Elasticity of single-crystal aragonite by Brillouin spectroscopy

The elastic constants of natural single-crystal aragonite (CaCO₃) have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃ and C₂₃ are 171.1±1.0, 110.1±0.9, 98.4±1.2, 39.3±0.6, 24.2±0.4, 40.2±0.6, 60.3±1.0, 27.8±1.6 and 41.9±2.0 GPa, respectively, for aragonite. The linear compressibilities of the a-, b- and c-axis for aragonite at ambient conditions were derived from our measured data to be 3.0±0.2, 4.2±0.2 and 7.3±0.6×10^–3 GPa^–1, respectively. The aggregate bulk and shear moduli for aragonite using the Voigt-Reuss-Hill (VRH) scheme are thus calculated to be 68.9±1.4 and 35.8±0.2 GPa, respectively. The value of bulk modulus is in remarkable contrast to the literature value of 46.9 GPa measured almost a century ago. Our new datum, however, is closer to that derived from recent atomistic simulation and static compression studies.     

Compressibility and crystal structure of sillimanite, Al2SiO5, at high pressure

The unit-cell dimensions and crystal structure of sillimanite at various pressures up to 5.29 GPa have been refined from single-crystal X-ray diffraction data. As pressure increases, a and b decrease linearly, whereas c decreases nonlinearly with a slightly positive curvature. The axial compression ratios at room pressure are β_a:β_b:β_c=1.22:1.63:1.00. Sillimanite exhibits the least compressibility along c, but the least thermal expansivity along a (Skinner et al. 1961; Winter and Ghose 1979). The bulk modulus of sillimanite is 171(1) GPa with K′=4 (3), larger than that of andalusite (151 GPa), but smaller than that of kyanite (193 GPa). The bulk moduli of the [Al1O₆], [Al2O₄], and [SiO₄] polyhedra are 162(8), 269(33), and 367(89) GPa, respectively. Comparison of high-pressure data for Al₂SiO₅ polymorphs reveals that the [SiO₄] tetrahedra are the most rigid units in all these polymorphic structures, whereas the [AlO₆] octahedra are most compressible. Furthermore, [AlO₆] octahedral compressibilities decrease from kyanite to sillimanite, to andalusite, the same order as their bulk moduli, suggesting that [AlO₆] octahedra control the compression of the Al₂SiO₅ polymorphs. The compression of the [Al1O₆] octahedron in sillimanite is anisotropic with the longest Al1-OD bond shortening by ～1.9% between room pressure and 5.29 GPa and the shortest Al1-OB bond by only 0.3%. The compression anisotropy of sillimanite is primarily a consequence of its topological anisotropy, coupled with the compression anisotropy of the Al-O bonds within the [Al1O₆] octahedron.     

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.     

High-pressure X-ray study of LiCrSi2O6 clinopyroxene and the general compressibility trends for Li-clinopyroxenes

High-pressure single-crystal X-ray diffraction measurements of synthetic LiCrSi₂O₆ clinopyroxene (with space group P2₁/c) were performed in a diamond-anvil cell up to 7.970 GPa. No phase transition has been observed within the pressure range investigated, but the elastic behavior at lower pressures (up to ~2.5 GPa) is affected by an anomalous softening due to the proximity of the phase transition to the HT-C2/c phase at 330 K and at ambient pressure. A third-order Birch–Murnaghan equation of state fitted to the compression data above 2.5 GPa yields a bulk modulus K _T0 = 93(2) GPa and its first derivative K′ = 8.8(6). The structural data measured up to 7.970 GPa confirm that the space group P2₁/c is maintained throughout the whole pressure range investigated. The atomic parameters, obtained from the integrated diffraction intensities, suggest that the Li coordination polyhedron changes its coordination number from 5 to 6 at 6–7 GPa by means of the approach of the bridging O atom, related to the increased kinking of the B tetrahedral chain. Furthermore, at higher pressures, the structural evolution of LiCrSi₂O₆ provides evidence in the variation of kinking angles and bond lengths of a potential phase transition above 8 GPa to the HP-C2/c space group. A comparison of the Li-clinopyroxenes (M1 = Cr, Al, Sc, Ga, Mg + Fe) previously investigated and our sample shows that their elastic behavior and structural mechanisms of compression are analogous.     

Compression of Na0.4Mg0.6Al1.6Si0.4O4 NAL and Ca-ferrite-type phases

Compression behaviors of two Al-rich phases in the lower mantle, hexagonal new aluminum-rich (NAL) phase and its high-pressure polymorph Ca-ferrite-type (CF) phase, were examined for identical Na_0.4Mg_0.6Al_1.6Si_0.4O₄ (40?% NaAlSiO₄–60?% MgAl₂O₄) composition. The volumes of the NAL and CF phases were obtained at room temperature up to 31 and 134?GPa, respectively, by a combination of laser-annealed diamond-anvil cell techniques and synchrotron X-ray diffraction measurements. Fitting of the third-order Birch–Murnaghan equation of state to such pressure–volume data yields bulk modulus K ₀?=?199(6) GPa at 1?bar and its pressure derivative K ₀′?=?5.0(6) for the NAL phase and K ₀?=?169(5) GPa and K ₀′?=?6.3(3) for the CF phase. These results indicate that the bulk modulus increases from 397 to 407 GPa across the phase transition from the NAL to CF phase at 43 GPa, where the NAL phase completely transforms into the CF phase on Na_0.4Mg_0.6Al_1.6Si_0.4O₄. Density also increases by 2.1?% across the phase transition.     

Displacive phase transitions in C-centred clinopyroxenes: spodumene, LiScSi2O6 and ZnSiO3

The clinopyroxenes spodumene (LiAlSi₂O₆), LiScSi₂O₆ and ZnSiO₃, all with space group C2/c at ambient conditions, were studied under high pressures by single-crystal X-ray diffraction in a diamond-anvil cell. Changes in the evolution of the unit-cell parameters, optical properties and the appearance of h + k odd reflections characteristic of a primitive lattice, indicate that all three pyroxenes undergo phase transitions. The transitions are mostly displacive in character, and are non-quenchable. Transition pressures are 3.19 GPa in spodumene, ∼0.6 GPa in LiScSi₂O₆ and 1.92 GPa in ZnSiO₃. The space group of all three high-pressure phases was determined to be P2₁/c by structure refinement to single-crystal X-ray intensity data collected in the DAC. In the ZnSiO₃ clinopyroxene the intermediate P2₁/c phase further transforms to a second C2/c phase (HP-C2/c) at 4.9 GPa (confirmed by structure refinement). The volume change at this transition is about 2.6%, three times larger than in the first phase transition, and typical of the P2₁/c→ HP-C2/c phase transitions found previously in MgSiO₃, FeSiO₃, etc. These results therefore provide the first direct evidence that the HP-C2/c and the HT-C2/c structures of pyroxenes are distinct polymorphs with the same space group. The phase transition from C2/c to P2₁/c symmetry in spodumene and LiScSi₂O₆ therefore occurs because the polymorphs stable at ambient conditions are isotypic to the high-temperature C2/c phases of clinopyroxenes such as pigeonite and clinoenstatite. Received: 22 December 1999 / Accepted: 7 June 2000     

High-pressure X-ray diffraction and Raman spectroscopy of CaFe<Subscript>2</Subscript>O<Subscript>4</Subscript>-type β-CaCr<Subscript>2</Subscript>O<Subscript>4</Subscript>

In situ high-pressure synchrotron X-ray diffraction and Raman spectroscopic studies of orthorhombic CaFe₂O₄-type β-CaCr₂O₄ chromite were carried out up to 16.2 and 32.0 GPa at room temperature using multi-anvil apparatus and diamond anvil cell, respectively. No phase transition was observed in this study. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a zero-pressure volume of V ₀ = 286.8(1) ų, an isothermal bulk modulus of K ₀ = 183(5) GPa and the first pressure derivative of isothermal bulk modulus K ₀′ = 4.1(8). Analyses of axial compressibilities show anisotropic elasticity for β-CaCr₂O₄ since the a-axis is more compressible than the b- and c-axis. Based on the obtained and previous results, the compressibility of several CaFe₂O₄-type phases was compared. The high-pressure Raman spectra of β-CaCr₂O₄ were analyzed to determine the pressure dependences and mode Grüneisen parameters of Raman-active bands. The thermal Grüneisen parameter of β-CaCr₂O₄ is determined to be 0.93(2), which is smaller than those of CaFe₂O₄-type CaAl₂O₄ and MgAl₂O₄.     

Room-temperature equation of state of Li<Subscript>2</Subscript>VOSiO<Subscript>4</Subscript> up to 8.5 GPa

High-pressure single-crystal X-ray diffraction measurements of lattice parameters of the compound Li₂VOSiO₄, which crystallises with a natisite-type structure, has been carried out to a pressure of 8.54(5) GPa at room temperature. Unit-cell volume data were fitted with a second-order Birch-Murnaghan EoS (BM-EoS), simultaneously refining V ₀ and K ₀ using the data weighted by the uncertainties in V. The bulk modulus is K ₀ = 99(1) GPa, with K′ fixed to 4. Refinements of third order equations-of-state yielded values of K′ that did not differ significantly from 4. The compressibility of the unit-cell is strongly anisotropic with the c axis (K ₀(c) = 49.7 ± 0.5 GPa) approximately four times more compressible than the a axis (K ₀(a) = 195 ± 3 GPa).     

The nonlinear anomalous lattice elasticity associated with the high-pressure phase transition in spodumene: a high-precision static compression study

The high-pressure behavior of the lattice elasticity of spodumene, LiAlSi₂O₆, was studied by static compression in a diamond-anvil cell up to 9.3 GPa. Investigations by means of single-crystal XRD and Raman spectroscopy within the hydrostatic limits of the pressure medium focus on the pressure ranges around ~3.2 and ~7.7 GPa, which have been reported previously to comprise two independent structural phase transitions. While our measurements confirm the well-established first-order C2/c–P2₁/c transformation at 3.19 GPa (with 1.2% volume discontinuity and a hysteresis between 0.02 and 0.06 GPa), both unit-cell dimensions and the spectral changes observed in high-pressure Raman spectra give no evidence for structural changes related to a second phase transition. Monoclinic lattice parameters and unit-cell volumes at in total 59 different pressure points have been used to re-calculate the lattice-related properties of spontaneous strain, volume strain, and the bulk moduli as a function of pressure across the transition. A modified Landau free energy expansion in terms of a one component order parameter has been developed and tested against these experimentally determined data. The Landau solution provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P _tr, thus giving Landau parameters of K ₀ = 138.3(2) GPa, K′ = 7.46(5), λ _V  = 33.6(2) GPa, a = 0.486(3), b = −29.4(6) GPa and c = 551(11) 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.     

Equation of state of Fe3+-bearing phase-X

We investigated the high-pressure behaviour of Fe³⁺-bearing hydrous phase-X, (K_1.307Na_0.015)(Mg_1.504Fe _0.373 ³⁺ Al_0.053Ti _0.004 ⁴⁺ )Si₂O₇H_0.36, up to 34?GPa at room temperature by synchrotron X-ray powder diffraction. The lattice parameters behave anisotropically, with the [001] direction stiffer than [100]. In the 10^?4 to 22?GPa pressure range, the axial bulk moduli are K _0a ?=?112(3) GPa and K′?=?4, and K _0c ?=?158(2) GPa and K′?=?4, and the anisotropy of the lattice parameters is β_0c :β_0a ?=?0.71:1. The cell volumes are fitted by a second-order Birch–Murnaghan equation of state giving a bulk modulus of K ₀?=?127(1) GPa and K′?=?4 in the same pressure range. After 22?GPa, a discontinuity in volume and lattice parameters can be recognized. Sample did not become amorphous up to 34?GPa. The coupled substitution K?+?Mg?=?[]?+?Fe³⁺ has only a limited influence on the bulk modulus and structural stability of phase-X.     

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.     

Synchrotron X-ray analysis of norbergite, Mg2.98Fe0.01Ti0.02Si0.99O4(OH0.31F1.69) structure at high pressure up to 8.2?GPa

The natural norbergite, Mg_2.98Fe_0.01Ti_0.02Si_0.99O₄(OH_0.31F_1.69) is examined by synchrotron X-ray diffraction analysis at pressures up to 8.2 GPa. The measured linear compressibilities of the crystallographic axes are β _a  = 2.18(4) × 10⁻³, β _b  = 2.93(7) × 10⁻³, and β _c  = 2.77(7) × 10⁻³ (GPa⁻¹), respectively and the calculated isothermal bulk modulus of the norbergite is K _T = 113(2) GPa based on the Birch–Murnaghan equation of state assuming a pressure derivative of K′ = 4. The crystal structures of norbergite are refined at room temperature and pressures of 4.7, 6.3, and 8.2 GPa, yielding R values for the structure refinements of 4.6, 5.3, and 5.3%, respectively. The bulk moduli of the polyhedral sites are 293(15) GPa for the tetrahedron, 106(5) GPa for the M2 octahedron, 113(2) GPa for the M3 octahedron, and 113(3) GPa for the total void space. The bulk modulus exhibits a good linear correlation with the filling factor for polyhedral sites in structures of the humite minerals and forsterite, reflecting the Si⁴⁺ + 4O²⁻ ⇔ □ + 4(OH, F)⁻ substitution in the humite minerals. Moreover, two simply linear trends were observed in the relationship between bulk modulus and packing index for natural minerals and dense hydrous magnesium silicate minerals. This relationship would reflect that the differences in compression mechanism were involved with hydrogen bonding in these minerals. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Elasticity of CaTiO3, SrTiO3 and BaTiO3 perovskites up to 3.0 Gpa: the effect of crystallographic structure

Elasticity of CaTiO₃, SrTiO₃ and BaTiO₃ perovskites has been experimentally investigated as a function of pressure up to 3.0 GPa in a liquid-medium piston cylinder apparatus using a high precision ultrasonic interferometric technique. Specimens used are hot-pressed fine-grained (3–10 μm) polycrystalline aggregates with low porosity (<1.5%). Compressional and shear wave velocities and their pressure derivatives have been measured. The results are compared with previous studies on other perovskites and the role of structural transitions is examined. We find that the role of Ti-O₆ polyhedral tilting (such as observed in CaTiO₃) is small in the sense that a single well-defined general trend exists in perovskites with a wide range of tilting angles, although there is suggestion that cubic perovskites have slightly higher bulk modulus than orthorhombic perovskites. In contrast, cation-anion displacement that changes crystal symmetry from cubic to tetragonal in BaTiO₃ has very large effects on elasticity. This distortion significantly reduces the bulk modulus (but not much the shear modulus) and results in an unusually large pressure derivative of bulk modulus (dK/dP～10). A large change in elasticity in BaTiO₃ associated with the structural transition (without a significant volume change) is a clear example of the breakdown of the Birch's law between densities and elastic wave velocities.     

Single-crystal elastic properties of chondrodite: implications for water in the upper mantle

Chondrodite, a member of the humite group of minerals, forms by hydration of olivine and is stable over a range of temperatures and pressures that includes a portion of the uppermost mantle. We have measured the single crystal elastic properties of a natural chondrodite specimen at ambient conditions using Brillouin spectroscopy. The isotropic aggregate bulk (K) and shear (μ) moduli calculated from the single-crystal elastic moduli, C_ij, are: K_S=118.4(16) GPa and μ=75.6(7) GPa. A comparison of the structures and elasticity of olivine and chondrodite indicate that the replacement of O with (OH,F) in M²⁺O₆ octahedra has a small effect on the elasticity of humite-group minerals. The slightly diminished elastic moduli of humite-group minerals (as compared to olivine) are likely caused by a smaller ratio of strong structural elements (SiO₄ tetrahedra) to weaker octahedra, and perhaps a more flexible geometry of edge-sharing MO₄(O,OH,F)₂ octahedra. In contrast to the humite-olivine group minerals, the incorporation of water into garnets and spineloids leads to a more substantial decrease in the elastic properties of these minerals. This contrasting behavior is due to formation of O₄H₄ tetrahedra and vacant hydroxyl-bearing octahedra in the garnets and spineloids, respectively. Therefore, the mechanism of incorporation of H/OH into mineral phases, not only degree of hydration, should be taken into account when estimating the effect of water on the elastic properties of minerals. The bulk elastic wave velocities of chondrodite and olivine are very similar. If humite-like incorporation of OH is predominant in the upper mantle, then the reaction of OH with olivine will have a minor or possibly no detectable effect on seismic velocities. Thus, it may be difficult to distinguish chondrodite-bearing rocks from “anhydrous” mantle on the basis of seismically determined velocities for the Earth. Received: 25 February 1998 / Revised, accepted: 18 August 1998     

On the elastic behaviour of zeolite mordenite: a synchrotron powder diffraction study

The high-pressure elastic behaviour of a synthetic zeolite mordenite, Na₆Al_6.02Si_42.02O₉₆·19H₂O [a=18.131(2), b=20.507(2), c=7.5221(5) Å, space group Cmc2₁], has been investigated by means of in situ synchrotron X-ray powder diffraction up to 5.68 GPa. No phase transition has been observed within the pressure range investigated. Axial and volume bulk moduli have been calculated using a truncated second-order Birch–Murnaghan equation-of-state (II-BM-EoS). The refined elastic parameters are: V ₀=2801(11) ų, K _T0= 41(2) GPa for the unit-cell volume; a ₀=18.138(32) Å, K _T0(a)=70(8) GPa for the a-axis; b ₀=20.517(35) Å, K _T0(b)=29(2) GPa for the b-axis and c ₀=7.531(5) Å, K _T0(c)=38(1) GPa for the c-axis [K _T0(a): K _T0(b): K _T0(c)=2.41:1.00:1.31]. Axial and volume Eulerian finite strain versus “normalized stress” plots (fe–Fe plot) show an almost linear trend and the weighted linear regression through the data points yields the following intercept values: Fe(0)=39(4) GPa for V; Fe _a (0)=65(18) GPa for a; Fe _b (0)=28(3) GPa for b; Fe _c (0)=38(2) GPa for c. The magnitudes of the principal Lagrangian unit-strain coefficients, between 0.47 GPa (the lowest HP-data point) and each measured P>0.47 GPa, were calculated. The unit-strain ellipsoid is oriented with ε₁ || b, ε₂ || c, ε₃ || a and |ε₁|> |ε₂|> |ε₃|. Between 0.47 and 5.68 GPa the relationship between the unit-strain coefficient is ε₁: ε₂: ε₃=2.16:1.81:1.00. The reasons of the elastic anisotropy are discussed.An erratum to this article can be found at     

The high-pressure C2/c–P21/c phase transition along the LiAlSi2O6–LiGaSi2O6 solid solution

Two synthetic single-crystals with composition Li(Al_0.53Ga_0.47)Si₂O₆ and LiGaSi₂O₆ and space group C2/c at room conditions have been studied under pressure by means of X-ray diffraction using a diamond anvil cell. The unit-cell parameters were determined at 12 and 10 different pressures up to P = 8.849 and P = 7.320 GPa for Li(Al_0.53Ga_0.47)Si₂O₆ and LiGaSi₂O₆, respectively. The sample with mixed composition shows a C2/c to P2₁/c phase transformation between 1.814 and 2.156 GPa, first-order in character. The transition is characterised by a large and discontinuous decrease in the unit-cell volume and by the appearance of the b-type reflections (h + k = odd) typical of the primitive symmetry. The Ga end-member shows the same C2/c to P2₁/c transformation at a pressure between 0.0001 and 0.39 GPa. The low-pressure value at which the transition occurred did not allow collecting any data in the C2/c pressure stability field except that on room pressure. Our results compared with those relative to spodumene (LiAlSi₂O₆, Arlt and Angel 2000a) indicate that the substitution of Al for Ga at the M1 site of Li-clinopyroxenes strongly affects the transition pressure causing a decrease from 3.17 GPa (spodumene) to less than 0.39 GPa (LiGaSi₂O₆) and decreases the volume discontinuity at the transition. As already found for other compounds, the C2/c low-pressure phases are more rigid than the P2₁ /c high-pressure ones. Moreover, the increase of the M1 cation radius causes a decrease in the bulk modulus K _T0. The axial compressibility among the Li-bearing clinopyroxenes indicates that the c axis is the most rigid for the C2/c phases while it becomes the most compressible for the P2₁ /c phases.     

Elasticity of CaTiO3–CaSiO3 perovskites

Polycrystalline specimens in the CaTiO₃–CaSiO₃ perovskite system have been hot-pressed in a 2000-ton uniaxial split-sphere apparatus (USSA-2000) at pressures up to 15 GPa and temperature of 1550°C, for the compositions CaTiO₃, Ca(Ti_0.75Si_0.25)O₃, Ca(Ti_0.5Si_0.5)O₃. For the specimens with the bulk densities within 1% of the X-ray density, compressional and shear wave velocity measurements have been conducted using ultrasonic interferometry. The measured adiabatic bulk moduli (K _s ) for the CaTiO₃ and Ca(Ti_0.5Si_0.5)O₃ perovskites are 175(1) and 188(1) GPa and shear moduli (G) of 106(1) and 109(1) GPa. In situ X-ray diffraction studies at high pressure and temperature resulted in isothermal values for K ₀ of 170(5) and 185(5) GPa, respectively. For the unquenchable CaSiO₃ perovskite, elasticity theory and systematics were used to predict K ₀=212(7) GPa and G ₀=112(5) GPa; this shear modulus is 37% less than that for (Mg,Fe)SiO₃ perovskite, suggesting that CaSiO₃ perovskite cannot be ignored in modeling the composition of the Earth’s lower mantle. Received: 27 June 1997 / Revised, accepted: 25 November 1997     

Elastic behaviour and structural evolution of topaz at high pressure

The elastic behaviour and the high-pressure structural evolution of a natural topaz, Al_2.00Si_1.05O_4.00(OH_0.26F_1.75), have been investigated by means of in situ single-crystal X-ray diffraction up to 10.55(5) GPa. No phase transition has been observed within the pressure range investigated. Unit-cell volume data were fitted 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: V ₀=345.57(7) ų, K _T0=164(2) GPa and K′=2.9(4). The axial-EoS parameters are: a ₀=4.6634(3) Å, K _T0(a)=152(2) GPa, K′(a)=2.8(4) for the a-axis; b ₀=8.8349(5) Å, K _T0(b)=224(3) GPa, K′(b)=2.6(6) for the b-axis; c ₀=8.3875(7) Å, K _T0(c)=137(2) GPa, K′(c)=2.9(4) for the c-axis. The magnitude and the orientation of the principal Lagrangian unit-strain ellipsoid were determined. At P−P ₀=10.55 GPa, the ratios ε₁:ε₂:ε₃ are 1.00:1.42:1.56 (with ε₁||b, ε₂||a, ε₃||c and |ε₃| > |ε₂| > |ε₁|). Four structural refinements, performed at 0.0001, 3.14(5), 5.79(5) and 8.39(5) GPa describe the structural evolution in terms of polyhedral distortions.     

The effect of composition and cation ordering on the compressibility of columbites up to 7 GPa

The unit-cell parameters of two columbite samples along the (Fe,Mn)Nb₂O₆ solid solution were measured by means of high-pressure single-crystal X-ray diffraction up to pressures of 7 GPa. The compressional behaviour of these minerals was studied as a function of composition and degree of order. The P–V data of all the samples were fitted with a third-order Birch–Murnaghan equation of state. For the two samples with different compositions but identical degree of order the substitution of Mn for Fe causes a decrease of the bulk modulus K _T0, from 153(1) to 146(1) GPa, without any effect on the pressure first derivative K′. For the two samples with the same composition, cation ordering causes an increase of the bulk modulus from 149(1) to 153(1) GPa and of the pressure first derivative from 4.1(2) to 4.8(3). The compressional behaviour is anisotropic with a linear axial compressibility scheme β _b > β _c ≥ β _a for all samples, regardless of composition and degree of order. Such anisotropy increases sligthly with increasing Mn content.