Calcite as polar biomineral with a tendency for glass formation

Calcite, $\mathrm{CaC}{\mathrm{O}}_{3}$, is a widely available biomaterial with remarkable properties. Its twin walls (TWs), formed during growth or deformation, show intriguing properties including a strong polarization. While calcite has no macroscopic dipole moment (by symmetry) the TWs show a big shift in the distance between $\mathrm{C}{\mathrm{a}}^{2+}$ and ${\mathrm{CO}}_{3}{}^{2\ensuremath{-}}$ resulting in dipole moments (polarization) estimated at $0.22\phantom{\rule{0.28em}{0ex}}\mathrm{C}/{\mathrm{m}}^{2}$. Such strong dipole moments have a substantial influence on the diffusion of atoms inside twin boundaries. Furthermore, deformation will also generate simple kinks inside the TWs. These kinks lead to local clusters of amorphized $\mathrm{CaC}{\mathrm{O}}_{3}$. Stressed calcite, in devices or in the natural environment, will be riddled with such kinks, which explains the tendency to form locally amorphized materials. The structural particularities of calcite originate from a sequence of phase transitions, thermal or by growth, from a cubic phase to a rhombohedral phase with $R\overline{3}m$ symmetry to the $R\overline{3}c$ phase known at room temperature. Symmetry aspects of these transitions are discussed. The complexity of the TW structure arises from both the odd-even effect at the twin boundary in the rhombohedral structure and the coupling between two order parameters in the phase transitions of calcite. The coupling scheme is linear quadratic and is discussed in detail.