Quantum-Mechanical Study of Single-Crystalline and Polycrystalline Elastic Properties of Mg-Substituted Calcite Crystals

We use quantum-mechanical calculations to study single-crystalline elastic properties of (Ca,Mg)CO3 crystals with concentrations ranging from calcite CaCO3 to magnesite MgCO3. By analyzing results for a dense set of distributions of Ca and Mg atoms within 30-atom supercells, our theoretical study shows that those atomic configurations, that minimize the total energy for a given concentration, are characterized by elastic constants that either increase with the Mg content or remain nearly constants. Employing these ab initio calculated single-crystalline elastic parameters, the polycrystalline elastic properties of (Ca,Mg)CO3 aggregates are determined using a mean-field self-consistent homogenization method. The computed integral elastic moduli (bulk and shear) show a significant stiffening impact of Mg atoms on calcite crystals. Our analysis also demonstrates that it is not advantageous to use a granular two-phase composite of stoichiometric calcite and magnesite instead of substituting individual Ca and Mg atoms. Such two-phase aggregates are not significantly thermodynamically favorable and do not offer any strong additional stiffening effect.