High-pressure disproportionation of Co2SiO4 spinel and implications for Mg2SiO4 spinel

Co₂SiO₄ spinel has been found to disproportionate into its isochemically mixed oxides with rocksalt and rutile structures at pressures between 170 and 190 kbar and temperatures between 1400 and 1800°C in a diamond-anvil press. The exact disproportionation pressure is not certain due to transient increases in pressure during the local and rapid heating by a continuous YAG laser. The slope of the phase boundary between the spinel phase and the mixed oxides is calculated to be?33 ± 20bar/deg. This negative slope is consistent with the observed anomalously large entropy of CoO (relative to its isostructural oxides) in entropy vs.(MV)^?1/2 systematics, whereM is the formula weight andV the molar volume. The sign of the slope for a phase boundary in the disproportionation of spinel depends on the values of entropy of the rocksalt oxides as well as the inverse character exhibited in the spinel phases. The normal entropy of MgO suggests that the phase boundary for the disproportionation of Mg₂SiO₄ spinel has positive slope.     

Synthesis of γ-Mg2SiO4

Magnesium orthosilicate with spinel structure (γ-Mg₂SiO₄) was synthesized at about 250 kbar and 1000°C. Unit cell dimension was established to be 8.076 ± 0.001Å. X-ray powder diffraction pattern revealed a significant difference between γ-Mg₂SiO₄ and other γ-M₂SiO₄ spinels (M = Fe, Co, and Ni) in the intensities of (111) and (331) reflections, both of which are virtually absent in the Mg₂SiO₄ spinel. This feature could be thoroughly understood by the calculation of the intensities for several silicate spinels.     

Ni2SiO4-enthalphy of the olivine-spinel transition by solution calorimetry at 713°C

The high pressure spinel polymorph of Ni₂SiO₄ persists metastably at 713°C and atmospheric pressure. The enthalpy of the olivine-spinel transition was obtained by measuring the heats of solution of both polymorphs in a molten oxide solvent, 2PbO · B₂O₃, at that temperature. For Ni₂SiO₄(ol)→Ni₂SiO₄, ΔH₉₈₆⁰ = +1.4 ± 0.7kcal/mol. The heat content increments, H₉₈₆ ? H₂₉₇, were found to be: olivine, 25.73 ± 0.42kcal/mol, and spinel, 25.39 ± 0.20kcal/mol. The measured enthalpy of the transformation is consistent with the low slope of the phase boundary, ?P/?T = ～ 12b/deg, observed by Akimoto and others. The entropy of the olivine-spinel transition in Ni₂SiO₄ is accordingly about a factor of three smaller in magnitude (ΔS = ～ ?1cal/deg mol) than that for Co₂SiO₄,Fe₂SiO₄,Mg₂SiO₄or Mg₂GeO₄ (ΔS = ?3to?3.5cal/deg mol).     

Disproportionation of spinels to mixed oxides: significance of cation configuration and implications for the mantle

Experimental study of the phase boundary for the disproportionation of the inverse spinel Mg₂SnO₄ into its isochemical mixed oxides indicates a slope dP/dT = 40 ± 10bars/°K. This positive slope is consistent with the large entropies of inverse (relative to normal) spinels predicted from high-temperature entropy-molar volume systematics. Thermodynamic data do not support the existence of a distinctly negative slope for the proposed disproportionation of Mg₂SiO₄ normal spinel. Evidence from X-ray and phase equilibria studies suggests the possibility that Si⁴⁺, Mg²⁺, and Fe²⁺ share the octahedral sites in silicate spinels under mantle conditions. The consequences of this partial inverse character are a positive slope for the postulated spinel-mixed oxide phase boundary near 650 km depth, removal of a widely accepted constraint on mantle-wide convection, and anomalous elasticity-density behaviour within the transition zone.     

High-pressure phases of Co2GeO4, Ni2GeO4, Mn2GeO4 and MnGeO3: implications for the germanate-silicate modeling scheme and the Earth's mantle

In a diamond-anvil press coupled with YAG laser heating, the spinels of Co₂GeO₄ and Ni₂GeO₄ have been found to disproportionate into their isochemical oxide mixtures at about 250 kbar and 1400–1800°C in the same manner as their silicate analogues. At about the same P-T conditions MnGeO₃ transforms to the orthorhombic perovskite structure (space group Pbnm); the lattice parameters at room temperature and 1 bar are a₀ = 5.084 ± 0.002, b₀ = 5.214 ± 0.002, and c₀ = 7.323 ± 0.003Å with Z = 4 for the perovskite phase. The zero-pressure volume change associated with the ilmenite-perovskite phase transition in MnGeO₃ is ?6.6%. Mn₂GeO₄ disproportionates into a mixture of the perovskite phase of MnGeO₃ plus the rocksalt phase of MnO at P = 250kbar and T = 1400–1800°C. The concept of utilizing germanates as high-pressure models for silicates is valid in general. The results of this study support the previous conclusion that the lower mantle comprises predominantly the orthorhombic perovskite phase of ferromagnesian silicate.     

Calorimetric study of the stability of high pressure phases in the systems CoOSiO2 and “FeO”SiO2, and calculation of phase diagrams in MOSiO2 systems

High temperature calorimetric measurements of the enthalpies of solution in molten if2 PbO · B₂O₃ of α- and γ-Fe₂SiO₄ and α-, β-, and γ-Co₂SiO₄ permit the calculation of phase relations at high pressure and temperature. The reported triple point involving α-, β-, and γ-Co₂SiO₄ is confirmed to represent stable equilibrium. The curvature in the α?β phase boundary in Co₂SiO₄ and of an α?γ boundary in Fe₂SiO₄ at high temperature is explained in part by the effects of compressibility and thermal expansion, but better agreement with the observed phase diagram is obtained when one considers the effect of small amounts of cation disorder in the spinel and/or modified spinel phases. The calculated ΔH⁰ and ΔS⁰ values for the α?β, α?γ, and β?γ transitions show that enthalpy and en changes both vary strongly in the series Mg, Fe, Co, and Ni, and are of equal importance in determining the stability relations. The disproportionation of Fe₂SiO₄ and Co₂SiO₄ spinel to rocksalt plus stishovite is calculated to occur in the 170–190 kbar region; cation disorder and/or changes in wüstite stoichiometry can affect the P?T slope. The calorimetric data for CoSiO₃ and FeSiO₃ are in good agreement with the observed phase boundary for pyroxene formation from olivine and quartz. The decomposition of pyroxene to spinel and stishovite at pressures near the coesite-stishovite transition is predicted in both iron and cobalt systems. The use of calorimetric data, obtained from small samples of high pressure phases, is very useful in predicting equilibrium phase diagrams in the 50–300 kbar range.     

Disproportionation of Ni2SiO4 to stishovite plus bunsenite at high pressures and temperatures

Samples of Ni₂SiO₄ in both olivine and spinel phases have been compressed to pressures above 140 kbar in a diamond-anvil cell and heated to temperatures of 1400–1800°C using a continuous YAG laser. After quenching and releasing pressure, X-ray diffraction examination indicates that the samples disproportionate to a mixture of stishovite (SiO₂) and bunsenite (NiO) at pressures between 140 and 190 kbar. The exact disproportionation pressure is not certain due to transient increases in pressure during the local and rapid heating. However, thermodynamic calculations suggest that the transition pressure is about 192 ± 4 kbar at 1545°C and that the equation of the spinel-mixed oxides phase boundary isP(kbar) = 121 + (0.046 ± 0.020) T (°C).     

Determination of the olivine-spinel transition in magnesium germanate (Mg2GeO4) up to 20 kilobars and 1300°C

Reversal experiments of the olivine-spinel transition in Mg₂GeO₄ up to 20 kbar indicate a reaction boundary with the formula P = 35 (T ? 805). Pressure (P) in bars and temperature (T) in degrees centigrade.     

High-pressure X-ray diffraction studies on β- and γ-Mg2SiO4

Pressure effects on the lattice parameters of β- and γ-Mg₂SiO₄ have been measured at room temperature and at pressures up to 100 kbar using a multi-anvil high-pressure X-ray diffraction apparatus. The volume changes (ΔV/V₀) at 90 kbar are 5.4 · 10^?2 and 4.2 · 10^?2 for β- and γ-Mg₂SiO₄, respectively. Isothermal bulk moduli at zero pressure have been calculated from least-square fits of the data to straight lines. They turn out to be 1.66 ± 0.4 and 2.13 ± 0.1 Mbar for β- and γ-Mg₂SiO₄, respectively. The α → γ transition obeys Wang's linear V_φ?ρ relation but the α → β transition does not.     

Pyroxene-garnet solid-solution equilibria in the systems Mg4Si4O12Mg3Al2Si3O12 and Fe4Si4O12Fe3Al2Si3O12 at high pressures and temperatures

Pyroxene-garnet solid-solution equilibria have been studied in the pressure range 41–200 kbar and over the temperature range 850–1,450°C for the system Mg₄Si₄O₁₂Mg₃Al₂Si₃O₁₂, and in the pressure range 30–105 kbar and over the temperature range 1,000–1,300°C for the system Fe₄Si₄O₁₂Fe₃Al₂Si₃O₁₂. At 1,000°C, the solid solubility of enstatite (MgSiO₃) in pyrope (Mg₃Al₂Si₃O₁₂) increases gradually to 140 kbar and then increases suddenly in the pressure range 140–175 kbar, resulting in the formation of a homogeneous garnet with composition Mg₃(Al_0.8Mg_0.6Si_0.6)Si₃O₁₂. In the MgSiO₃-rich field, the three-phase assemblage of β- or γ-Mg₂SiO₄, stishovite and a garnet solid solution is stable at pressures above 175 kbar at 1,000°C. The system Fe₄Si₄O₁₂Fe₃Al₂Si₃O₁₂ shows a similar trend of high-pressure transformations: the maximum solubility of ferrosilite (FeSiO₃) in almandine (Fe₃Al₂Si₃O₁₂) forming a homogeneous garnet solid solution is 40 mol% at 93 kbar and 1,000°C.If a pyrolite mantle is assumed, from the present results, the following transformation scheme is suggested for the pyroxene-garnet assemblage in the mantle. Pyroxenes begin to react with the already present pyrope-rich garnet at depths around 150 km. Although the pyroxene-garnet transformation is spread over more than 400 km in depth, the most effective transition to a complex garnet solid solution takes place at depths between 450 and 540 km. The complex garnet solid solution is expected to be stable at depths between 540 and 590 km. At greater depths, it will decompose to a mixture of modified spinel or spinel, stishovite and garnet solid solutions with smaller amounts of a pyroxene component in solution.     

High-pressure phase transformations in the system of MgSiO3-FeSiO3

Two synthetic pyroxenes (FeSiO₃, MgSiO₃) and five natural pyroxenes with compositions of about Fs₈₀En₂₀, Fs₆₀En₄₀, Fs₅₀En₅₀, Fs₄₀En₆₀, and Fs₂₀En₈₀ have been subjected to pressures up to250 ± 50kbars at a temperature of about1500 ± 200°C in a diamond anvil cell heated by an infrared laser beam. After quenching and unloading X-ray data analysis indicates that (1) those with Mg less than 50% undergo the following reactions: 2(Mg,Fe)SiO₃ (pyroxene) → (Mg,Fe)₂SiO₄ (spinel) + SiO₂ (stishovite) → 2(Mg,Fe)O (magnesiowu¨stite) + SiO₂ (stishovite) with increase of pressure, and (2) those with Mg higher than 60%, undergo the following reactions: 2(Mg,Fe)SiO₃ (pyroxene) → (Mg,Fe)₂SiO₄ (spinel) + SiO₂ (stishovite) → 2(Mg,Fe)SiO₃ (hexagonal phase) → 2(Mg,Fe)O (magnesiowu¨stite) + SiO₂ (stishovite) with increase of pressure.     

High-temperature elasticity of the fluorite-structure compounds CaF2, SrF2 and BaF2

The elastic moduli of single-crystal CaF₂, SrF₂ and BaF₂ have been determined by the ultrasonic pulse superposition technique as a function of temperature from T = 298 to T = 650°K. These new data are consistent with other data obtained by ultrasonic pulse techniques in the region of room temperature and are superior to previous high-temperature data from resonance experiments. The elastic moduli (c) are represented by quadratic functions in T over the experimental temperature range with the curvature in the same sense for all the moduli. Evaluation of the temperature derivatives of the elastic moduli at constant volume indicates that the dominant temperature effect is extrinsic for (?K_S/?T)_P and intrinsic for (?μ/?T)_P, where K_S and μ are the isotropic bulk and shear moduli, respectively. For the series CaF₂SrF₂BaF₂, |(?c/?T)_p| decreases with increasing molar volume for all moduli; however there are no theoretical or empirical grounds on which to derive a simple relationship between (?c/?T)_P and crystallographic parameters.     

The structure and sharpness of (Mg,Fe)2SiO4 phase transformations in the transition zone

To calculate accurately the pressure interval and mineral proportions (i.e. yields) across the olivine to wadsleyite and wadsleyite to ringwoodite transformations requires a detailed knowledge of the non-ideality of Fe-Mg mixing in these (Mg,Fe)₂SiO₄ solid solutions. In order to constrain the activity-composition relations that describe non-ideal mixing, Fe-Mg partitioning experiments have been conducted between magnesiowüstite and (Mg,Fe)₂SiO₄ olivine, wadsleyite and ringwoodite as a function of pressure at 1400°C. Using known activity-composition relations for magnesiowüstite the corresponding relations for the three polymorphs were determined from the partitioning data. In all experiments the presence of metallic iron ensured redox conditions compatible with the Earth’s transition zone. The non-ideality of the (Mg,Fe)₂SiO₄ solid solutions was found to decrease in the order W^wadsleyite_FeMg>W^ringwoodite_FeMg>W^olivine_FeMg. These partitioning data were used, along with published phase equilibria measurements for the Mg₂SiO₄ and Fe₂SiO₄ end-member transformations, to produce an internally consistent thermodynamic model for the Mg₂SiO₄-Fe₂SiO₄ system at 1400°C. Using this model the pressure interval of the olivine to wadsleyite transformation is calculated to be significantly smaller than previous determinations. By combining these results with Fe-Mg partitioning data for garnet, the widths of transition zone phase transformations in a peridotite composition were calculated. The olivine to wadsleyite transformation at 1400°C in dry peridotite was found to occur over a pressure interval equivalent to approximately 6 km depth and the mineral yields were found to vary almost linearly with depth across the transformation. This transformation is likely to be even sharper at higher temperatures or could be significantly broader in wet mantle or in regions with a significant vertical component of mantle flow. The entire range of estimated widths for the 410 km discontinuity (4-35 km) could, therefore, be explained by the olivine to wadsleyite transformation in a peridotite composition over a range of quite plausible mantle temperatures and H₂O contents. The wadsleyite to ringwoodite transformation in peridotite mantle was calculated to take place over an interval of 20 km at 1400°C. This transformation yield was also found to be near linear.     

Melting of the silica isotypes SiO 2, BeF 2 and GeO 2 at elevated pressures

The melting curves of the structural analogues SiO ₂, BeF ₂ and GeO ₂ have been studied at pressures ?40 kbar in a piston-cylinder apparatus. The initial slopes dT_m/dP of the β-quartz-liquid boundaries for SiO ₂ and BeF ₂ are ～35° while the slope of the rutile-liquid boundary for GeO ₂ is approximately 32°C/kbar. These large values of dT/dP reflect the unusually low entropies of fusion for these compounds in which strong structural similarities exist between the crystalline phases and the melt. Implications for the extended phase diagram of silica are discussed and it is concluded that either: (1) a maximum exists on the coesite melting curve, or (2) estimates of the melting temperature of stishovite need to be revised upwards.     

Melting of forsterite Mg2SiO4 up to 15 GPa

The melting curve of forsterite has been studied by static experiment up to a pressure of 15 GPa. Forsterite melts congruently at least up to 12.7 GPa. The congruent melting temperature is expressed by the Kraut-Kennedy equation in the following form: T_m(K)=2163 (1+3.0(V₀ ? V)/V₀), where the volume change with pressure was calculated by the Birch-Managhan equation of state with the isothermal bulk modulus K₀ = 125.4 GPa and its pressure derivative K′ = 5.33. The triple point of forsterite-β-Mg₂SiO₄-liquid will be located at about 2600°C and 20 GPa, assuming that congruent melting persists up to the limit of the stability field of forsterite. The extrapolation of the previous melting data on enstatite and periclase indicates that the eutectic composition of the forsterite-enstatite system should shift toward the forsterite component with increasing pressure, and there is a possibility of incongruent melting of forsterite into periclase and liquid at higher pressure, although no evidence on incongruent melting has been obtained in the present experiment.     

A new high-pressure phase of spinel

A new phase which is much denser than the component oxides of spinel (MgAl₂O₄) was synthesised at loading pressures greater than 250 kbar and at about 1000°C in a diamond-anvil press coupled with laser heating. The new phase (ε-MgAl₂O₄) was indexed on the basis of an orthorhombic cell with a = 8.507 ± 0.004, b = 2.740 ± 0.003, c = 9.407 ± 0.005Å, and Z = 4 at room temperature and 1 bar pressure. Thus the molar volume for ε-MgAl₂O₄ at the above conditions was calculated to be 33.01 ± 0.07 cm³, which is 10.3% less than that of the mixture corundum plus periclase. The dense phase of spinel found in shock-wave experiments can be reasonably interpreted as ε-MgAl₂O₄, and this may be a potentially important mineral component of the earth's lower mantle. The new structure may also provide a possible candidate for the dense phases of Fe₃O₄ and Mg₂SiO₄ which were found by shock experiments.     

Garnet-ilmenite-perovskite transitions in the system Mg4Si4O12-Mg3Al2Si3O12 at high pressures and high temperatures: phase equilibria, calorimetry and implications for mantle structure

Phase relations in the system Mg₄Si₄O₁₂-Mg₃Al₂Si₃O₁₂ were examined at pressures of 19-27 GPa and relatively low temperatures of 800-1000 °C using a multianvil apparatus to clarify phase transitions of pyroxene-garnet assemblages in the mantle. Both of glass and crystalline starting materials were used for the experiments. At 1000 °C, garnet solid solution (s.s.) transforms to aluminous ilmenite s.s. at 20-26 GPa which is stable in the whole compositional range in the system. In Mg₄Si₄O₁₂-rich composition, ilmenite s.s. transforms to a single-phase aluminous perovskite s.s., while Mg₃Al₂Si₃O₁₂-rich ilmenite s.s. dissociates into perovskite s.s. and corundum s.s. These newly determined phase relations at 1000 °C supersede preliminary phase relations determined at about 900 °C in the previous study. The phase relations at 1000 °C are quite different from those reported previously at 1600 °C where garnet s.s. transforms directly to perovskite s.s. and ilmenite is stable only very close to Mg₄Si₄O₁₂. The stability field of Mg₃Al₂Si₃O₁₂ ilmenite was determined at 800-1000 °C and 25-27 GPa by reversed phase boundaries. In ilmenite s.s., the a-axis slightly increases but the c-axis and molar volume decrease substantially with increasing Al₂O₃ content. Enthalpies of ilmenite s.s. were measured by differential drop-solution calorimetry method using a high-temperature calorimeter. The excess enthalpy of mixing of ilmenite s.s. was almost zero within the errors. The measured enthalpies of garnet-ilmenite and ilmenite-perovskite transitions at 298 K were 105.2±10.4 and 168.6±8.2 kJ/mol, respectively, for Mg₄Si₄O₁₂, and 150.2±15.9 and 98.7±27.3 kJ/mol, respectively, for Mg₃Al₂Si₃O₁₂. Thermodynamic calculations using these data give rise to phase relations in the system Mg₄Si₄O₁₂-Mg₃Al₂Si₃O₁₂ at 1000 and 1600 °C that are generally consistent with those determined experimentally, and confirm that the single-phase field of ilmenite expands from Mg₄Si₄O₁₂ to Mg₃Al₂Si₃O₁₂ with decreasing temperature. The earlier mentioned phase relations in the simplified system as well as those in the Mg₂SiO₄-Fe₂SiO₄ system are applied to estimate mineral proportions in pyrolite as a function of depth along two different geotherms: one is a horizontally-averaged temperature distribution in a normal mantle, and the other being 600 °C lower than the former as a possible representative geotherm in subducting slabs. Based on the previously described estimated mineral proportions versus depth along the two geotherms, density and compressional and shear wave velocities are calculated as functions of depth, using available mineral physics data. Along a normal mantle geotherm, jumps of density and velocities at about 660 km corresponding to the post-spinel transition are followed by steep gradients due to the garnet-perovskite transition between 660 and 710 km. In contrast, along a low-temperature geotherm, the first steep gradients of density and velocities are due to the garnet-ilmenite transition between 610 and 690 km. This is followed by abrupt jumps at about 690 km for the post-spinel transition, and steep gradients between 700 and 740 km that correspond to the ilmenite-perovskite transition. In the latter profile along the low-temperature geotherm, density and velocity increases for garnet-ilmenite and ilmenite-perovskite transitions are similar in magnitude to those for the post-spinel transition. The likely presence of ilmenite in cooler regions of subducting slabs is suggested by the fact that the calculated velocity profiles along the low-temperature geotherm are compatible with recent seismic observations indicating three discontinuities or steep velocity gradients at around 600-750 km depth in the regions of subducting slabs.     

The high-pressure phases of MgSiO3

The high-pressure and temperature phase transformations of MgSiO₃ have been investigated in a diamond-anvil cell coupled with laser heating from 150 to 300 kbar at 1000–1400°C. X-ray diffraction study of the quenched samples reveals that the sequence of phase transformations for this compound is clinoenstatite → β-Mg₂SiO₄ plus stishovite → Mg₂SiO₄(spinel) plus stishovite → ilmenite phase → perovskite phase with increasing pressure. The hexagonal form of MgSiO₃ observed by Kawai et al. is demonstrated to have the ilmenite structure and the “hexagonal form” of MgSiO₃ observed by Ming and Bassett is shown to be predominantly the orthorhombic perovskite phase plus the ilmenite phase. The mixture of oxides, periclase plus stishovite, reported by Ming and Bassett was not observed in this study. The very wide stability field for the ilmenite phase of MgSiO₃ found in this study suggests that this phase is of importance in connection with the observed rapid increase of velocity in the transition zone of the earth's mantle. On the basis of the extremely dense-packed structure of the perovskite phase of MgSiO₃, this phase should be the most important component for the lower mantle.     

Distribution of some trivalent ions between melt and single crystals of Mg2SiO4 grown by the Czochralski method

Partition coefficients for trace amounts of trivalent ions between artificial single crystals of Mg₂SiO₄ grown by the Czochralski method and the coexisting melt have been determined by neutron activation analysis. They are found to vary greatly with the amount of visible imperfections in the crystal and slightly with the concentration of the ions in the melt. Plots of the partition coefficients against ionic radius of the trace ions give a pattern which agrees qualitatively with that found in a natural olivine phenocryst-groundmass pair.     

Stability of forsterite + CO2 and its bearing on the role of CO2 in the mantle

An experimental determination of the reaction MgCO₃ + MgSiO₃ = Mg₂SiO₄ + CO₂ between 20 and 40 kbars and in the range 1000–1500°C yields an average pressure effect on the equilibrium of 44 bars/°C. This result shows that the assemblage forsterite and carbon dioxide is not stable under most pressure and temperature conditions expected in the upper mantle. Hypotheses requiring the presence of free CO₂ in the low-velocity zone, CO₂ as a drive mechanism for kimberlite emplacement, or action of a free CO₂ phase in ultramafic rocks may need considerable revision.