The shape of liquid miscibility gaps and short-range-order

The observed “flattened” shape of liquid miscibility gaps in binary alloys is not easily reproduced by a simple Gibbs energy equation involving a random-mixing Bragg–Williams (BW) expression for the configurational entropy and a polynomial expansion of the excess Gibbs energy since short-range-ordering (SRO) is not taken into account. It is shown that accounting for the SRO through a simple application of the modified quasi-chemical model (MQM) in the nearest-neighbour pair approximation is sufficient to provide a good representation of miscibility gaps using only a very few temperature-independent coefficients. For the many systems in which the only data available are the miscibility gap boundaries at lower temperatures, the MQM can therefore provide a good prediction of the gap boundaries at higher temperatures, as well as of the excess enthalpy. Furthermore, the MQM provides a significantly better prediction of the miscibility gap in a ternary system based only upon optimized model parameters of its three binary sub-systems than does the BW polynomial model. For binary systems in which deviations from ideal behaviour are not too large, it is shown that the MQM can be approximated by one additional term in the polynomial BW expression involving no additional empirical coefficients.

► Miscibility gaps calculated thermodynamically are generally too high and rounded.
► This is due to the neglect of short-range ordering.
► A simple quasichemical model in the pair approximation is sufficient to remedy this.
► This also yields better approximations of ternary gaps from binary parameters.
► Binary quasichemical equations can be approximated by an additional polynomial term.