Comparison of liquid-state anomalies in Stillinger-Weber models of water, silicon, and germanium

We use molecular dynamics simulations to compare and contrast the liquid-state anomalies in the Stillinger-Weber models of monatomic water (mW), silicon (Si), and germanium (Ge) over a fairly wide range of temperatures and densities. The relationships between structure, entropy, and mobility, as well as the extent of the regions of anomalous behavior, are discussed as a function of the degree of tetrahedrality. We map out the cascade of density, structural, pair entropy, excess entropy, viscosity, and diffusivity anomalies for these three liquids. Among the three liquids studied here, only mW displays anomalies in the thermal conductivity, and this anomaly is evident only at very low temperatures. Diffusivity and viscosity, on the other hand, show pronounced anomalous regions for the three liquids. The temperature of maximum density of the three liquids shows re-entrant behavior consistent with either singularity-free or liquid-liquid critical point scenarios proposed to explain thermodynamic anomalies. The order-map, which shows the evolution of translational versus tetrahedral order in liquids, is different for Ge than for Si and mW. We find that although the monatomic water reproduces several thermodynamic and dynamic properties of rigid-body water models (e.g., SPC/E, TIP4P/2005), its sequence of anomalies follows, the same as Si and Ge, the silica-like hierarchy: the region of dynamic (diffusivity and viscosity) anomalies encloses the region of structural anomalies, which in turn encloses the region of density anomaly. The hierarchy of the anomalies based on excess entropy and Rosenfeld scaling, on the other hand, reverses the order of the structural and dynamic anomalies, i.e., predicts that the three Stillinger-Weber liquids follow a water-like hierarchy of anomalies. We investigate the scaling of diffusivity, viscosity, and thermal conductivity with the excess entropy of the liquid and find that for dynamical properties that present anomalies there is no universal scaling of the reduced property with excess entropy for the whole range of temperatures and densities. Instead, Rosenfeld's scaling holds for all the three liquids at high densities and high temperatures, although deviations from simple exponential dependence are observed for diffusivity and viscosity at lower temperatures and intermediate densities. The slope of the scaling of transport properties obtained for Ge is comparable to that obtained for simple liquids, suggesting that this low tetrahedrality liquid, although it stabilizes a diamond crystal, is already close to simple liquid behavior for certain properties.