The error is investigated which results from the employment of tangential approximation in the calculation of line shift caused by specimen displacement from the recording circle in focusing systems (Guinier, Seemann–Bohlin). After an exact expression has been deduced and compared with the approximate formula in a numerical example, it is concluded that the error caused by the approximate formula may be important only in exceptional cases. The deduced exact formula is also compared with that given by Rafaja and Valvoda [Powder Diffr. 6, 200–203 (1991)] with the conclusion that both formulas are mathematically equivalent and complementary with respect to the theoretical and measured values of the diffraction angle 2θ.

Quantitative determination of phase abundances using X-ray powder diffraction is a technique in wide use today. Of the various methods employed, the Chung, or RIR method, is one of the most common because it can provide reliable results for all sample types. However, improvements can be made to the Chung method of analysis for phases which exhibit large chemical or preferred orientation effects. These effects can often be accommodated by using intensity regions that encompass several reflections, by averaging intensities from nonparallel reflections, or by using RIR values that are allowed to vary based on a predetermined functional relationship. To accommodate the effects of preferred orientation and variable composition in feldspars, RIR values versus the intensity ratio between two peaks of feldspar standards mixed with corundum have been determined. Curves of RIR have been formulated for: (1) feldspar RIR13.0−14.0° versus the intensity ratio (13.0–14.0° 2θ intensity region/27.0–28.75° 2θ intensity region); (2) feldspar RIR23.6° peak versus the intensity ratio (23.6° 2θ peak/27.0–28.75° 2θ intensity region); and (3) clinoptilolite RIR020 versus (020 reflection/22.1–23.0° 2θ intensity region). For example, RIR values for the highly variable 13.0–14.0° 2θ region for feldspar can be improved such that the quantitative results produced has a standard deviation of only 15% instead of 53% using a fixed-average value. From these curves, improved RIR values can be obtained for the quantitative analysis of unknowns. Additionally, intensity ratios can be determined between two peaks of a phase so that given the intensity of one peak, the intensity of the other peak can be readily calculated. This allows for subtraction of the intensity of a peak from one phase overlapping a peak from a second phase which is to be used for quantitative analysis but which cannot be decomposed by profile fitting.

Crystallographic data for Ni0.41Zn0.60Cu0.01Fe2.04−xSbxO4+δ (0.01≤x≤0.12) ferrites are significantly influenced by small additions of antimony. XRD analysis reveals that changes in crystal data for small Sb substitutions differ markedly from those for greater Sb substitutions. The differences are due to the contribution of the Sb ion. Complete crystal data for six solid solution compositions are reported. An X-ray powder diffraction pattern for Ni0.41Zn0.60Cu0.02Sn0.01Fe2.02Sb0.02O4+δ is given.

X-ray powder diffraction data for the spinels CoAl2O4 and CoGa2O4 were measured with synchrotron radiation using λ = 1.2033 Å, determined with Si as a standard (a = 5.4305 Å). The two blue compounds prepared hydrothermally are cubic with space group Fd3m. Profile refinements gave the results: CoAl2O4 had a = 8.0968(1) Å and composition (Co0.71Al0.29]Al1.71Co0.29]O4 and CoGa2O4 had a = 8.3229(1) Å and composition Ga[CoGa]O4. The degree of inversion is thus 0.29 for CoAl2O4 and one for CoGa2O4.

The kieserite-type solid-solution series of synthetic (Cu,Mg)SO4·H2O was investigated by TG-analysis and X-ray powder diffraction using the Rietveld method. Representatives with Cu≥20 mol% are triclinic distorted () analogous to the poitevinite (Cu,Fe)SO4·H2O compounds. Cation site ordering with preference of Cu for the more distorted M1 site was additionally proven by the structure refinement.

A comprehensive review of phases found in the Sr–Nd–Cu–O system which contains the high Tc superconductor phase Sr1−xNdxCuO2 has been prepared. This paper summarizes the crystal structures reported in the literature and the X-ray powder diffraction patterns reported in the ICDD Powder Diffraction File (PDF). In order to supplement the PDF with new patterns, calculated X-ray powder diffraction patterns generated from reported structures are provided for five ternary oxides: Sr0.86Nd0.14CuO2, SrNdCuO3.5, Sr6Nd3Cu6O17, Sr2NdCu2O5.66, and Sr1.2Nd1.8Cu2O6.

Indexed X-ray powder diffraction data are reported for the semiconducting compound Ba2Cl2Cu3O4. The structure was refined by the Rietveid technique on the basis of the space group I4/mmm. Refined unit cell dimensions are a = 5.5156(1) Å, c = 13.8221(3) Å, V = 420.49 Å3Dx = 4.74 g/cm3, F30 = 129(0.0075,30), M20 = 121, Rp = 6.58, Rwp = 8.66, and RB = 4.49.

The compounds BaR2O4, (R = Pr, Tb), where R are two of the less frequent trivalent lanthanides, have been prepared under reducing atmosphere from mixtures of BaO2, the R metals, and the oxides Pr2O3 and Tb4O7, respectively. The crystal structure of BaR2O4 have been refined from X-ray powder diffraction data by the Rietveld method of profile analysis using 31 parameters in each case. Both oxides are orthorhombic, isotypic with SrY2O4, of the perovskite-related CaFe2O4 structure type, S.G. Pnma (No. 62), Z = 4, a = 10.6113(8), b = 3.6303(3), c = 12.485(1) Å, and V = 480.93(5) Å3 for R = Pr; and a = 10.4282(8), b = 3.4893(3), c = 12.1809(6) Å, and V = 443.22(3) Å3 for R = Tb. The R–O distances vary between 2.15(6) to 3.40(6) Å for R = Pr, and between 2.15(3) to 2.91(5) Å for R = Tb.

X-ray powder diffraction data are reported for the trihydrated (A3N), the dihydrated (A2N), and the anhydrous ammonium trioxalatoaluminate (III) (AN). A3N is triclinic with space group . A2N and AN are monoclinic with space groups P21/c and P21/n respectively. The stability domains are A3N: –7.8 to 86 °C; A2N: 86 to 102 °C; AN: 102 to 180 °C.

X-ray powder diffraction data are reported for the monohydrated ammonium dioxalatotitanyl (IV). The crystal system is monoclinic with space group P21/c. Refined unitcell parameters are a = 13.484(3), b = 11.325(2), c = 17.673(3) Å, and β = 126.613(8)°.

This paper describes a straightforward method for the identification of the Miller indices associated with the face of a crystal of low symmetry. The method relies on orienting a crystal face parallel to the sample holder in the goniometer of a powder diffractometer. An intense diffractogram resulting from a single family of lattice planes parallel to the crystal face is obtained. The application of silicon powder to the surface of the crystal provides a means to correct 2Θ values for any misalignment of the crystal face. Calculated 2Θ and intensity values are used to assign the reflections from the corrected single-crystal diffractogram to a particular set of related lattice planes. In this paper are listed the corrected experimental 2Θ and intensity values for a particular face of a large single crystal of monoclinic hydroxylapatite and the theoretical 2Θ and intensity values for the h00 set of planes. Comparison of these parameters leads to the unambiguous assignment of that particular crystal face to the h00 Miller index.

X-ray powder diffraction data for a new potassium sodium silicate Na1.3K0.7Si2O5 are reported. The sample was prepared by calcining a mixture of NaOH, KOH, and sodium silicate (SiO2/Na2O=3.54, moisture content=60%) at 873 K for 2 h. The crystallographic data obtained by using the whole-powder-pattern decomposition method are Na1.3K0.7Si2O5, monoclinic, P21/c, a =4.8426(1) Å, b = 8.6892(2) Å, c = 11.9686(3) Å, β=90.373(2)°, V=503.60(2) Å3, Z=4, Dx = 2.51 g/cm3.

A perfect general purpose standard specimen for high accuracy line-profile analysis is shown to be an illusion. Balancing the partly contradictory requirements, an optimum standard specimen for a parafocusing diffractometer is developed. To obtain the optimum standard specimen, a 5–10 μm particle size fraction is taken from the NIST certified Si powder SRM640a, about 1.5 mg/cm2 of this powder is uniformly deposited on a (510) oriented Si single-crystal wafer and the assembly is heat treated for 2 h at 1273 K to remove lattice imperfections. All procedures necessary are precisely given, easily applicable, and reproducing. For the present standard specimens, the random errors due to crystal statistics are quantified and shown to be acceptable for spinning specimens; the systematic errors due to residual size and transparency broadening are determined semi-empirically and can be eliminated, if desired. Thus the proposed optimum standard specimen allows the determination of instrumental line profiles free from systematic errors and with random errors in the line width of the order of 0.001 °2θ, allowing a full use of the capacities of modern diffractometers and data evaluation procedures.

A synthetic catalyst precursor formed by sulfiding ferrihydrite (Fe3+O(OH)) in the presence of a hydrogen donor produces X-ray diffraction patterns resembling a mixture of both naturally occurring FeS2 polymorphs marcasite and pyrite. The diffraction peaks display a differential broadening, however, wherein only those peaks coincident to both marcasite and pyrite are strong and sharp, a feature that cannot be accounted for by a simple physical mixture. The broadening is analogous to that found in hexagonal cobalt, where occasional stacking faults produce interstratification of the hexagonal and cubic close-packed forms, resulting in strongly coherent diffraction only along the stacking direction. The crystal structures of marcasite and pyrite are virtually identical if viewed perpendicular to the (101) and (001) planes, respectively. Calculation of diffraction patterns based upon models of interstratifying marcasite and pyrite layers along these planes demonstrates that a sequence with marcasite-to-pyrite and pyrite-to-marcasite stacking fault probabilities of 0.22 provides a good fit to the experimental pattern. This interstratified material is a precursor to a species that shows catalytic activity for cleaving C-C bonds between aromatic rings and benzylic carbon atoms at low (<350 °C) temperatures.

A new diffraction pattern of the high-temperature and high-pressure polymorph Mg3(PO4)2-III (PDF 43-500) is given and indexed on the basis of a single-crystal structure refinement. It allows diffractogram indexing of the isostructural high-temperature and high-pressure form of Co3(PO4)2 (PDF 43-499).

Two complexes of gallium with 3-hydroxy-4-pyrones were synthesized as potential pharmaceutical compounds for oral administration. These compounds were analyzed by powder X-ray diffraction followed by computer indexing of the data. The first compound, tris(3-hydroxy-2-methyl-4-pyronato)gallium [Ga(C6H5O3)3], was found to be orthorhombic, a = 18.500(2), b = 16.948(2), c = 12.012(2) Å, V = 3766(1) Å3, Z = 8, Dm = 1.56(5), Dx = 1.570. The compound appears closely analogous to a similar compound containing Al instead of Ga, which crystallizes in space group Pbca. The second compound, tris(3-hydroxy-2-ethyl-4-pyronato)gallium [Ga(C7H7O3)3], was found to be monoclinic, a = 31.634(2), b = 8.7662(5), c = 7.8982(5) Å, β = 103.240(6)°, V = 2132.0(5) Å3, Z = 4, Dm = 1.50(5), Dx = 1.517, with a primitive space group.

A new semi-empirical approximation for the asymmetry function to be used in the X-ray Rietveld analysis has resulted in lower values of the so-called goodness-of-fit index, defined as S = Rwp/Rexp, where Rwp is the R-weighted pattern and Rexp is the R-expected [R. A. Young, The Rietveld Method (Oxford U.P., Oxford, 1993)], with respect to the corresponding values obtained with the classical approximation used by Rietveld in his fundamental paper. A comparing test of the two asymmetry functions was carried out for the cubic Y2O3 and for αAl2O3 using either pseudo-Voigt or Pearson VII symmetrical functions and two diffractometers. As in the case of the Rietveld approximation, the present one, which employs an exponential function, is optimized using only one fitting parameter. Experimentally, the asymmetry can be considerably diminished by using Soller slits with a small opening angle (≤2°).