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 th
e 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.
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 superco
oled 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.
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Free energy of crystal phases is commonly evaluated by thermodynamic integration (TDI) along a reversible path that involves an external potential. A persistent problem in this method is that a significant hysteresis is observed due to differences in
the center of mass position of the crystal phase in the presence and absence of the external potential. To alleviate this hysteresis, a constraint on the translational degrees of freedom of the crystal phase is imposed along the path and subsequently a correction term is added to the free energy to account for such a constraint. In this work, we propose a new methodology termed as error-biased Bennett Acceptance ratio (EBAR) method that effectively solves this problem without the need to impose any constraint. This method is simple to implement as it does not require any modification to the path or to the simulation code. We show the applicability of this method in the computation of crystal-melt interfacial energy by cleaving wall method [J. Chem. Phys., 118, 7651 (2003)] and bulk crystal-melt free energy difference by constrained fluid $lambda$-integration method [J. Chem. Phys., 120, 2122 (2004)] for a model potential of silicon.
