Beyond the point defect limit: solid solutions, phase diagrams and trace-element partitioning

Traditionally disorder in solid oxides has largely been investigated theoretically via classical point defect theory; such methods are not readily extended to solid solutions, liquid phases or grossly non-stoichiometric compounds. In this paper we show how Monte Carlo simulations in the semigrand canonical ensemble, which include the explicit interchange of cations and use configurational bias techniques, are an attractive method for situations involving finite and even high concentrations of defects or foreign atoms. We illustrate our approach with two examples involving CaO: (i) the phase diagram for the system CaO–MgO is calculated for both solid and liquid phases. All the characteristic features are reproduced, including the eutectic point and the regions of liquid–solid coexistence; (ii) the first direct calculation of trace-element partitioning between solid and melt phases. Our techniques take full account of local structural distortion and clustering due to the mismatch between the sizes of the cations involved.