2.2- Indexing powder patterns
You will not succeed in an automatic indexation, for a moderately difficult
case, without a very careful work. Do not expect any result from a routine
powder pattern as described in the previous talk, unless it is a trivial
case. Data accuracy should be the highest you can do. The maximum discrepancy
between the observed and calculated angular position of the reflections
should be less than ± 0.02° 2-theta. You can do even better.
There are 3 main programs which were used in 92% of the 300 ab initio
structure determinations up to the end of 1997 : they are TREOR, ITO (or
some variants) and DICVOL. Indexing is a real pleasure from a high resolution
powder pattern. I mean that finding the solution is quite exciting. It
is time to learn now how to realize a "long time, high quality pattern".
2.2.1- High quality pattern
Here is the end of routine work. In order to obtain an accuracy of ± 0.02° 2-theta, a high quality powder pattern should be recorded. The diffractometer should be adjusted to its highest resolution leading to patterns that could be fitted. On an old Siemens D500 diffractometer equipped with a graphite monochromator in the reflected beam, the 0.15° receiving slit leads to minimal Full Widths at Half Maximum (FWHM) of the order of 0.14 to 0.20° 2-theta, this may be sufficient. At the cost of a notable decrease in intensity (1/3 to 1/10), minimal FWHMs can be lowered to 0.08 or 0.06° 2-theta with a receiving slit of 0.05° or 0.018°. A monochromator in the incident beam allows the Kalpha-2 suppression, and some people think that there is no other way to do a good job, but not me. Care to fluorescency problems with this configuration. With such FWHMs, the counting step should be as low as 0.02° 2-theta, or even smaller. All this is possible on a conventional X-ray powder diffractometer.
Now, don't forget all the problems described previously related to the sample preparation on its holder (I mean preferred orientation and so on...). The most recent diffractometers equipped with variable aperture slits allow to obtain FWHMs as low as 0.04° 2-theta at low diffracting angles (<40° 2-theta). Such an excellent resolution at low angle is very decisive for succeeding in indexing a powder pattern, you need to decrease the counting step to 0.01° 2-theta or lower.
We were concerned in conventional in-laboratory diffractometers up to now. The 'Rolls' of the diffractometers consume monochromatic synchrotron radiation. This is another world. The recent performances claimed at the ESRF are FWHMs as low as 0.008° 2-theta. Such a value can be attained only if the sample is really free of structure imperfections and if the grain sizes are larger than 1 micron (should be lower than 60 or better, lower than 20 or even 5 microns for expecting good statistics in grain orientation). Imagine that 4 points are necessary for the description of this quite narrow peak for the upper part above the FWHM, then the full number of points for the description of a pattern becomes hardly manageable by most of the old Rietveld packages (77500 points for a pattern ranging from 5 to 160° 2-theta, but in fact, low wavelengths are selected and the maximum diffracting angle can be chosen as low as 70 or 80° 2-theta, because an unpacked sample fall down for larger values in most of the synchrotron facilities, unless it is inside a capillary). Small protein structure determination from powder diffraction data by means of these fantastic instruments is not utopia. These high (potential) performances are due to the quality of the synchrotron radiation allowing parallel beam geometry, few dispersion in the monochromatization process, high brilliance... there are only advantages to synchrotron radiation with one exception : it is generally not in your laboratory so that you cannot have immediate access, in principle. This example shows the comparison of a conventional X-ray and a synchrotron pattern of a cubic fullerene. The FWHM are reespectively 0.12 and 0.015° (2-theta). But in fact, dur to the short wavelength, you should consider 0.03 for a comparison at the same scale, so that the synchrotron is performing 4 times better in this case.
The neutron powder diffractometers cannot offer comparable performances. Their minimal FWHMs are near of 0.12 or 0.20 or even 0.30° 2-theta depending on the instrument (at NIST in the USA or instruments D2B ou D1A at the ILL in France). An interesting point is that these performances are attained at large angles (90-130° 2-theta), in a range where the conventional X-ray diffractometers cannot do better (they may eventually perform worst in this range). Instruments measuring Time of Flight (ToF) neutrons from spallation sources (see ISIS) give results comparable to those measuring neutrons with fixed wavelength.
We come back now to conventional X-ray diffractometers and to indexing problems. Samples which would have diffracted synchrotron radiation and/or neutrons without having before diffracted conventional X-rays will not be numerous. The access to these prestigious facilities is selective. You have to submit a proposal in which you demonstrate that synchrotron or neutron radiations are absolutely required for the research project (unless you are an industrial and are the owner of a beamline). This supposes that you have failed in solving your problem by conventional means or that you need an improvement in accuracy on atomic positions of light atoms (neutrons) or want to make use of the possibility of fine tuning the wavelength near of an absorption edge (synchrotron), etc.
Two techniques are useful in the objective of collecting perfect data for indexing purposes :
a- A standard is mixed with your sample for calibration, this is the best technique.
b- One or several families of reflections having clearly harmonics are identified on the powder pattern and can serve to an auto-calibration.
According to the technique selected, the high quality pattern which will produce data for indexation can be realized (on a standard in-laboratory instrument) :
from 5 to 80° 2-theta (or more if you wish) if a standard material for calibration is mixed with your sample,
from 5 to 130 or even to 160° 2-theta if the sample is pure for a final pattern. The counting step will depend on your resolution (0.02° 2-theta or less). The counting time should allow to almost eliminate the noise in the background (20 to 40 seconds per point is generally sufficient, so that you may need a full week-end).
The time needed for recording such a high quality pattern may be reduced to 1 or 2 hours or less if your apparatus is equipped with a linear detector or even now a bidimensional detector. Care that the resolution offered by such an instrument remains sufficiently good. Sometimes the whole data have to be corrected by applying a previously established calibration curve (for instance with the remarkable INEL detector covering 120° 2-theta).
Finally, we have yet discussed about the fact that excellent data (even better than those provided by some Bragg-Brentano diffractometers) can be obtained from a Guinier camera. This possibility should not be neglected.
2.2.2- "Automatic" indexing
Maybe your teacher said you that a simple manual calculation slide rule will suffice for indexing a powder pattern. That's true only if the problem is trivial. Serious problems need a computer. Telling that it is "automatic" is truly a lie. You, in person, will have to make the final choice, frequently among multiple propositions. Figures of merit as well as your common sense will help you in your choice. You should never have any full confidence in a cell proposed by an indexing program. The ultimate proof that the cell is correct is obtained when the structure has been determined and refined. Even at this point, you may realize that the cell is in fact larger with a higher symmetry or that you were in a wrong space group and so on...
This list of software is taken from the Structure Determination by Powder Diffractometry Database.
Don't try any indexing program before to be sure that your data are reliable. Never use only one indexing program. Here is the number of successful applications to a real case of structure determination from powder diffraction data. The most recommended actually which have proven their hability in dozens of structure determinations from powder data are TREOR, ITO and DICVOL (you can find elsewhere other indexing programs which were not listed in the SDPD-D because this databank gathers only successful experimental cases), each of them has qualities and deficiencies. You will have to read their manual and to test them on the cases included in the packages.
Test the program on some powder data of your own, corresponding to known materials, so that you will obtain some proof that you are ready to fight with a really unknown material. Gain some experience. Why these advices ? The indexing step is certainly one of the most difficult ! And you will not be able to go further if you do not succeed in that step.
The strategy applied to the samples in this scenario was generally the same and I will give details now :
It was expected to succeed in the calibration by using harmonics (prefer to mix a standard to your sample if you are not yet an expert.
Patterns were recorded in the range 5-130 or even up to 150° 2-theta ; with a 0.02° 2-theta step scan ; time being 20-40 seconds per point, corresponding to a long week-end ; sample holder with vertical loading : this could be the final pattern for publication in case of success. However, it is always verified if preferred orientation can occur by pressing a sample and doing a pattern.
Then the pattern is processed : the background is estimated and subtracted ; Kalpha-2 is eliminated ; in some case the data are smoothed (this is not really recommended, however the estimated angular positions with or without smoothing will be acceptable if the resolution is good enough and the step scan is as low as 0.02° 2-theta) ; peak positions are hunted by using an algorithm based on derivatives (using the EVA software from Socabim distributed by Siemens), another possibility would be to fit peaks or groups of peaks by using pseudo-Voigt or other profile shapes like split Pearson VII (...). I have not observed that profile fitting is better than a derivative method when there is severe reflection overlapping. To decide how many peaks are in a group can be a serious problem !
The result of the above efforts is a list of angular values to which are corresponding d(Å) values and observed intensities.
According to the calibration technique retained in this scenario, harmonics have to be found. For instance, if a reflection is observed at 6.2Å, one should find harmonics at 6.2/2=3.1; 6.2/3=2.066; 6.2/4=1.55... You have understood the principle. One should proceed tentatively up to find 3 series of harmonics if possible. Only one series could suffice if you detect up to 5 or more harmonics in it. Pressing the sample on its holder will favour the detection of harmonics if a preferred orientation occurs.
Using a software for cell refinement (as CELREF for instance) applied to the fictitious cell corresponding to the harmonics (an orthorhombic fictitious cell if 3 series of harmonics have been detected), the a, b, c parameters are refined together with a zeropoint (this zeropoint corresponding to a systematic error which could be due to the goniometer + an error associated with the fact that the sample is not exactly in the diffracting plane). The "calibration" is finished. In reality, the error cannot be reduced to a zeropoint because the discrepancy between observed and theoretical angular positions is not a constant and even does not vary linearly as a function of the angle.
However the approximation by a constant zeropoint is sufficient for our first objective, which is indexing, because we use generally data in the range 5-40° 2-theta where the error is almost a constant. Be careful, the maximum difference between the observed and calculated angular positions corresponding to your fictitious cell should be less than 0.01°(2-theta). If you have a larger error, then eliminate the harmonic which appears clearly wrong or eliminate a complete series of harmonics and replace it by another one. Finally, if your result is not excellent, then calibrate your sample by the first option : add a standard material to it and measure another pattern. Taking the angular positions of the standard reflections, it may be sufficient to refine a zeropoint which will be applied to the unknown. If really your cell refinement gives discrepancies largest than 0.01°(2-theta), maybe this is not a job for you :-).
Now begins the indexing stage strictly speaking. You have to choose data, discarding the dubious ones. In principle the 20 first reflections at low angle will suffice. In this scenario, up to 3 programs will be tested (TREOR, ITO and DICVOL).
One should proceed slowly, realizing numerous tries enlarging progressively the maximum cell volume, starting from, say 200Å3, selecting first the highest symmetry and going progressively down to the lowest symmetries. The DICVOL program has no tolerance for unindexed lines. Personally, I am usually uncertain of the sample purity. So that I tend to reserve DICVOL for an ultimate confirmation and verification of the propositions made by TREOR and ITO. OK, and what to do now if a cell proposition seems convincing ? You should use a program able to generate interreticular distances, choosing a P lattice in the crystal system of the cell proposition. You have to convince yourself evenmore that the cell is really correct and also you need a space group proposition. If you try to determine a structure from powder data with a wrong cell or a wrong space group, then you will waste one or two weeks of your existence, if not more. Thanks to this list of interreticular distances generated by programs like LAZY-PULVERIX or ERADIS or even a Rietveld program able to work in "calculated pattern" mode (like FULLPROF), one can index the experimental data, noting possible extinctions. Doing this, the unambiguously indexed reflections have to be selected in the objective to realize a definitive cell parameters refinement. This final refinement should be perfect (errors <0.01° 2-theta). The experts could avoid this unpleasing step, if they are really sure of themselves, going directly to the next step. This next step consists in an attempt to extract structure factors by the Pawley method or the Le Bail method. The space group can be estimated at this next step too, realizing an intensity extraction in a space group without extinction (for instance choosing P2/m if the system is monoclinic, P4/mmm if it is tetragonal...). Extracted intensities have to be carefully checked in order to determine systematic extinctions if any. The visual examination of a zoomed part of the pattern showing the refinement result is essential for concluding to the absence or presence of a reflection. If the cell was false, this step of extracting structure factors will reveal it by a very bad correspondence between the observed and cell-constrained calculated patterns.
We will see now in details the results of this general strategy as applied to the experimental cases retained in this scenario (just a warning : you cannot escape reading the manuals of all the programs mentioned) :
The pattern was recorded in the range 10-130° 2-theta (because the absence of any reflection below 10° was known from previous tests, however the best is to begin to record at the lowest possible angle as authorized by the beam stop. Weak reflections unperceptible on a routine pattern may become obvious on the long-time pattern. The measurement was made on a Siemens D500 diffractometer, CuKalpha, 28 mA - 38 KV, graphite monochromator in the reflected beam, receiving slit 0.15°, sample holder loaded vertically, counting 26 sec. per step, 0.02° 2-theta counting step. This figure shows the step of estimating a background with the EVA-2 software (Socabim Inc.). The background shape is a bit curious, well, probably due to plastic constituting the back of the sample holder (the beam would have passed through the whole sample - 0.5 mm ? probably yes), it is subtracted anyway. Then the Kalpha-2 contribution is estimated and subtracted. Finally a search for peak positions is done and the result is shown on the screen and saved in a file. Remember that the routine study of this sample led to a positive identification because a JCPDS-ICDD card in the PDF-2 database corresponded well to the experimental pattern. A Search/Match using the EVA-2 default options placed the good proposition at the head of the list (card 20-1149). The card has a cell and a space group propositions. No specification is given about the question "has the structure been determined ?". Searching in the ICSD databank fails. Searching in the CSD bank shows that the structure was determined. The data in CSD confirms the cell and space group which were in the PDF-2 card. Contrarily to PDF-2 which does not mention the fact that the structure was determined, the CSD mentions kindly a publication of the NBS (now NIST) which was at the origin of the 20-1149 card. Theoretically, the job stops here because the crystal structure is known. We will continue as if the identification had been negative. Maybe this would have happen without the CSD consultation.
Examination of the list of angular reflection positions allows to propose hypotheses for the presence of harmonics and to test these hypotheses. The data selected for the test are prepared for a software able to refine cell parameters (here fictitious) named ERACEL. The results are gathered into a file. In green are overlined the differences between observed and calculated theta, they are less than 0.004° theta, hence satisfying. The quite important value which was expected here is the zeropoint, overlined in red. The next step can be tackled with some confidence now (less confidence however, than if the calibration had been done with a standard material mixed with the sample).
For indexing, the choice will be to retain the 20 first reflections having an intensity larger than 0.1 % of the most intense, carefully discarding harmonics of the lowest angle reflections. Let us see the data as prepared for TREOR, together with the results (a local version modified in order to include a zeropoint correction). This local TREOR version works easily on a PC under Windows 95 (32 bits). Double-click on treor90.exe in the file explorer, then a DOS box is opened and the data name is asked for (here naoxa.dat). A few seconds later (on a Pentium 100 at least), it is finished. A quite satisfying proposition is made in the monoclinic system. Things seem too much that simple ? Yes, rarely it is made so fast, we will see why in the other examples. What would have been proposed by the ITO software ? The version used here is the CCP14 distributed version calling by default a file named itoinp.dat, asking nothing in interactive mode. Click on ito.exe, a DOS box is opened and it is finished. Files with predetermined names are created containing the results. In that case, ITO gives seven times the same result as TREOR, but too much is not a real problem if it is good :-). Finally, data prepared for DICVOL (a 1991 version, locally modified for a zeropoint introduction) are shown here, together with the results. This DICVOL version is executed in the same way as the above TREOR90 version, opening a DOS box. Same success for the three softwares, considered as being the stars in the indexing discipline. This will not be always true. We will see that the three programs may have different behaviours.
Before to continue, we have to confirm the cell proposition. Being an expert, you may try the Pawley or Le Bail methods. We will apply here the Le Bail method included in the FULLPROF software. The Le Bail method allows the structure factors extraction from a powder pattern by iterating the Rietveld decomposition formula. As in the Pawley method a secondary objective could be to refine the cell parameters from the whole pattern and finally to test a cell proposition. FULLPROF is one of the numerous Rietveld programs which are now able to extract structure factors without the need of an initial model.
Although FULLPROF is able to locate and refine a background with various options including a sixth order polynomial expression, the first step will be to estimate visually a background which will be kept fixed during the process. DMPLOT is a shareware which can help you to do that interactively. Frequently, format compatibility between sofwares can be a problem. Being able to create quickly a software (for PC or another computer) is good for your autonomy as a researcher. Here, a small program named DAT2RIT has been used for the transformation of a .dat file as prepared by the Siemens CVRAW program from a .raw file into a .rit file read in by DMPLOT (!!). Then the background was estimated by using DMPLOT. The commands file (with .pcr extension) for FULLPROF has been prepared for 20 iterations by the Le Bail method choosing the P2/m spacegroup (because free of extinction) with the cell parameters issued from TREOR, the zeropoint revealed previously and some standard profile parameters (U, V, W and eta for pseudo-Voigt profile shape) corresponding to the Siemens D500 diffractometer with a 0.15° receiving slit. Only one parameter is refined at the beginning : the zeropoint. Reliabilities before the first iteration are relatively high with Rp near of 72%, however after 20 iterations, the profile R factor Rp is yet very satisfying, belo 8%. You cannot obtain such a result if the cell has no relationship with reality. For those wishing to do the whole calculation, the data ready for the first step are downloadable at the Internet Web site of the Structure Determination by Powder Diffractometry Database. Since the first step results are encouraging, a second step will consist in the refinement of all the possible parameters. Improvement is obtained (with Rp ~ 6.5%) which strengthens us in the idea that the cell is the correct one. Here are the extracted structure factors. The next figure shows a zoomed view of the observed and calculated patterns as realized by DMPLOT able to read directly an output file from FULLPROF for visualization purposes (with .prf extension).
Really, we are not yet at the stage of extracting structure factors. This stage should be done after a space group proposition. Examining the reflections list at the end of the Fullprof output, looking carefully at the observed and calculated patterns allows to conclude to a P lattice and to suspect that the P21/a space group could characterize the studied compound because of conditions limiting possible reflections for 0k0: k=2n et h0l: h=2n. In many cases, reflection overlapping can lead to ambiguities so that several space groups could remain as possible and should be tested successively.
The ab initio structure determination is even not really decided at this stage because we have a few verifications to perform before to be sure that the structure has never been determined (in this fictitious example). Indeed, attempts of identification knowing the cell have to be done. If these attempts were successful, then it would be useless to go further.
This chromium palladium amine sample is extremely sensitive to hand-pressure, leading to an extraordinary preferred orientation effect (compare the patterns recorded by pressing the sample on a glass slide or dusted through a sieve, a side-loaded holder giving an intermediate result). Identification is positive by a default search in the PDF-2 database, two cards were corresponding when this job was done a few years ago: 40-1486 and 39-1422. These two cards were absolutely identical before this job, both proposed with a triclinic cell (Powder Diffraction 4, 1989, 217). Since the publication of the structure (Powder Diffraction 10, 1995, 159), the 39-1422 card is marked as "DELETED" remaining however with a "Quality : I" mark, meaning that it was indexed (this early proposed triclinic cell did not passed successfully the test by the Le Bail method, the fit was really disgusting). The 40-1486 JCPDS-ICDD card has been rejuvenated by adding the cell parameters included in the recent structure determination. However, the old d(obs) were kept which were indexed according to the new cell ! The corresponding FOM (figure of merit) are of course of very low quality : F30=8(0.028, 140). Really this is amazing because the FOM given in the 1995 paper was F20=51(0.0077, 48) corresponding to new d(obs) which were not inserted in the modified card ! The rules applied by ICDD for the publications of a JCPDS card remain a mystery for me. This case was discussed in the "Rietveld Mailing List'. This was just another example showing that you should not completely trust databases.
We come back to our study. After fruitless research in all databanks made in order to verify if a structure was known for this compound, and after having concluded that the triclinic cell is not orrect, indexing is undertaken. Angular reflection positions are estimated by EVA2. As for the sodium oxalate, the zeropoint is evaluated by the harmonics method, refining fictitious cell parameters by the ERACEL program. The zeropoint is -0.002° theta, this value is reported into TREOR90 (twice this value with a changed sign because the zeropoint is added to the experimental data in 2-theta in this locally modified version). The 20 first reflections observed on the pattern, excluding second or third order harmonics, are selected. TREOR90 is first executed by selecting the high symmetries (orthorhombic or more) without success. Tests in monoclinic symmetry allow to obtain a proposition after having increased the maximum cell volume successively to 200, 400, 600, 800, 1000 and finally 1200 A3. I mean that if you use a too large maximum volume, the program may not propose a cel that you would have been obtained with a lower voluml limit. When you have a proposition, in order to convince yourself that the cell is credible, ITO and DICVOL91 are applied too. ITO does not provide the same cell, even testing the discrepancy parameter with values 0.01, 0.02... and up to 0.06° 2-theta. A cell with twice the volume of the TREOR result is located among the ITO propositions. The ITO proposition with the highest FOM (figure of merit) is triclinic with a volume of 950 A3. DICVOL91 gives the same result as TREOR90, this was expected because DICVOL is the unique really exhaustive program. The dichotomy process in DICVOL explores all possibilities with the disadvantage that no unindexable reflection should be among the data. Here are the TREOR90 and DICVOL91 results. The ultimate verification of the cell quality remains to be done. We have yet seen for the sodium oxalate that this verification may consist in an application of the Le Bail method by FULLPROF. This time too, the P2/m, space group is chosen because no systematic extinction is associated with it. The Rp factor decreases to 6% (calculated after background subtraction), giving confidence for further efforts. Moreover, examination of the extracted intensities (1127 reflections up to 100° 2-theta), and in the meantime looking at the observed and experimental patterns, allows to suggest the P21/c space group, a centrosymmetrical group without ambiguity. You will be able to try by yourself, downloading the full data at the SDPD Database Web site.
This compound is obtained from an amorphous AlF3.xH2O
or from a complex aluminum fluoride hydrate by dehydration (J. Solid State
Chem. 100, 1992, 151-159). It transformed into the cubic AlF3
variety at high temperature without anymore weight loss so that it was
unbelievably a new AlF3 variety. See the negative result from
a PDF-2 search by EVA-2 : this is probably the most exciting case of all
my career ! Such disclosing is more and more rare so that the structural
study was quickly undertaken. Some proof that t-AlF3
is really interesting may be found in the fact that it was recently redetermined,
also from powder data three years later by guys working at the Dupont Company
(Chem. Mater. 7, 1995, 75-93) and evenmore, it was renamed theta-AlF3.
We found no possibility for obtaining single crystal from this soft chemistry
synthesis. Impurities were always present in large quantity when the sample
was made from the amorphous starting material. Fortunately, the second
preparation was purest with only small residue. The powder pattern was
recorded from 10 to 150° 2-theta on a Siemens D500 diffractometer,
using the side-loaded sample holder. The guessed harmonics method provided
a zeropoint of 0.02° 2-theta. The TREOR90/ITO/DICVOL91 results were
finally consistent with a tetragonal cell although many orthorhombic or
even cubic cells were proposed. By carefully examining the data, then the
space groups P4/nmm or P4/n were obvious. The cell confirmation was concluded
by the Le Bail method, excluding a few angular zones where the impurities
were contributing. I encourage you to try it by yourself, downloading the
Although this problem was solved from conventional X-ray data (J. Solid State Chem. 89, 1990, 282-291), it was interesting to try to determine the structure from the neutron powder data (which were used for structure accuracy improvement). The neutron data were collected from the Institut Laue Langevin D2B instrument in low resolution mode (wavelength 1.5945 A), so that the U, V ,W are respectively 0.071, -0.166, 0.190 corresponding to very large FWHMs. With such high profile widths, can we expect to index the data? ITO and TREOR90 proved not to be useful in such a case. DICVOL91 produced the expected cell with very low figures of merit so that it was not very credible. Applying the Le Bail method was encouraging as you can see from this plot. However there are 1387 reflections up to 147° 2-theta ! What confidence can we have in such a structure factors extraction when the FWHMs are so large ? The next step will give a response. Those neutron data are also available on the Internet.
This sample corresponds to a school case. Synchrotron data were collected at Daresbury (wavelength 1.52904 A). Cimetidine is in the PDF-2 (two cards). The search by EVA-2 limited to organic data is successfull. With such high quality data, it could be sufficient to get the reflection positions as corresponding to peak maxima. The three stars of indexation give the same result. As expected from synchrotron, the FOM (figure of merit) are quite brilliant : M(20) = 100 and F(20) = 248.(0.0032, 25) from TREOR90 results without searching for any zeropoint (the FOM are even better with a zeropoint = -0.008° 2-theta added to the observed positions, this zeropoint value being that refined at the last stage by the Rietveld method).
The cell is monoclinic. Applying the Le Bail method for cell confirmation,
a quite good fit is obtained with the P2/m space group selected for a further
hunting of possible systematic extinctions (in order to be consistent with
the original already published work, the cell will be later considered
in the non-standard setting P21/n space group).
2.3- Trying to identify a material knowing the cell
At this stage, one has to be sure of the cell proposition, of course. This is the same position as if the cell had been obtained from a single crystal by a four circle diffractometer or by photographic methods. The big question is : knowing the cell, should we now record the complete data for a structure determination or has the compound been already characterized ? From powder data, the whole dataset may have been yet registered but not necessarily. For a single crystal study, a classical four circle diffractometer may be immobilized for one day or two weeks depending of the cell complexity so that one should be sure that this is not waste of time and money. Maybe an isostructural compound will be found in databases so that reasons for performing a work presenting a low degree of originality should be found elsewhere (special properties or something else) than in the objective of adding a chapter in a PhD thesis.
The exact formulation of the compound is not always known at this stage. Now that you have the cell, you may divide the volume by nearly 20 and you will not be far from obtaining the number of anions if your material is an oxyde or a fluoride. If you have an estimation of the formula by chemical analysis (possibly by means of electronic microscopy) then you may estimate Z, the number of formula units per cell. You can measure the density if you dispose of a sufficiently large quantity of pure compound and compare it to the calculated one. Thermal analysis (DSC, TGA) is something to do absolutely. Then you dispose of informations allowing you to explore all the databanks, not only the PDF-2 one which is really almost empty if one considers that 300000 compounds or more have been the subject of a structure determination. In principle the JCPDS-ICDD files have yet been examined since this is a powder work. Either your compound is not inside, or there is a doubt about a possible structure determination which would have been already published (PDF-2 is rarely explicit on that point). Nevertheless it is recommended to try an ultimate search in PDF-2 with these new data wich are the cell parameters, the volume and eventually the space group.
With an inorganic compound, the first bank your should consult is ICSD. Possibilities for a query are numerous (the manual has more than 80 pages). The question may consist in providing the chemical elements that you are sure to be included in your sample, without excluding other possibilities by a too much strict query, but we have already seen that. The crystal system may be given to the search software as well as a cell volume with some tolerance range. The search result may consist in several possibilities which you should examine or try to reduce their number by adding other indications. If the query is too much precise then isostructural compounds may be missed. Use the same approach for an organic or organometallic material with the CSD databank.
If ICSD or CSD consultation are negative, then you should consult CRYSTAL DATA from N.I.S.T.. This is easy because a query consisting in the cell parameters with a tolerance factor may suffice, addind the possibility for finding sub- or supercells. CRYSTAL DATA can allow you to conclude that your compound or an isostructural material exists somewhere in a publication and that its cell at least has been established. You should not conclude that the structure has been determined necessarily until you have seen the atomic coordinates.
WARNING : You will have to examine the 3 or 4 recent years bibliography by using the Current Contents, the Chemical Abstract or the other (commercially) available databanks (PASCAL... see INIST). Do not neglect the more than 16000 indexed periodical iin the Uncover database to which you can access too by Telnet (URL database.carl.org). Indeed, searching by keywords is free in this bank, only the order of a publication costs something : an example which should be followed by the other data sources. Last but not least, most of the scientific revues have placed their content together with a summary in a catalog of references searchable by keyword (see Acta Crystallographica and all the IUCr journals for instance indexed since 1983).
If all attempts for identification failed, an ab initio structure determination from powder data is not always the best thing to do :
If you have sufficiently large single crystal, turn in the four-circle diffractometer direction (avoid wasting time with isostructural compounds unless you have good reasons). If really you have only a powder : have you tried all the possible means for synthesis available to you which could enlarge the crystal size ? If yes, we continue (but see the alternative).
3- The structure determination from powder data is decided
In this kind of job, you cannot rush without to think a bit. Applicability limits have been estimated. See if your problem dimensions are not quite out of these limits and make use of your common sense.
3.1.1- Conventional in-laboratory diffractometer
One can estimate limits by considering the recognized maximum number of parameters refinable by the Rietveld method which is the normal ultimate stage of the whole process. The values proposed here are personnal estimations which you may try to pass beyond. Corresponding to minimal FWHM (Full Width at Half Maximum) of the order of 0.12° 2-theta somewhere on the pattern (usually in the 20-40° range), 50 to 70 free atomic coordinates (x,y,z) are refinable reasonably (without taking account of fixed coordinates due to special positions nor of thermal parameters). This corresponds to 17 up to 23 independent atoms in general position (or more if some atoms occupy special positions).
Corresponding to these limits, cell volumes can be more or less estimated, depending on the crystal system and on the Bravais lattice. For centrosymmetrical space groups, these maximal volumes are the following :
Translated in maximal number of reflections, any of these above maximal possibilities corresponds to approximately 1000 to 1500 reflections for a pattern extending from 5 to 150° 2-theta recorded with a ~1.5 Å wavelength. One will have approximately 20 reflections per xyz refined parameter. In a single crystal study, 10 reflections per parameter, including the thermal ones, is something considered as normal. The fact that a larger value is proposed for powder data is a consequence of reflection overlapping. I hope that you will find these limits impressive after all. You shall divide the above volumes by 2 if you are working with an acentric space group. Divide them also by two if you wish accuracy otherwise you may have to present dubious interatomic distances in your manuscript and the reviewers will not be happy. At the beginning of the real expansion of this new sub-discipline (1986-1987) I had to face a lot of incredulity. Some reviewers simply reply to the editor that such a job was impossible...
3.1.2- Synchrotron data
Now if your minimal FWHMs decrease down to 0.06° or 0.02° or even 0.01° 2-theta, all you have to do is to multiply the maximum volumes previously listed (given for minimal FWHM ~ 0.12° 2-theta) by 2 or 6. This is much more comfortable than with conventional X-ray data. It can be expected really to play with 150 or 300 independent atoms, corresponding to 450 or 900 xyz refinable parameters. Up to 10000 or 15000 reflections could be extracted from a synchrotron powder pattern. Triclinic centrosymmetrical cells with up to 6000 Å3 volume or cubic cells with F lattice as large as 600000 Å3 are the theoretical upper limits which one could expect to attain by using high resolution synchrotron data ! No study has approached such limits up to now. This is because no try has been done. Actually, the largest problems solved (up to 60 independent atoms, 180 xyz parameters refined) are already considerable. However they are far from the limits suggested here. A list of complex experimental cases already published may be found as a Top 50 inside the SDPD-Databank. On another hand, the maximal limits suggested for conventional in-laboratory diffractometers have been already reached without too much difficulties for triclinic, monoclinic or orthorhombic cells. Consequently, one can predict exceptional results in a very near future from synchrotron data.
3.1.3- Neutron data
Neutron conventional theta-2theta diffractometers present at best minimal
FWHMs ~ 0.12° or at worst ~ 0.25 to 0.30° 2-theta. As a consequence,
the maximal cell volumes would be respectively applicable or would need
to be divided by 2 or 3. Nevertheless, the maximum number of parameters
that one could expect to refine by the Rietveld method is not a sufficient
criterion for an estimation of the feasibility limits of an ab initio
structure determination from powder diffraction data. Indeed, winning the
game depends on the successful application of the Patterson or Direct methods.
One has to obtain a starting model sufficiently large for being able to
start the refinement and then complete the structure by difference Fourier
syntheses. With the presence of atoms distinctly heavier than the others,
in the sense of having distinctly higher diffusion factors or Fermi lengths,
it is generally sufficient to locate them for the initial structure model
building. Without these heavy atoms, one has to locate almost the whole
structure before to be able to refine. Neutron data place you almost systematically
in this later case. Indeed, the Fermi lengths are of the same order for
all atoms. Therefore, a structure determination from exclusively neutron
data is generally much more difficult than from X-ray data, however organic
compounds are difficult whatever the data. It is advisable to make use
of both X-ray and neutron data, playing with their complementary advantages.
A structure can be determined partly from X-ray data by locating heavy
atoms, and it can be completed or the accuracy on the light atom positions
can be improved from neutron data. Finally, one can refine the structure
simultaneously from both data, a few softwares allow this. In the SDPD-Databank,
the top 30 lists the most complex structures according to the criterion
of the largest number of atoms simultaneously located at the stage of applying
the Patterson or Direct methods. The upper limit is relatively low with
18 atoms from X-ray data (6 only from neutron data). This rather small
record should be broken soon by using synchrotron data with the highest
resolution. More people have to be convinced that structure determination
has become a quasi routine task by using powder diffraction data with some
expertize. The difference with solving a structure from single crystal
data is that much expertize is needed for powder data because several essential
steps in the whole process are not 'automatized' : the goal is to locate
goodies among garbages.