Nesting of thermodynamic, structural, and dynamic anomalies in liquid silicon

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.

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.

Thermodynamic anomalies in silicon and the relationship to the phase diagram

The evolution of thermodynamic anomalies are investigated in the pressure-temperature (pT) plane for silicon using the well-established Stillinger-Weber potential. Anomalies are observed in the density, compressibility and heat capacity. The relationships between them and with the liquid stability limit are investigated and related to the known thermodynamic constraints. The investigations are extended into the deeply supercooled regime using replica exchange techniques. Thermodynamic arguments are presented to justify the extension to low temperature, although a region of phase space is found to remain inaccessible due to unsuppressible crystallisation. The locus corresponding to the temperature of minimum compressibility is shown to display a characteristic 'S'-shape in thepTprojection which appears correlated with the underlying crystalline phase diagram. The progression of the anomalies is compared to the known underlying phase diagrams for both the crystal/liquid and amorphous/liquid states. The locations of the anomalies are also compared to those obtained from previous simulation work and (limited) experimental observations.

Dispersion of acoustic excitations in tetrahedral liquids

Investigation of the longitudinal and transverse excitations in liquids is of great importance for understanding the fundamentals of the liquid state of matter. One of the important questions is the temperature and density dependence of the frequency of the excitations. In our recent works it was shown that while in simple liquids the frequency of longitudinal excitations increases when the temperature is increased isochorically, in water the frequency can anomalously decrease with the temperature increase. In the present manuscript we study the dispersion curves of longitudinal and transverse excitations of water and liquid silicon modelled by Stillinger-Weber (SW) potential. We show that both in liquid silicon and SW model of water the frequencies of longitudinal excitations slightly increase with temperature which is in contrast to the results for SPC/E model of water.

Viscous properties of nickel-containing binary metal melts

The paper presents the results of molecular dynamics study of the viscosity of nickel-containing binary metal melts for a wide range of temperatures, including the region of the equilibrium liquid phase and supercooled melt. It is shown that the temperature dependencies of the viscosity of binary metal melts are described by the Kelton's quasi-universal model. Based on the analysis of the viscosity coefficient of the binary melt composition within the framework of the Rosenfeld's scale transformations, it has been established that to correctly describe the viscosity of binary/multicomponent metal melts within the framework of entropy models, it is necessary to use a more complex representation of the excess entropy S _ex than in the approximation of pair correlation entropy S ₂.

Perspective: Excess-entropy scaling

This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.

Breakdown of the Stokes-Einstein relation above the melting temperature in a liquid phase-change material

The dynamic properties of liquid phase-change materials (PCMs), such as viscosity η and the atomic self-diffusion coefficient D, play an essential role in the ultrafast phase switching behavior of novel nonvolatile phase-change memory applications. To connect η to D, the Stokes-Einstein relation (SER) is commonly assumed to be valid at high temperatures near or above the melting temperature T m and is often used for assessing liquid fragility (or crystal growth velocity) of technologically important PCMs. However, using quasi-elastic neutron scattering, we provide experimental evidence for a breakdown of the SER even at temperatures above T m in the high-atomic mobility state of a PCM, Ge1Sb2Te4. This implies that although viscosity may have strongly increased during cooling, diffusivity can remain high owing to early decoupling, being a favorable feature for the fast phase switching behavior of the high-fluidity PCM. We discuss the origin of the observation and propose the possible connection to a metal-semiconductor and fragile-strong transition hidden below T m.

Relationship between structural order and water-like anomalies in metastable liquid silicon: Ab initio molecular dynamics

The relationship between structural order and water-like anomalies in tetrahedral liquids is still open. Here, first-principle molecular dynamics are performed to study it in metastable liquid Si. It is found that in T-P phase diagram, there indeed exists a structural anomaly region, which encloses density anomaly but not diffusivity anomaly. This is consistent with that of SW Si and BKS SiO₂ but different from that of SPC/E water. Two-body excess entropy anomaly can neither capture the diffusivity, structural, and density anomalies, as it can in a two-scale potential fluid. In structural anomaly region, tetrahedrality order q_tetra (measuring the extent to which an atom and its four nearest neighbours adopt tetrahedral arrangement) and translational order t_trans (measuring the tendency of two atoms to adopt preferential separation) are not perfectly correlated, which is different from that in SW Si and renders it impossible to use the isotaxis line to quantify the degree of structural order needed for water-like anomalies to occur. Along the isotherm of critical temperature T_c, t_trans/q_tetra is approximately linear with pressure. With decreasing pressure along the isotherm below T_c, t_trans/q_tetra departs downward from the line, while it is the opposite case above T_c.

Excess Entropy Scaling Law for Diffusivity in Liquid Metals

Understanding how dynamic properties depend on the structure and thermodynamics in liquids is a long-standing open problem in condensed matter physics. A very simple approach is based on the Dzugutov contribution developed on model fluids in which a universal (i.e. species-independent) connection relates the pair excess entropy of a liquid to its reduced diffusion coefficient. However its application to "real" liquids still remains uncertain due to the ability of a hard sphere (HS) reference fluid used in reducing parameters to describe complex interactions that occur in these liquids. Here we use ab initio molecular dynamics simulations to calculate both structural and dynamic properties at different temperatures for a wide series of liquid metals including Al, Au, Cu, Li, Ni, Ta, Ti, Zn as well as liquid Si and B. From this analysis, we demonstrate that the Dzugutov scheme can be applied successfully if a self-consistent method to determine the packing fraction of the hard sphere reference fluid is used as well as the Carnahan-Starling approach to express the excess entropy.

Equilibrium and nonequilibrium dynamics of soft sphere fluids

We use computer simulations to test the freezing-point scaling relationship between equilibrium transport coefficients (self-diffusivity, viscosity) and thermodynamic parameters for soft sphere fluids. The fluid particles interact via the inverse-power potential (IPP), and the particle softness is changed by modifying the exponent of the distance-dependent potential term. In the case of IPP fluids, density and temperature are not independent variables and can be combined to obtain a coupling parameter to define the thermodynamic state of the system. We find that the rescaled coupling parameter, based on its value at the freezing point, can approximately collapse the diffusivity and viscosity data for IPP fluids over a wide range of particle softness. Even though the collapse is far from perfect, the freezing-point scaling relationship provides a convenient and effective way to compare the structure and dynamics of fluid systems with different particle softness. We further show that an alternate scaling relationship based on two-body excess entropy can provide an almost perfect collapse of the diffusivity and viscosity data below the freezing transition. Next, we perform nonequilibrium molecular dynamics simulations to calculate the shear-dependent viscosity and to identify the distinct role of particle softness in underlying structural changes associated with rheological properties. Qualitatively, we find a similar shear-thinning behavior for IPP fluids with different particle softness, though softer particles exhibit stronger shear-thinning tendency. By investigating the distance and angle-dependent pair correlation functions in these systems, we find different structural features in the case of IPP fluids with hard-sphere like and softer particle interactions. Interestingly, shear-thinning in hard-sphere like fluids is accompanied by enhanced translational order, whereas softer fluids exhibit loss of order with shear. Our results provide a systematic evaluation of the role of particle softness in equilibrium and nonequilibrium transport properties and their underlying connection with thermodynamic and structural properties.