Calculated powder pattern

FIGURE 2. Calculated powder patterns for spin-1 (a) and spin-3/2 (b) nuclei with a dominating quadrupolar interaction (QUASAR simulation) tj is the asymmetry parameter of the quadmpolar interaction (equation (9))... 

Examination of the peak positions and intensities for the calculated powder patterns reveals relatively few lines which would differentiate the four structures. The values marked with an asterisk in Table II appear to... 

A data set with 2°<20 140° CuKa was collected for a barrelshaped crystal on an Enraf Nonius CAD4 diffractometer with a 3.5° variable-speed 6-20 scan to accommodate the broad diffractions. From 196 unique diffractions above background (2o) out of 2170 measured diffractions, the structure was solved independently by the Multan direct method and a search of hypothetical structures. The resulting framework (Figure 2) is 81 predicted by J.V. Smith(4). Refinement to R 16% yielded the framework geometry, but the T-0 distances did not correspond satisfactorily to Al, P alternation, and the TPAOH was not located. Nevertheless the framework topology appeared correct, and the calculated powder pattern (Figure lb) was satisfactory. 

Fig. 4.9. Calculated powder pattern ESR absorption spectra for an axial defect such as the dangling bond, showing the effect of disorder broadening (increasing values of ga/Ag). The spectra are calculated using the g-values obtained from the crystalline Si-SiOj interface (Street and Biegelsen 1984).

For example, the calculated powder patterns for four of the polymorphs of sul-phapyridine are given in Fig. 4.22. The calculated pattern represents that of a pure sample. Using some of the more sophisticated programs to calculate the powder pattern, one can assume the absence of preferred orientation or alternatively some specified degree of preferred orientation. The line shape can be varied to match experimentally observed line shapes. If the crystal structures of all the polymorphic forms (and impurities) in the mixture are known, then the diffraction patterns... 

Calculated powder patterns are shown in Fig. 12-4 for the eight alloys designated by number in the phase diagram of Fig. 12-3. It is assumed that the alloys have been brought to equilibrium at room temperature by slow cooling. Examination of these patterns reveals the following ... 

Fig. 12-4 Calculated powder patterns of alloys 1 to 8 in the alloy system shown in Fig. 12-3.

Fig. 14-3 Calculated powder patterns of austenite and martensite, each containing 1.0 percent carbon in solution. Cr Ka radiation.

While most Rietveld programs can calculate powder patterns, it can be easier to use a dedicated program. An excellent program for pattern calculation is the Powder Cell program. However, if attempting to calculate accurate patterns for non-tube wavelengths, the Poudrix software should be considered (Table 17.31). 

Figure 3-1. (a) Powder XRD of 1 at 28°C (top) and 69°C (bottom). Peaks that disappear upon heating are marked with an arrow. Note the increase in intensity of peaks and overall simplification of profile at higher temperature, (b) Experimental powder XRD of 3 at 69°C (black line) matches well with the calculated powder pattern of polymorph A (dotted line). Least squares refinement in Powder Cell 2.3 Rp = 14.39, R yp = 18.81. The starting solid in (a) was a mixture of forms A-D... 

The calculated XRPD patterns show distinctly different peak positions and intensities for the reactant and product. This is because the loss of water results in an entirely new crystal structure, unlike the situation noted for cromolyn sodium [21], in which the lattice contracts upon water loss without changing the crystal form. XRPD patterns collected on samples stored at 31% and 70% relative humidity show similar behavior (Figs. 22a and 23a). Notice that several diffraction peaks not present in the calculated powder pattern of the reactant are present in the measured powder pattern of material stored at 70% RH (Fig. 22). The same situation is noted for the calculated XRPD... 

Leopold et a/. (1982) observe two distinct deuterium lines, one of which is relatively narrow and one of which exhibits a resolved quadrupolar splitting. Figure 5 shows the Fourier transform of the echo observed after a 90° -t-90° pulse sequence in which the rf phase of the second pulse is 90° with respect to that of the first. The solid line in the 39 °K trace of Fig. 5 represents a calculated powder pattern of the broad (Pake doublet) component of the line. This component comprises 21 at. % of the sample. The... 

The lattice parameters for Ti and TiC are shown in Table 1. Values are given for the quenched-in phase boundary composition at room temperature. The cubic )S-Ti cannot be retained upon cooling. Calculated powder patterns for Ti and TiCi.o are listed in Tables 2 and 3, respectively. 

The lattice parameters for pure Hf and HfC are listed in Table 11 for the quenched-in phase boundary composition. Cubic jS-Hf cannot be retained upon cooling. The calculated powder patterns of a-Hf and HfCo.98 are listed in Tables 12 and 13, respectively. 

The structure and lattice parameters for the established phases V, jS-VjC, and VC are shown in Table 15 and the calculated powder patterns are listed in Tables 16, 17, and 18, respectively. Because of the fairly wide composition range exhibited by the compounds, the lattice parameters are given for the composition at the phase boundary after a quench from 1300°. Between these extremes the parameters will change with composition. 

The structure, lattice parameter and calculated powder pattern of the established phases (Nb, Nb2C, and NbC) are shown in Tables 20 through 24. Lattice parameters are given for the phase boundaries quenched from 2000°. 

Phase boundary lattice parameter values are given in Table 31 for the phases Ta, Ta2C, and TaC. In addition, the calculated powder patterns for Ta, a-Ta2C, l -Ta2C, and TaCo.99 are listed in Tables 32 through 35. 

Chromium metal is bcc (A2) with Uq = 2.8829 A (S. Muller and Dunner, 1965). A calculated powder pattern is given in Table 39. 

CrjsCg is reported to be complex face-centered-cubic crystal (D84 type) with 116 atoms per unit cell and Uq = 10.66 A (Westgren, 1933). A calculated powder pattern based on these data is given in Table 40. The structure designation is supported by electron diffraction work of J. F. Brown and Clark (1951). When this phase was formed in steel, Allten et al. (1954) referred to it as (Cr, Fe)23Cg and gave Uq = 10.60 A. Stecher et al. (1964) report Uq = 10.655 A. 

A calculated powder pattern for each phase in this system is shown in Tables 55 through 58. 

Because the lattice parameter of a-Th increases with dissolved carbon, nitrogen, and oxygen, the value given in Table 60 is the lowest reported. A calculated powder pattern is listed in Table 61, on this basis. fi-Th cannot be retained upon quenching. 

Fig. 4.33 Calculated powder pattern for4 -azido-2,2 6, 2"-terpyridine (compound 4.14) using single crystal X-ray diffraction data. The pattern is a fingerprint of the bulk powder material.

Importantly, the calculated diffraction pattern is not affected by the typical sources of errors of experimental powder diffraction (preferential orientation, mixtures, presence of amorphous phase) that often complicate or render uncertain the interpretation of measured powder diffractograms hence the calculated powder pattern is often referred to as the gold standard pattern for a crystal form. 

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