A method for automated determination of the crystal structures from X-ray powder diffraction data

An algorithm is proposed for determining the crystal structure of compounds. In the framework of this algorithm, X-ray powder diffraction patterns are compared using a new similarity index. Unlike the indices traditionally employed in X-ray powder diffraction analysis, the new similarity index can be applied even in the case of overlapping peaks and large differences in unit cell parameters. The capabilities of the proposed procedure are demonstrated by solving the crystal structures of a number of organic pigments (PY111, PR181, Me-PR170).     

Crystal structure refinement of CuxAg1‐xInTe2 bulk material determined from X‐ray powder diffraction data using the Rietveld method

The influence of the Cu‐content in the quaternary compounds Cu_xAg_1‐xInTe₂ (0 ≤ x ≤1) on the structural properties of the bulk material was discussed. Bulk ingot materials of Cu_xAg_1‐xInTe₂ solid solutions (x = 0.0, 0.25, 0.50, 0.75 and 1.0) have been synthesized by fusion of the constituent elements in the stoichiometric ratios in vacuum‐sealed silica tubes. The materials compositions were confirmed by using energy dispersive analysis of X‐rays (EDAX). X‐ray powder diffraction measurements were performed for all the prepared samples at 300 K in step scanning mode. The analysis of X‐ray data has indicated that the crystal structure of the prepared materials with different compositions is single‐phase polycrystalline materials corresponding to the tetragonal chalcopyrite structure with space group I 2d. The crystal structural parameters were refined by Rietveld method using the Full Prof program. The refined lattice constants (a and c), anion positional parameter, u, and the determined bond distances and angles were found to vary with composition, x, attaining zero tetragonal distortion at x ≈ 0.75, which corresponds to an ideal tetragonal unit cell. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure determination of two asymmetrically substituted oxadiazoles from powder diffraction data

The crystal structures of the 1,3,4 oxadiazole compounds N,N‐dimethyl‐N‐[4‐(1,3,4‐oxadiazol‐2‐yl)phenyl]amine ( 1 ) and 2‐methyl‐5‐phenyl‐1,3,4‐oxadiazole ( 2 ) have been determined. In case of 1 no adequate crystals were available; therefore the structure was solved at room temperature from X‐ray powder diffraction data using the method of simulated annealing. This solution is compared to a second one obtained by applying the molecular replacement method. Subsequent Rietveld refinements combined with the so called two stage method based on the data collected to 1.6 Å resolution yielded an R_wp value of 7.27% for 1 . Compound 1 crystallizes in the orthorhombic space group P2₁2₁2₁ with lattice parameters of a = 7.599(4) Å, b = 6.004(2) Å, c = 21.736(3) Å. The crystal structure of 2 was solved by means of single crystal structure analysis (monoclinic space group P2₁/c, a = 8.010(3) Å, b = 10.783(4) Å, c = 19.234(7) Å, β = 90.794(9)°). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure of ultraphosphate glasses with small rare-earth ions by X-ray diffraction

Rare-earth ultraphosphate glasses with nominal R₂O₃ fractions of 10 and 15 mol% and small ionic radius (large atomic number) R³⁺ ions (R = Tb, Tm, Lu) are measured by X-ray diffraction at a synchrotron with photons of 119 keV (maximum scattering vector 260 nm^− 1). The total correlation functions T(r) show well-resolved R-O and O-O first-neighbor peaks. In contrast to all ultraphosphate RP₅O₁₄ crystals and the ultraphosphate glasses of larger R³⁺ ions, where RO₈ polyhedra (mean R-O coordination numbers of ~ 8 for the glasses) are observed, the R³⁺ ions in glasses with R = Lu, Tm, Tb have mean R-O coordination numbers of ~ 7.5. The R-O first-neighbor peaks extracted from the T(r) functions are compared with those obtained from atomic coordinates of related RP₅O₁₄ and RP₃O₉ crystals. The R-O distances of the ultraphosphate glasses studied are found to fall between those of the two crystals but with tails to the side of longer bonds.     

Structure of rare-earth phosphate glasses by X-ray and neutron diffraction

Previous diffraction studies of the structures of rare-earth phosphate glasses (R₂O₃)_x(P₂O₅)_1−x are extended to glasses with smaller R³⁺ ions with R = Sm, Gd, Dy, Er, Yb, Y for x = ∼0.25 and with R = Nd, Sm, Gd for x = ∼0.15. Parameters for the P–O, R–O and O–O first-neighbor peaks were obtained by Gaussian fitting. P–P and R–P distances were estimated from the positions of peak maxima. Effects of residual silica or alumina contents present as a result of glass processing were taken into account for selected samples. The P–O coordination number, N_PO, and the P–O, O–O, P–P distances are consistent with the presence of phosphate tetrahedra and are insensitive to the R species and the R₂O₃ content. Rare-earth coordination numbers, N_RO, decrease from ∼8 to ∼6.5 when x is increased from ∼0.15 to ∼0.25. N_OO and N_PP decrease with increasing R₂O₃ content indicating the network disintegration. The numbers N_RO of the metaphosphate glasses (x = ∼0.25) decreases from ∼7 to ∼6 when R is changed from La to Yb. This change is also indicated by the behavior of the R–O distances and by constant number densities of atoms. The decrease in N_RO with increasing R₂O₃ content is due to the reduction in the number of terminal O (O_T) available for coordination of the R³⁺ ions (six at metaphosphate composition). Especially for smaller R³⁺ ions sharing O_T between two R sites is not favored. The decrease by ∼0.04 nm of the prominent R–R first-neighbor distance with a change of R from La to Yb at the metaphosphate composition is indicated by a shift to higher magnitude of scattering vector of the shoulder occurring in front of the first main diffraction peak.     

Structure of titanophosphate glasses studied by X-ray and neutron diffraction

The structure of binary (TiO₂)_x(P₂O₅)_1−x glasses with x = 0.60, 0.65 and a ternary K₂O–TiO₂–P₂O₅ (KTP) glass were studied by X-ray and neutron diffraction. The experiments were performed at the high-energy beamline BW5 of the synchrotron DORIS (Hamburg/Germany) and at the GEM instrument of the neutron source ISIS (Chilton/UK). Gaussian fitting of well-resolved first-neighbor peaks in the correlation functions of the binary glasses with TiO₂ contents of 0.65 and 0.60 result in Ti–O coordination numbers of 5.65 ± 0.2 and 5.9 ± 0.2, respectively. Distorted TiO₆ octahedra and isolated PO₄ units form the glassy networks, with a small number of lower coordinated Ti sites for the 0.65 TiO₂ glass. For comparison, only TiO₆ octahedra are found for a ternary K₂O–TiO₂–P₂O₅ glass. The Ti–O coordination numbers are compared with a structural model where all oxygen atoms occupy sites in Ti–O–Ti, Ti–O–P or P–O–P bridges. The presence of three-coordinated oxygens must be assumed for the binary glasses, whereas a structure with nearly all oxygen atoms forming network bridges exists for the ternary KTP glass.     

Identification of predominant point defects in nonstoichiometric CuInse2 by X-ray powder diffraction

Refinement of structural parameter, occupancy factors and temperature factors of three indium rich samples enabled type and concentration of intrinsic point defects to be determined. Vacancies on copper and indium sites (8 and 5%, respectively) and indium atoms on copper sites (5%) were identified. Indium atoms exhibit a large thermal vibration amplitude.     

Crystal structure refinement of the ternary compound Cu2SnTe3 by X‐ray powder diffraction

The ternary compound Cu₂SnTe₃ crystallizes in the Imm2 (Nº 44) space group, Z = 2, with a = 12.833(4) Å, b = 4.274(1) Å, c = 6.043(1) Å, V = 331.5(1) ų. Its structure was refined from X‐ray powder diffraction data using the Rietveld method. The refinement of 25 instrumental and structural variables led to R_p = 10.2%, R_wp = 11.8%, R_exp = 7.7%, R_B = 10.6%, S = 1.6 and χ² = 2.6, for 5501 step intensities and 163 independent reflections. This compound is isostructural with Cu₂GeSe₃, and consists of a three‐dimensional arrangement of slightly distorted CuTe₄ and SnTe₄ tetrahedra connected by common corners. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The crystal structure of Zr2Se reinvestigated by electron crystallography and X-ray powder diffraction

The metal-rich compound Zr₂Se is of particular interest for electron crystallography, since it was one of the first examples that proved that heavy-atom structures can be solved via quasi-automatic direct methods from selected area electron diffraction intensities [1]. For this reason, Zr₂Se has been chosen as a model to discuss the possibilities and the limits of the quasi-kinematical approach that has been successfully used to determine this and related structures from high-resolution electron microscopy (HREM) images and selected area electron diffraction. In order to quantify the achievable accuracy of the electron crystallography techniques used, the corresponding structures are compared with results from structural analysis with X-ray powder data and with a model received from first-principles calculations. The latter structure was chosen in this study as a reference, since the calculations do not depend on experimental parameters. Analysis of the obtained result from electron diffraction structural analysis (EDSA) shows that the structural model is, on average, only off by 0.08 Å, despite the investigated crystal having an effective thickness of 286 Å. The corresponding result from Rietveld refinement with X-ray powder data agrees to within 0.04 Å with the structure from calculation and within 0.03 Å with the result from an earlier single crystal X-ray study [2].     

Structure of amorphous LaNi5D3.3 studied by neutron and X-ray diffraction

In situ neutron and X-ray diffraction measurements in a D₂ gas atmosphere at a constant pressure of 1 MPa were performed on amorphous LaNi₅D_3.3, which was prepared by mechanical alloying in a D₂ gas atmosphere. Reverse Monte Carlo (RMC) simulation based on the neutron and X-ray diffraction data was applied to construct a three-dimensional atomic arrangement of this amorphous alloy. The RMC model shows that more than 90% of the deuterium atoms occupy tetrahedral sites consisting of La and/or Ni atoms. Furthermore, the local environments around the Ni and La atoms were investigated by Voronoi polyhedral analysis of the RMC configuration of the metal atoms. The results show the presence of a number of prismatic-like polyhedra around a Ni atom.     

Structure analysis by normalized data. I. Increase of relative accuracy of diffraction data

A new method for obtaining physically reliable values of atomic parameters in the refinement of the structure model by the least squares method has been suggested. The method requires the use of experimental data reduced to a scale corresponding to the Bragg scattering from an ideal defect-free crystal. The reduced experimental data can be obtained by interexperimental-minimization (IEM) method—a new algorithm minimizing the difference “experiment 1-experiment 2” (between the data obtained in two experiments, 1 and 2) used in addition to the model-experiment minimization performed in the conventional least square procedure. The use of four different experimental data sets for alexandrite crystals, Al₂BeO₄: Cr³⁺, allowed us to show that the application of the IEM algorithm considerably increases the reproducibility level of the experimental data, which, in turn, increases by 30–60% the agreement between the model and the experiment.     

A method for implementing the diffraction of a widely divergent X-ray beam

A method for implementing the diffraction of a widely divergent characteristic X-ray beam from a standard X-ray tube with a linear focal spot was improved. X rays, passing through a diaphragm 30 μm in diameter, diffract from a crystal adjacent to the diaphragm. The crystal, together with a photographic plate, rotates around the axis perpendicular to the plate. It is shown that the diffraction image is a set of hyperbolas in this case. The equations of the hyperbolas are obtained and investigated. A method for interpreting the diffraction images in the case of small crystal asymmetry is proposed.     

Structure of amorphous NaCl–glucose system studied by X-ray diffraction and IR methods

X-ray diffraction and diffuse reflection IR spectroscopic measurements have been carried out on amorphous NaCl–glucose mixtures, a-(NaCl)_x(glucose)_1−x, with x = 0, 0.05, 0.1 and 0.15, in order to obtain structural information on the intermolecular hydrogen-bonded interaction between glucose molecules affected by the presence of NaCl. The difference distribution function Δg^inter(r) was derived from the Fourier transform of the difference intermolecular interference term Δi^inter(Q) between X-ray intermolecular interference terms observed from amorphous NaCl-glucose and pure glucose samples. A negative peak appears at r ≈ 2.5 Å in the Δg^inter(r) observed for the 10 mol% NaCl sample, while, the Δg^inter(r) for the 15 mol% NaCl sample does not show pronounced negative peak. On the other hand, the IR spectra for the O–H stretching region (2300 ⩽ ν ⩽ 3800 cm⁻¹) indicate that hydrogen bonds between glucose molecules are significantly collapsed in the samples containing 5–15 mol% NaCl. These results imply that the contribution from the Na⁺⋯Cl⁻ contact ion pair is dominated in the 15 mol% NaCl sample.     

Structure analysis by reduced data: V. New approach to refinement of crystal structures

A new approach to refining crystal structures using reduced experimental data is considered. The data reduction, which requires the establishment of the common and different characteristics of the measured data, can be done using the method of interexperimental minimization. The method is used to analyze the thermal motion of atoms. The method can also be used for the detailed study of different groups of those model parameters that are especially important for each specific case.     

Structure of potassium germanophosphate glasses by X-ray and neutron diffraction: 2. Medium-range order

Characteristics of the medium-range order (MRO) of K₂O-GeO₂-P₂O₅ (KGP) glasses are obtained from X-ray and neutron scattering data. The behavior of the MRO is expressed in changes of pre-peaks and smooth contributions in the structure factors, S(Q), for Q < 12 nm^-1. Peaks at Q = (7.5 ± 0.5) nm^-1 (Q - magnitude of the scattering vector) are the outstanding features and reach maximum intensity for a glass of ∼25/50/25 mol% K₂O/GeO₂/P₂O₅. The pre-peaks are explained by a structural model in which K-rich and Ge-rich regions are separated by PO₄ units. The distance of repetition of similar regions (∼1 nm) is responsible for the pre-peak at ∼7.5 nm^-1. The intensity of this pre-peak is reduced and finally eliminated for glass compositions approaching the binary GeO₂-P₂O₅ system. The pre-peak is changed to a smooth scattering contribution and finally shifted to ∼9 nm^-1 for glass compositions approaching the binary K₂O-GeO₂ system. The strong tendency of the PO₄ units to coordinate K⁺ and Ge neighbors at their four corners is the source for the special MRO of the KGP glasses.     

Structure of potassium germanophosphate glasses by X-ray and neutron diffraction. Part 1: Short-range order

It has been reported that the addition of K₂O or P₂O₅ to binary germanate glasses increases the Ge−O coordination numbers (N_GeO). The present work describes X-ray and neutron diffraction studies aimed at clarifying the concomitant effects of both oxides on the structures of ternary K₂O-GeO₂-P₂O₅ glasses. The Ge−O coordination numbers obtained range from 4.2 to 5.1, less than what is predicted according to a model which assumes all oxygen atoms form network bridges similar to those found in the related crystal structures. This implies that the glass structures must include terminal oxygen sites, likely associated with the PO₄ tetrahedra, that are neutralized by coordinating K⁺ ions. The shapes of the high resolution first-neighbor diffraction peaks do not indicate distinctly different species of P−O and Ge−O bonds. The model for the increase of N_GeO which is based on an increase of the fraction of GeO₆ units, at the expense of GeO₄ units, is supported by the analysis of the two main components of the Ge−O peak used in the fits. However, the existence of a GeO₅ fraction cannot be excluded from the present data sets. A linear relation between the total Ge−O coordination numbers and mean Ge−O distances exists, assuming end members of units GeO₄ and GeO₆ with bond lengths of ∼0.175 and ∼0.190 nm, respectively.     

Study of synthetic hydroxyapatite by the method of high-resolution transmission electron microscopy: Morphology and growth direction

Hydroxyapatite crystals grown from aqueous solutions have been studied by the methods of high-resolution electron microscopy and transmission electron diffraction. Processing of the experimental electron micrographs with the use of the Digital Micrograph program and the study of the corresponding Fourier trans-forms showed that the submicron microcrystals grow mainly along the [0001] direction. The (0001) and the $(01\bar 10)$ planes are perpendicular and parallel to the long edge of the crystals, respectively. The good accord between the experimental electron-microscopy images and the electron microscopy images calculated by the EMS program was attained only for crystals with the thicknesses ranging from one to five lattice periods. This allows us to state that hydroxyapatite grows from aqueous solutions in the form of very thin (with the thickness of the order of several lattice parameters) platelike crystals.     

Structure analysis by reduced data. IV. IEM—A new program for refinement of structure models of crystals

A new program for the refinement of models of atomic structures by the X-ray, neutron, and electron diffraction data has been described. The program is based on a special form of the goal function including the term responsible for minimizing the difference between the normalized measurements [the interexperimental minimization (IEM) method] and the adaptive nonlinear algorithm of minimization based on the Lavrent’ev-Levenberg-Marquardt regularization. As a result, it became possible to determine a new solution to the problem different from that obtained by the classical least squares method. To a large extent, the program allows one to overcome the effect of parameter correlations on the procedure of refinement and the results obtained. The test of the program on 17 experimental data sets showed the fast and stable convergence in all the cases. Under the identical initial conditions, the new program provided lower reliability factors for most of the crystals studied.     

Structure of potassium germanophosphate glasses by X-ray and neutron diffraction: 3. Reverse Monte Carlo simulations

Reverse Monte Carlo (RMC) is used to investigate the origin of the first sharp diffraction peaks (FSDP) found for K₂O–GeO₂–P₂O₅ glasses at very small scattering vector Q = ～7.5 nm^?1. Structures of the ternary glass with the greatest intensity of FSDP (KGeP5 – 25/50/25 mol% K₂O/GeO₂/P₂O₅), of the binary combinations of the three oxides and of vitreous GeO₂ are modeled. Results are deduced from comparisons of the partial structure factors and inspections of model sections. The P sites are uniformly distributed in the structure of KGeP5. The K⁺ ions interact more with the PO₄ units (via O_T-corners) than with Ge-centered units. Main component of the FSDP comes from the S_GeGe(Q) factor. The FSDP is due to separations of ～1 nm between the longish Ge-rich clusters which are visible in the corresponding models. Different to our tentative structural models reported before, the PO₄ tetrahedra possess a broad distribution of numbers of O_T corners. The FSDP’s of the binary K₂O–GeO₂ and K₂O–P₂O₅ glasses (～10 nm^?1) are due to a chemical order between network former and network modifier regions. The MRO of a mixed GeO₂–P₂O₅ glass of small P₂O₅ content (FSDP at ～16 nm^?1) shows great similarity to the MRO of vitreous GeO₂.