Equilibrium, stability, and density anomalies in a lattice model with core-softening and directional bonding

The cluster-variation method has been used to investigate the phase behavior, thermal expansion characteristics, and stability limits of the Bell-Meijer lattice model; the model includes directional bonding and second neighbor repulsion. Both of these mechanisms are in principle capable of stabilizing open ground states and can therefore give rise to negative thermal expansion. A canonical implementation of the natural iteration solution technique facilitated the calculation of metastable states and stability limits. The four types of phase behavior previously found by Van Royen and Meijer³⁴ have been mapped as a function of the relative strength of the second neighbor repulsion and the bonding interaction over a wide range of parameter space. One of the types of phase behavior is water-like: it exhibits expansion upon freezing. As the strength of the bonding interaction increases, so does the range of second neighbor repulsion within which expansion upon freezing occurs. Density anomalies appear as a low-temperature locus of density minima that merges with a higher-temperature locus of density maxima. Of the two, density minima are the more prevalent feature, always spanning a greater range of pressure. Density maxima disappear at low enough values of the second neighbor repulsion. The peculiar features of thermal expansion in this model bear little relation to the known behavior in water, heavy water, and silica, and they persist throughout the wide range of parameter space explored. An undesirable feature of the Bell-Meijer model is that bonding only contributes to long-range orientational order and not to ground-state stability.