(10.4), (01.8), (01.2), and (00.1) Twin Laws of Calcite (CaCO₃): Equilibrium Geometry of the Twin Boundary Interfaces and Twinning Energy

Abstract

The “Four Twin Laws of Calcite”, expressed by their twin planes (10.4, 01.8, 01.2 and 0.01, hexagonal frame) have been investigated in order to assess the structure of the interfaces between twinned individuals. Athermal twinning and adhesion energies were evaluated by calculations using empirical potential functions: the relaxed interfaces were modeled to minimize the surface energy. To this end, different configurations of the twin interfaces have been considered when surface reconstructions were needed to cancel out the surface dipole moment, which is intrinsic to the ideal interfaces of both the (00.1) and (01.2) twins. Calculation shows that (i) the (00.1) twin law is the most likely to occur, and (ii) the minimum of the twinning energy is obtained if the twin operation is a diad axis perpendicular to the (00.1) interface. Finally, it has been demonstrated that the (00.1) twins are the only ones that can be generated by a 2D heterogeneous nucleation mechanism, while the 3D (either homogeneous or heterogeneous) nucleation is the dominating mechanism for the other twins.