Recipes are given to assist in setting up rigid bodies for common molecules and coordination polyhedra, to define satellite groups, to perform rotations around arbitrary axes through the origin of the rigid body, and to refine intramolecular degrees of freedom under consideration of the special needs of powder diffraction. To the greatest possible extent, the notation follows that of the well known Rietveld refinement program GSAS (Larson and Von Dreele, 1994).

Two new solubility-limiting phases relevant to nuclear waste disposal are reported, namely CeSiO4 and Ca2Ce8(SiO4)O2, produced by hydrothermal synthesis at 180 °C. X-ray diffraction data are presented for both compounds. Rietveld refinement was performed for each of these phases. CeSiO4 was confirmed to be a zircon structure type, with space group I41/amd, unit celltype="bold">abold=6.9564(3),type="bold">cbold=6.1953(4) Å. Bond lengths for SiO4 are in excellent agreement with published values; Ce4+ is coordinated to eight oxygen atoms with four regular and four short bonds. Ca2Ce8(SiO4)O2 was shown to have an apatite structure, with space group P63/m and unit celltype="bold">abold=9.4343(3),type="bold">cbold=6.8885(4) Å. The unit cell and bond lengths were found to be slightly smaller than would be expected from other lanthanide-containing analogs; possible reasons for this are discussed.

Crystalline phases present in the three NIST SRM Standard Portland cement clinkers 8486, 8487, and 8488 have been quantified from XRD powder patterns, (CoKα radiation), using the full-profile Rietveld method. Included in the Rietveld refinement are rhombohedral (R), monoclinic (M), and triclinic (T) crystal polymorphic forms of C3S, as well as crystal polymorphs of C2S and C3A. It is necessary to specify the phase crystallography including polymorphs, because of the extreme superposition of alite and belite XRD lines in the clinker patterns. Unsatisfactory results occur when only one or two of the C3S polymorphs are used in the Rietveld quantification; best results occur when all three polymorphs for C3S are included. The latter are called RMT-type refinements. The Rietveld full-profile XRD method is as precise as the microscope point-counting (MPC) method, but much less labor-intensive. The Rietveld method can quantify the C3S phase polymorphs, as well as total C3S. Rietveld and MPC methods give the same phase weight percentages for the three NIST standard clinkers. Calculated oxide weight percentages obtained from Rietveld phase weight percentages agree well with oxide percentages determined by XRF analysis. Bogue mineral weight percentages do not agree with Rietveld or MPC data, while transformation of the Bogue mineral percentages to oxides does not compare well with XRF analysis.

The National Institute of Standards and Technology (NIST) certifies a variety of standard reference materials (SRM) to address specific aspects of instrument performance for divergent beam diffractometers. This paper describes SRM 640d, the fifth generation of this powder diffraction SRM, which is certified with respect to the lattice parameter. It consists of approximately 7.5 g silicon powder specially prepared to produce strain-free particles in a size range between 1 and 10 μm to eliminate size-broadening effects. It is typically used for calibrating powder diffractometers for the line position and line shape. A NIST built diffractometer, incorporating many advanced design features, was used to certify the lattice parameter of the silicon powder measured at 22.5 °C. Both type A, statistical, and type B, systematic, errors have been assigned to yield a certified value for the lattice parameter of a=0.543 159±0.000 020 nm.

Structural characterization from powder diffraction of compounds not containing isolated molecules but three-dimensional infinite structure (alloys, intermetallics, framework compounds, extended solids) by direct space methods has been largely improved in the last 15 years. The success of the method depends very much on a proper modeling of the structure from building blocks. The modeling from larger building blocks improves the convergence of the global optimization algorithm by a factor of up to 10. However, care must be taken about the correctness of the building block, like its rigidity, deformation, bonding distances, and ligand identity. Dynamical occupancy correction implemented in the direct space program FOX has shown to be useful when merging excess atoms, and even larger building blocks like coordination polyhedra. It also allows joining smaller blocks into larger ones in the case when the connectivity was not a priori evident from the structural model. We will show in several examples of nonmolecular structures the effect of the modeling by correct structural units.

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.

X-ray powder diffraction data for Ba0.5Sr0.5Co0.8Fe0.2O3−δ are reported. The powder was prepared using a metal-EDTA complexing method. The XRD data could be fitted with a primitive cubic unit cell in space group Pm3m (No. 221). The Rietveld refined unit cell parameter is ac=0.398 30(3) nm with Z=1 and Dx=5.75 g/cm3.

The structure of the oxyphosphate Ni0.50TiO(PO4) has been determined ab initio from conventional X-ray powder diffraction data by the “heavy atom” method. The cell is monoclinic (space group P21/c, Z=4) with a=7.3830(5) Å, b=7.3226(5) Å, c=7.3444(5) Å, and β=120.233(6)°. Refinement of 46 parameters by the Rietveld method, using 645 reflexions, leads to cRwp=0.152, cRp=0.120, and RB=0.043. The structure of Ni0.50TiO(PO4) can be described as a TiOPO4 framework constituted by chains of tilted corner-sharing TiO6 octahedra running parallel to the c axis, crosslinked by phosphate tetrahedra and in which one-half of octahedral cavities created are occupied by Ni atoms. Ti atoms are displaced from the center of octahedra units in alternating long (2.231) and short (1.703 Å) Ti–O bonds along chains.

The measurement of x-ray diffraction line intensities is the basis for quantitative phase analysis (see for example, Chung (1974), Davis (1986), and Hubbard and Snyder (1988)). While there are many sources of error in such measurements, in recent years computer automation of powder diffractometers and associated analytical software has made such measurements more practical and accurate. For example, profile fitting software has made it possible to determine integrated peak areas and to deconvolute overlapping lines. Another problem which affects quantitative analysis is the systematic error in instrument sensitivity as a function of 20 diffraction angle. This effect has been partially responsible for poor reproducibility of relative intensities between laboratories (Schreiner and Kimmel (1987), and Jenkins and Schreiner (1989)). But, because the error is systematic, corrections may be made by using a standard such as the National Institute of Standards and Technology SRM 1976 alumina plate (NIST 1991). These and other advances have led to a renewed interest in the determination of I/Ic (also called RIR - Reference Intensity Ratio) values for crystalline substances (e.g., Snyder (1992)). I/Ic is defined as the ratio of the intensity of the strongest line of an analyte to the corundum (113) line when the analyte is mixed 50:50 by weight with corundum. We present here a standard procedure used in our laboratory to experimentally measure I/Ic values, and which explicitly incorporates profile fitting and instrument sensitivity corrections. The procedure is written in the format of an ASTM (American Society for Testing and Materials) standard test method, however, inter-laboratory round robin tests have not been carried out to determine precision and bias associated with the method. While the method calls for corundum as the internal standard, another standard material, s, may be used, in which case the procedure will result in a ratio I/Is. Hubbard and Snyder (1988) have shown how to convert between I/Is and I/Ic. This method is based on the procedure routinely published in NBS Monograph 25 until 1986. It is augmented with corrections for the angularly dependent instrument sensitivity and with calculations of I/Ic for both variable and fixed divergence slit configurations. A Quattro Pro spreadsheet is used in our laboratory to do the calculations. An example of the spreadsheet is given in the appendix for one of two I/Ic runs of MgCO3. We also utilize the corundum in the I/Ic runs as an internal standard to determine displacement error corrections for preparation of digitized patterns of pure analyte phases. These patterns are submitted to the International Centre for Diffraction Data for inclusion in a whole pattern data file planned for some time in the future. The notation used here is the standard notation developed for the RIR method by Hubbard and Snyder (1988) and systematically extended by Snyder (1992). A table of the notation is given in the Terminology section below.

Surface roughness of planar samples causes an additional attenuation of X-ray diffraction intensity measured in Bragg–Brentano geometry. The decrease of intensity becomes stronger with decreasing scattering angle. This is part of the microabsorption effect. Two quantitative expressions describing the microabsorption effect are incorporated into the DBWS 9006-PC Rietveid program [D. B. Wiles and R. A. Young, J. Appl. Crystallogr. 15, 149–151 (1981)]. The procedure is applied to scattering data obtained from YBa2Cu3O7-powder samples with different degree of surface roughness but approximately identical bulk structure. The procedure is proved to work well. However, the values obtained for the parameters of the temperature factors and the microabsorption effect are correlated, and careful discussion is necessary to interpret the results.

The solid solutions Y2−xDyxO3 (x=0.20,0.50,0.74,1.40,1.80) were obtained by ceramic technology. The crystal structures were refined from X-ray and neutron diffraction data measurements in the cubic space group Ia3 by the Rietveld method. The unit cell dimensions varied from 10.6056(4) Å to 10.6624(1) Å. The structure characteristics were analyzed in relation to the concentration of the magnetic ion. The selected cation–anion–cation bonds, important for the understanding of the superexchange interaction and the magnetic properties, are given. In all samples the Dy3+ ions are randomly distributed in the cation sites 8(b) and 24(d). Comparing the random cation distribution in Y2−xDyxO3 and the preferential distribution in Y2−xGdxO3, it has been concluded that the type of distribution depends on the difference of the lattice constants between RE2O3 and Y2O3. Hence, in this cubic Mn2O3-type of structure, a preferential distribution can be expected in Y2−xNdxO3, Y2−xSmxO3, Y2−xEuxO3, Y2−xLuxO3, and a random distribution in Y2−xHoxO3.

The results from a third structure determination by powder diffractometry (SDPD) round robin are discussed. From the 175 potential participants having downloaded the powder data, nine sent a total of 12 solutions (8 and 4 for samples 1 and 2, respectively, a tetrahydrated calcium tartrate and a lanthanum tungstate). Participants used seven different computer programs for structure solution (ESPOIR, EXPO, FOX, PSSP, SHELXS, SUPERFLIP, and TOPAS), applying Patterson, direct methods, direct space methods, and charge flipping approach. It is concluded that solving a structure from powder data remains a challenge, at least one order of magnitude more difficult than solving a problem with similar complexity from single-crystal data. Nevertheless, a few more steps in the direction of increasing the SDPD rate of success were accomplished since the two previous round robins: this time, not only the computer program developers were successful but also some users. No result was obtained from crystal structure prediction experts.

K2YZr(PO4)3and K2GdZr(PO4)3were found to have the langbeinite-type structure (K2Mg2(SO4)3). We determined the crystal structure of these compounds from powder diffraction data. They are cubic P213 (no. 198), with a = 10.3346(1)Å and a = 10.3457(3)Å respectively. The intensity values we observed and calculated are reported. Intensity measurements indicate a random distribution of Y3+(Gd3+) and Zr4+on both Mg2+sites of langbeinite.

In conventional multiphase Rietveld refinement, now being used for quantitative phase determination, the crystal structure of each phase needs to be known in order to generate a calculated standard pattern of the phase to be refined against the measured XRD pattern. This is a disadvantage when the structural data for a phase are imperfect or unknown and may prevent an analysis.

A method is given whereby a phase with an imperfectly known or unknown crystal structure can be included in a multiphase Rietveld refinement, with other well-characterised phases, by use of an empirical or “observed” hkl file for that phase, with the SIROQUANT software package. The amplitudes 1F(hkl)1 in the empirical hkl file of the phase generate a reference profile for it which agrees with a measured standard pattern of the phase. Methods are given for the creation and scaling of empirical or “observed” phase hkl datasets. The Rietveld variable parameters (preferred orientation, linewidth, lineshape and unit cell) are refinable in the usual way for a phase with an empirical hkl dataset.

Micro X-ray fluorescence (MXRF) offers the analyst a new approach to materials characterization. The range of applications is expanding rapidly. Single point analysis has been demonstrated for nanoliter volumes with detection limits at the 0.5 ng level. MXRF can be used as an element specific detector for capillary electrophoresis. Elemental imaging applications include analysis of sample corrosion and polymers, use as a combinatorial chemistry screening tool, and integration with molecular spectroscopic imaging methods to provide a more comprehensive characterization. Three-dimensional elemental imaging is a reality with the development of a confocal X-ray fluorescence microscope. Stereoview elemental X-ray imaging can provide unique views of materials that flat two-dimensional images cannot achieve. Spectral imaging offers chemical imaging capability, moving MXRF into a higher level of information content. The future is bright for MXRF as a materials characterization tool.

Fluorellestadite, Ca10(SiO4)3(SO4)3F2, has been synthesized as single phase. This compound crystallizes in the apatite type structure, s.g. P63/m, with parameters a=9.4417(1) Å, c=6.9396(1) Å and V=535.76(1) Å3. The refinement of its crystal structure converged to RWP=12.33% and RF=4.58%. The atomic parameters have been used to analyze the phase content of mineralized white Portland clinkers. These clinkers contain Ca3SiO5, Ca2SiO4, Ca12Al14O32F2 and Ca10(SiO4)3(SO4)3F2. The agreement between the elemental composition inferred from the Rietveld phase analysis and that measured by XRF is noteworthy. This comparison does not take into account the presence of amorphous phases and unmodeled elemental substitutions in crystalline phases. Similar Rietveld studies on commercial white Portland clinkers are also shown to be feasible.

X-ray powder diffraction was used to study the phase composition of human renal calculi. The stones were collected from 56 donors in Vitória, Espírito Santo state, southeastern Brazil. An XRD phase quantification revealed that 61% of the studied renal stones were composed exclusively of calcium oxalate [34% formed only by calcium oxalate monohydrate (COM) and 27% presents both monohydrate and dihydratate calcium oxalate]. The 39% multi-composed calculi have various other phases such as uric acid and calcium phosphate. Rietveld refinement of XRD data of one apparent monophasic (COM) renal calculus revealed the presence of a small amount of hydroxyapatite. The presence of this second phase and the morphology of the stone (ellipsoidal) indicated that this calculus can be classified as non-papillary type and its nucleation process developed in closed kidney cavities. In order to show some advantages of the X-ray powder diffraction technique, a study of the phase transformation of monohydrate calcium oxalate into calcium carbonate (CaCO3) was carried out by annealing of a monophasic COM calculi at 200, 300, and 400 °C for 48 h in a N2 gas atmosphere. The results of the XRD for the heat treated samples is in good agreement with the thermogravimetric analysis found in the literature and shows that X-ray powder diffraction can be used as a suitable technique to study the composition and phase diagram of renal calculi.

Magnesiumchromite, MgCr2O4, undergoes a structural transition from a cubic spinel structure [space group Fd3m, a=8.32768(4) Å at 16 K] into a tetragonal distorted structure [space group I41/amd, a=5.89199(5) Å, c=8.31677(8) Å at 10 K], isotypic with Hausmannite, Mn3O4. This phase transition is translationengleich and takes place very close or at the antiferromagnetic ordering temperature.

Eighty specimens of cellulosic materials were analyzed over a period of several years to study the diffraction characteristics resulting from polymorphism, crystallinity, and chemical substitution. The aim of the study was to produce and verify the quality of reference data useful for the diffraction analyses of cellulosic materials. These reference data can be used for material identification, polymorphism, and crystallinity measurements. Overall 13 new references have been characterized for publication in the Powder Diffraction File (PDF) and several others are in the process of publication.

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.