Structural modifications of CaGeO3-wollastonite under room temperature pressurization

 In-situ X-ray diffraction measurements of CaGeO₃-wollastonite at high pressure at room temperature have been performed using a diamond anvil cell with an X-ray source. A new structural modification of CaGeO₃-wollastonite is observed at about 6GPa and the characteristic reflections of the high pressure form are preserved on decompression to an ambient pressure. A rhodonite-like structure is proposed as a high pressure form from the crystal chemical consideration. The rhodonite-like phase is further transformed into a perovskite-form at about 15 GPa. The rhodonite-like-form of CaGeO₃ seems not to be a stable phase from the heating experiments under high pressures. The metastable transition path from the wollastonite to the perovskite polymorph through the rhodonite-like structure is kinetically favored under room temperature pressurization. No pressure-induced amorphization is observed during the transition into the perovskite-form, although the transition is accompanied by the coordination change of Ge atoms from fourfold to sixfold. Received: July 19, 1995 / Revised, accepted: August 1996     

A high-temperature and high-pressure Raman spectroscopic study of CaGeO3 garnet

 High-pressure and high-temperature Raman spectra of CaGeO₃ tetragonal garnet have been collected to 11.5 GPa and 1225 K, respectively, in order to investigate possible intrinsic anharmonic behaviour in this phase. The Raman peak positions were observed to vary linearly with pressure and temperature within the ranges studied, with the higher-energy peaks showing larger P- and T-induced shifts than the low energy modes. The observed T-induced shifts are similar to those reported for grossular and andradite, while the observed P-induced shifts are generally larger than those of aluminosilicate and MgSiO₃ majorite garnets (Gillet et al. 1992; Rauch et al. 1996) due to the larger bulk modulus of CaGeO₃ garnet. The observed mode shifts of CaGeO₃ garnet were used to determine the isothermal and isobaric mode Grüneisen parameters for this phase. These parameters are similar in value to those reported previously for grossular and andradite (Gillet et al. 1992). The calculated intrinsic anharmonic parameters, a _i , for CaGeO₃ garnet were determined to be nonzero, indicating significant anharmonic behaviour for this phase. These values, which range from −3.8 × 10⁻⁵ K⁻¹ to −1.3 × 10⁻⁵ K⁻¹, are also similar to those reported for andradite and grossular, but smaller than those determined for pyrope (Gillet et al. 1992). Hence, we expect MgSiO₃ majorite to show greater anharmonicity than the germanate analogue studied by us. The anharmonic parameters determined for CaGeO₃ tetragonal garnet may now be introduced into quasiharmonic vibrational heat capacity models to account for the observed anharmonic behaviour. Received: 21 April 1999 / Revised, accepted: 11 September 1999     

Do carbonate liquids become denser than silicate liquids at pressure? Constraints from the fusion curve of K<Subscript>2</Subscript>CO<Subscript>3</Subscript> to 3.2 GPa

Brackets on the melting temperature of K₂CO₃ were experimentally determined at 1.86 ± 0.02 GPa (1,163–1,167°C), 2.79 ± 0.03 GPa (1,187–1,195°C), and 3.16 ± 0.04 GPa (1,183–1,189°C) in a piston-cylinder apparatus. These new data, in combination with published experiments at low pressure (<0.5 GPa), establish the K₂CO₃ fusion curve to 3.2 GPa. On the basis of these experiments and published thermodynamic data for crystalline and liquid K₂CO₃, the high-pressure density and compressibility of K₂CO₃ liquid were derived from the fusion curve. The pressure dependence of the liquid compressibility (K′₀ = dK ₀/dP, where K ₀ = 1/β₀) is between 16.2 and 11.6, with a best estimate of 13.7, in a third-order Birch–Murnaghan equation of state (EOS). This liquid K′₀ leads to a density of 2,175 ± 36 kg/m³ at 4 GPa and 1,500°C, which is ∼30% lower than that reported in the literature on the basis of the falling-sphere method at the same conditions. The uncertainty in the liquid K′₀ leads to an error in melt density of ± 2% at 4 GPa; the error decreases with decreasing pressure. With a K′₀ of 13.7, the compressibility of K₂CO₃ at 1,500°C and 1 bar (K ₀ = 3.8 GPa) drops rapidly with increasing pressure ( ), which prevents a density crossover with silicate melts, such as CaAlSi₂O₈ and CaMgSi₂O₆, at upper mantle depths.     

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 CaSnO3 perovskite

The elastic properties of CaSnO₃ perovskite have been measured by both ultrasonic interferometry and single-crystal X-ray diffraction at high pressures. The single-crystal diffraction data collected using a diamond-anvil cell show that CaSnO₃ perovskite does not undergo any phase transitions at pressures below 8.5?GPa at room temperature. Ultrasonic measurements in the multianvil press to a maximum pressure of ～8?GPa at room temperature yielded S- and P-wave velocity data as a function of pressure. For a third-order Birch-Murnaghan EoS the adiabatic elastic moduli and their pressure derivatives determined from these velocity data are K _S0=167.2±3.1?GPa, K ^′ _S0=4.89±0.17, G ₀=89.3±1.0?GPa, G ^′ ₀=0.90±0.02. The quoted uncertainties include contributions from uncertainties in both the room pressure length and density of the specimen, as well as uncertainties in the pressure calibration of the multianvil press. Because the sample is a polycrystalline specimen, this value of K _S0 represents an upper limit to the Reuss bound (conditions of uniform stress) on the elastic modulus of CaSnO₃ perovskite. If the value of αγT is assumed to be 0.01, the value of K _S0 corresponds to K _T0=165.5±3.1?GPa. The 10 P-V data obtained by single-crystal diffraction were fit with a third-order Birch–Murnaghan equation-of-state to obtain the parameters V ₀=246.059±0.013 ų, K _T0=162.6±1.0?GPa, K ^′ _T0=5.6±0.3. Because single-crystal measurements under hydrostatic conditions are made under conditions of uniform stress, they yield bulk moduli equivalent to the Reuss bound on a polycrystalline specimen. The results from the X-ray and ultrasonic experiments are therefore consistent. The bulk modulus of CaSnO₃ perovskite lies above the linear trend of K ₀ with inverse molar volume, previously determined for Ca perovskites. This prevents an estimation of the bulk modulus of CaSiO₃ perovskite by extrapolation. However, our value of G ₀ for CaSnO₃ perovskite combined with values for CaTiO₃ and CaGeO₃ forms a linear trend of G ₀ with octahedral tilt angle. This allows a lower bound of 150?GPa to be placed on the shear modulus of CaSiO₃ by extrapolation.     

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

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

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).     

Composition of aqueous fluid coexisting with mantle minerals at high pressure and its bearing on the differentiation of the Earth’s mantle

In order to understand the role of aqueous fluid on the differentiation of the mantle, the compositions of aqueous fluids coexisting with mantle minerals were investigated in the system MgO-SiO₂-H₂O at pressures of 3 to 10 GPa and temperatures of 1000 to 1500°C with an MA8-type multianvil apparatus. Phase boundaries between the stability fields of forsterite + aqueous fluid, forsterite + enstatite + aqueous fluid, and enstatite + aqueous fluid were determined by varying the bulk composition at constant temperature and pressure. The composition of aqueous fluid coexisting with forsterite and enstatite can be defined by the intersection of these two phase boundaries. The solubility of silicate components in aqueous fluid coexisting with forsterite and enstatite increases with increasing pressure up to 8 GPa, from about 30 wt% at 3 GPa to about 70 wt% at 8 GPa. It becomes almost constant above 8 GPa. The Mg/Si weight ratio of these aqueous fluids is much higher than at low pressure (0.2 at 1.5 GPa) and almost constant (1.2) at pressures between 3 and 8 GPa. At 10 GPa, it becomes about 1.4. Aqueous fluid migrating upward through the mantle can therefore dissolve large amounts of silicates, leaving modified Mg/Si ratios of residual materials. It is suggested that the chemical stratification of Mg/Si in the Earth may have been formed as a result of aqueous fluid migration.     

High-pressure Raman studies and heat capacity measurements on the MgSiO<Subscript>3</Subscript> analogue CaIr<Subscript>0.5</Subscript>Pt<Subscript>0.5</Subscript>O<Subscript>3</Subscript>

Raman spectroscopy and heat capacity measurements have been used to study the post-perovskite phase of CaIr_0.5Pt_0.5O₃, recovered from synthesis at a pressure of 15 GPa. Laser heating CaIr_0.5Pt_0.5O₃ to 1,900 K at 60 GPa produces a new perovskite phase which is not recoverable and reverts to the post-perovskite polymorph between 20 and 9 GPa on decompression. This implies that Pt-rich CaIr_1−xPt_xO₃ perovskites including the end member CaPtO₃ cannot easily be recovered to ambient pressure from high P–T synthesis. We estimate an increase in the thermodynamic Grüneisen parameter across the post-perovskite to perovskite transition of 34%, of similar magnitude to those for (Mg,Fe)SiO₃ and MgGeO₃, suggesting that CaIr_0.5Pt_0.5O₃ is a promising analogue for experimental studies of the competition in energetics between perovskite and post-perovskite phases of magnesium silicates in Earth’s lowermost mantle. Low-temperature heat capacity measurements show that CaIrO₃ has a significant Sommerfeld coefficient of 11.7 mJ/mol K² and an entropy change of only 1.1% of Rln2 at the 108 K Curie transition, consistent with the near-itinerant electron magnetism. Heat capacity results for post-perovskite CaIr_0.5Rh_0.5O₃ are also reported.     

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.     

Pressure-induced structural changes and densification of vitreous MgSiO3

Compression of MgSiO₃ glass in a 6/8 multianvil apparatus to 10.0 ± 0.5 GPa results in demonstrable changes in density and silicon coordination. Under high-pressure, samples were heated over a range of temperatures from 300 to 773 K, quenched to room temperature and decompressed at rates of 10.4 and 0.08 GPa/min. Recovered glasses have bulk densities that are 2.6-11.0% higher than the non-compressed glass. ²⁹Si MAS NMR spectra of compressed glasses show narrowing of the ^[4]Si peak resulting from a reduction in the spread of the Si-O-Si bond angle distribution. After heating and rapid decompression, ²⁹Si MAS NMR spectra of recovered glasses exhibit peaks assignable to ^[4]Si, ^[5]Si, and ^[6]Si with relative fractions of 0.945, 0.045, and 0.008, respectively. These changes in Si coordination and in Si-O-Si bond angle distribution with pressure only represent part of the structural changes associated with permanent densification of heated and unheated samples. The abundance of ^[6]Si is found to be insensitive to decompression rate, while ^[5]Si reverts to ^[4]Si on slow decompression at room temperature. These observations demonstrate that high-coordinated silicon species in MgSiO₃ glass are formed on compression below glass transition temperatures and that pressure-induced structural changes can be preserved with rapid decompression. The ease with which ^[5]Si reverts to ^[4]Si during decompression suggests that the conversion of ^[4]Si → ^[5]Si principally involves short-range atomic displacement. The reversible and irreversible features of densification of MgSiO₃ glass, provide insights into the fundamental structural and rheological properties of refractory silicate melts similar to those found in the Earth’s mantle.     

Polysynthetically-twinned structures of enstatite and wollastonite

Crystal structures of clinoenstatite, orthoenstatite, wollastonite-1T and wollastonite-2M (parawollastonite) were refined to an R factor 3–4 percent level. Molar volumes at room temperature are 31.270(15), 31.315(8), 39.842(5) and 39.901(10) cm³/MSiO₃, in the above-mentioned order, indicating that one-layer polytypes (clinoenstatite and wollastonite-1T) are stable at higher pressures than two-layer polytypes (orthoenstatite and wollastonite-2M). The polytypic relation of the enstatite polytypes can be described by four twinning operations — b glide ∥ to (110), a glide ∥ to (001), twofold screw axis ∥ to a (of orthoenstatite) and a twofold screw axis ∥ to c. For the wollastonite polytypes, twinning operations are twofold screw axis ∥ to b and a glide ∥ to (010). Structural adjustments after twinning are not necessarily the largest at the twin boundary (true in enstatite but not so in wollastonite). In both cases octahedral sites that involve bridging oxygens tend to show relatively large changes. Lattice strain ellipsoids associated with twinning are also different for enstatite and wollastonite, which implies that wollastonite may react differently from enstatite to non-hydrostatic pressure.     

Phase transition and compression behavior of gibbsite under high-pressure

In situ high-pressure synchrotron X-ray diffraction and infrared absorption experiments for gibbsite were performed at room temperature up to 53 and 25 GPa, respectively. A phase transition was confirmed at about 2.5 GPa. The high-pressure phase is indexed as an orthorhombic structure, rather than a triclinic structure as reported in previous studies. The compressibility of gibbsite and its high-pressure polymorph were studied, and their bulk moduli K₀ were determined to be 49 and 75 GPa, respectively with K₀ as 4. The in situ high-pressure infrared absorption spectra revealed the gradual disordering of hydrogen substructure above 15 GPa in quasihydrostatic compression.     

In situ observation of a garnet/perovskite transition in CaGeO<Subscript>3</Subscript>

We used an in situ measurement method to investigate the phase transition of CaGeO₃ polymorphs under high pressures and temperatures. A multi-anvil high-pressure apparatus combined with intense synchrotron X-ray radiation was used. The transition boundary between a garnet and a perovskite phase at T = 900–1,650 K and P = 3–8 GPa was determined as occurring at P (GPa) = 9.0−0.0023 × T (K). The transition pressure determined in our study is in general agreement with that observed in previous high-pressure experiments. The slope, dP/dT, of the transition determined in our study is consistent with that calculated from calorimetry data.     

Phase transformations of enstatite in spherical shock waves

The analysis of available theoretical evaluations and experimental data reveals discrepancies and makes it possible to formulate the goals for the comprehensive study of the behavior of enstatite MgSiO₃ in shock isentropic waves of various scale and intensity. The paper presents the layout and results of an explosion experiment on the compression of an enstatite sphere with spherical shock waves and the subsequent recovery of the experimental material and its examination in discrete zones (along the sphere radius) that were produced by shock waves in the material. The latter were examined with the application of scanning electron microscopy, Raman spectroscopy, and X-ray diffraction analysis. The comparison of the systematic variations in the texture, chemistry, and phase composition of enstatite along the sphere radius with calculated pressure P(R, t) and temperature T(R, t) values led us to the following conclusions: enstatite starts melting on an isentrope upon pressure relief after shock wave compression at ?? _xx ?? 80 GPa and melts on the front of the spherically converging shock wave at ?? _xx ?? 160 GPa and T ?? 6300 K. Our laboratory experiments with shock waves were the world??s first in which enstatite was loaded with spherical converging shock isentropic waves and which provided evidence that shock wave-loaded MgSiO₃ shows certain morphological and mineralogical features never before detected in this mineral loaded with plane shock wave of smaller amplitude and duration. Goals are formulated for the further studying of shock wave-loaded materials, and the necessity is discussed for conducting an explosion experiment with a five to seven times greater spherical system in order to increase the duration of the shock wave loading impulse.     

Synthetic lead bromapatite: X-ray structure at ambient pressure and compressibility up to about 20 GPa

Lead bromapatite [Pb₁₀(PO₄)₆Br₂] has been synthesized via solid-state reaction at pressures up to 1.0 GPa, and its structure determined by single-crystal X-ray diffraction at ambient temperature and pressure. The large bromide anion is accommodated in the c-axis channel by lateral displacements of structural elements, particularly of Pb2 cations and PO₄ tetrahedra. The compressibility of bromapatite was also investigated up to about 20.7 GPa at ambient temperature, using a diamond-anvil cell and synchrotron X-ray radiation. The compressibility of lead bromapatite is significantly different from that of lead fluorapatite. The pressure–volume data of lead bromapatite (P < 10 GPa) fitted to the third-order Birch-Murnaghan equation yield an isothermal bulk modulus (K _T ) of 49.8(16) GPa and first pressure derivative (K_T^￠ K_{T}^{\prime } ) of 10.1(10). If K_T^￠ K_{T}^{\prime } is fixed at 4, the derived K _T is 60.8(11) GPa. The relative difference of the bulk moduli of these two lead apatites is thus about 12%, which is about two times the relative difference of the bulk moduli (~5%) of the calcium apatites fluorapatite [Ca₁₀(PO₄)₆F₂]_, chlorapatite [Ca₁₀(PO₄)₆Cl₂] and hydroxylapatite [Ca₁₀(PO₄)₆(OH)₂]. Another interesting feature apparently related to the replacement of F by Br in lead apatite is the switch in the principle axes of the strain ellipsoid: the c-axis is less compressible than the a-axis in lead bromapatite but more compressible in lead fluorapatite.     

Refractive index and compressibility of Di64An36 glass over a pressure range of 0–5.0 GPa

Data on the refractive index, density, and bulk modulus variations of Di₆₄An₃₆ glass, which is used as a model basalt melt, were obtained with a polarization interference microscope and a high-pressure diamond anvil cell at ambient temperature and pressure up to 5.0 GPa. An anomalous decrease in the bulk modulus, K _t , was observed in the pressure range 0?C1.0 GPa. The values of the zero-pressure isothermal bulk modulus, K _t,0 = 22.2, and variation of the bulk modulus with pressure, ??K _t /??P = 11.35, were derived using a linear equation relating K _t and P over the pressure range with the normal behavior of the compressibility. A comparison of our results with previous data on other glasses and melts showed that the bulk moduli of silicate glasses are similar to those of corresponding melts. The values of the pressure coefficient of the bulk moduli, ??K _t /??P, for glasses derived from linear equations are 2.5 times higher than the pressure derivative of the bulk modulus, K?? _T , derived using the Birch-Murnaghan equation for corresponding melts. The difference in ??K _t /??P and K?? _T has an effect on the compressibility of glasses and melts. The compressibility of glasses up to 5.0 GPa calculated as (d ? d ₀)/d is almost two times lower than that of corresponding melts.     

Hydrostatic compression of ilmenite phase of ZnSiO3 and MgGeO3

Accurate measurements of cell parameters were performed on the ilmenite phases of ZnSiO₃ and MgGeO₃ using an X-ray diffraction method under hydrostatic conditions. The linear changes in cell parameter are represented by 1?a/a ₀=(1.06±0.04)×10^?4 P(kbar) and 1?c/c ₀=(2.11±0.04)×10^?4 P for ZnSiO₃, and 1?a/a ₀=(1.37±0.03)×10^?4 P and 1?c/c ₀=(2.05±0.04)×10^?4 P for MgGeO₃. A least-squares calculation using the first-order Birch-Murnaghan equation gives K _T =2.16±0.02 Mbar and K _T =1.87±0.02 Mbar for ZnSiO₃ and MgGeO₃, respectively. Elastic systematics assuming K _T V _m =constant give a predicted value K _T =2.14 Mbar for the ilmenite phase of MgSiO₃.     

High-pressure transitions and thermochemistry of MGeO3 (M=Mg, Zn and Sr) and Sr-silicates: systematics in enthalpies of formation of A2+B4+O3 perovskites

Phase transitions in MgGeO₃ and ZnGeO₃ were examined up to 26 GPa and 2,073 K to determine ilmenite–perovskite transition boundaries. In both systems, the perovskite phases were converted to lithium niobate structure on release of pressure. The ilmenite–perovskite boundaries have negative slopes and are expressed as P(GPa)=38.4–0.0082T(K) and P(GPa)=27.4−0.0032T(K), respectively, for MgGeO₃ and ZnGeO₃. Enthalpies of SrGeO₃ polymorphs were measured by high-temperature calorimetry. The enthalpies of SrGeO₃ pseudowollasonite–walstromite and walstromite–perovskite transitions at 298 K were determined to be 6.0±8.6 and 48.9±5.8 kJ/mol, respectively. The calculated transition boundaries of SrGeO₃, using the measured enthalpy data, were consistent with the boundaries determined by previous high-pressure experiments. Enthalpy of formation (ΔH _f°) of SrGeO₃ perovskite from the constituent oxides at 298 K was determined to be −73.6±5.6 kJ/mol by calorimetric measurements. Thermodynamic analysis of the ilmenite–perovskite transition boundaries in MgGeO₃ and ZnGeO₃ and the boundary of formation of SrSiO₃ perovskite provided transition enthalpies that were used to estimate enthalpies of formation of the perovskites. The ΔH _f° of MgGeO₃, ZnGeO₃ and SrSiO₃ perovskites from constituent oxides were 10.2±4.5, 33.8±7.2 and −3.0±2.2 kJ/mol, respectively. The present data on enthalpies of formation of the above high-pressure perovskites were combined with published data for A²⁺B⁴⁺O₃ perovskites stable at both atmospheric and high pressures to explore the relationship between ΔH _f° and ionic radii of eightfold coordinated A²⁺ (R _A) and sixfold coordinated B⁴⁺ (R _B) cations. The results show that enthalpy of formation of A²⁺B⁴⁺O₃ perovskite increases with decreasing R _A and R _B. The relationship between the enthalpy of formation and tolerance factor ( R _o: O²⁻ radius) is not straightforward; however, a linear relationship was found between the enthalpy of formation and the sum of squares of deviations of A²⁺ and B⁴⁺ radii from ideal sizes in the perovskite structure. A diagram showing enthalpy of formation of perovskite as a function of A²⁺ and B⁴⁺ radii indicates a systematic change with equienthalpy curves. These relationships of ΔH _f° with R _A and R _B can be used to estimate enthalpies of formation of perovskites, which have not yet been synthesized.