Powder pattern recording
The pattern was recorded in the range 10-130° 2-theta (because the absence of any reflection below 10° was known, 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) 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.
Estimation of angular position of the reflections - phase identification
The figure 11 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 (figure 12) and subtracted. Finally a search for peak positions is done (figure 13) and the result is shown on the screen (figure 14) and saved in a file. Remember that the routine study of this sample led to a positive identification (figure 15) 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 the file naoxa2.html. 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 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. Data as prepared for the TREOR software (a 1990 version locally modified in order to include a zeropoint) as well as the result are in the file naoxa3.html. This local TREOR90 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 (figure 16). 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 (figure 17). Files with predetermined names are created containing the results (see naoxa4.html). ITO gives seven times the same result as TREOR, too much is not a real problem :-). Finally, data prepared for DICVOL (a 1991 version, locally modified for a zeropoint introduction) are in the file naoxa5.html together with the results. This DICVOL version is executed in the same way as the above TREOR90 version, opening a DOS box (figure 18). 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.
Cell confirmation - space group proposition
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 (see CCP14 or bali.saclay.cea.fr by anonymous FTP). 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 only one of the numerous Rietveld programs which are now able to apply the Le Bail method (a list is available).
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 Le Bail method iterations. 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 CVRAW from a Siemens .raw file into a .rit file read in by DMPLOT (!!). Then the background was estimated by using DMPLOT (figure 19). The commands file (.pcr) 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 by ERACEL 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 (figure 20) however at the 20th iteration, the profile R factor Rp is yet very satisfying (figure 21). You cannot obtain such a result (see naoxa6.html) 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 naoxa0.zip. 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%, figure 22) which strengthen us in the idea that the cell is the correct one. Results with the 120 first reflections as they are extracted by the Le Bail method are in the file naoxa7.html. The figure 23 shows a zoomed view of the observed and calculated patterns as realized by DMPLOT able to read directly the .prf output file from FULLPROF.
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 naoxa7.html, 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. 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.