High-temperature ab initio calculations on FeSi and NiSi at conditions relevant to small planetary cores.

The Fe-Ni-Si system is potentially a very important component of terrestrial planetary cores. However, at present, even the behaviour of the FeSi and NiSi end members is poorly understood, especially at low to moderate pressures-the data for FeSi are contradictory and NiSi has been little studied. For FeSi, there is general agreement that there is a phase transition from the ε-FeSi to the CsCl structure with increasing pressure, but, in experiments, there is disagreement as to the position and slope of the phase boundary and the range of coexistence of the two phases. In this paper we have used ab initio lattice dynamics calculations to determine the phase boundary between the ε-FeSi and CsCl structures as a function of pressure and temperature in both FeSi and NiSi. For FeSi, we find that the transition pressure at zero Kelvin is ~11 GPa and that the boundary between the ε-FeSi and CsCl phases varies little with temperature, having a slight negative Clapeyron slope, going from ~11 GPa at 300 K to ~3 GPa at 2000 K. For NiSi, there is much greater variation of the transition pressure with temperature, with a much shallower negative Clapeyron slope, going from ~156 GPa at 300 K to ~94 GPa at 2000 K.

Neutron powder diffraction studies of sulfuric acid hydrates. II. The structure, thermal expansion, incompressibility, and polymorphism of sulfuric acid tetrahydrate (D2SO4.4D2O).

We report results of the first neutron powder diffraction study of sulfuric acid tetrahydrate (SAT); D(2)SO(4)4D(2)O is tetragonal, space group P42(1)c, with two formula units per unit cell. At 1.7 K the unit-cell dimensions are a=b=7.475 12(6) A, c=6.324 66(5) A and V=353.405(5) A(3). At 225 K the unit-cell dimensions are a=b=7.4833(1) A, c=6.4103(1) A, and V=358.98(1) A(3). The deuteron positions refined from the neutron data are in excellent agreement with the single crystal x-ray analysis of Kjallman and Olovsson [Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. B28, 1692 (1972)]; the structure consists of SO(4) (2-) and D(5)O(2) (+) ions hydrogen bonded to form a three dimensional network. Although no structural change is observed between 2 K and the melting point at approximately 232 K, the thermal expansion and incompressibility of the crystal are highly anisotropic. The bulk modulus of SAT at 200 K is 9.2(2) GPa, ( partial differentialK partial differentialP)(T)=7.9(8), and -( partial differentialK partial differentialT)(P)=10.6(5) MPa K(-1), values which are very similar to D(2)O ice Ih. A new polymorph of SAT has been discovered above 235 K at 5.5 kbars. The structure of this phase could not be determined, but we have indexed the diffraction pattern with a monoclinic unit cell of likely space-group P2(1)a (Z=2). SAT-II has a lower density than SAT-I under the same PT conditions; the refined unit-cell parameters at 235 K, 5.435 kbars are a=6.1902(3) A, b=11.1234(5) A, c=5.6446(3) A, beta=110.287(4) degrees , and V=364.56(2) A(3). This phase has been quenched to low pressures and temperatures, and we have obtained estimates of the thermal expansivity and incompressibility which reveal SAT-II to be significantly stiffer and more isotropic than SAT-I.

Ab initio melting curve of copper by the phase coexistence approach.

Ab initio calculations of the melting properties of copper in the pressure range 0-100 GPa are reported. The ab initio total energies and ionic forces of systems representing solid and liquid copper are calculated using the projector augmented wave implementation of density functional theory with the generalized gradient approximation for exchange-correlation energy. An initial approximation to the melting curve is obtained using an empirical reference system based on the embedded-atom model, points on the curve being determined by simulations in which solid and liquid coexist. The approximate melting curve so obtained is corrected using calculated free energy differences between the reference and ab initio system. It is shown that for system-size errors to be rendered negligible in this scheme, careful tuning of the reference system to reproduce ab initio energies is essential. The final melting curve is in satisfactory agreement with extrapolated experimental data available up to 20 GPa, and supports the validity of previous calculations of the melting curve up to 100 GPa.

The ab initio simulation of the Earth's core.

The Earth has a liquid outer and solid inner core. It is predominantly composed of Fe, alloyed with small amounts of light elements, such as S, O and Si. The detailed chemical and thermal structure of the core is poorly constrained, and it is difficult to perform experiments to establish the properties of core-forming phases at the pressures (ca. 300 GPa) and temperatures (ca. 5000-6000 K) to be found in the core. Here we present some major advances that have been made in using quantum mechanical methods to simulate the high-P/T properties of Fe alloys, which have been made possible by recent developments in high-performance computing. Specifically, we outline how we have calculated the Gibbs free energies of the crystalline and liquid forms of Fe alloys, and so conclude that the inner core of the Earth is composed of hexagonal close packed Fe containing ca. 8.5% S (or Si) and 0.2% O in equilibrium at 5600 K at the boundary between the inner and outer cores with a liquid Fe containing ca. 10% S (or Si) and 8% O.

Phonon density of states of iron up to 153 gigapascals.

We report phonon densities of states (DOS) of iron measured by nuclear resonant inelastic x-ray scattering to 153 gigapascals and calculated from ab initio theory. Qualitatively, they are in agreement, but the theory predicts density at higher energies. From the DOS, we derive elastic and thermodynamic parameters of iron, including shear modulus, compressional and shear velocities, heat capacity, entropy, kinetic energy, zero-point energy, and Debye temperature. In comparison to the compressional and shear velocities from the preliminary reference Earth model (PREM) seismic model, our results suggest that Earth's inner core has a mean atomic number equal to or higher than pure iron, which is consistent with an iron-nickel alloy.

Structures and physical properties of epsilon-FeSi-type and CsCl-type RuSi studied by first-principles pseudopotential calculations

An investigation of the relative stability of the two known polymorphs of RuSi, having the epsilon-FeSi and CsCl structures, has been made by first-principles pseudopotential calculations. The resulting cell volumes and fractional coordinates at P = 0 are in good agreement with experiment. Application of high pressure to the epsilon-FeSi phase of RuSi is predicted to produce a structure having almost perfect sevenfold coordination. However, it appears that RuSi having the CsCl-type structure will be the thermodynamically most stable phase for pressures greater than 3.6 GPa. Fitting of the calculated internal energy versus volume to a fourth-order logarithmic equation of state led to values (at T = 0 K) for the bulk modulus, K0, of 202 and 244 GPa for the epsilon-FeSi and CsCl phases, respectively, in excellent agreement with experiment. Band-structure calculations for both phases are also presented.

Crystal structure, compressibility and possible phase transitions in \boldvarepsilon-FeSi studied by first-principles pseudopotential calculations.

An investigation of the relative stability of the FeSi structure and of some hypothetical polymorphs of FeSi has been made by first-principles pseudopotential calculations. It has been shown that the observed distortion from ideal sevenfold coordination is essential in stabilizing the FeSi structure relative to one of the CsCl type. Application of high pressure to FeSi is predicted to produce a structure having nearly perfect sevenfold coordination. However, it appears that FeSi having a CsCl-type structure will be the thermodynamically most stable phase for pressures greater than 13 GPa. Fitting of the calculated internal energy vs volume for the FeSi structure to a third-order Birch-Murnaghan equation of state led to values, at T = 0 K, for the bulk modulus, K(0), and for its first derivative with respect to pressure, K(0)', of 227 GPa and 3.9, respectively.