Tilting and distortion of CaSnO<Subscript>3</Subscript> perovskite to 7 GPa determined from single-crystal X-ray diffraction

The structural changes of CaSnO₃, a GdFeO₃-type perovskite, have been investigated to 7 GPa in a diamond-anvil cell at room temperature using single-crystal X-ray diffraction. Significant changes are observed in both the octahedral Sn–O bond lengths and tilt angles between the SnO6 octahedra. The octahedral (SnO6) site shows anisotropic compression and consequently the distortion of SnO6 increases with pressure. Increased pressure also results in a decrease of both of the inter-octahedral angles, Sn–O1–Sn and Sn–O2–Sn, indicating that octahedral tilting increases with increasing pressure, chiefly equivalent to rotation of the SnO6 octahedra about the pseudocubic <001>_p axis. The distortion in the CaO12 and SnO6 sites, along with the octahedral SnO6 tilting, is attributed to the SnO6 site being less compressible than the CaO12 site.Acknowledgments The authors acknowledge with gratitude the financial support for this work from NSF grant EAR-0105864. Ruby pressure measurements were conducted with the Raman system in the Vibrational Spectroscopy Laboratory in the Department of Geosciences at Virginia Tech with the help of Mr. Charles Farley.     

Peierls dislocation modelling in perovskite (CaTiO<Subscript>3</Subscript>): comparison with tausonite (SrTiO<Subscript>3</Subscript>) and MgSiO<Subscript>3</Subscript> perovskite

We present here a numerical modelling study of dislocations in perovskite CaTiO₃. The dislocation core structures and properties are calculated through the Peierls–Nabarro model using the generalized stacking fault (GSF) results as a starting model. The GSF are determined from first-principles calculations using the VASP code. The dislocation properties such as collinear, planar core spreading and Peierls stresses are determined for the following slip systems: [100](010), [100](001), [010](100), [010](001), [001](100), [001](010), and All dislocations exhibit lattice friction, but glide appears to be easier for [100](010) and [010](100). [001](010) and [001](100) exhibit collinear dissociation. Comparing Peierls stresses among tausonite (SrTiO₃), perovskite (CaTiO₃) and MgSiO₃ perovskite demonstrates the strong influence of orthorhombic distortions on lattice friction. However, and despite some quantitative differences, CaTiO₃ appears to be a satisfactory analogue material for MgSiO₃ perovskite as far as dislocation glide is concerned.     

Aluminum substitution mechanisms in perovskite-type MgSiO<Subscript>3</Subscript>: an investigation by Rietveld analysis

Al-containing MgSiO₃ perovskites of four different compositions were synthesized at 27 GPa and 1,873 K using a Kawai-type high-pressure apparatus: stoichiometric compositions of Mg_0.975Si_0.975Al_0.05O₃ and Mg_0.95Si_0.95Al_0.10O₃ considering only coupled substitution Mg²⁺ + Si⁴⁺ = 2Al³⁺, and nonstoichiometric compositions of Mg_0.99Si_0.96Al_0.05O_2.985 and Mg_0.97Si_0.93Al_0.10O_2.98 taking account of not only the coupled substitution but also oxygen vacancy substitution 2Si⁴⁺ = 2Al³⁺ + V_O¨. Using the X-ray diffraction profiles, Rietveld analyses were performed, and the results were compared between the stoichiometric and nonstoichiometric perovskites. Lattice parameter–composition relations, in space group Pbnm, were obtained as follows. The a parameters of both of the stoichiometric and nonstoichiometric perovskites are almost constant in the X _Al range of 0–0.05, where X _Al is Al number on the basis of total cation of two (X _Al = 2Al/(Mg + Si + Al)), and decrease with further increasing X _Al. The b and c parameters of the stoichiometric perovskites increase linearly with increasing Al content. The change in the b parameter of the nonstoichiometric perovskites with Al content is the same as that of the stoichiometric perovskites within the uncertainties. The c parameter of the nonstoichiometric perovskites is slightly smaller than that of the stoichiometric perovskites at X _Al of 0.10, though they are the same as each other at X _Al of 0.05. The Si(Al)–O1 distance, Si(Al)–O1–Si(Al) angle and minimum Mg(Al)–O distance of the nonstoichiometric perovskites keep almost constant up to X _Al of 0.05, and then the Si(Al)–O1 increases and both of the Si(Al)–O1–Si(Al) angle and minimum Mg(Al)–O decrease with further Al substitution. These results suggest that the oxygen vacancy substitution may be superior to the coupled substitution up to X _Al of about 0.05 and that more Al could be substituted only by the coupled substitution at 27 GPa. The Si(Al)–O1 distance and one of two independent Si(Al)–O2 distances in Si(Al)O₆ octahedra in the nonstoichiometric perovskites are always shorter than those in the stoichiometric perovskite at the same Al content. These results imply that oxygen defects may exist in the nonstoichiometric perovskites and distribute randomly.     

An infrared and <Superscript>1</Superscript>H MAS NMR investigation of strong hydrogen bonding in ussingite,Na<Subscript>2</Subscript>AlSi<Subscript>3</Subscript>O<Subscript>8</Subscript>(OH)

The mineral ussingite, Na₂AlSi₃O₈(OH), an interrupted tectosilicate, has strong hydrogen bonding between OH and the other nonbridging oxygen atom in the structure. Infrared spectra contain a strongly polarized, very broad OH-stretching band with an ill-defined maximum between 1500 and 1800 cm^–1, and a possible OH librational bending mode at 1295 cm^–1. The IR spectra confirm the orientation of the OH vector within the triclinic unit cell as determined from X-ray refinement (Rossi et al. 1974). There are three distinct bands in the ¹H NMR spectrum of ussingite: a predominant band at 13.5 ppm (TMS) representing 90% of the structural hydrogen, a second band at 15.9 ppm corresponding to 8% of the protons, and a third band at 11.0 ppm accounting for the remaining 2% of structural hydrogen. From the correlation between hydrogen bond length and ¹H NMR chemical shift (Sternberg and Brunner 1994), the predominant hydrogen bond length (H...O) was calculated to be 1.49 Å, in comparison to the hydrogen bond length determined from X-ray refinement (1.54 Å). The population of protons at 15.9 ppm is consistent with 5–8% Al–Si disorder. Although the ussingite crystal structure and composition are similar to those of low albite, the bonding environment of OH in low albite and other feldspars, as characterized through IR and ¹H NMR, is fundamentally different from the strong hydrogen bonding found in ussingite.     

High-pressure phase transitions of CaRhO<Subscript>3</Subscript> perovskite

High-pressure phase transitions of CaRhO₃ perovskite were examined at pressures of 6–27 GPa and temperatures of 1,000–1,930°C, using a multi-anvil apparatus. The results indicate that CaRhO₃ perovskite successively transforms to two new high-pressure phases with increasing pressure. Rietveld analysis of powder X-ray diffraction data indicated that, in the two new phases, the phase stable at higher pressure possesses the CaIrO₃-type post-perovskite structure (space group Cmcm) with lattice parameters: a = 3.1013(1) Å, b = 9.8555(2) Å, c = 7.2643(1) Å, V _m  = 33.43(1) cm³/mol. The Rietveld analysis also indicated that CaRhO₃ perovskite has the GdFeO₃-type structure (space group Pnma) with lattice parameters: a = 5.5631(1) Å, b = 7.6308(1) Å, c = 5.3267(1) Å, V _m  = 34.04(1) cm³/mol. The third phase stable in the intermediate P, T conditions between perovskite and post-perovskite has monoclinic symmetry with the cell parameters: a = 12.490(3) Å, b = 3.1233(3) Å, c = 8.8630(7) Å, β = 103.96(1)°, V _m  = 33.66(1) cm³/mol (Z = 6). Molar volume changes from perovskite to the intermediate phase and from the intermediate phase to post-perovskite are –1.1 and –0.7%, respectively. The equilibrium phase relations determined indicate that the boundary slopes are large positive values: 29 ± 2 MPa/K for the perovskite—intermediate phase transition and 62 ± 6 MPa/K for the intermediate phase—post-perovskite transition. The structural features of the CaRhO₃ intermediate phase suggest that the phase has edge-sharing RhO₆ octahedra and may have an intermediate structure between perovskite and post-perovskite.     

LiFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript> and NaFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript> at low temperatures: an infrared spectroscopic study

 Synthetic aegirine LiFeSi₂O₆ and NaFeSi₂O₆ were characterized using infrared spectroscopy in the frequency range 50–2000 cm⁻¹, and at temperatures between 20 and 300 K. For the C2/c phase of LiFeSi₂O₆, 25 of the 27 predicted infrared bands and 26 of 30 predicted Raman bands are recorded at room temperature. NaFeSi₂O₆ (with symmetry C2/c) shows 25 infrared and 26 Raman bands. On cooling, the C2/c–P2₁/c structural phase transition of LiFeSi₂O₆ is characterized by the appearance of 13 additional recorded peaks. This observation indicates the enlargement of the unit cell at the transition point. The appearance of an extra band near 688 cm⁻¹ in the monoclinic P2₁/c phase, which is due to the Si–O–Si vibration in the Si₂O₆ chains, indicates that there are two non-equivalent Si sites with different Si–O bond lengths. Most significant spectral changes appear in the far-infrared region, where Li–O and Fe–O vibrations are mainly located. Infrared bands between 300 and 330 cm⁻¹ show unusually dramatic changes at temperatures far below the transition. Compared with the infrared data of NaFeSi₂O₆ measured at low temperatures, the change in LiFeSi₂O₆ is interpreted as the consequence of mode crossing in the frequency region. A generalized Landau theory was used to analyze the order parameter of the C2/c–P2₁/c phase transition, and the results suggest that the transition is close to tricritical. Received: 21 January 2002 / Accepted: 22 July 2002     

Low-temperature heat capacities,entropies and high-pressure phase relations of MgSiO<Subscript>3</Subscript> ilmenite and perovskite

Low-temperature isobaric heat capacities (C _p ) of MgSiO₃ ilmenite and perovskite were measured in the temperature range of 1.9–302.4 K with a thermal relaxation method using the Physical Properties Measurement System. The measured C _p of perovskite was higher than that of ilmenite in the whole temperature range studied. From the measured C _p , standard entropies at 298.15 K of MgSiO₃ ilmenite and perovskite were determined to be 53.7 ± 0.4 and 57.9 ± 0.3 J/mol K, respectively. The positive entropy change (4.2 ± 0.5 J/mol K) of the ilmenite–perovskite transition in MgSiO₃ is compatible with structural change across the transition in which coordination of Mg atoms is changed from sixfold to eightfold. Calculation of the ilmenite–perovskite transition boundary using the measured entropies and published enthalpy data gives an equilibrium transition boundary at about 20–23 GPa at 1,000–2,000 K with a Clapeyron slope of −2.4 ± 0.4 MPa/K at 1,600 K. The calculated boundary is almost consistent within the errors with those determined by high-pressure high-temperature in situ X-ray diffraction experiments.     

Thermodynamics of mixing in diopside–jadeite,CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>–NaAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>, solid solution from static lattice energy calculations

Static lattice energy calculations (SLEC), based on empirical interatomic potentials, have been performed for a set of 800 different structures in a 2 × 2 × 4 supercell of C2/c diopside with compositions between diopside and jadeite, and with different states of order of the exchangeable Na/Ca and Mg/Al cations. Excess static energies of these structures have been cluster expanded in a basis set of 37 pair-interaction parameters. These parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the range of 273–2,023 K and to calculate a temperature–composition phase diagram. The simulations predict the order–disorder transition in omphacite at 1,150 ± 20°C in good agreement with the experimental data of Carpenter (Mineral Petrol 78:433–440, 1981). The stronger ordering of Mg/Al within the M1 site than of Ca/Na in the M2 site is attributed to the shorter M1–M1 nearest-neighbor distance, and, consequently, the stronger ordering force. The comparison of the simulated relationship between the order parameters corresponding to M1 and M2 sites with the X-ray refinement data on natural omphacites (Boffa Ballaran et al. in Am Mineral 83:419–433, 1998) suggests that the cation ordering becomes kinetically ineffective at about 600°C.     

High-pressure phase behavior of MnTiO<Subscript>3</Subscript>: decomposition of perovskite into MnO and MnTi<Subscript>2</Subscript>O<Subscript>5</Subscript>

The phase relations and compression behavior of MnTiO₃ perovskite were examined using a laser-heated diamond-anvil cell, X-ray diffraction, and analytical transmission electron microscopy. The results show that MnTiO₃ perovskite becomes unstable and decomposes into MnO and orthorhombic MnTi₂O₅ phases at above 38 GPa and high temperature. This is the first example of ABO₃ perovskite decomposing into AO + AB₂O₅ phases at high pressure. The compression behavior of volume, axes, and the tilting angle of TiO₆ octahedron of MnTiO₃ perovskite are consistent with those of other A²⁺B⁴⁺O₃ perovskites, although no such decomposition was observed in other perovskites. FeTiO₃ is also known to decompose into two phases, instead of transforming into the CaIrO₃-type post-perovskite phase and we argue that one of the reasons for the peculiar behavior of titanate is the weak covalency of the Ti–O chemical bonds.     

Structural properties of (Mn1-x Fe x )Nb2O6 columbites from X-ray diffraction and IR spectroscopy

A suite of (Mn_1-x Fe _x )Nb₂O₆ (x=0, 0.05, 0.25, 0.50, 0.75, 1) columbite samples has been prepared by solid-state reaction from oxides. X-ray diffraction and spectroscopic investigations have been carried out in order to gain different perspectives on how the solid solution adapts at different length scales to cation mixing. X-ray powder diffraction and powder absorption IR spectroscopy data are presented. The powder diffraction data show that there is no significant excess volume of mixing on the Fe–Mn columbite join. All the unit-cell parameters decrease linearly as a function of increasing Fe content. Substitution of Fe²⁺ for the larger Mn²⁺ cation causes a decrease in the volume of the A polyhedron, which also becomes more regular with respect to both bond-length and edge-length distortion parameters. No significant variation of the B site has been observed. Wavenumber shifts of the IR peaks nearly all vary linearly with composition, consistent with linear variations of the lattice parameters. Line broadening has been quantified by autocorrelation analysis of the IR spectra. This is interpreted as suggesting that there is some element of local strain or positional disorder at the length scale of second or third nearest neighbours around sites occupied by Fe.     

Atomistic model of diopside-K-jadeite (CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>-KAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>) solid solution

Atomistic model was proposed to describe the thermodynamics of mixing in the diopside-K-jadeite solid solution (CaMgSi₂O6-KAlSi₂O₆). The simulations were based on minimization of the lattice energies of 800 structures within a 2 × 2 × 4 supercell of C2/c diopside with the compositions between CaMgSi₂O₆ and KAlSi₂O₆ and with variable degrees of order/disorder in the arrangement of Ca/K cations in M2 site and Mg/Al in Ml site. The energy minimization was performed with the help of a force-field model. The results of the calculations were used to define a generalized Ising model, which included 37 pair interaction parameters. Isotherms of the enthalpy of mixing within the range of 273–2023 K were calculated with a Monte Carlo algorithm, while the Gibbs free energies of mixing were obtained by thermodynamic integration of the enthalpies of mixing. The calculated T-X diagram for the system CaMgSi₂O₆-KAlSi₂O₆ at temperatures below 1000 K shows several miscibility gaps, which are separated by intervals of stability of intermediate ordered compounds. At temperatures above 1000 K a homogeneous solid solution is formed. The standard thermodynamic properties of K-jadeite (KAlSi₂O₆) evaluated from quantum mechanical calculations were used to determine location of several mineral reactions with the participation of the diopside-K-jadeite solid solution. The results of the simulations suggest that the low content of KalSi₂O₆ in natural clinopyroxenes is not related to crystal chemical factors preventing isomorphism, but is determined by relatively high standard enthalpy of this end member.     

Thermal expansion of Mg(OH)<Subscript>2</Subscript> brucite under high pressure and pressure dependence of entropy

An equation of state for Mg(OH)₂ brucite under high-pressure and high-temperature conditions has been obtained by measuring temperature dependence of volume up to 600 K at ambient pressure and pressure dependence of volume up to 16 GPa at 300, 473, 673, and 873 K with in situ X-ray diffraction. Pressure dependence of entropy of brucite has been calculated with thermal expansion coefficient and volume which are derived from the present EoS. This dependence indicates that generation of secondary OH dipoles affects entropy. The OH dipoles probably appear around 2 GPa and the number seems not to change over 8 GPa at 300 K.     

Crystal chemistry of ferric iron in (Mg,Fe)(Si,Al)O<Subscript>3</Subscript> majorite with implications for the transition zone

Fifteen samples of (Mg,Fe)SiO₃ majorite with varying Fe/Mg composition and one sample of (Mg,Fe)(Si,Al)O₃ majorite were synthesized at high pressure and temperature under different conditions of oxygen fugacity using a multianvil press, and examined ex situ using X-ray diffraction and Mössbauer and optical absorption spectroscopy. The relative concentration of Fe³⁺ increases both with total iron content and increasing oxygen fugacity, but not with Al concentration. Optical absorption spectra indicate the presence of Fe²⁺–Fe³⁺ charge transfer, where band intensity increases with increasing Fe³⁺ concentration. Mössbauer data were used in conjunction with electron microprobe analyses to determine the site distribution of all cations. Both Al and Fe³⁺ substitute on the octahedral site, and charge balance occurs through the removal of Si. The degree of Mg/Si ordering on the octahedral sites in (Mg,Fe)SiO₃ majorite, which affects both the c/a ratio and the unit cell volume, is influenced by the thermal history of the sample. The Fe³⁺ concentration of (Mg,Fe)(Si,Al)O₃ majorite in the mantle will reflect prevailing redox conditions, which are believed to be relatively reducing in the transition zone. Exchange of material across the transition boundary to (Mg,Fe) (Si,Al)O₃ perovskite would then require a mechanism to oxidize sufficient iron to satisfy crystal-chemical requirements of the lower-mantle perovskite phase.     

In situ X-ray observations of phase transitions in MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> spinel to 40 GPa using multianvil apparatus with sintered diamond anvils

 Phase transitions in MgAl₂O₄ spinel have been studied at pressures 22–38 GPa, and at temperatures up to 1600 °C, using a combination of synchrotron radiation and a multianvil apparatus with sintered diamond anvils. Spinel dissociated into a mixture of MgO plus Al₂O₃ at pressures to 25 GPa, while it transformed to the CaFe₂O₄ (calcium ferrite) structure at higher pressures via the metastably formed oxide mixture upon increasing temperature. Neither the e-phase nor the CaTi₂O₄-type MgAl₂O₄, which were reported in earlier studies using the diamond-anvil cell, were observed in the present pressure and temperature range. The zero-pressure bulk modulus of the calcium-ferrite-type MgAl₂O₄ was calculated as K=213 (3) GPa, which is significantly lower than that reported by Yutani et al. (1997), but is consistent with a more recent result by Funamori et al. (1998) and that estimated by an ab initio calculation by Catti (2001). Received: 2 April 2002 / Accepted: 29 July 2002 Acknowledgements The authors thank Y. Higo, Y. Sueda, T.␣Ueda, Y. Tanimoto, A. Fukuyama, K. Ochi, F. Kurio and T. Kawahara for help in the in situ X-ray observations at SPring-8 (No: 2000A0061-CD-np and 2000B0093-ND-np). We also thank W.␣Utsumi, J. Ando and O. Shimomura for advice and encouragement during this study, and N. Funamori and an anonymous reviwer for comments on the article. The present study is partly supported by the grant-in-aid for Scientific Research (A) of the Ministry of Education, Science, Sport and Culture of the Japanese government (no: 11694088).     

Magnetic properties and neutron diffraction study of two manganese sulfosalts: monoclinic MnSb<Subscript>2</Subscript>S<Subscript>4</Subscript> and benavidesite (MnPb<Subscript>4</Subscript>Sb<Subscript>6</Subscript>S<Subscript>14</Subscript>)

Mn²⁺Sb₂S₄, a monoclinic dimorph of clerite, and benavidesite (Mn²⁺Pb₄Sb₆S₁₄) show well-individualized single chains of manganese atoms in octahedral coordination. Their magnetic structures are presented and compared with those of iron derivatives, berthierite (Fe²⁺Sb₂S₄) and jamesonite (Fe²⁺Pb₄Sb₆S₁₄). Within chains, interactions are antiferromagnetic. Like berthierite, MnSb₂S₄ shows a spiral magnetic structure with an incommensurate 1D propagation vector [0, 0.369, 0], unchanged with temperature. In berthierite, the interactions between identical chains are antiferromagnetic, whereas in MnSb₂S₄ interactions between chains are ferromagnetic along c-axis. Below 6 K, jamesonite and benavidesite have commensurate magnetic structures with the same propagation vector [0.5, 0, 0]: jamesonite is a canted ferromagnet and iron magnetic moments are mainly oriented along the a-axis, whereas for benavidesite, no angle of canting is detected, and manganese magnetic moments are oriented along b-axis. Below 30 K, for both compounds, one-dimensional magnetic ordering or correlations are visible in the neutron diagrams and persist down to 1.4 K.     

Low-temperature heat capacities of MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> and spinels of the MgCr<Subscript>2</Subscript>O<Subscript>4</Subscript>–MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> solid solution

We present results from low-temperature heat capacity measurements of spinels along the solid solution between MgAl₂O₄ and MgCr₂O₄. The data also include new low-temperature heat capacity measurements for MgAl₂O₄ spinel. Heat capacities were measured between 1.5 and 300 K, and thermochemical functions were derived from the results. No heat capacity anomaly was observed for MgAl₂O₄ spinel; however, we observe a low-temperature heat capacity anomaly for Cr-bearing spinels at temperatures below 15 K. From our data we calculate standard entropies (298.15 K) for Mg(Cr,Al)₂O₄ spinels. We suggest a standard entropy for MgAl₂O₄ of 80.9 ± 0.6 J mol⁻¹ K⁻¹. For the solid solution between MgAl₂O₄ and MgCr₂O₄, we observe a linear increase of the standard entropies from 80.9 J mol⁻¹ K⁻¹ for MgAl₂O₄ to 118.3 J mol⁻¹ K⁻¹ for MgCr₂O₄.     

Ab-initio calculations of the proton location in topaz-OH,Al<Subscript>2</Subscript>SiO<Subscript>4</Subscript>(OH)<Subscript>2</Subscript>

The position of hydrogen in the structure of topaz-OH was determined by means of ab-initio quantum-mechanic calculations. Static lattice energy calculations predict the existence of four non-equivalent positions of protons, which are characterized by O4–H1... O1, O4–H2... O2, O4–H3... O3 and O4–H4... O4 hydrogen bonds. The distribution of the protons between positions of local equilibrium is controlled by the proton–proton avoidance rule and the strength of the hydrogen bonds. The most favourable configuration of hydrogen atoms is achieved for adjacent protons, which form O4–H3... O3 and O4–H4... O4 hydrogen bonds, respectively. The thermal excitation of atoms at a temperature of 55 K is large enough for the hydrogen atoms occasionally to change their positions to form O4–H1... O1 and O4–H2... O2 bonds. At ambient pressures and higher temperatures the protons are in a dynamic exchange between the allowed positions of local minima. As a consequence, for nearly room-temperature conditions, the dynamic change between different structural configurations leads to the violation of all possible symmetry elements and with that to space group #E5/E5#1. The flipping of the protons between different sites is achieved by simple rotation of the OH-dipole and does not produce any significant distortion of the framework of topaz, whose symmetry remains that of the space group Pbnm. Therefore, no reduction of symmetry has been observed in former X-ray studies on topaz-OH. Calculated IR absorption spectra of topaz-OH were found to be in good agreement with measured spectra. According to the calculations, the two favourable configurations of protons might correspond to the measured peak splitting within the OH-stretching range. An experimentally observed low-frequency band at 3520 cm^–1 was assigned to the OH-stretching of the O4–H3... O3 bond, while the band at 3600 cm^–1 was attributed to OH-stretching of the O4–H4... O4 hydrogen bond. The broad peak in FAR-IR frequency range at 100–150 cm^–1 is attributed to the stretching of H3... O3 and H4... O4 contacts. The rate of proton exchange at 670 K among different sites was estimated by ab-inito molecular dynamic simulations. The calculations predict that flipping of adjacent protons between O4–H3... O3 and O4–H4... O4 bonds at 670 K occur at a rate of about 1.96 THz.     

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.