Accurate X-ray diffraction data required for proper evaluation of bond valence sums and global instability indexes: redetermination of the crystal structures of diamond-like Cu2CdSiS4 and Cu2HgSnS4 as a case study.

Our calculations of the global instability index (G) values for some diamond-like materials with the general formula I2-II-IV-VI4 have indicated that the structures may be unstable or incorrectly determined. To compute the G value of a given compound, the bond valence sums (BVSs) must first be calculated using a crystal structure. Two examples of compounds with high G values, based on data from the literature, are the wurtz-stannite-type dicopper cadmium silicon tetrasulfide (Cu2CdSiS4) and the stannite-type dicopper mercury tin tetrasulfide (Cu2HgSnS4), which were first reported in 1967 and 1965, respectively. In the present study, Cu2CdSiS4 and Cu2HgSnS4 were prepared by solid-state synthesis at 1000 and 900 °C, respectively. The phase purity was assessed by powder X-ray diffraction. Optical diffuse reflectance UV/Vis/NIR spectroscopy was used to estimate the optical bandgaps of 2.52 and 0.83 eV for Cu2CdSiS4 and Cu2HgSnS4, respectively. The structures were solved and refined using single-crystal X-ray diffraction data. The structure type of Cu2CdSiS4 was confirmed, where Cd2+, Si4+ and two of the three crystallographically unique S2- ions lie on a mirror plane. The structure type of Cu2HgSnS4 was also verified, where all ions lie on special positions. The S2- ion resides on a mirror plane, the Cu+ ion is situated on a fourfold rotary inversion axis and both the Hg2+ and the Sn4+ ions are located on the intersection of a fourfold rotary inversion axis, a mirror plane and a twofold rotation axis. Using the crystal structures solved and refined here, the G values were reassessed and found to be in the range that indicates reasonable strain for a stable crystal structure. This work, together with some examples gathered from the literature, shows that accurate data collected on modern instrumentation should be used to reliably calculate BVSs and G values.

Multifunctional Cu2TSiS4 (T = Mn and Fe): Polar Semiconducting Antiferromagnets with Nonlinear Optical Properties.

Cu2TSiS4 (T = Mn and Fe) polycrystalline and single-crystal materials were prepared with high-temperature solid-state and chemical vapor transport methods, respectively. The polar crystal structure (space group Pmn21) consists of chains of corner-sharing and distorted CuS4, Mn/FeS4, and SiS4 tetrahedra, which is confirmed by Rietveld refinement using neutron powder diffraction data, X-ray single-crystal refinement, electron diffraction, energy-dispersive X-ray spectroscopy, and second harmonic generation (SHG) techniques. Magnetic measurements indicate that both compounds order antiferromagnetically at 8 and 14 K, respectively, which is supported by the temperature-dependent (100-2 K) neutron powder diffraction data. Additional magnetic reflections observed at 2 K can be modeled by magnetic propagation vectors k = (1/2,0,1/2) and k = (1/2,1/2,1/2) for Cu2MnSiS4 and Cu2FeSiS4, respectively. The refined antiferromagnetic structure reveals that the Mn/Fe spins are canted away from the ac plane by about 14°, with the total magnetic moments of Mn and Fe being 4.1(1) and 2.9(1) µB, respectively. Both compounds exhibit an SHG response with relatively modest second-order nonlinear susceptibilities. Density functional theory calculations are used to describe the electronic band structures.

Crystal structure, electronic structure, and optical properties of the novel Li4CdGe2S7, a wide-bandgap quaternary sulfide with a polar structure derived from lonsdaleite.

The novel quaternary thiogermanate Li4CdGe2S7 (tetralithium cadmium digermanium heptasulfide) was discovered from a solid-state reaction at 750 °C. Single-crystal X-ray diffraction data were collected and used to solve and refine the structure. Li4CdGe2S7 is a member of the small, but growing, class of I4-II-IV2-VI7 diamond-like materials. The compound adopts the Cu5Si2S7 structure type, which is a derivative of lonsdaleite. Crystallizing in the polar space group Cc, Li4CdGe2S7 contains 14 crystallographically unique ions, all residing on general positions. Like all diamond-like structures, the compound is built of corner-sharing tetrahedral units that create a relatively dense three-dimensional assembly. The title compound is the major phase of the reaction product, as evidenced by powder X-ray diffraction and optical diffuse reflectance spectroscopy. While the compound exhibits a second-harmonic generation (SHG) response comparable to that of the AgGaS2 (AGS) reference material in the IR region, its laser-induced damage threshold (LIDT) is over an order of magnitude greater than AGS for λ = 1.064 µm and τ = 30 ps. Bond valence sums, global instability index, minimum bounding ellipsoid (MBE) analysis, and electronic structure calculations using density functional theory (DFT) were used to further evaluate the crystal structure and electronic structure of the compound and provide a comparison with the analogous I2-II-IV-VI4 diamond-like compound Li2CdGeS4. Li4CdGe2S7 appears to be a better IR nonlinear optical (NLO) candidate than Li2CdGeS4 and one of the most promising contenders to date. The exceptional LIDT is likely due, at least in part, to the wider optical bandgap of ∼3.6 eV.

Cu4MnGe2S7 and Cu2MnGeS4: two polar thiogermanates exhibiting second harmonic generation in the infrared and structures derived from hexagonal diamond.

The new, quaternary diamond-like semiconductor (DLS) Cu4MnGe2S7 was prepared at high-temperature from a stoichiometric reaction of the elements under vacuum. Single crystal X-ray diffraction data were used to solve and refine the structure in the polar space group Cc. Cu4MnGe2S7 features [Ge2S7]6- units and adopts the Cu5Si2S7 structure type that can be considered a derivative of the hexagonal diamond structure. The DLS Cu2MnGeS4 with the wurtz-stannite structure was similarly prepared at a lower temperature. The achievement of relatively phase-pure samples, confirmed by X-ray powder diffraction data, was nontrival as differential thermal analysis shows an incongruent melting behaviour for both compounds at relatively high temperature. The dark red Cu2MnGeS4 and Cu4MnGe2S7 compounds exhibit direct optical bandgaps of 2.21 and 1.98 eV, respectively. The infrared (IR) spectra indicate potentially wide windows of optical transparency up to 25 µm for both materials. Using the Kurtz-Perry powder method, the second-order nonlinear optical susceptibility, χ(2), values for Cu2MnGeS4 and Cu4MnGe2S7 were estimated to be 16.9 ± 2.0 pm V-1 and 2.33 ± 0.86 pm V-1, respectively, by comparing with an optical-quality standard reference material, AgGaSe2 (AGSe). Cu2MnGeS4 was found to be phase matchable at λ = 3100 nm, whereas Cu4MnGe2S7 was determined to be non-phase matchable at λ = 1600 nm. The weak SHG response of Cu4MnGe2S7 precluded phase-matching studies at longer wavelengths. The laser-induced damage threshold (LIDT) for Cu2MnGeS4 was estimated to be ∼0.1 GW cm-2 at λ = 1064 nm (pulse width: τ = 30 ps), while the LIDT for Cu4MnGe2S7 could not be ascertained due to its weak response. The significant variance in NLO properties can be reasoned using the results from electronic structure calculations.

Synthesis, crystal structure, and electronic structure of Li2PbSiS4: a quaternary thiosilicate with a compressed chalcopyrite-like structure.

The new quaternary thiosilicate, Li2PbSiS4 (dilithium lead silicon tetrasulfide), was prepared in an evacuated fused-silica tube via high-temperature, solid-state synthesis at 800 °C, followed by slow cooling. The crystal structure was solved and refined using single-crystal X-ray diffraction data. By strict definition, the title compound crystallizes in the stannite structure type; however, this type of structure can also be described as a compressed chalcopyrite-like structure. The Li+ cation lies on a crystallographic fourfold rotoinversion axis, while the Pb2+ and Si4+ cations reside at the intersection of the fourfold rotoinversion axis with a twofold axis and a mirror plane. The Li+ and Si4+ cations in this structure are tetrahedrally coordinated, while the larger Pb2+ cation adopts a distorted eight-coordinate dodecahedral coordination. These units join together via corner- and edge-sharing to create a dense, three-dimensional structure. Powder X-ray diffraction indicates that the title compound is the major phase of the reaction product. Electronic structure calculations, performed using the full potential linearized augmented plane wave method within density functional theory (DFT), indicate that Li2PbSiS4 is a semiconductor with an indirect bandgap of 2.22 eV, which compares well with the measured optical bandgap of 2.51 eV. The noncentrosymmetric crystal structure and relatively wide bandgap designate this compound to be of interest for IR nonlinear optics.

Syntheses and crystal structures of the quaternary thio-germanates Cu4FeGe2S7 and Cu4CoGe2S7.

The quaternary thio-germanates Cu4FeGe2S7 (tetra-copper iron digermanium hepta-sulfide) and Cu4CoGe2S7 (tetra-copper cobalt digermanium hepta-sulfide) were prepared in evacuated fused-silica ampoules via high-temperature, solid-state synthesis using stoichiometric amounts of the elements at 1273 K. These isostructural compounds crystallize in the Cu4NiSi2S7 structure type, which can be considered as a superstructure of cubic diamond or sphalerite. The monovalent (Cu+), divalent (Fe2+ or Co2+) and tetra-valent (Ge4+) cations adopt tetra-hedral geometries, each being surrounded by four S2- anions. The divalent cation and one of the sulfide ions lie on crystallographic twofold axes. These tetra-hedra share corners to create a three-dimensional framework structure. All of the tetra-hedra align along the same crystallographic direction, rendering the structure non-centrosymmetric and polar (space group C2). Analysis of X-ray powder diffraction data revealed that the structures are the major phase of the reaction products. Thermal analysis indicated relatively high melting temperatures, near 1273 K.

Practical issues in imaging hydraulic conductivity through hydraulic tomography.

Hydraulic tomography has been developed as an alternative to traditional geostatistical methods to delineate heterogeneity patterns in parameters such as hydraulic conductivity (K) and specific storage (S(s)). During hydraulic tomography surveys, a large number of hydraulic head data are collected from a series of cross-hole tests in the subsurface. These head data are then used to interpret the spatial distribution of K and S(s) using inverse modeling. Here, we use the Sequential Successive Linear Estimator (SSLE) of Yeh and Liu (2000) to interpret synthetic pumping test data created through numerical simulations and real data generated in a laboratory sandbox aquifer to obtain the K tomograms. Here, we define "K tomogram" as an image of K distribution of the subsurface (or the inverse results) obtained via hydraulic tomography. We examine the influence of signal-to-noise ratio and biases on results using inverse modeling of synthetic and real cross-hole pumping test data. To accomplish this, we first show that the pumping rate, which affects the signal-to-noise ratio, and the order of data included into the SSLE algorithm both have large impacts on the quality of the K tomograms. We then examine the role of conditioning on the K tomogram and find that conditioning can improve the quality of the K tomogram, but can also impair it, if the data are of poor quality and conditioning data have a larger support volume than the numerical grid used to conduct the inversion. Overall, these results show that the quality of the K tomogram depends on the design of pumping tests, their conduct, the order in which they are included in the inverse code, and the quality as well as the support volume of additional data that are used in its computation.