I hope that we will have interesting debates this day. The subject is how to go ab initio (that is to say, almost from scratch) from a powder diffraction pattern of an unknown compound to its crystal structure. In the ten last years the discipline has exploded in a large number of methods for data analysis so that a beginner may have difficulties in choosing the most appropriate way for solving his own problem. I will try to give you a broad view on methods which are possible to use in relation with different kinds of problems, needing either standard or special strategies. This diagram shows you that Structure Determination by Powder Diffractometry is becoming more and more routine job, but you may guess from the small number of applications that the job is not that easy.
For succeeding in a structure determination from powder diffraction data, the way is long and difficult before the final step which is the refinement. Everybody here know that this final step is commonly realized by using the famous Rietveld method of which Professor Ray Young spoke about all yesterday. In fact, here we are interested in the whole route between an unknown material and a known crystal structure and to the pitfails which may prevent from being able to refine something.
Powder diffraction is an ancient technique. It would be an error to believe that it is obsolete. There is no sign that powder diffraction could disappear, on the contrary. Thanks to a series of spectacular recent developments (being the consequences mainly of progresses in computers technology and software), powder diffraction is a tool more essential than ever for characterization in materials science. This method is predominantly selected for a first contact with an inorganic solid state compound.
The day will be divided in four parts :
We will see first how to be sure that a structure is unknown and deserves powder diffractometry, and then, how to index and finally decide to perform the structure determination.
Afterthat, we will see the classical approach consisting in extracting the structure factors and solving by Patterson or direct methods followed by Fourier recycling. And finally the non-classical other methods including molecular replacement or, if you prefer, molecule location methods, will be discussed. We will finish by some words on the Internet offer in powder diffractometry and more generally in crystallography.
This is the list of chapters corresponding to the first part, which comes from a tutorial available on Internet.
So, we start by the preliminaries. I take the risk to bore you with the description of the routine job in a research laboratory because the key for success resides in a very careful work during the whole process. The people you have to convince that a step has been successfully realized is first yourself. Only one error and you will waste your time considerably in unfruitful efforts. We will suppose that the job is made by an unprivileged researcher in solid state "physico-crystallo-chemistry" : this poor guy has not easy access to a neutron nuclear reactor nor to a synchrotron. However, he does his best in a "modern" laboratory (as far as the financial support is maintained), equipped at least with an automatized conventional X-ray powder diffractometer, with specialized databanks and with unlimited means for calculations (a PC with a Pentium processor is sufficient those days !). We will make the hypothesis that this researcher has just done an original synthesis by any method, or that his job is the characterization of a compound a priori unknown. This scenario will serve as the basis for examination of a large part of the capacities offered by powder diffraction in materials science. Indeed, a structure determination from powder data makes use of the trivial aspects as well as of the more sophisticated ones. Also, it is a last chance method : you should not use it if there is another more appropriate and more accurate possibility for determining the structure of your compound. Not many mathematical formulae will be given in this workshop. If really you follow this tutorial for solving a concrete case, then it will not be too late for examining mathematics behind the methods involved. Concrete examples will illustrate the successive scenario steps.
1- First routine contact with a material a priori unknown
The material can be any solid (inorganic, organometallic,..., synthetic or natural).
In this scenario, nothing should be done by diffraction methods before
a careful examination of the sample by optical microscopy under polarized
and natural light. This examination can reveal inhomogeneities in the sample
(to a point where a polyphasic nature could be suspected) and the presence
of single crystals sufficiently large for being characterized by using
a four-circle diffractometer. The scenario is highly dependent of this
first examination : powder or not powder diffraction, that is the question.
A routine X-ray diffraction pattern takes 15-30 minutes on an automated
powder diffractometer. Searching in a powder pattern databank will take
a few minutes more. The powder diffraction technique is preferred for material
identification because it may be really fast. Nevertheless, the success
will depends on your know how and on the databanks exhaustivity, we will
discuss later on this point. Even if the sample is constituted of sufficiently
large single crystals, an identification by powder diffraction may be preferable
to a preliminary study by Weissenberg, Laue or Buerger techniques or even
to a fast automated search for the cell with a four circle diffractometer.
Though the use of image plate is now also extremely fast. If the optical
examination has revealed inhomogeneities, then you should make several
powder patterns on selected different parts (isolated crystals for instance).
We will see some practical aspects of the first contact in the next part.
1.1- Camera or diffractometer ?
- Cameras (Debye, Gandolfi, Guinier) have a low cost advantage. Because of the need to impressed a photographic film and to develop it, cameras cannot rival with diffractometers on the speed point of view for a routine identification. However, structure refinements and even full structure determinations have been realized from data provided by powder cameras. One should emphasize that Guinier cameras offer one of the highest resolution attainable by a laboratory instrument with Full Width at Half Maximum as low as 0.06° or 0.08° (2-theta) for the minimum. Cameras may come back 'à la mode' if some multidetectors and bidimensional detectors make progresses and replace film/densitometers. Such progresses are expected because they are necessary for using fully the fantastic possibilities offered by synchrotron radiations, conventional X-ray sources will benefit of them. That revolution is really marching on, I think.
- Commercial diffractometers are dominated by the Bragg-Brentano geometry up to 90%, the other 10% are Seeman-Bohlin diffractometers. The present scenario considers most of the time a Bragg-Brentano mounting, with a fine focus anode, a diffracted-beam monochromator (eliminating Kß and a large part of fluorescency problems, but not removing Kalpha-2), a scintillation counter, Soller slits before and after the sample, allowing to measure on horizontal samples (which will fall down near 130°2-theta if not compacted, anyway). Current performances of the Bragg-Brentano diffractometers allow minimal FWHM as low as 0.04° (2-theta) by using variable slits.
1.2- The routine powder diffraction pattern
The scope of a fast recorded powder pattern is mainly for identifying your sample in order to avoid redetermining a known structure.
1.2.1- Preparing the sample
It should be kept in mind that problems could arise from small grain sizes, preferred orientation effects , sensitivity to hydration...
About grain size : by definition, a powder adequate for X-rays should present a large number of very small crystals oriented in all directions. The optimal grain size is near of one micron, this is very difficult to realize. As a minimum, one should mill the sample by hands, pass it through a 63µ (or less) sieve. Not all samples let you to do that easily, it is extremely difficult to do it manually through a smaller sieve, you will need to produce vibrations. Be careful, milling can reduce the crystallinity degree of your sample (this is unusual if the milling is by hand, but this is almost general if a powerful crushing machine is used).
Once the powder prepared, you have to deposit it on the holder :
- It can be pressed on the holder with a glass slide. Doing this will probably lead to favouring a preferred orientation of the individual grains. This can prevent the later use of reflection intensities. Preferred orientation effects can be reduced by making a suspension of the sample in chloroforme that will be evaporated on the sample holder (but care to not alter the sample). The mixture could be spread over the holder with a glass slide just before the full liquid evaporation.
- A very efficient way for avoiding preferred orientation is to dust the sample through a sieve on the holder. The disadvantage is that a flat surface will be diifficult to prepare, such a flat surface being absolutely necessary for not to degrade the resolution (excepted when working with synchrotron parallel beam).
- If you have enough sample (500 mg or 1 g), use a special sample holder which can be vertically loaded. However don't shake it down too much. Samples very sensitive to preferred orientation can show a non-negligible effect even with this special holder.
In short, the ideal sample is quite hard to prepare.
1.2.2- Measurement conditions
Just another warning : the sample must be in the diffracting plane otherwise systematic errors will occur on the reflection positions. Verify the diffractometer settings, the zero, the theta-2-theta coupling...
For a routine pattern with a 0.15° receiving slit, the following recording conditions may lead to a successful identification :
a- From 5 to 77°2-theta, with a counting step of 0.08°2-theta, a total of 900 points measured in 30 minutes if counting 2 seconds per point.
b- From 5 to 41°2-theta could be sufficient with 4 seconds per point, all other conditions similar.
Here are two patterns for the same sample by testing two preparation ways (sample pressed on a glass slide and sample inserted in the vertical loading holder) : a preferred orientation is obvious as can be concluded from notable differences on intensities.
Here is shown the effect of a quite rough surface produced by dusting the sample through a sieve. No preferred orientation but the resolution is quite bad if compared with the pattern obtained from a plane surface produced by using a side-loaded sample holder.
1.2.3- Data treatment
Now, what to do with this routine pattern ?
According to the scenario (Bragg Brentano diffractometer with a diffracted
beam monochromator), the alpha 1-2 doublet and the background have to be
subtracted first. This operation is usually done very fast by a PC software
generally proposed by the diffractometer vendor (for instance EVA as part
of the DIFFRACT-AT suite from the Socabim society is proposed with the
Bruker, ex-Siemens diffractometers). You will probably learn how this is
done by a Rigaku system also this afternoon. This point will be examined
more in details at the stage of recording a high quality pattern. Once
the pattern cleaned, it can be compared with those inside your databank,
expecting for identification.
1.3- Using the PDF-2 database (ICDD)
PDF-2 is a database (on CD-ROM or other support) gathering approximately 115000 powder diffraction patterns. The bank contains the pattern of your sample, maybe. There are two ways for using the bank. It is not always necessary to make use of it if you know yet the chemical system you are studying. Sometimes you may visually recognize immediately which sample you have prepared. The mammoth is there for recalling that this ICDD is really an old house, and that old houses do not change easily. ICDD has long resisted before to decide to include systematically calculated patterns in the database. This was done only last year !
1.3.1- Automatic search
Software exist which are able to examine in a few seconds all the powder diffraction patterns of the database (at least on a PC Pentium II 300 MHz or better) and to propose a list of patterns supposed to fit with your experimental data. The final decision is yours : you will have to compare each pattern proposed by the software and to accept or not the identification attempt. Now, an example of automatic search for the sample chosen in the scenario. The software is EVA 2 (now version 4 available) from the Socabim Inc. Very easily, the background was subtracted and then the default options in the search/match process were applied, the result is a list of possible compounds which may correspond. Examining all the propositions, it becomes clear that the sample is KAlF4. It was placed at the head of the list proposed by the EVA 2 program.
When your sample is really unknown, you should not be able to obtain any match or the PDF database contains only an unindexed pattern, etc. In this example, we were sure that the sample would only contain aluminum and fluorine. I was impossible to obtain any matching with the PDF-2 database.
1.3.2- Half automatic search or by hand
Preferably, don't have a full confidence in an automatic search when it is negative. Usually you know what chemical elements are in your sample and so you should sort and examine the complete list of JCPDS-ICDD cards corresponding to various combinations of these elements. This is a laborious work, it is decisive time to time, due for instance to large zeropoint error on your data. You should even include in the list the patterns corresponding to some permutations of chemical elements for some well known isostructural substitutions.
For instance, in fluorides, you could have synthesized an aluminum-based material, previously unknown, which could be isostructural with a compound in which the Al atoms would be replaced by Cr, V, Ga or Fe. This possible isostructural compound could be present inside the database with neighbouring cell parameters, too much different however for an automatic recognition by the search/match process.
A manual search by the Hanawalt method (using a classification according to the most intense reflections) gives sometimes ideas for isostructural compounds, sometimes it gives a positive identification when the automatic search fails.
1.3.3- Comments about PDF-2
Continuing this scenario, we will consider powders of unknown materials. Nevertheless a failure to identify a compound by means of PDF-2 is not a sufficient proof that it is really unknown or that an evident isostructural compound does not exist, one should be conscious of that.
Multiple works concerning the same compound are inside the bank, some JCPDS-ICDD cards carry the mention "Deleted" meaning invariably that a more recent card, corresponding to more accurate data, is in the bank. However, the old "deleted" card is still there. The quality of numerous cards is really dubious (some carry the mention "questionable") and many cards inside the bank do not propose a cell indexation. Some cards do not mention if the crystal structure has been determined in a subsequent or even previous work which made not use of powder diffraction methodology. This is the case of the sample chosen at the beginning of the scenario. The recent 40-0549 card about KAlF4 is given for 1986 and presents a false cell, a false spacegroup, a very bad figure of merit characterizing the cell parameters refinement. This is not understandable because the structure was published in 1981 par J. Nouet, J. Pannetier and J.L. Fourquet , Acta Crystallographica, B37, pp 32-34)... It is surprising to observe an increase of 10000 new entries per year in the Cambridge (CSD) databank of organic and organometallic compounds whereas PDF-2 increases of approximately 2000 cards of which 25% are organic. I suggest that the ICDD should quickly :
Actualize cards which are not mentioning structure determination for the concerned compound ; introduce systematically the patterns calculated according to the published crystal structure data.
More serious critics could be made last year, but ICDD has undoubtedly progressed by including the ICSD calculated patterns!
Possibly, the CSD crystal structures will be used to calculate 200000 powder patterns of organic and metallo-organic compounds in a near future.
2- Materials unidentified by the routine approach with PDF-2
If the search/match failed by using the PDF-2 databank, one should try more. Other databanks contain crystallography related informations :
- ICSD (Inorganic Crystal Structure Databank), on CD-ROM, contains nearly about 50000 phases of which the structures were determined from single crystal or powder diffraction data. The atomic coordinates are generally given (not for 3000 entries) together with the full reference and some other details. One can observe the presence of multiple entries for one compound in this bank too. There are also a huge quantity of isotypical compounds but this is unavoidable. The user should be very careful and make use of his common critical sense with any databank, including this one.
Here is an example of search in ICSD, choosing the possibility of search by the chemical composition. You just have to select elements on a periodic table, define a range for the number of elements if you wish, and start the search. For aluminum, potassium and fluorine, and no other element, the base contains seven entries. An entry contains typically all those informations.
- CSD (Cambridge Structural Databank) on CD-ROM contains about 180000 entries for small organic molecules and organometallic compounds. This number increases by 10000 each year !
- N.I.S.T. CRYSTAL DATA, on CD-ROM, contains about 200000 entries corresponding to 60000 single phases (inorganic/organic). Are gathered a large number of published propositions of indexation. These could be false or the structure (which is the final proof that a cell is correct) was not necessarily determined. There are numerous multiple entries and isotypical compounds in this bank.
- CRYSMET is a compilation of data concerning metallic compounds. Let us have a demonstration for this database....
To be able to use these databanks, complementary of the powder diffraction databank, one information which may suffice is the sample composition. However the best way is to add the cell knowledge. Several methods giving access to the cell are to be considered depending on the presence or not of large enough single crystals in your preparation.
The PDB (Protein Data Bank of Brookhaven, 5400 entries) has been excluded from this discussion. Indeed, you have little chance to succeed in a protein structure determination from standard powder diffraction data (unless it is a very small protein or you are working with a high resolution diffractometer using synchrotron radiation, eventually at low temperature). A discussion about the limits of what you can expect to do from powder data will be given later.
The scenario will continue with the study of at least seven real cases :
One compound identified in the ICDD databank, given with a cell proposition ; absent from ICSD although compounds classified as organometallic like Ni(CO)4 are included ; found in CSD : Na2(COO)2. This is a simple case chosen as a school case. The study will be by conventional X-ray data.
[Pd(NH3)4]Cr2O7, a typical case with heavy atoms for testing the Patterson method (and also, why not, the direct methods). The study will make use of conventional X-ray data. This compound was peviously listed in the ICDD databank with a false cell proposition.
t-AlF3, more complex than the two previous ones because the initial model necessary before to begin to refine the structure by the Rietveld method was the whole structure. Indeed, Al3+ and F- are isoelectronic and thus their X-ray diffusion factors are not very different. This is a typical case for applying direct methods : eleven independent sites should be found simultaneously. The study was realized by using conventional X-ray data. This is a beautiful example of the contribution of the powder diffraction methodologies to the advancing of Science and basic knowledge. The result was a crystal structure based on an unknown new way to arrange octahedra exclusively by corner sharing.
beta-BaAlF5, examined by neutron diffraction, to show how more difficult is the structure determination from neutron data (remember that determination is not refinement : for a refinement, at least a large part of the structure should be known). In the reality, his structure was determined from X-ray data and the accuracy (on F and Al atomic coordinates) was later improved by refinement from neutron data.
Cimetidine C10H16N6S, a famous example, previously known from a single crystal study. This case was examined by synchrotron radiation in order to estimate the feasibility limits by the powder methods several years ago (see R.J. Cernik, A.K. Cheetham, C.K. Prout, D.J. Watkin, A.P. Wilkinson & B.T.M. Willis, J. Appl. Cryst. 24 ,1991, 222-226).
We will also see the 2 samples of the SDPD Round Robin, if we have time.
The various (standard) strategies used in structure determinations from powder diffraction data will be examined at each step of the whole process for one or several of those examples, successively in the next parts of this tutorial. The corresponding data are made available (together with other data) in the SDPD-D (Structure Determination from Powder Diffraction - Database).
2.1- Crystals or not crystals
If you have sufficiently large single crystals in your sample, it would be logical that your structure approach make use of single crystal techniques, not powder. The faster approach for an identification is an automatic cell search on a four-circle diffractometer. Once the crystal sticked, you could obtain the cell in one or a few hours later, depending on your diffractometer characteristics (classic or 2D detector). Of course, the diffractometer should not be yet occupied otherwise you will have to wait for the end of the current campaign of data recording. This could be long.
You can follow the old good way, in fact the normal way, the most advisable way because you will be able to detect twinning, diffusion, superstructures, incomensurability (...) if any : use the photographic techniques (Laue, Weissenberg, Buerger..) unless your single crystal diffractometer is equipped with a 2D detector. If you have patience and choose this way, you could leave us and come back after the end of the next part of the talk concerning indexing from powder data.
If you don't have crystals or if you have no patience and you consider
that it could be easier/faster to try an automatic indexing by using powder
diffraction data, then stay with us. Remember of electronic microdiffraction
as a possibility, not as easy as you could think, and don't forget to confirm
the result by refining the cell parameters according to the powder diffraction