Juichiro Hama

First-principles calculation of the elastic stiffness tensor of aluminium nitride under high pressure

The first-principles method for calculating the elastic stiffness tensor of composite crystals has been given. Applying the present method to the wurtzite and rocksalt structures of AlN under normal and elevated pressure up to 25.8 GPa, we have determined the elastic stiffness tensor completely from first principles. The theoretical values for the wurtzite structure at normal pressure are in good agreement with the experimental ones given by Tsubouchi and Mikoshiba. The elastic stiffness constants have been evaluated from the total energies of the deformed static lattices. These energies have been calculated by using a calculation method based on the variational principle.

Thermoelastic properties of periclase and magnesiowüstite under high pressure and high temperature

Abstract A simple thermodynamic model for calculating the high-pressure and high-temperature properties of MgO consistently is presented. The model explains experimental equation of state (EOS) to ∼220 GPa at room temperature and shock-wave EOS to ∼200 GPa very well. The calculated Hugoniot temperature amounts to 3400 K at 200 GPa. The input parameters are the volume of the unit cell, V0, bulk modulus, K0, its pressure derivative, K0′, Debye temperature, Θ0, and a parameter relating to the shear modulus, f44, all in the static lattice at zero pressure which are estimated from experimental data at room temperature and zero pressure. The calculated thermal expansivity, α, and Anderson–Gruneisen parameters, δT and δS, at zero pressure are in agreement with experimental data to 1000–1250 K and those to 1800 K, respectively. Our model explains also experimental velocities vp and vs of compressional and shear waves to 1800 K at zero pressure very well. The pressure-dependence of α, vp and vs at room temperature agree reasonably with experimental data to 36 GPa at room temperature. Applying our model to magnesiowustite, we have calculated the thermal EOS and shock-wave EOS in agreement with experimental data. The implication of our result together with our previous one of magnesium-silicate perovskite for the composition of the lower mantle is briefly discussed.

Anomalously high metallization pressure of solid neon

Abstract The equation of state of solid fcc neon at T = 0 K is calculated by the local density functional theory in the muffin-tin approximation. The calculated equation of state is in good agreement with Hawke et al.s experimental value at about 6 Mbar by magnetic flux compression and also agrees remarkably well with that by the quantum statistical model in the region of extremely high pressures. If no structural phase transition occurs up to metallization, solid neon becomes metallic at a molar volume of 0.256 cm 3 /mole or at a pressure of 1.58 × 10 3 Mbar. This is the highest metallization pressure ever reported.

HIGH-TEMPERATURE EQUATION OF STATE OF CASIO3 PEROVSKITE AND ITS IMPLICATIONS FOR THE LOWER MANTLE

Abstract A method for calculating thermal equation of state (EOS) of solids is presented and is applied to CaSiO3 perovskite. The input parameters are the volume, V0, the bulk modulus, K0, its pressure derivative, K′0, and the Debye temperature, Θ0, all in the static lattice at zero pressure. These were determined from experimental data at room temperature. The present values of V0, K0 and K′0 agree well with recent theoretical values by Wentzcovitch et al. The present EOS is in good agreement with the high-temperature data to 1600 K and to 13 GPa by Wang et al. as well as the room-temperature data to 134 GPa by Mao et al., those to 112 GPa by Yagi et al. and those to 90 GPa by Tarrida and Richet. The calculated density and thermal expansivity of CaSiO3 perovskite under lower mantle conditions are in agreement, respectively, with PREM (Preliminary Reference Earth Model) within −1.2 −1.2% and with thermal expansivity of the lower mantle estimated by O.L. Anderson within 6.8 to −3.1% over the depth from 670 km to 2891 km. A method of calculating Lame constants, λS and μS, for an isotropic medium is also presented and is applied to CaSiO3 perovskite under lower mantle conditions. The calculated sound velocities, νp and νs, agree with PREM within 1.3–2.7% and −1.2 to −4.5%, respectively. The present results suggest that CaSiO3 perovskite behaves as an invisible component in the lower mantle.

Equation of state of MgSiO3 perovskite and its thermoelastic properties under lower mantle conditions

A simple four-parameter model for calculating thermoelastic properties of MgSiO3 perovskite is presented based on the Vinet model for static lattice and the Debye approximation for lattice vibration. The input parameters are the volume of the unit cell, V0, the bulk modulus, K0, its pressure derivative, K0′, and the Debye temperature, Θ0, in the static lattice at zero pressure. For V0, K0 and K0′ the theoretical values by Stixrude and Cohen [1993] are used and Θ0 is determined to reproduce the experimental value at ambient conditions, 980 K, by Akaogi and Ito [1993]. The resulting isobars are in good agreement with experimental data to 1300 K and 11 GPa by Wang et al. [1994], with those to 1200 K at 20 GPa by Utsumi et al. [1995], and with those to 1500 K and to 2000 K, respectively, by Kato et al. [1995] and Funawori et al. [1996] both at 25 GPa. Using the present equation of state together with the method for calculating adiabatic Lame constants λS and μS for isotropic medium given in the present paper, density ρ, and sound velocities νp and νs of MgSiO3 perovskite under lower mantle conditions have been calculated where the constant-entropy model is assumed with the temperature at the core-mantle boundary being taken to be 3000 K. The results for ρ, νp, and νs are in agreement with the preliminary reference Earth model (PREM) within −2.4%∼ −3.7%, +3.3%∼+1.1%, and +0.8%∼−6.8%, respectively, over the lower mantle from 670 to 2891 km in depth. The calculated thermal expansivity under lower mantle conditions is in good agreement with that of the lower mantle estimated by Anderson [1982]. Using the present model with the parameters determined from experimental data at room temperature by Knittle and Jeanloz [1987], assuming Θ0 to be the same as that of MgSiO3 perovskite, thermoelastic properties of (Mg0.9, Fe0.1)SiO3 perovskite under lower mantle conditions have been calculated. The density becomes in much better agreement (+0.4%∼−0.8 %) with PREM and νp and νs remain almost unchanged from those of MgSiO3 perovskite.

Pressure induced insulator-metal transition of solid LiH

Abstract The equation of state and the electronic band structure of solid LiH have been calculated using the local-density functional theory with Ceperley and Alders exchange-correlation potential in the muffin-tin approximation. The band gap is the direct gap with the X1 minus; X′4 symmetries up to the band closing at VM=3.35 cm3 mole−1. At further compression, the band crossing occurs between the state with the Z1 symmetry and that of the Z3 symmetry. The transition pressure of metallization is estimated to be PM=226 GPa. Using the Debye model, the zero-point pressure is also calculated with the Debye temperature theoretically determined. The Debye temperature of 7LiH at normal density is 1115 K in agreement with the experimental value 1190 ± 80 K.

Structural change of compressed Xe as a phase transition preceding metallization

Abstract A structural transition from f.c.c. to b.c.c. is suggested to occur for solid Xe at high pressure. This phase transition is shown to precede the metallization, and accordingly brings about a metallization pressure 0.82 Mbar which is closer to the experimental value 0.33 Mbar than the previous estimate 1.30 Mbar with f.c.c. as the assumed structure. The first-order effect of the spin-orbit coupling is also studied with an improved transition pressure 0.66 Mbar. These studies have been done consistently by means of the APW method combined with the local-density scheme.

Correctly weighted tetrahedron method for k-space integration

The analytical integration of a linearly interpolated function commonly used in the tetrahedron integration (TI) method is not correct and the calculated quantities do not satisfy crystal symmetry. The authors propose an improved method wherein the integration is restricted to a minimal volume which covers the irreducible part of the Brillouin zone with microcubes in contrast to those by Kleinman (1983) and Hanke and co-workers (1984). They also extend this to a hexagonal crystal. The k-points in the correctly weighted TI method are shown to have the characteristics of special points and give accurate values for an insulator. The efficiency of the present method is discussed in comparison with the conventional TI method.

Equation of state and metallization of ice under very high pressure

The equation of state and the electronic bandstructure of ice have been calculated in the recently proposed high-pressure phase XI (anti-fluorite structure) by using the local-density approximation with the augmented-plane-wave method. The calculated pressure of metallization 1.76 TPa is in agreement with the value of 1.0-1.5 TPa conjectured by Besson (1986), but it is 2.5 times higher than that estimated by the classical Herzfeld theory (1927) and Thomas-Fermi-Dirac model. It has been also shown that the ionic model proposed for the ice XI phase is not adequate even for ultra-high pressure from the viewpoint of the bandstructure calculation.

Equation of state and electronic structure of solid CaO under high pressure

Abstract The equations of state (EOSs) and the electronic structures of solid CaO both in the B1 and in the B2 structure have been calculated by using the local-density functional theory with the APW method in the muffin-tin approximation. The EOS of the B1 phase is in excellent agreement with the diamond-anvil-cell experiments. The metallization at T = 0 K is shown to occur in the B2 phase at a pressure of 480 GPa. By using the Debye temperature and the Gruneisen constant, both of which are theoretically determined, the hugoniot has also been calculated. The agreement with experiment is good for the B1 phase and is moderate for the B2 phase.