High-<Emphasis Type="Italic">P</Emphasis>, <Emphasis Type="Italic">T</Emphasis> phase relations in the NaAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript> system from first principles computation

Vibrational density of states of the NaAlSi₂O₆ jadeite and NaAlSiO₄ calcium ferrite (CF)-type, and SiO₂ stishovite is calculated as a function of pressure up to 50 GPa using density functional perturbation theory. The calculated frequencies are used to determine the thermal contribution to the Helmholtz free energy within the quasi-harmonic approximation and to derive the equation of state and several thermodynamic properties of interest. A dissociation of jadeite into a mixture of a CF-type phase and stishovite is predicted to occur at 23.4 GPa and 1,800 K with a positive Clapeyron slope of 2.8 MPa/K. Elastic anisotropy for jadeite, the CF-type phase, and stishovite also computed clearly shows that stishovite and the CF-type phase are the most anisotropic and isotropic in these three phases, respectively.     

Subsolidus and melting phase relations of basaltic composition in the uppermostlower mantle

The phase relations and the element partitioning in a mid-oceanic ridge basalt composition were determined for both above-solidus and subsolidus conditions at 22 to 27.5 GPa by means of a multianvil apparatus. The mineral assemblage at the solidus changes remarkably with pressure; majorite and stishovite at 22 GPa, joined by Ca-perovskite at 23 GPa, further joined by CaAl₄Si₂O₁₁-rich CAS phase at 25.5 GPa, and Mg-perovskite, stishovite, Ca-perovskite, CF phase (approximately on the join NaAlSiO₄-MgAl₂O₄), and NAL phase ([Na,K,Ca]₁[Mg,Fe²⁺]₂[Al,Fe³⁺,Si]_5.5-6.0O₁₂) above 27 GPa. The liquidus phase is Ca-perovskite, and stishovite, a CAS phase, a NAL phase, Mg-perovskite, and a CF phase appear with decreasing temperature at 27.5 GPa. Partial melt at 27 to 27.5 GPa is significantly depleted in SiO₂ and CaO and enriched in FeO and MgO compared with those formed at lower pressures, reflecting the narrow stability of (Fe,Mg)-rich phases (majorite or Mg-perovskite) above solidus temperature. The basaltic composition has a lower melting temperature than the peridotitic composition at high pressures except at 13 to 18 GPa (Yasuda et al., 1994) and therefore can preferentially melt in the Earth’s interior. Recycled basaltic crusts were possibly included in hot Archean plumes, and they might have melted in the uppermost lower mantle. In this case, Ca-perovskite plays a dominant role in the trace element partitioning between melt and solid. This contrasts remarkably with the case of partial melting of a peridotitic composition in which magnesiowüstite is the liquidus phase at this depth.     

First-principles simulation of high-pressure polymorphs in MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript>

We have used density functional theory to investigate the stability of MgAl₂O₄ polymorphs under pressure. Our results can reasonably explain the transition sequence of MgAl₂O₄ polymorphs observed in previous experiments. The spinel phase (stable at ambient conditions) dissociates into periclase and corundum at 14 GPa. With increasing pressure, a phase change from the two oxides to a calcium-ferrite phase occurs, and finally transforms to a calcium-titanate phase at 68 GPa. The calcium-titanate phase is stable up to at least 150 GPa, and we did not observe a stability field for a hexagonal phase or periclase + Rh₂O₃(II)-type Al₂O₃. The bulk moduli of the phases calculated in this study are in good agreement with those measured in high-pressure experiments. Our results differ from those of a previous study using similar methods. We attribute this inconsistency to an incomplete optimization of a cell shape and ionic positions at high pressures in the previous calculations.     

Compression of Na0.4Mg0.6Al1.6Si0.4O4 NAL and Ca-ferrite-type phases

Compression behaviors of two Al-rich phases in the lower mantle, hexagonal new aluminum-rich (NAL) phase and its high-pressure polymorph Ca-ferrite-type (CF) phase, were examined for identical Na_0.4Mg_0.6Al_1.6Si_0.4O₄ (40?% NaAlSiO₄–60?% MgAl₂O₄) composition. The volumes of the NAL and CF phases were obtained at room temperature up to 31 and 134?GPa, respectively, by a combination of laser-annealed diamond-anvil cell techniques and synchrotron X-ray diffraction measurements. Fitting of the third-order Birch–Murnaghan equation of state to such pressure–volume data yields bulk modulus K ₀?=?199(6) GPa at 1?bar and its pressure derivative K ₀′?=?5.0(6) for the NAL phase and K ₀?=?169(5) GPa and K ₀′?=?6.3(3) for the CF phase. These results indicate that the bulk modulus increases from 397 to 407 GPa across the phase transition from the NAL to CF phase at 43 GPa, where the NAL phase completely transforms into the CF phase on Na_0.4Mg_0.6Al_1.6Si_0.4O₄. Density also increases by 2.1?% across the phase transition.     

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.     

Pressure and temperature dependence of the viscosity of a NaAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript> melt

The viscosity of a silicate melt of composition NaAlSi₂O₆ was measured at pressures from 1.6 to 5.5 GPa and at temperatures from 1,350 to 1,880°C. We employed in situ falling sphere viscometry using X-ray radiography. We found that the viscosity of the NaAlSi₂O₆ melt decreased with increasing pressure up to 2 GPa. The pressure dependence of viscosity is diminished above 2 GPa. By using the relationship between the logarithm of viscosity and the reciprocal temperature, the activation energies for viscous flow were calculated to be 3.7 ± 0.4 × 10² and 3.7 ± 0.5 × 10² kJ/mol at 2.2 and 2.9 GPa, respectively.     

Hydrostatic compression of galenobismutite (PbBi<Subscript>2</Subscript>S<Subscript>4</Subscript>): elastic properties and high-pressure crystal chemistry

A single-crystal sample of galenobismutite was subjected to hydrostatic pressures in the range of 0.0001 and 9 GPa at room temperature using the diamond-anvil cell technique. A series of X-ray diffraction intensities were collected at ten distinct pressures using a CCD equipped 4-circle diffractometer. The crystal structure was refined to R1(|F₀| > 4σ) values of approximately 0.05 at all pressures. By fitting a third-order Birch-Murnaghan equation of state to the unit-cell volumes V ₀ = 700.6(2) ų, K ₀ = 43.9(7) GPa and dK/dP = 6.9(3) could be determined for the lattice compression. Both types of cations in galenobismutite have stereochemically active lone electron pairs, which distort the cation polyhedra at room pressure. The cation eccentricities decrease at higher pressure but are still pronounced at 9 GPa. Galenobismutite is isotypic with CaFe₂O₄ (CF) but moves away from the idealised CF-type structure during compression. Instead of the two octahedral cation sites and one bi-capped trigonal-prismatic site, PbBi₂S₄ attains a new high-pressure structure characterised by one octahedral site and two mono-capped trigonal-prismatic sites. Analyses of the crystal structure at high pressure confirm the preference of Bi for the octahedral site and the smaller one of the two trigonal-prismatic sites.     

Elasticity and equation of state of Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript>

A single crystal X-ray diffraction study on lithium tetraborate Li₂B₄O₇ (diomignite, space group I4₁ cd) has been performed under pressure up to 8.3 GPa. No phase transitions were found in the pressure range investigated, and hence the pressure evolution of the unit-cell volume of the I4₁ cd structure has been described using a third-order Birch–Murnaghan equation of state (BM-EoS) with the following parameters: V ₀  = 923.21(6) ų, K ₀  = 45.6(6) GPa, and K′ = 7.3(3). A linearized BM-EoS was fitted to the axial compressibilities resulting in the following parameters a ₀  = 9.4747(3) Å, K _0a  = 73.3(9) GPa, K′ _a  = 5.1(3) and c ₀  = 10.2838(4) Å, K _0c  = 24.6(3) GPa, K′ _c  = 7.5(2) for the a and c axes, respectively. The elastic anisotropy of Li₂B₄O₇ is very large with the zero-pressure compressibility ratio β _0c /β _0a  = 3.0(1). The large elastic anisotropy is consistent with the crystal structure: A three-dimensional arrangement of relatively rigid tetraborate groups [B₄O₇]²⁻ forms channels occupied by lithium along the polar c–axis, and hence compression along the c axis requires the shrinkage of the lithium channels, whereas compression in the a direction depends mainly on the contraction of the most rigid [B₄O₇]²⁻ units. Finally, the isothermal bulk modulus obtained in this work is in general agreement with that derived from ultrasonic (Adachi et al. in Proceedings-IEEE Ultrasonic Symposium, 228–232, 1985; Shorrocks et al. in Proceedings-IEEE Ultrasonic Symposium, 337–340, 1981) and Brillouin scattering measurements (Takagi et al. in Ferroelectrics, 137:337–342, 1992).     

Sound velocities of Na0.4Mg0.6Al1.6Si0.4O4 NAL and CF phases to 73 GPa determined by Brillouin scattering method

The sound velocities of two aluminum-rich phases in the lower mantle, hexagonal new Al-rich phase (NAL) and its corresponding high-pressure polymorph orthorhombic Ca-ferrite-type phase (CF), were determined with the Brillouin scattering method in a pressure range from 9 to 73 GPa at room temperature. Both NAL and CF samples have identical chemical composition of Na_0.4Mg_0.6Al_1.6Si_0.4O₄ (40 % NaAlSiO₄–60 % MgAl₂O₄). Infrared laser annealing in the diamond anvil cell was performed to minimize the stress state of the sample and obtain the high-quality Brillouin spectra. The results show shear modulus at zero pressure G ₀ = 121.960 ± 0.087 GPa and its pressure derivative G’ = 1.961 ± 0.009 for the NAL phase, and G ₀ = 129.653 ± 0.059 GPa and G’ = 2.340 ± 0.004 for the CF phase. The zero-pressure shear velocities of the NAL and CF phases are obtained to be 5.601 ± 0.005 km/sec and 5.741 ± 0.001 km/sec, respectively. We also found that shear velocity increases by 2.5 % upon phase transition from NAL to CF at around 40 GPa.     

In situ X-ray observations of phase transitions in MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> spinel to 40 GPa using multianvil apparatus with sintered diamond anvils

 Phase transitions in MgAl₂O₄ spinel have been studied at pressures 22–38 GPa, and at temperatures up to 1600 °C, using a combination of synchrotron radiation and a multianvil apparatus with sintered diamond anvils. Spinel dissociated into a mixture of MgO plus Al₂O₃ at pressures to 25 GPa, while it transformed to the CaFe₂O₄ (calcium ferrite) structure at higher pressures via the metastably formed oxide mixture upon increasing temperature. Neither the e-phase nor the CaTi₂O₄-type MgAl₂O₄, which were reported in earlier studies using the diamond-anvil cell, were observed in the present pressure and temperature range. The zero-pressure bulk modulus of the calcium-ferrite-type MgAl₂O₄ was calculated as K=213 (3) GPa, which is significantly lower than that reported by Yutani et al. (1997), but is consistent with a more recent result by Funamori et al. (1998) and that estimated by an ab initio calculation by Catti (2001). Received: 2 April 2002 / Accepted: 29 July 2002 Acknowledgements The authors thank Y. Higo, Y. Sueda, T.␣Ueda, Y. Tanimoto, A. Fukuyama, K. Ochi, F. Kurio and T. Kawahara for help in the in situ X-ray observations at SPring-8 (No: 2000A0061-CD-np and 2000B0093-ND-np). We also thank W.␣Utsumi, J. Ando and O. Shimomura for advice and encouragement during this study, and N. Funamori and an anonymous reviwer for comments on the article. The present study is partly supported by the grant-in-aid for Scientific Research (A) of the Ministry of Education, Science, Sport and Culture of the Japanese government (no: 11694088).     

High-pressure phase behavior of MnTiO<Subscript>3</Subscript>: decomposition of perovskite into MnO and MnTi<Subscript>2</Subscript>O<Subscript>5</Subscript>

The phase relations and compression behavior of MnTiO₃ perovskite were examined using a laser-heated diamond-anvil cell, X-ray diffraction, and analytical transmission electron microscopy. The results show that MnTiO₃ perovskite becomes unstable and decomposes into MnO and orthorhombic MnTi₂O₅ phases at above 38 GPa and high temperature. This is the first example of ABO₃ perovskite decomposing into AO + AB₂O₅ phases at high pressure. The compression behavior of volume, axes, and the tilting angle of TiO₆ octahedron of MnTiO₃ perovskite are consistent with those of other A²⁺B⁴⁺O₃ perovskites, although no such decomposition was observed in other perovskites. FeTiO₃ is also known to decompose into two phases, instead of transforming into the CaIrO₃-type post-perovskite phase and we argue that one of the reasons for the peculiar behavior of titanate is the weak covalency of the Ti–O chemical bonds.     

Electrical conductivity of dry and hydrous NaAlSi<Subscript>3</Subscript>O<Subscript>8</Subscript> glasses and liquids at high pressures

We report the first study of electrical conductivities of silicate melts at very high pressures (up to 10 GPa) and temperatures (up to 2,173 K). Impedance spectroscopy was applied to dry and hydrous albite (NaAlSi₃O₈) glasses and liquids (with 0.02–5.7 wt% H₂O) at 473–1,773 K and 0.9–1.8 GPa in a piston-cylinder apparatus, using a coaxial cylindrical setup. Measurements were also taken at 473–2,173 K and 6–10 GPa in two multianvil presses, using simple plate geometry. The electrical conductivity of albite melts is found to increase with temperature and water content but to decrease with pressure. However, at 6 GPa, conductivity increases rapidly with temperature above 1,773 K, so that at temperatures beyond 2,200 K, conductivity may actually increase with pressure. Moreover, the effect of water in enhancing conductivity appears to be more pronounced at 6 GPa than at 1.8 GPa. These observations suggest that smaller fractions of partial melt than previously assumed may be sufficient to explain anomalously high conductivities, such as in the asthenosphere. For dry melt at 1.8 GPa, the activation energy at T > 1,073 K is higher than that at T < 1,073 K, and the inflection point coincides with the rheological glass transition. Upon heating at 6–10 GPa, dry albite glass often shows a conductivity depression starting from ~1,173 K (due to crystallization), followed by rapid conductivity enhancement when temperature approaches the albite liquidus. For hydrous melts at 0.9–1.8 GPa, the activation energies for conductivity at ≥1,373 K are lower than those at <973 K, with a complex transition pattern in between. Electrical conductivity and previously reported Na diffusivity in albite melt are consistent with the Nernst–Einstein relation, suggesting the dominance of Na transport for electrical conduction in albite melts.     

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.     

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     

Pressure induced phase transition in Pb<Subscript>6</Subscript>Bi<Subscript>2</Subscript>S<Subscript>9</Subscript>

The crystal structure of Pb₆Bi₂S₉ is investigated at pressures between 0 and 5.6 GPa with X-ray diffraction on single-crystals. The pressure is applied using diamond anvil cells. Heyrovskyite (Bbmm, a = 13.719(4) Å, b = 31.393(9) Å, c = 4.1319(10) Å, Z = 4) is the stable phase of Pb₆Bi₂S₉ at ambient conditions and is built from distorted moduli of PbS-archetype structure with a low stereochemical activity of the Pb²⁺ and Bi³⁺ lone electron pairs. Heyrovskyite is stable until at least 3.9 GPa and a first-order phase transition occurs between 3.9 and 4.8 GPa. A single-crystal is retained after the reversible phase transition despite an anisotropic contraction of the unit cell and a volume decrease of 4.2%. The crystal structure of the high pressure phase, β-Pb₆Bi₂S₉, is solved in Pna2 ₁ (a = 25.302(7) Å, b = 30.819(9) Å, c = 4.0640(13) Å, Z = 8) from synchrotron data at 5.06 GPa. This structure consists of two types of moduli with SnS/TlI-archetype structure in which the Pb and Bi lone pairs are strongly expressed. The mechanism of the phase transition is described in detail and the results are compared to the closely related phase transition in Pb₃Bi₂S₆ (lillianite).     

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.     

Vibrational and thermodynamic properties of Ni<Subscript>3</Subscript>S<Subscript>2</Subscript> polymorphs from first-principles calculations

We have calculated the compressional, vibrational, and thermodynamic properties of Ni₃S₂ heazlewoodite and the high-pressure orthorhombic phase (with Cmcm symmetry) using the generalized gradient approximation to the density functional theory in conjunction with the quasi-harmonic approximation. The predicted Raman frequencies of heazlewoodite are in good agreement with room-temperature measurements. The calculated thermodynamic properties of heazlewoodite at room conditions agree very well with experiments, but at high temperatures (especially above 500 K) the heat capacity data from experiments are significantly larger than the quasi-harmonic results, indicating that heazlewoodite is anharmonic. On the other hand, the obtained vibrational density of states of the orthorhombic phase at 20 GPa reveals a group of low-frequency vibrational modes which are absent in heazlewoodite. These low-frequency modes contribute substantially to thermal expansivity, heat capacity, entropy, and Grüneisen parameter of the orthorhombic phase. The calculated phase boundary between heazlewoodite and the orthorhombic phase is consistent with high-pressure experiments; the predicted transition pressure is 17.9 GPa at 300 K with a negative Clapeyron slope of −8.5 MPa/K.     

Raman spectra of bixbyite,Mn<Subscript>2</Subscript>O<Subscript>3</Subscript>, up to 40 GPa

The Raman spectra of bixbyite, Mn₂O₃, were measured up to 40 GPa at room temperature. Mn₂O₃ undergoes a phase transition from the C-type rare earth structure to the CaIrO₃-type (post-perovskite) structure at 16–25 GPa. The transition pressure measured in Raman spectroscopy is significantly lower than the pressure reported previously by an X-ray diffraction study. This could be due to the greater polarizability in the CaIrO₃-type structure, consistent with high-pressure observation on the CaIrO₃ type in MgGeO₃, although it is still possible that experimental differences may cause the discrepancy. Unlike the change at the perovskite to CaIrO₃-type transition, the spectroscopic Grüneisen parameter does not decrease at the C-type to CaIrO₃-type transition. The spectroscopic Grüneisen parameter of the low-pressure phase (C type) is significantly lower than thermodynamic Grüneisen parameter, suggesting significant magnetic contributions to the thermodynamic property of this material. Our Raman measurements on CaIrO₃-type Mn₂O₃ contribute to building systematic knowledge about this structure, which has emerged as one of the common structures found in geophysically important materials.     

High-pressure stability, structure and compressibility of Cmcm -MgAl2O4: an ab initio study

 Quantum-mechanical solid-state calculations have been performed on the highest-pressure polymorph of magnesium aluminate (CaTi₂O₄-type structure, Cmcm space group), as well as on the low-pressure (Fd3ˉm) spinel phase and on MgO and Al₂O₃. An ab initio all-electron periodic scheme with localized basis functions (Gaussian-type atomic orbitals) has been used, employing density-functional-theory Hamiltonians based on LDA and B3LYP functionals. Least-enthalpy structure optimizations in the pressure range 0 to 60 GPa have allowed us to predict: (1) the full crystal structure, the pV equation of state and the compressibility of Cmcm-MgAl₂O₄ as a function of pressure; (2) the phase diagram of the MgO–Al₂O₃–MgAl₂O₄ system (with exclusion of CaFe₂O₄-type Pmcn-MgAl₂O₄), and the equilibrium pressures for the reactions of formation/decomposition of the Fd3ˉm and Cmcm polymorphs of MgAl₂O₄ from the MgO + Al₂O₃ assemblage. Cmcm-MgAl₂O₄ is predicted to form at 39 and 57 GPa by LDA and B3LYP calculations, with K ₀=248 (K′=3.3) and 222 GPa (K′=3.8), respectively. Results are compared to experimental data, where available, and the performance of different DFT functionals is discussed. Received: 31 January 2001 / Accepted: 16 May 2001     

Equation of state of synthetic qandilite Mg<Subscript>2</Subscript>TiO<Subscript>4</Subscript> at ambient temperature

Using a diamond-anvil cell and synchrotron X-ray diffraction, the compressional behavior of a synthetic qandilite Mg_2.00(1)Ti_1.00(1)O₄ has been investigated up to about 14.9 GPa at 300 K. The pressure–volume data fitted to the third-order Birch–Murnaghan equation of state yield an isothermal bulk modulus (K _T0) of 175(5) GPa, with its first derivative \(K_{T0}^{{\prime }}\) attaining 3.5(7). If \(K_{T0}^{{\prime }}\) is fixed as 4, the K _T0 value is 172(1) GPa. This value is substantially larger than the value of the adiabatic bulk modulus (K _S0) previously determined by an ultrasonic pulse echo method (152(7) GPa; Liebermann et al. in Geophys J Int 50:553–586, 1977), but in general agreement with the K _T0 empirically estimated on the basis of crystal chemical systematics (169 GPa; Hazen and Yang in Am Miner 84:1956–1960, 1999). Compared to the K _T0 values of the ulvöspinel (Fe₂TiO₄; ~148(4) GPa with \(K_{T0}^{{\prime }} = 4\)) and the ringwoodite solid solutions along the Mg₂SiO₄–Fe₂SiO₄ join, our finding suggests that the substitution of Mg²⁺ for Fe²⁺ on the T sites of the 4–2 spinels can have more significant effect on the K _T0 than that on the M sites.