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Register a new userThe freezing tendency towards 4-coordinated amorphous network causes increase in heat capacity of supercooled Stillinger-Weber silicon
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The supercooled liquid silicon, modeled by Stillinger-Weber potential, shows anomalous increase in heat capacity $C_p$, with a maximum $C_p$ value close to 1060 K at zero pressure. We study equilibration and relaxation of the supercooled SW Si, in the temperature range of 1060 K--1070 K at zero pressure. We find that as the relaxation of the metastable supercooled liquid phase initiates, a straight line region (SLR) is formed in cumulative potential energy distributions. The configurational temperature corresponding to the SLR is close to 1060 K, which was earlier identified as the freezing temperature of 4-coordinated amorphous network. The SLR is found to be tangential to the distribution of the metastable liquid phase and thus influences the broadness of the distribution. As the bath temperature is reduced from 1070 K to 1060 K, the effective temperature approaches the bath temperature which results in broadening of the metastable phase distribution. This, in turn, causes an increase in overall fluctuations of potential energy and hence an increase of heat capacity. We also find that during initial stages of relaxation, 4-coordinated atoms form 6-membered rings with a chair--like structure and other structural units that indicate crystallization. Simultaneously a strong correlation is established between the number of chair-shaped 6-membered rings and the number of 4-coordinated atoms in the system. This shows that all properties related to 4-coordinated particles are highly correlated as the SLR is formed in potential energy distributions and this can be interpreted as a consequence of `freezing of amorphous network formed by 4-coordinated particles.
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Using a recently developed thermodynamic integration method, we compute the precise values of the excess Gibbs free energy (G^e) of the high density liquid (HDL) phase with respect to the crystalline phase at different temperatures (T) in the supercooled region of the Stillinger-Weber (SW) silicon [F. H. Stillinger and T. A. Weber, Phys. Rev. B. 32, 5262 (1985)]. Based on the slope of G^e with respect to T, we find that the absolute entropy of the HDL phase increases as its enthalpy changes from the equilibrium value at T ge 1065 K to the value corresponding to a non-equilibrium state at 1060 K. We find that the volume distribution in the equilibrium HDL phases become progressively broader as the temperature is reduced to 1060 K, exhibiting van-der-Waals (VDW) loop in the pressure-volume curves. Our results provides insight into the thermodynamic cause of the transition from the HDL phase to the low density phases in SW silicon, observed in earlier studies near 1060 K at zero pressure.
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.
We have obtained by Monte Carlo NVT simulations the constant-volume excess heat capacity of square-well fluids for several temperatures, densities and potential widths. Heat capacity is a thermodynamic property much more sensitive to the accuracy of a theory than other thermodynamic quantities, such as the compressibility factor. This is illustrated by comparing the reported simulation data for the heat capacity with the theoretical predictions given by the Barker-Henderson perturbation theory as well as with those given by a non-perturbative theoretical model based on Baxters solution of the Percus-Yevick integral equation for sticky hard spheres. Both theories give accurate predictions for the equation of state. By contrast, it is found that the Barker-Henderson theory strongly underestimates the excess heat capacity for low to moderate temperatures, whereas a much better agreement between theory and simulation is achieved with the non-perturbative theoretical model, particularly for small well widths, although the accuracy of the latter worsens for high densities and low temperatures, as the well width increases.
We investigate the relaxation mechanism of a supercooled tetrahedral liquid at its limit of stability using isothermal isobaric ($NPT$) Monte Carlo (MC) simulations. In similarity with systems which are far from equilibrium but near the onset of jamming [OHern et.al., Phys. Rev. Lett. {bf 93}, 165702 (2004)], we find that the relaxation is characterized by two time-scales: the decay of long-wavelength (slow) fluctuations of potential energy is controlled by the the slope $[partial (G/N)/partial phi]$ of the Gibbs free energy ($G$) at a unique value of per particle potential energy $phi = phi_{mid}$. The short-wavelength (fast) fluctuations are controlled by the bath temperature $T$. The relaxation of the supercooled liquid is initiated with a dynamical crossover after which the potential energy fluctuations are biased towards values progressively lesser than $phi_{mid}$. The dynamical crossover leads to the change of time-scale, i.e., the decay of long-wavelength potential energy fluctuations (intermediate relaxation). Because of the condition [$partial^2 (G/N)/partial phi^2 = 0$] at $phi = phi_{mid}$, the slope $[partial (G/N)/partial phi]$ has a unique value and governs the intermediate stage of relaxation, which ends just after the crossover. In the subsequent stage, there is a relatively rapid crystallization due to lack of long-wavelength fluctuations and the instability at $phi_{mid}$, i.e., the condition that $G$ decreases as configurations with potential energies lower than $phi_{mid}$ are accessed. The dynamical crossover point and the associated change in the time-scale of fluctuations is found to be consistent with the previous studies.
A novel liquid-liquid phase transition has been proposed and investigated in a wide variety of pure substances recently, including water, silica and silicon. From computer simulations using the Stillinger-Weber classical empirical potential, Sastry and Angell [1] demonstrated a first order liquid-liquid transition in supercooled silicon, subsequently supported by experimental and simulation studies. Here, we report evidence for a liquid-liquid critical end point at negative pressures, from computer simulations using the SW potential. Compressibilities exhibit a growing maximum upon lowering temperature below 1500 K and isotherms exhibit density discontinuities below 1120 K, at negative pressure. Below 1120 K, isotherms obtained from constant volume-temperature simulations exhibit non-monotonic, van der Waals-like behavior signaling a first order transition. We identify Tc ~ 1120 +/- 12 K, Pc -0.60 +/- 0.15 GPa as the critical temperature and pressure for the liquid-liquid critical point. The structure of the liquid changes dramatically upon decreasing the temperature and pressure. Diffusivities vary over 4 orders of magnitude, and exhibit anomalous pressure dependence near the critical point. A strong relationship between local geometry quantified by the coordination number, and diffusivity, is seen, suggesting that atomic mobility in both low and high density liquids can usefully be analyzed in terms of defects in the tetrahedral network structure. We have constructed the phase diagram of supercooled silicon. We identify the lines of compressibility, density extrema (maxima and minima) and the spinodal which reveal the interconnection between thermodynamic anomalies and the phase behaviour of the system as suggested in previous works [2-9]
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