Thermodynamic anomalies in silicon and the relationship to the phase diagram

Abstract

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 the pT projection 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.

Thermodynamic anomalies, polyamorphism and all that

“…The temperature below which full equilibration is not possible is indicated as Teq in figure 1. Teq is determined by observing the arrest in the decay of the time correlation function extracted from the local tetrahedrality (see [110]). The results presented are an attempt to extend the equations of state into unstable parts of the phase diagram in order to obtain a more complete picture of behaviour of thermodynamic anomalies.…”

“…To model the covalent systems we employ molecular dynamics (MD) on systems containing 500 atoms, in the NVT ensemble using LAMMPS [107] with the temperature maintained using Nosé–Hoover thermostats [108,109]. Isochores are obtained over a range of volumes and temperatures within the stability limit of the potential model as discussed in [110]. Typically systems are equilibrated for t∼2 ns with production runs of t∼2.5 ns.…”

“…We analyse the thermodynamic state space adjacent to the liquid–vapour stability limit using longer production runs of t∼150 ns and with increased temperature and volume sampling [2]. At state points for which dynamical arrest was observed on the simulation time-scale replica exchange molecular dynamics (REMD) [111,112] were employed to enable a more complete exploration of the disordered state configurational space and as described in [110]. The thermodynamic data are analysed using the NumPy and SciPy packages [113] and the anomalies and related properties are identified as described in [110].…”

“…At state points for which dynamical arrest was observed on the simulation time-scale replica exchange molecular dynamics (REMD) [ 111 , 112 ] were employed to enable a more complete exploration of the disordered state configurational space and as described in [ 110 ]. The thermodynamic data are analysed using the NumPy and SciPy packages [ 113 ] and the anomalies and related properties are identified as described in [ 110 ]. Note that the liquid–vapour stability limits are identified by isolating the lowest pressure point on an isotherm for each temperature which gives an upper bound estimate of the liquid–vapour spinodal line.…”