Calcite–magnesite solid solutions: using genetic algorithms to understand non-ideality

Abstract

We show how a genetic algorithm (GA) generates efficiently the energy landscape of the equimolar calcite–magnesite (CaCO3—MgCO3) solid solution. Starting from a random configuration of cations and a supercell containing 480 atoms, the lowest energy form of ordered dolomite was found in all runs, in 94% of which it was located with less than 20,000 fitness evaluations. Practical implementation and operation of the GA are discussed in detail. The method can also generate both low-lying and high-lying excited states. Detailed analysis of the energy-minimised structures of the different configurations reveals that low energies are associated with reduction of strain associated with rotation of the carbonate groups, a mechanism possible only when a carbonate layer lies between a layer of just Ca and a layer of just Mg. Such strain relief is not possible in the equimolar MgO–CaO solid solution despite the similarity of the crystal structures of these binary oxides to calcite–magnesite, and therefore, the enthalpy of mixing is very high. Implications for thermodynamic configurational averaging over the minima in the energy landscape are briefly considered. Overall, the genetic algorithm is shown to be a powerful tool in probing non-ideality in solid solutions and revealing the ordering patterns that give rise to such behaviour.