The structure of a birefringent andradite–grossular sample was refined using single-crystal X-ray diffraction (SCD) and synchrotron high-resolution powder X-ray diffraction (HRPXRD) data. Electron-microprobe results indicate a homogeneous composition of {Ca2.88Mn2+0.06Mg0.04Fe2+0.03}Σ3[Fe3+1.29Al0.49Ti4+0.17Fe2+0.06] Σ2(Si2.89Al0.11) Σ3O12. The Rietveld refinement reduced χ2 = 1.384 and overall R (F2) = 0.0315. The HRPXRD data show that the sample contains three phases. For phase-1, the weight %, unit-cell parameter (Å), distances (Å), and site occupancy factor (sof) are 62.85(7)%, a = 12.000 06(2), average <Ca–O> = 2.4196, Fe–O = 1.9882(5), Si–O = 1.6542(6) Å, Ca(sof) = 0.970(2), Fe(sof) = 0.763(1), and Si(sof) = 0.954(2). The corresponding data for phase-2 are 19.14(9)%, a = 12.049 51(2), average <Ca–O> = 2.427, Fe–O = 1.999(1), Si–O = 1.665(1) Å, Ca(sof) = 0.928(4), Fe(sof) = 0.825(3), and Si(sof) = 0.964(4). The corresponding data for phase-3 are 18.01(9)%, a = 12.019 68(3), average <Ca–O> = 2.424, Fe–O = 1.992(2), Si–O = 1.658(2) Å, Ca(sof) = 0.896(5), Fe(sof) = 0.754(4), and Si(sof) = 0.936(5). The fine-scale coexistence of the three phases causes strain that arises from the unit-cell and bond distances differences, and gives rise to strain-induced birefringence. The results from the SCD are similar to the dominant phase-1 obtained by the HRPXRD, but the SCD misses the minor phases.

GSAS instrument parameters are tabulated for a variety of laboratory and synchrotron diffractometers to give users an idea of the typical ranges of profile parameters when they generate their own instrument parameter files. For modern high-resolution laboratory diffractometers, the parameters fall in the ranges 0<U<3, V=0, 0<W<4, 1<X<3, 0<Y<3, 1<asym<3, and 0<S/L<0.03. For synchrotron diffractometers, the parameters fall in the ranges 0<U<1.2, −1<V<0, 0<W<1, 0<X<1, 0<Y<1, 0<asym<0.5, 0<S/L<0.001, and 0<H/L<0.007. FULLPROF equivalents are also reported. The factors which are convoluted together to generate the instrument profile are described.

X-ray diffraction analysis on small samples or micro-area of large samples is always a challenge due to weak diffraction and poor statistics, especially when dealing with samples containing large grain size, inhomogeneous phase distribution, and preferred orientation. Two-dimensional X-ray diffraction has many advantages in microdiffraction analysis. A two-dimensional detector can collect a large amount of data both in terms of speed and angular coverage. This paper covers some aspects about instrumentation of two-dimensional X-ray diffraction and its applications in phase identification and stress analysis on small samples and micro-area of large samples.

An interlaboratory study (ILS, round robin) was conducted to assess the accuracy and precision of the phase quantification of calcium phosphate (CaP) bioceramics by X-ray diffraction (XRD) and Rietveld refinement. For that purpose, a mixture of hydroxyapatite and β-tricalcium phosphate, two CaP phases commonly used in synthetic bone graft substitutes, was prepared and sent to 12 laboratories for XRD analysis. Results from 26 different instruments were received and evaluated statistically according to ASTM E691 – 13. The statistical analysis revealed that the reproducibility standard deviation of phase quantities was approximately two times greater than the repeatability standard deviation, which is obtained by repeating the analysis on a single instrument configuration multiple times. The 95% reproducibility limit for phase quantities was R = ±1.67 wt%. The study also demonstrated that several participants overinterpreted their data in an attempt to refine crystallite sizes of the minor phase.

Without experimental or predicted literature crystal structures for succinonitrile at low temperature, structure solution was attempted from powder diffraction data taken at 173 and 90 K from a solid sample. Its room-temperature plastic-crystal state makes production of a sample with good particle statistics and random orientation almost impossible. Combining constrained models, simulated annealing, and careful application of second-order spherical harmonic corrections nevertheless produced viable-looking structures at 90 and 173 K, yielding two distinct structure models with the same projection down c. VASP optimization of atom coordinates in the experimental cell agreed well with the 90 K model but poorly with the model derived from the 173 K data. The refined 90 K structure changed little on optimization and fitted all datasets from 85 to 225 K. Plots of cell data, torsion angles, and isotropic displacement parameters against temperature suggest possible phase transitions around 100, 120, and 180 K. Cell data at 90 K: monoclinic P21/a, a=9.0851(5) Å, b=8.5617(5) Å, c=5.8343(3) Å, β=79.295(2)°, and Z=4. Succinonitrile has gauche conformation, in agreement with literature spectroscopy 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.

Since Boeke's finding of a reversible phase transition of calcite (calcium carbonate, CaCO3) at elevated temperatures [Boeke, H. E. (1912). Neues Jahrb. Mineral. 1, 91–121], and following W. L. Bragg's determination of the structure of the room-temperature Phase I [Bragg, W. L. (1914). Proc. R. Soc. Lond. A 89, 468–489.], the high-temperature Phase V of calcite has been an enduring mystery. Here, we summarize a paper on the structure of Phase V [Ishizawa, N., Setoguchi, H. and Yanagisawa, K. (2013). Sci. Rep. 3, 2832], as well as the intermediate Phase IV which exists between Phases I and V, and add new aspects. An in situ single-crystal X-ray diffraction study revealed that the I–IV and IV–V transitions occurred reversibly at approximately 985 and 1240 K, respectively, in a carbon dioxide atmosphere. Phase V was stable only over a narrow temperature range between 1240 and 1275 K. The crystal decomposed immediately at temperatures above 1275 K, leaving a nanoporous calcium oxide reaction product which retained the shape of the parent calcite crystal. The I–IV transition can be described as an orientational order/disorder transition of the carbonate group, occurring within the same space group $R\bar 3c$. In Phase V, the oxygen sublattice is melted. The joint-probability density function obtained from the anharmonic atomic displacement parameters of the oxygen atoms revealed that the oxygen triangles of the carbonate group in Phase V do not sit still at specified Wyckoff positions in the space group $R\bar 3m$, but are instead distributed with equal probability along the undulated circular orbital about the central carbon. The carbonate group in Phase V is no longer flat on the basal plane when the oxygen triangle comes to troughs or peaks in the undulated orbital, but is instead deformed like an umbrella. Assuming that the oxygen triangle migrates about carbon, the carbonate group should repeat the umbrella inversion in Phase V as a function of time. Finally, possible thermal decomposition mechanisms of calcite are briefly discussed.

Amino acids often cocrystallize with water molecules, which make them pseudopolymorphs of their anhydrous forms. In this work, we discuss in detail the hydrogen bond patterns in anhydrous L-proline and DL-proline and its pseudopolymorphic forms: L-proline monohydrate and DL-proline monohydrate. For this propose, the crystal structure of L-proline anhydrous was determined from synchrotron X-ray powder diffraction data and refined using the Rietveld method. Special emphasis is given to the role played by the water molecule in the hydrogen bond network observed in the crystalline structures.

The importance of software continues to grow for all areas of scientific research, no less for powder diffraction. Knowing how to program a computer is a basic and useful skill for scientists. This paper explains the three approaches for programming languages and why scripting languages are preferred for non-expert programmers. The Python-scripting language is extremely efficient for science and its use by scientists is growing. Python is also one of the easiest languages to learn. The language is introduced, as well as a few of the many add-on packages available that extend its capabilities, for example, for numerical computations, scientific graphics, and graphical user interface programming. Resources for learning Python are also provided.

Novel plate-stratiform nanostructured Bi12O17Cl2 was studied with its visible-light photocatalytic performance. The Bi12O17Cl2 photocatalyst synthesized by a solid-state reaction was constructed of dozens of primary nanosheets, which were stacked by a parallel array of ultrathin secondary nanosheets. The microstructure and crystal structure of Bi12O17Cl2 primary and secondary nanosheets were discovered by high-resolution transmission electron microscopy and selected-area electron diffraction analyses. Its absorption edge was determined as about 590 nm and the band gap energy was 2.1 eV. The Bi12O17Cl2 nanomaterial exhibited superior visible-light-responsive photocatalytic activity and confirmed successful photodegradation of methyl orange (MO) under visible-light irradiation. The degradation efficiency was up to 97% in 90 min. Furthermore, the Bi12O17Cl2 photocatalyst exhibited excellent photostability and high mineralization capacity for MO photodegradation reaction. The MO photodegradation process was dominated by the direct photocatalytic mechanism. The contribution from its morphology and microstructure to superior photocatalytic activity was discussed.

A computer program is presented that allows for the merging of diffraction patterns collected at multiple positions on the Powder Diffraction beamline of the Australian Synchrotron. It is also generally applicable to detector systems based on other modular detectors. The program allows for the interpolation of data to a constant 2θ step size and to normalise intensities to beam current and/or monitor count rate.

ZnGa2Te4 was found to crystallize in a defect tetrahedral structure with possible space group I4(82) with Z=2. Complete X-ray powder diffraction data were obtained and the unit cell parameters a and c and X-ray density were calculated. These were a=0.5930(1) nm, c=1.1859(3) nm, and Dx=5.7×103 kg/m3.

Indexed X-ray powder diffraction data are reported for the homologous compound (ZnO)5(In1−xYx)2O3. The structures of (ZnO)5In2O3 and of (ZnO)5(In1−xYx)2O3 were refined by the Rietveld technique on the basis of the space group R3¯m. Refined unit cell dimensions are a=3.3285(1) Å, c=58.127(2) Å, V=557.71(3) Å3, Dx=6.11 g/cm3, Rwp=10.52, RB=8.56 for (ZnO)5In2O3, and a=3.3505(1) Å, c=57.863(1) Å, V=562.53(2) Å3, Dx=5.97 g/cm3, Rwp=9.05, RB=6.94 for (ZnO)5(In0.8Y0.2)2O3. The structure of (ZnO)5In2O3 was shown to be isostructural with (ZnO)5LuFeO3. Y3+ ions were determined to be arranged at the 3a-metal sites substituting for In3+ ions.

Synchrotron X-ray diffraction was used to monitor the hydrothermal precipitation of akaganeite (β-FeOOH) and its transformation to hematite (Fe2O3) in situ. Akaganeite was the first phase to form and hematite was the final phase in our experiments with temperatures between 150 and 200 °C. Akaganeite was the only phase that formed at 100 °C. Rietveld analyses revealed that the akaganeite unit-cell volume contracted until the onset of dissolution, and subsequently expanded. This reversal at the onset of dissolution was associated with a substantial and rapid increase in occupancy of the Cl site, perhaps by OH− or Fe3+. Rietveld analyses supported the incipient formation of an OH-rich, Fe-deficient hematite phase in experiments between 150 and 200 °C. The inferred H concentrations of the first crystals were consistent with “hydrohematite.” With continued crystal growth, the Fe occupancies increased. Contraction in both a- and c-axes signaled the loss of hydroxyl groups and formation of a nearly stoichiometric hematite.

XLENS is a traditional direct methods program working exclusively in reciprocal space. The distinctive feature of XLENS is the use of the modulus sum function as target function for the phase refinement. Due to its efficiency, robustness, and no need of weighting schemes, this function is specially well suited for treating powder diffraction data. The mathematical basis as well as the significance of the most important control parameters of the program will be described here. To illustrate how XLENS works, three different examples will be shown. Due to its simplicity, the modulus sum function can be easily combined with real-space filtering procedures to produce even more efficient crystal structure solving strategies.

The crystal structures of some nickel hexacyanoferrates (II, III), including mixed compositions containing Na+, K+ and Cs+, were resolved and refined from XRD powder patterns. Data from infrared, Mössbauer and adsorption techniques provided complementary structural information. The crystal structures of Ni3[Fe(CN)6]2⋅16H2O and NiCs2[Fe(CN)6] were refined in space group Fm3m. NiNa2[Fe(CN)6]⋅2H2O and NiK2[Fe(CN)6]⋅2H2O were found to be orthorhombic (space group Pmn21). This structure (Pmn21) results from a distortion around the alkali ion, which appears as a monohydrated interstitial species. On ionic exchange in an aqueous solution containing Cs+, the orthorhombic distortion disappears and the cubic cell is obtained. Cs+ is a large cation and space is not available for interstitial water molecules. This orthorhombic model is also supported by the Mössbauer spectra of the ferrous analogs, FeK2[Fe(CN)6]⋅xH2O and Fe[Pt(CN)6]. © 2004 International Centre for Diffraction Data.

Detailed structural properties of La1−xBaxCoO3 (LBCO) have been investigated by means of X-ray powder diffraction and Rietveld analysis. A structural phase transformation from R3c to Pm3m at x=0.30–0.35 has been detected based on a comparison between the refinements of R3c and Pm3m. The Co–O bond length of the CoO6 octahedron expanded rapidly with increasing Ba content when x<0.1, and then it leveled off and kept constant at 0.1⩽x⩾0.35, where the Co–O–Co bond angle reaches 180°. The Co–O bond length expansion resumed with increasing Ba content beyond x=0.35.

Bright apple green millimeter-sized crystals of tavorite from the Tip Top pegmatite, near Custer, South Dakota are triclinic, space group , with refined unit-cell parameters a = 5.340(2), b = 7.283(2), c = 5.110(2)Å, α = 109.29(2)°, β = 97.86(3)°, γ = 106.32(3)°, V = 174.1(3)Å3, a:b:c = 0.7332:1:0.7016, Z = 2, D(m) (suspension in methylene iodide) = 3.32(1) and D(x) = 3.33 g/cm3 (for the theoretical formula). A fully indexed X-ray powder pattern is presented. Semiquantitative electron microprobe and secondary ion mass spectroscopic analyses indicate a formula near end-member LiFe + 3(PO4)(OH). The Tip Top tavorite is biaxial positive, α = 1.795(5), β = 1.81(1), γ = 1.86(1), 2V(meas.) = 50(2)°, 2V(calc.) = 59°, XΛa ≃ 15°, YΛb ≃ 0°, and ZΛc ≃ 38°. There is no evidence for optical absorption, pleochroism or dispersion.

The crystal structures of calcium citrate hexahydrate, calcium citrate tetrahydrate, and anhydrous calcium citrate have been solved using laboratory and synchrotron X-ray powder diffraction data, and optimized using density functional techniques. Both the hexahydrate and tetrahydrate structures are characterized by layers of edge-sharing Ca coordination polyhedra, including triply chelated Ca. An additional isolated Ca is coordinated by water molecules, and two uncoordinated water molecules occur in the hexahydrate structure. The previously reported polymorph of the tetrahydrate contains the same layers, but only two H2O coordinated to the isolated Ca and two uncoordinated water molecules. Anhydrous calcium citrate has a three-dimensional network structure of Ca coordination polyhedra. The new polymorph of calcium citrate tetrahydrate is the major crystalline phase in several commercial calcium supplements.

The crystal structures of two manganese hexacyanometallates(II), Mn2[Fe(CN)6].8H2O and Mn2[Os(CN)6].8H2O, were refined from X-ray powder diffraction data using the Rietveld method, with the reported structure for Mn2[Ru(CN)6].8H2O used as a structural model. These compounds are isomorphous and crystallize in the monoclinic space group P21/n. Their crystallization water is not firmly bound and can be removed without disrupting the M–C≡N–Mn network. In the dehydrated complexes, the outer cation (Mn) remains linked to only three N atoms from CN ligands while the inner cation (Fe,Os) preserves its coordination sphere. The IR, Raman, and Mössbauer spectra for the hydrated and anhydrous forms are explained based on the refined structures.