Indexing powder patterns

The subceU a dimensions and angles as welt as the corresponding unit cell parameters were estimated indirectly from indexed powder patterns analogous to tochilmite... 

Although indexing powder patterns for crystals with more unit cell parameters than cubic may be carried out by similar procedures as just described, the task increases in difficulty with the number of parameters to be determined. For example, in the case of tetragonal crystals, we have... 

The problem of indexing powder patterns becomes more difficult as the number of unknown parameters increases. There is only one unknown parameter for cubic crystals, the cell edge a, but noncubic crystals have two or more, and special graphical and analytical techniques have had to be devised in order to index the patterns of such crystals. 

A bright gray LaSeF was obtained by low temperature (600 to 650" C) synthesis of LaFg and La2Se3 in evacuated vitreous silica ampules. The material was intermediately ground and pressed to tablets. The reaction product probably is orthorhombic, with lattice parameters a = 7.709, b =10.08, c = 6.402 A Z = 8 D25p = 6.16, D<-aic = 6.323 g/cm. For a table of the indexed powder pattern, see the paper, Schmid, Hahn [3]. 

Of the other hydrates of the 1 1 compounds, CsSc(S04)2 I2H2O appears particularly interesting because it is the only known rare earth sulfate having the alum structure (Bashkov et al., 1972). Its thermal stability is low and it has been prepared only at 0°C. The indexed powder pattern indicates that the unit cell parameter a = 12.51 A and the volume V = 1957 All other scandium compounds with Cs are anhydrous, viz. CSSCSO4 and Cs3Sc(S04)3 (Komissarova et al., 1970b). 

Indexings and Lattice Parameter Determination. From a powder pattern of a single component it is possible to determine the indices of many reflections. From this information and the 20-values for the reflections, it is possible to determine the unit cell parameters. As with single crystals this information can then be used to identify the material by searching the NIST Crystal Data File (see "SmaU Molecule Single Stmcture Determination" above). 

The crystal group or Bravais lattice of an unknown crystalline material can also be obtained using SAD. This is achieved easily with polycrystalline specimens, employing the same powder pattern indexing procedures as are used in X-ray diffraction. ... 

Preliminary X-ray work on CrSBr crystals, probably formed via a chemical-transport reaction, shows rhombic symmetry (181). Powder patterns of the iodides can be indexed with respect to a hexagonal lattice, and are similar to those of Cris (17, 181). 

When stored under increasing relative humidities (RH), cromolyn sodium absorbed water, resulting in a continuous series of interstitial solid solutions [11]. The amount of water absorbed was proportional to the relative humidity of the environment and could be up to about nine molecules of water per molecule of drug. Such an unusual system was characterized by combining XPD with single-crystal x-ray studies. The unit cell parameters of cromolyn sodium were obtained from single-crystal x-ray studies, and this permitted the authors to index the powder pattern. The b axis spacing was found to increase dramatically as a function of the relative humidity up to 20% RH (Table 2). Above 40% RH, the unit cell dimensions were nearly constant. 

These nitridooxophosphates are stable in water and 1 N HC1, which is useful to extract eventual by-products. Their composition has been undoubtedly established by a complete chemical analysis. The XRD powder patterns can be indexed with hexagonal parameters (Z = 6) as illustrated for the potassium compounds ... 

The identity of the polytype present in a given LDH sample may, in principle at least, be determined from the powder XRD pattern, although as we shall see for many LDHs this is not possible, as the amoimt of useful information therein is limited. By convention, the indexing of powder patterns for rhombohedral polytypes is based on a triple hexagonal unit cell (see Fig. 3). 

The X-ray powder patterns were reported for the XFg type (34, 64, 246) and the BF4 (64) adduct and were tentatively indexed in the orthorhombic system. 

In a high symmetry crystal system, very few peaks occur in the powder pattern, and they are often well resolved and well separated. It is then possible to measure their position and intensity with accuracy, and by the methods we described earlier, index... 

The x-ray diffraction powder pattern for Mg2NiH4 was indexed on the basis of a tetragonal crystal system with unit cell dimensions of a = 6.464 A and c = 7.033 A. The measured density was 2.57 g/cm3, compatible with four formula units of Mg2NiH4 per unit cell. 

Fig. 72. Graphical method for indexing the powder pattern of a tetragonal crystal. The pattern shown is that of urea.

For powder photographs, the use of the charts described on p. 143 and in Appendix 3 will show whether the substance is cubic, tetragonal, or hexagonal if it is not, the numerical methods of indexing the patterns of crystals of low symmetry may be tried or, if it is. possible to pick out single crystals, or if the specimen can be recrystallized to give suitable crystals, the unit cell dimensions may be determined by the methods described earlier. A search may then be made in the tables of Donnay and Nowacki (1954), in which, for each crystal system, the species are arranged in order of the axial ratios. 

Characterization.— The LSFTO powder was calcined at a series of temperatures (1250, 1300, and 1400°C) in air to investigate phase purity and densification behavior. X-ray diffraction (XRD) powder patterns are shown in Fig. 1. The sample is single phase after heating at 1250°C. At the higher sintering temperatures, the lines become sharper and the density increases. The density measured by the Archimedes method was 90.3% relative to theoretical value after annealing at 1400°C for 10 h. The XRD pattern sintered at 1400°C was completely indexed with a cubic unit cell with lattice parameter a = 3.898(8) A and V= 59.2(6) A3. The weak XRD peaks at 31, 43, 55, and 65° 20 are also from the perovskite phase and arise from a small amount of WL radiation in the incident beam. 

The powder pattern of etodolac is shown in Figure 3, and a summary of the observed scattering angles, d-spacings, and relative intensities is shown in Table 1. Since the unit cell parameters of etodolac are known [9], it was possible to index the observed lines to the PbCa and these assignments are also found in Table 1. 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

Powder X-ray diffiactograms of the alloys are taken using Fe Ka radiation. The X-ray powder patterns are indexed on the basis of hexagonal C14 Laves phase structure. The lattice constants are evaluated by least square refinement. 

---