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.

Two-dimensional proportional detectors with their faster data collection, large dynamic range, and more available information than point or linear proportional detectors make them ideal for microdiffraction analysis. The unique capabilities of these detectors coupled with a rotating anode source, capillary optics, and a variety of accessories allow for a wide range of applications.

Silver halide based photographic imaging elements have been utilized as detectors for X-rays for over 100 years. These elements comprised of gelatin dispersed silver halide coated on one or both sides of a support, have been utilized in diffraction experiments since the discovery of X-ray diffraction by Laue and co-workers. X-ray film has high spatial resolution and can be adapted to flat or curved two-dimensional detection geometries. This paper describes the use of X-ray film as a two-dimensional detector for X-ray diffraction analysis, and discusses X-ray film composition, exposure, and processing, along with considerations for analyzing X-ray diffraction data collected using X-ray film.

Advances in X-ray texture solutions require new methods and descriptions for the texture analysis process, e.g., when using general area detector diffraction systems. A new method is presented that defines a general pole figure resolution and provides the possibility to optimize strategies for efficient pole figure data collection. Application of the new method improves resolution and (!) speed. New software enables simultaneous monitoring of pole and detector space. This allows a fundamentally better understanding of the collected information, e.g., in situations where peaks overlap or high backgrounds compromise data quality.

A novel sealed gaseous parallel plate avalanche chamber detector is described which is significantly less prone to discharges and can consequently achieve high gas gains at high counting rates. The detector has demonstrated stable gains greater than 104 at counting rates in excess of 107 counts/mm2 s.

To test the effectiveness of phase identification software, a two-stage search/match round robin using powder X-ray diffraction data was organized, through the internet and world wide web. The first stage provided powder patterns and a vague sample origin, the second stage provided the chemistry and sample history. While the statistics are not robust, it shows that routine phase identification without chemistry can be performed, providing effective modern third generation search/match software is used; the most up to date databases are available; and well trained, experienced scientists perform the analysis.

Results of Rietveld refinement for indium nitride data collected in the temperature range 105–295 K are presented. Acicular microcrystals of indium nitride prepared by reaction of liquid indium with nitrogen plasma were studied by X-ray diffraction. The diffraction measurements were carried out at the Swiss-Norwegian Beamline SNBL (ESRF) using a MAR345 image-plate detector. Excellent counting statistics allowed for refinement of the lattice parameters of InN as well as those of the metallic indium secondary phase. In the studied temperature range, the InN lattice parameters show a smooth increase that can be approximated by a linear function. Lattice-parameter dependencies confirm the trends indicated earlier by data measured using a conventional equipment. The relative change of both the a and c lattice parameters with increasing the temperature in the studied range is about 0.05%. The axial ratio slightly decreases with rising temperature. The experimental value of the free structural parameter, u=0.3769(14), is reported for InN for the first time. Its temperature variation is found to be considerably smaller than the experimental error. The thermal-expansion coefficients (TECs), derived from the linearly approximated lattice-parameter dependencies, are αa=3.09(14)×10−6 K−1 and αc=2.79(16)×10−6 K−1. The evaluated TECs are generally consistent with the earlier data. For the present dataset, the accuracy is apparently higher for both, the lattice parameters and thermal-expansion coefficients, than for the earlier results. The refined lattice parameter cIn of the indium secondary phase exhibits the known strongly nonlinear behavior; a shift (ΔT equal about −50 K) of the maximum in cIn(T) dependence is observed with respect to the literature data.

Ba(3−x)Srx(PO4)2 orthophosphates (0≤x≤3) have been prepared by solid state reaction. The final temperature was 1000°C. The X-ray diffraction analyses show the existence of a continuous solid solution. Ba(3−x)Srx(PO4)2 orthophosphates (0≤x≤3) crystallize in the hexagonal system with the space group R3m. Their structure is based on a three-dimensional framework constructed of infinite layers of Ba1/Sr1O12 linked and parallel to infinite layers of Ba2/Sr2O10 polyhedra and PO4 tetrahedra.

The crystal structures of the chiolite-related room temperature phases α-Na5M3F14 (MIII=Cr,Fe,Ga) are determined. For all of them, the space group is P21/n, Z=2; a=10.5096(3) Å, b=7.2253(2) Å, c=7.2713(2) Å, β=90.6753(7)° (M=Cr); a=10.4342(7) Å, b=7.3418(6) Å, c=7.4023(6) Å, β=90.799(5)° (M=Fe), and a=10.4052(1) Å, b=7.2251(1) Å, c=7.2689(1), β=90.6640(4)° (M=Ga). Rietveld refinements produce final RF factors 0.036, 0.033, and 0.035, and RWP factors, 0.125, 0.116, and 0.096, for MIII=Cr, Fe, and Ga, respectively. The MF6 polyhedra in the defective isolated perovskite-like layers deviate very few from perfect octahedra. Subtle octahedra tiltings lead to the symmetry decrease from the P4/mnc space group adopted by the Na5Al3F14 chiolite aristotype to the P21/n space group adopted by the title series. Facile twinning precluded till now the precise characterization of these compounds.

Rietveld refinement of LixCoO2-type cathodes (where x=0.59–1.00) has been demonstrated to yield quantitative information about the Li occupancy with an error of about ∼10%. With careful X-ray diffraction (XRD) data collection, refinement, and proper calibration, accurate values can be obtained. Rietveld refinement tends to under-predict the Li occupancy values in charged (de-lithiated) cathodes as compared to ICP measurements. A Li-gradient model that assumes a decreasing concentration of Li from the particle core to its surface is discussed to explain this observation. The observed lattice parameters for the fully lithiated LiCoO2 standard phase (R-3m symmetry) were a=2.8155(1) Å, c=14.052(1) Å. The error convention used in this paper is 3σ of standard deviations obtained from Rietveld refinement output.

X-ray powder diffraction data for the anticancer drug PtCl2(C2H3O2)2(C6H13N)(NH3) are reported. The crystal structure of PtCl2(C2H3O2)2(C6H13N)(NH3) obtained from a Rietveld refinement are: space group P21/a, a=13.547(2) Å, b=8.260(1) Å, c=14.638(3) Å, β=110.429(2)°, V=1534.96 Å3, Z=4 and Dcalc.=2.068 Mg/m3.

Two novel copper and iron chelates have been studied by powder diffraction. The cell parameters for triclinic (space group P 1 (2)) C25H21CuN3SO4 are a=9.636(2) Å; b=11.014(1) Å; c=11.233(3) Å; α=83.55(2); β=82.45(6); γ=76.36(2); Z=2; Dx=1.456 g cm−3. The monoclinic cell parameters (space group P 21/c (14)) for C40H30Cl4Fe2N8S2 are a=11.464(8) Å; b=17.462(1) Å; c=20.550(6) Å; β=103.534(1); Z=2; Dx=1.356 g cm−3.

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.

Powder diffraction pattern of SP-1 graphite has been obtained using synchrotron X-ray diffraction. Unit cell dimensions were calculated using a least-squares analysis that refined to a |Δ2θ°| of no more than 0.007. A hexagonal cell was determined with a space group of P63/mmc (194), a=2.4617(2) and c=6.7106 (4) Å. The Smith/Synder figure of merit is 167 based upon 11 peaks, which indicates that the quality of this data set is superior to the existing PDF card for graphite, 41-1487. It is also emphasized that the interlayer spacing of graphite should be 3.355(1) Å. Using GAS and EXPGUI codes, a new set of calculated powder diffraction data based upon the interlayer spacing of 3.555 Å is generated. A comparison with the current calculated card, 75-1621, has also been made.

Improved X-ray powder diffraction data for orthorhombic phosphorus, S.G. C mca (64) obtained in situ at synthesis conditions of 1.2 GPa and 1100 K, are described. Representative, as synthesized, data include 2.552X, 3.3204, 2.5953, 5.1912, 1.6302, for least-squares unit-cell a=3.3182(6) Å, b=10.3744(18) Å and c=4.3227(9) Å. As an illustration of the quality of the data, the structure was solved from powder XRD and Rietveld refined to give a=3.3199(2) Å, b= 10.3678(4) Å, c=4.3154(2)Å, and V=148.535(12) Å3 with the P atom on 8f (1/2, y,z) with y=0.1044(22) and z=0.9179(7).

The crystal structures of LaCo0.5Ni0.5O3−δ and LaCo0.5Fe0.5O3−δ solid solutions, studied by powder X-ray diffraction, were found to be rhombohedral perovskite. The unit cell parameters in the hexagonal setting are a=5.491(6) Å and c=13.231(3) Å for LaCo0.5Fe0.5O3−δ, and a=5.464(4) Å and c=13.125(3) Å for LaCo0.5Ni0.5O3−δ. The space group is R3c (No. 167).

The compound ammonium D-gluconate (C6H11O7−NH4+) has been studied by X-ray powder diffraction. The powder diffraction pattern and data obtained at room temperature are presented (cell data and powder data summary).