Nonmonotonic Dependence of the Absolute Entropy on Temperature in Supercooled Stillinger-Weber Silicon

Abstract

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 ≥ 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.Keywords amorphous silicon · liquid-liquid transition IntroductionThe liquid-amorphous transition in silicon, modeled by the Stillinger-Weber (SW) potential [23], has been intensely studied [9,19,20,2,22,7,24,15,18] with an aim of understanding the phase behavior of real silicon. In the initial molecular dynamics (MD) studies on SW silicon [20,2], it was found

The freezing tendency towards 4-coordinated amorphous networks causes an increase in the heat capacity of supercooled Stillinger–Weber silicon

“…Note that since C p values are obtained by numerical differentiation, these are highly sensitive to the estimated enthalpies of the equilibrium states. 12 Nonetheless, these C p values show the same qualitative trend, i.e., a sharp rise at 1060 K, as in an earlier investigation. 4 In this work, we nd a link between the supercooled liquid properties (including the rise of C p near 1060 K) and the cooperative relaxation (freezing) of the 4-coordinated particles.…”

“…These investigations suggested that there is a free energy minimum associated with the liquid state of SW-Si at or above 1060 K but no such minimum is associated with the low density amorphous phases formed aer the relaxation of the supercooled liquid, which indicates that the amorphous phases are non-equilibrium phases. In previous work, 12 the properties of the equilibrium liquid states of supercooled SW-Si at and above 1060 K and zero pressure were ascertained on the basis of the fact that the excess enthalpy (with respect to those of the crystal phase at the same temperature) of such states, together with the computed excess Gibbs free energies G e , satisfy the Gibbs-Helmholtz equation within the computed error bars of G e (see Table 1…”

“…Based on the computed enthalpies of equilibrium states in ref. 12, we nd the heat capacities by numerically differentiating the enthalpy with respect to temperature using a central difference technique. Thus, the computed values of C p /Nk B are 29, 12.7 and 7 at 1062.5, 1067.5 and 1072.5 K, respectively.…”

“…2 The reason for this anomalous behavior is not fully understood. In a previous work, 3 the properties of metastable equilibrium liquid of SW-Si, in the temperature range of 1060-1070 K, were ascertained by means of free energy computations. Here we analyze the properties of the metastable equilibrium liquid in more detail vis-a-vis the nature of the relaxation process.…”

Dynamical Instability Causes the Demise of a Supercooled Tetrahedral Liquid

“…[4] In the case of Stillinger-Weber [16] silicon, the liquid state properties at the lower limit of stability of 1060 K [7,8] have been precisely estimated based on free energy computations. [1,2] Here we attempt to study the relaxation at the stability limit of supercooled water modeled by mW potential of Molinero and Moore. [9] mW is a coarse-grained model of water in which water is represented by a single atom with 3-body (tetrahedral) interactions to mimic the effect of hydrogen bonds of real water.…”