The Uhlenbeck-Ford model: Exact virial coefficients and application as a reference system in fluid-phase free-energy calculations

Melting conditions and entropies of superionic water ice: Free-energy calculations based on hybrid solid/liquid reference systems

Superionic (SI) water ices-high-temperature, high-pressure phases of water in which oxygen ions occupy a regular crystal lattice whereas the protons flow in a liquid-like manner-have attracted a growing amount of attention over the past few years, in particular due to their possible role in the magnetic anomalies of the ice giants Neptune and Uranus. In this paper, we consider the calculation of the free energies of such phases, exploring hybrid reference systems consisting of a combination of an Einstein solid for the oxygen ions occupying a crystal lattice and a Uhlenbeck-Ford potential for the protonic fluid that avoids irregularities associated with possible particle overlaps. Applying this approach to a recent neural-network potential-energy landscape for SI water ice, we compute Gibbs free energies as a function of temperature for the SI fcc and liquid phases to determine the melting temperature T_m at 340 GPa. The results are consistent with previous estimates and indicate that the entropy difference between both phases is comparatively small, in particular due to the large amplitude of vibration of the oxygen ions in the fcc phase at the melting temperature.

Uncovering the effects of interface-induced ordering of liquid on crystal growth using machine learning

The process of crystallization is often understood in terms of the fundamental microstructural elements of the crystallite being formed, such as surface orientation or the presence of defects. Considerably less is known about the role of the liquid structure on the kinetics of crystal growth. Here atomistic simulations and machine learning methods are employed together to demonstrate that the liquid adjacent to solid-liquid interfaces presents significant structural ordering, which effectively reduces the mobility of atoms and slows down the crystallization kinetics. Through detailed studies of silicon and copper we discover that the extent to which liquid mobility is affected by interface-induced ordering (IIO) varies greatly with the degree of ordering and nature of the adjacent interface. Physical mechanisms behind the IIO anisotropy are explained and it is demonstrated that incorporation of this effect on a physically-motivated crystal growth model enables the quantitative prediction of the growth rate temperature dependence.

Crystallization is a challenging process to model quantitatively. Here the authors use machine learning and atomistic simulations together to uncover the role of the liquid structure on the process of crystallization and derive a predictive kinetic model of crystal growth.

Uhlenbeck-Ford model: Phase diagram and corresponding-states analysis

Using molecular dynamics simulations and nonequilibrium thermodynamic-integration techniques we compute the Helmholtz free energies of the body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal close-packed, and fluid phases of the Uhlenbeck-Ford model (UFM) and use the results to construct its phase diagram. The pair interaction associated with the UFM is characterized by an ultrasoft, purely repulsive pair potential that diverges logarithmically at the origin. We find that the bcc and fcc are the only thermodynamically stable crystalline phases in the phase diagram. Furthermore, we report the existence of two reentrant transition sequences as a function of the number density, one featuring a fluid-bcc-fluid succession and another displaying a bcc-fcc-bcc sequence near the triple point. We find strong resemblances to the phase behavior of other soft, purely repulsive systems such as the Gaussian-core model (GCM), inverse-power-law, and Yukawa potentials. In particular, we find that the fcc-bcc-fluid triple point and the phase boundaries in its vicinity are in good agreement with the prediction supplied by a recently proposed corresponding-states principle [J. Chem. Phys. 134, 241101 (2011)JCPSA60021-960610.1063/1.3605659; Europhys. Lett. 100, 66004 (2012)EULEEJ0295-507510.1209/0295-5075/100/66004]. The particularly strong resemblance between the behavior of the UFM and GCM models are also discussed.