The fluorite-related anion-excess β-Pb1−xFexF2+x (0.25 ≤ x ≤ 0.27) orthorhombic crystal structure is approached from powder diffraction data. A 1 × 1 × 2 fluorite supercell is found to describe the main aspects of the structure, which would have ideally the Pb3FeF9 formula (x = 0.25) (space group Cmmm, a = 5.9926(1), b = 5.5781(1), c = 11.5208(3) Å), and would include a complete [FeF4]∝−1 perovskite plane, orthogonal to the c axis. However, there is large Pb substitution (44%) on the perovskite Fe site as well as Fe substitution (∼25%) on one of the two main Pb sites. A strong relationship with the fully ordered crystal structure of Pb8MnFe2F24, which can be expressed as Pb1−xMxF2+2/3x (x = 0.273), is discussed, suggesting that both phases may have infinite [M3F14]∝ ribbons in common.

The synthesis and X-ray powder diffraction data for the long-known CaSiF6 and CaSiF6·2H2O species are reported. Their crystal structures have been determined from laboratory powder diffraction data by simulated annealing and full-profile Rietveld refinement methods. CaSiF6·2H2O was found to crystallize in the monoclinic P21/n space group with unit-cell parameters: a = 10.48107(9), b = 9.18272(7), c = 5.72973(5) Å, β = 98.9560(6)°, V = 544.733(8) Å3, and Z = 4. The crystal structure of CaSiF6·2H2O, eventually found to be isomorphous with SrSiF6·2H2O (but not with the Mg analogue—a hexahydrate phase), contains centrosymmetric [Ca(μ-H2O)2Ca]4+ dimers, interconnected by hexafluorosilicate anions, in a dense 3D framework. The crystal structure is completed by a further water molecule, terminally bound to the Ca2+ ion, which, consequently, attains a F5O3 octacoordination. Thermodiffractometric measurements allowed the determination of the linear and volumetric thermal expansion coefficients of CaSiF6·2H2O, which showed a minor contraction, along a, on heating. CaSiF6 is trigonal, space group R-3, a = 5.3497(3), c = 13.5831(11) Å, V = 336.66(5) Å3, and Z = 3, and isomorphous with several other species of MIIAIVF6 or MIAVF6 formulation, among which several silicates, germanates, and stannates.

EXPO2011 is a new package for phasing crystal structures from powder diffraction diagrams. It is able to carry out all the steps necessary for crystal structure solution, from pattern indexation up to Rietveld method for structure refinement: for each step, the basic algorithm is described. Phasing is performed via ab initio (e.g., Direct Methods, integrated by real space refinement) and non ab initio techniques (e.g., simulated annealing algorithm, when molecular geometry is a priori known). Some emphasis is given to running procedures: the main commands and directives are described, to allow the user to run default and non-default phasing attempts.

The family of zeolitic imidazolate framework (ZIF) compounds is efficient sorbent materials that can be used for catalytic, ion exchange, gas storage, and gas separation applications. A high-resolution reference X-ray powder diffraction pattern for one of the ZIF members, bis(2-methylimidazolyl)-zinc, C8H10N4Zn (commonly known as ZIF-8), was determined using synchrotron diffraction data obtained at the Advanced Photon Source (APS) in Argonne, IL. The sample was confirmed to be cubic I-43m, with a = 17.01162(6) Å, V = 4932.08 Å3, and Z = 12. The reference X-ray powder diffraction pattern has been submitted for inclusion in the Powder Diffraction File (PDF).

A series of LiFe1−xZnxPO4 (0.0 ≤ x ≤ 1.0) compounds were prepared by solid-state reaction. Effects of the substitution of Zn for Fe on crystal structure and electrochemical properties of LiFe1−xZnxPO4 were investigated. The results show that single-phase regions of LiFe1−xZnxPO4 with orthorhombic (space group Pmna) and monoclinic (Cc) structures were found for the compounds with low Zn (or high Fe) contents of 0.0 ≤ x ≤ 0.30 and high Zn (or low Fe) contents of 0.90 ≤ x ≤ 1.0, respectively. The LiFe1−xZnxPO4 compounds with medium Zn (or Fe) contents of 0.35 ≤ x ≤ 0.80 are two-phase mixtures containing both the orthorhombic and the monoclinic phases. Systematic variations of unit-cell parameters a, b, c, and volume V with the Zn content determined by X-ray diffraction have also been obtained. Our electrochemical study show that the conductivity of LiFe1−xZnxPO4 increases by almost 2 orders of magnitude from 2.13 × 10−9 to 1.27 × 10−7 Scm−1 as the Zn content increasing from x = 0 to 0.3. The initial specific capacity decreases and the cycle performance increase with increasing Zn-doping content in the four orthorhombic LiFe1−xZnxPO4 compounds. Among the four LiFe1−xZnxPO4 compounds, LiFe0.8Zn0.2PO4 has the highest capacity retentions after 6 to 20 cycles and the capacity retention is 93.7% after 20 cycles, even though the initial discharge specific capacity of LiFe0.8Zn0.2PO4 is lower than those of LiFeZnPO4 and LiFe0.9Zn0.1PO4. LiFe0.7Zn0.3PO4 has the highest capacity retention of 97% after 20 cycles.

The crystal structure of Li2LaTa2O6N was determined from laboratory X-ray powder diffraction data (Cu Kα1) using the Rietveld method. The title compound is tetragonal with space group I4/mmm, Z=2, and unit-cell dimensions a=0.395 049(4) nm, c=1.850 97(3) nm, and V=0.288 869(6) nm3. The initial structural model was successfully derived by the direct methods and further refined by the Rietveld method, with the anisotropic atomic displacement parameters being assigned for all atoms. The final reliability indices were Rwp=5.73%, S=1.46, Rp=4.33%, RB=1.13%, and RF=0.53%. Li2LaTa2O6N has a layered perovskite structure similar to that of Li2LaTa2O7.

High-resolution powder X-ray diffraction has been used to determine the crystal structure of silver behenate, [Ag(O2C(CH2)20CH3]2. Using CASTEP density functional plane wave pseudopotential techniques to obtain an optimized structural model, Rietveld refinement of the structure gives Rwp = 8.66%. The unit cell is triclinic, space group P1, with cell dimensions of a = 4.1769(2) Å, b = 4.7218(2) Å, c = 58.3385(1) Å, α = 89.440(3)°, β = 89.634(3)°, γ = 75.854(1)°. The structure is characterized by an 8-membered ring dimer of Ag atoms and carboxyl groups with a fully extended all-trans configuration of the alkyl side chains. The dimers are joined by four-membered Ag-O rings creating a polymeric network, giving rise to one-dimensional chains along the b-axis. This structure is supported by EXAFS measurements of the local structure around the silver atoms and IR measurements.

Silver sulfide, Ag2S, is most commonly known as the tarnish that forms on silver surfaces due to the exposure of silver to hydrogen sulfide. The mineral acanthite is a monoclinic crystalline form of Ag2S that is stable to 176°C. Upon heating above 176°C, there is a phase conversion to a body-centered cubic (bcc) form referred to as argentite. Further heating above 586°C results in conversion of the bcc phase to a face-centered cubic (fcc) phase polymorph. Both high-temperature cubic phases are solid-state silver ion conductors. In situ high-temperature X-ray diffraction was used to better understand the polymorphs of Ag2S on heating. The existing powder diffraction file (PDF) entries for the high-temperature fcc polymorph are of questionable reliability, prompting a full Rietveld structure refinement of the bcc and fcc polymorphs. Rietveld analysis was useful to show that the silver atoms are largely disordered and can only be described by unreasonably large isotropic displacement parameters or split site models.

Rigid bodies provide a way to simplify the model used in a crystallographic refinement by removing parameters that describe degrees of freedom that are unlikely to change based on chemical experience. The GSAS software package provides a powerful implementation of rigid bodies that allows for refinement of classes of bond lengths, grouping of bodies to further reduce parameterization and where atomic motion can be described from group displacement parameters (TLS) representation. However, use of rigid bodies in GSAS is complex to learn and time-consuming to perform. This paper describes how the rigid body definition process has been simplified and extended through implementation in the EXPGUI interface to GSAS.

Computer algebra removes much of the drudgery from mathematics; it allows users to formulate models by using the language of mathematics and to have those models evaluated with little effort. This symbolic form of representation is often thought of as being separate to dedicated computational programs such as Rietveld refinement. These dedicated programs are often written in low level languages; they are relatively inflexible in what they do and modifying them to change functionality in a small manner is often a major programming task. This paper describes a symbolic system that is integrated into the dedicated Rietveld refinement program called TOPAS. The symbolic component allows large functional changes to be made at run time and with a relatively small amount of effort. In addition, the system as a whole reduces the programming complexity at the developmental stage.

The subsolidus phase relations of the Dy-Fe-Al system have been investigated by means of X-ray powder diffraction. There are 5 ternary compounds, 10 binary compounds, and 21 three-phase regions in this system. The solid-solution regions of Dy(Fe1−xAlx)2, DyFe3−xAlx, Dy2(Fe1−xAlx)17, and DyFe12−xAlx have been determined based on the dependence of their unit-cell parameters on the Al content.

A new barium copper niobate, Ba4CuNb3O12, was successfully prepared by high-temperature solid-state reaction in an inert atmosphere. Rietveld-refinement analysis of the XRD data of the compound showed that it has the 8H-type hexagonal perovskite structure with space group P63/mmc (#194), a = 5.830(1) Å, c = 19.123(1) Å, and chemical composition of Ba4Cu1.84Nb2.16O12-δ.

The structure of 3,4-diaminopyridin-1-ium dihydrogen phosphate, [C5H3(NH)(NH2)2]+ (H2PO4)−, is solved from conventional X-ray powder diffraction data in direct space (monoclinic unit cell with a = 16.0725(9) Å, b = 7.7301(3) Å, c = 14.6189(9) Å, β = 96.869(1)°, V = 1803.2(2) Å3, Z = 8, and space group I2/c), and optimized by energy minimization in the solid state. In the crystal structure of the title compound, dihydrogenphosphate tetrahedra are linked by strong hydrogen O-H…O bonds forming chains running parallel to the b-axis. Antiparallelly π–π stacked DAP cations form molecular columns in the spaces between the chains. Although the dominant interaction of the molecules with their surroundings is electrostatic, their bonding are further enhanced by N-H…O and C-H…O hydrogen bonds.

The crystal structures of marialite (Me6) from Badakhshan, Afghanistan and meionite (Me93) from Mt. Vesuvius, Italy were obtained using synchrotron high-resolution powder X-ray diffraction (HRPXRD) data and Rietveld structure refinements. Their structures were refined in space groups I4/m and P42/n, and similar results were obtained. The Me6 sample has a formula Ca0.24Na3.37K0.24[Al3.16Si8.84O24]Cl0.84(CO3)0.15, and its unit-cell parameters are a=12.047555(7), c=7.563210(6) Å, and V=1097.751(1) Å3. The average ⟨T1-O⟩ distances are 1.599(1) Å in I4/m and 1.600(2) Å in P42/n, indicating that the T1 site contains only Si atoms. In P42/n, the average distances of ⟨T2-O⟩=1.655(2) and ⟨T3-O⟩=1.664(2) Å are distinct and are not equal to each other. However, the mean ⟨T2,3-O⟩=1.659(2) Å in P42/n and is identical to the ⟨T2′-O⟩=1.659(1) Å in I4/m. The ⟨M-O⟩ [7]=2.754(1) Å (M site is coordinated to seven framework O atoms) and M-A=2.914(1) Å; these distances are identical in both space groups. The Me93 sample has a formula of Na0.29Ca3.76[Al5.54Si6.46O24]Cl0.05(SO4)0.02(CO3)0.93, and its unit-cell parameters are a=12.19882(1), c=7.576954(8) Å, and V=1127.535(2) Å3. A similar examination of the Me93 sample also shows that both space groups give similar results; however, the C–O distance is more reasonable in P42/n than in I4/m. Refining the scapolite structure near Me0 or Me100 in I4/m forces the T2 and T3 sites (both with multiplicity 8 in P42/n) to be equivalent and form the T2′ site (with multiplicity 16 in I4/m), but ⟨T2-O⟩ is not equal to ⟨T3-O⟩ in P42/n. Using different space groups for different regions across the series implies phase transitions, which do not occur in the scapolite series.