Hydrostatic compression of galenobismutite (PbBi<Subscript>2</Subscript>S<Subscript>4</Subscript>): elastic properties and high-pressure crystal chemistry

A single-crystal sample of galenobismutite was subjected to hydrostatic pressures in the range of 0.0001 and 9 GPa at room temperature using the diamond-anvil cell technique. A series of X-ray diffraction intensities were collected at ten distinct pressures using a CCD equipped 4-circle diffractometer. The crystal structure was refined to R1(|F₀| > 4σ) values of approximately 0.05 at all pressures. By fitting a third-order Birch-Murnaghan equation of state to the unit-cell volumes V ₀ = 700.6(2) ų, K ₀ = 43.9(7) GPa and dK/dP = 6.9(3) could be determined for the lattice compression. Both types of cations in galenobismutite have stereochemically active lone electron pairs, which distort the cation polyhedra at room pressure. The cation eccentricities decrease at higher pressure but are still pronounced at 9 GPa. Galenobismutite is isotypic with CaFe₂O₄ (CF) but moves away from the idealised CF-type structure during compression. Instead of the two octahedral cation sites and one bi-capped trigonal-prismatic site, PbBi₂S₄ attains a new high-pressure structure characterised by one octahedral site and two mono-capped trigonal-prismatic sites. Analyses of the crystal structure at high pressure confirm the preference of Bi for the octahedral site and the smaller one of the two trigonal-prismatic sites.     

Pressure induced phase transition in Pb<Subscript>6</Subscript>Bi<Subscript>2</Subscript>S<Subscript>9</Subscript>

The crystal structure of Pb₆Bi₂S₉ is investigated at pressures between 0 and 5.6 GPa with X-ray diffraction on single-crystals. The pressure is applied using diamond anvil cells. Heyrovskyite (Bbmm, a = 13.719(4) Å, b = 31.393(9) Å, c = 4.1319(10) Å, Z = 4) is the stable phase of Pb₆Bi₂S₉ at ambient conditions and is built from distorted moduli of PbS-archetype structure with a low stereochemical activity of the Pb²⁺ and Bi³⁺ lone electron pairs. Heyrovskyite is stable until at least 3.9 GPa and a first-order phase transition occurs between 3.9 and 4.8 GPa. A single-crystal is retained after the reversible phase transition despite an anisotropic contraction of the unit cell and a volume decrease of 4.2%. The crystal structure of the high pressure phase, β-Pb₆Bi₂S₉, is solved in Pna2 ₁ (a = 25.302(7) Å, b = 30.819(9) Å, c = 4.0640(13) Å, Z = 8) from synchrotron data at 5.06 GPa. This structure consists of two types of moduli with SnS/TlI-archetype structure in which the Pb and Bi lone pairs are strongly expressed. The mechanism of the phase transition is described in detail and the results are compared to the closely related phase transition in Pb₃Bi₂S₆ (lillianite).     

Compressibility of strontium orthophosphate Sr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> at high pressure

High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr₃(PO₄)₂ has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V ₀ = 498.0 ± 0.1 Å³, an isothermal bulk modulus of K _T  = 89.5 ± 1.7 GPa, and first pressure derivative of K _T ′ = 6.57 ± 0.34. If K _T ′ is fixed at 4, K _T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K _c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO₄ vibrations of Sr₃(PO₄)₂ is calculated to be 0.30(2).     

Equation of state of synthetic qandilite Mg<Subscript>2</Subscript>TiO<Subscript>4</Subscript> at ambient temperature

Using a diamond-anvil cell and synchrotron X-ray diffraction, the compressional behavior of a synthetic qandilite Mg_2.00(1)Ti_1.00(1)O₄ has been investigated up to about 14.9 GPa at 300 K. The pressure–volume data fitted to the third-order Birch–Murnaghan equation of state yield an isothermal bulk modulus (K _T0) of 175(5) GPa, with its first derivative \(K_{T0}^{{\prime }}\) attaining 3.5(7). If \(K_{T0}^{{\prime }}\) is fixed as 4, the K _T0 value is 172(1) GPa. This value is substantially larger than the value of the adiabatic bulk modulus (K _S0) previously determined by an ultrasonic pulse echo method (152(7) GPa; Liebermann et al. in Geophys J Int 50:553–586, 1977), but in general agreement with the K _T0 empirically estimated on the basis of crystal chemical systematics (169 GPa; Hazen and Yang in Am Miner 84:1956–1960, 1999). Compared to the K _T0 values of the ulvöspinel (Fe₂TiO₄; ~148(4) GPa with \(K_{T0}^{{\prime }} = 4\)) and the ringwoodite solid solutions along the Mg₂SiO₄–Fe₂SiO₄ join, our finding suggests that the substitution of Mg²⁺ for Fe²⁺ on the T sites of the 4–2 spinels can have more significant effect on the K _T0 than that on the M sites.     

Elastic behavior of vanadinite,Pb<Subscript>10</Subscript>(VO<Subscript>4</Subscript>)<Subscript>6</Subscript>Cl<Subscript>2</Subscript>, a microporous non-zeolitic mineral

The high-pressure behavior of a vanadinite (Pb₁₀(VO₄)₆Cl₂, a = b = 10.3254(5), c = 7.3450(4) Å, space group P6₃/m), a natural microporous mineral, has been investigated using in-situ HP-synchrotron X-ray powder diffraction up to 7.67 GPa with a diamond anvil cell under hydrostatic conditions. No phase transition has been observed within the pressure range investigated. Axial and volume isothermal Equations of State (EoS) of vanadinite were determined. Fitting the P–V data with a third-order Birch-Murnaghan (BM) EoS, using the data weighted by the uncertainties in P and V, we obtained: V ₀ = 681(1) Å³, K ₀ = 41(5) GPa, and K′ = 12.5(2.5). The evolution of the lattice constants with P shows a strong anisotropic compression pattern. The axial bulk moduli were calculated with a third-order “linearized” BM-EoS. The EoS parameters are: a ₀ = 10.3302(2) Å, K ₀(a) = 35(2) GPa and K′(a) = 10(1) for the a-axis; c ₀ = 7.3520(3) Å, K ₀(c) = 98(4) GPa, and K′(c) = 9(2) for the c-axis (K ₀(a):K ₀(c) = 1:2.80). Axial and volume Eulerian-finite strain (fe) at different normalized stress (Fe) were calculated. The weighted linear regression through the data points yields the following intercept values: Fe _a (0) = 35(2) GPa for the a-axis, Fe _c (0) = 98(4) GPa for the c-axis and Fe _V (0) = 45(2) GPa for the unit-cell volume. The slope of the regression lines gives rise to K′ values of 10(1) for the a-axis, 9(2) for the c-axis and 11(1) for the unit cell-volume. A comparison between the HP-elastic response of vanadinite and the iso-structural apatite is carried out. The possible reasons of the elastic anisotropy are discussed.     

New high-pressure phases in BaCO<Subscript>3</Subscript>

Barium carbonate (BaCO₃) was examined in a diamond anvil cell up to a pressure of 73 GPa using an in situ angle-dispersive X-ray diffraction technique. Three new phases of BaCO₃ were observed at pressures >10 GPa. From 10 to 24 GPa, BaCO₃-IV had a post-aragonite structure with space group Pmmn. There are two molecules in a single unit cell (Z = 2) of the orthorhombic phase, which is same as the high-pressure phases of CaCO₃ and SrCO₃. The isothermal bulk modulus of BaCO₃-IV is K ₀ = 84(4) GPa, with V ₀ = 129.0(7) Å³ when K ₀′ = 4. The c axis of the unit cell parameter is less compressible than the a and b axes. The relative change in volume that accompanies the transformation between BaCO₃-III and BaCO₃-IV is ～6%. BaCO₃-V, which has an orthorhombic symmetry, was synthesized at 50 GPa. As the pressure increases, BaCO₃-V is transformed into tetragonal BaCO₃-VI. This transformation is likely to be second order, because the diffraction pattern of BaCO₃-V is similar to that of BaCO₃-VI, and some single peaks in BaCO₃-VI become doublets in BaCO₃-V. After decompression, the new high-pressure phases transform into BaCO₃-II. Our findings resolve a dispute regarding the stable high-pressure phases of BaCO₃.     

Thermoelastic properties of chromium oxide Cr<Subscript>2</Subscript>O<Subscript>3</Subscript> (eskolaite) at high pressures and temperatures

A new synchrotron X-ray diffraction study of chromium oxide Cr₂O₃ (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K _0,T0), 206 ± 4 GPa; its pressure derivative K′_0,T , 4.4 ± 0.8; (?K _0,T /?T) = ?0.037 ± 0.006 GPa K^?1; a = 2.98 ± 0.14 × 10^?5 K^?1 and b = 0.47 ± 0.28 × 10^?8 K^?2, where α _0,T  = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr₂O₃ was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α _0,T0 was determined to be 2.95 × 10^?5 K^?1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α ₀ value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Grüneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K _0,T0 = 205 ± 3 GPa, K′_0,T  = 4.0, Grüneisen parameter (γ ₀) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr₂O₃ undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr₂O₃ is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data.     

Thermal equation of state of CaIrO<Subscript>3</Subscript> post-perovskite

The pressure–volume–temperature (P–V–T) relation of CaIrO₃ post-perovskite (ppv) was measured at pressures and temperatures up to 8.6 GPa and 1,273 K, respectively, with energy-dispersive synchrotron X-ray diffraction using a DIA-type, cubic-anvil apparatus (SAM85). Unit-cell dimensions were derived from the Le Bail full profile refinement technique, and the results were fitted using the third-order Birth-Murnaghan equation of state. The derived bulk modulus \( K_{T0} \) at ambient pressure and temperature is 168.3 ± 7.1 GPa with a pressure derivative \( K_{T0}^{\prime } \) = 5.4 ± 0.7. All of the high temperature data, combined with previous experimental data, are fitted using the high-temperature Birch-Murnaghan equation of state, the thermal pressure approach, and the Mie-Grüneisen-Debye formalism. The refined thermoelastic parameters for CaIrO₃ ppv are: temperature derivative of bulk modulus \( (\partial K_{T} /\partial T)_{P} \) = ?0.038 ± 0.011 GPa K^?1, \( \alpha K_{T} \) = 0.0039 ± 0.0001 GPa K^?1, \( \left( {\partial K_{T} /\partial T} \right)_{V} \) = ?0.012 ± 0.002 GPa K^?1, and \( \left( {\partial^{2} P/\partial T^{2} } \right)_{V} \) = 1.9 ± 0.3 × 10^?6 GPa² K^?2. Using the Mie-Grüneisen-Debye formalism, we obtain Grüneisen parameter \( \gamma_{0} \) = 0.92 ± 0.01 and its volume dependence q = 3.4 ± 0.6. The systematic variation of bulk moduli for several oxide post-perovskites can be described approximately by the relationship K _T0  = 5406.0/V(molar) + 5.9 GPa.     

Stability at high-pressure,elastic behaviour and pressure-induced structural evolution of CsAlSi<Subscript>5</Subscript>O<Subscript>12</Subscript>, a potential host for nuclear waste

The elastic and structural behaviour of the synthetic zeolite CsAlSi₅O₁₂ (a = 16.753(4), b = 13.797(3) and c = 5.0235(17) Å, space group Ama2, Z = 2) were investigated up to 8.5 GPa by in situ single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions. No phase-transition occurs within the P-range investigated. Fitting the volume data with a third-order Birch–Murnaghan equation-of-state gives: V ₀ = 1,155(4) ų, K _T0 = 20(1) GPa and K′ = 6.5(7). The “axial moduli” were calculated with a third-order “linearized” BM-EoS, substituting the cube of the individual lattice parameter (a ³, b ³, c ³) for the volume. The refined axial-EoS parameters are: a ₀ = 16.701(44) Å, K _T0a = 14(2) GPa (β_a = 0.024(3) GPa^?1), K′ _a = 6.2(8) for the a-axis; b ₀ = 13.778(20) Å, K _T0b = 21(3) GPa (β_b = 0.016(2) GPa^?1), K′ _b = 10(2) for the b-axis; c ₀ = 5.018(7) Å, K _T0c = 33(3) GPa (β_c = 0.010(1) GPa^?1), K′ _c = 3.2(8) for the c-axis (K _T0a:K _T0b:K _T0c = 1:1.50:2.36). The HP-crystal structure evolution was studied on the basis of several structural refinements at different pressures: 0.0001 GPa (with crystal in DAC without any pressure medium), 1.58(3), 1.75(4), 1.94(6), 3.25(4), 4.69(5), 7.36(6), 8.45(5) and 0.0001 GPa (after decompression). The main deformation mechanisms at high-pressure are basically driven by tetrahedral tilting, the tetrahedra behaving as rigid-units. A change in the compressional mechanisms was observed at P ≤ 2 GPa. The P-induced structural rearrangement up to 8.5 GPa is completely reversible. The high thermo-elastic stability of CsAlSi₅O_12, the immobility of Cs at HT/HP-conditions, the preservation of crystallinity at least up to 8.5 GPa and 1,000°C in elastic regime and the extremely low leaching rate of Cs from CsAlSi₅O₁₂ allow to consider this open-framework silicate as functional material potentially usable for fixation and deposition of Cs radioisotopes.     

High-pressure thermo-elastic properties of beryl (Al<Subscript>4</Subscript>Be<Subscript>6</Subscript>Si<Subscript>12</Subscript>O<Subscript>36</Subscript>) from ab initio calculations,and observations about the source of thermal expansion

Ab initio calculations of thermo-elastic properties of beryl (Al₄Be₆Si₁₂O₃₆) have been carried out at the hybrid HF/DFT level by using the B3LYP and WC1LYP Hamiltonians. Static geometries and vibrational frequencies were calculated at different values of the unit cell volume to get static pressure and mode-γ Grüneisen’s parameters. Zero point and thermal pressures were calculated by following a standard statistical-thermodynamics approach, within the limit of the quasi-harmonic approximation, and added to the static pressure at each volume, to get the total pressure (P) as a function of both temperature (T) and cell volume (V). The resulting P(V, T) curves were fitted by appropriate EoS’, to get bulk modulus (K ₀) and its derivative (K′), at different temperatures. The calculation successfully reproduced the available experimental data concerning compressibility at room temperature (the WC1LYP Hamiltonian provided K ₀ and K′ values of 180.2 Gpa and 4.0, respectively) and the low values observed for the thermal expansion coefficient. A zone-centre soft mode \( P6/mcc \to P\bar{1} \) phase transition was predicted to occur at a pressure of about 14 GPa; the reduction of the frequency of the soft vibrational mode, as the pressure is increased, and the similar behaviour of the majority of the low-frequency modes, provided an explanation of the thermal behaviour of the crystal, which is consistent with the RUM model (Rigid Unit Model; Dove et al. in Miner Mag 59:629–639, 1995), where the negative contribution to thermal expansion is ascribed to a geometric effect connected to the tilting of rigid polyhedra in framework silicates.     

Thermodynamic properties,low-temperature heat-capacity anomalies,and single-crystal X-ray refinement of hydronium jarosite, (H<Subscript>3</Subscript>O)Fe<Subscript>3</Subscript>(SO<Subscript>4</Subscript>)<Subscript>2</Subscript>(OH)<Subscript>6</Subscript>

Crystals of hydronium jarosite were synthesized by hydrothermal treatment of Fe(III)–SO₄ solutions. Single-crystal XRD refinement with R₁=0.0232 for the unique observed reflections (|F_o| > 4_F) and wR₂=0.0451 for all data gave a=7.3559(8) Å, c=17.019(3) Å, V^o=160.11(4) cm³, and fractional positions for all atoms except the H in the H₃O groups. The chemical composition of this sample is described by the formula (H₃O)_0.91Fe_2.91(SO₄)₂[(OH)_5.64(H₂O)_0.18]. The enthalpy of formation (H^o_f) is –3694.5 ± 4.6 kJ mol^–1, calculated from acid (5.0 N HCl) solution calorimetry data for hydronium jarosite, -FeOOH, MgO, H₂O, and -MgSO₄. The entropy at standard temperature and pressure (S^o) is 438.9±0.7 J mol^–1 K^–1, calculated from adiabatic and semi-adiabatic calorimetry data. The heat capacity (C_p) data between 273 and 400 K were fitted to a Maier-Kelley polynomial C_p(T in K)=280.6 + 0.6149T–3199700T^–2. The Gibbs free energy of formation is –3162.2 ± 4.6 kJ mol^–1. Speciation and activity calculations for Fe(III)–SO₄ solutions show that these new thermodynamic data reproduce the results of solubility experiments with hydronium jarosite. A spin-glass freezing transition was manifested as a broad anomaly in the C_p data, and as a broad maximum in the zero-field-cooled magnetic susceptibility data at 16.5 K. Another anomaly in C_p, below 0.7 K, has been tentatively attributed to spin cluster tunneling. A set of thermodynamic values for an ideal composition end member (H₃O)Fe₃(SO₄)₂(OH)₆ was estimated: G^o_f= –3226.4 ± 4.6 kJ mol^–1, H^o_f=–3770.2 ± 4.6 kJ mol^–1, S^o=448.2 ± 0.7 J mol^–1 K^–1, C_p (T in K)=287.2 + 0.6281T–3286000T^–2 (between 273 and 400 K).     

Single-crystal Raman spectra of YAlO<Subscript>3</Subscript> and GdAlO<Subscript>3</Subscript>: comparison to several orthorhombic ABO<Subscript>3</Subscript> perovskites

Room-temperature-polarized single-crystal Raman spectra have been measured for both GdAlO₃ and YAlO₃. Both aluminates crystallize in the orthorhombic (Pbnm) perovskite structure. Of the 24 possible Raman modes in 4 symmetries, 20 and 17 modes were observed for gadolinium and yttrium aluminates, respectively. Comparisons of the Raman spectra of these two aluminates to those of 28 other orthorhombic ABO₃ perovskites revealed remarkably similar spectral patterns, regardless of chemistry or valency of the cations. Closer examination of the effect of mass, valencies, and size of the cations on the Raman spectra versus composition revealed that for the observed modes, the A cation plays the dominant role in determining the Raman shift. In particular, the one to two lowest energy modes in each symmetry are determined by cation mass and valency no matter what the chemistry. For some perovskites with common A cations, higher energy modes were also strikingly similar. In particular, the calcium perovskites had almost all A_g modes at the same energies despite the greatly varying B cations. The second to the lowest mode in A_g and B_1g depended only on A cation mass for all perovskites. The volume plays a minor role throughout but is hard to separate from mass effects because the most massive cations are also the largest. However, if the B-cation is common, for example, aluminates or ferrites, the volume has a minor effect on the higher energy modes. These trends were not observed for all perovskites. Notable exceptions were found if a perovskite is near a phase transition or metastable, as found for three manganites. The effect of increased valency of the A cation from 2–4 to 3–3 perovskites expresses itself as relatively larger Raman shifts for the lowest energy modes. Analog studies of MgSiO₃ perovskites should be undertaken with only 2–4 perovskites. The increased understanding for the mode distributions of perovskites allows for better estimates of their thermodynamic properties through vibrational modeling.     

Experimental determination of liquidus H<Subscript>2</Subscript>O contents of haplogranite at deep-crustal conditions

The liquidus water content of a haplogranite melt at high pressure (P) and temperature (T) is important, because it is a key parameter for constraining the volume of granite that could be produced by melting of the deep crust. Previous estimates based on melting experiments at low P (≤0.5 GPa) show substantial scatter when extrapolated to deep crustal P and T (700–1000 °C, 0.6–1.5 GPa). To improve the high-P constraints on H₂O concentration at the granite liquidus, we performed experiments in a piston–cylinder apparatus at 1.0 GPa using a range of haplogranite compositions in the albite (Ab: NaAlSi₃O₈)—orthoclase (Or: KAlSi₃O₈)—quartz (Qz: SiO₂)—H₂O system. We used equal weight fractions of the feldspar components and varied the Qz between 20 and 30 wt%. In each experiment, synthetic granitic composition glass + H₂O was homogenized well above the liquidus T, and T was lowered by increments until quartz and alkali feldspar crystalized from the liquid. To establish reversed equilibrium, we crystallized the homogenized melt at the lower T and then raised T until we found that the crystalline phases were completely resorbed into the liquid. The reversed liquidus minimum temperatures at 3.0, 4.1, 5.8, 8.0, and 12.0 wt% H₂O are 935–985, 875–900, 775–800, 725–775, and 650–675 °C, respectively. Quenched charges were analyzed by petrographic microscope, scanning electron microscope (SEM), X-ray diffraction (XRD), and electron microprobe analysis (EMPA). The equation for the reversed haplogranite liquidus minimum curve for Ab_36.25Or_36.25Qz_27.5 (wt% basis) at 1.0 GPa is \(T = - 0.0995 w_{{{\text{H}}_{ 2} {\text{O}}}}^{ 3} + 5.0242w_{{{\text{H}}_{ 2} {\text{O}}}}^{ 2} - 88.183 w_{{{\text{H}}_{ 2} {\text{O}}}} + 1171.0\) for \(0 \le w_{{{\text{H}}_{ 2} {\text{O}}}} \le 17\) wt% and \(T\) is in °C. We present a revised \(P - T\) diagram of liquidus minimum H₂O isopleths which integrates data from previous determinations of vapor-saturated melting and the lower pressure vapor-undersaturated melting studies conducted by other workers on the haplogranite system. For lower H₂O (<5.8 wt%) and higher temperature, our results plot on the high end of the extrapolated water contents at liquidus minima when compared to the previous estimates. As a consequence, amounts of metaluminous granites that can be produced from lower crustal biotite–amphibole gneisses by dehydration melting are more restricted than previously thought.     

Fahlore thermochemistry: Gaps inside the (Cu,Ag)<Subscript>10</Subscript>(Fe,Zn)<Subscript>2</Subscript>(Sb,As)<Subscript>4</Subscript>S<Subscript>13</Subscript> cube

Possible topologies of miscibility gaps in arsenian (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores are examined. These topologies are based on a thermodynamic model for fahlores whose calibration has been verified for (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores, and conform with experimental constraints on the incompatibility between As and Ag in (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores, and with experimental and natural constraints on the incompatibility between As and Zn and the nonideality of the As for Sb substitution in Cu₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores. It is inferred that miscibility gaps in (Cu,Ag)₁₀(Fe,Zn)₂As₄S₁₃ fahlores have critical temperatures several °C below those established for their Sb counterparts (170 to 185°C). Depending on the structural role of Ag in arsenian fahlores, critical temperatures for (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores may vary from comparable to those inferred for (Cu,Ag)₁₀(Fe,Zn)₂As₄S₁₃ fahlores, if the As for Sb substitution stabilizes Ag in tetrahedral metal sites, to temperatures approaching 370°C, if the As for Sb substitution results in an increase in the site preference of Ag for trigonal-planar metal sites. The latter topology is more likely based on comparison of calculated miscibility gaps with compositions of fahlores from nature exhibiting the greatest departure from the Cu₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ and (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ planes of the (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlore cube.     

First-principles simulation of high-pressure polymorphs in MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript>

We have used density functional theory to investigate the stability of MgAl₂O₄ polymorphs under pressure. Our results can reasonably explain the transition sequence of MgAl₂O₄ polymorphs observed in previous experiments. The spinel phase (stable at ambient conditions) dissociates into periclase and corundum at 14 GPa. With increasing pressure, a phase change from the two oxides to a calcium-ferrite phase occurs, and finally transforms to a calcium-titanate phase at 68 GPa. The calcium-titanate phase is stable up to at least 150 GPa, and we did not observe a stability field for a hexagonal phase or periclase + Rh₂O₃(II)-type Al₂O₃. The bulk moduli of the phases calculated in this study are in good agreement with those measured in high-pressure experiments. Our results differ from those of a previous study using similar methods. We attribute this inconsistency to an incomplete optimization of a cell shape and ionic positions at high pressures in the previous calculations.     

Elasticity and equation of state of Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript>

A single crystal X-ray diffraction study on lithium tetraborate Li₂B₄O₇ (diomignite, space group I4₁ cd) has been performed under pressure up to 8.3 GPa. No phase transitions were found in the pressure range investigated, and hence the pressure evolution of the unit-cell volume of the I4₁ cd structure has been described using a third-order Birch–Murnaghan equation of state (BM-EoS) with the following parameters: V ₀  = 923.21(6) ų, K ₀  = 45.6(6) GPa, and K′ = 7.3(3). A linearized BM-EoS was fitted to the axial compressibilities resulting in the following parameters a ₀  = 9.4747(3) Å, K _0a  = 73.3(9) GPa, K′ _a  = 5.1(3) and c ₀  = 10.2838(4) Å, K _0c  = 24.6(3) GPa, K′ _c  = 7.5(2) for the a and c axes, respectively. The elastic anisotropy of Li₂B₄O₇ is very large with the zero-pressure compressibility ratio β _0c /β _0a  = 3.0(1). The large elastic anisotropy is consistent with the crystal structure: A three-dimensional arrangement of relatively rigid tetraborate groups [B₄O₇]²⁻ forms channels occupied by lithium along the polar c–axis, and hence compression along the c axis requires the shrinkage of the lithium channels, whereas compression in the a direction depends mainly on the contraction of the most rigid [B₄O₇]²⁻ units. Finally, the isothermal bulk modulus obtained in this work is in general agreement with that derived from ultrasonic (Adachi et al. in Proceedings-IEEE Ultrasonic Symposium, 228–232, 1985; Shorrocks et al. in Proceedings-IEEE Ultrasonic Symposium, 337–340, 1981) and Brillouin scattering measurements (Takagi et al. in Ferroelectrics, 137:337–342, 1992).     

Calorimetric study on high-pressure transitions in KAlSi<Subscript>3</Subscript>O<Subscript>8</Subscript>

KAlSi₃O₈ sanidine dissociates into a mixture of K₂Si₄O₉ wadeite, Al₂SiO₅ kyanite and SiO₂ coesite, which further recombine into KAlSi₃O₈ hollandite with increasing pressure. Enthalpies of KAlSi₃O₈ sanidine and hollandite, K₂Si₄O₉ wadeite and Al₂SiO₅ kyanite were measured by high-temperature solution calorimetry. Using the data, enthalpies of transitions at 298 K were obtained as 65.1 ± 7.4 kJ mol^–1 for sanidine wadeite + kyanite + coesite and 99.3 ± 3.6 kJ mol^–1 for wadeite + kyanite + coesite hollandite. The isobaric heat capacity of KAlSi₃O₈ hollandite was measured at 160–700 K by differential scanning calorimetry, and was also calculated using the Kieffer model. Combination of both the results yielded a heat-capacity equation of KAlSi₃O₈ hollandite above 298 K as C_p=3.896 × 10²–1.823 × 10³T^–0.5–1.293 × 10⁷T^–2+1.631 × 10⁹T^–3 (C_p in J mol^–1 K^–1, T in K). The equilibrium transition boundaries were calculated using these new data on the transition enthalpies and heat capacity. The calculated transition boundaries are in general agreement with the phase relations experimentally determined previously. The calculated boundary for wadeite + kyanite + coesite hollandite intersects with the coesite–stishovite transition boundary, resulting in a stability field of the assemblage of wadeite + kyanite + stishovite below about 1273 K at about 8 GPa. Some phase–equilibrium experiments in the present study confirmed that sanidine transforms directly to wadeite + kyanite + coesite at 1373 K at about 6.3 GPa, without an intervening stability field of KAlSiO₄ kalsilite + coesite which was previously suggested. The transition boundaries in KAlSi₃O₈ determined in this study put some constraints on the stability range of KAlSi₃O₈ hollandite in the mantle and that of sanidine inclusions in kimberlitic diamonds.     

Structural investigations of (Ca,Sr)ZrO<Subscript>3</Subscript> and Ca(Sn,Zr)O<Subscript>3</Subscript> perovskite compounds

(Ca _x ,Sr_1?x )ZrO₃ and Ca(Sn _y ,Zr_1-y )O₃ solid solutions were synthesized by solid-state reaction at high temperature before to be studied by powder X-ray diffraction and Raman Spectroscopy. Diffraction data allow the distortion of the ABO₃ perovskite structure to be investigated according to cations substitution on A and B-sites. It is shown that distortion, characterized by Φ, the tilt angle of BO₆ octahedra, slightly increases with decreasing y content in Ca(Sn _y ,Zr_1?y )O₃ compounds and strongly decreases with decreasing x content in (Ca _x ,Sr_1?x )ZrO₃ compounds. Such results are discussed in view of the relative A and B cation sizes. Raman data show that vibrational spectra are strongly affected by the cation substitution on A-site; the frequencies of most vibrational modes increase with increasing x content in (Ca _x ,Sr_1?x )ZrO₃ compounds, i.e. with the decreasing mean size of the A-cation; the upper shift is observed for the 358 cm^?1 mode (?ν/?r = ?60.1 cm^?1/Å). On the other hand, the cation substitution on B-sites, slightly affect the spectra; it is shown that in most cases, the frequency of vibrational modes increases with increasing y content in Ca(Sn _y ,Zr_1?y )O₃ compounds, i.e. with the decreasing mean size of the B-cation, but that two modes (287 and 358 cm^?1) behave differently: their frequencies decrease with the decreasing mean size of the B-cation, with a shift respectively equal to +314 and +162 cm^?1/Å. Such results could be used to predict the location of different elements such as trivalent cations or radwaste elements on A- or B-site, in the perovskite structure.     

Adsorption of H<Subscript>2</Subscript>O,NH<Subscript>3</Subscript> and C<Subscript>6</Subscript>H<Subscript>6</Subscript> on alkali metal cations in internal surface of mordenite and in external surface of smectite: a DFT study

Adsorption of H₂O, NH₃ and C₆H₆ on H- and alkali metal-exchanged structures of mordenite and on corresponding cations on the smectite layer is investigated by ab initio density-functional calculations. Proton or an alkali metal cation compensates one Al/Si framework substitution and resides in the extra-framework position of zeolite or above flat smectite layer close to the Al/Si substitution. Pronounced similarities between zeolite and smectite are observed in changes of the adsorption energies and location of the external cation with changing character of the external cation. Calculated adsorption energies exhibit the following trend: E(NH₃) > E(H₂O) > E(C₆H₆). Because of looser contact with the framework, zeolitic cations are stronger adsorption centers and calculated adsorption energies of zeolites are by ~20–30% larger than cations of smectites. The highest adsorption energy is calculated for H-exchanged structures and down the group of alkali metal cations a decrease of the adsorption energy is observed. Deviations from the smooth variation of the adsorption energy are caused by: (1) formation of strong hydrogen bonds in H-exchanged structures, (2) adsorption induced migration of the external Li⁺ cation, and (3) steric hindrances of the flat C₆H₆ molecule adsorbed on the cation in the cage of zeolite.