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

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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.

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Acknowledgements

NLA is grateful for valuable discussions with Victor Vinograd which prompted this work. This work was, in part, performed on the Abel Cluster, owned by the University of Oslo and the Norwegian metacenter for High Performance Computing (NOTUR), and operated by the Department for Research Computing at the University of Oslo IT-department. CM acknowledges support from the Research Council of Norway through its Centres of Excellence funding scheme, project number 223272.

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Authors and Affiliations

  1. School of Chemistry, University of Bristol, Cantock’s Close, Bristol, BS8 1TS, UK

    N. L. Allan & L. Thomas

  2. School of Materials Science and Engineering, UNSW Sydney, NSW, 2052, Australia

    J. N. Hart

  3. Department of Materials Science, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

    C. L. Freeman

  4. Centre for Earth Evolution and Dynamics, University of Oslo, P.O. Box 1048, Blindern, 0316, Oslo, Norway

    C. E. Mohn

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  1. N. L. Allan
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Correspondence to C. E. Mohn.

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Allan, N.L., Thomas, L., Hart, J.N. et al. Calcite–magnesite solid solutions: using genetic algorithms to understand non-ideality. Phys Chem Minerals 46, 193–202 (2019). https://doi.org/10.1007/s00269-018-0997-3

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