The Reference Intensity Ratio (RIR) is a general, instrument-independent constant for use in quantitative phase analysis by the X-ray powder diffraction internal standard method. When the reference standard is corundum, RIR is known as I/Ic; These constants are collected in the Powder Diffraction File (1987), can be calculated, and can be measured. Recommended methods for accurate measurement of RIR constants are presented, and methods of using these constants for quantitative analysis are discussed. The numerous, complex constants in Copeland and Bragg's method introduced to account for superimposed lines can be simply expressed in terms of RIR constants and relative intensities. This formalism also permits introduction of constraints and supplemental equations based on elemental analysis.

Crystal and X-ray powder diffraction data are presented for BaPbO3. The powder pattern was indexed and refined on an orthorhombic cell with a=6.0264(3)Å , b=8.5078(3)Å , c=6.0629(2)Å, Z=4, space group Imma. The phase may actually be monoclinic with space group I2/m, but no distortion from the orthorhombic cell was evident in the powder patterns, suggesting a β angle very close to 90.0°.

As is well known from literature, the grinding process, which is an unavoidable step in sample preparation, may strongly modify the physical properties of chrysotile through amorphisation. The aim of this work is to establish the proper milling time to apply to the samples before an accurate X-ray powder diffraction quantitative analysis. We have used the RIR (reference intensity ratio) analytical method, based on the measurement of the ratio I/Is between the intensity of the strongest line of an analyte and the intensity of the analytical peak of a standard material, when they are thoroughly mixed 50:50 by weight. We have studied how the RIR value changes as a function of the milling time of the sample and how the accuracy of this quantitative method is affected.

The intensity diffracted by a low-mass sample with negligible absorption may be expressed as It = I∞ (B/2μ*)/G, where I∞ = intensity diffracted by a bulk sample, B = cross section of the primary beam, μ* = mass absorption coefficient, and G = mass of the sample. Measurable intensity may be obtained from samples with less than 1 μg mass. In order to improve the limit of detection, the primary beam should be collimated so as to irradiate the sample and only a minimum volume of the sample support. The optimum spreading area of a low-mass sample is S sinθ≅10μ*. Comminution of low-mass samples to 1 — 2μm particles is adequate for reasonable intensity measurements.

A study has been conducted with gibbsite specimens, on the use of Rietveld X-ray powder diffraction (XRPD) pattern fitting for quantitating preferred orientation in powders. This study has shown that an earlier formula gives results which correlate closely with an empirical measure of morphology proposed recently for gibbsite powders, viz., the ratio of the XRPD intensities for the (002) line and the (110, 200) doublet lines. A method is proposed on the basis of this correlation for the correction for preferred orientation of line intensities in gibbsite powder patterns. The correction method appears to have excellent potential for XRPD quantification of gibbsite levels in mixtures, and could have general application for coping with preferred orientation effects in the quantitation of other phases.

The crystal structure of La1−xSrxCoO3−δ (0≤x≤0.6) has been studied, using powder X-Ray diffraction. The crystal structure shows a transition from rhombohedral distorted perovskite for LaCoO3−δ into cubic perovskite for La0.4Sr0.6CoO3−δ. The cubic unit cell parameter is ac=3.8342(1) Å for La0.4Sr0.6CoO3−δ, the space group probably being Pm3m. Using a hexagonal setting, the cell parameters for La0.5Sr0.5CoO3−δ, are a=5.4300(3) Å, c=13.2516(10) Å; a=5.4375(1) Å, c=13.2313(4) Å for La0.6Sr0.4CoO3−δ; a=5.4437(1) Å, c=13.2085(5) Å for La0.7Sr0.3CoO3−δ; a=5.4497(2) Å, c=13.1781(6) Å for La0.8Sr0.2CoO3−δ and a=5.4445(2) Å, c=13.0936(6) Å for LaCoO3−δ with the space group probably being R3c.

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.

I have made use of X-ray powder diffraction patterns for over sixty years. In the summer of 1922, in anticipation of my becoming a graduate student in chemistry, I read the book “X-Rays and Crystal Structure,” by W. H. and W. L. Bragg. Then in September 1922 I arrived in Pasadena, and immediately began to learn how to determine the structure of a crystal by a study of the X-ray diffraction pattern from Roscoe Gilkey Dickinson, who was the first person to have received a Ph.D. degree from the California Institute of Technology (1920). The procedure in use in Pasadena started with the preparation of a photograph showing lines obtained by Bragg reflection from a developed face of a large crystal with monochromatic radiation, usually molybdenum K alpha and beta. Measurement of the angle of reflection gave a set of possible values for the length of the edges of the unit of structure, usually of a cubic, hexagonal, or tetragonal crystal, since the methods were not powerful enough to permit the evaluation of more than two or three parameters. The next step was the preparation of Laue photographs, and their analysis. This was a powerful method, which often led to the correct structures.

The X-ray powder diffraction patterns of anilinium trimolybdate tetrahydrate, (C6H5NH3)2Mo3O10·4H2O, and anilinium trimolybdate dihyhydrate, (C6H5NH3)2Mo3O10·2H2O, have been measured in room temperature. The unit cell parameters were refined to a=11.0670(7) Å, b=7.6116(8) Å, c=25.554(3) Å, space group Pnma(62) and a=17.560(2) Å, b=7.5621(6) Å, c=16.284(2) Å, β=108.54(1)°, space group P21(4) or P21/m(11) for orthorhombic anilinium trimolybdate tetrahydrate and monoclinic anilinium trimolybdate dihydrate, respectively.

A powder X-ray diffraction technique has been developed to quantify the relative amounts of α-carbamazepine (A) and β-carbamazepine (B) when they occur as a mixture. The theoretical basis of this technique was developed in 1948 by Alexander and Klug (Anal. Chem., 20:886-889). The powder X-ray diffraction patterns of A and B revealed that the line with d-spacing of 10.1 Å was unique to A. The ratio of the integrated intensity of the 10.1 Å line in a mixture of A and B, to the intensity of the 10.1 Å line in a sample consisting of only A, was calculated as a function of weight fraction of A in the mixture. These ratios were also experimentally determined, and there was a good agreement between the theoretical and experimental intensity ratios. The particle size of the samples, the sample preparation technique and the experimental conditions were controlled so as to eliminate the major sources of error in powder X-ray diffractometry. In order to minimize preferred orientation of the particles, a sample holder was specially fabricated.

The following new or updated patterns are submitted by the JCPDS Research Associateship at the National Bureau of Standards. The patterns are a continuation of the series of standard X-ray diffraction powder patterns published previously in the NBS Circular 539, the NBS Monograph 25, and in this journal. The methods of producing these reference patterns are described in this journal, Vol. 1, No. 1, p. 40 (1986).

The data for each phase apply to the specific sample described. A sample was mixed with 1 or 2 internal standards: silicon (SRM640a), silver, tungsten, or fluorophlogopite (SRM675). Expected 2-theta values for these standards are specified in the methods described (ibid.). Data from which the reported 2-theta values were determined, were measured with a computer controlled diffractometer. Computer programs were used to locate peak positions and calibrate the patterns as well as to perform variable indexing and least squares cell refinement. A check on the overall internal consistency of the data was also provided by a computer program.

With the explosive growth in the number of highly automated powder diffraction systems, many types of analyses which were previously considered a specialty analysis are now performed on a routine basis. Algorithms have been developed for measuring peak profiles from which crystallite sizes, residual microstrain, and X-ray crystal structure (Rietveld techniques for example) can be determined. However, these techniques require an instrumental peak profile calibration standard to correct the experimental data for instrumental broadening due to the system optics.

Significant problems are encountered when laboratories try to cross-correlate or reproduce published data due to the lack of a common reference material for instrumental calibration. This is particularly distressing in microstrain and crystallite size calculations which can be dramatically affected by a poor choice of standard materials. Microstrain and crystallite size measurement are becoming increasingly important for the characterization of advanced materials and catalysts.

Crystal data for four p-dibromobenzene/p-chloroiodobenzene mixed crystals, (pDBB)x(pCIB)1-x, with x = 0.1, 0.4, 0.7, 0.9, synthesized by the fusion-quenching method, and a typical powder diffraction pattern are reported. The unit cell is monoclinic with S.G. = P21/a and Z = 2. Cell parameters of solid solution members varied almost linearly between the end member values.

Single crystals and powder samples of Ca2Bi5O5and Ca4Bi6O13have been synthesized and studied using single crystal X-ray diffraction as well as X-ray and neutron powder diffraction. Unit cell dimensions were calculated using a least squares analysis that refined to a δ2θof no more than 0.03°. A triclinic cell was found with space group , a = 10.1222(7), b = 10.1466(6), c = 10.4833(7) Å. α= 116.912(5), β= 107.135(6) and γ= 92.939(6)°, Z = 6 for the Ca2Bi2O5compound. An orthorhombic cell was found with space group C2mm, a = 17.3795(5), b = 5.9419(2) and c = 7.2306(2) Å, Z = 2 for the Ca4Bi6O13compound.

In most of the practical problems of the quantitative X-ray analysis, obtaining working equations including only intensity ratios without the sample mass-absorption coefficient is impossible, unless an internal standard is added to the sample. It is shown that the internal standard may be unnecessary if some chemical data are added to the XRD information used. Experimental results justify this claim.

The crystal structure of the high-temperature phase of Sr2ZnWO6 prepared by air quenching from 1200° C has been determined by means of X-ray powder diffraction. β-Sr2ZnWO6 belongs to the cubic system, with space group Fm3m and a lattice parameter a = 7.9266 Å at room temperature. Its measured density is Dm = 6.93g/cm3, and each unit cell contains four formula weights.

New powder and crystallographic data for gorceixite, a mineral of the crandallite subgroup of the alunite group, are reported and compared with current Powder Data File (PDF) patterns and with calculated patterns. Both d-spacings and intensities have been evaluated, and the results indicate a significant improvement over existing patterns. Indexing of the reflections is given for the true monoclinic symmetry, Cm (8), the pseudorhombohedral symmetry, (166) (to compare with structurally analogous minerals), and the pseudocubic symmetry, Fm3m (225). Because of the strong pseudosymmetry, the overall figure of merit is lower than would be the case for indexing in one of the pseudospace groups.