A free energy study of the liquid-liquid phase transition of the Jagla two-scale potential

Kinetic reconstruction of free energies as a function of multiple order parameters

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

Liquid-liquid phase transition in deeply supercooled Stillinger-Weber silicon

The existence of a phase transition between two distinct liquid phases in single-component network-forming liquids (e.g. water, silica, silicon) has elicited considerable scientific interest. The challenge, both for experiments and simulations, is that the liquid-liquid phase transition (LLPT) occurs under deeply supercooled conditions, where crystallization occurs very rapidly. Thus, early evidence from numerical equation of state studies was challenged with the argument that slow spontaneous crystallization had been misinterpreted as evidence of a second liquid state. Rigorous free-energy calculations have subsequently confirmed the existence of a LLPT in some models of water, and exciting new experimental evidence has since supported these computational results. Similar results have so far not been found for silicon. Here, we present results from free-energy calculations performed for silicon modeled with the classical, empirical Stillinger-Weber-potential. Through a careful study employing state-of-the-art constrained simulation protocols and numerous checks for thermodynamic consistency, we find that there are two distinct metastable liquid states and a phase transition. Our results resolve a long-standing debate concerning the existence of a liquid-liquid transition in supercooled liquid silicon and address key questions regarding the nature of the phase transition and the associated critical point.

Stability of the high-density Jagla liquid in 2D: sensitivity to parameterisation

We computed the pressure-temperature phase diagram of the hard-core two-scale ramp potential in two-dimensions, with the parameterisation originally suggested by Jagla [E. A. Jagla, Phys. Rev. E, 63, 061501 (2001)], as well as with a series of systematically modified variants of the model to reveal the sensitivity of the stability of phases. The nested sampling method was used to explore the potential energy landscape, allowing the identification of thermodynamically relevant phases, such as low- and high-density liquids and various crystalline forms, some of which have not been reported before. We also proposed a smooth version of the potential, which is differentiable beyond the hard-core. This potential reproduces the density anomaly, but forms a dodecahedral quasi-crystal structure at high pressure. Our results allow to hypothesise on the necessary modifications of the original model in order to improve the stability of the metastable high-density liquid phase in 3D.

Thermodynamics and kinetics of crystallization in deeply supercooled Stillinger-Weber silicon

We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three-body potential. The free energy barriers to crystallization are computed using umbrella sampling Monte Carlo simulations and from unconstrained molecular dynamics simulations using a mean first passage time formulation. We focus on state points that have been described in earlier work [S. Sastry and C. A. Angell, Nat. Mater. 2, 739 (2003)] as straddling a liquid-liquid phase transition (LLPT) between two metastable liquid states. It was argued subsequently [Ricci et al., Mol. Phys. 117, 3254 (2019)] that the apparent transition is due to the loss of metastability of the liquid state with respect to the crystalline state. The presence of a barrier to crystallization for these state points is therefore of importance to ascertain, which we investigate, with due attention to ambiguities that may arise from the choice of order parameters. We find a well-defined free energy barrier to crystallization and demonstrate that both umbrella sampling and mean first passage time methods yield results that agree quantitatively. Our results thus provide strong evidence against the possibility that the liquids at state points close to the reported LLPT exhibit slow, spontaneous crystallization, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallization at other state points over a broad range of temperatures and pressures and discuss the effect of changes in the microscopic structure of the metastable liquid on the free energy barrier heights.

Insight into Liquid Polymorphism from the Complex Phase Behavior of a Simple Model

We systematically explored the phase behavior of the hard-core two-scale ramp model suggested by Jagla [Phys. Rev. E 63, 061501 (2001)PRESCM1539-375510.1103/PhysRevE.63.061501] using a combination of the nested sampling and free energy methods. The sampling revealed that the phase diagram of the Jagla potential is significantly richer than previously anticipated, and we identified a family of new crystalline structures, which is stable over vast regions in the phase diagram. We showed that the new melting line is located at considerably higher temperature than the boundary between the low- and high-density liquid phases, which was previously suggested to lie in a thermodynamically stable region. The newly identified crystalline phases show unexpectedly complex structural features, some of which are shared with the high-pressure ice VI phase.

Structural properties of the Jagla fluid

The structural properties of the Jagla fluid are studied by Monte Carlo (MC) simulations, numerical solutions of integral equation theories, and the (semi-analytical) rational-function approximation (RFA) method. In the latter case, the results are obtained from the assumption (supported by our MC simulations) that the Jagla potential and a potential with a hard core plus an appropriate piecewise constant function lead to practically the same cavity function. The predictions obtained for the radial distribution function, g(r), from this approach are compared against MC simulations and integral equations for the Jagla model, and also for the limiting cases of the triangle-well potential and the ramp potential, with a general good agreement. The analytical form of the RFA in Laplace space allows us to describe the asymptotic behavior of g(r) in a clean way and compare it with MC simulations for representative states with oscillatory or monotonic decay. The RFA predictions for the Fisher-Widom and Widom lines of the Jagla fluid are obtained.

Nuclear quantum effects on the liquid–liquid phase transition of a water-like monatomic liquid

The liquid–liquid phase transition of a classical monatomic liquid shifts towards low-temperatures and high-pressures when nuclear quantum effects are included.