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.     

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.     

High-pressure phase transformations in baddeleyite and zircon,with geophysical implications

Phase transformations in baddeleyite (ZrO₂) and zircon (ZrSiO₄) have been investigated in the pressure range between 100 and 300 kbar at about 1000°C in a diamond-anvil press coupled with laser heating. Baddeleyite has been found to transform to an orthorhombic cotunnite-type structure at pressures greater than 100 kbar, and is the first oxide known to adopt this structure. The lattice parameters of the cotunnite-type ZrO₂ at room temperature and atmospheric pressure area = 3.328 ± 0.001 ,b = 5.565 ± 0.002 , andc = 6.503 ± 0.003A? withZ = 4 , and its volume is 14.3% smaller than baddeleyite and 7.6% smaller than the fluorite-type ZrO₂. It is suggested that all the polymorphic structures of ZrO₂ are possible high-pressure models for the post-rutile phase of SiO₂. The polyhedral coordination in these model structures varies from 7 to “9”, compared with 6 for stishovite. If SiO₂ were to adopt any of these structures in the deep mantle, Birch's hypothesis of a mixed-oxide lower mantle may still be viable, but the primary coordination of silicon would be greater than 6. Zircon has been found to transform to a scheelite-type structure at about 120 kbar as noted earlier. The scheelite-type ZrSiO₄ was found to decompose further into a mixture of ZrO₂ (cotunnite-type) plus SiO₂ (stishovite) in the pressure range 200–250 kbar. As implied by the transitions in zircon, the large cations of U and Th in the earth's deep mantle are most likely to occur in dioxides with structures such as the cotunnite-type, rather than to occur in silicates.     

Phase relations in the system LiFMgF2 at elevated pressures: Implications for the proposed mixed-oxide zone of the earth's mantle

Solvi and liquidi for various LiFMgF₂ mixtures have been determined at pressures up to 40 kbar by differential-thermal-analysis in a piston-cylinder high-pressure device. The melting curves of pure LiF and MgF₂ were also studied and the initial slopes (dT_m/dP)_{P = 0} were found to be 11.2 and 8.3°C/kbar, respectively. The eutectic composition (LiF)_0.64(MgF₂)_0.36 is independent of pressure to 35 kbar and the eutectic temperature rises approximately 6.3°C per kbar. Initial slopes of 11°C/kbar and 35°C/kbar are inferred for the melting curves of MgO and SiO₂ (stishovite) respectively, on the basis of data for their structural analogue compounds. The observed solid solution of LiF in MgF₂ and other evidence suggest the possibility of solid solution in the system (Mg,Fe)OSiO₂ (stishovite) under mantle conditions which may have important consequences for the elastic properties of a “mixed-oxide” zone of the earth's mantle.     

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).     

Electrical conductivity measurements on synthetic olivines and on olivine,enstatite and diopside from Dreiser Weiher,Eifel (Germany) under defined thermodynamic activities as a function of temperature and pressure

Results of electrical conductivity measurments on synthetic olivines of the system Mg₂SiO₄Fe₂SiO₄ and on minerals of Dreiser Weiher peridotite nodule Ib-8 (Eifel, Germany) are discussed in relation to the measuring procedure and to the variation of thermodynamic parameters.The measurements were performed in solid state high-pressure vessels between 340 and 1100°C and at a pressure of 10 kbar. It is shown that for ternary olivines and for pyroxenes, the control of two further variables, like the chemical activities of the components, is needed besides temperature and pressure control. The experimental set-up for the control of chemical activities and oxygen partial pressure is shown. From the slopes of the lines of log σ against 1/T the activation energies were calculated. Though in most cases the same oxygen fugacity ?_O2 is applied, the results reveal different values for synthetic and natural samples since the chemical activities of SiO₂ are different.     

Disproportionation of kyanite to corundum plus stishovite at high pressure and temperature

Natural kyanite (Al₂SiO₅) has been found to disproportionate into a mixture of its component oxides, corundum and stishovite, at a loading pressure of about 160 kbar and temperature between 1000–1400°C in a diamond-anvil press. The exact transition pressure is not certain due to transient increases in pressure during the local and rapid heating by a continuous YAG laser. The phase boundary, however, has been estimated to be P(kbar) = (138 ～ 174) + 0.011 T (°C) on the basis of the available thermodynamic data. The shock-wave Hugoniot data above 650 kbar for andalusite (Al₂SiO₅) and sillimanite (Al₂SiO₅) as starting materials are consistent with the present results.     

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.     

High-pressure decomposition of Ca2GeO4 and Ca2MnO4 with the K2NiF4-type structures

By using the diamond-anvil pressure cell coupled with laser heating, Ca₂GeO₄ in the K₂NiF₄-type structure has been found to decompose into the mixture Ca₃Ge₂O₇ plus CaO at pressures greater than 200 kbar and at about 1000°C, and the same type of structure for Ca₂MnO₄ has been found to decompose into the mixture CaMnO₃ (perovskite) plus CaO at pressures greater than 100 kbar and at about 1400°C. The decomposition product of Ca₃Ge₂O₇ is a new compound which is isostructural with Sr₃Ti₂O₇ and has the lattice parameters of a = 3.72 ± 0.01 and $\text{c = 19.32 ± 0.05}\text{A}\text{?}$ at room temperature and 1 bar pressure. The results of the study of Ca₂GeO₄ and Ca₂MnO₄ (both with the K₂NiF₄-type structure) strongly support the view that compounds possessing the K₂NiF₄-type structure are unstable relative to corresponding mixtures possessing the perovskite and rocksalt structures. It is concluded that, in the earth's mantle, the K₂NiF₄-type Ca₂SiO₄ would ultimately decompose into the mixture CaSiO₃ (perovskite) + CaO or would otherwise transform to other as-yet-unknown phase(s), and that the mixture of MgSiO₃ (perovskite) + MgO (the post-spinel phase of Mg₂SiO₄) would not adopt the K₂NiF₄-type structure.     

Melting of some alkaline-earth and transition-metal fluorides and alkali fluoroberyllates at elevated pressures: A search for melting systematics

The melting curves of the fluorides ZnF₂ and NiF₂ (rutile structure), CaF₂, SrF₂ and BaF₂ (fluorite structure), and of the fluoroberyllates Na₂BeF₄ and Li₂BeF₄ have been studied at pressures ? 40 kbar by differential thermal analysis in a piston-cylinder high-pressure device. The initial slopes (dT_m/dP)₀ of these melting curves are respectively 7.2, 5.8, 16.7, 15.2, 15.7, 15.1 and <0°C/kbar. A new Li₂BeF₄ polymorph, apparently of the olivine structure type, is stable at pressures > 10 kbar and its melting curve has an average slope of ～6.7°C/kbar. These new data and those for SiO₂, BeF₂, GeO₂, LiF and MgF₂, recently studied by Jackson, are combined with existing data for elements, ionic compounds and silicates to assess the influence of crystal structure, molar volume and the nature of interatomic bonding on the initial slopes of melting curves. It is found that the entropy of fusion (ΔS_m) is primarily a function of crystal structure while the volume change on fusion (ΔV_m) is controlled by crystal molar volume within each isostructural series. Such systematics have recently facilitated estimation of the initial slopes of the melting curves of periclase and stishovite. New and existing melting data for silicates and their analogues have been analysed and a systematic dependence of (dT_m/dP)₀ on SiO₂ concentration has been demonstrated. Possible implications of this trend for partial melting of upper-mantle garnet lherzolite are illustrated. Finally, the use of the traditional silicate-germanate and oxide-fluoride modelling schemes is reviewed in the light of information from this present study.     

Spinel disproportionation at high pressure: calorimetric determination of enthalpy of formation of Mg2SnO4 and Co2SnO4 and some implications for silicates

The enthalpies of formation from the oxides of Mg₂SnO₄ and Co₂SnO₄ were found by oxide melt solution calorimetry to be +1.13 ± 0.48 kcal/mol and ?2.31 ± 0.28 kcal/mol, respectively. Using these data, the slopes, ?P/?T, for disproportionation of these spinels to the component oxides at high pressure were calculated to be +30.4 ± 4.2 bar/K for Mg₂SnO₄ and ?10.3 ± 2.4 bar/K for Co₂SnO₄, in general agreement with the data of Jackson et al. (1974a,b). Using thermochemical data for the formation of olivines, for olivine-spinel transitions and for the transformation of quartz to stishovite, we calculate pressures for the disproportionation of silicate spinels to be in the range 150–200 kbar. Calculated slopes ?P/?T for the disproportionation reactions are ?10.7, ?24.9, ?11.2, and +7.6 bar/K for Mg₂SiO₄, Fe₂SiO₄, Co₂SiO₄, and Ni₂SiO₄. The large negative slope calculated for Fe₂SiO₄ results from a surprisingly large positive slope reported for the olivine-spinel transition in that compound (Akimoto et al., 1969). Further consideration of the systematic trends in the thermodynamics of spinel formation from the oxides suggests that the silicate spinels should have entropies of formation close to zero, resulting in values of ?P/?T which are zero or at most only slightly negative. This confirms the conclusion of Jackson, Liebermann, and Ringwood that values of ?P/?T for spinel disproportionation are unlikely to be more negative than ?10 bar/K and may well be slightly positive. Reaction of spinels to form other post-spinel phases, particularly ilmenite and perovskite, are discussed in terms of available thermochemical data.     

Compression and phase behavior of solid CO2 to half a megabar

CO₂ has been investigated up to 514 kbar at23 ± 2°C by both optical and in situ X-ray diffraction studies using a diamond-anvil pressure cell. CO₂ solidifies in an unknown structure in the pressure range 5 to 23 kbar, and transforms to ordinary dry-ice structure above 23 kbar at room temperature. Isothermal compression data for dry ice have been obtained above about 24 kbar. These appear to be the first data at room temperature known in the literature. The data fitted to the Birch equation of state yieldK₀ = 29.3 ± 1.0kbar andK₀^′ = 7.8 assuming the volume of the hypothetical dry ice at zero-pressure and room temperature is 31.4 ± 0.2 cm³/mole. The isothermal bulk modulus(K₀) thus derived is consistent with the compression data and compressibilities for dry ice obtained at low temperatures using dilatometry and ultrasonic techniques, respectively, reported in the literature. By comparing shock-wave data for relevant materials, it is suggested that CO₂ is not likely to transform to one of the crystalline forms of SiO₂ which is otherwise expected from empirical grounds, but may instead decompose into C (diamond) + O₂, at high pressures.     

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.     

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.     

The system enstatite-pyrope at high pressures and temperatures and the mineralogy of the earth's mantle

In a diamond-anvil pressure cell coupled with laser heating, the system enstatite (MgSiO₃)-pyrope (3 MgSiO₃ · Al₂O₃) has been studied in the pressure region between about 100 and 300 kbar at about 1000°C using glass starting materials. The high-pressure phase behavior of the intermediate compositions of the system contrasts greatly with that of the two end-members. Differences between MgSiO₃ and 95% MgSiO₃ · 5% Al₂O₃ are especially remarkable. The phase assemblages β-Mg₂SiO₄ + stishovite and γ-Mg₂SiO₄ (spinel) + stishovite displayed by MgSiO₃ were not observed in 95% MgSiO₃ · 5% Al₂O₃, and the garnet phase, which was observed in 95% MgSiO₃ · 5% Al₂O₃ at high pressure, was not detected in MgSiO₃. These results suggest that the high-pressure phase transformations found in pure MgSiO₃ would be inhibited under mantle conditions by the presence even of small amounts of Al₂O₃ (?4% by weight). On the other hand, pyrope displays a wide stability field, finally transforming at 240–250 kbar directly to an ilmenite-type modification of the same stoichiometry. The two-phase region, within which orthopyroxene and garnet solid solutions coexist, is very broad. The structure of the earth's mantle is discussed in terms of the phase transformations to be expected in a simple mixture of 90% MgSiO₃ · 10% Al₂O₃ and Mg₂SiO₄. The seismic discontinuity at a depth of 400 km in the earth's mantle is probably due entirely to the olivine → β-phase transition in Mg₂SiO₄, with the progressive solution of pyroxene in garnet (displayed in 90% MgSiO₃ · 10% Al₂O₃) occurring at shallower depths. The inferred discontinuity at 650 km is due to the combination of the phase changes spinel → perovskite + rocksalt in Mg₂SiO₄ and garnet → ilmenite in 90% MgSiO₃ · 10% Al₂O₃. The 650-km discontinuity is thus characterized by an increase in the primary coordination of silicon from 4 to 6. A further discontinuity in the density and seismic wave velocities at greater depth associated with the ilmenite-perovskite phase transformation in 90% MgSiO₃ · 10% Al₂O₃ is expected.     

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).     

Elasticity of polycrystalline stishovite

Ultrasonic data for the velocities of SiO₂-stishovite have been determined as a function of pressure to 10 kbar at room temperature for polycrystalline specimens hot-pressed at pressures P = 120kbar and temperatures T = 900°C. These cylindrical specimens are 2 mm in diameter and 0.9–1.4 mm long and have a grain size less than 10 μm. Compressional and shear wave velocities were measured both parallel and perpendicular to the axis of pressing and were found to be isotropic at 10 kbar with ν_p = 11.0 ± 0.2km/sec andν_s = 6.9 ± 0.3km/sec; this shear velocit is substantially higher than that of Mizutani et al. (1972) perhaps due to the presence of crack orientations in their specimen which affected ν_s but not ν_p. The Murnaghan P-V trajectories calculated from the ultrasonic data [bulk modulus K_s = 2.5 ± 0.3Mbar and assuming (?K_s/?P)_T = 6 ± 2] are consistent with recent hydrostatic compression data and with the shock wave compression data above 600 kbar. The combined evidence from the data of the ultrasonic and hydrostatic compression techniques suggests that the most probable value of the bulk modulus of stishovite at zero pressure is close to the upper limit of the uncertainty of our ultrasonically determined value, K₀ = 2.7?2.8Mbar. Elasticity data for rutile-type oxides are not compatible with normal K_s-V₀ systematics perhaps due to the neglect of non-central forces in the lattice model. These new stishovite data would make it impossible to satisfy the elasticity-density data of the lower mantle using an oxide mixture with either olivine or pyroxene stoichiometry.     

Hot pressing of polycrystals of high-pressure phases of mantle minerals in multi-anvil apparatus

In the 1960s, E. Schreiber and his colleagues pioneered the use of hot-pressed polycrystalline aggregates for studies of the pressure and temperature dependence of the elastic wave velocities in minerals. We have extended this work to the high-pressure polymorphs of mantle minerals by developing techniques to fabricate large polycrystalline specimens in a 2000-ton uniaxial split-sphere apparatus. A new cell assembly has been developed to extend this capability to pressures of 20 GPa and temperatures of 1700°C. Key elements in the new experimental design include: a telescopic LaCrO₃ forT>1200°C; Toshiba Tungaloy grade F tungsten carbide anvils; and the use of homogeneous glasses or seeded powder mixtures as starting material to enhance reactivity and maximize densities. Cell temperatures are linearly related to electrical power to 1700°C and uniform throughout the 3 mm specimens. Pressure calibrations at 25°C and 1700°C are identical to 15 GPa. Cylindrical specimens of the beta and spinel phases of Mg₂SiO₄, stishovite (SiO₂-rutile), and majorite-pyrope garnets have been synthesized within their stability fields in runs of 1–4 hr duration and recovered at ambient conditions by simultaneously decompressing and cooling along a computer-controlledP-T path designed to preserve the high-pressure phase and to relax intergranualar stress in the polycrystalline aggregate. These specimens are single-phased, fine-grained (<5 micron), free of microcracks and preferred orientation, and have bulk densities greater than 99% of X-ray density. The successful fabrication of these high-quality polycrystalline specimens has made possible experiments to determine the pressure dependence of acoustic velocities in the ultrasonics laboratory of S. M. Rigden and I. Jackson at the Australian National University.CHiPR: NSF Science and Technology Center for High Pressure Research.     

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.