High-pressure transformations of ilmenite to perovskite, and lithium niobate to perovskite in zinc germanate

In-situ X-ray powder diffraction measurements conducted under high pressure confirmed the existence of an unquenchable orthorhombic perovskite in ZnGeO₃. ZnGeO₃ ilmenite transformed into perovskite at 30.0 GPa and 1300±150 K in a laser-heated diamond anvil cell. After releasing the pressure, the lithium niobate phase was recovered as a quenched product. The perovskite was also obtained by recompression of the lithium niobate phase at room temperature under a lower pressure than the equilibrium phase boundary of the ilmenite–perovskite transition. Bulk moduli of ilmenite, lithium niobate, and perovskite phases were calculated on the basis of the refined X-ray diffraction data. The structural relations among these phases are considered in terms of the rotation of GeO₆ octahedra. A slight rotation of the octahedra plays an important role for the transition from lithium niobate to perovskite at ambient temperature. On the other hand, high temperature is needed to rearrange GeO₆ octahedra in the ilmenite–perovskite transition. The correlation of quenchability with rotation angle of GeO₆ octahedra for other germanate perovskites is also discussed.     

Clinopyroxene-perovskite phase transition of FeGeO3 under high pressure and room temperature

In order to confirm the possible existence of FeGeO₃ perovskite, we have performed in situ X-ray diffraction measurements of FeGeO₃ clinopyroxene at pressures up to 40 GPa at room temperature. The transition of FeGeO₃ clinopyroxene into orthorhombic perovskite is observed at about 33GPa. The cell parameters of FeGeO₃ perovskite are a=4.93(2) Å, b=5.06(6) Å, c=6.66(3) Å and V=166(3) ų at 40 GPa. On release of pressure, the perovskite phase transformed into lithium niobate structure. The previously reported decomposition process of clino-pyroxene into Fe₂GeO₄ (spinel)+GeO₂ (rutile) or FeO (wüstite) +GeO₂ (rutile) was not observed. This shows that the transition of pyroxene to perovskite is kinetically accessible compared to the decomposition processes under low-temperature pressurization.     

Molecular dynamics study of the crystal structure and phase relation of the GeO2 polymorphs

A two-body interatomic potential model for GeO₂ polymorphs has been determined to simulate the structure change of them by semi-empirical procedure, total lattice energy minimization of GeO₂ polymorphs. Based on this potential, two polymorphs of GeO₂; α-quartz-type and rutile-type, have been reproduced using the molecular dynamics (MD) simulation techniques. Crystal structures, bulk moduli, volume thermal expansion coefficients and enthalpies of these polymorphs of GeO₂ were simulated. In spite of the simple form of the potential, these simulated structural values, bulk moduli and thermal expansivities are in excellent agreement with the reliable experimental data in respect to both polymorphs. Using this potential, MD simulation was further used to study the structural changes of GeO₂ under high pressure. We have investigated the pressure-induced amorphization. As reported in previous experimental studies, quartz-type GeO₂ undergoes pressure-induced crystalline-to-amorphous transformation at room temperature, the same as other quartz compounds; SiO₂, AlPO₄. Under hydrostatic compression, in this study, α-quartz-type GeO₂ transformed to a denser amorphous state at 7.4 GPa with change of the packing of oxygen ions and increase of germanium coordination. At higher pressure still, rutile-type GeO₂ transformed to a new phase of CaCl₂-type structure as a post-rutile candidate. Received: 29 July 1996 / Revised, accepted: 30 April 1997     

Bonding character of SiO2 stishovite under high pressures up to 30 Gpa

 The charge density and bond character of the rutile-type structure of SiO₂ (stishovite) under compression to 30 GPa were investigated by X-ray diffraction study using synchrotron radiation and AgKα rotating anode X-ray generator through a newly devised diamond-anvil cell. The valence electron density was determined by least-squares refinement including the κ parameter and the electron population in the X-ray atomic scattering parameters. The oxygen κ-parameter of SiO₂ is 0.94 under ambient conditions and 1.11 at 29.1 GPa and the silicon valence changes from +2.12(8) at ambient pressure to +2.26(15) at 29.1 GPa. These values indicate that the electron distributions are more localized with increasing pressure. The difference Fourier map shows the deformation of the valence electron distribution and the bonding electron population in residual electron densities. The bonding electron observed from the X-ray diffraction study is interpreted by molecular orbital calculations. The deformation of SiO₆octahedra and the bonding electron density of stishovite structures are elucidated from the overlapping electron orbits. The O–O distances of shared and unshared edge of SiO₆ octahedra change with the cation ionicity. The repulsive force between the two cations in the adjacent octahedron makes its shared edge shorter. The pressure changes of the apical and equatorial Si–O interatomic distances are explained by the electron density of state (DOS) of Si and electron configuration. Received: 7 January 2002 / Accepted: 6 May 2002     

The cubic-tetragonal phase transition in the system majorite (Mg4Si4O12) – pyrope (Mg3Al2Si3O12), and garnet symmetry in the Earth's transition zone

 Garnets along the join Mg₄Si₄O₁₂ (majorite end member) – Mg₃Al₂Si₃O₁₂ (pyrope) synthesized at 2000 °C, 19 GPa are, after quench, tetragonal in the compositional range up to 20 mol% pyrope, but cubic at higher Al contents. Lattice constants a _tet and a _tet in the tetragonal compositional range converge with increasing pyrope contents towards the lattice constant of the cubic garnets. The elastic strain and the intensity of the (222) reflection as a function of composition indicate a second-order phase transition near 20 mol% pyrope. From the wedge-like shape of pseudomerohedral twins and their interaction near 90° twin-boundary corners, as well as from the absence of growth-induced dislocations, it is concluded that the Al-poor garnets are also cubic at synthesis conditions but invert by (Mg,Si) ordering on the octahedral sites into tetragonal phases of space group I4₁/a upon quench. This implies that the cubic-to-tetragonal phase transition in Mg₄Si₄O₁₂ garnet occurs below 2000 °C at 19 GPa and at even lower temperatures in more aluminous compositions. A composition-dependent Landau model is consistent with a direct transformation from Ia3d to I4₁/a. Comparison of the T-X stability field of majorite-pyrope garnets with the chemistry of majorite-rich garnets expected to occur in the Earth's transition zone shows that the latter will be cubic under all conditions. Softening of elastic constants, which commonly accompanies ferroelastic phase transitions, may affect the seismic velocities of garnets in the deeper transition zone where majorite contents are highest. Received July 5, 1996 / Revised, accepted September 24, 1996     

The influence of the Jahn–Teller effect at Fe<Superscript>2+</Superscript> on the structure of chromite at high pressure

The crystal structure of chromite FeCr₂O₄ was investigated to 13.7 GPa and ambient temperature with single-crystal X-ray diffraction techniques. The unit-cell parameter decreases continuously from 8.3832 (5) to 8.2398 (11) Å up to 11.8 GPa. A fit to the Birch–Murnaghan equation of state (EoS) based on the P–V data gives: K ₀ = 209 (13) GPa, K′ = 4.0 (fixed), and V ₀ = 588 (1) ų. The FeO₄ tetrahedra and CrO₆ octahedra are compressed isotropically with pressure with their Fe–O and Cr–O bond distances decreasing from 1.996 (6) to 1.949 (7) Å and from 1.997 (3) to 1.969 (7) Å, respectively. The tetrahedral site occupied by the Fe²⁺ cation is more compressible than the octahedral site occupied by the Cr³⁺ cation. The resulting EoS parameters for the tetrahedral and the octahedral sites are K ₀ = 147 (9) GPa, K′ = 4.0 (fixed), V ₀ = 4.07 (1) ų and K ₀ = 275 (24) GPa, K′ = 4.0 (fixed), V ₀ = 10.42 (2) ų, respectively. A discontinuous volume change is observed between 11.8 and 12.6 GPa. This change indicates a phase transition from a cubic (space group Fd-[`3]{\overline{3}} m) to a tetragonal structure (space group I4₁ /amd). At the phase transition boundary, the two Cr–O bonds parallel to the c-axis shorten from 1.969 (7) to 1.922 (17) Å and the other four Cr–O bonds parallel to the ab plane elongate from 1.969 (7) to 1.987 (9) Å. This anisotropic deformation of the octahedra leads to tetragonal compression of the unit cell along the c-axis. The angular distortion in the octahedron decreases continuously up to 13.7 GPa, whereas the distortion in the tetrahedron rises dramatically after the phase transition. At the pressure of the phase transition, the tetrahedral bond angles along the c-axis direction of the unit cell begin decreasing from 109.5° to 106.6 (7)°, which generates a “stretched” tetrahedral geometry. It is proposed that the Jahn–Teller effect at the tetrahedrally coordinated Fe²⁺ cation becomes active with compression and gives rise to the tetrahedral angular distortion, which in turn induces the cubic-to-tetragonal transition. A qualitative molecular orbital model is proposed to explain the origin and nature of the Jahn–Teller effect observed in this structure and its role in the pressure-induced phase transition.     

High pressure behaviour of lead feldspar (PbAl2Si2O8)

An in situ high pressure powder diffraction study, using high-brilliance synchrotron radiation, on lead feldspar (PbAl₂Si₂O₈) was performed. Two samples, with Q _od=0.68 and 0.76, were loaded in a diamond anvil cell and were compressed up to 11 GPa. Up to P=7.1 GPa the only phase present is lead feldspar. In the range 7.1–9.4 GPa sudden changes in the position of the reflections suggest the transformation of lead feldspar to a new phase (probably feldspar-like). The absence of split that would be compatible with triclinic symmetry rules out the monoclinic-triclinic transition, that was reported for the structurally similar strontium feldspar. At P>9.4 GPa some new extra reflections not indexable in the feldspar cell are present as well. During decompression the lead feldspar was the only phase present at P<6 GPa. Peak enlargement was observed with pressure, probably preliminary to amorphization. However almost complete amorphization was observed only after fortuitous shock compression at ∼18 GPa; the crystallinity was recovered at room pressure after decompression. The bulk modulus for lead feldspar was K=71.0(9) and 67.6(1.2) GPa for the two samples, in the range reported for feldspars. The cell parameters show a compression pattern which is similar to that observed in anorthite, with Δa/a ₀>Δc/c ₀>Δb/b ₀; comparison with the high temperature behaviour shows that for lead feldspar the strain tensor with pressure is more isotropic and the deformation along a is less prominent. A turnover in the behaviour of the β angle with pressure suggests a change in the compression behaviour at P∼2 GPa. Rietveld refinement of the Pb coordinates was performed in a series of spectra with pressure ranging from 0.6 to 6.5 GPa. The combined analysis of cell parameters and Pb coordinates with pressure showed that the compression of the structure is mainly achieved by an approach of Pb atoms along a *. Received: 21 July 1998 / Revised, accepted: 13 October 1998     

High-pressure metallization and electronic-magnetic propertiesof hexagonal cubanite (CuFe2S3)

^?57Fe Mössbauer studies at room temperature and temperature-dependent resistance studies have been performed on a natural specimen of cubanite (CuFe₂S₃) in a diamond-anvil cell at pressures up to ～10 GPa. An insulator-metal phase transition occurs in the range 3.4–5.8 GPa coinciding with a previously observed structural transition from an orthorhombic to a hexagonal NiAs (B8) structure. The room temperature data shows that the metallization process concurs with a gradual transition from a magnetically ordered phase at low pressure to a nonmagnetic or paramagnetic phase at high-pressure. The change in magnetic behaviour at the structural transition may be attributed to a reduction of the Fe-S-Fe superexchange angle formed by edge-sharing octahedra occurring in the high-pressure phase. The non-magnetic or paramagnetic metallic phase at high pressure is retained upon decompression to ambient pressure-temperature conditions, indicative of substantial hysteresis associated with the pressure driven orthorhombic→hexagonal structural transition. The pressure evolution of both the ⁵⁷Fe Mössbauer hyperfine interaction parameters and resistance behaviour is consistent with the transition from mixed-valence character in the low pressure orthorhombic structure to that of extended-electron delocalization in the hexagonal phase at high-pressure.     

Compression behaviors of distorted rutile-type hydrous phases, MOOH (M?=?Ga, In, Cr) and CrOOD

X-ray diffraction measurements of distorted rutile-type oxyhydroxides β-GaOOH, InOOH, β-CrOOH, and β-CrOOD were taken at a maximum pressure of up to 35 GPa under quasi-hydrostatic conditions, at ambient temperature. Anomalies in the evolution of the relative lattice constants and the axial ratios of β-GaOOH, InOOH, and β-CrOOD suggest anisotropic stiffening along the a- and/or b-axes where the hydrogen bond is formed. The changes were observed at 15 GPa in β-GaOOH and InOOH and at 4 GPa in β-CrOOD. The pressures were higher in oxyhydroxides that have longer O…O distances of the hydrogen bond at ambient pressure. In contrast, such stiffening behavior was not observed in CrOOH, which has a significant short O…O distance and strong hydrogen bond. The stiffening behaviors observed in the present study can be attributed to the symmetrization of the hydrogen bonds in oxyhydroxides, as was previously found in δ-AlOOH(D).     

Static compression of the hydrous magnesium silicate phase D to 30 GPa at room temperature

Phase D is a dense hydrous magnesium silicate (ideal formula MgSi₂H₂O₆) which contains silicon cations exclusively in octahedral coordination. Measurements of the unit cell parameters of phase D were made to pressures of 30 GPa using a diamond anvil cell and employing synchrotron X-ray diffraction. A neon pressure medium was used. Using a third order Birch-Murnaghan equation of state the isothermal bulk modulus of phase D was determined as 166(±3) GPa with K′ equal to 4.1(±0.3). The compression of phase D is anisotropic with the c-axis twice as compressible as the a-axis. Above 20 GPa, however, the c/a ratio becomes pressure independent. Received: 29 July 1998/ Revised, accepted: 5 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     

Evolution of the distortion of perovskites under pressure: An EXAFS study of BaZrO3, SrZrO3 and CaGeO3

We have investigated the evolution of the distortion of several oxide perovskites with increasing pressure, using EXAFS in the diamond anvil cell. Cubic perovskite BaZrO₃ remains cubic up to 52 GPa. Orthorhombic perovskite CaGeO₃ becomes less distorted as pressure increases, becomes tetragonal at about 12 GPa and evolves toward cubic structure, still not obtained at 23 GPa. The distortion of orthorhombic perovskite SrZrO₃ first increases with pressure up to 8 GPa, then decreases until the perovskite becomes cubic at 25 GPa. The results are interpreted in terms of a systematics, relating the distortion to the ratio f of the volumes of the AO₁₂ dodecahedron and the BO₆ octahedron, and to the compressibilities of the polyhedra. For cubic perovskites, f=5, which may correspond to a situation where the compressibilities of octahedra and dodecahedra are equal.The behavior of SrZrO₃ offers a clue to predict the evolution of the distortion of MgSiO₃ at lower mantle pressures. It is suggested that the increase in distortion experimentally observed at lower pressures should stop above about 10 GPa, and the distortion decrease until the perovskite undergoes ferroelastic transitions to tetragonal and cubic phases, at pressures possibly below the pressure at the core-mantle boundary.     

High-pressure crystal chemistry of MgSiO3 perovskite

A high-pressure single-crystal x-ray diffraction study of perovskite-type MgSiO₃ has been completed to 12.6 GPa. The compressibility of MgSiO₃ perovskite is anisotropic with b approximately 23% less compressible than a or c which have similar compressibilities. The observed unit cell compression gives a bulk modulus of 254 GPa using a Birch-Murnaghan equation of state with K set equal to 4 and V/V ₀ at room pressure equal to one. Between room pressure and 5 GPa, the primary response of the structure to pressure is compression of the Mg-O and Si-O bonds. Above 5 GPa, the SiO₆ octahedra tilt, particularly in the [bc]-plane. The distortion of the MgO₁₂ site increases under compression. The variation of the O(2)-O(2)-O(2) angles and bondlength distortion of the MgO₁₂ site with pressure in MgSiO₃ perovskite follow trends observed in GdFeO₃type perovskites with increasing distortion. Such trends might be useful for predicting distortions in GdFeO₃-type perovskites as a function of pressure.     

Elasticity of CaIrO<Subscript>3</Subscript> with perovskite and post-perovskite structure

Compression behaviors of CaIrO₃ with perovskite (Pv) and post-perovskite (pPv) structures have been investigated up to 31.0(1.0) and 35.3(1) GPa at room temperature, respectively, in a diamond-anvil cell with hydrostatic pressure media. CaIrO₃ Pv and pPv phases were compressed with the axial compressibility of β _a > β _c > β _b and β _b > β _a > β _c, respectively and no phase transition was observed in both phases up to the highest pressure in the present study. The order of axial compressibility for pPv phase is consistent with the crystallographic consideration for layer structured materials and previous experimental results. On the other hand, Pv phase shows anomalous compression behavior in b axis, which exhibit constant or slightly expanded above 13 GPa, although the applied pressure remained hydrostatic. Volume difference between Pv and pPv phases was gradually decreased with increasing pressure and this is consistent with the results of theoretical study based on the ab initio calculation. Present results, combined with theoretical study, suggest that these complicate compression behaviors in CaIrO₃ under high pressure might be caused by the partially filled electron of Ir⁴⁺. Special attention must be paid in case of using CaIrO₃ as analog materials to MgSiO₃, although CaIrO₃ exhibits interesting physical properties under high pressure.     

Quantum mechanical calculations of the vibrational spectra of quartz- and rutile-type GeO2

Heat-treatment and stepwise cooling of as-delivered, water-containing quartz-type GeO₂ powder resulted in transformation into a water-free form. A rutile-type modification could be prepared by impregnation of the quartz-type phase with RbOH solutions, drying and annealing. Raman- and FTIR-absorption spectra of quartz- and rutile-type GeO₂ were measured and compared to quantum-mechanical ab initio calculations based on a hybrid functional using the Perdew–Burke–Ernzerhof correlation functional with 16.7% Hartree–Fock exchange density functional. Maximum and mean deviations between measured spectral bands and assigned vibrational modes are 14 and ±8 cm⁻¹ for the quartz-type and 30 and ±13 cm⁻¹ for the rutile-type polymorphic form. Water is incorporated into GeO₄ entities of quartz-type GeO₂; a water-free and structurally stable form can be prepared by a heating up to 1,425 K, tempering at 1,323 K and stepwise cooling. Spectral bands not explained by the calculations suggest defects and distortions in both quartz- and rutile-type structures, in case of the quartz-type one by incomplete transformation into an ideal structure after removing the water, whereas the rutile-type modification most probably incorporates Rb during its synthesis.     

High-pressure behaviour of germanate olivines studied by X-ray diffraction and X-ray absorption spectroscopy

Germanate olivines Mg₂GeO₄, Ca₂GeO₄ and CaMgGeO₄ have been studied by high-pressure X-ray Diffraction and high-pressure X-ray Absorption Spectroscopy. The three compounds were compressed, in the 0–30 GPa pressure range, at room temperature in a diamond-anvil cell, silicon oil being used as the pressure transmitting medium. Values of K₀ are 166 ± 15, 117 ± 15 and 152 ± 14 GPa for Mg₂GeO₄, Ca₂GeO₄ and CaMgGeO₄ respectively. These olivines all exhibit compression anisotropy, the a axis being the least compressible. Crystal to crystal phase transitions have been observed in Mg₂GeO₄ and Ca₂GeO₄ above 12 GPa and 6 Gpa respectively. The nature of these structural changes remains unclear yet. The onset of amorphization has been observed in Mg₂GeO₄ and Ca₂GeO₄ at pressures above about 22 and 11 GPa respectively. These phase transitions and amorphization processes do not involve any detectable increase in the coordination number of germanium atoms. At higher pressure (P >23 GPa), we report the onset of a transition from a phase with fourfold coordinated germanium to a phase with higher germanium coordination number in CaMgGeO₄.     

Static compression of α-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>: linear incompressibility of lattice parameters and high-pressure transformations

The high-pressure behavior of -Fe₂O₃ has been studied under static compression up to 60 GPa, using a laser-heated diamond anvil cell. Synchrotron-based angular-dispersive X-ray diffraction shows that the sample remains in the corundum structure up to 50 GPa, but with the appearance of coexisting diffraction lines from a high-pressure phase at pressures above 45 GPa. A least-squares fit of low-pressure phase data to an Eulerian finite-strain equation of state yields linear incompressibilities of K _{a 0}=749.5 (± 18.4) GPa and K _{c 0}= 455.7 (± 21.4) GPa, differing by a factor of 1.6 along the two directions. The enhanced compressibility of the c axis may lead to breaking of vertex- or edge-sharing bonds between octahedra, inducing the high-pressure phase transformation at 50 GPa. Analysis of linear compressibilities suggests that the high-pressure phase above 50 GPa is of the Rh₂O₃ (II) structure. Continuous laser heating reveals a new structural phase transformation of -Fe₂O₃ at 22 GPa, to an orthorhombic structure with a=7.305(3) Å, b=7.850(3) Å, and c=12.877(14) Å, different from the Rh₂O₃ (II) structure.     

BaCO<Subscript>3</Subscript>: high-temperature crystal structures and the <Emphasis Type="Italic">Pmcn</Emphasis>→<Emphasis Type="Italic">R</Emphasis>3<Emphasis Type="Italic">m</Emphasis> phase transition at 811°C

The temperature (T) evolution of the barium carbonate (BaCO₃) structure was studied using Rietveld structure refinements based on synchrotron X-ray diffraction and a powdered synthetic sample. BaCO₃ transforms from an orthorhombic, Pmcn, α phase to a trigonal, R3m, β phase at 811°C. The orthorhombic BaCO₃ structure is isotypic with aragonite, CaCO₃. In trigonal R3m BaCO₃, the CO₃ group occupies one orientation and shows no rotational disorder. The average <Ba–O> distances increase while the <C–O> distances decrease linearly with T in the orthorhombic phase. After the 811°C phase transition, the <Ba–O> distances increase while C–O distances decrease. There is also a significant volume change of 2.8% at the phase transition.     

Melilite-type and melilite-related compounds: structural variations along the join Sr2?xBaxMgSi2O7 (0?≤?x?≤?2) and high-pressure behavior of the two end-members

The structural variations along the solid solution Sr_2−x Ba _x MgSi₂O₇ (0 ≤ x ≤ 2), combined to the high-pressure characterization of the two end-members, have been studied. A topological change from the tetragonal (melilite-type) to the monoclinic (melilite-related) structure along the join Sr₂MgSi₂O₇ (e.g., P[`4]2₁ m P\bar{4}2_{1} m )–Ba₂MgSi₂O₇ (e.g., C2/c) occurs with a Ba content higher than 1.6 apfu. Favored in the crystallization from a melt, the tetragonal form has a tetrahedral sheet topology exclusively based on five-membered rings, which provide a regular “4 up + 4 down” ligand arrangement. In contrast, the melilite-related structure, favored by solid-state reaction synthesis, is made by alternating six- and four-membered tetrahedral rings, which give an asymmetric arrangement of alternated “5 up + 3 down” and “3 up + 5 down” ligands around Sr or Ba. This latter configuration is characterized by an additional degree of freedom with Ba polyhedra hosted in the interlayer with a more irregular and compact coordination and longer Ba–O bond distances. Further insights into the relationships between the two melilite typologies were achieved by investigating the in situ high-pressure behavior of these systems. The synchrotron high-pressure experiments allowed to calculate the elastic moduli for the Sr melilite-type end-member and for the Ba monoclinic polymorph (Sr₂MgSi₂O₇: K _T0 = 107, K _a=b  = 121, and K _c  = 84 GPa; m-Ba₂MgSi₂O₇: K _T0 = 85, K _a  = 96, K _b  = 72, and K _c  = 117 GPa) and compare them with those reported in the literature for ?kermanite (Ca₂MgSi₂O₇). The results show that, although the volume of Ba polyhedron in tetragonal polymorphs is larger than in the monoclinic forms, the interlayer compressibility is significantly lower in the former structures due to the occurrence of very short Ba–O distances. This unfavored Ba environment also makes tetragonal Ba₂MgSi₂O₇ a metastable phase at room conditions, possibly favored by high pressure. However, no phase transition occurs from monoclinic to tetragonal form due to kinetic hindrance in reconstructing the sheet topology.     

Single-crystal elastic constants of fluorite (CaF2) to 9.3 GPa

 The second-order elastic constants of CaF₂ (fluorite) have been determined by Brillouin scattering to 9.3 GPa at 300 K. Acoustic velocities have been measured in the (111) plane and inverted to simultaneously obtain the elastic constants and the orientation of the crystal. A notable feature of the present inversion is that only the density at ambient condition was used in the inversion. We obtain high-pressure densities directly from Brillouin data by conversion to isothermal conditions and iterative integration of the compression curve. The pressure derivative of the isentropic bulk modulus and of the shear modulus determined in this study are 4.78 ± 0.13 and 1.08 ± 0.07, which differ from previous low-pressure ultrasonic elasticity measurements. The pressure derivative of the isothermal bulk modulus is 4.83 ± 0.13, 8% lower than the value from static compression, and its uncertainty is lower by a factor of 3. The elastic constants of fluorite increase almost linearly with pressure over the whole investigated pressure range. However, at P ≥ 9 GPa, C ₁₁ and C ₁₂ show a subtle structure in their pressure dependence while C ₄₄ does not. The behavior of the elastic constants of fluorite in the 9–9.3 GPa pressure range is probably affected by the onset of a high-pressure structural transition to a lower symmetry phase (α-PbCl₂ type). A single-crystal Raman scattering experiment performed in parallel to the Brillouin measurements shows the appearance of new features at 8.7 GPa. The new features are continuously observed to 49.2 GPa, confirming that the orthorhombic high-pressure phase is stable along the whole investigated pressure range, in agreement with a previous X-ray diffraction study of CaF₂ to 45 GPa. The high-pressure elasticity data in combination with room-pressure values from previous studies allowed us to determine an independent room-temperature compression curve of fluorite. The new compression curve yields a maximum discrepancy of 0.05 GPa at 9.5 GPa with respect to that derived from static compression by Angel (1993). This comparison suggests that the accuracy of the fluorite pressure scale is better than 1% over the 0–9 GPa pressure range. Received: 10 July 2001 / Accepted: 7 March 2002