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.

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.

Ultrahigh-pressure phase boundary between solid and liquid SiO₂ is still quite unclear. Here we present predictions of silica melting curve for the multimegabar pressure regime, as obtained from first principles molecular dynamics simulations. We calculate the melting temperatures from three high pressure phases of silica (pyrite-, cotunnite-, and Fe₂P-type SiO₂) at different pressures using the Z method. The computed melting curve is found to rise abruptly around 330 GPa, an increase not previously reported by any melting simulations. This is in close agreement with recent experiments reporting the α-PbO₂–pyrite transition around this pressure. The predicted phase diagram indicates that silica could be one of the dominant components of the rocky cores of gas giants, as it remains solid at the core of our Solar System’s gas giants. These results are also relevant to model the interior structure and evolution of massive super-Earths.

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.

The correct modeling of velocity distribution functions for particles in steady-state plasmas is a central element in the study of nuclear fusion and also in the description of space plasmas. In this paper, a statistical mechanical formalism for the description of collisionless plasmas in a steady state is presented, based solely on the application of the rules of probability and not relying on the concept of entropy. Beck and Cohen's superstatistical framework [Beck and Cohen, Physica A 322, 267 (2003)] is recovered as a limiting case, and a “microscopic” definition of inverse temperature $\beta$ is given. Nonextensivity is not invoked a priori but enters the picture only through the analysis of correlations between parts of the system.