Low-temperature heat capacities,entropies and enthalpies of Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> polymorphs,and α−β−γ and post-spinel phase relations at high pressure

The low-temperature isobaric heat capacities (C _p) of β- and γ-Mg₂SiO₄ were measured at the range of 1.8–304.7 K with a thermal relaxation method using the Physical Property Measurement System. The obtained standard entropies (S°₂₉₈) of β- and γ-Mg₂SiO₄ are 86.4 ± 0.4 and 82.7 ± 0.5 J/mol K, respectively. Enthalpies of transitions among α-, β- and γ-Mg₂SiO₄ were measured by high-temperature drop-solution calorimetry with gas-bubbling technique. The enthalpies of the α−β and β−γ transitions at 298 K (ΔH°₂₉₈) in Mg₂SiO₄ are 27.2 ± 3.6 and 12.9 ± 3.3 kJ/mol, respectively. Calculated α−β and β−γ transition boundaries were generally consistent with those determined by high-pressure experiments within the errors. Combining the measured ΔH°₂₉₈ and ΔS°₂₉₈ with selected data of in situ X-ray diffraction experiments at high pressure, the ΔH°₂₉₈ and ΔS°₂₉₈ of the α−β and β−γ transitions were optimized. Calculation using the optimized data tightly constrained the α−β and β−γ transition boundaries in the P, T space. The slope of α−β transition boundary is 3.1 MPa/K at 13.4 GPa and 1,400 K, and that of β−γ boundary 5.2 MPa/K at 18.7 GPa and 1,600 K. The post-spinel transition boundary of γ-Mg₂SiO₄ to MgSiO₃ perovskite plus MgO was also calculated, using the optimized data on γ-Mg₂SiO₄ and available enthalpy and entropy data on MgSiO₃ perovskite and MgO. The calculated post-spinel boundary with a Clapeyron slope of −2.6 ± 0.2 MPa/K is located at pressure consistent with the 660 km discontinuity, considering the error of the thermodynamic data.     

Phase boundary between ilmenite and perovskite structures in MnGeO3 determined by in situ X-ray diffraction measurements

In situ X-ray observations of the phase transition from ilmenite to perovskite structure in MnGeO₃ were carried out in a Kawai-type high-pressure apparatus interfaced with synchrotron radiation. The phase boundary between the ilmenite and perovskite structures in the temperature range of 700–1,400°C was determined to be P (GPa) = 16.5(±0.6) − 0.0034(±0.0006)T (°C) based on Anderson’s gold pressure scale. The Clapeyron slope, dP/dT, determined in this study is consistent with that for the transition boundary between the ilmenite and the perovskite structure in MgSiO₃.     

The ZnSiO3 clinopyroxene-ilmenite transition: Heat capacity,enthalpy of transition,and phase equilibria

ZnSiO₃ clinopyroxene stable above 3 GPa transforms to ilmenite at 10–12 GPa, which further decomposes into ZnO (rock salt) plus stishovite at 20–30 GPa. The enthalpy of the clinopyroxene-ilmenite transition was measured by high-temperature solution calorimetry, giving ΔH⁰=51.71 ±3.18 kJ/mol at 298 K. The heat capacities of clinopyroxene and ilmenite were measured by differential scanning calorimetry at 343–733 and 343–633 K, respectively. The C _p of ilmenite is 3–5% smaller than that of clinopyroxene. The entropy of transition was calculated using the measured enthalpy and the free energy calculated from the phase equilibrium data. The enthalpy, entropy and volume changes of the pyroxene-ilmenite transition in ZnSiO₃ are similar in magnitude to those in MgSiO₃. The present thermochemical data are used to calculate the phase boundary of the ZnSiO₃ clinopyroxene-ilmenite transition. The calculated boundary,

Pressure dependence of electrical conductivity of (Mg,Fe)SiO<Subscript>3</Subscript> ilmenite

The electrical conductivity of (Mg_0.93Fe_0.07)SiO₃ ilmenite was measured at temperatures of 500–1,200 K and pressures of 25–35 GPa in a Kawai-type multi-anvil apparatus equipped with sintered diamond anvils. In order to verify the reliability of this study, the electrical conductivity of (Mg_0.93Fe_0.07)SiO₃ perovskite was also measured at temperatures of 500–1,400 K and pressures of 30–35 GPa. The pressure calibration was carried out using in situ X-ray diffraction of MgO as pressure marker. The oxidation conditions of the samples were controlled by the Fe disk. The activation energy at zero pressure and activation volume for ilmenite are 0.82(6) eV and −1.5(2) cm³/mol, respectively. Those for perovskite were 0.5(1) eV and −0.4(4) cm³/mol, respectively, which are in agreement with the experimental results reported previously. It is concluded that ilmenite conductivity has a large pressure dependence in the investigated P–T range.     

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.     

Phase equilibrium and calorimetric study of the transition of MnTiO3 from the ilmenite to the lithium niobate structure and implications for the stability field of perovskite

The phase boundary between MnTiO₃ I (ilmenite structure) and MnTiO₃ II (lithium niobate structure) has been determined by analysis of quench products from reversal experiments in a cubic anvil apparatus at 1073–1673 K and 43–75 kbar using mixtures of MnTiO₃ I and II as starting materials. Tight brackets of the boundary give P(kbar)=121.2−0.045 T(K). Thermodynamic analysis of this boundary gives ΔH^o=5300±1000 J·mol⁻¹, ΔS^o = 1.98 ±1J·K⁻¹· mol⁻¹. The enthalpy of transformation obtained directly by transposed-temperature-drop calorimetry is 8359 ±2575 J·mol⁻¹. Possible topologies of the phase relations among the ilmenite, lithium niobate, and perovskite polymorphs are constrained using the above data and the observed (reversible with hysteresis) transformation of II to III at 298 K and 20–30 kbar (Ross et al. 1989). The observed II–III transition is likely to lie on a metastable extension of the II–III boundary into the ilmenite field. However the reversed I–II boundary, with its negative dP/ dT does represent stable equilibrium between ilmenite and lithium niobate, as opposed to the lithium niobate being a quench product of perovskite. We suggest a topology in which the perovskite occurs stably at low T and high P with a triple point (I, II, III) at or below 1073 K near 70 kbar. The I–II boundary would have a negative P-T slope while the II–III and I–III boundaries would be positive, implying that entropy decreases in the order lithium niobate, ilmenite, perovskite. The inferred positive slope of the ilmenite-perovskite transition in MnTiO₃ is different from the negative slopes in silicates and germanates. These thermochemical parameters are discussed in terms of crystal structure and lattice vibrations.     

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.     

Heat capacity of γ-Fe2SiO4 between 5 and 303 K and derived thermodynamic properties

A multi-anvil device was used to synthesize 24 mg of pure γ-Fe₂SiO₄ crystals at 8.5 GPa and 1,273 K. The low-temperature heat capacity (C _p) of γ-Fe₂SiO₄ was measured between 5 and 303 K using the heat capacity option of a physical properties measurement system. The measured heat capacity data show a broad λ-transition at 11.8 K. The difference in the C _p between fayalite and γ-Fe₂SiO₄ is reduced as the temperature increases in the range of 50–300 K. The gap in C _p data between 300 and 350 K of γ-Fe₂SiO₄ is an impediment to calculation of a precise C _p equation above 298 K that can be used for phase equilibrium calculations at high temperatures and high pressures. The C _p and entropy of γ-Fe₂SiO₄ at standard temperature and pressure (S°₂₉₈) are 131.1 ± 0.6 and 140.2 ± 0.4 J mol⁻¹ K⁻¹, respectively. The Gibbs free energy at standard pressure and temperature (ΔG° _f,298) is calculated to be −1,369.3 ± 2.7 J mol⁻¹ based on the new entropy data. The phase boundary for the fayalite–γ-Fe₂SiO₄ transition at 298 K based on current thermodynamic data is located at 2.4 ± 0.6 GPa with a slope of 25.4 bars/K, consistent with extrapolated results of previous experimental studies.     

Determination of the phase boundary between ilmenite and perovskite in MgSiO3 by in situ X-ray diffraction and quench experiments

Determination of the phase boundary between ilmenite and perovskite structures in MgSiO₃ has been made at pressures between 18 and 24 GPa and temperatures up to 2000 °C by in situ X-ray diffraction measurements using synchrotron radiation and quench experiments. It was difficult to precisely define the phase boundary by the present in situ X-ray observations, because the grain growth of ilmenite hindered the estimation of relative abundances of these phases. Moreover, the slow reaction kinetics between these two phases made it difficult to determine the phase boundary by changing pressure and temperature conditions during in situ X-ray diffraction measurements. Nevertheless, the phase boundary was well constrained by quench method with a pressure calibration based on the spinel-postspinel boundary of Mg₂SiO₄ determined by in situ X-ray experiments. This yielded the ilmenite-perovskite phase boundary of P (GPa) = 25.0 (±0.2) – 0.003 T (°C) for a temperature range of 1200–1800 °C, which is generally consistent with the results of the present in situ X-ray diffraction measurements within the uncertainty of ∼±0.5 GPa. The phase boundary thus determined between ilmenite and perovskite phases in MgSiO₃ is slightly (∼0.5 GPa) lower than that of the spinel-postspinel transformation in Mg₂SiO₄. Received: 19 May 1999 / Accepted: 21 March 2000     

Heat capacity calculations for Al2O3 corundum and MgSiO3 ilmenite

We have used Kieffer's vibrational model to calculate heat capacities and entropies for Al₂O₃ corundum and MgSiO₃ ilmenite, using available vibrational and elastic data for these phases. The calculated heat capacity for corundum is within 1–2 percent of the experimental values between 100 K and 1,800 K, while that for MgSiO₃ ilmenite is within 1–2 percent of the experimental data between 350 K and 500 K. We have calculated the heat capacity for MgSiO₃ ilmenite from 50 K to 1,800 K, which extends the range of available heat capacity data for this phase. The results of this calculation suggest that there may be differences in the vibrational properties of corundum and MgSiO₃ ilmenite. Finally, we have used the results of our calculation to obtain a transition entropy of near -18.8 J/mol.K for the MgSiO₃ pyroxene-ilmenite reaction.     

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.     

MgSiO3 ilmenite: Heat capacity,thermal expansivity,and enthalpy of transformation

A new determination, using high temperature drop-solution calorimetry, of the enthalpy of transformation of MgSiO₃ pyroxene to ilmenite gives H ₂₉₈ = 59.03 ±4.26 kJ/mol. The heat capacity of the ilmenite and orthopyroxene phases has been measured by differential scanning calorimetry at 170–700 K; C_p of MgSiO₃ ilmenite is 4–10 percent less than that of MgSiO₃ pyroxene throughout the range studied. The heat capacity differences are consistent with lattice vibrational models proposed by McMillan and Ross (1987) and suggest an entropy change of -18 ± 3 J-K^-1 ·mol^-1, approximately independent of temperature, for the pyroxene-ilmenite transition. The unit cell parameters of MgSiO₃ ilmenite were measured at 298–876 K and yield an average volume thermal expansion coefficient of 2.44 × 10^-5 K^-1. The thermochemical data are used to calculate phase relations involving pyroxene, -Mg₂SiO₄ plus stishovite, Mg₂SiO₄ spinel plus stishovite, and ilmenite in good agreement with the results of high pressure studies.     

Low-temperature heat capacities of MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> and spinels of the MgCr<Subscript>2</Subscript>O<Subscript>4</Subscript>–MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> solid solution

We present results from low-temperature heat capacity measurements of spinels along the solid solution between MgAl₂O₄ and MgCr₂O₄. The data also include new low-temperature heat capacity measurements for MgAl₂O₄ spinel. Heat capacities were measured between 1.5 and 300 K, and thermochemical functions were derived from the results. No heat capacity anomaly was observed for MgAl₂O₄ spinel; however, we observe a low-temperature heat capacity anomaly for Cr-bearing spinels at temperatures below 15 K. From our data we calculate standard entropies (298.15 K) for Mg(Cr,Al)₂O₄ spinels. We suggest a standard entropy for MgAl₂O₄ of 80.9 ± 0.6 J mol⁻¹ K⁻¹. For the solid solution between MgAl₂O₄ and MgCr₂O₄, we observe a linear increase of the standard entropies from 80.9 J mol⁻¹ K⁻¹ for MgAl₂O₄ to 118.3 J mol⁻¹ K⁻¹ for MgCr₂O₄.     

LiFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript> and NaFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript> at low temperatures: an infrared spectroscopic study

 Synthetic aegirine LiFeSi₂O₆ and NaFeSi₂O₆ were characterized using infrared spectroscopy in the frequency range 50–2000 cm⁻¹, and at temperatures between 20 and 300 K. For the C2/c phase of LiFeSi₂O₆, 25 of the 27 predicted infrared bands and 26 of 30 predicted Raman bands are recorded at room temperature. NaFeSi₂O₆ (with symmetry C2/c) shows 25 infrared and 26 Raman bands. On cooling, the C2/c–P2₁/c structural phase transition of LiFeSi₂O₆ is characterized by the appearance of 13 additional recorded peaks. This observation indicates the enlargement of the unit cell at the transition point. The appearance of an extra band near 688 cm⁻¹ in the monoclinic P2₁/c phase, which is due to the Si–O–Si vibration in the Si₂O₆ chains, indicates that there are two non-equivalent Si sites with different Si–O bond lengths. Most significant spectral changes appear in the far-infrared region, where Li–O and Fe–O vibrations are mainly located. Infrared bands between 300 and 330 cm⁻¹ show unusually dramatic changes at temperatures far below the transition. Compared with the infrared data of NaFeSi₂O₆ measured at low temperatures, the change in LiFeSi₂O₆ is interpreted as the consequence of mode crossing in the frequency region. A generalized Landau theory was used to analyze the order parameter of the C2/c–P2₁/c phase transition, and the results suggest that the transition is close to tricritical. Received: 21 January 2002 / Accepted: 22 July 2002     

Solid solution behaviour of CaSiO<Subscript>3</Subscript> and MgSiO<Subscript>3</Subscript> perovskites

Using density functional simulations within the generalized gradient approximation and projector-augmented wave method together with thermodynamic modelling, the reciprocal solubilities of MgSiO₃ and CaSiO₃ perovskites were calculated for pressures and temperatures of the Earth’s lower mantle from 25 to 100 GPa and 0 to 6,000 K, respectively. The solubility of Ca in MgSiO₃ at conditions along a mantle adiabat is found to be less than 0.02 atoms per formula unit. The solubility of Mg in CaSiO₃ is even lower, and most important, the extent of solid solution decreases with pressure. To dissolve CaSiO₃ perovskite completely in MgSiO₃ perovskite, a solubility of 7.8 or 2.3 mol% would be necessary for a fertile pyrolytic or depleted harzburgitic mantle, respectively. Thus, for any reasonable geotherm, two separate perovskites will be present in fertile mantle, suggesting that Ca-perovskite will be residual to low degree melting throughout the entire mantle. At the solidus, CaSiO₃ perovskite might completely dissolve in MgSiO₃ perovskite only in a depleted mantle with <1.25 wt% CaO. These implications may be modified if Ca solubility in MgSiO₃ is increased by other major mantle constituents such as Fe and Al.     

Thermodynamic properties of MgSiO3 ilmenite from vibrational spectra

Unpolarized infrared (IR) reflectance spectra for MgSiO₃ ilmenite taken from a single-crystal and from a densly packed polycrystalline sample possessed all eight peaks mandated by symmetry between 337 and 850 cm^?1. Polarizations were inferred from intensity differences between the two samples. IR peak positions differ by up to 250 cm^?1 from recent calculations, but on average are within 11%. Heat capacity C _p calculated from these data by using a Kieffer-type model are within the experimental uncertainty of calorimetric measurements from 170 to 700 K. Outside this range, calculated C _p is probably accurate within a few percent, based on recent results for garnets. Calculated entropy is only slightly less accurate, giving S ⁰ (298.15 K) as 54.1 ±0.5 J/ mol-K, which is 10% lower than recent estimates based on phase equilibria. The slope of the phase boundary between ilmenite and perovskite is used to predict S ⁰ (298.15 K) of perovskite as 58.7 ±1.4 J/mol-K, which is 10% lower than previous values.     

The transition of pyrope to perovskite

The stability field of Mg₃Al₂Si₃O₁₂-pyrope was examined for the first time under hydrostatic pressure conditions in a CO₂-laser heated diamond cell in the pressure range 21–30 GPa between 2300 and 3200 K. The phases were characterized using Raman and fluorescence spectroscopy. With increasing pressure pyrope transforms to an ilmenite phase above ∼21.5 GPa, to perovskite plus ilmenite above ∼24 GPa, and to perovskite above 29 GPa. The pressures of the first occurrence of perovskite in this study are about 2 GPa above the corresponding phase boundary between end-member MgSiO₃-ilmenite and perovskite. A small amount of Al₂O₃ coexists with perovskite up to 43 GPa, as evident from fluorescence spectra resembling those of ruby, but above 43 GPa the entire Al₂O₃ content of the pyrope starting material is accommodated in the perovskite structure. Received: 6 March 1997 / Revised, accepted: 23 July 1997     

Heat capacity and entropy of rutile (TiO<Subscript>2</Subscript>) and nepheline (NaAlSiO<Subscript>4</Subscript>)

 From heat capacities measured adiabatically at low temperatures, the standard entropies at 298.15 K of synthetic rutile (TiO₂) and nepheline (NaAlSiO₄) have been determined to be 50.0 ± 0.1 and 122.8 ± 0.3 J mol⁻¹ K, respectively. These values agree with previous measurements and in particular confirm the higher entropy of nepheline with respect to that of the less dense NaAlSiO₄ polymorph carnegieite. Received: 23 July 2001 / Accepted: 12 October 2001     

Heat capacity,entropy, and phase equilibria of dmitryivanovite

The heat capacity (C _p ) of dmitryivanovite synthesized with a cubic press was measured in the temperature range of 5–664 K using the heat capacity option of a physical properties measurement system and a differential scanning calorimeter. The entropy of dmitryivanovite at standard temperature and pressure (STP) was calculated to be 110.1 ± 1.6 J mol⁻¹ K⁻¹ from the measured C _p data. With the help of new phase equilibrium experiments done at 1.5 GPa, the phase transition boundary between krotite and dmitryivanovite was best represented by the equation: P (GPa) = −2.1825 + 0.0025 T (K). From the temperature intercept of this phase boundary and other available thermodynamic data for krotite and dmitryivanovite, the enthalpy of formation and Gibbs free energy of formation of dmitryivanovite at STP were calculated to be −2326.7 ± 2.1 and −2,208.1 ± 2.1 kJ mol⁻¹, respectively. It is also inferred that dmitryivanovite is the stable CaAl₂O₄ phase at STP and has a wide stability field at high pressures whereas the stability field of krotite is located at high temperatures and relatively low pressures. This conclusion is consistent with natural occurrences (in Ca–Al-rich inclusions) of dmitryivanovite and krotite, where the former is interpreted as the shock metamorphic product of originally present krotite.     

High-pressure phase transitions of CaRhO<Subscript>3</Subscript> perovskite

High-pressure phase transitions of CaRhO₃ perovskite were examined at pressures of 6–27 GPa and temperatures of 1,000–1,930°C, using a multi-anvil apparatus. The results indicate that CaRhO₃ perovskite successively transforms to two new high-pressure phases with increasing pressure. Rietveld analysis of powder X-ray diffraction data indicated that, in the two new phases, the phase stable at higher pressure possesses the CaIrO₃-type post-perovskite structure (space group Cmcm) with lattice parameters: a = 3.1013(1) Å, b = 9.8555(2) Å, c = 7.2643(1) Å, V _m  = 33.43(1) cm³/mol. The Rietveld analysis also indicated that CaRhO₃ perovskite has the GdFeO₃-type structure (space group Pnma) with lattice parameters: a = 5.5631(1) Å, b = 7.6308(1) Å, c = 5.3267(1) Å, V _m  = 34.04(1) cm³/mol. The third phase stable in the intermediate P, T conditions between perovskite and post-perovskite has monoclinic symmetry with the cell parameters: a = 12.490(3) Å, b = 3.1233(3) Å, c = 8.8630(7) Å, β = 103.96(1)°, V _m  = 33.66(1) cm³/mol (Z = 6). Molar volume changes from perovskite to the intermediate phase and from the intermediate phase to post-perovskite are –1.1 and –0.7%, respectively. The equilibrium phase relations determined indicate that the boundary slopes are large positive values: 29 ± 2 MPa/K for the perovskite—intermediate phase transition and 62 ± 6 MPa/K for the intermediate phase—post-perovskite transition. The structural features of the CaRhO₃ intermediate phase suggest that the phase has edge-sharing RhO₆ octahedra and may have an intermediate structure between perovskite and post-perovskite.