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.
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.
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.
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 2002:880–881.
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.
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
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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
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manganites
ZEITSCHRIFT FUR KRISTALLOGRAPHIE 2001, Vol 216,
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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
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CHEN PY; MOU CY
STATISTICAL-INFERENCE OF DISTRIBUTION OF CRYSTAL
SIZE BY X-RAY-POWDER DIFFRACTION
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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
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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
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
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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.
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
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.
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.