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

Abstract

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 crystallisation are computed using umbrella sampling Monte Carlo simulations, and for selected low temperature and zero pressure state points, using unconstrained molecular dynamics simulations to reconstruct the free energy from a mean first passage time formulation. We focus on state points that have been described in earlier work [Sastry and Angell, Nature Mater., 2, 739, 2003] as straddling a first order 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 phase transition is in fact due the loss of metastability of the liquid state with respect to the globally stable crystalline state. The presence or absence of a barrier to crystallization for these state points is therefore of importance to ascertain, with due attention to ambiguities that may arise from the choice of order parameters. We discuss our choice of order parameters and also our choice of methods to calculate the free energy at deep supercooling. We find a well-defined free energy barrier to crystallisation 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 crystallisation, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallisation 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.

References in corpus (16)

• Structural transformation in supercooled water controls the crystallization rate of ice
• The Putative Liquid-Liquid Transition is a Liquid-Solid Transition in Atomistic Models of Water
• Liquid-liquid critical point in supercooled silicon
• The Putative Liquid-Liquid Transition is a Liquid-Solid Transition in Atomistic Models of Water, Part II
• Liquid-liquid transition in supercooled silicon determined by first-principles simulation
• Two-state thermodynamics of the ST2 model for supercooled water
• Static and Dynamic Anomalies in a Repulsive Spherical Ramp Liquid: Theory and Simulation
• Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization
• Persistence of Covalent Bonding in Liquid Silicon Probed by Inelastic X-ray Scattering
• Local structure of liquid carbon controls diamond nucleation
• Forward-Flux Sampling with Jumpy Order Parameters
• Structural Relaxation of a Gel Modeled by Three Body Interactions
• Test of classical nucleation theory on deeply supercooled high-pressure simulated silica
• Crystal Nucleation in a Supercooled Liquid with Glassy Dynamics
• Free energy of formation of small ice nuclei near the Widom line in simulations of supercooled water
• Potential tuning in the S-W system. (i) Bringing Tc,2 to ambient pressure, and (ii) colliding Tc,2 with the liquid-vapor spinodal

Cited by in corpus (3)

• Solid-amorphous transition is related to the waterlike anomalies in a fluid without liquid-liquid phase transition
• Kinetic reconstruction of free energies as a function of multiple order parameters
• A general relation between the largest nucleus and all nuclei distributions for free energy calculations