The Earth solid inner core is mostly iron 1,2 , therefore, the question-what is the structure of iron in the Earth inner core-is central to our understanding of the Core. However, the stable phase of iron in the Core is still unknown. Currently, two major candidates are considered-hexagonal close-packed (hcp) and body centered cubic (bcc) structures. Neither of these structures received unanimous support 3,4. Here we demonstrate stability of the bcc phase under conditions in the center of the Core by performing novel constant pressure-temperature ab initio molecular dynamics simulations with varying shape and volume of the computational cell. The bcc phase is stabilized by the discovered unique diffusion mechanism that originates in the low temperature dynamical instability of the bcc phase. It appears that the bcc phase has already been observed in the recent experiments, however, the experimental data was misinterpreted. The diffusion of iron atoms in solid state is quite unique and might allow us to explain both the anisotropy and the low shear modulus of the inner Core. The Earth solid inner and liquid outer cores consist mainly of iron 1. The pressure range of the inner core is from 330 to 365 GPa 2. The temperature is known less precisely, since the melting temperatures of iron have not been measured at the core pressures. When extrapolated, the data from shockwave (SW) 3,4 and diamond anvil cell (DAC) 5 experiments place melting temperature of iron somewhat above 6000 K at the pressure of the inner core outer core (ICOC) boundary (330 GPa). The melting temperature of iron in the center of the Earth then could be close to 7000 K. Some DAC studies 6 place this number considerably lower, around 5000 K. Theory supports higher melting temperatures 7-9. Structure and properties of a crystal are intimately related. Therefore, elasticity of the core, its seismic response, density, heat capacity and heat conductivity, to name a few, critically depend on the structure of iron in the core. The interpretation of seismic data, our major source of information about deep Earth, is completely dependent on the phase diagram of iron at the core conditions 10-12. At high pressure and low temperature the stable phase of iron is hcp 13. There are two experimental studies that support transition of iron to another, yet unknown phase at pressures above 150-200 GPa and temperatures higher than 3000 K 3,14. The SW data 3 was interpreted as a transition from the hcp to the bcc phase. The DAC data 14 is consistent with stabilization of the bcc phase 15. Later SW studies 4 claim that the Brown and McQueen data 3 is not an evidence for a phase transition. We note, however, that a similar situation was recently resolved for the case of Mo. It was suggested 16 that there is no phase transition in Mo contrary to the discovery made by Hixson et al. 17 earlier. Recently, it was demonstrated 18 that the 'no-transition' scenario 16 is not consistent with theory and likely the original data by Hixson et al. 17 is indeed an evidence for a tran...

Earth's solid-iron inner core has a low rigidity that manifests itself in the anomalously low velocities of shear waves as compared to shear wave velocities measured in iron alloys. Normally, when estimating the elastic properties of a polycrystal, one calculates an average over different orientations of a single crystal. This approach does not take into account the grain boundaries and defects that are likely to be abundant at high temperatures relevant for the inner core conditions. By using molecular dynamics simulations, we show that, if defects are considered, the calculated shear modulus and shear wave velocity decrease dramatically as compared to those estimates obtained from the averaged single-crystal values. Thus, the low shear wave velocity in the inner core is explained.

First-principles molecular dynamics calculations of the structural, elastic, vibrational and electronic properties of amorphous Al(2)O(3), in a system consisting of a supercell of 80 atoms, are reported. A detailed analysis of the interatomic correlations allows us to conclude that the short-range order is mainly composed of AlO(4) tetrahedra, but, in contrast with previous results, also an important number of AlO(6) octahedra and AlO(5) units are present. The vibrational density of states presents two frequency bands, related to bond-bending and bond-stretching modes. It also shows other recognizable features present in similar amorphous oxides. We also present the calculation of elastic properties (bulk modulus and shear modulus). The calculated electronic structure of the material, including total and partial electronic density of states, charge distribution, electron localization function and the ionicity for each species, gives evidence of correlation between the ionicity and the coordination for each Al atom.

No abstract

For a continuous maximum-entropy distribution (obtained from an arbitrary number of simultaneous constraints), we derive a general relation connecting the Lagrange multipliers and the expectation values of certain particularly constructed functions of the states of the system. From this relation, an estimator for a given Lagrange multiplier can be constructed from derivatives of the corresponding constraining function. These estimators sometimes lead to the determination of the Lagrange multipliers by way of solving a linear system, and, in general, they provide another tool to widen the applicability of Jaynes's formalism. This general relation, especially well suited for computer simulation techniques, also provides some insight into the interpretation of the hypervirial relations known in statistical mechanics and the recently derived microcanonical dynamical temperature. We illustrate the usefulness of these new relations with several applications in statistics.