Stability and equation of state of face-centered cubic and hexagonal close packed phases of argon under pressure

Ab initio determination of melting and sound velocity of neon up to the deep interior of the Earth

The thermophysical properties and elemental abundances of the noble gases in terrestrial materials can provide unique insights into the Earth's evolution and mantle dynamics. Here, we perform extensive ab initio molecular dynamics simulations to determine the melting temperature and sound velocity of neon up to 370 GPa and 7500 K to constrain its physical state and storage capacity, together with to reveal its implications for the deep interior of the Earth. It is found that solid neon can exist stably under the lower mantle and inner core conditions, and the abnormal melting of neon is not observed under the entire temperature (T) and pressure (P) region inside the Earth owing to its peculiar electronic structure, which is substantially distinct from other heavier noble gases. An inspection of the reduction for sound velocity along the Earth's geotherm evidences that neon can be used as a light element to account for the low-velocity anomaly and density deficit in the deep Earth. A comparison of the pair distribution functions and mean square displacements of MgSiO3-Ne and Fe-Ne alloys further reveals that MgSiO3 has a larger neon storage capacity than the liquid iron under the deep Earth condition, indicating that the lower mantle may be a natural deep noble gas storage reservoir. Our results provide valuable information for studying the fundamental behavior and phase transition of neon in a higher T-P regime, and further enhance our understanding for the interior structure and evolution processes inside the Earth.

Correlations in randomly stacked solids

Packing of spheres is a problem with a long history dating back to Kepler's conjecture in 1611. The highest density is realized in face-centered-cubic (FCC) and hexagonal-close-packed (HCP) arrangements. These are only limiting examples of an infinite family of maximal-density structures called Barlow stackings. They are constructed by stacking triangular layers, with each layer shifted with respect to the one below. At the other extreme, Torquato-Stillinger stackings are believed to yield the lowest possible density while preserving mechanical stability. They form an infinite family of structures composed of stacked honeycomb layers. In this article, we characterize layer-correlations in both families when the stacking is random. To do so, we take advantage of the Hägg code-a mapping between a Barlow stacking and a one-dimensional Ising magnet. The layer correlation is related to a moment-generating function of the Ising model. We first determine the layer correlation for random Barlow stacking, finding exponential decay. We next introduce a bias favoring one of two stacking chiralities-equivalent to a magnetic field in the Ising model. Although this bias favors FCC ordering, there is no long-ranged order as correlations still decay exponentially. Finally, we consider Torquato-Stillinger stackings, which map to a combination of an Ising magnet and a three-state Potts model. With random stacking, the correlations decay exponentially with a form that is similar to the Barlow problem. We discuss relevance to ordering in clusters of stacked solids and for layer-deposition-based synthesis methods.

Lattice sum for a hexagonal close-packed structure and its dependence on the c/a ratio of the hexagonal cell parameters

We continue the work by Lennard-Jones and Ingham, and later by Kane and Goeppert-Mayer, and present a general lattice sum formula for the hexagonal close packed (hcp) structure with different c/a ratios for the two lattice parameters a and c of the hexagonal unit cell. The lattice sum is expressed in terms of fast converging series of Bessel functions. This allows us to analytically examine the behavior of a Lennard-Jones potential as a function of the c/a ratio. In contrast to the hard-sphere model, where we have the ideal ratio of c/a=sqrt[8/3] with 12 kissing spheres around a central atom, we observe the occurrence of a slight symmetry-breaking effect and the appearance of a second metastable minimum for the (12,6) Lennard-Jones potential around the ratio c/a=2/3. We also show that the analytical continuation of the (n,m) Lennard-Jones potential to the domain n,m<3 such as the Kratzer potential (n=2,m=1) gives unphysical results.

First principles molecular dynamics calculations of the mechanical properties of endofullerenes containing noble gas atoms or small molecules

The mechanical properties of endofullerenes have been investigated by performing compression tests using finite temperature first principles molecular dynamics calculations. We considered various X@C₆₀ systems, with X a single noble gas atom (He, Ne, Ar, Kr, or Xe), small molecules (H₂O, CH₄), or small helium clusters. In the absence of compression, it is observed that there is no or at best a negligible effect of X on the properties of C₆₀. The compression simulations revealed several original findings. First, the influence of X on the stiffness of X@C₆₀ can be quantified, although it is at most 12% for the studied cases. Next, both energy and contact force variations as a function of strain are demonstrated to depend on X. However, this is not the case for the yield strain and for the failure mechanism of the C₆₀ shell. Finally, it is shown that the X@C₆₀ compression could bring X to be in a high stress state. In the specific cases of H₂O and CH₄ molecules, a mechanism of stress assisted dissociation is observed.