Ab-initio study of the structural, linear and nonlinear optical properties of CdAl2Se4 defect-chalcopyrite

The complex density functional theory (DFT) calculations of structural, electronic, linear and nonlinear optical properties for the defect chalcopyrite CdAl₂Se₄ compound have been reported using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code. We employed the Wu and Cohen generalized gradient approximation (GGA-WC), which is based on exchange-correlation energy optimization to calculate the total energy. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure, density of states and the spectral features of the linear and nonlinear optical properties. This compound has a wide direct energy band gap of about 2.927 eV with both the valence band maximum and conduction band minimum located at the center of the Brillouin zone. The ground state quantities such as lattice parameters (a, c, x, y and z), bulk modulus B and its pressure derivative B′ are evaluated. We have calculated the frequency-dependent complex ε(ω), its zero-frequency limit ε₁(0), refractive index n(ω), birefringence Δn(ω), the reflectivity R(ω) and electron energy loss function L(ω). Calculations are reported for the frequency-dependent complex second-order nonlinear optical susceptibilities. We find opposite signs of the contributions of the 2ω and 1ω inter/intra-band to the imaginary part for the dominant component through the wide optical frequency range.     

Electronic and optical properties of ZnSc2S4 and CdSc2S4 cubic spinels by the modified Becke–Johnson density functional

Structural, electronic and optical properties of the ZnSc₂S₄ and CdSc₂S₄ cubic spinels have been investigated by means of the full-potential (linearized) augmented plane wave plus local orbitals based on density functional theory. The exchange-correlation potential is treated by the GGA–PBEsol [J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100 (2008) 136406] and the recently proposed modified Becke–Johnson potential approximation (mBJ) [F. Tran, P. Blaha, Phys. Rev. Lett. 102 (2009) 226401], which successfully corrects the band-gap problem found with GGA for a wide range of materials. The obtained structural parameters are in good agreement with the available experimental data. This gives support for the predict properties for ZnSc₂S₄ and CdSc₂S₄. The band structures reveal that both compounds are semiconductor with a direct gap. The obtained gap values show that mBJ is superior for estimating band gap energy. We have calculated the electron and hole effective masses in different directions. The density of states has been analyzed. Based on our electronic structure obtained using the mBJ method we have calculated various optical properties, including the complex dielectric function ɛ(ω), complex index of refraction n(ω), reflectivity coefficient R(ω), absorption coefficient α(ω) and electron energy-loss function L(ω) as functions of the photon energy. We find that the values of zero-frequency limit ɛ₁(0) increase with decreasing the energy band gap in agreement with the Penn model. The origin of the peaks and structures in the optical spectra is determined in terms of the calculated energy band structures.     

Structural, thermodynamic and optical properties of MgF2 studied from first-principles theory

A detailed theoretical study of structural, electronic, elastic, thermodynamic and optical properties of rutile type MgF₂ has been carried out by means of first-principles Density Functional Theory (DFT) calculations using plane wave pseudo-potentials within the local density approximation and generalized-gradient approximation for the exchange and correlation functionals. The calculated ground state properties and elastic constants agree quite well with experimental values. From the calculated elastic constants we conclude that MgF₂ is relatively hard when compared to other alkaline-earth fluorides and ductile in nature. The thermodynamic properties such as heat capacity, entropy, free energy, phonon density of states and Debye temperatures are calculated at various temperatures from the lattice dynamical data obtained through the quasi-harmonic Debye model. From free energy and entropy it is found that the system is thermodynamically stable up to 1200 K. The imaginary part of the calculated dielectric function ε₂(ω) could reproduce the six prominent peaks which are observed in experiment. From the calculated ε(ω), other optical properties such as refractive index, reflectivity and electron energy-loss spectrum are obtained up to the photon energy range of 30 eV.     

Vaporization chemistry and thermodynamics in the CdGa2S4-Ga2S3 system

The chemistry and thermodynamics of vaporization of CdGa₂S₄(s), CdGa₈S₁₃(s), and Ga₂S₃(s) were studied by computer-automated, simultaneous Knudsen-effusion and torsion-effusion, vapor pressure measurements in the temperature range 967–1280 K. The vaporization was incongruent with loss of Cd(g) + 1/2 S₂(g) and production of CdGa₈S₁₃(s), a previously unknown compound, in equilibrium with CdGa₂S₄(s), until the solid became CdGa₈S₁₃ only. Then, incongruent vaporization continued with production of Ga₂S₃(s) until the solid was Ga₂S₃ only. The latter vaporized congruently. The ΔH°(298 K) of combination of one mole of CdS(s) with one mole of Ga₂S₃(s) to give CdGa₂S₄(s) was ?22.6 ± 0.9 kJ mole^?1. The 2H2(298 K) of combination of one mole of CdS(s) with four moles of Ga₂S₃(s) to give CdGa₈S₁₃(s) was ?25.5 ± 1.1 kJ mole^?1. The 2H2(298K) of CdGa₈S₁₃(s) with respect to disproportionation into CdGa₂S₄(s) and 3 Ga₂S₃(s) was ?2.8 ± 0.6 kJ mole^?1. CdGa₈S₁₃(s) was not observed at room temperature. The 2H2(298 K) of vaporization of the residual Ga₂S₃(s) was 663.4 ± 0.8 kJ mole^?1, which compared well with a value of 661.4 ± 0.3 kJ mole^?1 already available from the literature. Implications of small variations in stoichiometry of compounds in this study were observed and are discussed.     

Crystal structures of CsFe2S3 and RbFe2S3: synthetic analogs of rasvumite KFe2S3

The isostructural alkali thioferrate compounds CsFe₂S₃, RbFe₂S₃ and KFe₂S₃ have been synthesized by reacting Fe and S with their corresponding AFeS₂ (A=K, Rb, Cs) precursors. The crystal structures of these and binary compounds of intermediate composition were determined by Rietveld analysis of laboratory powder X-ray diffraction patterns. All of the synthesized compounds adopt the space group Cmcm (#63), Z=4 with: a=9.5193(8) Å, b=11.5826(10) Å, c=5.4820(4) Å for CsFe₂S₃; a=9.2202(7) Å, b=11.2429(9) Å, c=5.4450(3) Å for RbFe₂S₃; and a=9.0415(13) Å, b=11.0298(17) Å, c=5.4177(6) Å for KFe₂S₃. These mixed valence alkali thioferrates show regular changes in cell dimensions, AS₁₀ (A=K, Rb, Cs) polyhedron volumes, polyhedron distortion parameters, and calculated oxidation state of Fe with respect to increasing size of the alkali element cation. The calculated empirical oxidation state of iron varies from +2.618 (CsFe₂S₃), through +2.666 (RbFe₂S₃) to +2.77 (KFe₂S₃).     

Ta4P4S29: A new tunnel structure with inserted polymeric sulfur

Ta₄P₄S₂₉ was prepared from the elements heated together in stoichiometric proportions in an evacuated Pyrex tube for 10 days at 500°C. The crystal symmetry is tetragonal, space group P4₃2₁2, with the cell parameters: a = b = 15.5711(7) Å, c = 13.6516(8) Å, V = 3309.9(5) ų, and Z = 4. The structure calculations were conducted from 2335 reflections and 146 variables, leading to R = 0.033. The structure basic framework, corresponding to the chemical composition [TaPS₆], is made of biprismatic bicapped [Ta₂S₁₂] units (average d_TaS = 2.539 Å), including sulfur pairs (average d_SS = 2.039 Å), bonded to each other through [PS₄] tetrahedral groups (average d_PS = 2.044 Å) sharing sulfurs. This framework leaves large tunnels running along the c axis of the cell and in which (S₁₀)_∞ sulfur chains are found to be inserted (average d_SS = 2.052 Å and SSS = 105.75°). Diamagnetic and semiconducting Ta₄P₄S₂₉ can be formulated: Ta^V₄P^V₄(S^?II)₁₆(S^?II₂)₄(S⁰₅).     

Syntheses, crystal structures, and characterization of As(III) and As(V) thioarsenates, [Mn2(phen)(As2S5)]n and [Mn3(phen)3(AsS4)2]n·nH2O

The hydrothermal reactions of As, Mn, S, phen (phen=1,10-phenanthroline), and en (en=ethylenediamine) yield two manganese As(III) and As(V) thioarsenates, [Mn₂(phen)(As^III₂S₅)]_n (1) and [Mn₃(phen)₃(As^VS₄)₂]_n·nH₂O (2), respectively. Single-crystal X-ray diffraction analyses reveal that compound 1 is a two-dimensional (2D) layer of (6,3) topology. The 18-membered rings within the 2D porous layers are formed by corner-, edge-, and face-sharing cubane-like [Mn₂As₂S₄] units along the [100] direction. Whereas compound 2 is a one-dimensional (1D) chain structure. They are both characterized by IR, elemental analysis, EDS, and X-ray powder diffraction. The thermogravimetric analysis of 1 and 2 are discussed. Both the compounds are semiconductors with the band gap of E_g (compound 1)=2.01 eV (617 nm) and E_g (compound 2)=1.97 eV (629 nm), respectively. In addition, the variable-temperature magnetic susceptibility data suggest weak antiferromagnetic interactions between the Mn²⁺ ions in these two compounds.     

Syntheses, crystal structures and spectroscopic properties of Ag2Nb[P2S6][S2] and KAg2[PS4]

Ag₂Nb[P₂S₆][S₂] (1) was obtained from the direct solid state reaction of Ag, Nb, P₂S₅ and S at 500 °C. KAg₂[PS₄] (2) was prepared from the reaction of K₂S₃, Ag, Nd, P₂S₅ and extra S powder at 700 °C. Compound 1 crystallizes in the orthorhombic space group Pnma with a=12.2188(11), b=26.3725(16), c=6.7517(4) Å, V=2175.7(3) Å³, Z=8. Compound 2 crystallizes in the non-centrosymmetric tetragonal space group with lattice parameters a=6.6471(7), c=8.1693(11) Å, V=360.95(7) Å³, Z=2. The structure of Ag₂Nb[P₂S₆][S₂] (1) consists of [Nb₂S₁₂], [P₂S₆] and new found puckered [Ag₂S₄] chains which are along [001] direction. The Nb atoms are located at the center of distorted bicapped trigonal prisms. Two prisms share square face of two [S₂²⁻] to form one [Nb₂S₁₂] unit, in which Nb-Nb bond is formed. The [Nb₂S₁₂] units share all S²⁻ corners with ethane-like [P₂S₆] units to form 14-membered rings. The novel puckered [Ag₂S₄] chains are composed of distorted [AgS₄] tetrahedra and [AgS₃] triangles that share corners with each other. These chains are connected with [P₂S₆] units and [Nb₂S₁₂] units to form three-dimensional frame work. The structural skeleton of 2 is built up from [AgS₄] and [PS₄] tetrahedra linked by corner-sharing. The three-dimensional anionic framework contains orthogonal, intersecting tunnels directed along [100] and [010]. This compound possesses a compressed chalcopyrite-like structure. The structure is compressed along [001] and results from eight coordination sphere for K⁺. Both compounds are characterized with UV/vis diffuse reflectance spectroscopy and compound 1 with IR and Raman spectra.     

Tl2S-Sb2S3-Bi2S3 quasi-ternary system

The Tl₂S-Sb₂S₃-Bi₂S₃ quasi-ternary system (system A) was studied using DTA, X- ray powder diffraction, microstructure examination, and microhardness measurements. TlSbS₂-Tl₄Bi₂S₅(TlBiS₂, Bi₂S₃), Sb₂S₃-TlBiS₂, Tl₃SbS₃-TlBiS₂(Bi₂S₃), and [TlSb_0.5Bi_0.5S₂]-Tl₂S isopleths; isothermal sections at 500 K; and liquidus surface projection of system A were constructed. Characteristic features of the title system are extensive fields of solid solutions extended along the TlSbS₂-TlBiS₂ quasi-binary section and a continuous solubility belt 1–2 mol % wide extended along the Sb₂S₃-Bi₂S₃ binary subsystem. Primary separation fields of phases and the types and coordinates of invariant and monovariant equilibria in system A were determined.     

Preparation and photocatalytic activity of Sb2S3/Bi2S3 doped TiO2 from complex precursor via gel-hydrothermal treatment

Sb₂S₃/Bi₂S₃ doped TiO₂ were prepared with the coordination compounds [M(S₂CNEt)₃] (M=Sb, Bi; S₂CNEt=pyrrolidinedithiocarbamate) as precursors via gel-hydrothermal techniques. The doped TiO₂ were characterized by XRD, SEM, XPS and UV-vis diffuse reflectance means. The photocatalyst based on doped TiO₂ for photodecolorization of 4-nitrophenol (4-NP) was examined. The optimal Bi₂S₃/Sb₂S₃ content, pH and different doped techniques have been investigated. Photocatalytic tests reveal that M₂S₃ doped TiO₂ via the gel-hydrothermal route performs better photocatalytic activity for photodegradation reaction of 4-nitrophenol (4-NP).     

Solvothermal synthesis of three new dimeric thiogermanates (enH)4Ge2S6, [Mn(en)3]2Ge2S6 and [Ni(en)3]2Ge2S6 from germanium dioxide and sulfur powder

Three new thiogermanates (enH)₄Ge₂S₆ (1) and [M(en)₃]₂Ge₂S₆ (M=Mn (2), Ni (3); en=ethylenediamine) were synthesized using GeO₂ and S₈ as starting materials in molar ratio of 1:0.5 under solvothermal conditions. These compounds suggest that the dimeric [Ge₂S₆]⁴⁻ anion is likely to be the main germanium-containing species in en system and it also might be preferred as counter anions by the transition metal complex cations in crystallization. The cations of [Mn(en)₃]²⁺ and [Ni(en)₃]²⁺ are even better mineralizers than the protonated amine of [enH]⁺. The crystal systems of [Ge₂S₆]⁴⁻ compounds are related to entities of cations and intermolecular reactions between cations and [Ge₂S₆]⁴⁻ anions. The compounds remove ethylenediamine and H₂S molecules in multi steps when being heated under nitrogen stream.     

Ab-initio calculation of structural, electronic, and optical characterizations of the intermetallic trialuminides ScAl3 compound

We present first-principles study of the electronic and the optical properties for the intermetallic trialuminides ScAl₃ compound using the full-potential linear augmented plane wave method within density-functional theory. We have employed the generalized gradient approximation (GGA), which is based on exchange-correlation energy optimization to calculate the total energy. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for calculating the electronic band structure and optical properties. The electronic specific heat coefficient (γ), which is a function of density of states, can be calculated from the density of states at Fermi energy N(E_F). The N(E_F) of the phase L1₂ is found to be lower than that of D0₂₂ structure which confirms the stability of L1₂ structure. We found that the dispersion of the band structure of D0₂₂ is denser than L1₂ phase. The linear optical properties were calculated. The evaluations are based on calculations of the energy band structure.     

Crystal structures of V3S4 and V5S8

Crystal structures of the ordered phases of V₃S₄ and V₅S₈ were refined with single crystal data. Both are monoclinic. Chemical compositions, space groups and lattice constants are as follows: VS_1.47, $\text{I2}\text{m}$ (No. 12), a = 5.831(1), b = 3.267(1), c = 11.317(2)Å, β = 91.78(1)° and VS_1.64, $\text{F}\text{2}\text{m}$ (No. 12), a = 11.396(11), b = 6.645(7), c = 11.293(4), Å, β = 91.45(6)°. In both structures, short metal-metal bonds were found between the layers as well as within them. In comparison with the structure of Fe₇S₈, the stability of NiAs-type structure was discussed based on the detailed metal-sulfur distances.     

Thermodynamic studies on SrFe12O19(s), SrFe2O4(s), Sr2Fe2O5(s) and Sr3Fe2O6(s)

The citrate-nitrate gel combustion route was used to prepare SrFe₂O₄(s), Sr₂Fe₂O₅(s) and Sr₃Fe₂O₆(s) powders and the compounds were characterized by X-ray diffraction analysis. Different solid-state electrochemical cells were used for the measurement of emf as a function of temperature from 970 to 1151 K. The standard molar Gibbs energies of formation of these ternary oxides were calculated as a function of temperature from the emf data and are represented as (SrFe₂O₄, s, T)/kJ mol⁻¹ (±1.7)=−1494.8+0.3754 (T/K) (970?T/K?1151). (Sr₂Fe₂O₅, s, T)/kJ mol⁻¹ (±3.0)=−2119.3+0.4461 (T/K) (970?T/K?1149). (Sr₃Fe₂O₆, s, T)/kJ mol⁻¹ (±7.3)=−2719.8+0.4974 (T/K) (969?T/K?1150).Standard molar heat capacities of these ternary oxides were determined from 310 to 820 K using a heat flux type differential scanning calorimeter (DSC). Based on second law analysis and using the thermodynamic database FactSage software, thermodynamic functions such as Δ_fH°(298.15 K), S°(298.15 K) S°(T), C_p°(T), H°(T), {H°(T)-H°(298.15 K)}, G°(T), free energy function (fef), Δ_fH°(T) and Δ_fG°(T) for these ternary oxides were also calculated from 298 to 1000 K.     

Synthesis and properties of pyrazine-pillared Ag3Mo2O4F7 and AgReO4 layered phases

The new pyrazine-pillared solids, AgReO₄(C₄H₄N₂) (I) and Ag₃Mo₂O₄F₇(C₄H₄N₂)₃ (C₄H₄N₂=pyrazine, pyz) (II), were synthesized by hydrothermal methods at 150 °C and characterized using single crystal X-ray diffraction (I—P2₁/c, No. 14, Z=4, a=7.2238(6) Å, b=7.4940(7) Å, c=15.451(1) Å, β=92.296(4)°; II—P2/n, No. 13, Z=2, a=7.6465(9) Å, b=7.1888(5) Å, c=19.142(2) Å, β=100.284(8)°), thermogravimetric analysis, UV-Vis diffuse reflectance, and photoluminescence measurements. Individual Ag(pyz) chains in I are bonded to three perrhenate ReO₄^- tetrahedra per layer, while each layer in II contains sets of three edge-shared Ag(pyz) chains (π-π stacked) that are edge-shared to four Mo₂O₄F₇^3- dimers. A relatively small interlayer spacing results from the short length of the pyrazine pillars, and which can be removed at just slightly above their preparation temperature, at >150-175 °C, to produce crystalline AgReO₄ for I, and Ag₂MoO₄ and an unidentified product for II. Both pillared solids exhibit strong orange-yellow photoemission, at 575 nm for I and 560 nm for II, arising from electronic excitations across (charge transfer) band gaps of 2.91 and 2.76 eV in each, respectively. Their structures and properties are analyzed with respect to parent ‘organic free’ silver perrhenate and molybdate solids which manifest similar photoemissions, as well as to the calculated electronic band structures.     

Magnetic susceptibility and torque measurements of FeV2S4, FeV2Se4 and FeTi2Se4

Magnetic susceptibility and torque measurements of FeV₂S₄, FeV₂Se₄ and FeTi₂Se₄ were made using the powder and the single crystal samples. The inverse susceptibility of FeV₂S₄, FeV₂Se₄ and FeTi₂Se₄ changed its slope at 850, 820 and 700 K, respectively, at which temperature the order-disorder transition of cation vacancies should seem to take place. Above these temperatures the paramagnetic moment obtained for these compounds was in the range of 5.26–5.37 μ_B, close to that of the high spin state Fe²⁺. Below these temperatures the paramagnetic moment was reduced to 4.23–4.35 μ_B.The antiferromagnetic spin axis of FeV₂S₄ was in the neighborhood of the [101] direction and that of FeV₂Se₄ and FeTi₂Se₄ in the direction of the c-axis. The large magnetic anisotropy observed and the preference of the magnetic moments for the direction of the c-axis were attributed to the spin-orbit interaction of Fe²⁺ electrons in the trigonal crystal field.     

Syntheses, structures, physical properties, and electronic structures of KLn2CuS4 (Ln=Y, Nd, Sm, Tb, Ho) and K2Ln4Cu4S9 (Ln=Dy, Ho)

Seven new quaternary metal sulfides, KY₂CuS₄, KNd₂CuS₄, KSm₂CuS₄, KTb₂CuS₄, KHo₂CuS₄, K₂Dy₄Cu₄S₉, and K₂Ho₄Cu₄S₉, were prepared by the reactive flux method. All crystallographic data were collected at 153 K. The isostructural compounds KLn₂CuS₄ (Ln=Y, Nd, Sm, Tb, Ho) crystallize in space group Cmcm of the orthorhombic system with four formula units in cells of dimensions (Ln, a, b, c (Å)): Y, 3.9475(9), 13.345(3), 13.668(3); Nd, 4.0577(3), 13.7442(10), 13.9265(10); Sm, 4.0218(4), 13.6074(14), 13.8264(14); Tb, 3.9679(5), 13.4243(17), 13.7102(18); Ho, 3.9378(3), 13.3330(11), 13.6487(11). The corresponding R₁ indices for the refined structures are 0.0197, 0.0153, 0.0158, 0.0181, and 0.0178. The isostructural compounds K₂Dy₄Cu₄S₉ and K₂Ho₄Cu₄S₉ crystallize in space group C2/m of the monoclinic system with two formula units in cells of dimensions (Ln, a, b, c (Å), β (°)): Dy, 13.7061(13), 3.9482(4), 15.8111(15), 109.723(1); Ho, 13.6760(14), 3.9360(4), 15.7950 (16), 109.666(2). The corresponding R₁ indices are 0.0312 and 0.0207. Both structure types are closely related three-dimensional tunnel structures. The tunnels are filled with bicapped trigonal-prismatically coordinated K atoms. Their anionic frameworks are built from LnS₆ octahedra and CuS₄ tetrahedra. KLn₂CuS₄ contains _∞¹[CuS₃⁵⁻] chains of vertex-sharing tetrahedra and K₂Ln₄Cu₄S₉ contains _∞¹[Cu₄S₈¹²⁻] chains of tetrahedra. K₂Ho₄Cu₄S₉ shows Curie-Weiss paramagnetic behavior between 5 and 300 K, and has an effective magnetic moment of 10.71 μ_B for Ho³⁺ at 293 K. Optical band gaps of 2.17 eV for KSm₂CuS₄ and 2.43 eV for K₂Ho₄Cu₄S₉ were deduced from diffuse reflectance spectra. A first-principles calculation of the density of states and the frequency-dependent optical conductivity was performed on KSm₂CuS₄. The calculated band gap of 2.1 eV is in good agreement with the experimental value.     

Tight binding prediction of the α-Gd2S3 magnetic structure

Spin-dependent extended Hückel tight binding (EHTB) calculations were carried out for the magnetic solid Gd₂S₃ by considering 20 different variations in the ordering of the 4f⁷ moments. The tight-binding calculations are used to interpolate the band structure of a nonmagnetic congener (Y₂S₃) and the 4f/5d,6s exchange interactions are introduced as perturbations via the introduction of spin-dependent H_dd and H_ss parameters. The calculations predict that Gd₂S₃ adopts an antiferromagnetic ordering of the 4f⁷ moments that is consistent with published neutron diffraction results. Our attempt to account for the calculated energies of the spin patterns using an Ising model was unsuccessful.     

High-Pressure Synthesis and Crystal Structure of B2S3

Two new high-pressure phases of binary boron-sulfur compounds, B₂S₃-II and B₂S₃-III, were synthesized at 3-6.2 GPa. A single crystal of B₂S₃-III was grown and the structure was determined (tetragonal, space group I4₁/a, a=16.086(2) Å, c=30.488(4) Å; V=7888(1) ų, Z=100, R=3.0% and R_w=2.8% for 3047 observed data [I>3.00σ(I)]. The structure of B₂S₃-III consists of two kinds of macrotetrahedra built up from 20 and 34 BS₄-tetrahedra. These macrotetrahedra connect each other to form an interpenetrating zincblende-type structure by sharing BS₄-tetrahedra at the corners of those. B₂S₃-III is anticipated having a rather disordered structure. From the UV-Vis diffuse reflectance spectrum, the optical band gap of B₂S₃-III was estimated to be 3.7 eV.     

Structural behavior of the ferromagnetic spinels AlxMo2S4 and GaxMo2S4, containing tetrahedral clusters of molybdenum atoms

The structure of the ferromagnetic spinels Al_xMo₂S₄ and Ga_xMo₂S₄ (x ～ 0.5) was determined from powder diffraction data. The Al and Ga atoms order on the tetrahedral sites. The space group is $\text{F}\text{4}\text{3m; a = 9.726}$ Å for Al_xMo₂S₄ and 9.739 Å for Ga_xMo₂S₄. The Mo atoms were found to shift towards the tetrahedral site vacancies, created by the lower Al and Ga concentrations. This results in tetrahedral clusters of Mo around the vacancies. Their semiconducting and magnetic behavior was explained on the basis of the structural behavior of the molybdenum lattice in these spinel compounds.