Special "New" Methods

Last update : February 2007

This list is largely uncomplete since indexation, structure factors extraction, direct and Patterson methods, refinement by the Rietveld method... are part of the whole process. Some of the following publications may contain tests on previously known structures. Some methods proposing an alternative to equipartition at the stage of structure factors extraction, Monte Carlo, model building approaches, etc, are listed. New methods for single crystals which could be soon translated into methods for powders are also partly listed. The classification is questionable, since "global optimization", "direct space", "simulated annealing", etc may be the subject of a same unique paper. Anyway, here is the list !

Search among papers


Indexing

VISSER JW
A FULLY AUTOMATIC PROGRAM FOR FINDING THE UNIT CELL FROM POWDER DATA
JOURNAL OF APPLIED CRYSTALLOGRAPHY, 1969, Vol 2, pp 89-95

WERNER, PE; ERIKSSON, L; WESTDAHL, M
TREOR, A SEMI-EXHAUSTIVE TRIAL-AND-ERROR POWDER INDEXING PROGRAM FOR ALL SYMMETRIES
JOURNAL OF APPLIED CRYSTALLOGRAPHY, 1985, Vol 18, pp 367-370

DE WOLFF PM
J. APPL. CRYST., 1968, Vol 1, pp 108-

SMITH GS; SNYDER RL
FN - CRITERION FOR RATING POWDER DIFFRACTION PATTERNS AND EVALUATING THE RELIABILITY OF POWDER-PATTERN INDEXING
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1979, Vol 12, pp 60-65

BOULTIF, A; LOUER, D
INDEXING OF POWDER DIFFRACTION PATTERNS FOR LOW-SYMMETRYLATTICES BY THE SUCCESSIVE DICHOTOMY METHOD
JOURNAL OF APPLIED CRYSTALLOGRAPHY, 1991, Vol 24, pp 987-993

ITO T
X-ray studies on polymorphism, Tokyo : Maruzen, 1950

WERNER PE
Z. kristallogr., 1964, Vol 120, pp 275-

LIPSON H
ACTA CRYSTALLOGRAPHICA, 1949, Vol 2, pp 43-

DE WOLFF PM
ACTA CRYSTALLOGRAPHICA, 1957, Vol 10, pp 590-

TAUPIN D
J. Appl. Cryst., 1973, Vol 6, 380-385

HESSE R
ACTA CRYSTALLOGRAPHY, 1948, Vol 1, pp 200-

LOUER, D; VARGAS, R
AUTOMATIC INDEXATION OF POWDER DIAGRAMS BASED ON SUCCESSIVE DICHOTOMIES
JOURNAL OF APPLIED CRYSTALLOGRAPHY, 1982, Vol 15, pp 542-545

TAUPIN D
J. APPL CRYST., 1968, Vol 1, pp 178-

ITO T
NATURE, LONDON, 1949, Vol 164, pp 755-

WERNER PE
DETERMINATION OF UNIT-CELL DIMENSIONS FROM INACCURATE POWDER DIFFRACTION DATA
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1976, Vol 9, pp 216-219

BENOIT PH
ADAPTATION TO MICROCOMPUTER OF THE APPLEMAN-EVANS PROGRAM FOR INDEXING AND LEAST-SQUARES REFINEMENT OF POWDER-DIFFRACTION DATA FOR UNIT-CELL DIMENSIONS
AMERICAN MINERALOGIST 1987, Vol 72, pp 1018-1019

KOHLBECK F; HORL EM
INDEXING PROGRAM FOR POWDER PATTERNS ESPECIALLY SUITABLE FOR TRICLINIC, MONOCLINIC AND ORTHORHOMBIC LATTICES
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1976, Vol 9, Iss FEB1, pp 28-33

RUNGE C
Z. PHYSIK, 1917, Vol 18, pp 509-

SHIRLEY R
Data accuracy for powder indexing
Natl. Bur. Stand. (US) Spec. Publ. N°567, 1980, pp 361-382

TAKAKI Y; TANIGUCHI T; HORI K
PROGRAM PACKAGE FOR OBTAINING UNIT-CELL CONSTANTS AND POSSIBLE SPACE-GROUPS FROM X-RAY-POWDER DIFFRACTION DATA
NIPPON SERAMIKKUSU KYOKAI GAKUJUTSU RONBUNSHI-JOURNAL OF THE CERAMIC SOCIETY OF JAPAN 1993, Vol 101, Iss 3, pp 373-376

ALBERTI A
USE OF STRUCTURE FACTORS IN REFINEMENT OF UNIT-CELL PARAMETERS FROM POWDER DIFFRACTION DATA
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1976, Vol 9, Iss OCT1, pp 373-374

WU E
POWD, AN INTERACTIVE PROGRAM FOR POWDER DIFFRACTION DATA INTERPRETATION AND INDEXING
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1989, Vol 22, pp 506-510

KOHLBECK F; HORL EM
TRIAL AND ERROR INDEXING PROGRAM FOR POWDER PATTERNS OF MONOCLINIC SUBSTANCES
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1978, Vol 11, Iss FEB, pp 60-61

SERYKH VP
UNAMBIGUOUS INDEXING OF POWDER PATTERNS FROM MONOCLINIC AND ORTHORHOMBIC CRYSTALS
KRISTALLOGRAFIYA 1975, Vol 20, Iss 6, pp 1170-1174

MIGHELL AD
REDUCED CELL - ITS USE IN IDENTIFICATION OF CRYSTALLINE MATERIALS
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1976, Vol 9, Iss DEC1, pp 491-498

JAMARD C; TAUPIN D; GUINIER A
BULL. SOC. FRANC. MINER. CRIST., 1966, Vol 89, pp 312-

SMITH GS; KAHARA E
AUTOMATED COMPUTER INDEXING OF POWDER PATTERNS - MONOCLINIC CASE
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1975, Vol 8, Iss DEC1, pp 681-683

LOUER D
Automatic Indexing : procedures and applications
NIST Special Publication 846 (1992) pp 92-104

GREIS O
SYSTEMATIC PROCEDURE FOR INDEXING X-RAY POWDER PATTERNS OF SUPERSTRUCTURE PHASES
MONATSHEFTE FUR CHEMIE 1977, Vol 108, Iss 1, pp 205-211

PASZKOWICZ W
APPLICATION OF OPTIMIZATION TO POWDER-PATTERN INDEXING
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1987, Vol 20, pp 166-172

SMITH GS
ESTIMATING UNIT-CELL VOLUMES FROM POWDER DIFFRACTION DATA - TRICLINIC CASE
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1976, Vol 9, Iss DEC1, pp 424-428

MIGHELL AD; SANTORO A
GEOMETRICAL AMBIGUITIES IN INDEXING OF POWDER PATTERNS
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1975, Vol 8, Iss JUN1, pp 372-374

TAUPIN D
INFORMATION IN POWDER PATTERN INDEXING
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1988, Vol 21, pp 485-489

SHIRLEY R; LOUER D
NEW POWDER INDEXING PROGRAMS FOR ANY SYMMETRY WHICH COMBINE GRID-SEARCH WITH SUCCESSIVE DICHOTOMY
ACTA CRYSTALLOGRAPHICA SECTION A 1978, Vol 34, pp S382-S382

TAUPIN D
ENHANCEMENTS IN POWDER-PATTERN INDEXING
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1989, Vol 22, pp 455-459

PASZKOWICZ W
INDEXING - PROGRAM FOR INDEXING POWDER PATTERNS OF CUBIC, TETRAGONAL, HEXAGONAL AND ORTHORHOMBIC SUBSTANCES ON PERSONAL COMPUTERS
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1989, Vol 22, pp 186-187

WU E
A MODIFICATION OF THE DEWOLFF FIGURE OF MERIT FOR RELIABILITY OF POWDER PATTERN INDEXING
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1988, Vol 21, pp 530-535

Cabeza A; Aranda MAG; MartinezLara M; Bruque S
How to solve the problems for the indexation of complex materials using laboratory powder diffraction: Application to metal phosphonates
EUROPEAN POWDER DIFFRACTION: EPDIC IV, PTS 1 AND 2 1996, Vol 228, pp 165-170

BAILEY SW
PRACTICAL NOTES CONCERNING THE INDEXING OF X-RAY-POWDERDIFFRACTION PATTERNS OF CLAY-MINERALS
CLAYS AND CLAY MINERALS 1991, Vol 39, Iss 2, pp 184-190

Kariuki BM; Belmonte SA; McMahon MI; Johnston RL; Harris KDM; Nelmes RJ
A new approach for indexing powder diffraction data based on whole-profile fitting and global optimization using a genetic algorithm
JOURNAL OF SYNCHROTRON RADIATION 1999, Vol 6, pp 87-92

Paszkowicz W
Application of the smooth genetic algorithm for indexing powder patterns - Tests for the orthorhombic system
EUROPEAN POWDER DIFFRACTION: EPDIC IV, PTS 1 AND 2 1996, Vol 228, pp 19-24

CERNIK RJ
INDEXING UNIT CELLS FROM SYNCHROTRON X-RAY-POWDER DIFFRACTION DATA
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1993, Vol 26, pp 277-280

ZABOLOTNYI VA; OVCHINNIKOV VE; SOLOVYEVA LP; SHCHEDRIN BM PROGRAMS FOR POWDER X-RAY-PATTERNS INDEXING
KRISTALLOGRAFIYA 1983, Vol 28, Iss 1, pp 51-55

ISHIDA T; WATANABE Y
A CRITERION METHOD FOR INDEXING UNKNOWN POWDER DIFFRACTION PATTERNS
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 1982, Vol 160, Iss 1-2, pp 19-32

YAO T; JINNO H
COMPUTER-PROGRAMS FOR INDEXING X-RAY-POWDER PATTERNS
NIPPON KAGAKU KAISHI 1980, Iss 4, pp 529-536

Ferraris G; Prencipe M
A warning in indexing triclinic powder diffraction data
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 1998, Vol 213, Iss 2, pp 82-84

SERYKH VP; VERKHOROBIN LF
FULL-PROFILE POWDER PATTERNS INDEXING
KRISTALLOGRAFIYA 1983, Vol 28, Iss 6, pp 1199-1200

SERYKH VP
THE USE OF EXTINCTIONS IN POWDER PATTERNS INDEXING PROGRAMS
KRISTALLOGRAFIYA 1982, Vol 27, Iss 5, pp 994-994

SERYKH VP; SERCHENKO AI
PROGRAM FOR INDEXING A POWDER X-RAY-DIFFRACTION PATTERN OF ORTHORHOMBIC CRYSTALS ON A MIR DIGITAL-COMPUTER
KRISTALLOGRAFIYA 1976, Vol 21, Iss 4, pp 820-821

Altomare A; Giacovazzo C; Guagliardi A; Moliterni AGG; Rizzi R; Werner PE
New techniques for indexing: N-TREOR in EXPO
JOURNAL OF APPLIED CRYSTALLOGRAPHY 2000, Vol 33, pp 1180-1186
 
 

Paszkowicz, W
Properties of a genetic algorithm extended by a random self-learning
   operator and asymmetric mutations: A convergence study for a task of
   powder-pattern indexing
ANALYTICA CHIMICA ACTA 566, 2006, 81-98.
Genetic algorithms represent a powerful global-optimisation tool
   applicable in solving tasks of high complexity in science, technology,
   medicine, communication, etc. The usual genetic-algorithm calculation
   scheme is extended here by introduction of a quadratic self-learning
   operator, which performs a partial local search for randomly selected
   representatives of the population. This operator is aimed as a minor
   deterministic contribution to the (stochastic) genetic search. The
   population representing the trial solutions is split into two equal
   subpopulations allowed to exhibit different mutation rates (so called
   asymmetric mutation). The convergence is studied in detail exploiting a
   crystallographic-test example of indexing of powder diffraction data of
   orthorhombic lithium copper oxide, varying such parameters as imitation
   rates and the learning rate. It is shown through the averaged (over the
   subpopulation) fitness behaviour, how the genetic diversity in the
   population depends on the mutation rate of the given subpopulation.
   Conditions and algorithm parameter values favourable for convergence in
   the framework of proposed approach are discussed using the results for
   the mentioned example. Further data are studied with a somewhat
   modified algorithm using periodically varying mutation rates and a
   problem-specific operator. The chance of finding the global optimum and
   the convergence speed are observed to be strongly influenced by the
   effective mutation level and on the self-learning level. The optimal
   values of these two parameters are about 6 and 5%, respectively. The
   periodic changes of mutation rate are found to improve the explorative
   abilities of the algorithm. The results of the study confirm that the
   applied methodology leads to improvement of the classical genetic
   algorithm and, therefore, it is expected to be helpful in constructing
   of algorithms permitting to solve similar tasks of higher complexity.
 
 

Louer, D   Boultif, A
Indexing with the successive dichotomy method, DICVOL04
ZEITSCHRIFT FUR KRISTALLOGRAPHIE Suppl. 23, part1, 2006, 225-230.
A new version of the program based on the dichotomy principle for
   powder pattern indexing is reported. The new facilities of the program
   DICVOL04 include a tolerance for spurious diffraction lines, a
   refinement of the zero-point shift together with that of cell
   parameters, an a priori search for a zero-point offset in the input
   data, a reviewing of all available powder data from the indexing
   solution found from, generally, the first twenty lines. New strategies
   have been introduced to limit the risk to miss a solution. The program
   efficiency is shown with many tests. Additionally, the robustness of
   the program with respect to the minimum of lines required for finding
   solutions is presented and examples of two-phases patterns are used to
   test the performance of the program.
 
 

Boultif, A
History of the dichotomy method for powder pattern indexing
POWDER DIFFRACTION 20, 2005, 284-287.
A short history of the developments of the successive dichotomy method
   for powder pattern indexing is presented. In the first computer powder
   indexing programs (P1 and P2), only high lattice symmetries, down to
   orthorhombic, were considered [Louer and Louer, J. Appl. Crystallogr.
   5, 271-275 (1972)]. Later on, an extension to the monoclinic symmetry
   was reported in DICVOL, including a partition of the volume space to
   first search solutions with smaller unit cell volumes [Louer and
   Vargas, J. Appl. Crystallogr. 15, 542-545 (1982)]. However, CPU times
   were slow in some monoclinic examples. A thorough mathematical analysis
   resulted in a significant optimization of the CPU times [Boultif and
   Louer, J. Appl. Crystallogr. 24, 987-993 (199 1)]. Simultaneously, the
   method is extended to triclinic lattices. The stages of development of
   the various versions of the DICVOL program are described, with a
   particular emphasis on DICVOL91 (Boultif and Louer, 1991) and DICVOL04
   [Boultif and Louer, J. Appl. Crystallogr. 37, 724-731 (2004)]. This
   article is written to testify to and emphasize the major role played by
   Daniel Louer, who introduced the successive dichotomy method and
   continued to its evolution and optimization over almost 40 years.
 
 
 

2004
 
 

Boultif, A   Louer, D
Powder pattern indexing with the dichotomy method
JOURNAL OF APPLIED CRYSTALLOGRAPHY 37, 2004, 724-731.
The efficiency of the successive dichotomy method for powder
   diffraction pattern indexing [Louer & Louer (1972). J. Appl. Cryst. 5,
   271-275] has been proved over more than 30 years of usage. Features
   implemented in the new version of the computer program DICVOL04 include
   (i) a tolerance to the presence of impurity (or inaccurately measured)
   diffraction lines, (ii) a refinement of the 'zero-point' position,
   (iii) a reviewing of all input lines from the solution found from,
   generally, the first 20 lines, (iv) a cell analysis, based on the
   concept of the reduced cell, to identify equivalent monoclinic and
   triclinic solutions, and (v) an optional analysis of input powder data
   to detect the presence of a significant 'zero-point' offset. New search
   strategies have also been introduced, e. g. each crystal system is
   scanned separately, within the input volume limits, to limit the risk
   of missing a solution characterized by a metric lattice singularity.
   The default values in the input le have been extended to 25 A for the
   linear parameters and 2500 A 3 for the cell volume. The search is
   carried out exhaustively within the input parameter limits and the
   absolute error on peak position measurements. Many tests with data from
   the literature and from powder data of pharmaceutical materials,
   collected with the capillary technique and laboratory monochromatic
   X-rays, have been performed with a high success rate, covering all
   crystal symmetries from cubic to triclinic. Some examples reported as
   'difficult' cases are also discussed. Additionally, a few
   recommendations for the correct practice of powder pattern indexing are
   reported.
 
 
 
 
 

Le Bail, A
Monte Carlo indexing with McMaille
POWDER DIFFRACTION 19, 2004, 249-254.
A Monte Carlo code for indexing powder diffraction patterns is
   presented. Cell parameters are generated randomly and tested against an
   idealized powder profile generated from the extracted d's and I's.
 

Mighell, AD
Ambiguities in powder indexing: Conjunction of a ternary and binary
   lattice metric singularity in the cubic system
JOURNAL OF RESEARCH OF THE NATIONAL INSTITUTE OF STANDARDS AND
   TECHNOLOGY 109, 2004, 569-579.
A lattice metric singularity occurs when unit cells defining two (or
   more) lattices yield the identical set of unique calculated d-spacings.
   The existence of such singularities, therefore, has a practical and
   theoretical impact on the indexing of powder patterns. For example, in
   experimental practice an indexing program may find only the lower
   symmetry member of a singularity. Obviously, it is important to
   recognize such cases and know how to proceed. Recently, we described:
   (1) a binary singularity involving a monoclinic and a rhombohedral
   lattice in a subcell-supercell relationship and (2) a second type of
   singularity - a ternary singularity - in which two of the three
   lattices are in a derivative composite relationship. In this work, we
   describe a ternary lattice metric singularity involving a cubic P, a
   tetragonal P, and an orthorhombic C lattice. Furthermore, there is a
   binary singularity, involving a hexagonal P and orthorhombic P lattice,
   which is characterized by a set of unique d-spacings very close to that
   of the ternary singularity. The existence of such singularities is more
   common than once thought and requires a paradigm shift in experimental
   practice. In addition singularities provide opportunities in material
   design as they point to highly specialized lattices that may be
   associated with unusual physical properties.
 

Habershon, S   Cheung, EY   Harris, KDM   Johnston, RL
Powder diffraction indexing as a pattern recognition problem: A new
   approach for unit cell determination based on an artificial neural
   network
JOURNAL OF PHYSICAL CHEMISTRY A, 108, 2004, 711-716.
An artificial neural network, in combination with local optimization,
   is shown to be an effective approach for determining unit cell
   parameters directly from powder diffraction data. The viability of this
   new approach is initially demonstrated using simulated powder
   diffraction data. Subsequently, the successful application of the
   method to determine unit cell parameters is illustrated for two
   materials using experimental powder X-ray diffraction data recorded on
   a standard laboratory diffractometer.

2003

Neumann, MA
X-Cell: a novel indexing algorithm for routine tasks and difficult cases
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 356-365.
X-Cell is a novel indexing algorithm that makes explicit use of
   systematic absences to search for possible indexing solutions from
   cells with low numbers of calculated reflections to cells with high
   numbers of reflections. Space groups with the same pattern of
   systematic absences are grouped together in powder extinction classes,
   and for a given peak number range an independent search is carried out
   in each powder extinction class. The method has the advantage that the
   correct cell is likely to be found before the rapid increase of
   possible solutions slows down the search significantly. A successive
   dichotomy approach is used to establish a complete list of all possible
   indexing solutions. The dichotomy procedure is combined with a search
   for the zero-point shift of the diffraction pattern, and impurity peaks
   can be dealt with by allowing for a user-defined portion of unindexed
   reflections. To rank indexing solutions with varying numbers of
   unindexed reflections, a new figure of merit is introduced that takes
   into account the highest level of agreement typically obtained for
   completely incorrect unit cells. The indexing of long and flat unit
   cells is facilitated by the possibility to search for rows or zones in
   reciprocal space first and then to use the lattice parameters of the
   dominant row or zone in the unit-cell search. The main advantages of
   X-Cell are robustness and completeness, as demonstrated by a validation
   study on a variety of compounds. The dominant phase of phase mixtures
   can be indexed in the presence of up to 50% of impurity peaks if
   high-quality synchrotron data are available.
 
 

Coelho, AA
Indexing of powder diffraction patterns by iterative use of singular
   value decomposition
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 86-95
A fast method for indexing powder diffraction patterns has been
   developed for large and small lattices of all symmetries. The method is
   relatively insensitive to impurity peaks and missing high d-spacings:
   on simulated data, little effect in terms of successful indexing has
   been observed when one in three d-spacings are randomly removed.
   Comparison with three of the most popular indexing programs, namely
   ITO, DICVOL91 and TREOR90, has shown that the present method as
   implemented in the program TOPAS is more successful at indexing
   simulated data. Also significant is that the present method performs
   well on typically noisy data with large diffractometer zero errors.
   Critical to its success, the present method uses singular value
   decomposition in an iterative manner for solving linear equations
   relating hkl values to d-spacings.
 
 
 

Florence, AJ   Baumgartner, B   Weston, C   Shankland, N
   Kennedy, AR   Shankland, K   David, WIF
Indexing powder patterns in physical form screening: Instrumentation
   and data quality
JOURNAL OF PHARMACEUTICAL SCIENCES 92, 2003, 1930-1938.
Two multisample laboratory powder diffractometers have been evaluated
   for the purpose of pattern indexing in the context of physical form
   screening. Both diffractometers utilise foil transmission geometry,
   primary monochromated radiation, and a position-sensitive detector.
   Data collected from six compounds (sotalol hydrochloride,
   hydroflumethiazide, verapamil hydrochloride, captopril, clomipramine
   hydrochloride, and famotidine) showed good angular resolution (FWHM as
   small as ca. 0.06degrees) and lattice parameters were easily obtained
   using the indexing program DICVOL-91. The extent of preferred
   orientation in each pattern was estimated using the DASH implementation
   of the March-Dollase function and is most evident with clomipramine
   hydrochloride and famotidine. Otherwise, the data compare favorably
   with reference capillary data sets. In conclusion, where there is a
   requirement to analyze 20-30 samples per day, with an emphasis on
   obtaining the high-quality data that are important in pattern
   recognition and imperative in indexing, the combination of foil
   transmission geometry, primary monochromated radiation, plus a
   position-sensitive detector is highly effective. The data also afford
   opportunities for crystal structure determination.
 
 

Hageman, JA   Wehrens, R   De Gelder, R   Buydens, LMC
Powder pattern indexing using the weighted crosscorrelation and genetic
   algorithms
JOURNAL OF COMPUTATIONAL CHEMISTRY 24, 2003, 1043-1051.
X-ray diffraction is a powerful technique for investigating the
   structure of crystals and crystalline powders. Unfortunately, for
   powders, the first step in the structure elucidation process,
   retrieving the unit cell parameters (indexing), is still very critical.
   In the present article, an improved approach to powder pattern indexing
   is presented. The proposed method matches peak positions from
   experimental X-ray powder patterns with peak positions from trial cells
   using a recently published method for pattern comparison (weighted
   crosscorrelation). Trial cells are optimized with Genetic Algorithms.
   Patterns are not pretreated to remove any existing zero point shift, as
   this is determined during optimization. Another improvement is the peak
   assignment procedure. This assignment is needed for determining the
   similarity between lines from trial cells and experiment. It no longer
   allows calculated peaks to be assigned twice to different experimental
   peaks, which is beneficial for the indexing process. The procedure
   proves to be robust with respect to false peaks and accidental or
   systematic absensences of reflections, and is successfully applied to
   powder patterns originating from orthorhombic, monoclinic, and
   triclinic compounds measured with synchrotron as well as with
   conventional laboratory X-ray diffractometers.
 



Structure Factors Extraction

PAWLEY GS
UNIT-CELL REFINEMENT FROM POWDER DIFFRACTION SCANS
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1981, Vol 14, pp 357-361

LE BAIL A; DUROY H; FOURQUET JL
ABINITIO STRUCTURE DETERMINATION OF LISBWO6 BY X-RAY-POWDER DIFFRACTION
MATERIALS RESEARCH BULLETIN 1988, Vol 23, Iss 3, pp 447-452

A. Le Bail,
Extracting structure factors from powder diffraction data by iterating full pattern profile fitting,
NIST Special Pubication 846 (1992) 213.

RODRIGUEZCARVAJAL J
RECENT ADVANCES IN MAGNETIC-STRUCTURE DETERMINATION BY NEUTRON POWDER DIFFRACTION
PHYSICA B 1993, Vol 192, Iss 1-2, pp 55-69

TORAYA H
WHOLE-POWDER-PATTERN FITTING WITHOUT REFERENCE TO A STRUCTURAL MODEL - APPLICATION TO X-RAY-POWDER DIFFRACTOMETER DATA
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1986, Vol 19, pp 440-447

Altomare, A; Burla, MC; Cascarano, G; Giacovazzo, G; Guagliardi, A; Moliterni, AGG; Polidori, G
EXTRA: A program for extracting structure factor amplitudes from powder diffraction data.
JOURNAL OF APPLIED CRYSTALLOGRAPHY, 1995, Vol 28, pp 842-846

JANSEN, J; PESCHAR, R; SCHENK, H
ON THE DETERMINATION OF ACCURATE INTENSITIES FROM POWDER DIFFRACTION DATA .1. WHOLE-PATTERN FITTING WITH A LEAST-SQUARES PROCEDURE
JOURNAL OF APPLIED CRYSTALLOGRAPHY, 1992, Vol 25, pp 231-236

JANSEN, J; PESCHAR, R; SCHENK, H
ON THE DETERMINATION OF ACCURATE INTENSITIES FROM POWDER DIFFRACTION DATA .2. ESTIMATION OF INTENSITIES OF OVERLAPPING REFLECTIONS
JOURNAL OF APPLIED CRYSTALLOGRAPHY, 1992, Vol 25, pp 237-243

SIVIA DS; DAVID WIF
A BAYESIAN-APPROACH TO EXTRACTING STRUCTURE-FACTOR AMPLITUDES FROM POWDER DIFFRACTION DATA
ACTA CRYSTALLOGRAPHICA SECTION A 1994, Vol 50, pp 703-714

DAVID WIF
THE PROBABILISTIC DETERMINATION OF INTENSITIES OF COMPLETELY OVERLAPPING REFLECTIONS IN POWDER DIFFRACTION PATTERNS
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1987, Vol 20, pp 316-319

ESTERMANN MA; GRAMLICH V
IMPROVED TREATMENT OF SEVERELY OR EXACTLY OVERLAPPINGBRAGG-REFLECTIONS FOR THE APPLICATION OF DIRECT-METHODS TO POWDER DATA
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1993, Vol 26, pp 396-404

TORAYA H
ARRAY-TYPE UNIVERSAL PROFILE FUNCTION FOR POWDER PATTERN FITTING
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1990, Vol 23, pp 485-491

Altomare A; Cascarano G; Giacovazzo C; Guagliardi A; Moliterni AGG; Burla MC; Polidori G
On the number of statistically independent observations in a powder diffraction pattern
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1995, Vol 28, pp 738-744

Carrozzini B. Giacovazzo C. Guagliardi A. Rizzi R. Burla MC. Polidori G.
SOLVING CRYSTAL STRUCTURES FROM POWDER DATA .3. THE USE OF THE PROBABILITY DISTRIBUTIONS FOR ESTIMATING THE |F|S
J. Appl. Crystallogr. 30(1997) 92-97.

Altomare A; Foadi J; Giacovazzo C; Moliterni AGG; Burla MC; Polidori G
Solving crystal structures from powder data. IV. The use of patterson information for estimating the |F|'s
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1998, Vol 31, pp 74-77

Rius J; Sane J; Miravitlles C; Amigo JM; Reventos MM; Louer D
Determination of crystal structures from powder diffraction data by direct methods: Extraction of integrated intensities from partially overlapping Bragg reflections
ANALES DE QUIMICA 1996, Vol 92, Iss 4, pp 223-227

Altomare-A; Giacovazzo-C; Moliterni-AGG; Rizzi-R
A random procedure for the decomposition of a powder pattern in EXPO.
J. Appl. Cryst. 34 (2001) 704-709

B. Grzeta & H. Toraya,
Powder-pattern-fitting methods in structure determination,
Croatica Chemica Acta 67 (1994) 273-288.

Lasocha W. Schenk H.
A SIMPLIFIED, TEXTURE-BASED METHOD FOR INTENSITY DETERMINATION OF OVERLAPPING REFLECTIONS IN POWDER DIFFRACTION
Journal of Applied Crystallography 30 (1997) 561-564.

Cerny R.
Powder pattern decomposition with the aid of preferred orientation - use of the whole Debye-Scherrer ring.
Mater. Sci. Forum 378-381 (2001) 24-29.
 
 
 

Feng, ZJ   Dong, C
GENEFP: a full-profile fitting program for X-ray powder patterns using
   the genetic algorithm
JOURNAL OF APPLIED CRYSTALLOGRAPHY 39, 2006, 615-617.
GENEFP is a full-profile fitting program, employing a
   fundamental-parameters method, for Cu-target X-ray powder patterns. In
   this program, the Le Bail method is used to determine integrated
   intensities and the genetic algorithm is used to search for the proper
   fundamental parameters. When some parameters, such as the grain size,
   have large uncertainties, the genetic algorithm has an advantage over
   conventional least-squares methods in finding the global extremum.
 
 
 

Altomare, A   Cuocci, C   Giacovazzo, C   Moliterni, AGG   Rizzi, R
The combined use of Patterson and Monte Carlo methods for the
   decomposition of a powder diffraction pattern
JOURNAL OF APPLIED CRYSTALLOGRAPHY 39, 2006, 145-150.
The success of ab initio crystal structure solution by powder
   diffraction data is strictly related to the quality of the integrated
   intensity estimates. A new method that is able to improve the pattern
   decomposition step has been developed. It combines the inversion of a
   suitably modified Patterson map with the use of the Hamming codes
   [13,10] and [40,36] in order to explore more decomposition trials. The
   new approach has been introduced in EXPO2005, an updated version of
   EXPO2004, and successfully applied to a set of known organic and
   inorganic structures.
 
 
 

2005

Altomare, A   Cuocci, C   da Silva, I   Giacovazzo, C   Moliterni, AGG   Rizzi, R
Full powder pattern decomposition and direct phasing in EXPO2004: A
   statistical study
POWDER DIFFRACTION 20, 2005, 327-333.
Ab initio crystal structure solution by powder diffraction data is
   based on the experimental full pattern decomposition process: the
   resulting structure factor moduli are used for direct phasing. The
   extracted intensity estimates are scarcely accurate (overlapping,
   background, and preferred orientation are the main causes of the lack
   of accuracy), no matter if Le Bail or Pawley method is adopted:
   consequently the structure solution process is not straightforward. We
   have focused our attention on the relation between the efficiency of
   the EXP02004 phasing process and the various parameters which are
   normally used in the full pattern decomposition process, e.g., the peak
   shape function, the number of refinement cycles, the degree of
   overlapping. Different steps of the phasing process are considered: the
   definition of the unit cell, the determination of the space group, and
   the application of direct methods.
 

2004
 

 
Altomare, A   Caliandro, R   Cuocci, C   da Silva, I   Giacovazzo, C
   Moliterni, AGG   Rizzi, R
The use of error-correcting codes for the decomposition of a powder
   diffraction pattern
JOURNAL OF APPLIED CRYSTALLOGRAPHY 37, 2004, 204-209.
The decomposition of a powder diffraction pattern consists of the
   extraction of the intensities of the individual reflections from the
   experimental profile. The process is crucial for structure
   determination from powder diffraction data, but its accuracy is limited
   by the intrinsic peak overlap. A substantial improvement is achieved by
   considering clusters of reflections in strong overlap and partitioning
   in a systematic way the total intensity of each cluster among the
   constituent reflections. In this paper, error-correcting codes are used
   to explore the set of decomposition trials obtained by combining the
   partitions of various clusters of overlapping reflections. Linear
   ternary codes resulting from modifications of the Hamming codes [ 13,
   10] and [ 40, 36] have been considered as the most suited for the
   present problem. They have been included in the EXPO program via their
   generator matrices. Tests on a set of experimental powder patterns show
   that an efficient decomposition procedure consists of performing only
   27 decomposition trials, determined as the codewords of an [ndoub, 3]
   code, where ndoub is the number of doublets of strong overlapping
   reflections found in the experimental profile. This allows a reduction
   in the number of trials, thus processing about 2% of the number used in
   a previous design of the same procedure, leading to a reduction of the
   total execution time by nearly the same amount.
 

2003
 

 
Guo, LP   Cheng, ZX   Han, FT   Liu, Y   Zhao, ZX
Simulated annealing method for powder diffraction pattern decomposition
ACTA PHYSICA SINICA 52, 2003, 2842-2848.
Simulated annealing algorithm was applied in the decomposition of
   neutron and x-ray powder diffraction pattern. The method described in
   this paper has two main advantages: first, the pattern decomposition
   results do not depend on the starting peak parameters, thus the
   difficulty in the choice of initial solutions, which occurs in fitting
   a complex pattern composed of severely overlapped peaks by a
   conventional least-squares profile fitting method, is overcome;
   secondly, it has the ability of searching for global other than local
   optimal solutions, thus can effectively resolve the multi-solution
   problem mathematically, and this advantage is the most useful when
   decomposing complex patterns with several local optimal solutions. The
   computing step is described in detail, the setting of relative
   parameters is discussed, and the simulated annealing method is compared
   with a conventional least-squares profile fitting method through both
   simulated pattern and actual pattern to demonstrate its unique
   advantage in the decomposition, of, complex pattern. In principle, the
   method can also be applied in other kinds of spectra which can be
   described by profile shape function.
 
 
 
 
 

 
Altomare, A   Caliandro, R   Cuocci, C   Giacovazzo, C   Moliterni, AGG   Rizzi, R
A systematic procedure for the decomposition of a powder diffraction
   pattern
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 906-913.
Ab initio crystal structure solution from powder diffraction data can
   be attained by means of the two-stage method: first the integrated
   intensities of individual reflections are extracted from the
   experimental profile; then the extracted intensities are processed by
   direct methods to recover their phase. The efficiency of the
   direct-methods process is strongly affected by the accuracy of the
   extracted intensities and this is a serious drawback for the solution
   of organic compounds, where the presence of light atoms leads to a
   rapid decrease of the scattering at high angles. In order to overcome
   this problem, a procedure is proposed which generates a set of
   different intensity partitions for groups of reflections in strong
   overlap: the resulting decomposition trials are supplied to direct
   methods. The procedure is able to reduce the phase error at the end of
   the phasing process by up to 50degrees and enables the solution of
   organic structures with data resolution not worse than 1.5 Angstrom in
   a reasonable computing time. The procedure has been implemented in the
   EXPO program, which makes use of the Le Bail extraction algorithm.
 
 
 

Peterson, VK
Lattice parameter measurement using Le Bail versus structural
   (Rietveld) refinement: A caution for complex, low symmetry systems
POWDER DIFFRACTION 20, 2005, 14-17.
The measurement of lattice parameters using the Le Bail method was
   shown to be inappropriate for a complex, low symmetry, structure, even
   with high resolution synchrotron diffraction data. The method failed as
   a result of ambiguous indexing in the absence of constraints on
   diffraction intensities, that arise when a structural model is used,
   combined with the large number of reflections. A caution for the use of
   the Le Bail and other whole-powder pattern decomposition methods is
   presented, particularly for high reflection density data.
 
 

Wright, JP
Extraction and use of correlated integrated intensities with powder
   diffraction data
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 219, 2005, 791-802.
The transformation of a powder diffraction profile into a set of
   correlated integrated intensities allows crystallographic calculations
   to be performed without modelling raw diffractometer counts. By
   carrying out this transformation it is possible to preserve the
   information about peak overlap without needing to retain the multitude
   of experimental details and description of the peak shape function. An
   implementation is described which allows problems of significant size
   to be tackled. Least squares refinement. issues of data quality and the
   generation and importance of free R-factors are discussed.
 

 
 

Ma, HW   Liang, JK   Liu, GY   Rao, GH
UACIEM: A new method to extract reliable intensities of nonequivalent
   systematical overlapping reflections from powder diffraction data
POWDER DIFFRACTION 19, 2004, 333-339.
A new method, namely UACIEM, to extract reliable intensities of
   nonequivalent systematical overlapping reflections has been proposed
   and tested by simulated powder diffraction data from known crystal
   structures. Using both crystallographic and structural chemistry
   information, the method reconstructs diffraction intensities and solves
   a crystal structure through an iterative procedure. Our study shows
   that UACIEM is successful for cases where more than 30% of the total
   scattering power is located with precision from equivalent systematical
   overlapping reflections. The UACIEM process is not needed when
   equivalent systematical overlapping reflections are sufficient to
   reveal a crystal structure. UACIEM may fail in cases when: (i) only a
   small portion of the total scattering power (e.g., less than 7%) can be
   located, and (ii) most of the total scattering power (e.g., 95%) is
   located, but the atomic coordinates are not accurately known. The
   UACIEM method is superior to the simple equipartition methods for
   nonequivalent systematical overlapping reflections.
 

 
Ma, HW   Liang, JK
A new approach to extract reliable intensities of non-equivalent
   systematical overlapping reflections from powder diffraction data
ACTA PHYSICA SINICA 53, 2004, 829-834.
A new approach to extract reliable intensities from systematical
   non-equivalent overlapping reflections has been proposed and tested by
   simulated powder diffraction pattern of known structures. By using both
   crystallographic and structural chemistry knowledge, the IDM-UAIC
   reconstructs the intensities and solves the structure through an
   iterative procedure. The results show that IDM-UAIC succeeds when more
   than 30% of the total scattering power can be located in a reasonable
   precise from the equivalent systematical overlapping reflections. The
   IDM-UAIC procedure is superior to the simple equi-partition methods for
   the nonequivalent systematical overlapping reflections while it is
   equivalent to simple equi-partition methods for the equivalent
   systematical overlapping reflections.
 

 

Tucker, MG   Dove, MT   Keen, DA
Application of the reverse Monte Carlo method to crystalline materials
JOURNAL OF APPLIED CRYSTALLOGRAPHY 34, 2001, 630-638.
An implementation of the reverse Monte Carlo (RMC) method for the study
   of crystalline materials from polycrystalline neutron total scattering
   data is presented. The new feature is that explicit account is taken of
   the intensities of Bragg peaks, which are extracted from the data using
   the Pawley method. The use of Bragg peaks ensures that the RMC models
   reproduce both the long-range and the short-range order reflected in
   the experimental data. The relative effects of different contributions
   to the data sets in the RMC method are assessed and successful
   applications are illustrated using the quartz and cristobalite
   polymorphs of silica as examples.
 
 
 
 

Space group determination
 
 

Altomare, A   Caliandro, R   Camalli, M   Cuocci, C   da Silva, I
   Giacovazzo, C   Moliterni, AGG   Spagna, R
Space-group determination from powder diffraction data: a probabilistic
   approach
JOURNAL OF APPLIED CRYSTALLOGRAPHY 37, 2004, 957-966.
Experimental powder diffraction diagrams, once indexed and decomposed
   into single diffraction intensities, can be submitted to statistical
   analysis for the determination of space-group symmetry. A new algorithm
   is illustrated, which is able to provide, on a quantitative basis, a
   probability value for each extinction symbol compatible with the
   previously established lattice symmetry. The algorithm has been
   implemented in EXPO2004 [Altomare, Caliandro, Camalli, Cuocci,
   Giacovazzo, Moliterni & Rizzi ( 2004). J. Appl. Cryst. 37, 1025 - 1028]
   and has been successfully tested using a large set of experimental data.
 
 
 
 
 

 
Markvardsen, AJ   David, WIF   Johnson, JC   Shankland, K
A probabilistic approach to space-group determination from powder
   diffraction data
ACTA CRYSTALLOGRAPHICA SECTION A 57, 2001, 47-54.
An algorithm for the determination of the space-group symmetry of a
   crystal from powder diffraction data, based upon probability theory, is
   described. Specifically, the relative probabilities of different
   extinction symbols are assessed within a particular crystal system. In
   general, only a small number of extinction symbols are relatively
   highly probable and a single extinction symbol is often significantly
   more probable than any other. Several examples are presented to
   illustrate this approach.
 
 


Direct methods / Patterson

A. Altomare, G. Cascarano, C. Giacovazzo, A. Guagliardi, M.C. Burla, G. Polidori & M. Camalli,
SIRPOW.92
J. Appl. Cryst. 27 (1994) 435-436.

C. Cascarano, L. Favia & C. Giacovazzo,
SIRPOW.91- a direct-methods package optimized for powder data,
J. Appl. Cryst. 25 (1992) 310-317.

Altomare A; Burla MC; Camalli M; Carrozzini B; Cascarano GL; Giacovazzo C; Guagliardi A; Moliterni AGG; Polidori G; Rizzi R
EXPO: a program for full powder pattern decomposition and crystal structure solution
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1999, Vol 32, pp 339-340

Altomare A. Burla MC. Cascarano G. Giacovazzo C. Guagliardi A. Moliterni AGG. Polidori G.
EARLY FINDING OF PREFERRED ORIENTATION - APPLICATIONS TO DIRECT METHODS
Journal of Applied Crystallography. 29(1996) 341-345.

J. Jansen, R. Peschar & H. Schenk,
Application of direct methods to powder data. A weighting scheme for intensities in the optimal symbolic addition program SIMPEL88,
Z. Kristallogr. 206 (1993) 33-43.

W. Prandl,
Phase determination and Patterson maps from multiwavelength powder data,
Acta Cryst. A46 (1990) 988-992.

W. Prandl,
Phase determination from X-ray powder diffraction data II. Partial Patterson maps and the localization of anomalously scattering atoms,
Acta Cryst. A50 (1994) 52-55.

Burger K. Prandl W. Doyle S.
STRUCTURE DETERMINATION FROM POWDER DATA USING ANOMALOUS SCATTERING - DIFFERENCE AND PARTIAL, PATTERSON DENSITIES, AND PHASES OF STRUCTURE FACTORS
Zeitschrift fur Kristallographie. 212 (1997) 493-505.

Rius J. Miravitlles C. Gies H. Amigo JM.
A tangent formula derived from Patterson-function arguments. VI. Structure solution from powder patterns with systematic overlap
J. Appl. Crystallogr. 32(Part 1):89-97, 1999.

Rius-J; Torrelles-X; Miravitlles-C; Ochando-LE; Reventos-MM; Amigo-JM
A tangent formula derived from Patterson-function arguments. VII. Solution of inorganic structures from powder data with accidental overlap
JOURNAL-OF-APPLIED-CRYSTALLOGRAPHY. OCT 1 2000; 33 Part 5 : 1208-1211

Rius J
XLENS, a direct methods program based on the modulus sum function: Its application to powder data
POWDER-DIFFRACTION. DEC 1999; 14 (4) : 267-273
 
 

Burla, MC   Caliandro, R   Carrozzini, B   Cascarano, GL   De Caro, L
   Giacovazzo, C   Polidori, G   Siliqi, D
The revenge of the Patterson methods. I. Protein ab initio phasing
JOURNAL OF APPLIED CRYSTALLOGRAPHY 39, 2006, 527-535.
Direct methods combined with direct-space refinement procedures are the
   standard tools for ab initio crystal structure solution of
   macromolecules via diffraction data collected up to atomic or
   quasi-atomic resolution. An entirely direct-space approach is described
   here: it includes an automated Patterson deconvolution method, based on
   the minimum superposition function, followed by an effective
   direct-space refinement, consisting of cycles of electron density
   modification. The new approach has been implemented in a new version of
   the SIR2004 program and tested on a large set of test structures
   selected from the Protein Data Bank, with data resolution better than
   1.6 angstrom and number of non-hydrogen atoms in the asymmetric unit up
   to 2000. The new procedure proved to be extremely efficient and very
   fast in solving crystal structures with atomic resolution data and
   heavy atoms: their solution and refinement requires a computing time
   roughly comparable with that necessary for solving small-molecule
   crystal structures via a modern computer program. It markedly overcomes
   direct methods, even for crystal structures with atomic data resolution
   and heaviest atomic species up to calcium, as well as for crystal
   structures with quasi-atomic data resolution (i.e. 1.2 - 1.6 angstrom).
   The Patterson approach proved to be loosely dependent on the structure
   complexity.
 

Rius, J
Advances and some recent applications of the origin-free modulus sum
   function
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 219, 2005, 826-832.
Since its discovery, the direct methods origin-free modulus sum
   function [Rius, J., Acta Cryst A49 (1993) 406-409] has been responsible
   for the solution of a number of difficult crystal structures of
   minerals and other inorganic compounds from powder diffraction data.
   This is principally due to the efficiency, robustness and simplicity of
   implementation of this phase refinement function. The first part of the
   contribution describes some recent examples on the application of the
   origin-free modulus sum function to complex structures. In the second
   part, a powerful variant of this function is introduced which
   discriminates even better the correct solutions from the wrong ones.
   This is illustrated with its application to single-crystal data of
   three selected organic structures. One of these test structures
   contains 317-atom molecules and is regarded as one of the most
   difficult structures to be solved with reciprocal space direct methods.
   This variant could also be useful for those phase refinement strategies
   based on alternating reciprocal- and real-space procedures, provided
   that the weak reflections are known.
 

Caliandro, R   Carrozzini, B   Cascarano, GL   De Caro, L
   Giacovazzo, C   Siliqi, D
Phasing at resolution higher than the experimental resolution
ACTA CRYSTALLOGRAPHICA SECTION D-BIOLOGICAL CRYSTALLOGRAPHY 61, 2005, 556-565.
Limited experimental resolution is a unavoidable feature in
   macromolecular crystallography: it may hinder or make difficult the
   determination of the crystal structure. A novel procedure is presented
   which from an approximate electron-density map extrapolates the moduli
   and phases of non-measured reflections beyond and behind the
   experimental resolution limit. Applications to a set of test structures
   show that the extrapolation can be successfully accomplished. As a
   consequence, the phase estimates of the observed reflections are
   subsequently improved and the interpretability of the corresponding
   electron-density map increases. The use of the extrapolated values for
   the non-measured reflections provides additional information for the
   map, which shows a resolution higher than the experimental resolution.
 
 

 
Rius-Palleiro, J   Peral, I   Margiolaki, I   Torrelles, X
Solving centrosymmetrical zeolites from powder diffraction data by
   combining the direct-methods origin-free modulus sum function with the
   isomorphous replacement technique. X
JOURNAL OF APPLIED CRYSTALLOGRAPHY 38, 2005, 906-911.
A new two-stage strategy for the solution of zeolite crystal structures
   with centrosymmetrical frameworks is proposed; this strategy exploits
   the information contained in multiple powder diffraction patterns. In
   the first stage, the structure-directing agent (SDA), i.e. the template
   molecule, is located by combining the isomorphous replacement technique
   with direct methods. In the second stage, the framework atoms are found
   by applying direct methods strengthened with additional information
   coming from the located SDA. All phase refinements are based on the
   maximization of the origin-free modulus sum function as implemented in
   the direct-methods program XLENS [Rius (2004). Z. Kristallogr. 219,
   826-832], with data resolution limits equal to 3.2 angstrom for the
   first and 2.21 angstrom for the second stage. The viability of this new
   two-stage strategy is illustrated with the solution of the novel
   zeolite ITQ-32, containing nine Si atoms in the asymmetric unit, from
   synchrotron powder diffraction data. Especially important is the
   confirmation that the intensity differences involved in the SDA
   isomorphous replacement are significantly greater than the
   experimentally measured errors.
 
 
 
 

2004
 

 Altomare, A   Caliandro, R   Camalli, M   Cuocci, C   Giacovazzo, C
   Moliterni, AGG   Rizzi, R   Spagna, R   Gonzalez-Platas, J
Towards EXPO2005
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 219, 2004, 833-837
New procedures have been introduced in EXPO2004 (Altomare. A..
   Caliandro, R., Camalli, M., Cuocci, C., da Silva, I., Giacovazzo, C.,
   Moliterni, A. G. G. & Rizzi, R., J. Appl. Cryst. Submitted) aiming at
   making the solution process more straightforward, particularly for
   cases very resistant to the ab-initio approach.
 
 

Altomare, A   Caliandro, R   Camalli, M   Cuocci, C   Giacovazzo, C
   Moliterni, AGG   Rizzi, R
Automatic structure determination from powder data with EXPO2004
JOURNAL OF APPLIED CRYSTALLOGRAPHY37, 2004, 1025-1028
EXPO2004 is the updated version of the EXPO program [Altomare et al.
   (1999). J. Appl. Cryst. 32, 339 - 340]. The traditional steps of the ab
   initio powder solution process are performed automatically: indexing,
   space-group determination, decomposition of the pattern for extracting
   the observed structure-factor moduli, structure solution by direct
   methods, model refinement by Rietveld technique. Special strategies may
   be applied to improve both the estimates of the extracted
   structure-factor moduli and the quality of the structure model. In
   addition, the use of special procedures exploiting available
   supplementary information on molecular geometry can be successfully
   adopted. The graphical interface has also been improved.
 
 

Altomare, A   Giacovazzo, C   Grazia, A   Moliterni, G   Rizzi, R
Direct methods optimised for solving crystal structure by powder
   diffraction data: Limits, strategies, and prospects
JOURNAL OF RESEARCH OF THE NATIONAL INSTITUTE OF STANDARDS AND
   TECHNOLOGY 109, 2004, 125-132.
ab-initio crystal structure solution by powder diffraction data
   requires great efforts because of the collapse of the experimental
   information onto the one dimensional 2theta axis of the pattern.
   Different strategies will be described aiming at improving the process
   of extraction of the integrated intensities from the experimental
   pattern in order to make more straightforward the structure solution
   process by direct methods. Particular attention will be devoted to the
   EXPO program. Some of its performance will be analysed and results will
   be shown.
 

Altomare, A   Cuocci, C   Giacovazzo, C   Grazia, A   Moliterni, G   Rizzi, R
Completion of crystal structure with polyhedral coordination: A new
   procedure
EUROPEAN POWDER DIFFRACTION EPDIC 8  - MATERIALS SCIENCE FORUM 443-4, 2004, 23-26.
The ab-initio crystal structure solution via powder diffraction data is
   often uncomplete. A recent procedure POLPO [1] aims at completing a
   partial structure model provided by Direct Methods by exploiting the
   prior information on the polyhedral coordination of the located atoms
   (tetrahedral or octahedral) and their connectivity has been developed.
   The POLPO procedure requires that all the cations are correctly
   labelled and rightly located. This condition does not always occur,
   particularly when the data quality is poor. A new method is described
   which is able to locate missing cations and surrounding anions when the
   cation coordination is tetrahedral or octahedral.

Altomare, A   Cuocci, C   Giacovazzo, C   Moliterni, AGG   Rizzi, R
Powder diffraction: the new automatic least-squares Fourier recycling
   procedure in EXPO2005
JOURNAL OF APPLIED CRYSTALLOGRAPHY 39, 2006, 558-562.
The Rietveld method is the most widely used approach for refining
   crystal structures from powder diffraction patterns. It requires
   sufficiently accurate structure models and user skill. A method is
   described which is often able to complete and refine a structure model
   by using an automatic least-squares procedure applicable to reflection
   integrated intensities. A weighting scheme has been devised that is
   capable of taking into account the lower accuracy of the estimates of
   the overlapping reflections.
 

Giacovazzo, C   Altomare, A   Cuocci, C   Moliterni, AGG   Rizzi, R
Completion of crystal structure by powder diffraction data: a new
   method for locating atoms with polyhedral coordination
JOURNAL OF APPLIED CRYSTALLOGRAPHY 35, 2002, 422-429.
Ab initio crystal structure solution via powder diffraction data is
   often incomplete: frequently, the heavy atoms are correctly located but
   the light-atom positions are usually unreliable. The recently developed
   procedure POLPO [Altomare et al. (2000). J. Appl. Cryst. 33,
   1305-1310], implemented in the EXPO program [Altomare et al. (1999). J.
   Appl. Cryst. 32, 339-340], aims at completing a partial structure model
   provided by direct methods by exploiting the prior information on the
   polyhedral coordination of the located atoms (tetrahedral or
   octahedral) and their connectivity. The POLPO procedure requires that
   all the cations are correctly labelled and rightly located. This
   condition does not always occur, particularly when the data quality is
   poor. A new method is described which is able to locate missing cations
   and surrounding anions when the cation coordination is tetrahedral or
   octahedral. The procedure has been successfully checked on different
   test structures.
 

 
Altomare, A   Cuocci, C   Giacovazzo, C   Guagliardi, A   Moliterni, AGG   Rizzi, R
Real-space technique applied to crystal structure determination from
   powder data
JOURNAL OF APPLIED CRYSTALLOGRAPHY 35, 2002, 182-184.
Real-space techniques used for phase extension and refinement in the
   modern direct procedures for ab initio crystal structure solution of
   proteins have been optimized for application to powder diffraction
   data. The new process has been implemented in a modified version of
   EXPO [Altomare et al. (1999). J. Appl. Cryst. 32, 339-340]. The method
   is able to supply a structural model that is more complete than that
   provided by the standard EXPO program. The model is then refined via a
   diagonal least-squares procedure, but only when the ratio of the number
   of observations to the number of structure parameters to be refined is
   larger than a given threshold.
 

Altomare, A   Giacovazzo, C   Ianigro, M   Moliterni, AGG   Rizzi, R
Peak labelling in electron density maps from powder data: the use of
   crystal chemical information
JOURNAL OF APPLIED CRYSTALLOGRAPHY 35, 2002, 21-27.
Direct methods applied to powder diffraction data often provide
   electron density maps of which the quality is usually affected by
   systematic and/or random phase errors, by amplitude truncation effects
   in the series representation of the electron density, etc. The frequent
   incorrect labelling of the peaks can strongly affect the efficiency of
   the procedures used for crystal structure refinement. For example, the
   success of alternative techniques, such as POLPO [Altomare et al.
   (2000). J. Appl. Cryst. 33, 1305-1310], requires that all the heavy
   atoms be positioned and exactly labelled.
 
 
 
 



Monte Carlo / Simulated annealing / Direct space / Real space / Global optimization

DEEM MW; NEWSAM JM
FRAMEWORK CRYSTAL-STRUCTURE SOLUTION BY SIMULATED ANNEALING - TEST APPLICATION TO KNOWN ZEOLITE STRUCTURES
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY 1992, Vol 114, Iss 18, pp 7189-7198

HARRIS KDM; TREMAYNE M; LIGHTFOOT P; BRUCE PG
CRYSTAL-STRUCTURE DETERMINATION FROM POWDER DIFFRACTION DATA BY MONTE-CARLO METHODS
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY 1994, Vol 116, Iss 8, pp 3543-3547

CATLOW CRA; BELL RG; GALE JD
COMPUTER MODELING AS A TECHNIQUE IN MATERIALS CHEMISTRY
JOURNAL OF MATERIALS CHEMISTRY 1994, Vol 4, Iss 6, pp 781-792

Falcioni M; Deem MW
A biased Monte Carlo scheme for zeolite structure solution
JOURNAL OF CHEMICAL PHYSICS 1999, Vol 110, Iss 3, pp 1754-1766

FREEMAN CM; NEWSAM JM; LEVINE SM; CATLOW CRA
INORGANIC CRYSTAL-STRUCTURE PREDICTION USING SIMPLIFIED POTENTIALS AND EXPERIMENTAL UNIT CELLS - APPLICATION TO THE POLYMORPHS OF TITANIUM-DIOXIDE
JOURNAL OF MATERIALS CHEMISTRY 1993, Vol 3, Iss 5, pp 531-535

Engel GE; Wilke S; Konig O; Harris KDM; Leusen FJJ
PowderSolve - a complete package for crystal structure solution from powder diffraction patterns
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1999, Vol 32, pp 1169-1179

CHEETHAM AK; BULL LM
THE STRUCTURE AND DYNAMICS OF ADSORBED MOLECULES IN MICROPOROUS SOLIDS - A COMPARISON BETWEEN EXPERIMENTS AND COMPUTER-SIMULATIONS
CATALYSIS LETTERS 1992, Vol 13, Iss 3, pp 267-275

Tremayne M; Kariuki BM; Harris KDM
The development of Monte Carlo methods for crystal structure solution from powder diffraction data: Simultaneous translation and rotation of a structural fragment within the unit cell
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1996, Vol 29, pp 211-214

Kariuki BM; Zin DMS; Tremayne M; Harris KDM
Crystal structure solution from powder X-ray diffraction data: The development of monte carlo methods to solve the crystal structure of the gamma-phase of 3-chloro-trans-cinnamic acid
CHEMISTRY OF MATERIALS 1996, Vol 8, Iss 2, pp 565-569

N. Masciocchi, R. Bianchi, P. Cairati, G. Mezza, T. Pilati, A. Sironi,
P-RISCON: a real-space scavenger for crystal structure determination from powder diffraction data,
J. Appl. Cryst. 27 (1994) 426-429.

Andreev YG; Lightfoot P; Bruce PG
A general Monte Carlo approach to structure solution from powder-diffraction data: Application to poly(ethylene oxide)(3):LiN(SO2CF3)(2)
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1997, Vol 30, pp 294-305

DINUNZIO PE; MARTELLI S; BITTI RR
A MONTE-CARLO ESTIMATE OF CRYSTALLITE-SIZE AND MICROSTRAIN DISTRIBUTION-FUNCTIONS FROM X-RAY-LINE BROADENING
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1995, Vol 28, pp 146-159

Newsam JM; Freeman CM; Gorman AM; Vessal B
Simulating non-framework cation location in aluminosilicate zeolites
CHEMICAL COMMUNICATIONS 1996, Iss 16, pp 1945-1946

Harris KDM; Kariuki BM; Tremayne M
Crystal structure solution from powder diffraction data by the Monte Carlo method
EPDIC 5, PTS 1 AND 2 1998, Vol 278-2, pp 32-37

Andreev YG; Bruce PG
Solving crystal structures of molecular solids without single crystals: a simulated annealing approach
JOURNAL OF THE CHEMICAL SOCIETY-DALTON TRANSACTIONS 1998, Iss 24, pp 4071-4080

Takahashi N; Ebihara K; Yoshida K; Nakata T; Ohashi K; Miyata K
Investigation of simulated annealing method and its application to optimal design of die mold for orientation of magnetic powder
IEEE TRANSACTIONS ON MAGNETICS 1996, Vol 32, Iss 3, pp 1210-1213

Andreev YG; Bruce PG
Solution of flexible structures from powder diffraction data using a simulated annealing technique
EPDIC 5, PTS 1 AND 2 1998, Vol 278-2, pp 14-19

Coelho AA
Whole-profile structure solution from powder diffraction data using simulated annealing
JOURNAL OF APPLIED CRYSTALLOGRAPHY 2000, Vol 33, Iss 2, pp 899-908

Tremayne M; Kariuki BM; Harris KDM; Shankland K; Knight KS
Crystal structure solution from neutron powder diffraction data by a new Monte Carlo approach incorporating restrained relaxation of the molecular geometry
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1997, Vol 30, pp 968-974

Montfrooij W; McGreevy RL; Hadfield R; Andersen NH
Reverse Monte Carlo analysis of powder patterns
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1996, Vol 29, pp 285-290

AREAN CO; GONZALEZ JMR
APPLICATION OF A MONTE-CARLO METHOD TO THE DETERMINATION OF CATION DISTRIBUTION IN SPINELS BY POWDER DIFFRACTOMETRY
JOURNAL OF SOLID STATE CHEMISTRY 1986, Vol 63, Iss 2, pp 336-340

Wechsler D; Zsigmond G; Streffer F; Stride JA; Mezei F
Monte-Carlo simulations for instrumentation at pulsed and continuous sources
PHYSICA B 2000, Vol 276, pp 71-72

EUTSCH PW; STANIK TD
A TEMPERATURE-DEPENDENT SIMULATION OF THE X-RAY-POWDER SPECTRUM OF ICE IH USING METROPOLIS MONTE-CARLO SAMPLING
JOURNAL OF CHEMICAL PHYSICS 1986, Vol 85, Iss 8, pp 4660-4666

Mellergard A; McGreevy RL
Reverse Monte Carlo modelling of neutron powder diffraction data
ACTA CRYSTALLOGRAPHICA SECTION A 1999, Vol 55, pp 783-789

Di Nunzio PE; Martelli S
Size distribution of single-crystal nanoparticles by Monte Carlo fitting of wide-angle X-ray scattering peak shape
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1999, Vol 32, pp 546-548

Altomare A; Giacovazzo C; Guagliardi A; Moliterni AGG; Rizzi R
Completion of crystal structures from powder data: the use of the coordination polyhedra
JOURNAL OF APPLIED CRYSTALLOGRAPHY 2000, Vol 33, pp 1305-1310

Toby BH; Khosrovani N; Dartt CD; Davis ME; Parise JB
Structure-directing agents and stacking faults in the CON system: a combined crystallographic and computer simulation study
MICROPOROUS AND MESOPOROUS MATERIALS 2000, Vol 39, Iss 1-2, pp 77-89

Zetterstrom P; McGreevy RL
Improved Monte Carlo program MCGR, for determining G(r)
PHYSICA B 2000, Vol 276, pp 187-188

Zhukov SG; Chernyshev VV; Babaev EV; Sonneveld EJ; Schenk H
Application of simulated annealing approach for structure solution of molecular crystals from X-ray laboratory powder data
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 2001, Vol 216, Iss 1, pp 5-9

Reinaudi L; Carbonio RE; Leiva EPM
Inclusion of symmetry for the enhanced determination of crystalline structures from powder diffraction data using simulated annealing
CHEMICAL COMMUNICATIONS 1998, Iss 2, pp 255-256

Reinaudi L; Leiva EPM; Carbonio RE
Simulated annealing prediction of the crystal structure of ternary inorganic compounds using symmetry restrictions
JOURNAL OF THE CHEMICAL SOCIETY-DALTON TRANSACTIONS 2000, Iss 23, pp 4258-4262

Popa NC; Ionita I
The instrumental profile for a neutron powder diffractometer in focusing geometry
PHYSICA B 2000, Vol 276, pp 192-194

Stoica AD; Popovici M; Yelon WB
Instrumental line shapes in neutron powder diffraction with focusing monochromators
JOURNAL OF APPLIED CRYSTALLOGRAPHY 2000, Vol 33, pp 137-146

Favre-Nicolin-V; Cerny-R
FOX, 'free objects for crystallography': a modular approach to ab initio structure determination from powder diffraction
JOURNAL-OF-APPLIED-CRYSTALLOGRAPHY. DEC 2002; 35 Part 6 : 734-743
global-optimization algorithms to solve the structure by performing trials in direct space.

Seaton CC, Tremayne M.
Differential evolution: crystal structure determination of a triclinic polymorph of adipamide from powder diffraction data.
Chem Commun 2002:880881.
The crystal structure of a previously unknown triclinic polymorph of adipamide has been solved from laboratory X-ray powder diffraction data using a new direct space global optimisation method based on differential evolution.

JOHNSTON-John-C; DAVID-William-I-F; MARKVARDSEN-Anders-J; SHANKLAND-Kenneth
A hybrid Monte Carlo method for crystal structure determination from powder diffraction data
Acta-crystallographica-Section-A-Foundations-of-crystallography. 2002; 58 (p.5) : 441-447

A. Altomare, C. Cuocci, C. Giacovazzo, A. Guagliardi, A.G. Moliterni and R. Rizzi,
Real-space technique applied to crystal structure determination from powder data
J. Appl. Cryst. 35 (2002) 182-184.

Rodriguez-Carvajal,-J.
Magnetic structure determination from powder diffraction symmetry analysis and simulated annealing
Materials-Science-Forum. 2001; 378-381 pt. 1: 268-73

Le-Bail,-A.
ESPOIR: a program for solving structures by Monte Carlo analysis of powder diffraction data
Materials-Science-Forum. 2001; 378-381 pt. 1: 65-70

O.J. Lanning, S. Habershon, K.D.M. Harris, R.L. Johnston, B.M. Kariuki, E. Tedesco and G.W. Turner,
Definition of a 'guiding function' in global optimization: a hybrid approach combining energy and R-factor in structure solution from powder diffraction data
Chem. Phys. Letters 317 (2000) 296-303.
 
 

Earl, DJ   Deem, MW
Parallel tempering: Theory, applications, and new perspectives
PHYSICAL CHEMISTRY CHEMICAL PHYSICS 7, 2005, 3910-3916.
We review the history of the parallel tempering simulation method. From
   its origins in data analysis, the parallel tempering method has become
   a standard workhorse of physicochemical simulations. We discuss the
   theory behind the method and its various generalizations. We mention a
   selected set of the many applications that have become possible with
   the introduction of parallel tempering, and we suggest several
   promising avenues for future research.
 

Chong, SY   Tremayne, M
Combined optimization using cultural and differential evolution:
   application to crystal structure solution from powder diffraction data
CHEMICAL COMMUNICATIONS iss 39, 2006, 4078-4080.
The principles of social and biological evolution have been combined in
   a Cultural Differential Evolution hybrid global optimization technique
   and applied to crystal structure solution.
 
 
 

 
David, WIF   Shankland, K   van de Streek, J   Pidcock, E   Motherwell, WDS   Cole, JC
DASH: a program for crystal structure determination from powder
   diffraction data
JOURNAL OF APPLIED CRYSTALLOGRAPHY 39, 2006, 910-915.
DASH is a user-friendly graphical-user-interface-driven computer
   program for solving crystal structures from X-ray powder diffraction
   data, optimized for molecular structures. Algorithms for multiple peak
   fitting, unit-cell indexing and space-group determination are included
   as part of the program. Molecular models can be read in a number of
   formats and automatically converted to Z-matrices in which flexible
   torsion angles are automatically identified. Simulated annealing is
   used to search for the global minimum in the space that describes the
   agreement between observed and calculated structure factors. The
   simulated annealing process is very fast, which in part is due to the
   use of correlated integrated intensities rather than the full powder
   pattern. Automatic minimization of the structures obtained by simulated
   annealing and automatic overlay of solutions assist in assessing the
   reproducibility of the best solution, and therefore in determining the
   likelihood that the global minimum has been obtained.
 
 

Charge flipping
 

Wu, JS   Leinenweber, K   Spence, JCH   O'Keeffe, M
Ab initio phasing of X-ray powder diffraction patterns by charge
   flipping
NATURE MATERIALS 5, 2006, 647-652.
Determining crystal structures from powder X- ray diffraction data
   remains a challenging problem in materials science. By embedding a
   Le-Bail-like procedure within the recently discovered charge-flipping
   phasing algorithm, an extremely simple, fast and effective ab initio
   method has been developed to determine phases directly from indexed
   powder diffraction patterns. The algorithm solves the degeneracy
   problem by applying spherical averaging for overlapping Bragg
   reflections, while solving the phase problem by using the Oszlanyi-Suto
   charge-flipping algorithm. The processes of peak decomposition and
   phasing are integrated within the same iteration, and a dynamic support
   is used. The Fienup hybrid input-output algorithm is also incorporated
   to minimize stagnation. The ability of the algorithm to find
   structure-factor phases rapidly is found to assist with the fundamental
   problem of degeneracy ( overlapping reflections) which is intrinsic to
   powder diffraction data. Space-group and chemical-composition
   information are not needed as inputs, and can be determined from the
   result. The method is illustrated using several experimental powder
   patterns of indifferent quality.
 
 

Palatinus, L
Ab initio determination of incommensurately modulated structures by
   charge flipping in superspace
ACTA CRYSTALLOGRAPHICA SECTION A 60, 2004, 604-610.
The charge flipping algorithm proposed by Oszlanyi & Suto [Acta Cryst.
   (2004), A60, 134-141] for ab initio reconstruction of crystal
   structures is generalized towards superspace. Its efficiency is
   demonstrated by successful reconstruction of eight known
   incommensurately modulated structures from experimental data. The
   output of the charge flipping algorithm is an electron density with
   symmetry P1. The symmetry of the structure is recovered by locating the
   positions of symmetry operators and averaging the density over the
   symmetry-related pixels. The reconstruction of a modulated structure by
   the charge flipping algorithm and the accuracy of the result is
   demonstrated in detail on the modulated structure of
   tetraphenylphosphonium hexabromotellurate(IV) bis{dibromoselenate(I)}.
 
 
 
 
 
 
 

2005
 

Markvardsen, AJ   Shankland, K   David, WIF   Didlick, G
Characterization of a hybrid Monte Carlo search algorithm for structure
   determination
JOURNAL OF APPLIED CRYSTALLOGRAPHY 38, 2005, 107-111.
A hybrid Monte Carlo (HMC) search algorithm has recently been shown to
   be a promising method for structure determination from powder
   diffraction data [ Johnston, David, Markvardsen & Shankland ( 2002).
   Acta Cryst. A58, 441 - 447]. Here, the performance of the algorithm on
   a number of different crystal structures is investigated as a function
   of its control parameters. This detailed analysis required the use of a
   system for distributed computing in order to keep the calculation times
   within a reasonable time frame. The results obtained confirm previous
   findings and a detailed discussion of the effect of the control
   parameters on the efficiency of the HMC method is provided. The results
   suggest a method for setting these parameters automatically, which is
   an essential step if HMC is to find routine use in the determination of
   crystal structures.

Cerny, R   Favre-Nicolin, V
FOX: A friendly tool to solve nonmolecular structures from powder
   diffraction
POWDER DIFFRACTION 20, 2005, 359-365.
Structural characterization from powder diffraction of compounds not
   containing isolated molecules but three-dimensional infinite structure
   (alloys, intermetallics, framework compounds, extended solids) by
   direct space methods has been largely improved in the last 15 years.
   The success of the method depends very much on a proper modeling of the
   structure from building blocks. The modeling from larger building
   blocks improves the convergence of the global optimization algorithm by
   a factor of up to 10. However, care must be taken about the correctness
   of the building block, like its rigidity, deformation, bonding
   distances, and ligand identity. Dynamical occupancy correction
   implemented in the direct space program FOX has shown to be useful when
   merging excess atoms, and even larger building blocks like coordination
   polyhedra. It also allows joining smaller blocks into larger ones in
   the case when the connectivity was not a priori evident from the
   structural model. We will show in several examples of nonmolecular
   structures the effect of the modeling by correct structural units.

Favre-Nicolin, V   Cerny, R
FOX, 'free objects for crystallography': a modular approach to ab
   initio structure determination from powder diffraction
JOURNAL OF APPLIED CRYSTALLOGRAPHY 35, 2002, 734-743.
A new program has been developed for ab initio crystal structure
   determination from powder diffraction data (X-ray and neutron). It uses
   global-optimization algorithms to solve the structure by performing
   trials in direct space. It is a modular program, capable of using
   several criteria for evaluating each trial configuration (e.g.
   multi-pattern). It is also modular in the description of the crystal
   content, with the possibility of describing building blocks in the
   sample, such as polyhedra or molecules, and with automatic adaptive
   handling of special positions and sharing of identical atoms between
   neighbouring building blocks. It can therefore find the correct
   structure without any assumption about the connectivity of the building
   blocks and is suitable for any kind of material. Several optimization
   algorithms (simulated annealing, parallel tempering) are available,
   with the possibility of choosing the convergence criterion as a
   combination of available cost functions. This program is freely
   available for Linux and Windows platforms; it is also fully 'open
   source', which, combined with an object-oriented design and a complete
   developer documentation, ensures its future evolution.
 
 

Favre-Nicolin-, V   Cerny, R
A better FOX: using flexible modelling and maximum likelihood to
   improve direct-space ab initio structure determination from powder
   diffraction
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 219, 2004, 847-856.
Ab initio structure determination using direct-space methods, although
   relying on an essentially bruteforce approach, can be greatly improved
   through smarter algorithms. The most basic improvement involves the use
   C, of prior information to reduce the number of configurations
   evaluated to find the structure solution. It is however vitally
   important that the parametrization used to incorporate this prior
   information does not reduce the efficiency with which the configuration
   space is explored. We will show that this can be achieved by defining
   molecules and polyhedra through a set of restraints associated to
   dedicated random changes. allowing to solve structures up to three
   times as fast as with the 'standard' approach where atomic positions
   are parametrized directly from bond lengths, bond angles and dihedral
   angles.
   To further enhance the efficiency of the algorithm, it is also possible
   to 'tune' the convergence criterion used to compare the structural
   model to the observed diffraction data (usually chi(2) or R-wp). By
   using Maximum Likelihood principles. it is shown that incorporating the
   fact that the model is approximate in the chi(2) evaluation can improve
   the algorithm convergence towards the structure solution.
 
 

 
Favre-Nicolin, V     Cerny, R
FOX: Modular approach to crystal structure determination from powder
   diffraction
EUROPEAN POWDER DIFFRACTION EPDIC 8  MATERIALS SCIENCE FORUM 443-4, 2004, 35-38.
Program FOX for ab initio crystal structure determination from powder
   diffraction uses global optimization algorithms to find the correct
   structure by making trials in the direct space. It is a modular
   program, capable of using several criteria for evaluating each trial
   configuration, e.g. combining neutron and X-ray diffraction patterns.
   The program describes the structural building blocks (polyhedrons,
   molecules etc.) with their internal coordinates (Z-matrices), thus all,
   owing natural constraints on interatomic distances and angles.
   Identical atoms shared between neighboring building blocks, and special
   positions are handled with an automatic, adaptive method (Dynamical
   Occupancy Correction). Several algorithms (Simulated Annealing,
   Parallel Tempering) are currently available. The program is based on an
   object-oriented crystallographic library ObjCryst++ (programming
   language c++). The program and the library are available for Linux and
   Windows on http://objcryst.sourceforge.net. Inorganic and organic
   structures with the complexity up to 26 independents atoms are
   routinely solved from laboratory X-ray, synchrotron or neutron data.

 
Harris, KDM   Habershon, S   Cheung, EY   Johnston, RL
Developments in genetic algorithm techniques for structure solution
   from powder diffraction data
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 219, 2004, 838-846.
DE X-ray powder diffraction; structure analysis; structure solution;
   genetic algorithm; molecular crystals
ID CRYSTAL-STRUCTURE DETERMINATION; X-RAY-DIFFRACTION; MONTE-CARLO
   APPROACH; R-FACTOR; ACID; ENERGY; SYSTEM; UNIT
AB This paper presents an overview of developments that have taken place
   in recent years in the genetic algorithm technique for structure
   solution from powder diffraction data. After a brief resume of the
   essential features of the genetic algorithm technique for structure
   solution, the paper highlights recent developments in fundamental
   aspects of the technique, including the development of parallel
   computing concepts, the analysis of the evolutionary history in genetic
   algorithm structure solution calculations and the combination of energy
   information together with the powder diffraction data in structure
   solution. Several examples are also given to illustrate the application
   of the genetic algorithm technique to solve crystal structures of
   different types of organic molecular materials, including oligopeptides
   and multi-component co-crystals.
 
 
 

Brodski, V   Peschar, R   Schenk, H
Organa - a program package for structure determination from powder
   diffraction data by direct-space methods
JOURNAL OF APPLIED CRYSTALLOGRAPHY 38, 2005, 688-693.
A new software package has been developed, named Organa, for ab initio
   solution of crystal structures from powder diffraction data by
   direct-space methods. The package contains energy-guiding Monte Carlo
   and grid-search algorithms and is based on a combined global
   minimization of the R factor and a potential energy function of the
   system with the option of local minimization of the cost function for
   each generated trial structure. Basically, the potential energy
   function consists of van der Waals interactions, but harmonic
   potentials can be added to impose soft distance restraints. The program
   was successfully applied to the structure determination of a series of
   melamine phosphate compounds. The program is freely available ( for all
   Windows platforms) from the correspondence author upon request.

Altomare, A   Caliandro, R   Giacovazzo, C   Moliterni, AGG   Rizzi, R
Solution of organic crystal structures from powder diffraction by
   combining simulated annealing and direct methods
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 230-238.
The ab initio crystal structure solution from powder diffraction data
   can be attempted via direct methods. If heavy atoms are present, they
   are usually correctly located; then some crystal chemical information
   can be exploited to complete the partial structure model. Organic
   structures are more resistant to direct methods; as an alternative,
   their molecular geometry is used as prior information for Monte Carlo
   methods. In this paper, a new procedure is described which combines the
   information contained in the electron density map provided by direct
   methods with a Monte Carlo method which uses simulated annealing as a
   minimization algorithm. A figure of merit has been designed based on
   the agreement between the experimental and calculated profiles, and on
   the positions of the peaks in the electron density map. The procedure
   is completely automatic and has been included in EXPO; its performance
   has been validated and tested for a set of known molecular structures.
 

 
Habershon, S   Harris, KDM   Johnston, RL
Development of a multipopulation parallel genetic algorithm for
   structure solution from powder diffraction data
JOURNAL OF COMPUTATIONAL CHEMISTRY 24, 2003, 1766-1774.
Previously, the genetic algorithm (GA) approach for direct-space
   crystal structure solution from powder diffraction data has been
   applied successfully in the structure determination of a range of
   organic molecular materials. In this article, we present a further
   development of our approach, namely a multipopulation parallel GA
   (PGA), which is shown to give rise to increased speed, efficiency, and
   reliability of structure solution calculations, as well as providing
   new opportunities for further optimizing our GA methodology. The
   multipopulation PGA is based on the independent evolution of different
   subpopulations, with occasional interaction (e.g., transfer of
   structures) allowed to occur between the different subpopulations.
   Different strategies for carrying out this interpopulation
   communication are considered in this article, and comparisons are made
   to the conventional single-population GA. The increased power offered
   by the PGA approach creates the opportunity for structure determination
   of molecular crystals of increasing complexity.
 
 

 
Brodski, V   Peschar, R   Schenk, H
A Monte Carlo approach to crystal structure determination from powder
   diffraction data
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 239-243.
A new direct-space method for ab initio solution of crystal structures
   from powder diffraction data is presented. The approach consists of a
   combined global minimization of R-wp and the potential energy of the
   system. This method was tested on two organic compounds with known
   structure and also applied successfully in the structure determination
   of the previously unknown structure of melamine pyrophosphate.
 

Johnston, JC   David, WIF   Markvardsen, AJ   Shankland, K
A hybrid Monte Carlo method for crystal structure determination from
   powder diffraction data
ACTA CRYSTALLOGRAPHICA SECTION A 58, 2002, 441-447.
A hybrid Monte Carlo algorithm for crystal structure determination from
   powder diffraction data is presented. The algorithm combines the key
   components of molecular dynamics and Monte Carlo simulations to achieve
   efficient sampling of phase space, allowing the crystal structure of
   capsaicin to be determined from powder diffraction data more
   effectively than by a simulated-annealing approach. The implementation
   of the algorithm, the choice of the simulation parameters and the
   performance of the algorithm are discussed.
 
 
 
 

Markvardsen, AJ   David, WIF   Shankland, K
A maximum-likelihood method for global-optimization-based structure
   determination from powder diffraction data
ACTA CRYSTALLOGRAPHICA SECTION A 58, 2002, 316-326.
A maximum-likelihood algorithm has been incorporated into a crystal
   structure determination from a powder diffraction data framework that
   uses an integrated-intensity-based global optimization technique. The
   algorithm is appropriate when the structural model being optimized is
   not a complete description of the crystal structure under study.
 
 

 
Nakamura, H   Yamazaki, S   Ohnishi, T   Ida, T   Toraya, H
The Monte Carlo method for finding missing atoms in solving crystal
   structures from powder diffraction data without applying a rigid-body
   approximation
POWDER DIFFRACTION 16, 2001, 65-70.
The Monte Carlo method is applied to finding missing atoms in solving
   inorganic crystal structures without applying a rigid-body
   approximation. Whole powder patterns of alpha -SiO2 and Mg2SiO4 were
   used for testing a procedure. Four atoms among the six in the
   asymmetric unit of Mg2SiO4 could be found in the present analysis. The
   use of well-refined profile parameters enhanced the frequency of
   correct structure configurations in the Monte Carlo search. Utilizing
   structural information available for constructing a trial configuration
   is also considered to be important for efficiently searching the
   structure solution. A procedure for assignment of equivalent positions
   to respective atoms is presented. The method can be used as a powerful
   tool for finding missing atoms in a partially solved structure. A
   histogram of weighted reliability index in Monte Carlo calculations is
   very informative for evaluating the performance of the method. (C) 2001
   International Centre for Diffraction Data.
 
 
 



Maximum Entropy / Likelihood

BRICOGNE G
DIRECT PHASE DETERMINATION BY ENTROPY MAXIMIZATION AND LIKELIHOOD RANKING - STATUS-REPORT AND PERSPECTIVES
ACTA CRYSTALLOGRAPHICA SECTION D-BIOLOGICAL CRYSTALLOGRAPHY 1993, Vol 49, pp 37-60

KUMAZAWA S; KUBOTA Y; TAKATA M; SAKATA M; ISHIBASHI Y
MEED - A PROGRAM PACKAGE FOR ELECTRON-DENSITY-DISTRIBUTION CALCULATION BY THE MAXIMUM-ENTROPY METHOD
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1993, Vol 26, pp 453-457

BRICOGNE G
A MULTISOLUTION METHOD OF PHASE DETERMINATION BY COMBINED MAXIMIZATION OF ENTROPY AND LIKELIHOOD .3. EXTENSION TO POWDER DIFFRACTION DATA
ACTA CRYSTALLOGRAPHICA SECTION A 1991, Vol 47, pp 803-829

GILMORE CJ; HENDERSON K; BRICOGNE G
A MULTISOLUTION METHOD OF PHASE DETERMINATION BY COMBINED MAXIMIZATION OF ENTROPY AND LIKELIHOOD .4. THE ABINITIO SOLUTION OF CRYSTAL-STRUCTURES FROM THEIR X-RAY-POWDER DATA
ACTA CRYSTALLOGRAPHICA SECTION A 1991, Vol 47, pp 830-841

C.J. Gilmore, K. Shankland & G. Bricogne,
Applications of the maximum entropy method to powder diffraction and electron crystallography,
Proc. R. Soc. Lond. A 442 (1993) 97-111.

K. Shankland & C.J. Gilmore,
The ab initio determination of crystal structures from their powder diffraction patterns using a combination of entropy maximisation and likelihood ranking,
Materials Sci. Forum 133/136 (1993) 189.

SAKATA M; MORI R; KUMAZAWA S; TAKATA M; TORAYA H
ELECTRON-DENSITY DISTRIBUTION FROM X-RAY-POWDER DATA BY USE OF PROFILE FITS AND THE MAXIMUM-ENTROPY METHOD
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1990, Vol 23, pp 526-534

SAKATA M; UNO T; TAKATA M; HOWARD CJ
MAXIMUM-ENTROPY-METHOD ANALYSIS OF NEUTRON-DIFFRACTION DATA
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1993, Vol 26, pp 159-165

GILMORE CJ; HENDERSON AN; BRICOGNE G
A MULTISOLUTION METHOD OF PHASE DETERMINATION BY COMBINED MAXIMIZATION OF ENTROPY AND LIKELIHOOD .5. THE USE OF LIKELIHOOD AS A DISCRIMINATOR OF PHASE SETS PRODUCED BY THE SAYTAN PROGRAM FOR A SMALL PROTEIN
ACTA CRYSTALLOGRAPHICA SECTION A 1991, Vol 47, pp 842-846

VOIGTMARTIN IG; YAN DH; YAKIMANSKY A; SCHOLLMEYER D; GILMORE CJ; BRICOGNE G
STRUCTURE DETERMINATION BY ELECTRON CRYSTALLOGRAPHY USING BOTH MAXIMUM-ENTROPY AND SIMULATION APPROACHES
ACTA CRYSTALLOGRAPHICA SECTION A 1995, Vol 51, pp 849-868

SHANKLAND K; GILMORE CJ; BRICOGNE G; HASHIZUME H
A MULTISOLUTION METHOD OF PHASE DETERMINATION BY COMBINED MAXIMIZATION OF ENTROPY AND LIKELIHOOD .6. AUTOMATIC LIKELIHOOD ANALYSIS VIA THE STUDENT T TEST, WITH AN APPLICATION TO THE POWDER STRUCTURE OF MAGNESIUM BORON-NITRIDE, MG3BN3
ACTA CRYSTALLOGRAPHICA SECTION A 1993, Vol 49, pp 493-501

PAPOULAR RJ; COX DE
MODEL-FREE SEARCH FOR EXTRA-FRAMEWORK CATIONS IN ZEOLITES USING POWDER DIFFRACTION
EUROPHYSICS LETTERS 1995, Vol 32, Iss 4, pp 337-342

Gilmore C; Dong W; Bricogne G
A multisolution method of phase determination by combined maximization of entropy and likelihood. VI. The use of error-correcting codes as a source of phase permutation and their application to the phase problem in powder, electron and macromolecular crystallography
ACTA CRYSTALLOGRAPHICA SECTION A 1999, Vol 55, pp 70-83

KUMAZAWA S; TAKATA M; SAKATA M
ON THE SINGLE-PIXEL APPROXIMATION IN MAXIMUM-ENTROPY ANALYSIS
ACTA CRYSTALLOGRAPHICA SECTION A 1995, Vol 51, pp 47-53

Sakata M; Takata M
The principle of the maximum entropy method
HIGH PRESSURE RESEARCH 1996, Vol 14, Iss 4-6, pp 327-333

Elliott JA; Hanna S
A model-independent maximum-entropy method for the inversion of small-angle X-ray diffraction patterns
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1999, Vol 32, pp 1069-1083

Knorr K; Madler F; Papoular RJ
Model-free density reconstruction of host/guest compounds from high-resolution powder diffraction data
MICROPOROUS AND MESOPOROUS MATERIALS 1998, Vol 21, Iss 4-6, pp 353-363

Xie Y; Hao Q
Evaluation of reflection intensities for the components of multiple Laue diffraction spots by the maximum-entropy method
ACTA CRYSTALLOGRAPHICA SECTION A 1997, Vol 53, pp 643-648

ESTERMANN MA
SOLVING CRYSTAL-STRUCTURES WITH THE SYMMETRY MINIMUM FUNCTION
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT 1995, Vol 354, Iss 1, pp 126-133

Gilmore CJ
Maximum entropy methods in electron crystallography
MICROSCOPY RESEARCH AND TECHNIQUE 1999, Vol 46, Iss 2, pp 117-129

Burger K; Prandl W
A new type of constraint in the maximum-entropy method using ambiguous phase information from anomalous-scattering powder data
ACTA CRYSTALLOGRAPHICA SECTION A 1999, Vol 55, pp 719-728

Burger K; Cox D; Papoular R; Prandl W
The application of resonant scattering techniques to ab initio structure solution from powder data using SrSO4 as a test case
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1998, Vol 31, pp 789-797

Dong W; Gilmore CJ
The ab initio solution of structures from powder diffraction data: the use of maximum entropy and likelihood to determine the relative amplitudes of overlapped reflections using the pseudophase concept
ACTA CRYSTALLOGRAPHICA SECTION A 1998, Vol 54, pp 438-446

Burger K
Enhanced versions of the maximum entropy program MEED for X-ray and neutron diffraction
POWDER DIFFRACTION 1998, Vol 13, Iss 2, pp 117-120

Takata M; Nishibori E; Sakata M
Charge density studies utilizing powder diffraction and MEM. Exploring of high Tc superconductors, C-60 superconductors and manganites
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 2001, Vol 216, Iss 2, pp 71-86

Kirihara K; Nakata T; Takata M; Kubota Y; Nishibori E; Kimura K; Sakata M
Electron-density distribution of approximants of the icosahedral Al-based alloys by the maximum-entropy method and the Rietveld refinement
MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 2000, Vol 294, pp 492-495

Dorset DL
Low-resolution direct phase determination in protein electron crystallography - breaking globular constraints
ACTA CRYSTALLOGRAPHICA SECTION A 2000, Vol 56, pp 529-535

Armstrong N; Kalceff W
A maximum entropy method for determining column-length distributions from size-broadened X-ray diffraction profiles
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1999, Vol 32, pp 600-613

CHEN PY; MOU CY
STATISTICAL-INFERENCE OF DISTRIBUTION OF CRYSTAL SIZE BY X-RAY-POWDER DIFFRACTION
JOURNAL OF THE CHINESE CHEMICAL SOCIETY 1994, Vol 41, Iss 1, pp 65-73

DAVID WIF
EXTENDING THE POWER OF POWDER DIFFRACTION FOR STRUCTURE DETERMINATION
INSTITUTE OF PHYSICS CONFERENCE SERIES 1990, Iss 107, pp 93-100

ESTERMANN MA; GRAMLICH V
IMPROVED TREATMENT OF SEVERELY OR EXACTLY OVERLAPPING BRAGG-REFLECTIONS FOR THE APPLICATION OF DIRECT-METHODS TO POWDER DATA
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1993, Vol 26, pp 396-404

MOENS P; DEVOLDER P; HOOGEWIJS R; CALLENS F; VERBEECK R
MAXIMUM-LIKELIHOOD COMMON-FACTOR ANALYSIS AS A POWERFUL TOOL IN DECOMPOSING MULTICOMPONENT EPR POWDER SPECTRA
JOURNAL OF MAGNETIC RESONANCE SERIES A 1993, Vol 101, Iss 1, pp 1-15

ANTONIADIS A; BERRUYER J; FILHOL A
MAXIMUM-LIKELIHOOD METHODS IN POWDER DIFFRACTION REFINEMENTS
ACTA CRYSTALLOGRAPHICA SECTION A 1990, Vol 46, pp 692-711

Tsur Y; Randall CA
Analysis of X-ray powder diffraction data using the maximum likelihood estimation method
JOURNAL OF THE AMERICAN CERAMIC SOCIETY 2000, Vol 83, Iss 8, pp 2062-2066

BYROM PG; LUCAS BW
POLISH - A COMPUTER-PROGRAM FOR IMPROVING THE ACCURACY OF STRUCTURE-FACTOR MAGNITUDES OBTAINED FROM POWDER DATA
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1993, Vol 26, pp 137-139

A. J. Markvardsen, W. I. F. David and K. Shankland
A maximum-likelihood method for global-optimization-based structure determination from powder diffraction data
Acta Cryst. (2002). A58, 316-326

F. Izumi, A. Yamamoto, N.R. Khasanova, S. Kumazawa, W.Z. Hu and T. Kamiyama,
Novel techniques of neutron powder diffraction and their applications to superconducting oxides
Physica C 335 (2000) 239-244.
Program REMEDY : whole pattern-fitting combined with maximum entropy



Genetic Algorithm

Shankland K; David WIF; Csoka T
Crystal structure determination from powder diffraction data by the application of a genetic algorithm
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 1997, Vol 212, Iss 8, pp 550-552

Harris KDM; Johnston RL; Kariuki BM
The genetic algorithm: Foundations and applications in structure solution from powder diffraction data
ACTA CRYSTALLOGRAPHICA SECTION A 1998, Vol 54, pp 632-645

Kariuki BM; Serrano-Gonzalez H; Johnston RL; Harris KDM
The application of a genetic algorithm for solving crystal structures from powder diffraction data
CHEMICAL PHYSICS LETTERS 1997, Vol 280, Iss 3-4, pp 189-195

WIENKE D; LUCASIUS C; KATEMAN G
MULTICRITERIA TARGET VECTOR OPTIMIZATION OF ANALYTICAL PROCEDURES USING A GENETIC ALGORITHM .1. THEORY, NUMERICAL SIMULATIONS AND APPLICATION TO ATOMIC EMISSION-SPECTROSCOPY
ANALYTICA CHIMICA ACTA 1992, Vol 265, Iss 2, pp 211-225

Woodley SM; Battle PD; Gale JD; Catlow CRA
The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation
PHYSICAL CHEMISTRY CHEMICAL PHYSICS 1999, Vol 1, Iss 10, pp 2535-2542

Harris KDM; Johnston RL; Kariuki BM; Tremayne M
A genetic algorithm for crystal structure solution from powder diffraction data
JOURNAL OF CHEMICAL RESEARCH-S 1998, Iss 7, pp 390-+

Putz H; Schon JC; Jansen M
Combined method for ab initio structure solution from powder diffraction data
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1999, Vol 32, pp 864-870

Wessels T; Baerlocher C; McCusker LB
Single-crystal-like diffraction data from polycrystalline materials
SCIENCE 1999, Vol 284, Iss 5413, pp 477-479

Hammond RB; Roberts KJ; Smith EDL; Docherty R
Application of a computational systematic search strategy to study polymorphism in phenazine and perylene
JOURNAL OF PHYSICAL CHEMISTRY B 1999, Vol 103, Iss 37, pp 7762-7770

Kariuki BM; Belmonte SA; McMahon MI; Johnston RL; Harris KDM; Nelmes RJ
A new approach for indexing powder diffraction data based on whole-profile fitting and global optimization using a genetic algorithm
JOURNAL OF SYNCHROTRON RADIATION 1999, Vol 6, pp 87-92

Reardon BJ
Optimization of densification modelling parameters of beryllium powder using a fuzzy logic based multiobjective genetic algorithm
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING 1998,
Vol 6, Iss 6, pp 735-746

Csoka T; David WIF; Shankland K
Crystal structure determination from powder diffraction data by the application of a genetic algorithm
EPDIC 5, PTS 1 AND 2 1998, Vol 278-2, pp 294-299

Paszkowicz W
Application of the smooth genetic algorithm for indexing powder patterns - Tests for the orthorhombic system
EUROPEAN POWDER DIFFRACTION: EPDIC IV, PTS 1 AND 2 1996, Vol 228, pp 19-24

De Gelder R; Wehrens R; Hageman JA
A generalized expression for the similarity of spectra: Application to powder diffraction pattern classification
JOURNAL OF COMPUTATIONAL CHEMISTRY 2001, Vol 22, Iss 3, pp 273-289

Bond AD; Feeder N; Teat SJ; Jones W
The solid-state structure of 3-hydroxy-4-methyl-2(3H)-thiazolethione: Prediction and measurement
TETRAHEDRON 2000, Vol 56, Iss 36, pp 6617-6624

Turner GW; Tedesco E; Harris KDM; Johnston RL; Kariuki BM
Implementation of Lamarckian concepts in a Genetic Algorithm for structure solution from powder diffraction data
CHEMICAL PHYSICS LETTERS 2000, Vol 321, Iss 3-4, pp 183-190

Reardon BJ; Bingert SR
Inversion of tantalum micromechanical powder consolidation and sintering models using Bayesian inference and genetic algorithms
ACTA MATERIALIA 2000, Vol 48, Iss 3, pp 647-658

Reardon BJ
Inversion of micromechanical powder consolidation and sintering models using Bayesian inference and genetic algorithms
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING 1999, Vol 7, Iss 6, pp 1061-1081

Harris KDM; Johnston RL; Kariuki BM
An evolving technique for powder structure solution - fundamentals and applications of the genetic algorithm
ANALES DE QUIMICA-INTERNATIONAL EDITION 1998, Vol 94, Iss 6, pp 410-416

Kariuki BM; Johnston RL; Harris KDM; Psallidas K; Ahn S; Serrano-Gonzalez H
Application of a Genetic Algorithm in structure determination from powder diffraction data
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY 1998, Iss 38, pp 123-135

Yan JQ; Zhang PX; Wu WQ; Shan SG; Sui ZT
Artificial neural networks and genetic algorithm used to optimize process parameters of reaction-sintered ZrO2-SiC(p) ceramics
JOURNAL OF INORGANIC MATERIALS 1998, Vol 13, Iss 6, pp 937-940

Knorr K; Madler F
The application of evolution strategies to disordered structures
JOURNAL OF APPLIED CRYSTALLOGRAPHY 1999, Vol 32, pp 902-910

Weber-T; Burgi-HB
Determination and refinement of disordered crystal structures using evolutionary algorithms in combination with Monte Carlo methods
ACTA-CRYSTALLOGRAPHICA-SECTION-A. NOV 2002; 58 Part 6 : 526-540

HABERSHON-Scott; HARRIS-Kenneth-D-M; JOHNSTON-Roy-L; TURNER-Giles-W; JOHNSTON-Jennifer-M
Gaining insights into the evolutionary behaviour in genetic algorithm calculations, with applications in structure solution from powder diffraction data
Chemical-physics-letters. 2002; 353 (3-4) : 185-194
A general strategy is introduced for analysing the evolutionary events that occur during a genetic algorithm calculation, and the application of this approach is illustrated for the specific case of understanding the evolutionary trajectory leading to the correct structure solution in structure determination from powder diffraction data.



Grid Search

Chernyshev VV; Schenk H
A grid search procedure of positioning a known molecule in an unknown crystal structure with the use of powder diffraction data
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 1998, Vol 213, Iss 1, pp 1-3

Mora AJ; Fitch AN
The low-temperature crystal structure of RS-camphor
JOURNAL OF SOLID STATE CHEMISTRY 1997, Vol 134, Iss 1, pp 211-214



Structure Prediction

FREEMAN CM; NEWSAM JM; LEVINE SM; CATLOW CRA
INORGANIC CRYSTAL-STRUCTURE PREDICTION USING SIMPLIFIED POTENTIALS AND EXPERIMENTAL UNIT CELLS - APPLICATION TO THE POLYMORPHS OF TITANIUM-DIOXIDE
JOURNAL OF MATERIALS CHEMISTRY 1993, Vol 3, Iss 5, pp 531-535

Buttar D; Charlton MH; Docherty R; Starbuck J
Theoretical investigations of conformational aspects of polymorphism. Part 1: O-acetamidobenzamide
JOURNAL OF THE CHEMICAL SOCIETY-PERKIN TRANSACTIONS 2 1998, Iss 4, pp 763-772

van Eijck BP; Kroon J
UPACK program package for crystal structure prediction: Force fields and crystal structure generation for small carbohydrate molecules
JOURNAL OF COMPUTATIONAL CHEMISTRY 1999, Vol 20, Iss 8, pp 799-812

Filippini G; Gavezzotti A; Novoa JJ
Modelling the crystal structure of the 2-hydronitronylnitroxide radical (HNN): observed and computer-generated polymorphs
ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE 1999, Vol 55, pp
543-553

Breu J; Domel H; Norrby PO
Chiral recognition among trisdiimine-metal complexes, 7 - Racemic compound formation versus conglomerate formation with [M(bpy)(3)](PF6)(2) (M = Ni, Zn, Ru); Lattice energy minimisations and implications for structure prediction
EUROPEAN JOURNAL OF INORGANIC CHEMISTRY 2000, Iss 11, pp 2409-2419

Lommerse JPM; Motherwell WDS; Ammon HL; Dunitz JD; Gavezzotti A; Hofmann DWM; Leusen FJJ; Mooij WTM; Price SL; Schweizer B; Schmidt MU; van Eijck BP; Verwer P; Williams DE
A test of crystal structure prediction of small organic molecules
ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE 2000, Vol 56, pp 697-714

van Eijck BP; Kroon J
Structure predictions allowing more than one molecule in the asymmetric unit
ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE 2000, Vol 56, pp 535-542

Newsam JM; Freeman CM; Leusen FJJ
Crystal structure solution and prediction via global and local optimization
CURRENT OPINION IN SOLID STATE & MATERIALS SCIENCE 1999, Vol 4, Iss 6, pp
515-528

Bond AD; Feeder N; Teat SJ; Jones W
The solid-state structure of 3-hydroxy-4-methyl-2(3H)-thiazolethione: Prediction and measurement
TETRAHEDRON 2000, Vol 56, Iss 36, pp 6617-6624

Smrcok L; Durik M
On reliability of R-wp in structure modelling
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 2000, Vol 215, Iss 7, pp 384-385

Chin DN; Palmore GTR; Whitesides GM
Predicting crystalline packing arrangements of molecules that form hydrogen-bonded tapes
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY 1999, Vol 121, Iss 10, pp 2115-2122

A. Gavezzotti & G. Filippini,
Computer prediction of organic crystal structures using partial X-ray diffraction data,
J. Amer. Chem. Soc. 118 (1996) 7153-7157.

Gavezzotti-A
Structure and intermolecular potentials in molecular crystals
MODELLING-AND-SIMULATION-IN-MATERIALS-SCIENCE-AND-ENGINEERING. MAY 2002; 10 (3) : R1-R29
Polymorphism, phase transitions and the attempts at crystal structure prediction are examined, together with models for the reproduction and possible prediction of crystal morphology. Simulations of crystal growth and nucleation, also extremely important for prediction and control of organic crystal structures, are discussed.

Mellot-Draznieks-C; Girard-S; Ferey-G; Schon-JC; Cancarevic-Z; Jansen-M
Computational design and prediction of interesting not-yet-synthesized structures of inorganic materials by using building unit concepts
CHEMISTRY-A-EUROPEAN-JOURNAL. SEP 16 2002; 8 (18) : 4103-4113

A. D. Bond and W. Jones
Structure prediction as a tool for solution of the crystal structures of metallo-organic complexes using powder X-ray diffraction data
Acta Cryst. (2002). B58, 233-243

Schon-JC; Jansen-M
Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems - Part I
ZEITSCHRIFT-FUR-KRISTALLOGRAPHIE. 216 (2001) : 307-325

Schon-JC; Jansen-M
Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems - Part III
ZEITSCHRIFT-FUR-KRISTALLOGRAPHIE. 216 (2001) 361-383
These include structure prediction of extended and molecular crystals, structure prediction and folding of proteins, structure analysis of zeolites, and structure determination of crystals from powder diffraction data.

Potter BS. Palmer RA. Withnall R. Chowdhry BZ. Price SL.
Aza analogues of nucleic acid bases: experimental determination and computational prediction of the crystal structure of anhydrous 5-azauracil
J. Mol. Struct. 486(Special Issue SI):349-361, 1999.

T.S. Bush, C.R.A. Catlow and P.D. Battle,
Evolutionary programming techniques for predicting inorganic crystal structures
J. Mater. Chem. 5 (1995) 1269-1272.
 
 
 
 

Molecule packing prediction, blind tests, etc
 
 

Day, GM   Motherwell, WDS
An experiment in crystal structure prediction by popular vote
CRYSTAL GROWTH & DESIGN 6, 2006, 1985-1990.
The ability to identify the crystal structures of small molecules by
   visual inspection, given a list of computer-generated low-energy
   possibilities, has been tested in an experiment conducted at an
   international crystallographic conference. The surprising result of the
   test was that the experimentally observed crystal structures were the
   least popular of five choices for the two molecules included in the
   test, casting doubt on the reliability of crystallographic intuition as
   a complement to computational methods in crystal structure prediction.
 

 
Day, GM   Motherwell, WDS   Ammon, HL   Boerrigter, SXM   Della Valle, RG
   Venuti, E   Dzyabchenko, A   Dunitz, JD   Schweizer, B   van Eijck, BP
   Erk, P   Facelli, JC   Bazterra, VE   Ferraro, MB   Hofmann, DWM
   Leusen, FJJ   Liang, C   Pantelides, CC   Karamertzanis, PG
   Price, SL   Lewis, TC   Nowell, H   Torrisi, A   Scheraga, HA
   Arnautova, YA   Schmidt, MU   Verwer, P
A third blind test of crystal structure prediction
ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE 61, 2005, 511-527.
Following the interest generated by two previous blind tests of crystal
   structure prediction (CSP1999 and CSP2001), a third such collaborative
   project (CSP2004) was hosted by the Cambridge Crystallographic Data
   Centre. A range of methodologies used in searching for and ranking the
   likelihood of predicted crystal structures is represented amongst the
   18 participating research groups, although most are based on the global
   minimization of the lattice energy. Initially the participants were
   given molecular diagrams of three molecules and asked to submit three
   predictions for the most likely crystal structure of each. Unlike
   earlier blind tests, no restriction was placed on the possible space
   group of the target crystal structures. Furthermore, Z' = 2 structures
   were allowed. Part-way through the test, a partial structure report was
   discovered for one of the molecules, which could no longer be
   considered a blind test. Hence, a second molecule from the same
   category (small, rigid with common atom types) was offered to the
   participants as a replacement. Success rates within the three submitted
   predictions were lower than in the previous tests - there was only one
   successful prediction for any of the three 'blind' molecules. For the
   'simplest' rigid molecule, this lack of success is partly due to the
   observed structure crystallizing with two molecules in the asymmetric
   unit. As in the 2001 blind test, there was no success in predicting the
   structure of the flexible molecule. The results highlight the necessity
   for better energy models, capable of simultaneously describing
   conformational and packing energies with high accuracy. There is also a
   need for improvements in search procedures for crystals with more than
   one independent molecule, as well as for molecules with conformational
   flexibility. These are necessary requirements for the prediction of
   possible thermodynamically favoured polymorphs. Which of these are
   actually realised is also influenced by as yet insufficiently
   understood processes of nucleation and crystal growth.
 

Day, GM   Motherwell, WDS   Jones, W
Beyond the isotropic atom model in crystal structure prediction of
   rigid molecules: Atomic multipoles versus point charges
CRYSTAL GROWTH & DESIGN 5, 2005, 1023-1033.
The lattice energies of predicted and known crystal structures for 50
   small organic molecules with constrained (rigid) geometries have been
   calculated with a model potential whose electrostatic component is
   described by atom-centered multipoles. In comparison to previous
   predictions using atomic point charge electrostatics, there are
   important improvements in the reliability of lattice energy
   minimization for the prediction of crystal structures. Half of the
   experimentally observed crystal structures are found either to be the
   global minimum energy structure or to have calculated lattice energies
   within 0.5 kJ/mol (0.1 kcal/mol) of the global minimum. Furthermore, in
   69% of cases, there are five or fewer unobserved structures with
   lattice energies calculated to be lower than that of the observed
   structure. The results are promising for the advancement of global
   lattice energy minimization for the ab initio prediction of crystal
   structures and confirm the utility of representing electrostatic
   contributions to the energy with atom-centered multipoles.
 

Day, GM   Chisholm, J   Shan, N   Motherwell, WDS   Jones, W
Assessment of lattice energy minimization for the prediction of
   molecular organic crystal structures
CRYSTAL GROWTH & DESIGN 4, 2004, 1327-1340.
Lattice energy searches for theoretical low-energy crystal forms are
   presented for 50 small organic molecules, and we compare the
   experimentally observed crystal forms to these lists of hypothetical
   polymorphs. For each known crystal, the relative stability is
   calculated with respect to the global minimum energy structure, and we
   determine the number of unobserved structures lower in energy than the
   experimental form. The distributions of these relative energies and
   their rankings in the predicted lists are used to determine the
   efficacy of lattice energy minimization in crystal structure
   prediction. Although a simple form for the interaction energies has
   been used, the calculations produce almost a third of the known
   crystals as the global minimum in energy, and approximately a half of
   the known structures are within 1 kJ/mol of the global minimum.
   Molecules with no hydrogen-bonding capacity are most likely to be found
   close to the global minimum in lattice energy, while increasing the
   number of possible hydrogen-bond donor-acceptor combinations leads to
   less reliable predictions.
 

Pidcock, E   Motherwell, WDS
A novel description of the crystal packing of molecules
CRYSTAL GROWTH & DESIGN 4, 2004, 611-620.
The question of why molecules pack to form particular crystal
   structures is occupying many researchers throughout the scientific
   community. Much emphasis has been placed on the study of intermolecular
   interactions and the search for "structure-directing" motifs. However,
   examination of experimental crystal structures contained within the
   Cambridge Structural Database has led us to propose a new, conceptually
   simple model of crystal packing that describes the arrangements
   molecules adopt in unit cells. The model was inspired by consideration
   of arrangements of boxes (with three unequal dimensions) stacked with
   faces touching and edges aligned. For a fixed number of boxes, there
   are only a limited number of arrangements possible, and these
   arrangements, or packing patterns, are of the same volume but different
   surface area. Applied to crystal structures, the model describes unit
   cells in terms of multiples (pattern coefficients) of molecular
   dimensions. The different packing patterns are not populated equally by
   experimental crystal structures, and it is found that the most
   populated packing patterns are those that are characterized by low
   surface area. Correlations between broadly defined molecular shapes and
   packing patterns have been observed which indicate that molecular
   aggregation is a useful method for moderating awkward (high surface
   area for volume) molecular shapes. A limited number of crystal
   structure prediction trials were performed with the reduced search
   space afforded by estimated unit cell dimensions (from molecular
   dimensions), and an increase in success rate was observed.
 

Motherwell, WDS   Ammon, HL   Dunitz, JD   Dzyabchenko, A   Erk, P
   Gavezzotti, A   Hofmann, DWM   Leusen, FJJ   Lommerse, JPM
   Mooij, WTM   Price, SL   Scheraga, H   Schweizer, B   Schmidt, MU
   van Eijck, BP   Verwer, P   Williams, DE
Crystal structure prediction of small organic molecules: a second blind
   test
ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE 58, 2002, 647-661.
The first collaborative workshop on crystal structure prediction
   (CSP1999) has been followed by a second workshop (CSP2001) held at the
   Cambridge Crystallographic Data Centre. The 17 participants were given
   only the chemical diagram for three organic molecules and were invited
   to test their prediction programs within a range of named common space
   groups. Several different computer programs were used, using the
   methodology wherein a molecular model is used to construct theoretical
   crystal structures in given space groups, and prediction is usually
   based on the minimum calculated lattice energy. A maximum of three
   predictions were allowed per molecule. The results showed two correct
   predictions for the first molecule, four for the second molecule and
   none for the third molecule (which had torsional flexibility). The
   correct structure was often present in the sorted low-energy lists from
   the participants but at a ranking position greater than three. The use
   of non-indexed powder diffraction data was investigated in a secondary
   test, after completion of the ab initio submissions. Although no one
   method can be said to be completely reliable, this workshop gives an
   objective measure of the success and failure of current methodologies.
 

 
Motherwell, WDS
Crystal structure prediction and the Cambridge Structural Database
MOLECULAR CRYSTALS AND LIQUID CRYSTALS 356, 2001, 559-567.
A computer program has been written to attempt prediction of likely
   polymorphs of small organic molecules, using a genetic algorithm. The
   cost function used is based not on energy but the intermolecular atom
   pair distances as seen in the Cambridge database, for selected similar
   molecules to the target. Some successful results are described, showing
   possible applications to molecules not easily treated with empirical
   energy potentials.
 
 

Lommerse, JPM   Motherwell, WDS   Ammon, HL   Dunitz, JD   Gavezzotti, A
   Hofmann, DWM   Leusen, FJJ   Mooij, WTM   Price, SL   Schweizer, B
   Schmidt, MU   van Eijck, BP   Verwer, P   Williams, DE
A test of crystal structure prediction of small organic molecules
ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE 56, 2000, 697-714.
A collaborative workshop was held in May 1999 at the Cambridge
   Crystallographic Data Centre to test how well currently available
   methods of crystal structure prediction perform when given only the
   atomic connectivity for an organic compound. A blind test was conducted
   on a selection of four compounds and a wide range of methodologies
   representing the principal computer programs currently available were
   used. There were 11 participants who were allowed to propose at most
   three structures for each compound. No program gave consistently
   reliable results. However, seven proposed structures were close to an
   experimental one and were classified as 'correct'. One compound
   occurred in two polymorphs, but only one form was predicted correctly
   among the calculated structures. The basic problem with lattice energy
   based methods of crystal structure prediction is that many structures
   are found within a few kJ mol(-1) of the global minimum. The fine
   detail of the force-field methodology and parametrization influences
   the energy ranking within each method. Nevertheless, present methods
   may be useful in providing a set of structures as possible polymorphs
   for a given molecular structure.
 
 
 
 

Prediction
 
 

 
 

 
Cancarevic, Z   Schon, JC   Jansen, M
Alkali metal carbonates at high pressure
ZEITSCHRIFT FUR ANORGANISCHE UND ALLGEMEINE CHEMIE 632, 2006, 1437-1448.
The possible existence of crystalline alkali metal carbonates as
   high-pressure modifications in the system M2CO3, where M = Li, Na, K,
   Rb, and Cs are investigated. The results agree well with the
   experimental observations at standard pressure, and several new
   modifications are proposed that should be thermodynamically stable at
   high and effective negative pressures.
 
 

 
Le Bail, A   Calvayrac, F
Hypothetical AlF3 crystal structures
JOURNAL OF SOLID STATE CHEMISTRY 179, 2006, 3159-3166.
Applying a structure prediction computer programme (GRINSP =
   Geometrically Restrained INorganic Structure Prediction), the
   occurrence of 6-connected 3D networks was investigated, through AlF6
   octahedra exclusive corner sharing. The five known AlF3 varieties were
   reproduced (alpha-, beta-, eta-, K- and tau-AlF3) and seven
   hypothetical models were predicted. Among these still to be synthesized
   AlF3 phases, one can recognize two known structure types (TICa2Ta5O15,
   Ba4CoTa10O30) and some easy to imagine intergrowths; however, a few
   others are completely unexpected, though simple. A comparison of the ab
   initio total energies of all the structures is provided, leading to the
   conclusion that the virtual models could well be viable.
 
 

 
Florence, AJ   Leech, CK   Shankland, N   Shankland, K   Johnston, A
Control and prediction of packing motifs: a rare occurrence of
   carbamazepine in a catemeric configuration
CRYSTENGCOMM 8, 2006, 746-747.
A predicted orthorhombic crystal structure of carbamazepine is
   isostructural with an experimentally determined dihydrocarbamazepine
   crystal structure, providing a rationale for synthesising a novel 1 : 1
   solid solution that has carbamazepine in a rare catemeric configuration.
 
 
 

 
Mellot-Draznieks, C   Ferey, G
Assembling molecular species into 3D frameworks: Computational design
   and structure solution of hybrid materials
PROGRESS IN SOLID STATE CHEMISTRY 33, 2005, 187-197.
We present here the computational prediction of hybrid
   organic-inorganic extended lattices. The production of candidate
   crystal structures is successfully performed by direct-space assembly
   of building-units using the AASBU (Automated Assembly of Secondary
   Building Units) method, mixing independent organic and inorganic units.
   Hybrid candidates that are compatible with the imposed metal:organic
   ratio are generated with their cell parameters, space group, atomic
   positions, along with their simulated diffraction pattern. Since no
   explicit limit regarding the nature, number, and size of the inorganic
   and organic units, or hybrid building-block is involved, the method
   offers boundless potential for exploring hybrid frameworks in terms of
   the topological diversity. The most appealing development arises from
   the computer-assisted design of hybrid frameworks. Indeed, in a
   significant number of systems, it is well-known that controlled
   synthesis conditions can promote the occurrence of specific
   building-units, which serve to "propagate" the infinite crystal
   structure. We believe that the computational approach presented herein
   is valuable to create virtual libraries of viable hybrid polymorphs. We
   further show how it has proven to be, for the first time in the realm
   of hybrids, a tangible route towards structure solution in direct
   space, exemplified here with the computational structure determination
   of two complex hybrid structures, MIL-100 and MIL-101. This challenging
   area is of special interest when high quality diffraction data are not
   available or when very large cell sizes are involved. The development
   of a structural model in direct space, starting with minimal knowledge
   such as the metal:organic ratio, is shown here to be possible. With
   such a method in hand, formerly intractable structural problems when
   using methods based on conventional reciprocal space become feasible in
   direct space.
 

Mellot-Draznieks, C   Ferey, G
Simulations of inorganic crystal structures recent advances in
   structure elucidation
CURRENT OPINION IN SOLID STATE & MATERIALS SCIENCE 7, 2003, 13-19.
The aim of this paper is to show some recent developments of simulation
   approaches in the structure elucidation of inorganic crystalline
   compounds, highlighting at each step their role either as a
   complementary technique or as a tool to anticipate structure/properties
   relationships or even to imagine new inorganic architectures. Specific
   examples are taken in the area of zeolites to illustrate the use of
   energy minimizations and (N, V, T) Monte Carlo techniques as a
   complement to experimental diffraction approaches, typically for the
   disordered placement of extra-framework species (cations, water
   molecules). In the still extending area of the synthesis of templated
   open-framework inorganic structures, we show that lattice energy
   minimizations may possibly be used to estimate or even anticipate the
   structures and energetics of the related template-free structures. A
   third section tackles the development of more sophisticated methods for
   the computational design of not-yet-synthesized structures using
   building block concepts.

 
Le Bail, A
Inorganic structure prediction with GRINSP
JOURNAL OF APPLIED CRYSTALLOGRAPHY 38, 2005, 389-395.
A new computer program is described, GRINSP ( geometrically restrained
   inorganic structure prediction), which allows the exploration of the
   possibilities of occurrence of 3-, 4-, 5- and 6-connected
   three-dimensional networks. Hypothetical ( as well as known structure)
   models for binary compounds are produced with exclusive connection of
   polyhedra by corners, such as [MX3] triangles in M2X3 formulation,
   [MX4] tetrahedra in MX2 ( zeolites or dense SiO2 polymorphs), [MX5]
   polyhedra in M2X5, and finally [MX6] octahedra in MX3 polymorphs.
   Moreover, hypothetical ternary compounds are built up by combinations
   of either two different polyhedra or two different radii for two
   different cations adopting the same coordination. The cost function is
   based on the agreement of the model interatomic distances with ideal
   distances provided by the user. The Monte Carlo algorithm first finds
   structure candidates selected after the verification of the expected
   geometry, and then optimizes the cell parameters and the atomic
   coordinates. A satellite software ( GRINS) uses the predicted models
   and produces the characteristics of isostructural compounds which would
   be obtained by cationic substitutions. A huge list of CIF files of
   hypothetical boron oxide polymorphs ( including nanotubes), zeolites,
   aluminium and 3d-element fluorides, fluoroaluminates, borosilicates,
   titanosilicates, gallophosphates etc., is freely available at the PCOD
   ( Predicted Crystallography Open Database).
 

 
Schon, JC   Cancarevic, Z   Jansen, M
Structure prediction of high-pressure phases for alkali metal sulfides
JOURNAL OF CHEMICAL PHYSICS 121, 2004, 2289-2304.
For a given chemical system we present a systematic approach to predict
   structures, which may exist at high pressure, by investigating the
   global enthalpy landscape. We combine global optimizations, based on
   empirical potential energy functions, and local optimizations (volume,
   cell shape, and atomic positions) on both Hartree-Fock and density
   functional theory level. We predict the existence of high-pressure
   phases for the alkali metal sulfides of the composition M2S (M=Li, Na,
   K, Rb, Cs), together with the transition pressures among these phases.

 
Gibbons, PC   Hennig, RG   Huett, VT   Kelton, KF
Ti-Zr-Ni and Ti-Hf-Ni quasicrystals and approximants as hydrogen
   storage alloys
JOURNAL OF NON-CRYSTALLINE SOLIDS 334, 2004, 461-465.
X-ray and neutron powder diffraction data previously collected from the
   Ti-Zr-Ni quasicrystal have been analyzed. The data were modeled by an
   8/5 rational approximant (RA) that was constructed using the known
   structure of the 1/1 RA and then refined. Ab initio total energy
   calculations were made for small structures with between 81 and 123
   atoms, in which atomic positions were allowed to vary while minimizing
   the energy. The final structure is in good agreement with that obtained
   from the scattering data. Interstitial sites in which H is stable in
   the 1/1 model, and the H binding energies, were identified. An
   excellent fit to existing pressure-composition isotherms was obtained,
   but those data cannot be inverted to obtain experimental site binding
   energies. At 250 degreesC the Ti-Hf-Ni alloy can be loaded with H
   without the formation of any detectable crystal hydride phase, which is
   always found in similarly loaded Ti-Zr-Ni alloys.
 
 
 

Cancarevic, ZP   Schon, JC   Jansen, M
Structure prediction of solids: Heuristic algorithms for local
   optimization on Hartree-Fock level
PROGRESS IN ADVANCED MATERIALS AND PROCESSES
MATERIALS SCIENCE FORUM 453-454, 2004, 71-76.
In recent years, the prediction of new not-yet-synthesized solid phases
   and the theoretical determination of the structure of already
   synthesized compounds from cell information only have become of
   increasing importance. For example, it would be of great advantage in
   the identification of newly generated phases in high-pressure
   experiments, if one could supplement the experimental results with
   theoretical studies on the same system.
   The prediction of high pressure phases of a chemical system is realized
   as a two-step process: identification of structure candidates via
   global exploration of the energy landscapes over a range of different
   pressures followed by a local optimization of the candidates on
   ab-initio level. From the completed E(V)-curves, one could then
   calculate the stable phase at a given pressure and the transition
   pressures among the phases.
   In this work we will focus on the local optimization of the cell
   parameters and relative atom positions on the Hartree-Fock level. We
   present a heuristic algorithm for the full local optimization of all
   structural parameters and show, taking Na2S as an example, how this
   leads to a significant improvement in e.g. the agreement between
   computed and measured transition pressures.

 
Nagayoshi, K   Ikeda, T   Kitaura, K   Nagase, S
Computational procedure of lattice energy using the ab initio MO method
JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2, 2003, 233-234.
Recently, we have proposed a computational procedure for calculations
   of lattice energies of molecular crystals using the ab initio MO
   method. This procedure does not use potential functions and is
   applicable to a variety of molecular crystals. The procedure has been
   successfully applied to calculation of packing structure of electron
   donor-acceptor complex, H3N-BF3, and hydrogen bonding crystal, CH3OH.
   In this work, we present a full account of the computational procedure.
   This method is applied to the packing structure calculations of
   hydrocarbon crystals, C2H2, C2H4 and C6H6. The lattice parameters
   optimized at the MP2/6-311++G** level are in good agreement with the
   experimental values. The basis set dependence of the lattice constants
   is also discussed for several crystals.
 
 

Kratochvil, B   Husak, M   Jegorov, A
Polymorphism and solvatomorphism of solid substances in pharmacy
CHEMICKE LISTY 96, 2002, 330-335.
The ability of a particular substance to exist in several different
   crystal forms (unsolvated or solvated) is called polymorphism or
   solvatomorphism. These phenomena are frequently observed in solid
   pharmaceuticals. Polymorphs and solvatomorphs of a compoud differ in
   their physical and biological properties (crystal shape, hardness,
   melting point, solubility, pharmacokinetics, bioavailability, etc.).
   This influences commercial drug formulations and their therapeutical
   effect, The exact theoretical prediction of all polymorphs and
   solvatomorphs is not yet possible. The most frequently used analytical
   method of detection and characterization of polymorphic and
   solvatomorphic forms is X-ray diffraction (single-crystal structure
   analysis and collection of powder patterns), Producers of original
   pharmaceuticals endeavour to patent all crystal forms of the developed
   active substance, while generic producers search for new polymorphs
   (solvatomorphs) or technologies. Clearly this can cause lawsuits.
 
 

Van Droogenbroeck, J   Swerts, B   Schafer, L   Van Alsenoy, C
Solids modeled by ab initio crystal field methods, Part 22: The Fock
   matrix transformed supermolecule model and the structure determination
   of D-erythronic acid-3,4-carbonate
JOURNAL OF COMPUTATIONAL CHEMISTRY 25, 2004, 2065-2072.
To eliminate the cutoff effects in the supermolecule model (SM), the
   Fock matrix transformed supermolecule model (FTSM) is developed. In
   this model a cyclization of the cluster is performed by means of
   transformations of elements of the Fock matrix, thereby restoring the
   translational symmetry. Besides this fundamental enhancement,
   significant CPU time savings are realized because, in this new
   procedure, not all Fock matrix elements need to be calculated. The
   method is applied in a study of the structure of D-erythronic
   acid-3,4-carbonate in the crystal phase, where the new model is
   compared to the supermolecule model as well as the XRD experiment. The
   results are found to be in good agreement with experimental data.
 
 
 
 
 
 

 
Hofmann, DWM   Apostolakis, J
Crystal structure prediction by data mining
JOURNAL OF MOLECULAR STRUCTURE 647, 2003, 17-39.
The ever increasing number of experimentally determined crystal.
   structures allows for the use of data mining methods to, address
   crystallographic questions. Here we study the application of data
   mining for predicting the arrangement of molecules in unit cells of
   unknown dimensions (crystal structure prediction) as well as in unit
   cells of predetermined dimensions (fractional coordinate prediction).
   In this work, data mining is used to derive an atom-pair potential,
   which is then compared-to known force fields. It is shown that the
   potential is-physically reasonable when the data are sufficient in
   quality and quantity. For validation the energy function is applied to
   the problems of crystal structure prediction and fractional coordinate
   prediction. In both cases a large number of structures-was generated
   and the structures were ranked according to their energies. Structure
   prediction was considered successful if a structure similar to the
   experimentally observed one was ranked highest.
   For crystal structure prediction the energy function is tested on
   an-independent set of crystal, structures taken from the P1 and P (1)
   over bar space groups. We show that approximately 76% of the 218
   molecules tested-in, space group P1 are predicted correctly. For the
   more complex space group P (1) over bar the success rate is 24%.
   If the powder diffraction can be indexed, the problem simplifies to
   fractional coordinate prediction. With the assumption of known cell
   parameters the structure has been resolved in 92% of the test-cases for
   P1 and 29% for P1.
 
 
 
 

Tedesco, E   Giron, D   Pfeffer, S
Crystal structure elucidation and morphology study of pharmaceuticals
   in development
CRYSTENGCOMM 2002, 393-400.
The structural characterization of drug substances by X- ray
   diffraction plays a central role during the development of
   pharmaceuticals. While powder diffraction is usually employed for the
   identification of solid phases, the single crystal technique yields
   detailed structural information, which is needed for purity control,
   understanding of polymorphism or pseudo-polymorphic behavior,
   physico-chemical property elucidation and morphology characterization.
   The structure determination of three active ingredients is discussed in
   this context. In the first case, we have solved the structure directly
   from high- resolution powder X-ray data, using the `direct-space'
   methodology. The polymorphic behavior of the second substance has been
   rationalized by analyzing the intermolecular interactions and packing
   motifs of the two modifications in the solid state. For the third
   compound, we have predicted the morphology from the knowledge of its
   crystal structure. Solvent mixtures have been used to control the
   external crystal habit, based upon a detailed analysis of chemical
   groups emerging from the cleaved crystal surfaces of the calculated
   morphology.
 
 
 
 

 
Mellot-Draznieks, C   Girard, S   Ferey, G   Schon, JC   Cancarevic, Z   Jansen, M
Computational design and prediction of interesting not-yet-synthesized
   structures of inorganic materials by using building unit concepts
CHEMISTRY-A EUROPEAN JOURNAL 8, 2002, 4103-4113.
The computational design of new and interesting inorganic materials is
   still an ongoing challenge. The motivation of these efforts is to aid
   the often difficult task of crystal structure determination, to
   rationalize different but related structure types, or to help limit the
   domain of structures that are possible in a given system. Over the past
   decade, simulation methods have continuously evolved towards the
   prediction of new structures using minimal input information in terms
   of symmetry, cell parameters, or chemical composition. So far, this
   task of identifying candidate structures through an analysis of the
   energy landscape of chemical systems has been particularly successful
   for predominantly ionic systems with relatively small numbers of atoms
   or ions in the simulation cell. After an introductory section, the
   second section of this work presents the historical developments of
   such simulation methods in this area. The following sections of the
   work are dedicated to the introduction of the building unit concept in
   simulation methods: we present simulation approaches to structure
   prediction employing both primary (aggregate of atoms) and secondary
   (aggregate of coordination polyhedra) building units. While structure
   prediction with primary units is a straightforward extension of
   established approaches, the AASBU method (automated asssembly of
   secondary building units) focusses on the topology of network-based
   structures. This method explores the possible ways to assemble
   predefined inorganic building units in three-dimensional space, opening
   the way to the manipulation of very large building units (up to 84
   atoms in this work). As illustrative examples we present the prediction
   of candidate structures for Li4CO4, the identification of topological
   relationships within a family of metalphosphates, ULM-n and MIL-n, and
   finally the generation of new topologies by using predefined large
   building units such as a sodalite or a double-four-ring cage, for the
   prediction of new and interesting zeolite-type structures.
 

 
Bond, AD   Jones, W
Structure prediction as a tool for solution of the crystal structures
   of metallo-organic complexes using powder X-ray diffraction data
ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE 58, 2002, 233-243.
A simulated-annealing direct-space approach has been applied to predict
   the crystal structures of a series of metallo-organic complexes
   containing Zn, Cu and Ni. The prediction methodology generates a set of
   energetically reasonable crystal structures among which the actual
   structure is present, but it is not always possible to specify
   unambiguously the known crystal structure solely on the basis of
   energy. In each case, however, the ambiguity may be resolved by
   recourse to laboratory powder X-ray diffraction (PXRD) data. In this
   manner, structure prediction is shown to be a powerful tool for
   structure solution using PXRD data, with the additional advantage that
   indexing of the PXRD profile is not required at the outset.
 
 
 
 

2001

Schon, JC   Jansen, M
Determination, prediction, and understanding of structures, using the
   energy landscapes of chemical systems - Part III
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 216, 2001, 361-383.
In the past decade, new theoretical approaches have been developed to
   determine, predict and understand the structure of chemical compounds.
   The central element of these methods has been the investigation of the
   energy landscape of chemical systems. Applications range from extended
   crystalline and amorphous compounds over clusters and molecular
   crystals to proteins. In this review, we are going to give an
   introduction to energy landscapes and methods for their investigation,
   together with a number of examples. These include structure prediction
   of extended and molecular crystals, structure prediction and folding of
   proteins, structure analysis of zeolites, and structure determination
   of crystals from powder diffraction data.
 
 
 
 



Other
 
 
 
 

Instruments
 

 
Ferreira, FF   Granado, E   Carvalho, W   Kycia, SW   Bruno, D   Droppa, R
X-ray powder diffraction beamline at D10B of LNLS: application to the
   Ba2FeReO6 double perovskite
JOURNAL OF SYNCHROTRON RADIATION 13, 2006, 46-53.
A new beamline, fully dedicated to X-ray powder diffraction (XPD)
   measurements, has been installed after the exit port B of the bending
   magnet D10 at the Brazilian Synchrotron Light Laboratory (LNLS) and
   commissioned. The technical characteristics of the beamline are
   described and some performance indicators are listed, such as the
   incoming photon flux and the angular/energy resolutions obtainable
   under typical experimental conditions. The results of a Rietveld
   refinement for a standard sample of Y2O3 using high-resolution data are
   shown. The refined parameters match those found in the literature,
   within experimental error. High-resolution XPD measurements on
   Ba2FeReO6 demonstrate a slight departure from the ideal cubic
   double-perovskite structure at low temperatures, not detected by
   previous powder diffraction experiments. The onset of the structural
   transition coincides with the ferrimagnetic ordering temperature,
   T(c)similar or equal to 315 K. Subtle structural features, such as
   those reported here for Ba2FeReO6, as well as the determination and/or
   refinement of complex crystal structures in polycrystalline samples are
   ideal candidate problems to be investigated on this beamline.
 
 

Knapp, M   Baehtz, C   Ehrenberg, H   Fuess, H
The synchrotron powder diffractometer at beamline B2 at HASYLAB/DESY:
   status and capabilities
JOURNAL OF SYNCHROTRON RADIATION 11, 2004, 328-334.
The synchrotron powder diffraction beamline B2 at HASYLAB/DESY is
   described. The beamline is capable of high-resolution powder
   diffraction as well as time-resolved studies and offers several
   sophisticated ancillary equipments for special applications. A newly
   developed image-plate system allows for kinetic studies with good
   resolution in the minutes range. Numerous sample environments allow for
   various standard applications including structure solution, kinetic
   studies and in situ observations under flexible and well defined
   conditions. Representative examples are shown for these setups, which
   are also supported for experiments of external users.
 

 
Fitch, AN
The high resolution powder diffraction beam line at ESRF
JOURNAL OF RESEARCH OF THE NATIONAL INSTITUTE OF STANDARDS AND
   TECHNOLOGY 109, 2004, 133-142.
The optical design and performance of the high-resolution powder
   diffraction beam line BM16 at ESRF are discussed and illustrated. Some
   recent studies carried out on BM16 are described, including crystal
   structure solution and refinement, anomalous scattering, in situ
   measurements, residual strain in engineering components, investigation
   of microstructure, and grazing-incidence diffraction from surface
   layers. The beam line is built on a bending magnet, and operates in the
   energy range from 5 keV to 40 keV. After the move to an undulator
   source in 2002, it will benefit from an extented energy range up to 60
   keV and increased flux and resolution. It is anticipated that
   enhancements to the data quality will be achieved, leading to the
   solution of larger crystal structures, and improvements in the accuracy
   of refined structures. The systematic exploitation of anisotropic
   thermal expansion will help reduce the effects of peak overlap in the
   analysis of powder diffraction data.
 
 

 
Krimmer, B   Gilles, R   Zeitelhack, K   Schneider, R
   Montermann, G   Boysen, H   Fuess, H
A new detector system for the structure powder diffractometer SPODI at
   the FRM-II in Garching
APPLIED PHYSICS A-MATERIALS SCIENCE & PROCESSING 74, 2002, S154-S156.
This article describes the concept of one of the new technical features
   of the structure powder diffractometer SPODI: the array of
   position-sensitive detectors including the read-out electronics. 80
   single-He3 detectors each with an active length of 300 mm will be
   arranged vertically in a detector bank. The position sensitivity
   enables us to evaluate larger parts of the Debye-Scherrer rings and to
   improve the determination of the 2theta positions of the Bragg peaks.
   The set-up of this detector system, which is called an individual
   counter array, is described. Test measurements with the prototype of
   the read-out electronics are presented. A software package will store
   the signals in a 2D matrix and allow various evaluation procedures of
   the data.
 
 

Etc
 

Hundt, R   Schon, JC   Jansen, M
CMPZ - an algorithm for the efficient comparison of periodic structures
JOURNAL OF APPLIED CRYSTALLOGRAPHY 39, 2006, 6-16.
The systematic comparison of the atomic structure of solid compounds
   has become an important task in crystallography, chemistry, physics and
   materials science, in particular in the context of structure prediction
   and structure determination of crystalline solids. In this work, an
   efficient and robust algorithm for the comparison of periodic
   structures is presented, which is based on the mapping of the point
   patterns of the two structures into each other. This algorithm has been
   implemented as the module CMPZ in the structure visualization and
   analysis program KPLOT.
 

Norrman, M    Stahl, K   Schluckebier, G   Al-Karadaghi, S
Characterization of insulin microcrystals using powder diffraction and
   multivariate data analysis
JOURNAL OF APPLIED CRYSTALLOGRAPHY 39, 2006, 391-400.
Twelve different microcrystalline insulin formulations were
   investigated by X-ray powder diffraction and were shown to have very
   characteristic patterns.
 
 
 

Koudelka-B; Capkova-P
Supramol - a program for structure analysis of intercalates using molecular simulations: the structure of VOPO4.C6H4O2
JOURNAL-OF-MOLECULAR-MODELING. 2002; 8 (5) : 184-190
A method of structure analysis of intercalates has been developed that uses a combination of molecular simulations with powder diffraction.

Altomare A., Giacovazzo C., Ianigro M., Moliterni AGG, Rizzi R
Peak labelling in electron density maps from powder data: the use of crystal chemical information
J. Appl. Cryst. 35 (2002) 21-27.

Hsu-HP; Lin-SC; Hansmann-UHE
Energy landscape paving for X-ray structure determination of organic molecules
ACTA-CRYSTALLOGRAPHICA-SECTION-A. MAY 2002; 58 Part 3 : 259-264
The new approach has been tested using the example of 9-(methylamino)-1H-phenalen-1-one 1,4-dioxan-2-y1 hydroperoxide solvate (C14H11NO.C4H8O4). The results indicate that, for this example, ELP outperforms standard techniques such as simulated annealing.

Weirich-TE; Winterer-M; Seifried-S; Mayer-J
Structure of nanocrystalline anatase solved and refined from electron powder data
ACTA-CRYSTALLOGRAPHICA-SECTION-A. JUL 2002; 58 Part 4 : 308-315
Energy-filtered Debye-Scherrer electron powder data have been successfully employed to determine the structure of nanocrystalline anatase (TiO2). The performed structure analysis includes determining the unit cell, space group, solving the structure via direct methods from extracted intensities and refining the structure using the Rietveld technique. The result of the present study shows that the methods originally developed for determining structures from X-ray powder data work equally well with data from electron powder diffraction.

Middleton-DA; Peng-X; Saunders-D; Shankland-K; David-WIF; Markvardsen-AJ
Conformational analysis by solid-state NMR and its application to restrained structure determination from powder diffraction data
CHEMICAL-COMMUNICATIONS. 2002; (17) : 1976-1977
Solid-state NMR is used to dramatically improve the efficiency and reliability of molecular crystal structure determination from X-ray powder diffraction data.

BETHANIS-K; TZAMALIS-P; HOUNTAS-A; TSOUCARIS-G
Ab initio determination of a crystal structure by means of the Schrodinger equation
Acta-crystallographica-Section-A-Foundations-of-crystallography. 2002; 58 (p.3) : 265-269
It is shown that the use of the Schrodinger equation may lead to the ab initio determination of the positions of the nuclei in a crystal, given a limited number of diffracted-beam intensities.

IDA-T; TORAYA-H
Deconvolution of the instrumental functions in powder X-ray diffractometry
Journal-of-applied-crystallography. 2002; 35 (p.1) : 58-68

S. Brenner, L.B. McCusker and C. Baerlocher,
The application of structure envelopes in structure determination from powder diffraction data
J. Appl. Cryst. 35 (2002) 243-252.

Hao,-Q
Phasing from an envelope.
Acta-Crystallogr-D-Biol-Crystallogr. 2001 Oct; 57(Pt 10): 1410-4

D.M. Ockwell, M.A. Hough, J.G. Grossmann, S.S. Hasnain and Q. Hao
Implementation of cluster analysis for ab initio phasing using the molecular envelope from solution X-ray scattering
Acta Cryst. D56 (2000) 1002-1006.
Program FSEARCH

Heuer-M
The determination of site occupancies using a new strategy in Rietveld refinements
JOURNAL-OF-APPLIED-CRYSTALLOGRAPHY, 34 (2001) 271-279
The purpose of the study reported here was to determine if the LOT method can also be used in Rietveld refinements.

David WIF
Robust Rietveld refinement in the presence of impurity phases
J. Appl. Cryst. 34 (2001) 691-698.

A.J. Markvardsen, W.I.F. David, J.C. Johnson & K. Shankland,
A probabilistic approach to space-group determination from powder diffraction data.
Acta Cryst. A57 (2001) 47-54.

Shiono-M; Takakura-H; Yamamoto-A
Ab initio structure solutions of quasicrystals by a density modification method
FERROELECTRICS-. 2001; 250 (1-4) : 293-296

Turner GW, Tedesco E, Harris KDM, Johnston RL, Kariuki BM
A method for understanding characteristics of multi-dimensional hypersurfaces, illustrated by energy and powder profile R-factor hypersurfaces for molecular crystals
Z. Kristallogr. 216 (2001) 187-189.

V.Y. Lunin, L.N. Lunina, T.E. Petrova, T.P. Skovoroda, A.G. Urzhumtsev and A.D. Podjarny,
Low-resolution ab initio phasing: problems and advances
Acta Cryst. D56 (2000) 1223-1232.

C.L. Henley, V. Elser and M. Mihalkovic,
Structure determinations for random-tiling quasicrystals
Z. Kristallogr. 215 (2000) 553-568.

K. Pilz and K.F. Fischer,
Solving crystal structures without Fourier mapping. II. Non-centrosymmetric case
Z. Kristallogr. 215 (2000) 640-649.

V.I. Korsunsky,
The investigation of structure of heavy metal clusters and polynuclear complexes in powder-samples with the radial distribution function method
Coordination Chem. Reviews 199 (2000) 55-87.

D.I. Svergun,
Advanced solution scattering data analysis methods and their applications
J. Appl. Cryst. 33 (2000) 530-534.

Guo-Liping; Cheng-Zhixu (China Inst. of Atomic Energy, Beijing (China)
A profile fitting software package (CPOWDER) and its application in powder diffraction research
Atomic-Energy-Science-and-Technology (Mar 2000) v. 34(2) p. 120-124

Y. X. Gu, Y. D. Liu, Q. Hao and H. F. Fan
Solving crystal structures from two-wavelength X-ray powder diffraction data - breaking the phase ambiguity in the noncentrosymmetric case
Acta Cryst. (2000). A56, 592-595

Wessels T. Baerlocher C. McCusker LB.
Single-crystal-like diffraction data from polycrystalline materials
Science. 284(5413):477-479, 1999.

Grosse-Kunstleve RW. McCusker LB. Baerlocher C.
Zeolite structure determination from powder diffraction data: applications of the FOCUS method
J. Appl. Crystallogr. 32(Part 3):536-542, 1999.

Lunin VY. Lunina NL. Urzhumtsev AG.
Seminvariant density decomposition and connectivity analysis and their application to very low resolution macromolecular phasing
Acta Crystallogr. Sect. A. 55(Part 5):916-925, 1999.

Li BH. Jin QH. Zhu SP. Guo ZY. Ding DT. Sun PC.
Development of three-dimensional, four-connected framework structures with extra-large open pores
Microporous Mesoporous Mat. 31(1-2):123-127, 1999.

Altomare A. Giacovazzo C. Guagliardi A. Moliterni AGG. Rizzi R.
Solving crystal structures from powder data. V. Located molecular fragment and powder-pattern decomposition
J. Appl. Crystallogr. 32(Part 5):963-967, 1999.

Dong C. Wu F. Chen H.
Correction of zero shift in powder diffraction patterns using the reflection-pair method
J. Appl. Crystallogr. 32(Part 5):850-853, 1999.

P. W. Stephens
Phenomenological model of anisotropic peak broadening in powder diffraction
J. Appl. Cryst. (1999). 32, 281 - 289.

R. W. Cheary and A. A. Coelho
Axial Divergence in a Conventional X-ray Powder Diffractometer. II. Realization and Evaluation in a Fundamental-Parameter Profile Fitting Procedure
J. Appl. Cryst. (1998). 31, 862 - 868

P. Riello, G. Fagherazzi and P. Canton
Scale Factor in Powder Diffraction
Acta Cryst. (1998). A54, 219 - 224

Dorset DL.
DIRECT DETERMINATION OF POLYMER CRYSTAL STRUCTURES FROM FIBRE AND POWDER X-RAY DATA
Polymer. 38 (1997) 247-253.

R. W. Grosse-Kunstleve, L. B. McCusker and Ch. Baerlocher
Powder Diffraction Data and Crystal Chemical Information Combined in an Automated Structure Determination Procedure for Zeolites
J. Appl. Crystallogr. 30 (1997) 985-995.

Hammond RB. Roberts KJ. Docherty R. Edmondson M.
COMPUTATIONALLY ASSISTED STRUCTURE DETERMINATION FOR MOLECULAR MATERIALS FROM X-RAY POWDER DIFFRACTION DATA
Journal of Physical Chemistry B. 101 (1997) 6532-6536.

Le Bail A. Jouanneaux A.
A QUALITATIVE ACCOUNT FOR ANISOTROPIC BROADENING IN WHOLE-POWDER-DIFFRACTION-PATTERN FITTING BY SECOND-RANK TENSORS
Journal of Applied Crystallography. 30 (1997) 265-271.

Norby P.
SYNCHROTRON POWDER DIFFRACTION USING IMAGING PLATES - CRYSTAL STRUCTURE DETERMINATION AND RIETVELD REFINEMENT
Journal of Applied Crystallography. 30 (1997) 21-30.

Parise JB. Chen J.
STUDIES OF CRYSTALLINE SOLIDS AT HIGH PRESSURE AND TEMPERATURE USING THE DIA MULTI-ANVIL APPARATUS
European Journal of Solid State & Inorganic Chemistry. 34 (1997) 809-821.

Altomare A. Carrozzini B. Giacovazzo C. Guagliardi A. Moliterni AGG. Rizzi R.
SOLVING CRYSTAL STRUCTURES FROM POWDER DATA .1. THE ROLE OF THE PRIOR INFORMATION IN THE TWO-STAGE METHOD
Journal of Applied Crystallography, 29 (1996) 667-673.

Altomare A. Foadi J. Giacovazzo C. Guagliardi A. Moliterni AGG.
SOLVING CRYSTAL STRUCTURES FROM POWDER DATA .2. Etc
Journal of Applied Crystallography, 29 (1996) 674-681.

Y.G. Andreev,T. Lundsrtöm & N.I. Sorokin,
Powder diffraction pattern fitting and structure refinement by means of the CPSR v.3.1 software package,
Nucl. Instr. & Meth. in Phys. Res. A354 (1995) 134-138.

J-J Liang, F.C. Hawthorne, M. Novak & P. Cerny,
Crystal-structure refinement of boromuscovite polytypes using a coupled Rietveld - static-structure energy minimization method,
The Canadian Mineralogist 33 (1995) 859-865.

R.E. Marsh,
Some thoughts on choosing the correct space group,
Acta Cryst. B51 (1995) 897-907.

M. Ohmasa and K. Ohsume,
Determination of Laue class from diffraction data of polycrystalline materials,
Acta Cryst. A51 (1995) 87-91.

R. Peschar, H. Schenk & P. Capkova,
Preferred-orientation correction and normalization procedure for ab initio structure determination from powder data,
J. Appl. Cryst. 28 (1995) 127-140.

P. G. Byrom & B.W. Lucas,
Crystal structure determination by neutron powder diffraction using structural and packing constraints,
J. Appl. Cryst. 24 (1991) 1005-1008.

C.C Wilson & J.W. Wadsworth,
Crystal structure determination from low-resolution X-ray powder diffraction data.
Acta Cryst. A46 (1990) 258-262.

C.C. Wilson,
Determination of crystal structures from poor-quality data using Patterson methods,
Acta Cryst. A45 (1989) 833-839.

Sivia-DS; David-WIF
A Bayesian approach to phase extension
JOURNAL-OF-PHYSICS-AND-CHEMISTRY-OF-SOLIDS. DEC 2001; 62 (12) : 2119-212

David-WIF; Sivia-DS
Background estimation using a robust Bayesian analysis
JOURNAL-OF-APPLIED-CRYSTALLOGRAPHY. JUN 2001; 34 Part 3 : 318-324
 
 

 
Helliwell, M   Jones, RH   Kaucic, V   Logar, NZ
The use of softer X-rays in the structure elucidation of microporous
   materials
JOURNAL OF SYNCHROTRON RADIATION 12, 2005, 420-430.
Microporous materials, such as zeolites and aluminophosphates, have
   many applications as molecular sieves and shape-selective catalysts.
   This is due to their three-dimensional frameworks, which contain
   regular pores and channels, to their high acidity, arising from
   Bronsted and Lewis acid active sites, and to the incorporation of
   transition metal atoms into framework sites. This review firstly
   provides an introduction into the nature and properties of these
   materials, and their important applications; the difficulties in their
   full characterization and possible methods of elucidating their
   structures are then outlined; finally, methods of characterization,
   utilizing 'softer X-rays' are introduced. The first method is the
   determination of low concentrations of transition metals, incorporated
   into the frameworks using single crystal anomalous dispersion
   crystallography; synchrotron radiation is used to tune to the
   absorption edge of the metal atom in question, in order to change its
   signal relative to that of the rest of the structure, thereby allowing
   the pinpointing of its positions and the determination of its
   concentration at each site in the framework. Secondly, the use of
   longer wavelengths in powder diffraction studies is described, which,
   by stretching out the powder pattern, thereby reduces the overlapping
   of the diffraction peaks, thus allowing the structure to be solved by
   conventional direct methods. Finally, the use of X-ray absorption
   spectroscopy to determine the metal incorporation and the nature of
   coordination at the metal atom sites, in Mn silicalite-1 and FAPO-36,
   are described.
 
 
 

Vaughan, GBM   Schmidt, S   Poulsen, HF
Multicrystal approach to crystal structure solution and refinement
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 219, 2005, 813-825.
We present a method in which the contributions from the individual
   crystallites in a polycrystalline sample are separated and treated as
   essentially single crystal data sets. The process involves the
   simultaneous determination of the orientation matrices of the
   individual crystallites in the sample, the subsequent integration of
   the individual peaks, and filtering and summing of the subsequent
   integrated intensities, in order to arrive at a single-crystal like
   data set which may be treated normally. In order to demonstrate the
   method, we consider as a test case a small molecule structure, cupric
   acetate monohyrade. We show that it is possible to obtain a
   single-crystal quality structure solution and refinement, in which
   accurate anisotropic thermal parameters and hydrogen atom positions are
   obtained.
 
 
 

Brouwer, DH   Darton, RJ   Morris, RE   Levitt, MH
A solid-state NMR method for solution of zeolite crystal structures
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY 127, 2005, 10365-10370.
Since zeolites are notoriously difficult to prepare as large single
   crystals, structure determination usually relies on powder X-ray
   diffraction (XRD). However, structure solution (i.e., deriving an
   initial structural model) directly from powder XRD data is often very
   difficult due to the diffraction phase problem and the high degree of
   overlap between the individual reflections, particularly for materials
   with the structural complexity of most zeolites. Here, we report a
   method for structure determination of zeolite crystal structures that
   combines powder XRD and nuclear magnetic resonance (NMR) spectroscopy
   in which the crucial step of structure solution is achieved using
   solid-state Si-29 double-quantum dipolar recoupling NMR, which probes
   the distance-dependent dipolar interactions between naturally abundant
   Si-29 nuclei in the zeolite framework. For two purely siliceous zeolite
   blind test samples, we demonstrate that the NMR data can be combined
   with the unit cell parameters and space group to solve structural
   models that refine successfully against the powder XRD data.
 

Coelho, AA
A bound constrained conjugate gradient solution method as applied to
   crystallographic refinement problems
JOURNAL OF APPLIED CRYSTALLOGRAPHY 38, 2005, 455-461.
Small modifications to the conjugate gradient method for solving
   symmetric positive definite systems have resulted in an increase in
   performance over LU decomposition by a factor of around 84 for solving
   a dense system of 1325 unknowns. Performance is further increased in
   the case of applying upper- and lower-bound parameter constraints. For
   structure solution employing simulated annealing and the Newton -
   Raphson method of non-linear least squares, the overall performance
   gain can be a factor of four, depending on the applied constraints. In
   addition, the new algorithm with bounding constraints often seeks out
   lower minima than would otherwise be attainable without constraints.
   The behaviour of the new algorithm has been tested against the
   crystallographic problems of Pawley refinement, rigid-body and general
   crystal structure refinement.
 
 

Masciocchi, N   Sironi, A
Structural powder diffraction characterization of organometallic
   species: the role of complementary information
COMPTES RENDUS CHIMIE 8, 2005, 1617-1630.
X-ray powder diffraction (XRPD) has been employed in the last years as
   an active structural tool, well beyond its classical usage in
   qualitative, quantitative and microstructural analyses. The complexity
   of the materials studied by this method has steadily grown, allowing
   the full structural characterization of molecular systems, of organic
   and organometallic nature. Here we emphasize that, when dealing with
   such moderately complex molecular materials, the power of XRPD can be
   enhanced not only by increasing the radiation flux or the instrumental
   resolution, but also (and cheaply) by using additional (experimental or
   computational) information.
 
 

 
Hofmann, DWM   Kuleshova, L
New similarity index for crystal structure determination from X-ray
   powder diagrams
JOURNAL OF APPLIED CRYSTALLOGRAPHY 38, 2005, 861-866.
A new similarity index for automated comparison of powder diagrams is
   proposed. In contrast to traditionally used similarity indices, the
   proposed method is valid in cases of large deviations in the cell
   constants. The refinement according to this index closes the gap
   between crystal structure prediction and automated crystal structure
   determination. The opportunities of the new procedure have been
   demonstrated by crystal structure solution of un-indexed powder
   diagrams of some organic pigments (PY111, PR181 and Me-PR170).
 
 

Trask, AV   van de Streek, J   Motherwell, WDS   Jones, W
Achieving polymorphic and stoichiometric diversity in cocrystal
   formation: Importance of solid-state grinding, powder X-ray structure
   determination, and seeding
CRYSTAL GROWTH & DESIGN 5, 2005, 2233-2241.
Solid-state grinding is explored as a means of selectively preparing
   specific stoichiometric or polymorphic modifications of crystalline
   supramolecular complexes, or cocrystals. In research involving
   cocrystals of the model pharmaceutical compound caffeine prepared via
   solid-state grinding and solution crystallization, it has been
   demonstrated that these two methods of preparation are not always
   coterminous with respect to the cocrystal product obtained. Examined
   herein are the structures of five previously unreported caffeine
   cocrystals with monocarboxylic acids, including formic acid, acetic
   acid, and trifluoroacetic acid. This system illustrates three different
   possibilities in performing cocrystal preparation via the dual methods
   of solid-state grinding and solution crystallization: (1) the same
   cocrystal can result from both methods; (2) different cocrystal
   stoichiometries can result from each method; (3) different cocrystal
   polymorphs can result from each method. Materials that at first could
   be prepared only by solid-state grinding were later induced to
   crystallize from solution by seeding with the grinding material.
   Because some cocrystals from grinding contained minor residual
   unreacted starting components, a phase-subtraction method was used to
   enable subsequent crystal structure determination from powder X-ray
   diffraction data. The findings herein assign a significance to
   solid-state grinding as a technique of choice in widespread screening
   efforts for novel supramolecular materials.
 
 

Basso, S   Fitch, AN   Fox, GC   Margiolaki, I   Wright, JP
High-throughput phase-diagram mapping via powder diffraction: a case
   study of HEWL versus pH
ACTA CRYSTALLOGRAPHICA SECTION D-BIOLOGICAL CRYSTALLOGRAPHY 61, 2005, 1612-1625.
44 samples of tetragonal hen egg-white lysozyme (HEWL) were obtained as
   a series of polycrystalline precipitates at 277 K and room temperature
   in the pH range between 6.56 and 3.33. The precipitates were
   investigated by the collection of high-resolution powder X-ray
   diffraction data at 295 K, which reveal the tetragonal or orthorhombic
   forms of lysozyme depending on the temperature and pH of
   crystallization. The use of a new robotic sample changer greatly
   facilitated these measurements. LeBail analyses of the powder patterns
   display a characteristic behaviour for the pH dependence of the
   tetragonal unit-cell parameters of HEWL crystallized at both
   temperatures. More detailed analysis shows that molecular replacement
   can give a suitable starting point for structural refinements,
   illustrating that powder data can be sufficient for this approach.
   Pawley or Rietveld refinements that fit a single model to four data
   sets simultaneously from four samples crystallized at pH values across
   the range studied benefit from improved powder data quality via the
   anisotropic changes in the unit cell. The Rietveld analysis gave an
   average structural model with excellent goodness of fit and
   stereochemistry.
 
 
 

Margiolaki, I   Wright, JP   Fitch, AN   Fox, GC   von Dreele, RB
Synchrotron X-ray powder diffraction study of hexagonal turkey
   egg-white lysozyme
ACTA CRYSTALLOGRAPHICA SECTION D-BIOLOGICAL CRYSTALLOGRAPHY 61, 2005, 423-432.
The structure of turkey egg-white lysozyme (TEWL) has been refined from
   high-resolution X-ray powder diffraction data. The sample was rapidly
   obtained as a polycrystalline precipitate at high protein concentration
   using 0.5 M NaCl solvent pH 6 and was deposited in the PDB with code
   1xft. The diffraction data were collected at room temperature.
   Molecular replacement was shown to give a suitable starting point for
   refinement, illustrating that powder data can be sufficient for this
   approach. Crystallographic models were then refined by combined
   Rietveld and stereochemical restraint analysis of the powder data
   (d(min) = 3.35 angstrom), resulting in the extraction of reliable
   lattice parameters and the refinement of the molecular conformation at
   room temperature. The structure is hexagonal [space group P6(1)22,
   unit-cell parameters a = 71.0862 (3), c = 85.0276 (5) angstrom] with 12
   symmetry-related molecules in the unit cell, in agreement with previous
   studies. The results of our analysis are indicative of specific amino
   acids being disordered at this temperature. Upon cooling, a sudden drop
   in the lattice parameters at similar to 250 K is observed concurrently
   with the freezing of the mother liquor. The observation of severe peak
   broadening below this temperature indicates strain effects accompanying
   the freezing transition, which are found to be reversible. Finally, a
   correlation between the unit-cell parameters and the pH of the buffer
   solution is evident, in a similar manner to earlier observations on
   HEWL.

 
Evans, JSO   Evans, IR
Beyond classical applications of powder diffraction
CHEMICAL SOCIETY REVIEWS 33, 2004, 539-547.
This article provides a short tutorial review of how laboratory powder
   diffraction methods can be used to establish a variety of
   "non-traditional'' pieces of information about solid state
   materials-information beyond simple phase identification or structure
   determination at a specific temperature. The examples show how unique
   insights into synthetic pathways, reaction mechanisms, reaction
   kinetics, polymorphism, phase transitions and physical properties can
   be obtained for a variety of different types of materials.
 
 

Gilmore, CJ   Barr, G   Paisley, J
High-throughput powder diffraction. I. A new approach to qualitative
   and quantitative powder diffraction pattern analysis using full pattern
   profiles
JOURNAL OF APPLIED CRYSTALLOGRAPHY 37, 2004, 231-242.
A new integrated approach to full powder diffraction pattern analysis
   is described. This new approach incorporates wavelet-based data
   pre-processing, non-parametric statistical tests for full-pattern
   matching, and singular value decomposition to extract quantitative
   phase information from mixtures. Every measured data point is used in
   both qualitative and quantitative analyses. The success of this new
   integrated approach is demonstrated through examples using several test
   data sets. The methods are incorporated within the commercial software
   program SNAP-1D, and can be extended to high-throughput powder
   diffraction experiments.
 
 
 

Bhuvanesh, NSP   Reibenspies, JH
A novel approach to micro-sample X-ray powder diffraction using nylon
   loops
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 1480-1481.
A novel method for sample mounting to obtain powder diffraction from
   very small amounts of samples ( ranging from micrograms down to a few
   nanograms), by using a combination of multiwire area detector, three-
   circle diffractometer, monochromatic Cu K alpha radiation and 10 mum
   nylon loops, has been developed. This method exploits customary single-
   crystal approaches to collect the powder diffraction pattern, which
   overcomes many of the limitations of conventional powder X- ray
   diffraction.
 
 
 
 

Gozzo, F   Schmitt, B   Bortolamedi, T   Giannini, C   Guagliardi, A
   Lange, M   Meister, D   Maden, D   Willmott, P   Patterson, BD
First experiments at the Swiss Light Source Materials Science beamline
   powder diffractometer
JOURNAL OF ALLOYS AND COMPOUNDS 362, 2004, 206-217.
The Materials Science beamline at the Swiss Light Source saw 'first
   light' in Spring 2001 and is presently undergoing commissioning and
   pilot experiment operation. In this article we concentrate on one of
   the three MS beamline stations, the Powder Diffractometer, and report
   on resolution tests and first experimental results. Using the
   high-resolution multi-crystal analyzer detector, full widths at half
   maximum (FWHM) smaller than 0.01degrees were measured with standard
   powders and FWHMs smaller than 0.003degrees were measured with a single
   Si(111) crystal and a very low-divergent incident beam. With the same
   detector, first residual stress measurements on low pressure plasma
   sprayed coatings were performed. Dynamic electric field-induced strain
   effects in relaxor perovskite crystals and the influence of
   water-soluble polymers on the early hydration of cement were studied
   using a fast read-out multistrip solid-state detector.
 

 

 
Baerlocher, C   McCusker, LB   Prokic, S   Wessels, T
Exploiting texture to estimate the relative intensities of overlapping
   reflections
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 219, 2004, 803-812.
Additional information about the relative intensities of reflections
   that overlap in a powder diffraction pattern can be obtained from a
   polycrystalline sample in which the crystallites are preferentially
   oriented. If the data are collected and analyzed appropriately, more
   single-crystal-like reflection intensities can be extracted, and
   thereby more complex structures solved. This 'texture method' was
   implemented initially in reflection mode and its power demonstrated
   with the solution of the 117-atom structure of the hi-h-silica zeolite
   UTD-1F However, the experiment required a minimum of 3 days of
   synchrotron beamtime per sample. In an attempt to reduce the amount of
   beamtime needed and to simplify the experiment itself, a transmission
   mode alternative using an area detector was developed. Details of the
   sample preparation, data collection and data analysis for both
   geometries are described. The solution of the structures of the
   aluminophosphates Mu-9 (R(3) over bar c, a = 14.0696(1) Angstrom, c =
   42.3113(4) Angstrom) and AIPO-M (Pbca, a = 9.7493(1) Angstrom, b =
   29.1668(2) Angstrom, c = 9.3528(1) Angstrom) using reflection and
   transmission mode data, respectively, are provided as examples of the
   method.
 
 
 
 

Habershon, S   Cheung, EY   Harris, KDM   Johnston, RL
An efficient algorithm for calculating whole-profile functions in
   crystal structure solution from powder diffraction data
CHEMICAL PHYSICS LETTERS 390, 2004, 394-398.
A method for calculation of the whole-profile powder diffraction
   R-factor R-wp, adapted specifically for use in direct-space structure
   solution, is shown to be faster by a factor of approximately 20 than
   standard methods for calculating R-wp.
 
 

Dutour, J   Guillou, N   Huguenard, C   Taulelle, F
   Mellot-Draznieks, C   Ferey, G
Chiolite, a case study for combining NMR crystallography, diffraction
   and structural simulation
SOLID STATE SCIENCES, 6, 2004, 1059-1067.
Chiolite has been selected as a test case for developing a general
   approach to solve inorganic structures from powders by combining NMR,
   modeling, and X-ray diffraction. The different steps of the strategy
   are successfully performed, building the candidate integrant units
   using NMR, simulating candidate crystal structures using the
   computational AASBU method, and checking the consistency of the
   candidate structures against the diffraction data analyzed with FOX
   computer program.
 
 
 

Li, ZG   Harlow, RL   Foris, CM   Li, H   Ma, P   Vickery, RD   Maurin, MB   Toby, BH
New applications of electron diffraction in the pharmaceutical
   industry: Polymorph determination by using a combination of electron
   diffraction and synchrotron X-ray powder diffraction techniques
MICROSCOPY AND MICROANALYSIS 8, 2002, 134-138.
Electron diffraction has been recently used in the pharmaceutical
   industry to study the polymorphism in crystalline drug substances.
   While conventional X-ray diffraction patterns could not be used to
   determine the cell parameters of two forms of the microcrystalline GP
   IIb/IIIa receptor antagonist roxifiban, a combination of electron
   single-crystal and synchrotron powder diffraction techniques were able
   to clearly distinguish the two polymorphs. The unit-cell parameters of
   the two polymorphs were ultimately determined using new software
   routines designed to take advantage of each technique's unique
   capabilities. The combined use of transmission electron microscopy
   (TEM) and synchrotron patterns appears to be a good general approach
   for characterizing complex (low-symmetry, large-unit- cell,
   micron-sized) polymorphic pharmaceutical compounds.
 
 
 

Brenner, S   McCusker, LB   Baerlocher, C
The application of structure envelopes in structure determination from
   powder diffraction data
JOURNAL OF APPLIED CRYSTALLOGRAPHY 35, 2002, 243-252.
A structure envelope is a special type of periodic nodal surface that
   separates regions of high electron density from those of low electron
   density. Once such a surface has been generated, it can be used in
   combination with direct-space methods to facilitate structure solution
   from powder data. To generate an informative structure envelope, the
   phases of the structure factors of a few strong low-order reflections
   must be determined; an algorithm has been developed for this purpose.
   The program SayPerm combines (a) the use of error-correcting codes
   (e.c.c.'s) to sample phase space efficiently, (b) a pseudo-atom
   approximation of structure fragments to simulate atomic resolution at
   ca 2.5 Angstrom, and (c) phase extension and phase set ranking using
   the Sayre equation. The effect of using a structure envelope in
   structure solution was first tested in combination with a subroutine
   for finding zeolite topologies in the program FOCUS. Then extension to
   molecular structures in combination with a simulated-annealing program
   was explored. This resulted in the development of the program Safe and
   the subsequent determination of the structure of a tri-beta-peptide
   (C32N3O6H53) with 17 variable torsion angles.
 
 
 

Brunelli, M   Wright, JP   Vaughan, GRM   Mora, AJ   Fitch, AN
Solving larger molecular crystal structures from powder diffraction
   data by exploiting anisotropic thermal expansion
ANGEWANDTE CHEMIE-INTERNATIONAL EDITION 42, 2003, 2029-2032.
 
 
 

 
Pichon, C   Palancher, H   Hodeau, JL   Berar, JF
Towards operando characterisation by powder diffraction techniques of
   molecular sieves
OIL & GAS SCIENCE AND TECHNOLOGY-REVUE DE L INSTITUT FRANCAIS DU PETROLE
   60, 2005, 831-848.
Working molecular sieves imply numerous and various atoms and for their
   characterisation we need chemical selective probes. Thus they can be
   studied either by neutron powder diffiraction or by anomalous X-ray
   powder diffiraction techniques to extract structural information. We
   will illustrate the complementarities of these methods in the analysis
   of two different chemical processes on X-type zeolite.
   In the first case, a fully exchanged barium X-type zeolite was,
   firstly, characterised by neutron powder diffiraction after an ex situ
   preparation step. During the preparation step, the sample was saturated
   with a mixture of heavy water and deuterated para-xylene. The
   selectivity of neutron diffraction for light elements allows the
   precise location of both water and xylene molecules.
   In the second example, an X-type zeolite exchanged by both strontium
   and rubidium cations was studied during the dehydration process. The in
   situ structural characterisation was performed by recording, for each
   state of the zeolite (hydrated, dehydrated), three X-ray powder
   patterns. Two of them were measured at an energy close to the
   absorption edge of each compensating cation (Sr2+ and Rb+) and one far
   from both absorption edges. The chemical selectivity of resonant
   diffraction allows an accurate determination of the distribution of
   compensating cations (location, distribution and mobility) during the
   dehydration process.
   Finally a comparison of some specificities and limitations of both
   methods are summarized.
 

 
Schmidt, S   Poulsen, HF   Vaughan, GBM
Structural refinements of the individual grains within polycrystals and
   powders
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 326-332.
A method is presented for simultaneous structural refinement of up to
   several hundred grains inside powders or polycrystals. The method is
   based on the use of hard X-rays and the indexing program GRAINDEX,
   where grain orientations are found by scanning in Euler space.
   Conventional experimental setups and refinement programs for
   single-crystal work can be applied. The method is validated by a study
   of a sintered plate of alpha-Al2O3, containing of the order of 1500
   grains in the gauge volume. 57 of the largest grains were refined with
   respect to the Al z and O x positions as well as the isotropic atomic
   displacement parameters. The R1 values were 3.4% and 3.8% for the grain
   average and the best grain, respectively. A discussion of the potential
   of the method is presented, as well as the main limitation: grain size
   and overlap of diffraction spots.
 
 
 
 
 
 
 

Redeterminations
 
 

Florence, AJ   Shankland, N   Shankland, K   David, WIF   Pidcock, E
   Xu, XL   Johnston, A   Kennedy, AR   Cox, PJ   Evans, JSO
   Steele, G   Cosgrove, SD   Frampton, CS
Solving molecular crystal structures from laboratory X-ray powder
   diffraction data with DASH: the state of the art and challenges
JOURNAL OF APPLIED CRYSTALLOGRAPHY 38, 2005, 249-259.
The crystal structures of 35 molecular compounds have been redetermined
   from laboratory monochromatic capillary transmission X-ray powder
   diffraction data using the simulated-annealing approach embodied within
   the DASH structure solution package. The compounds represent
   industrially relevant areas ( pharmaceuticals; metal coordination
   compounds; nonlinear optical materials; dyes) in which the research
   groups in this multi-centre study are active. The molecules were
   specifically selected to form a series within which the degree of
   structural complexity (i.e. degrees of freedom in the global
   optimization) increased systematically, the degrees of freedom
   increasing with increasing number of optimizable torsion angles in the
   structural model and with the inclusion of positional disorder or
   multiple fragments ( counterions; crystallization solvent; Z' > 1). At
   the lower end of the complexity scale, the structure was solved with
   excellent reproducibility and high accuracy. At the opposite end of the
   scale, the more complex search space offered a significant challenge to
   the global optimization procedure and it was demonstrated that the
   inclusion of modal torsional constraints, derived from the Cambridge
   Structural Database, offered significant benefits in terms of
   increasing the frequency of successful structure solution by
   restricting the magnitude of the search space in the global
   optimization.
 
 
 

Graphism
 

 
Hinrichsen, B   Dinnebier, RE   Jansen, M
Powder3D: An easy to use program for data reduction and graphical
   presentation of large numbers of powder diffraction patterns
ZEITSCHRIFT FUR KRISTALLOGRAPHIE suppl 23, part 1, 2006, 231-236.
The presented software facilitates data reduction of multiple powder
   diffraction patterns. Many operations are automated for the application
   to huge sets of patterns collected during diffraction experiments in
   dependence of time, temperature, pressure and composition. The features
   include basic data reduction procedures, such as background reduction,
   K-alpha stripping, smoothing and Le Bail fitting. Many file formats are
   supported to provide interoperability with GSAS, Fullprof and Crysfire
   (amongst others). The software is freely available for non-profit use
   at http://www.fkf.mpg.de/xray/.
 
 

Rietveld, DDM
 

Toby, BH
R factors in Rietveld analysis: How good is good enough?
POWDER DIFFRACTION 21, 2006, 67-70.
The definitions for important Rietveld error indices are defined and
   discussed. It is shown that while smaller error index values indicate a
   better fit of a model to the data, wrong models with poor quality data
   may exhibit smaller values error index values than some superb models
   with very high quality data.
 

 
Solovyov, LA
Full-profile refinement by derivative difference minimization
JOURNAL OF APPLIED CRYSTALLOGRAPHY 37, 2004, 743-749.
A new method of full-profile refinement is developed on the basis of
   the minimization of the derivatives of the pro le difference curve. The
   use of the derivatives instead of the absolute difference between the
   observed and calculated pro le intensities allows refinement
   independently of the background. The procedure is tested on various
   powder diffraction data sets and is shown to be fully functional.
   Besides having the capability of powder diffraction structure analysis
   without modelling the background curve, the method is shown to allow
   the derivation of structure parameters of even higher quality than
   those obtained by Rietveld refinement in the presence of systematic
   errors in the model background function. The derivative difference
   minimization principles may be used in many different areas of powder
   diffraction and beyond.
 
 

 
Dusek, M   Petricek, V
Three years of developing JANA2000 305, 2004, 267-271.
FERROELECTRICS
We present the latest state of the computing system JANA2000. The main
   improvement comparing with the previous version JANA98 consists in the
   possibility to use powder diffraction data of one or more
   three-dimensional or modulated phases. The current development of
   JANA2000 comprises (1) generalization of the program from four to six
   dimensions, (2) improvement of the powder option, (3) developing of
   complex tools for transformations and (4) automatic determination of
   the (super)space symmetry.
 
 
 
 
 

David, WIF
On the equivalence of the Rietveld method and the correlated integrated
   intensities method in powder diffraction
JOURNAL OF APPLIED CRYSTALLOGRAPHY 37, 2004, 621-628.
The Rietveld method is the most straightforward and statistically
   correct approach for the refinement of crystal structure parameters
   from powder diffraction data. The equivalent two-stage approach,
   involving the refinement of structural parameters based on integrated
   intensities extracted using the Pawley method, is extremely useful in
   circumstances such as the global optimization methods of structure
   determination, where a great many refinements need to be performed very
   quickly. The equivalence is emphasized in a simple mathematical
   relationship between the goodness of fits obtained in Rietveld, Pawley
   and correlated integrated intensities refinements. A rationale is given
   for determining the estimated standard deviations for structural
   variables from powder diffraction data.
 
 
 

David, WIF
Powder diffraction: Least-squares and beyond
JOURNAL OF RESEARCH OF THE NATIONAL INSTITUTE OF STANDARDS AND
   TECHNOLOGY 109, 2004, 107-123.
This paper addresses some of the underlying statistical assumptions and
   issues in the collection and refinement of powder diffraction data.
   While standard data collection and Rietveld analysis have been
   extremely successful in providing structural information on a vast
   range of materials, there is often uncertainty about the true accuracy
   of the derived structural parameters. In this paper, we discuss a
   number of topics concerning data collection and the statistics of data
   analysis. We present a simple new function, the cumulative chi-squared
   distribution, for assessing regions of misfit in a diffraction pattern
   and introduce a matrix which relates the impact of individual points in
   a powder diffraction pattern with improvements in the estimated
   standard deviation of refined parameters. From an experimental
   viewpoint, we emphasise the importance of not over-counting at
   low-angles and the routine use of a variable counting scheme for data
   collection. Data analysis issues are discussed within the framework of
   maximum likelihood, which incorporates the current least-squares
   strategies but also enables the impact of systematic uncertainties in
   both observed and calculated data to be reduced.
 
 

 
Shankland, K
Global Rietveld refinement
JOURNAL OF RESEARCH OF THE NATIONAL INSTITUTE OF STANDARDS AND
   TECHNOLOGY 109, 2004, 143-154.
Global optimisation methods of structure determination from powder
   diffraction data have risen to prominence in a relatively short space
   of time and they now constitute a key approach in the examination of
   polycrystalline molecular organic materials. A correctly formulated
   global optimisation approach may be regarded as a "global Rietveld
   refinement" that is capable of delivering accurate crystal structures
   from high-quality powder diffraction data. This paper focuses on how
   accuracy at all stages of a powder diffraction experiment impacts upon
   the overall structure solution process and particular attention is paid
   to assessing the degree of accuracy with which structures are returned
   from the global optimisation process.
 

 
Izumi, F
Beyond the ability of Rietveld analysis: MEM-based pattern fitting
SOLID STATE IONICS 172, 2004, 1-6.
A multipurpose pattern-fitting program, RIETAN-2000, and a software
   package, VENUS, for three-dimensional (3D) visualization were
   substantially combined to grow into an integrated system for
   whole-pattern fitting (w.p.f) based on the maximum entropy method
   (MEM). In MEM-based pattern fitting (MPF), 'observed' structure factors
   resulting from Rietveld analysis are analyzed by MEM to yield improved
   structure factors, F-c(MEM). Then, we carry out w.p.f where structure
   factors are fixed at the F-c(MEM)s. F-o(w.p.f) data estimated after
   w.p.f. are analyzed again by MEM. MEM analysis and w.p.f are
   alternately repeated until R factors in the latter no longer decrease.
   These iterative processes enable us to minimize a bias imposed by a
   structural model for the Rietveld analysis on final electron/nuclear
   densities. MPF is flexible enough to be capable of modeling static and
   dynamic disorder, chemical bonds, nonlocalized electrons, and
   anharmonic thermal motion better than the Rietveld method. Applications
   of MPF to structure refinements of five compounds with disordered
   structures have demonstrated its excellent performance and
   effectiveness.
 
 
 

Izumi, F   Kumazawa, S   Ikeda, T   Hu, WZ   Yamamoto, A   Oikawa, K
MEM-based structure-refinement system REMEDY and its applications
EPDIC 7: EUROPEAN POWDER DIFFRACTION, PTS 1 AND 2
MATERIALS SCIENCE FORUM 378-3, 2001, 59-64.
A Rietveld-analysis program RIETAN was combined with MEED for a
   maximum-entropy method (MEM) to grow into an integrated software
   REMEDY. At first, 'observed' structure factors, F-o, estimated after
   Rietveld analysis are analyzed by the MEM to give electron/nuclear
   densities biased by a structural model. Then, we evaluate structure
   factors, (FeMEM)-M-(), by the Fourier transform of the densities and
   fit the whole powder pattern calculated from the F-e(MEM) data to the
   observed one to refine parameters irrelevant to the structure. F-o data
   obtained in such a manner are analyzed again by the MEM. MEM analysis
   and whole-pattern fitting are alternately repeated until R factors in
   the pattern fitting no longer decrease. REMEDY was utilized to
   investigate (a) positional disorder of K+ ions interlayered in
   KxTi2-x/3Li(x)/O-3(4), (b) atomic arrangement of K clusters in K-type
   LTA, and (c) nuclear/electron-density distribution in HgBa2CUO4+delta.
 

 

Izumi, F
Development and applications of the pioneering technology of structure
   refinement from powder diffraction data
JOURNAL OF THE CERAMIC SOCIETY OF JAPAN 111, 2003, 617-623.
A couple of Rietveld-analysis programs, RIETAN, for angle-dispersive
   diffraction and time-of-flight neutron diffraction have been
   extensively used for structural studies of many compounds. The history
   of their developments is briefly reviewed. The latest versions,
   RIETAN-2000 for angle-dispersive diffraction and RIETAN-2001T for the
   Vega and Sirius diffractometers at KENS have a practical feature of
   partial profile relaxation. In this technique, primary profile
   parameters of (nearly) isolated reflections can be individually refined
   independent of secondary profile parameters. It was combined with split
   profile functions to improve fits between observed and calculated
   patterns, particularly in samples exhibiting anisotropic profile
   broadening and reflections with very large lattice-plane spacings.
   RIETAN-2000 and our own program for the maximum-entropy method (MEM),
   PRIMA, were virtually integrated into a structure-refinement system,
   REMEDY, whereby the pattern calculated from structure factors obtained
   by MEM is fit to the whole observed pattern. 'Observed' structure
   factors estimated at the end of the whole-pattern fitting are analyzed
   again by MEM. Whole-pattern fitting and MEM analysis are alternately
   repeated until R factors in the former no longer decrease. Applications
   of this technology to three inorganic compounds having highly
   disordered structures are demonstrated, showing its excellent
   performance and effectiveness.
 
 
 
 
 

Jouanneaux, A   Le Gonidec, X   Fitch, AN
WinMProf: Visual Rietveld software
EPDIC 7: EUROPEAN POWDER DIFFRACTION, PTS 1 AND 2
MATERIALS SCIENCE FORUM 378-3, 2001, 112-117.
WinMProf is a Windows application that can be used for powder
   diffraction analysis, with data collected at constant wavelength, using
   the MPROF Rietveld refinement routine. The main features of the
   software are described in detail.
 
 
 

 

energy-dispersive X-ray diffraction
 
 
 

Dong, YH   Liu, J   Li, YC   Li, XD
A full-pattern fitting algorithm for energy-dispersive X-ray diffraction
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 1123-1127.
A full-pattern fitting algorithm for energy-dispersive X-ray
   diffraction is proposed, especially for high-pressure X-ray diffraction
   studies. The algorithm takes into account the errors in measuring the
   energy and the diffraction angle. A lognormal function is introduced to
   represent the background. All the peaks that are detectable in the
   diffraction spectra, including fluorescence and diffraction peaks, are
   considered together. Because all the data points in the spectra are
   used, the accuracy of the cell parameters obtained by this method is
   very high. This is very helpful in the analysis of the equation of
   state and the identification of new phases under high pressure.
 
 

Size-strain, faulting
 

Masson, O   Dooryhee, E   Fitch, AN
Instrument line-profile synthesis in high-resolution synchrotron powder
   diffraction
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 286-294.
An accurate method for synthesizing the instrumental line profile of
   high-resolution synchrotron powder diffraction instruments is
   presented. It is shown that the instrumental profile can be modelled by
   the convolution of four physical aberration functions: the equatorial
   intensity distribution, the monochromator and analyser transfer
   functions, and the axial divergence aberration function. Moreover, each
   equatorial aberration is related to an angle-independent function by a
   scale transform factor. The principles of the instrument line-profile
   calculation are general. They are applied in the case of the
   angle-dispersive powder X-ray diffraction beamline BM16 at the ESRF.
   The effects of each optical element on the overall instrument profile
   are discussed and the importance of the quality of the different
   optical elements of the instrument is emphasized. Finally, it is shown
   that the high resolution combined with the precise modelling of the
   instrument profile shape give access to a particle size as large as 3
   mum.
 
 
 
 

Kaszkur, Z   Mierzwa, B   Pielaszek, J
Ab initio test of the Warren-Averbach analysis on model palladium
   nanocrystals
JOURNAL OF APPLIED CRYSTALLOGRAPHY 38, 2005, 266-273.
Model powder diffraction patterns were calculated via the Debye formula
   from atom positions of a range of energy-relaxed closed-shell
   cubooctahedral clusters. The energy relaxation employed the Sutton-Chen
   potential scheme with parameters for palladium. The assumed cluster
   size distribution followed lognormal distribution of a crystallite
   volume centred with the diameter of 5 nm, as well as two bimodal
   lognormal distributions centred around 4 nm and 7 nm. These models
   allowed an in-depth analysis of the Warren - Averbach method of
   separating strain and size effects in a peak shape Fourier analysis.
   The atom-displacement distribution in the relaxed clusters could be
   directly computed, as well as the strain Fourier coefficients. The
   results showed that in the case of the unimodal size distribution, the
   method can still be successfully used for obtaining the column length
   distribution. However, the strain Fourier coefficients obtained from
   three reflections ( 002, 004 and 008) cannot be reliably estimated with
   the Warren - Averbach method. The primary cause is a non-Gaussian
   strain distribution and a shift of the diffraction maximum, inherent to
   the nanoparticles, differing for every constituent cluster in the size
   distribution. For the bimodal size distributions, the obtained column
   length distributions tend to be shifted towards the centres of the
   modes and are less sensitive to the larger size mode.
 

 
Balzar, D   Audebrand, N   Daymond, MR   Fitch, A   Hewat, A   Langford, JI
   Le Bail, A   Louer, D   Masson, O   McCowan, CN   Popa, NC   Stephens, PW
   Toby, BH
Size-strain line-broadening analysis of the ceria round-robin sample
JOURNAL OF APPLIED CRYSTALLOGRAPHY 37, 2004, 911-924.
The results of both a line-broadening study on a ceria sample and a
   size - strain round robin on diffraction line-broadening methods, which
   was sponsored by the Commission on Powder Diffraction of the
   International Union of Crystallography, are presented. The sample was
   prepared by heating hydrated ceria at 923 K for 45 h. Another ceria
   sample was prepared to correct for the effects of instrumental
   broadening by annealing commercially obtained ceria at 1573 K for 3 h
   and slowly cooling it in the furnace. The diffraction measurements were
   carried out with two laboratory and two synchrotron X-ray sources, two
   constant-wavelength neutron and a time-of-flight (TOF) neutron source.
   Diffraction measurements were analyzed by three methods: the model
   assuming a lognormal size distribution of spherical crystallites,
   Warren-Averbach analysis and Rietveld refinement. The last two methods
   detected a relatively small strain in the sample, as opposed to the
   first method. Assuming a strain-free sample, the results from all three
   methods agree well. The average real crystallite size, on the
   assumption of a spherical crystallite shape, is 191 (5) Angstrom. The
   scatter of results given by different instruments is relatively small,
   although significantly larger than the estimated standard
   uncertainties. The Rietveld refinement results for this ceria sample
   indicate that the diffraction peaks can be successfully approximated
   with a pseudo-Voigt function. In a common approximation used in
   Rietveld refinement programs, this implies that the size-broadened
   profile cannot be approximated by a Lorentzian but by a full Voigt or
   pseudo-Voigt function. In the second part of this paper, the results of
   the round robin on the size - strain line-broadening analysis methods
   are presented, which was conducted through the participation of 18
   groups from 12 countries. Participants have reported results obtained
   by analyzing data that were collected on the two ceria samples at seven
   instruments. The analysis of results received in terms of coherently
   diffracting, both volume-weighted and area-weighted apparent domain
   size are reported. Although there is a reasonable agreement, the
   reported results on the volume-weighted domain size show significantly
   higher scatter than those on the area-weighted domain size. This is
   most likely due to a significant number of results reporting a high
   value of strain. Most of those results were obtained by Rietveld
   refinement in which the Gaussian size parameter was not refined, thus
   erroneously assigning size-related broadening to other effects. A
   comparison of results with the average of the three-way comparative
   analysis from the first part shows a good agreement.
 
 
 

Estevez-Rams, E   Leoni, M   Scardi, P   Aragon-Fernandez, B   Fuess, H
On the powder diffraction pattern of crystals with stacking faults
PHILOSOPHICAL MAGAZINE 83, 2003, 4045-4057.
The so-called direct solution of the powder diffraction pattern for a
   faulted layered crystal is discussed. It is shown how, in the general
   case, peak profiles can be split into a symmetric and an antisymmetric
   component. The relationships between peak profile parameters and the
   underlying faulting structure, as given by the probability correlation
   function, are evidenced. The formalism reduces to known equations when
   applied to particular faulting models. Warren's equations for peak
   profile of fcc materials with {111} planar faulting are derived within
   the framework of a general theory. Possible strategies for
   incorporating the proposed formalism into a general powder pattern
   refinement procedure are also discussed.
 

 
Cervellino, A   Giannini, C   Guagliardi, A
Determination of nanoparticle structure type, size and strain
   distribution from X-ray data for monatomic f.c.c.-derived
   non-crystallographic nanoclusters
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 1148-1158.
Whole-profile-fitting least-squares techniques are applied to simulated
   and experimental X-ray diffraction patterns of monatomic face-centred
   cubic (f.c. c.)derived non-crystallographic nanoclusters to extract
   structure and size information. Three main structure types have been
   considered (cuboctahedral, icosahedral and decahedral). Nanocluster
   structure models have been generated within an original mathematical
   approach so as to be independent of a specific material. For each
   structure type, a log-normal size distribution is assumed and a
   phenomenological function is introduced to model possible additional
   size-related strain effects. The Debye function method (modified to
   increase computational efficiency) has been used to obtain the
   diffracted intensities of the nanocluster. Tests revealed the
   effectiveness of the method to recognize the structure types correctly
   and to estimate with good accuracy structure concentrations and size
   distributions. Application to a thiol-passivated gold nanoparticle
   sample is presented.
 

Scardi, P   Leoni, M
Whole powder pattern modelling
ACTA CRYSTALLOGRAPHICA SECTION A 58, 2002, 190-200.
A new approach for the modelling of diffraction patterns without using
   analytical profile functions is described and tested on ball milled
   f.c.c. Ni powder samples. The proposed whole powder pattern modelling
   (WPPM) procedure allows a one-step refinement of microstructure
   parameters by a direct modelling of the experimental pattern. Lattice
   parameter and defect content, expressed as dislocation density, outer
   cut-off radius, contrast factor, twin and deformation fault
   probabilities), can be refined together with the parameters (mean and
   variance) of a grain-size distribution. Different models for lattice
   distortions and domain size and shape can be tested to simulate or
   model diffraction data for systems as different as plastically deformed
   metals or finely dispersed crystalline powders. TEM pictures support
   the conclusions obtained by WPPM and confirm the validity of the
   proposed procedure.
 
 
 
 
 
 
 
 
 

parallel beam with laboratory instrument

 
Whitfield, PS
Use of double Gobel mirrors with high-temperature stages for powder
   diffraction - a strategy to avoid severe intensity fade
JOURNAL OF APPLIED CRYSTALLOGRAPHY 36, 2003, 926-930.
This paper describes an approach for countering an issue that can occur
   when using a high-temperature stage with a diffractometer equipped with
   double Gobel mirrors. The optical characteristics of the dual-mirror
   configuration make it more susceptible to intensity loss with sample
   displacement than conventional parallel-beam secondary optics. This
   issue has been apparent in the use of a high-temperature stage on a
   diffractometer equipped with dual mirrors, where data could not be
   obtained from the full room temperature to 1273 K range without
   resetting the sample height manually part way through the experiment. A
   simple technique involving controlled contouring of the sample surface
   has been demonstrated to allow data to be collected uninterrupted over
   the full temperature range, while retaining satisfactory intensities.
   The extent to which this technique extends the tolerable sample
   displacement range has been quantified using a computer-controlled XYZ
   stage.
 
 

Texture

Morales, M   Chateigner, D   Lutterotti, L   Ricote, J
X-ray combined QTA using a CPS applied to a ferroelectric ultrastructure
TEXTURES OF MATERIALS, PTS 1 AND 2 MATERIALS SCIENCE FORUM 408-4, 2002, 113-118.
The new combined methodology for quantitative description of texture,
   structure and other microstructural parameters of thin layers using
   X-ray diffraction is presented and applied to the case of a
   ferroelectric thin film of Pb0.76Ca0.24TiO3 on a Pt/TiO2/SiO2/Si
   substrate. The approach allows the quantitative texture analysis of the
   ferroelectric thin film and the Pt electrode, refining simultaneously
   their structure, layers thickness, mean crystallite size and
   microstrain state. The layer thickness determination is estimated by
   the refinement of the thicknesses inserted in the absorption and
   volumic correction factors. The powerfulness of this methodology is
   discussed and compared with other approaches.
 

Modulated structures
 
 

 
Dusek, M   Petricek, V   Wunschel, M   Dinnebier, RE   van Smaalen, S
Refinement of modulated structures against X-ray powder diffraction
   data with JANA2000
JOURNAL OF APPLIED CRYSTALLOGRAPHY 34, 2001, 398-404.
JANA is a computer program for the refinement and analysis of periodic
   and aperiodic (incommensurately modulated structures and composite
   crystals) crystal structures. Here a new module is introduced that
   allows Rietveld refinements against powder diffraction data. It is
   shown that JANA2000 provides a state-of-the-art description of the peak
   profiles. A re-analysis of the low-temperature structure of (CO)(x)C-60
   showed that the application of icosahedral symmetry restrictions to the
   C-60 molecule leads to a better description of the electron density and
   to a corrected position of the CO molecule as compared with a
   rigid-body refinement. The incommensurately modulated structure of
   NbTe4 has been successfully refined against X-ray powder diffraction
   data. The structural parameters are equal to, but less accurate, than
   the parameters obtained from a single-crystal study.
 
 
 
 

Electron crystallography
 

 
Weirich, TE   Portillo, J   Cox, G   Hibst, H   Nicolopoulos, S
Ab initio determination of the framework structure of the heavy-metal
   oxide CsxNb2.54W2.46O14 from 100 kV precession electron diffraction data
ULTRAMICROSCOPY 106, 2006, 164-175.
The present work deals with the ab initio determination of the heavy
   metal framework in Cs-x(Nb, W)(5)O-14 from precession electron
   diffraction intensities. The target structure was first discovered by
   Lundberg and Sundberg [Ultramicroscopy 52 (1993) 429-435], who
   succeeded in deriving a tentative structural model from high-resolution
   electron microsopy (HREM) images. The metal framework of the compound
   was solved in this investigation via direct methods from hk0 precession
   electron diffraction intensities recorded with a Philips EM400 at 100
   kV. A subsequent (kinematical) least-squares refinement with electron
   intensities yielded slightly improved co-ordinates for the I I heavy
   atoms in the structure. Chemical analysis of several crystallites by
   EDX is in agreement with the formula Cs0.44Nb2.54W2.46O14. Moreover,
   the structure was independently determined by Rietveld refinement from
   X-ray powder data obtained from a multi-phasic sample. The compound
   crystallises in the orthorhombic space group Pbam with refined lattice
   parameters a = 27.145(2), b = 21.603(2), and c = 3.9463(3) angstrom.
   Comparison of the framework structure from electron diffraction with
   the result from Rietveld refinement shows an average agreement for the
   heavy atoms within 0.09 angstrom.
 
 

Weirich, TE
First-principles calculations as a tool for structure validation in
   electron crystallography
ACTA CRYSTALLOGRAPHICA SECTION A 60, 2004, 75-81.
The crystal structures of Ti11Se4 [Weirich, Ramlau, Simon, Hovmoller &
   Zou ( 1996). Nature ( London), 382, 144 - 146] and Ti45Se16 [ Weirich (
   2001). Acta Cryst. A57, 183 - 191] determined previously from
   selected-area electron diffraction ( SAED) data have been checked for
   their correctness by means of total energy calculations within the
   non-local density functional theory. The reliability of the used method
   was verified by test calculations carried out for the structurally
   related compound Ti8Se3, which is well known from single-crystal X-ray
   diffraction [ Weirich, Pottgen & Simon ( 1996). Z. Kristallogr. 212,
   929 - 930]. For Ti8Se3, structural models from both experiment and
   calculation show a perfect match (average agreement 0.01 Angstrom).
   This proves that the geometrical optimized models from first-principles
   calculation can be used as a reliable alternative when good-quality
   X-ray results cannot be obtained. Calculations carried out for the two
   structures determined from electron crystallography yielded average
   improvement of the atomic coordinates of 0.04 and 0.09 Angstrom for
   Ti11Se4 and Ti45Se16, respectively. The optimized cell parameters of
   the monoclinic structures ( both space group C2/m, No. 12) are a =
   25.51, b = 3.43, c = 19.19 Angstrom, beta = 117.9degrees for Ti11Se4
   and a = 36.31, b = 3.45, c = 16.59 Angstrom, beta = 92.1degrees for
   Ti45Se16. These results prove that crystals that are too small for
   single-crystal X-ray diffraction and are difficult to solve by powder
   diffraction may nevertheless be amenable to accurate structure
   determination by electron diffraction structure analysis using data
   from standard SAED and the assumption of quasi-kinematical scattering.
   Moreover, this study shows that geometry optimization by
   first-principles calculations is the perfect tool for validation and
   improvement of complex structural models, which are suspected to have
   errors owing to the poor quality of experimental data.
 
 

 
Zou, XD   Mo, ZM   Hovmoller, S   Li, XZ   Kuo, KH
Three-dimensional reconstruction of the nu-AlCrFe phase by electron
   crystallography
ACTA CRYSTALLOGRAPHICA SECTION A 59, 2003, 526-539.
The three-dimensional (3D) structure of the huge quasicrystal
   approximant nu-AlFeCr (space group P6(3)/m, a = 40.687 and c = 12.546
   Angstrom) was solved by electron crystallography. High-resolution
   transmission-electron-microscopy (HREM) images and selected-area
   electron diffraction patterns from 13 different zone axes were combined
   to give a 3D potential map. 124 out of 129 unique atoms were found in
   the 3D map. Procedures for ab initio structure determination by 3D
   reconstruction are given. It is demonstrated that 3D reconstruction
   from HREM images is very powerful for solving structures - even very
   complicated ones. There is no limit in terms of the number of unique
   atoms in a structure that can be solved by 3D reconstruction.
 
 

 
Dorset, DL
Applications of direct methods for structure determination to problems
   in electron and x-ray fibre diffraction of polymers
REPORTS ON PROGRESS IN PHYSICS 66, 2003, 305-338.
In this review, the prospect of determining polymer crystal structures
   directly from single crystal electron or x-ray powder/fibre diffraction
   intensity data is explored. When care is taken to collect the best data
   set from a polymer, i.e. sampling the most intense regions of the
   three-dimensional reciprocal lattice, structure analyses can be carried
   out effectively by the conventional direct phasing methods employed in
   small molecule crystallography, even though the data sets are
   relatively small. This means that constraints imposed by multiple beam
   interactions in electron diffraction and reflection overlap in x-ray
   diffraction often do not limit the structure analysis.
   Several three-dimensional single crystal electron diffraction structure
   analyses are presented to illustrate the problems encountered. These
   include: polyethylene, poly(epsilon-caprolactone), isotactic
   poly(butene-1) form III, isotactic polypropylene
   beta-form,poly(p-oxybenzoate) and poly(ethylene sulfide). Techniques
   for sampling the complete reciprocal lattice are discussed. If an
   adequate number of data is collected, it is also possible to refine the
   structure by constrained least squares. In any case Fourier refinement
   is always useful.
   From powder x-ray diffraction the crystal structure of polyethylene has
   been determined by direct methods; from fibre x-ray intensities, this
   review reports the direct analyses of poly(epsilon-caprolactone),
   poly(ethylene terephthalate) and poly(tetramethyl-p-silphenylene
   siloxane). Rietveld methods might also be useful for the structure
   refinement.
   Direct structure analyses are advantageous in that they circumvent a
   priori assumptions about the molecular model and also the linkage bonds
   to base conformational refinement. Instead, individual atomic positions
   or molecular envelopes are observed directly in potential or electron
   density maps, to which the model can then be fit, a situation analogous
   to current practice in protein crystallography.
 
 
 

Dorset, DL
Correlations, convolutions and the validity of electron crystallography
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 218, 2003, 237-147.
Although often an object of controversy, electron crystallography has
   emerged as a useful technique for characterization of the
   microcrystalline state, capable of elucidating crystal structures of
   unknown substances. Despite the complicated multiple scattering
   perturbations to diffracted intensities, experimental conditions can be
   adjusted to favor data collection where the experimental Patterson
   function still resembles the autocorrelation function of the actual
   crystal structure. Satisfying this condition is often sufficient to
   permit structure solution from such data by direct methods. While the
   application to organic structures may seem obvious, there are
   surprising successes with data sets from inorganic materials. The
   account given in this paper, in part, portrays work leading to the A.
   L. Patterson Award to the author from the American Crystallographic
   Association.
 
 
 

Kolb, U   Matveeva, GN
Electron crystallography on polymorphic organics
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 218, 2003, 259-268.
Organic materials, such as non-linear optical active compounds
   (1-(2-furyl)-3-(4-aminophenyl)-2-propene-1-one (FBAPPO) and
   1-(2-furyl)-3-(4-benzamidophenyl)-2-propene-1-one (FAPPO)), polymeric
   materials like the metal coordinated polyelectrolyte (Fe(II) [ditopic
   bis-terpyridin] (MEPE)) or polymorphic materials (e.g.
   Cu-phthalocyanine), which do not crystallize big enough for single
   crystal x-ray structure analysis have been investigated by electron
   diffraction (ED) at 100 and 300 kV acceleration voltage. Sample
   preparation (direct crystallization, ultra sonication, ultra
   microtomy), diffraction strategies (selected area diffraction, nano
   diffraction, use of double-tilt rotation holder), data collection and
   data processing as well as structure solution strategies have been
   chosen dependent on the different requirements of the compounds under
   investigation. Structure analysis was carried out by simulation using
   ab initio quantum-mechanical methods like density functional theory
   (DFT), semi-empirical approach (MNDO/AM1/PM3) and force field packing
   energy calculations (DREIDING). The structure models resulting from
   simulation were refined kinematically as rigid bodies. Subsequently,
   refinements by multi-slice least squares (MSLS) procedures taking
   dynamical scattering into account were performed. The described
   combination of different methods which was used successfully on
   crystallizable materials is also adaptable to insoluble organic
   materials (e.g. pigments) and polymorphic systems.
 
 

NMR

 
Elena, B   Pintacuda, G   Mifsud, N   Emsley, L
Molecular structure determination in powders by NMR crystallography
   from proton spin diffusion
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY 128, 2006, 9555-9560.
The inability to determine molecular structures from powdered samples
   is a key barrier to progress in many areas of molecular and materials
   science. We report an approach to structure determination that combines
   molecular modeling with experimental spin diffusion data obtained from
   the high-resolution solid-state nuclear magnetic resonance of protons,
   and which allows the determination of the three-dimensional structure
   of an organic compound, in powder form and at natural isotopic
   abundance.
 
 
 

 
Senker, J   Seyfarth, L   Voll, J
Determination of rotational symmetry elements in NMR crystallography
SOLID STATE SCIENCES 6, 2004, 1039-1052.
In this work we present a consistent set of NMR experiments including
   high-resolution as well as wideline techniques, which allow to
   determine crystallographic rotational symmetry elements in crystalline
   solids. I D spectra acquired with fast sample spinning about the magic
   angle provide the number of crystal lographically inequivalent nuclei.
   By making use of the anisotropic properties of the chemical shift
   interaction the sets of crystallographically equivalent nuclei can be
   divided into subgroups of magnetically equivalent spins by means of
   radio-frequency-driven spin-diffusion wide-line exchange experiments.
   Maximum information can be achieved from these experiments by a
   combination of time- and frequency- domain analyses. We could
   demonstrate that the number of subgroups is equal to the order of the
   rotational symmetry element in which the crystallographically
   equivalent nuclei are arranged. From the evolution of the polarisation
   transfer as a function of the mixing time distances of these spins can
   be estimated quite accurately. Furthermore, it is often possible to
   distinguish between rotation and rotoinversion axes. The potential of
   this strategy for ab initio structure determination is demonstrated on
   the crystal structure of triphenyl phosphite, where eighteen molecules
   are arranged in a R-centred trigonal unit cell.
 
 

Harris, RK
NMR crystallography: the use of chemical shifts
SOLID STATE SCIENCES 6, 2004, 1025-1037.
Measurements of chemical shifts obtained from magic-angle spinning NMR
   spectra (together with quantum mechanical computations of shielding)
   can provide valuable information on crystallography. Examples are given
   of the determination of crystallographic asymmetric units, of molecular
   symmetry in the solid-state environment, and of crystallographic space
   group assignment. Measurements of full tensor components for (199)Ha
   have given additional coordination information. The nature of
   intermolecular hydrogen bonding in cortisone acetate polymorphs and
   solvates is obtained from chemical shift information, also involving
   measurement of the full tensor parameters. The resulting data have been
   used as restraints, built into the computation algorithm, in the
   analysis of powder diffraction patterns to give full crystal
   structures. A combination of quantum mechanical computation of
   shielding and measurement of proton chemical shifts (obtained by
   high-speed MAS) leads to the determination of the position of a proton
   in an intermolecular hydrogen bond. A recently-developed computer
   program specifically based on crystallographic repetition has been
   shown to give acceptable results. Moreover, NMR chemical shifts can
   distinguish between static and dynamic disorder in crystalline
   materials and can be used to determine modes and rates of molecular
   exchange motion.
 
 

Middleton, DA   Peng, X   Saunders, D   Shankland, K
   David, WIF   Markvardsen, AJ
Conformational analysis by solid-state NMR and its application to
   restrained structure determination from powder diffraction data
CHEMICAL COMMUNICATIONS 17, 2002, 1876-1977.
Solid-state NMR is used to dramatically improve the efficiency and
   reliability of molecular crystal structure determination from X-ray
   powder diffraction data.
 
 

Femtosecond

 
Miao, JW   Chapman, HN   Kirz, J   Sayre, D   Hodgson, KO
Taking X-ray diffraction to the limit: Macromolecular structures from
   femtosecond X-ray pulses and diffraction microscopy of cells with
   synchrotron radiation
ANNUAL REVIEW OF BIOPHYSICS AND BIOMOLECULAR STRUCTURE 33, 2004, 157-176.
Recent work is extending the methodology of X-ray crystallography to
   the structure determination of noncrystalline specimens. The phase
   problem is solved using the oversampling method, which takes advantage
   of "continuous" diffraction patterns from noncrystalline specimens.
   Here we review the principle of this newly developed technique and
   discuss the ongoing experiments of imaging nonperiodic objects, such as
   cells and cellular structures, using coherent and bright X rays
   produced by third-generation synchrotron sources. In the longer run,
   the technique may be applicable to image single biomolecules using
   anticipated X-ray free electron lasers. Here, computer simulations have
   so far demonstrated two important steps: (a) by using an extremely
   intense femtosecond X-ray pulse, a diffraction pattern can be recorded
   from a macromolecule before radiation damage manifests itself; and (b)
   the phase information can be retrieved in an ab initio fashion from a
   set of calculated noisy diffraction patterns of single protein
   molecules.
 

PDF
 
 

 
Juhas, P   Cherba, DM   Duxbury, PM   Punch, WF   Billinge, SJL
Ab initio determination of solid-state nanostructure
NATURE 440, 2006, 655-658.
Advances in materials science and molecular biology followed rapidly
   from the ability to characterize atomic structure using single
   crystals(1-4). Structure determination is more difficult if single
   crystals are not available(5). Many complex inorganic materials that
   are of interest in nanotechnology have no periodic long-range order and
   so their structures cannot be solved using crystallographic methods(6).
   Here we demonstrate that ab initio structure solution of these
   nanostructured materials is feasible using diffraction data in
   combination with distance geometry methods. Precise, sub-angstrom
   resolution distance data are experimentally available from the atomic
   pair distribution function (PDF)(6,7). Current PDF analysis consists of
   structure refinement from reasonable initial structure guesses(6,7) and
   it is not clear, a priori, that sufficient information exists in the
   PDF to obtain a unique structural solution. Here we present and
   validate two algorithms for structure reconstruction from precise
   unassigned interatomic distances for a range of clusters. We then apply
   the algorithms to find a unique, ab initio, structural solution for
   C-60 from PDF data alone. This opens the door to sub-angstrom
   resolution structure solution of nanomaterials, even when
   crystallographic methods fail.
 
 
 
 

Bruhne, S   Sterzel, R   Uhrig, E   Gross, C   Assmus, W
Medium range real atomic structure of face-centred icosahedral
   Ho9Mg26Zn65
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 219, 2004, 245-258.
A complementary approach to quasicrystalline atomic structures in
   3-dimensional (3D) real space is presented: The atomic pair
   distribution function (PDF) of face centred icosahedral Ho9Mg26Zn65
   [a(6D) = 2 x 5.18(3) Angstrom] has been obtained from in-house powder
   X-ray diffraction data (MoKalpha(1)). For the first time, full profile
   PDF refinements of a quasicrystal were performed: Starting with
   rational approximant models, derived from 1/1- and 2/1-Al-Mg-Zn, its
   local and medium range structure was refined (r < 27 Angstrom; R =
   12.9%) using the PDF data. 85% of all atoms show Frank-Kasper (FK) type
   coordinations. The basic structural unit is the 3-shell, 104-atom
   Bergman cluster (d approximate to 15 A) comprising a void at its
   center. The clusters are interconnected sharing common edges and
   hexagonal faces of the 3rd shells. The remaining space is filled by
   some glue atoms (9% of all atoms), yielding an almost tetrahedrally
   close packed structure. All Ho atoms are surrounded by 16 neighbours
   (FK-polyhedron "P"). Most of them (89%) are situated in the 2nd shell
   and form a Ho-8 cube (edge length 5.4 Angstrom); they are completed by
   12 Mg atoms to a pentagon dodecahedron. Cubes in neighbouring clusters
   are tilted with respect to each other; their superposition generates
   diffraction symmetry 2/m35. The remaining Ho atoms act as glue atoms.
   As a result and as can be expected for real matter, local atomic
   coordinations in quasicrystals are similar when compared to common
   crystalline intermetallic compounds. From our results, the long range
   quasiperiodic structure of icosahedral Mg-Zn-RE (RE = Y and some rare
   earths) is anticipated to be a canonical cell tiling (CCT, after
   Henely) decorated with Bergman clusters.

 
Proffen, T   Billinge, SJL   Egami, T   Louca, D
Structural analysis of complex materials using the atomic pair
   distribution function - a practical guide
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 218, 2003, 132-143.
Modem materials and their properties are often characterized by varying
   degrees of disorder. Routine crystallographic structure solution only
   reveals the average structure. The study of Bragg and diffuse
   scattering yields the local atomic arrangements holding the key to
   understanding increasingly complex materials. In this paper we review
   the pair distribution function technique used to unravel the local
   structure. We aim to give a practical overview and make this method
   easily accessible to the wider scientific community.
 
 
 
 

Bruhne, S   Uhrig, E   Gross, C   Assmus, W
Local 3D real space atomic structure of the simple icosahedral
   Ho11Mg15Zn74 quasicrystal from PDF data
CRYSTAL RESEARCH AND TECHNOLOGY 38, 2003, 1023-1036.
We present a new complementary strategy to quasicrystalline structure
   determination: The local atomic structure of simple icosahedral (si)
   Ho11Mg15Zn74 [a(6D) = 5.144(3)Angstrom] in a sphere of up to r =
   17Angstrom was refined using the atomic pair distribution function
   (PDF) from in-house X-ray powder diffraction data (MoKalpha(1), Q(max)
   = 13.5Angstrom(-1); R = 20.4%). The basic building block is a 105-atom
   Bergman-Cluster {Ho8Mg12Zn85}. Its center is occupied by a Zn atom - in
   contrast to a void in face centred icosahedral (fci) Ho9Mg26Zn65. The
   center is then surrounded by another 12 Zn atoms, forming an
   icosahedron (1st shell). The 2nd shell is made up of 8 Ho atoms
   arranged on the vertices of a cube which in turn is completed to a
   pentagon dodecahedron by 12 Mg atoms, the dodecahedron then being
   capped by 12 Zn atoms. The 3rd shell is a distorted soccer ball. of 60
   Zn atoms, reflecting the higher Zn content of the si phase compared to
   the fci phase. In our model, 7% of all atoms are situated in between
   the clusters. The model corresponds to a hypothetical 1/1-approximant
   of the icosahedral (i) phase. The local coordinations of the single
   atoms are of a much distorted Frank-Kasper type and call to mind those
   present in 0/1-Mg2Zn11.
 
 
 

Resonant diffraction
 
 

Attfield, JP
Multidataset refinement resonant diffraction, and magnetic structures
JOURNAL OF RESEARCH OF THE NATIONAL INSTITUTE OF STANDARDS AND
   TECHNOLOGY 109, 2004, 99-106.
The scope of Rietveld and other powder diffraction refinements
   continues to expand, driven by improvements in instrumentation,
   methodology and software. This will be illustrated by examples from our
   research in recent years. Multidataset refinement is now commonplace;
   the datasets may be from different detectors, e. g., in a
   time-of-flight experiment, or from separate experiments, such as at
   several x-ray energies giving resonant information. The complementary
   use of x rays and neutrons is exemplified by a recent combined
   refinement of the monoclinic superstructure of magnetite, Fe3O4, below
   the 122 K Verwey transition, which reveals evidence for Fe2+/Fe3+
   charge ordering. Powder neutron diffraction data continue to be used
   for the solution and Rietveld refinement of magnetic structures.
   Time-of-flight instruments on cold neutron sources can produce data
   that have a high intensity and good resolution at high d-spacings. Such
   profiles have been used to study incommensurate magnetic structures
   such as FeAsO4 and beta-CrPO4. A multiphase, multidataset refinement of
   the phase-separated perovskite (Pr0.35Y0.07Th0.04Ca0.04Sr0.5) MnO3 has
   been used to fit three components with different crystal and magnetic
   structures at low temperatures.
 
 

Chen, JR   Gu, YX   Fan, HF
Solving a superstructure from two-wavelength x-ray powder diffraction
   data - a simulation
CHINESE PHYSICS 12, 2003, 310-314.
Two different kinds of phase ambiguities are intrinsic in
   two-wavelength x-ray powder diffraction from acentric crystal
   structures having pseudo-translation symmetry. In a test calculation we
   have solved the problem for the first time by two different phasing
   procedures developed originally in single-crystal structure analysis.
   They are the direct method of breaking enantiomorphous phase ambiguity
   in protein crystallography and that of breaking translational phase
   ambiguity for superstructures. An artificial structure was used in the
   test, which is based on atomic coordinates of the known structure, SHAS
   (C5H6O5N3K), with the atom K replaced by Rb. The arrangement of Rb
   atoms possesses a subperiodicity of t = (a + b + c)/2. Two-wavelength
   synchrotron x-ray powder diffraction data were simulated with
   lambda(1)=0.0816nm and lambda(2)=0.1319nm. Overlapped reflections were
   uniformly decomposed at the beginning and redecomposed afterward when
   the partial-structure information became available. The enantiomorphous
   phase ambiguity was resolved only for reflections with h + k + l even.
   Phases of reflections with h + k + 1 odd were derived by the direct
   method of solving superstructures. A fragment was then obtained, which
   led to the complete structure in five cycles of Fourier iteration.
 
 
 
 

preferred orientation
 
 
 

Cheung, EY   Harris, KDM   Foxman, BM
A straightforward and effective procedure to test for preferred
   orientation in polycrystalline samples prior to structure determination
   from powder diffraction data
CRYSTAL GROWTH & DESIGN 3, 2003, 705-710.
If a polycrystalline sample exhibits preferred orientation, the
   relative peak intensities in the powder diffraction pattern deviate
   from the intrinsic relative diffraction intensities, and can cause
   major difficulties in attempts to determine structural information from
   the powder diffraction pattern. To circumvent this problem, we report a
   straightforward and effective test that we use routinely as a screening
   procedure to ensure that polycrystalline samples are free of preferred
   orientation before recording high quality powder diffraction data for
   use in structure determination calculations.
 
 

identification
 

Le Meins, JM   Cranswick, LMD   Le Bail, A
Results and conclusions of the internet based "Search/match round robin
   2002"
POWDER DIFFRACTION 18, 2003, 106-113.
To test the effectiveness of phase identification software, a two-stage
   search/match round robin using powder X-ray diffraction data was
   organized, through the internet and world wide web. The first stage
   provided powder patterns and a vague sample origin, the second stage
   provided the chemistry and sample history. While the statistics are not
   robust, it shows that routine phase identification without chemistry
   can be performed, providing effective modem third generation
   search/match software is used; the most up to date databases are
   available; and well trained, experienced scientists perform the
   analysis.
 
 

Phase transition
 
 
 

Depmeier, W
Observation and characterization of structural phase transitions by
   X-ray powder diffraction
PARTICLE & PARTICLE SYSTEMS CHARACTERIZATION 22, 2006, 367-377.
Some of the basic properties of powder diffraction are summarized after
   a short introduction into the theory. Then it is described
   phenomenologically how various kinds of structural transformations
   affect the powder diffraction pattern. This is achieved on emphasizing
   that diffraction studies on powders are statistically more sound than
   those on single crystals, thus allowing the reliable determination of
   the generic properties of a given crystal structure.
 
 
 

Proteins
 

Von Dreele, RB   Lee, PL   Zhang, Y
Protein polycrystallography
ZEITSCHRIFT FUR KRISTALLOGRAPHIE Suppl 23, part 1, 2006, 3-8.
The application of powder diffraction to polycrystalline proteins has
   seen a number of significant advances. Faster data collection
   techniques have reduced the sample size requirement to less than 1mg
   and allowed acquisition of high quality data in < 30 s permitting in
   situ exploration of protein crystallization, reactions and radiation
   damage effects. Recent developments include the formation of heavy atom
   derivatives that possibly provide a route to protein structure solution.
 

Pore volumes, shapes
 
 

Kuppers, H   Lieba, F   Spek, AL
The determination of pore volumes, pore shapes and diffusion paths in
   microporous crystals
JOURNAL OF APPLIED CRYSTALLOGRAPHY 39, 2006, 338-346.
The original option SOLV of the program PLATON, which is primarily
   devoted to the study of organic structures, has been extended to
   studies of microporous inorganic crystals. The space that is available
   for a potential spherical guest within a pore can be regarded as being
   outlined by rolling a sphere of the guest's radius over the surfaces of
   the host atoms that form the pore. The volumes of the pores are
   determined in angstrom(3) and the pore shapes can be drawn. The pore
   volumes of several microporous phases have been calculated and compared
   with results obtained with other methods. An essential feature of the
   program is the option to vary a parameter called `probe radius', which
   models the size of a guest. The decision whether a void is a pore or
   not and the dimensionality of a pore depend on the radius of the guest,
   which is approximated by a sphere. This is demonstrated for the
   structure of the zeolite afghanite. With decreasing probe radius, cages
   can coalesce into larger cages and finally into channels and channel
   systems. The variation of the probe radius allows one to determine
   whether a window between adjacent pores is permeable to guests; in
   addition, diffusion paths in zeolites and zeolite-like structures can
   be determined and visualized.
 

DFT
 
 

Martinez, JR   Mohn, CE   Stolen, S   Sondena, R
What can a "quantum black-box'' do for the inorganic thermochemist?
PHYSICAL CHEMISTRY CHEMICAL PHYSICS 8, 2006, 2036-2039.
Enthalpies of formation of ABO(3) (A = Ca, Sr, Ba; B = Ti, Zr, Hf) from
   the binary constituent oxides have been calculated by ab initio density
   functional theory. The resulting values compare well with the large
   number of experimental determinations reported in literature. The
   trends in the calculated enthalpies of formation correlate with the
   difference in acidity between the binary constituent oxides. Density
   functional theory is shown to be a valuable tool that should be used
   routinely in thermochemical studies of inorganic compounds.
 
 

Topology
 

Krivovichev, S
Topology of microporous structures
MICRO- AND MESOPOROUS MINERAL PHASES
REVIEWS IN MINERALOGY & GEOCHEMISTRY 57, 2005, 17-68.
 

 
Rocha, J    Lin, Z
Microporous mixed octahedral-pentahedral-tetrahedral framework silicates
MICRO- AND MESOPOROUS MINERAL PHASES
REVIEWS IN MINERALOGY & GEOCHEMISTRY 57, 2005, 173-201.
 
 

 

SDPD Round Robin
 
 

A. Le Bail & L. Cranswick,
SDPD Round Robin 2002 Results
IUCr Commission on Powder Diffraction Newsletter 29 (2003) 31-34.
 
 

A. Le Bail and L.M.D. Cranswick,
Revisiting the 1998 SDPD Round Robin
IUCr Commission on Powder Diffraction Newsletter 25 (2001) 7-9.
 
 
 
 
 



Armel Le Bail