Two-dimensional X-ray diffraction refers to X-ray diffraction applications with two-dimensional detector and corresponding data reduction and analysis. The two-dimensional diffraction pattern contains far more information than a one-dimensional profile collected with the conventional diffractometer. In order to take advantage of two-dimensional diffraction, new theories and approaches are necessary to configure the two-dimensional X-ray diffraction system and to analyze the two-dimensional diffraction data. This paper is an introduction to some fundamentals about two-dimensional X-ray diffraction, such as geometry convention, diffraction data interpretation, and advantages of two-dimensional X-ray diffraction in various applications, including phase identification, stress, and texture measurement.

This study was performed to suggest convenient equations for quantifying Fe and K within the illite structure using relative intensities for the illite basal reflections. The 002/005 and 003/005 ratios were available for Fe and K quantifications, and equations could be derived as the following: CFe=(ln I002/005−1.807 ln I003/005+1.29)/(1.241 ln I003/005−3.843), CK=−(ln I002/005+0.121 ln I003/005−2.592)/(1.308 ln I003/005+1.984). The equations may obtain Fe and K contents within ca. ±0.05 atoms per half-unit cell, if incident radiation loss is minimized and basal reflection modification caused by expandable layers is eliminated. © 2004 International Centre for Diffraction Data.

Two-phase polycrystalline powder mixtures of YBa2Cu3O7−δ (YBCO) and xBaCuO2 (x=0, 0.05, 0.1, 0.2, and 0.3) were prepared by solid reaction. The Rietveld refinements of X-ray powder diffraction data show that BaCuO2 addition was successfully produced in superconductor YBCO and the unit-cell parameters of YBCO reach a maximum at x=0.05. The critical current density (Jc) also reaches a maximum at x=0.05 and then decreases sharply with increasing amount of BaCuO2. The change of Jc as a function of x was found to be similar to those of the unit-cell parameters. The characteristic behavior of Jc may come from the structure-parameter change of YBCO caused by BaCuO2 addition.

Methods of chemical preparation and crystal data are reported for four new condensed phosphates: two hydrated cyclotriphosphates with a general formula SrMIP3O9⋅3H2O (MI=K+,Tl+) and their corresponding anhydrous cyclotriphosphates SrMIP3O9 (MI=K+,Tl+). The two hydrated condensed phosphates, SrKP3O9⋅3H2O and SrTlP3O9⋅3H2O, belong to previously investigated structure types. SrKP3O9⋅3H2O and SrTlP3O9⋅3H2O are orthorhombic, Z=4, space group Pnma, with respectively the following unit-cell dimensions: a=9.082(2) Å, b=8.133(2) Å, c=15.009(2) Å, M(20)=49, F(25)=61(0.0052;79) and a=9.115(7) Å, b=8.139(7) Å, c=15.221(2) Å, M(20)=285, F(30)=522(0.000 411;140). SrKP3O9 and SrTlP3O9 are monoclinic, space group P21/m or P21, Z=4, with, respectively, the following unit-cell dimensions: a=14.957(1) Å, b=8.372(1) Å, c=7.909(1) Å, β=102.27(1)°, M(20)=81, F(24)=95(0.000 025;92) and a=14.544(2) Å, b=8.639(1) Å, c=7.727(1) Å, β=102.05(1)°, M(20)=66, F(30)=78(0.003 098;125).

Direct methods and Rietveld analysis were applied to high-resolution synchrotron X-ray powder diffraction data to solve the crystal structure of dicalcium chromate hydrate (Ca2CrO5⋅3H2O). The compound crystallizes in monoclinic symmetry (space group Cm, Z=2), with a=8.23575(5) Å, b=7.90302(4) Å, c=5.20331(3) Å, and β=98.0137(3)°. The structure is built from double-layers of CrO4 tetrahedra and CaO8 polyhedra that run parallel to the (001) plane.

The X-ray powder diffraction patterns for three 4-tert-butylcalix(4)arenes were determined. The similarity and differences between them were compared and discussed.

A new polymorph of HfMo2O8 (β-form) is synthesized under high pressure and high temperature conditions. The powder X-ray diffraction (XRD) data could be explained based on a monoclinic lattice (Space Group: C2/c No. 15) with the unit cell parameters as: a=11.415(3), b=7.906(2), c=7.438(2) Å and β=122.37(2)°, V=566.9(2) Å3. The detailed powder XRD data and analysis are reported herein.

Na4CrNi(PO4)3 orthophosphate powder was prepared from acid solutions of NiO, Na2CO3 and aqueous solutions of Cr(NO3)3.9H2O, and (NH4)2HPO4 at a final temperature of 750 °C. The hexagonal unit cell parameters were determined to be ah≈8.789 Å and ch≈21.481 Å in space group R3¯c. These parameters were compared to those of Na4AA′(PO4)3 (AA′=CrMg, CrCo, TiNa, ZrNa). The linear variations of these parameters versus the mean A cation radius (rAA′) are consistent with the atomic distribution found for the structure of Na4NiCr(PO4)3. The ah and ch parameters are functions of the An+ ion size.

Materials with systematic absence of X-ray diffraction (XRD) peaks are desirable for conducting some special researches using X-ray diffraction or time-resolved X-ray scattering. This paper proposes a method for designing this kind of materials. It utilizes solid solution to reduce the structure factor of a selected reflection to zero by choosing proper components and their contents to let the reflection amplitudes from different atomic layers in a unit cell of the solid solution cancel each other completely. This method on how to select a solid solvent and how to calculate its content was illustrated using SrTiO3 as an example. A solid solution Sr1−xCaxTiO3 with a systematic absence of the (001) diffraction can be designed, and the value of x can be determined to be x=0.54 using an iteration calculation process. This result was verified by the experimental XRD pattern of a Sr0.46Ca0.54TiO3 sample.

Methods of chemical preparation and crystal data are reported for two new anhydrous cyclotriphosphates MIIK4(P3O9)2 (MII=Co2+ and Mn2+). These anhydrous cyclotriphosphates CoK4(P3O9)2 and MnK4(P3O9)2 were obtained by total dehydration of corresponding hydrated cyclotriphosphates CoK4(P3O9)2.7H2O and MnK4(P3O9)2.2H2O. CoK4(P3O9)2 is triclinic, space group P−1, Z=1 with the following unit-cell dimensions: a=6.29(3) Å, b=8.00(1)Å, c=13.05(8)Å, α=86.03(5)°, β=98.00(1)°, γ=68.11(2)°. MnK4(P3O9)2 crystallizes in the rhombohedral system, space group P−31c, Z=2 with the following unit-cell dimensions: a=b=7.337(3)Å, c=19.920(1)Å.

The Rietveld method allows a precise quantitative phase analysis of building materials. Thanks to the development of stable-functioning software and the use of high-performance detectors, a quantitative phase analysis by X-ray, including sample preparation, and measurement and evaluation, can be performed in fewer than ten minutes. This has made it possible to integrate the method into existing laboratory automation systems for process and quality control to provide a means of online monitoring. Due to the completely automated operating principle of the Rietveld software, no additional staff is required and the results are user-independent. The Rietveld method is now being employed in industrial laboratories and also in various cement plants owned by the Lafarge Group as the standard method of quantitative analysis of Portland Cement clinkers and Portland Cements (CEM I, CEM II A-L).

PLZT of the compositions 0≤L≤12, and 0≤T≤10 was studied in order to describe the structure of the phases as a function of composition. This range contains a mixed region with PLZT+La2Zr2O7, an orthorhombic, a rhombohedral (hexagonal) phase, a tetragonal phase, and a mixture of different PLZT phases. Each phase pure composition is described by X-ray diffraction.

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.

Two new bimetallic and trimetallic compounds (NH4)1.5Ni2V2O7(OH)1.5 · H2O and (NH4)1.5Cu1.125 Ni1.125V2O7(OH)2 · H2O were synthesized by hydrothermal method and characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), thermogravimetric analysis (TGA), and X-Ray fluorescence (XRF). Crystallographic studies showed that both compounds are hexagonal with space group P-62c.

Rietveld neutron powder profile analysis of the (Na1−xKx)0.5Bi0.5TiO3 (NKBT) series (x=0, 0.2, 0.4, 0.5, 0.6, 0.8, 1.0) is reported over the temperature range 293–993 K. A detailed characterization of the structures and phase transitions occurring across this series as a function of temperature has been made. Room-temperature refinements have revealed a rhombohedral phase, space group R3c for x=0, 0.2, and 0.4, which exhibits an antiphase, a−a−a− oxygen tilt system with parallel cation displacements along [111]p. An intermediate zero-tilt rhombohedral phase, space group R3m possessing cation displacements along [111]p, has been established for x=0.5 and 0.6. At the potassium-rich end of the series at x=0.8 and 1.0, a tetragonal phase, space group P4mm is observed possessing cation displacements along [001]. At the sodium-rich end of the series for x=0.2, the unusual tetragonal structure with space group P4bm is seen for Na0.5Bi0.5TiO3 which possesses a combination of in-phase a0a0c+ tilts and antiparallel cation displacements along the polar axis. Temperature-induced phase transitions are reported and structural modifications are discussed.

The laboratory implementation of grazing incidence in-plane X-ray diffraction, using an unmodified commercial diffractometer, is described. Low resolution, high intensity measurements are illustrated in the study of the in-plane lattice parameters and texture of a thin polycrystalline ZnO film on glass, the in-plane order in Cd arachidate Langmuir–Blodgett films, and the depth dependence of the lattice parameter in graded Si–Ge epilayers. Use of an asymmetrically cut Ge crystal to compress and monochromate the beam provides a high resolution setting, appropriate to measurement of the in-plane mosaic of mismatched epilayers such as GaN on sapphire.

Five new aliphatic-aromatic thiodiols: 1,2-bis[4-(2′-hydroxyethylthio)phenyl]ethane (C18H22O2S2), 1,2-bis[4-(3′-hydroxypropylthio)phenyl]ethane (C20H26O2S2), 1,2-bis[4-(6′-hydroxyhexylthio)phenyl]ethane (C26H38O2S2), 1,2-bis[4-(10′-hydroxydecylthio)phenyl]ethane (C34H54O2S2), 1,2-bis[4-(11′-hydroxyundecylthio)phenyl]ethane (C36H58O2S2) have been characterized by X-ray powder diffraction. These thiodiols can be used for synthesis of thermoplastic nonsegmented polyurethanes. Experimental 2θ peaks positions, relative peak intensities, values of d and Miller indices as well as unit cell parameters are reported.

The crystal structure of the common expectorant guaifenesin, 3-(2-methoxyphenoxy)-1, 2-propanediol (C10H14O4) was solved by applying Monte Carlo simulated annealing techniques to synchrotron powder data, and refined using the Rietveld method. Initial structure solutions yielded an unreasonable conformation, and an unacceptable refinement. Quantum chemical geometry optimizations were used to identify the correct conformation. Guaifenesin crystallizes in the orthorhombic space group P212121 (#19), with a=7.657 05(7), b=25.670 20(24), c=4.979 66(4) Å, V=978.79(2) Å3, and Z=4. Both hydroxyl groups act as hydrogen bond donors and acceptors, resulting in the formation of a two-dimensional network of strong hydrogen bonds in the ac plane. The solid state conformation is ∼4 kcal/mol higher in energy than the minimum-energy conformation of an isolated molecule, but the formation of the hydrogen bonds results in an energy gain of ∼100 kcal/mol. Knowledge of the crystal structure permits quantitative phase analysis of guaifenesin-containing pharmaceuticals (such as Duratuss GP 120-1200) by the Rietveld method.

Transparent p-type conducting Ga-doped SnO2 thin films were prepared using reactive rf-magnetron sputtering. Good p-type conduction was directly realized without the need of postdeposition annealing. The p-type conductivity was found to be very sensitive to the growth condition and process, suggesting that the carrier behavior is strongly related to the fine microstructure of the films. The microstructures of the films were characterized using synchrotron X-ray diffraction and specular reflectivity techniques. The valence state of the Ga dopant was measured from X-ray photoelectron spectra to explain the origin of net holes presented in the films.