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The lowermost portion of Earth's mantle (D″) above the core-mantle boundary shows anomalous seismic features, such as strong seismic anisotropy, related to the properties of the main mineral MgSiO 3 postperovskite. But, after over a decade of investigations, the seismic observations still cannot be explained simply by flow models which assume dislocation creep in postperovskite. We have investigated the chemical diffusivity of perovskite and postperovskite phases by experiment and ab initio simulation, and derive equations for the observed anisotropic diffusion creep. There is excellent agreement between experiments and simulations for both phases in all of the chemical systems studied. Single-crystal diffusivity in postperovskite displays at least 3 orders of magnitude of anisotropy by experiment and simulation ( D a = 1,000 D b ; D b ≈ D c ) in zinc fluoride, and an even more extreme anisotropy is predicted ( D a = 10,000 D c ; D c = 10,000 D b ) in the natural MgSiO 3 system. Anisotropic chemical diffusivity results in anisotropic diffusion creep, texture generation, and a strain-weakening rheology. The results for MgSiO 3 postperovskite strongly imply that regions within the D″ region of Earth dominated by postperovskite will 1) be substantially weaker than regions dominated by perovskite and 2) develop a strain-induced crystallographic-preferred orientation with strain-weakening rheology. This leads to strain localization and the possibility to bring regions with significantly varying textures into close proximity by strain on narrow shear zones. Anisotropic diffusion creep therefore provides an attractive alternative explanation for the complexity in observed seismic anisotropy and the rapid lateral changes in seismic velocities in D″.

The equation of state of the orthorhombic phase of NiSi with Pmmn symmetry has been determined at room temperature from synchrotron-based X-ray diffraction measurements of its lattice parameters, made in a diamond anvil cell. Measurements were performed up to 44 GPa, using Ne as the pressure medium and Au as the pressure standard. The resulting pressure-volume ( P - V ) data have been fitted with a Birch-Murnaghan equation of state of third order to yield V 0 = 11.650 (7) Å 3  atom -1 , K 0 = 162 (3) GPa and K 0 ' = 4.6 (2). In addition, P - V data have been collected on Ni 53 Si 47 in the B20 structure using both Ne and He as the pressure media and Cu and Au as the pressure standards, also to 44 GPa. A fit using the same Birch-Murnaghan equation of state of third order yields V 0 = 11.364 (6) Å 3  atom -1 , K 0 = 171 (4) GPa and K 0 ' = 5.5 (3).

The observed shear-wave velocity VS in Earth's core is much lower than expected from mineralogical models derived from both calculations and experiments. A number of explanations have been proposed, but none sufficiently explain the seismological observations. Using ab initio molecular dynamics simulations, we obtained the elastic properties of hexagonal close-packed iron (hcp-Fe) at 360 gigapascals up to its melting temperature Tm. We found that Fe shows a strong nonlinear shear weakening just before melting (when T/Tm > 0.96), with a corresponding reduction in VS. Because temperatures range from T/Tm = 1 at the inner-outer core boundary to T/Tm ≈ 0.99 at the center, this strong nonlinear effect on VS should occur in the inner core, providing a compelling explanation for the low VS observed.

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 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 nature of the stable phase of iron in the Earth's solid inner core is still highly controversial. Laboratory experiments suggest the possibility of an uncharacterized phase transformation in iron at core conditions and seismological observations have indicated the possible presence of complex, inner-core layering. Theoretical studies currently suggest that the hexagonal close packed (h.c.p.) phase of iron is stable at core pressures and that the body centred cubic (b.c.c.) phase of iron becomes elastically unstable at high pressure. In other h.c.p. metals, however, a high-pressure b.c.c. form has been found to become stabilized at high temperature. We report here a quantum mechanical study of b.c.c.-iron able to model its behaviour at core temperatures as well as pressures, using ab initio molecular dynamics free-energy calculations. We find that b.c.c.-iron indeed becomes entropically stabilized at core temperatures, but in its pure state h.c.p.-iron still remains thermodynamically more favourable. The inner core, however, is not pure iron, and our calculations indicate that the b.c.c. phase will be stabilized with respect to the h.c.p. phase by sulphur or silicon impurities in the core. Consequently, a b.c.c.-structured alloy may be a strong candidate for explaining the observed seismic complexity of the inner 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.

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.

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.

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.