Equation of state of MgGeO3 perovskite to 65 GPa: comparison with the post-perovskite phase

The equation of state of MgGeO₃ perovskite was determined between 25 and 66 GPa using synchrotron X-ray diffraction with the laser-heated diamond anvil cell. The data were fit to a third-order Birch–Murnaghan equation of state and yielded a zero-pressure volume (V ₀) of 182.2 ± 0.3 Å³ and bulk modulus (K ₀) of 229 ± 3 GPa, with the pressure derivative (K′₀ = (?K ₀/?P) _T ) fixed at 3.7. Differential stresses were evaluated using lattice strain theory and found to be typically less than about 1.5 GPa. Theoretical calculations were also carried out using density functional theory from 0 to 205 GPa. The equation of state parameters from theory (V ₀ = 180.2 Å³, K ₀ = 221.3 GPa, and K′₀ = 3.90) are in agreement with experiment, although theoretically calculated volumes are systematically lower than experiment. The properties of the perovskite phase were compared to MgGeO₃ post-perovskite phase near the observed phase transition pressure (～65 GPa). Across the transition, the density increased by 2.0(0.7)%. This is in excellent agreement with the theoretically determined density change of 1.9%; however both values are larger than those for the (Mg,Fe)SiO₃ phase transition. The bulk sound velocity change across the transition is small and is likely to be negative [?0.5(1.6)% from experiment and ?1.2% from theory]. These results are similar to previous findings for the (Mg,Fe)SiO₃ system. A linearized Birch–Murnaghan equation of state fit to each axis yielded zero-pressure compressibilities of 0.0022, 0.0009, and 0.0016 GPa^?1 for the a, b, and c axis, respectively. Magnesium germanate appears to be a good analog system for studying the properties of the perovskite and post-perovskite phases in silicates.     

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).     

Compression of Fe3C to 30 GPa at room temperature

Polycrystalline Fe₃C (cementite) was compressed in a neon pressure medium to 30.5 GPa at 300 K using diamond-anvil cell techniques. Angular dispersive X-ray diffraction of Fe₃C was measured using monochromatic synchrotron radiation and imaging plates. No phase transition was observed up to the highest pressure studied. The pressure–volume data were fitted to a third-order Birch–Murnaghan equation of state. With V ₀ constrained to a measured value of 155.28 ų, the best fit yielded a 300-K isothermal bulk modulus K ₀ = 174 ± 6 GPa, and its pressure derivative at constant temperature K ₀ ^′ =(K ₀ /P) _T = 4.8±0.8.     

Compressibility of Ca3Al2Si3O12 perovskite up to 55 GPa

Compressibility of perovskite-structured Ca₃Al₂Si₃O₁₂ grossular (GrPv) was investigated at high pressure and high temperature by means of angle-dispersive powder X-ray diffraction using a laser-heated diamond anvil cell. We observed the Pbnm orthorhombic distortion for the pure phase above 50 GPa, whereas below this pressure, Al-bearing CaSiO₃ perovskite coexists with an excess of corundum. GrPv has a bulk modulus (K ₀ = 229 ± 5 GPa; \(K_{0}^{{\prime }}\) fixed to 4) almost similar to that reported for pure CaSiO₃ perovskite. Its unit-cell volume extrapolated to ambient conditions (V ₀ = 187.1 ± 0.4 Å³) is found to be ~2.5 % larger than for the Al-free phase. We observe an increasing unit-cell anisotropy with increasing pressure, which could have implications for the shear properties of Ca-bearing perovskite in cold slabs subducted into the Earth’s mantle.     

High-pressure single-crystal X-ray diffraction study of jadeite and kosmochlor

The crystal structures of natural jadeite, NaAlSi₂O₆, and synthetic kosmochlor, NaCrSi₂O₆, were studied at room temperature, under hydrostatic conditions, up to pressures of 30.4 (1) and 40.2 (1) GPa, respectively, using single-crystal synchrotron X-ray diffraction. Pressure–volume data have been fit to a third-order Birch–Murnaghan equation of state yielding V ₀ = 402.5 (4) Å³, K ₀ = 136 (3) GPa, and K ₀ ^′  = 3.3 (2) for jadeite and V ₀ = 420.0 (3) Å³, K ₀ = 123 (2) GPa and K ₀ ^′  = 3.61 (9) for kosmochlor. Both phases exhibit anisotropic compression with unit-strain axial ratios of 1.00:1.95:2.09 for jadeite at 30.4 (1) GPa and 1:00:2.15:2.43 for kosmochlor at 40.2 (1) GPa. Analysis of procrystal electron density distribution shows that the coordination of Na changes from 6 to 8 between 9.28 (Origlieri et al. in Am Mineral 88:1025–1032, 2003) and 18.5 (1) GPa in kosmochlor, which is also marked by a decrease in unit-strain anisotropy. Na in jadeite remains six-coordinated at 21.5 (1) GPa. Structure refinements indicate a change in the compression mechanism of kosmochlor at about 31 GPa in both the kinking of SiO₄ tetrahedral chains and rate of tetrahedral compression. Below 31 GPa, the O3–O3–O3 chain extension angle and Si tetrahedral volume in kosmochlor decrease linearly with pressure, whereas above 31 GPa the kinking ceases and the rate of Si tetrahedral compression increases by greater than a factor of two. No evidence of phase transitions was observed over the studied pressure ranges.     

High-pressure behaviour and equation of state of calcite, CaCO3

The high-pressure response of the cell parameters of calcite, CaCO₃, has been investigated by single crystal X-ray diffraction. The unit cell parameters have been refined from 0 to 1.435?GPa, and the linear and volume compressibilities have been measured as β _a =2.62(2)?×?10^?3?GPa^?1,β _c =7.94(7)?×?10^?3?GPa^?1, β _v =13.12?×?10^?3?GPa^?1. The bulk modulus has been obtained from a fit to the Birch-Murnaghan equation of state, giving K ₀=73.46?±?0.27?GPa and V ₀=367.789 ±?0.004?ų with K′=4. Combined with earlier data for magnesite, ankerite and dolomite, these data suggest that K ₀ V ₀ is a constant for the Ca-Mg rhombohedral carbonates.     

P–V–T equation of state of Mn3Al2Si3O12 spessartine garnet

The thermoelastic parameters of synthetic Mn₃Al₂Si₃O₁₂ spessartine garnet were examined in situ at high pressure up to 13 GPa and high temperature up to 1,100 K, by synchrotron radiation energy dispersive X-ray diffraction within a DIA-type multi-anvil press apparatus. The analysis of room temperature data yielded K ₀ = 172 ± 4 GPa and K ₀ ^′  = 5.0 ± 0.9 when V _0,300 is fixed to 1,564.96 Å³. Fitting of P–V–T data by means of the high-temperature third-order Birch–Murnaghan EoS gives the thermoelastic parameters: K ₀ = 171 ± 4 GPa, K ₀ ^′  = 5.3 ± 0.8, (?K _0,T /?T) _P  = ?0.049 ± 0.007 GPa K^?1, a ₀ = 1.59 ± 0.33 × 10^?5 K^?1 and b ₀ = 2.91 ± 0.69 × 10^?8 K^?2 (e.g., α _0,300 = 2.46 ± 0.54 × 10^?5 K^?1). Comparison with thermoelastic properties of other garnet end-members indicated that the compression mechanism of spessartine might be the same as almandine and pyrope but differs from that of grossular. On the other hand, at high temperature, spessartine softens substantially faster than pyrope and grossular. Such softening, which is also reported for almandine, emphasize the importance of the cation in the dodecahedral site on the thermoelastic properties of aluminosilicate garnet.     

A high P-T single-crystal X-ray diffraction study of thermoelasticity of MgSiO3 orthoenstatite

P-V-T data of MgSiO₃ orthoenstatite have been measured by single-crystal X-ray diffraction at simultaneous high pressures (in excess of 4.5 GPa) and temperatures (up to 1000 K). The new P-V-T data of the orthoenstatite, together with previous compression data and thermal expansion data, are described by a modified Birch-Murnaghan equation of state for diverse temperatures. The fitted thermoelastic parameters for MgSiO₃ orthoenstatite are: thermal expansion ?α/?P with values of a=2.86(29)×10^-5 K^-1 and b=0.72(16)×10^-8 K^-2; isothermal bulk modulus K _{T o} =102.8(2) GPa; pressure derivative of bulk modulus K′=?K/?P=10.2(1.2); and temperature derivative of bulk modulus K=?K/?T=-0.037(5) GPa/K. The derived thermal Grüneisen parameter is γ _th=1.05 for ambient conditions; Anderson-Grüneisen parameter is δ _{T o} =11.6, and the pressure derivative of thermal expansion is ?α/?P=-3.5×10^-6K^-1 GPa^-1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at two constant pressures of 1.5 GPa and 4.0 GPa are calculated. The resulting pressure dependence of thermal expansion is Δα/ΔP=-3.2(1)× 10^-6 K^-1 GPa^-1. The significantly large values of K′, K, δ _T and ?α/?P indicate that compression/expansion of MgSiO₃ orthoenstatite is very sensitive to changes of pressure and temperature.     

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.     

High-temperature and high-pressure equation of state for the hexagonal phase in the system NaAlSiO4 – MgAl2O4

Thermal equation of state of an Al-rich phase with Na_1.13Mg_1.51Al_4.47Si_1.62O₁₂ composition has been derived from in situ X-ray diffraction experiments using synchrotron radiation and a multianvil apparatus at pressures up to 24 GPa and temperatures up to 1,900 K. The Al-rich phase exhibited a hexagonal symmetry throughout the present pressure–temperature conditions and the refined unit-cell parameters at ambient condition were: a=8.729(1) Å, c=2.7695(5) Å, V ₀=182.77(6) Å³ (Z=1; formula weight=420.78 g/mol), yielding the zero-pressure density ρ₀=3.823(1) g/cm³ . A least-square fitting of the pressure-volume-temperature data based on Anderson’s pressure scale of gold (Anderson et al. in J Appl Phys 65:1534–543, 1989) to high-temperature Birch-Murnaghan equation of state yielded the isothermal bulk modulus K ₀=176(2) GPa, its pressure derivative K ₀ ^′ =4.9(3), temperature derivative (?K _T /?T) _P =?0.030(3) GPa K^?1 and thermal expansivity α(T)=3.36(6)×10^?5+7.2(1.9)×10^?9 T, while those values of K ₀=181.7(4) GPa, (?K _T /?T) _P =?0.020(2) GPa K^?1 and α(T)=3.28(7)×10^?5+3.0(9)×10^?9 T were obtained when K ₀ ^′ was assumed to be 4.0. The estimated bulk density of subducting MORB becomes denser with increasing depth as compared with earlier estimates (Ono et al. in Phys Chem Miner 29:527–531 2002; Vanpeteghem et al. in Phys Earth Planet Inter 138:223–230 2003; Guignot and Andrault in Phys Earth Planet Inter 143–44:107–128 2004), although the difference is insignificant (<0.6%) when the proportions of the hexagonal phase in the MORB compositions (～20%) are taken into account.     

Structural and vibrational behaviour of fluorapatite with pressure. Part I: in situ single-crystal X-ray diffraction investigation

Using single-crystal X-ray diffraction from a diamond anvil cell, the compressibility of a synthetic fluorapatite was determined up to about 7?GPa. The compression pattern was anisotropic, with greater change along a than c. Unit cell parameters varied linearly with β _a =3.32(8)?10^?3 and β _c =2.40(5)?10^?3 GPa^?1, giving a ratio β _a :β _c =1.38:1. Data fitted with a third-order Birch-Murnaghan EOS yielded a bulk modulus of K ₀=93(4)?GPa with K′=5.8(1.8). The evolution of the crystal structure of fluorapatite was analysed using data collected at room pressure, at 3.04 and 4.72?GPa. The bulk modulus of phosphate tetrahedron is about three times greater than the bulk modulus of calcium polyhedra. The values were 270(10), 100(4) and 86(3) GPa for P, Ca1 (nine-coordinated) and Ca2 (seven-coordinated) respectively. While the calcium polyhedra became more regular with pressure, the distortion of the phosphate tetrahedron remained unchanged. The size of the channel extending along the [001] direction represented the most compressible direction. The Ca2–Ca2 distance decreased from 3.982 to 3.897?Å on compression from 0.0001 to 4.72?GPa. The anisotropic compressional pattern may be understood in terms of the greater compressibility of the channel size over the polyhedral units. The reduction of the channel volume was measured by the evolution of the trigonal prism, having the Ca2–Ca2–Ca2 triangle as its base and the c lattice parameter as its height. This prism volume changed from 47.3?ų at room pressure to 44.78?ų at 4.72?GPa. Its relatively high bulk moduli, 86(3) GPa, indicated that the channel did not collapse with pressure and the apatite structure could remain stable at very high pressure.     

Equation of state of hexagonal aluminous phase in basaltic composition to 63 GPa at 300 K

A laser-heated diamond-anvil cell that is capable of operating up to a pressure of 63 GPa, with X-ray diffraction facilities using a synchrotron radiation source at the SPring-8, has been developed to observe the compressibility of a hexagonal aluminous phase, [K_0.15Na_1.66Ca_0.11Mg_1.29Fe²⁺ _0.86Al_3.13Ti_0.09Si_1.98] _Σ9.27O₁₂. The hexagonal aluminous phase is a potassium host mineral from the subducted oceanic crust in the Earth's lower mantle. A sample was heated using a YAG laser at each pressure increment to relax the deviatoric stress in the sample. X-ray diffraction measurements were carried out at 300 K using an angle-dispersive technique. Pressure was measured using an internal platinum pressure calibrant. The observed unit-cell volumes were used to obtain a third-order Birch–Murnaghan equation of state: unit-cell volume V _o=185.94(±16) ų, density ρ _o=4.145 g/cm³, and bulk modulus K _o=198(±3) GPa when the first pressure is derivative of the bulk modulus K ^′ _o is fixed to 4. The density of hexagonal aluminous phase is lower than that of coexisting Mg-perovskite in the subducted oceanic crust.     

The compressibility of Fe- and Al-bearing phase D to 30 GPa

High-pressure in situ X-ray diffraction experiment of Fe- and Al-bearing phase D (Mg_0.89Fe_0.14Al_0.25Si_1.56H_2.93O₆) has been carried out to 30.5 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields values of V ₀ = 86.10 ± 0.05 ų; K ₀ = 136.5 ± 3.3 GPa and K′ = 6.32 ± 0.30. If K′ is fixed at 4.0 K ₀ = 157.0 ± 0.7 GPa, which is 6% smaller than Fe–Al free phase D reported previously. Analysis of axial compressibilities reveals that the c-axis is almost twice as compressible (K _c  = 93.6 ± 1.1 GPa) as the a-axis (K _a  = 173.8 ± 2.2 GPa). Above 25 GPa the c/a ratio becomes pressure independent. No compressibility anomalies related to the structural transitions of H-atoms were observed in the pressure range to 30 GPa. The density reduction of hydrated subducting slab would be significant if the modal amount of phase D exceeds 10%.     

Equations of state of magnesium silicates anhydrous B and superhydrous B

High-pressure single crystal X-ray diffraction experiments of phase anhydrous B and superhydrous B have been carried out to 7.3 and 7.7?GPa, respectively, at room temperature. Fitting a third-order Birch-Murnaghan equation of state to the P-V data yields values of V ₀?=?838.86?±?0.04?ų, K_T,0?=?151.5?±?0.9?GPa and K′?=?5.5?±?0.3 for Anhy-B and V ₀?=?624.71?± 0.03?ų, K_T,0?=?142.6?±?0.8?GPa and K′?=?5.8?±?0.2 for Shy-B. A similar analysis of the axial compressibilities in Anhy-B reveals that the c-axis is most compressible (K_c?=?137?±?3?GPa), the b-axis is least compressible (K_b?=?175?±?4?GPa), and the a-axis is intermediate (K_a?=?148?±?1?GPa). In Shy-B, the a-axis is most compressible (K_a?=?135?±?1?GPa), followed by the b- and c-axes which have similar compressibilities (K_b?=?146?±?3?GPa; K_c?=?148?±?3?GPa). The fact that the b-axis of Shy-B is approximately 16% more compressible than Anhy-B is primarily due to differences in the O-T layer in which the H atoms are located and the linkages with the adjacent O layers. The rigid edge-sharing chains of MgO₆ and SiO₆ octahedra in the O layer control compressibility along the a- and c-axes in both structures. The net result is a reduction in the overall anisotropic compression from ～22% in Anhy-B to ～9% in Shy-B.     

Structural control of polyhedral compression in synthetic braunite, Mn2+Mn3+ 6O8SiO4

The compression of synthetic braunite, Mn²⁺Mn³⁺ ₆O₈SiO₄, was studied by high-pressure single-crystal X-ray diffraction carried out in a diamond-anvil cell. The equation of state at room temperature (third-order Birch-Murnaghan equation of state: V ₀=1661.15(8) ų, K _0,298=180.7±0.9 GPa, K′=6.5±0.3) was determined from unit-cell volume data to 9.18 GPa. Crystal structures were determined at 6 different pressures to 7.69 GPa. Compression of the structure (space group I4₁/acd) was found to be slightly anisotropic (a ₀=9.4262(4) Å, K _a =499±4 GPa, K _a ′=19.7±0.9; c ₀=18.6964(6) Å, K _c =657±6 GPa, K _c ′=15.7±1.4) which can be attributed to the fact that the Mn³⁺-O bonds, which are the most compressible bonds, are aligned closer to the (001) plane than to the c axis. The large bulk modulus is the result of the structural topology in which 2/3 and 1/2 of the edges of the Mn²⁺O₈ and Mn³⁺O₆ polyhedra share edges with other polyhedra. The Mn²⁺O₈ polyhedra were found to compress isotropically, whereas anisotropic compressional behaviour was observed for all three Mn³⁺O₆ octahedra. Although the polyhedral geometry of all three crystallographically independent Mn³⁺ sites shows the same type of uniaxially elongated distortion, the compression of the individual octahedral configurations was found to be strongly dependent upon both the geometry of the polyhedron itself and the types of, and the connectivity to, the neighbouring polyhedra. The differences in the configuration of the different oxygen atoms, and therefore the structural topology, is one of the major factors determining the type and degree of the pressure-induced distortion, while the Jahn-Teller effect plays a subordinate role.     

Density variations of Cr-rich garnets in the upper mantle inferred from the elasticity of uvarovite garnet

The thermoelastic parameters of Ca₃Cr₂Si₃O₁₂ uvarovite garnet were examined in situ at high pressure up to 13 GPa and high temperature up to 1100 K by synchrotron radiation energy-dispersive X-ray diffraction within a 6-6-type multi-anvil press apparatus. A least-square fitting of room T data to a third-order Birch–Murnaghan (BM3) EoS yielded K₀ = 164.2 ± 0.7 GPa, V₀ = 1735.9 ± 0.3 ų (K’₀ fixed to 4.0). P–V–T data were fitted simultaneously by a modified HT-BM3 EoS, which gave the isothermal bulk modulus K₀ = 163.6 ± 2.6 GPa, K’₀ = 4.1 ± 0.5, its temperature derivative (?K_0,T/?T)_P = –0.014 ± 0.002 GPa K^?1, and the thermal expansion coefficients a₀ = 2.32 ± 0.13 ×10^?5 K^?1 and b₀ = 2.13 ± 2.18 ×10^?9 K^?2 (K’₀ fixed to 4.0). Our results showed that the Cr³⁺ enrichment in natural systems likely increases the density of ugrandite garnets, resulting in a substantial increase of mantle garnet densities in regions where Cr-rich spinel releases chromium through a metasomatic reaction.     

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.     

High pressure single-crystal synthesis, structure and compressibility of the garnet Mn2+ 3Mn3+ 2[SiO4]3

Single crystals of the garnet Mn²⁺ ₃Mn³⁺ ₂[SiO₄]₃ and coesite were synthesised from MnO₂-SiO₂ oxide mixtures at 1000°C and 9 GPa in a multianvil press. The crystal structure of the garnet [space group Ia3¯d, a=11.801(2) Å] was refined at room temperature and 100 K from single-crystal X-ray data to R1=2.36% and R1=2.71%, respectively. In contrast to tetragonal Ca₃Mn³⁺ ₂[GeO₄]₃ (space group I4₁/a), the high-pressure garnet is cubic and does not display an ordered Jahn-Teller distortion of octahedral Mn³⁺. A disordered Jahn-Teller distortion either dynamic or static is evidenced by unusual high anisotropic displacement parameters. The room temperature structure is characterised by following bond lengths: Si-O=1.636(4) Å (tetrahedron), Mn³⁺-O=1.995 (4) Å (octahedron), Mn²⁺-O=2.280(5) and 2.409(4) Å (dodecahedron). The cubic structure was preserved upon cooling to 100 K [a=11.788(2) Å] and upon compressing up to 11.8 GPa in a diamond-anvil cell. Pressure variation of the unit cell parameter expressed by a third-order Birch-Murnaghan equation of state led to a bulk modulus K ₀=151.6(8) GPa and its pressure derivatives K′=6.38(19). The peak positions of the Raman spectrum recorded for Mn²⁺ ₃Mn³⁺ ₂[SiO₄]₃ were assigned based on a calderite Mn²⁺ ₃Fe³⁺ ₂[SiO₄]₃ model extrapolated from andradite and grossular literature data.     

Elastic behavior and pressure-induced structure evolution of topaz up to 45 GPa

The behavior of a natural topaz, Al_2.00Si_1.05O_4.00(OH_0.26F_1.75), has been investigated by means of in situ single-crystal synchrotron X-ray diffraction up to 45 GPa. No phase transition or change in the compressional regime has been observed within the pressure-range investigated. The compressional behavior was described with a third-order Birch–Murnaghan equation of state (III-BM-EoS). The III-BM-EoS parameters, simultaneously refined using the data weighted by the uncertainties in P and V, are as follows: K _V = 158(4) GPa and K _V ′ = 3.3(3). The confidence ellipse at 68.3 % (Δχ² = 2.30, 1σ) was calculated starting from the variance–covariance matrix of K _V and K′ obtained from the III-BM-EoS least-square procedure. The ellipse is elongated with a negative slope, indicating a negative correlation of the parameters K _V and K _V ′, with K _V = 158 ± 6 GPa and K _V ′ = 3.3 ± 4. A linearized III-BM-EoS was used to obtain the axial-EoS parameters (at room-P), yielding: K(a) = 146(5) GPa [β _a = 1/(3K(a)) = 0.00228(6) GPa^?1] and K′(a) = 4.6(3) for the a-axis; K(b) = 220(4) GPa [β _b = 0.00152(4) GPa^?1] and K′(b) = 2.6(3) for the b-axis; K(c) = 132(4) GPa [β _c = 0.00252(7) GPa^?1] and K′(c) = 3.3(3) for the c-axis. The elastic anisotropy of topaz at room-P can be expressed as: K(a):K(b):K(c) = 1.10:1.67:1.00 (β _a:β _b:β _c = 1.50:1.00:1.66). A series of structure refinements have been performed based on the intensity data collected at high pressure, showing that the P-induced structure evolution at the atomic scale is mainly represented by polyhedral compression along with inter-polyhedral tilting. A comparative analysis of the elastic behavior and P/T-stability of topaz polymorphs and “phase egg” (i.e., AlSiO₃OH) is carried out.