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.

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).

The broadening of powder pattern peaks of metals is normally caused by small crystallite size and by distortions within the crystallites as a consequence of dislocation configurations. In addition, the experimental diffraction geometry contributes to the line broadening. Using Cu Kα radiation, we recorded the peak profiles of the cold-worked and annealed filings of tungsten, niobium, aluminum, and silver-indium alloys with a standard focusing diffractometer. The Rachinger method was applied to separate the Kα1 and Kα2 peaks, and the Kα1 peaks were subjected to a Fourier analysis. Elimination of the instrumental broadening was carried out by the Stokes method, which does not require any assumptions concerning the mathematical description of the diffraction peak profile.

The Fourier coefficients, AL, were separated into the fraction produced by particle size, ALFF, and by strains, ALe, by the Warren-Averbach method and plotted as a function of the distance L = ndhkl, normal to the reflecting planes (hkl) of spacing dhkl. The negative, reciprocal initial slope of the ALPF vs. L curve is equal to the effective particle size Deff, which contains the effects of the true crystallite size and faulting. The coefficients ALβ = AL/ALPF are used to calculate the root mean square strain <∊L2>1/2. The sum of the ALPF, which is proportional to a reciprocal integral breadth, leads to a different particle size, DWAPF, which is also dependent upon the crystallite size and faulting. The sum of the AL6 values is a measure of the strain ƐWA.

The integral breadths bst, corrected by the Stokes method, i.e.,

are separated into a particle size term bstPF and distortion term bSts using the relations . It is found that only the first relation leads to particle sizes DG,StPF and strains ∊G,st similar to those obtained by the summation of the ALPF and AL6, i.e., DWAPF and ∊wA, respectively. The integral breadths of the cold-worked peaks Bew and of the annealed standards bA. were also calculated, using the Lauc definition of B equal to area per peak maximum. A comparison of the values of bst/Bcw with bA/Bew for bA/Bew < 0.6 shows that all data follow the parabolic relation b/Bew = 1 − bA2/Bew2. The maximum deviation of bst/Bew from the parabola is less than 10%.

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.

Fluorescent X-ray spectrometers bave a high inherent reproducibility. It is possible to achieve results, on a routine basis, which have a coefficient of variation of less than 0.1%. Given extremely good chemical standards and the absence of interelemental effects, these readings can be interpreted into percentage concentrations with the same order of accuracy. Results, with this accuracy of analyses of copper in a straight brass will be given. With samples of greater complexity and more elements the interelement effects are large and have to be tackled. A correction method has been established and will be explained in detail.

As an example of the method it was decided to tackle the determination of chromium at high concentrations (7-32 %) in high-alloy steels containing additions in the following ranges: Si, 0.2-2.4%; Al, 0,07-5%; Cu, 1,3-3.6%; W, 0.25-3%; V, 0.1-0.3%; Nb, 0.1-0.3%; Mo, 0.1-4.4%; Ti, 0.05-1%; Mn, 0.35-10%; Ni, 0.2-24%. These very wide alloy specifications were a severe test on the accuracy of the chromium determination & the correction for interelement effects.

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 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.

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.

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.

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.

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.

Mn2+ and Cd2+ form a family of isostructural hexacyanoferrates(II,III). Their crystal structures, including those of mixed compositions containing K+ and Cs+ as charge balance cations, were resolved and refined from XRD powder patterns. The crystal structures of M3[Fe(CN)6]2⋅xH2O and MCs2[Fe(CN)6] (where M=Mn, Cd) were refined in the space group Fm3m. The mixed salts, MK2[Fe(CN)6]⋅2H2O, were found to be orthorhombic (space group Pmn21). The orthorhombic structure results from a local distortion due to monohydrated potassium ions located in interstitial sites. On ionic exchange in an aqueous solution containing Cs+, the orthorhombic distortion disappears and the cubic cell is obtained. Cs+ is a large ion, which practically fills the available interstitial voids stabilizing the cubic structure. In solutions of K+ and Cs+ the single salts, M2[Fe(CN)6]⋅8H2O (monoclinic P21/n) also transform, in this case liberating M2+ ions and forming the corresponding mixed salts. An analogous but slow structural transformation was also observed in the anhydrous forms of these single salts. These structural transformations could be relevant to the use of these compounds as ion exchangers and particularly for the sorption of 137Cs+ from radioactive waste solutions. The XRD data were complemented with structural information from infrared (IR), Mössbauer and water vapor adsorption techniques. © 2004 International Centre for Diffraction Data.

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.

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.

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.

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 brief review of the different topographic methods is given in order to attempt a classification of the various types of contrast observed. Depending on whether the image is obtained by a reflection or transmission method, is simple or integrated, dynamic, direct, or intermediary, the contrast and image width vary greatly. A detailed analysis is given in the case of transmission section topographs.

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.