The mathematical relationships are developed which are pertinent to the quantitative analysis of powder mixtures for the case of diffraction from the surface of a flat powder specimen. These formulas relate the diffracted intensity to the absorptive properties of the sample. Three important cases are treated: (1) Mixture of n components; absorbing powder of the unknown equal to that of the matrix; concentration proportional to intensity. Direct analysis is permitted. (2) Binary mixture; absorbing powder of the unknown not equal to that of the diluent; concentration not proportional to intensity. Direct analysis is possible by means of calibration curves prepared from synthetic mixtures. (3) Mixture of n components; absorbing power of the unknown not equal to that of the matrix; general case. Analysis is accomplished by the addition of an internal standard. Concentration is proportional to the ratio of the intensity of a selected reflection from the unknown to the intensity of a reflection from the internal standard.

The absorption of X-rays in a heterogeneous material depends on the linear absorption coefficients and volume fractions of the components, and on die geometrical peculiarities of their distribution. The latter is called the microabsorption effect, it can be separated into a bulk and a surface contribution. Within the framework of a well-defined stochastic structure model, the bulk contribution to the microabsorption is calculated for arbitrary random multiphase systems in terms of dependence on volume fractions and mean chord lengths of particles. Expressions are derived which are suitable for eliminating the experimental errors of scattering intensities caused by the bulk contribution of microabsorption.

If only one wavelengtii of radiation is used, the mean chord lengths of the phases of the sample must be determined by other experimental techniques. A method is proposed to overcome this difficulty by using two or more wavelengths of radiation; this correction procedure works without the knowledge of the particle sizes of the phases.

A series of BaO:RxOy:CuO materials has been prepared where R=Y, La, Ce, Pr, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. They have been characterized by X-ray powder diffraction methods. All BaR2CuO5 phases, commonly referred to as the “green phases”, are orthorhombic with space group Pbnm(62) and are isostructural. These single phase materials could be prepared with most lanthanides, except for La, Ce, Pr, Nd and Tb. Possible reasons for the exceptions are discussed. Both La and Nd tend to form a brown solid solution of Ba2+2xR4-2xCu2-xO10-2x with a tetragonal space group of P4/mbm(127). The major phases found in the Ce, Pr and Tb compositions are the perovskite-related structures BaRO3, and in the Pr case, Ba2PrCu3O6+x as well. The cell parameters of the green phase materials increase progressively from the Lu compound to the Sm compound: a ranges from 7.0506(6) to 7.2754(4) Å, b from 12. 0534(8) to 12. 4029(7) Å, c from 5.6099(5) to 5. 7602(3) Å, and the cell volume from 476.75(6) to 519.78(4) Å3. A correlation of the crystallographic data with the size of the R elements is given.

The procedure of whole-powder-pattern fitting without reference to a structural model has been applied to the determination of direction-dependent crystallite size and strain. The fitting function used is defined as the sum of (1) background intensity and (2) contributions from individual reflections given as the convolution of the observed instrumental function with the true data function in analytical form. Crystallite size and strain parameters are adjustable, together with unit-cell parameters and the integrated intensities of all reflections, during the whole-powder-pattern fitting. The procedure requires neither structural parameters nor intensity correction for preferred orientation in calculating profile intensity. The two models are incorporated for line broadening, one for isotropic size and strain effects and the other for the anisotropic size effect of cylindrical shape. The procedure has been tested for these two models using the observed data of 4 mole % Y2O3-doped tetragonal ZrO2 and hydroxyapatite, Ca5(PO4)3OH, respectively, and been shown to be effective for determining crystallite size and strain from the powder pattern with a relatively high peak density.

A powder diffraction method was applied to the quantitative analysis of amorphous silica in several quartz powders. Two calibration methods, i.e., direct analysis and the standard addition method were examined. Calibration mixtures were made by mixing a standard silica gel powder ground to under 5 μm particle size with a matrix quartz powder which was ground to 10 to 40 μm particle size and treated with NaOH solution to remove the amorphous phase caused by grinding. Intensity of the amorphous halo was measured at 23.0° 2θ, and the background intensity at 53.0° 2θ was subtracted. Linear calibration curves were obtained over the ranges of 0 to 50 wt% by direct analysis and 0 to 20 wt% by standard addition methods, respectively. The analytical results obtained by the two calibration methods were in good agreement with each other. The relative standard deviations for 4.3 wt% of amorphous silica were 4.6% by the direct analysis and 5.4% by the standard addition method. These methods were successfully applied to a correction of reference intensity ratios (RIR) for several quartz powders containing amorphous silica. After the correction for amorphous content, the relative standard deviations of the RIR values for quartz powders became smaller.

A quantitative phase analysis often requires advanced numerical studies to determine the appropriate intensity values. In this paper the method of fitting analytical functions to the experimental profile is applied to X-ray powder diffraction patterns obtained with FeK radiation. In the present work, the authors examine some problems connected with numerical studies, especially the function describing the experimental profile. The usefulness of the α2 elimination procedure and the angular dependence FWHM are also examined.

Quantitative phase analysis of n-phase mixtures can be performed if at least n samples composed of no more than n identical phases are available. The fact that there is no need for pure phases (analytical standards) constitutes the main advantage of the method presented here. However, substitution for the pure phases by an unknown mixture of these phases decreases the diversity of the sample set and also the precision of the analysis. The crucial step in a standardless method is the creation of an initial sample set. A simple test is developed to estimate the suitability of the sample set for analysis and to evaluate the analysis error. Application of this test to 13 four-phase mixtures has confirmed its high quality.

A new Peltier-cooled solid-state Si(Li) detector has been compared to a traditional scintillation detector/diffracted-beam graphite monochromator system in conventional X-ray powder diffraction applications. Parameters studied included absolute count rates, detector linearity, peak-to-background ratios, detection limits, fluorescent radiation elimination, and peak profile shapes. Comparisons were performed on a Siemens D-500 θ-2θ diffractometer using constant sample and nondetector instrumental parameters. Advantages of the Si(Li) detector include a significantly increased count rate (3.4 - 3.8 times), primarily due to the elimination of the graphite monochromator, slightly lower background count rates, and the ability to change the analysis energy quickly. The higher count rate and slightly lower background count rate of the Si(Li) detector allow collection of data more rapidly than possible with a scintillation detector/diffracted-beam monochromator system and yield improved peak-to-background ratios and detection limits. Significant disadvantages of the Si(Li) detector include pronounced deviation from linearity at low count rates, making accurate measurement of even moderate countrate peaks difficult, and detector shutdown due to 100% deadtime between 4 and 5 × 10 4 counts/s (cps). The Si(Li) detector and the scintillation detector/diffracted-beam monochromator system are comparable in terms of fluorescence radiation elimination, resolution, and peak shape, although it appears tfiat die diffracted-beam monochromator measurably reduces the low-angle portion of the half width of all reflections.

Crystals of sodium copper oxalate dihydrate [Na2Cu (C2O4)2.2H2,O] were obtained by the gel method, from solutions of oxalic acid and copper chloride. The crystals form blue needles with idiomorphic faces of brilliant luster, permitting goniometric measurements and the determination of the morphology with the aid of crystallographic parameters. Optically the crystals are biaxial negative, 2V = 38°, with a weak dispersion r<v. The orientation of the indicatrix was determined using a universal stage.

Crystals of sodium copper oxalate dihydrate, Na2Cu (C2O4)2.2H2O, were apparently first obtained in 1929 by Riley. Gleizes et al. (1980) undertook a preliminary crystallographic study of crystals obtained by a different technique from Riley's. In the first case, a solution of 33.5 g/L of sodium oxalate was heated and then poured gradually into a nearly saturated solution of copper sulfate until slight turbidity appeared. The turbidity was eliminated and the solution clarified by the addition of a little more sodium oxalate solution. In this way Riley obtained a dark blue solution which after filtration yielded extremely fine sky-blue needle-like crystals, rarely more than 8mm long. In the method of Gleizes et al. (1980), copper oxalate was dissolved in an aqueous solution of sodium oxalate; those authors observed complete dissolution when the molar ratio of sodium oxalate to copper oxalate was near 2. By evaporating the solution, they obtained long, prismatic crystals whose crystallographic constants they determined.

In order to obtain crystals large enough for further crystallographic study, we set out to produce crystals of sodium copper oxalate by the gel method (Triché, 1984). We found that slow crystallization did encourage the formation of large crystals.

Fourier self-deconvolution has been successfully applied as a means of obtaining semi-quantitative information by resolving the overlapping peaks in X-ray powder diffractograms collected from mixtures of kaolinite and ripidolite. A series of diffractograms were collected from known mixtures of the two minerals. The diffractograms were then processed using Fourier self-deconvolution over a selected range between 23 and 27° 2θ (encompassing the overlapping peaks of kaolinite (002) and ripidolite (004) at 24.85 and 25.13° 2θ, respectively). Once deconvoluted, areas under individual peaks of kaolinite and ripidolite were calculated using curve fitting. The calculated percentage of kaolinite in the mixtures was then plotted versus the true weight percent of kaolinite. The same procedure was conducted on the original diffractograms using only curve fitting without first deconvoluting. A comparison of results shows that, provided the number of peaks are known, both methods give nearly equal results. However, Fourier self-deconvolution, by increasing the resolution, greatly improves the ability to detect overlapping peaks.

This is a second and considerably expanded edition of the RIR table. We are pleased that considerable interest is now being generated in the RIR table; several contributors have provided measured data for this second edition. We have also added many entries of common minerals and simple compounds from the JCPDS data base and will continue to add more from this source with each succeeding table published. In this regard where we receive requests for a particular class of RIR's (alloys, or rare earth oxides, for examples) we can give higher priority to extracting these values from the JCPDS data base.

The reader should refer to the text explanation of the first published table in Vol. 3, No. 4 of this journal. In the first text two important errors are noted here; Equation (3) should have read RIRcorr = RIRobs/Wj; and the second sample preparation category of section 4 Specific Parameters should read “(w) Methods including well mounts with side or back loading or similar process”.

The intensity round-robin is one of a series of round-robins sponsored by the International Centre for Diffraction Data. The purpose of these round-robins is to attempt to quantify problems encountered in the acquisition, analysis and interpretation of powder diffraction data. Previous International Centre sponsored round-robins have addressed topics including: manual and automated search match methods; sample preparation methods; d-spacing accuracy; cell parameter refinement and peak profile calibration.

The primary focus of the intensity round-robin was to study measured intensities obtained from modern computer controlled powder diffractometers. However, the tests were designed in such a way as to also yield information on the performance of data treatment software packages. To this end, participants were asked to submit both raw and treated data, thus allowing evaluation of, for example, the efficiency of peak hunting algorithms in finding peaks.

Room temperature crystalline structures of La2-xSrxCuO4 samples with uncommonly high hole concentrations (p) up to p=0.4, annealed under 1 and 100 bars of oxygen pressure have been analyzed by X-ray diffraction. Results show that the x=0 sample with p=0.09 and superconducting below 20K is orthorhombic at room temperature. The orthorhombic distortion at 300K decreases with increasing x and becomes tetragonal when x reaches 0.08. This orthorhombic-to-tetragonal phase transformation is consistent with previous work. Samples with x≥0.28 and p≥0.31 remain tetragonal but are nonsuperconducting down to 5K. Lattice dimension anomalies have also been observed and are correlated with the sudden appearance of oxygen vacancies, as seen by the hole concentration measurements. Initially, the value of the lattice dimension a decreases and c increases monotonically with increasing x. A sudden increase in a and decrease in c begins when x reaches 0.28 for samples prepared under 1 bar of oxygen indicating a sudden loss of oxygen from the structure. This sudden reversal in lattice dimensions a and c is not present in samples annealed under 100 bars of oxygen pressure suggesting essentially no oxygen vacancies. The increase in c with x of the La2-xSrxCuO4 samples with no oxygen vacancies can be attributed mainly to the result of substituting smaller La+3 ions by larger Sr+2 ions. A study of the variation of c with the hole concentration reveals that the c lattice dimension drops sharply with no change in the hole concentration when oxygen is continuously removed from the lattice caused by an increase of the Sr content in La2-xSrxCuO4.

Crystal data and a representative X-ray powder diffraction pattern are reported for a series of isomorphous compounds, LnKFe(CN)6.4H2O where Ln = La, Ce, Pr and Nd. They crystallize in the hexagonal space group P63/m (176) with Z = 2. A plot of the unit cell volume (V) versus the cube of the Ln ionic radius (r3) yields linearity with a correlation coeficient of 0.9998.

The unit cell dimensions of minerals in the smectite group, regular and random mixed-layer groups, and halloysite shown in the Mineral Powder Diffraction File (1986) have been refined by least-squares analysis in the hexagonal system with a primitive lattice with indices restricted to hk or 00l reflections. Trioctahedral minerals have larger a unit-cell dimensions than dioctahedral minerals.

A commercially available photoconductor material, p-diethylaminobenzaldehyde diphenylamine hydrazone, C23H25N3, has been purified and recrystallized from an absolute alcohol solution. The triclinic compound has been characterized by X-ray powder diffraction. Experimental 2θ values corrected for systematic errors, relative peak intensities, values of d, and the Miller indices of 74 observed reflections with 2θ up to 30.5° are reported. The powder diffraction data have been evaluated, and figures of merit are reported. Unit-cell parameters least-squares refined from the 74 observed reflections of the triclinic compound are in good agreement with those obtained from the single-crystal structure analysis.

Quartz in dolostone can be determined quantitatively down to 0.03 weight percent using a standard preparation procedure for the sample and absolute integrated intensity measurements. Measurement reproducibilities of 3.2% were obtained. Calibration curves determined by spiking low-quartz dolostone allowed concentrations of 2.0 weight percent or lower to be established. Higher concentrations of quartz in some related soil samples were determined by comparing the absolute integrated intensity with that obtained from a pure quartz sample prepared in the same manner.

Based on analysis of its powder diffraction pattern, tetracycline hydrochloride is orthorhombic; the space group is probably P212121(19) or P21212(18). Indexed powder data and refined cell parameters are presented.

Observed powder diffraction data for two tetracyclines were interpreted with the aid of calculated patterns based upon the crystal structures determined from a single crystal of the same batch for each compound. The results consist of high quality standard powder patterns with the usual supporting data.

The Powder Diffraction File (PDF) X-ray diffraction pattern for SnO2 (cassiterite, syn), determined in the early 1950's at the National Bureau of Standards, was evaluated using the NBS*AIDS83 editorial review program and a calculated powder pattern. Systematic errors in d-spacings and relative intensities were attributed to the lack of an iterative least-squares refinement of unit cell parameters, to inadequate precision in reporting d-spacings, to poor sensitivity to high angle reflections, and to detector dead time. A new SnO2 pattern was prepared and used to illustrate criteria for evaluation of powder patterns. An R-Factor for quantifying agreement between observed and calculated relative intensities was utilized. The systematic errors in the earlier pattern occurred at higher angles and did not hinder its usefulness for identification purposes.