Application of Phase Transition Theory to a Glass-Forming System

Abstract

We have investigated the crystallization of a monatomic simple liquid in equilibrium, where the constituents interact through the Lennard-Jones-Gauss (LJG) potential. By incorporating a perturbation expansion into a density functional approach, we obtain a phase diagram covering a wide range of the parameter space. The phase diagram agrees qualitatively with that obtained by molecular dynamics (MD) simulations. The MD simulations show that the system cannot be crystallized, even if the temperature is sufficiently low, in a certain region of the parameter space. In this parameter region, we find that the coexisting density of the fcc crystal is unexpectedly high owing to a decrease in the free energy and show that the third-nearest-neighbor site of the fcc crystal coincides with the second minimum in the LJG potential.

Effects of interactions between depletants in phase diagrams of binary hard-sphere systems

“…The size ratios of q = 1/10 and 1/6 were examined to study the effects of the second minimum on the IE potential because the coexistence densities are affected by the location of the second minimum (see fig. 1) in the previous results for the Lennard-Jones-Gauss systems [37][38][39]. Here, the second minimum for q = 1/6 was located at the peak of g HS LL (r) of the bcc crystal.…”

“…It seems that the contribution of the second minimum in the potential φ ef f (r) is not always small. It has been shown that the second minimum affects the coexistence density and pressure in the Lennard-Jones-Gauss system [37][38][39]. The second peak of g HS LL (r) around r = 1.17σ l is large for a bcc crystal (fig.…”

“…To obtain the Helmholtz free energy, F , the thermodynamic perturbation theory should be applied to the AO and IE potential systems [33][34][35][36][37][38][39]. The free energy F is expanded into a power series of φ dep (r), and we ignore items beyond the second term.…”

“…The Carnahan-Starling [26] and Verlet-Weis [40] formulas were adopted to calculate F HS and g HS LL (r) in the fluid phase, respectively. In the solid phase, F HS was calculated by the modified weighted density approximation [41], which is one of the density functional theories (DFT), and we applied a method developed by Rascón et al [17,34,[36][37][38][39]42,43] to calculate g HS LL (r). As the packing fraction η r s increases, the oscillation in the effective potential becomes stronger, and the molecular simulation becomes harder.…”

“…As the packing fraction η r s increases, the oscillation in the effective potential becomes stronger, and the molecular simulation becomes harder. The above method was adopted in the present study because its validity has been confirmed based on the comparison with the results of simulations [17,34,[36][37][38][39]42,43].…”