Elastic and breaking properties of epitaxial face-centered crystals in neutron star crusts and white dwarf cores

Crystallization of dense matter in neutron star crusts and white dwarf cores may be similar to epitaxial crystal growth in terrestrial laboratories. However, in stellar crystals, the spacing between horizontal planes has to gradually increase with the outward movement of the crystallization front, tracing decrease of the electron density. This process produces Coulomb crystals with stretched rather than cubic elementary cells. We extend the analysis of the elastic and breaking properties of such crystals to the face-centered (fc) lattice. Shear deformations orthogonal to the stretch direction have been studied for 22 crystallographic shear planes. A common property for all these planes is the reduction and eventual nulling of the breaking shear strain with deviation from the unstretched configuration. The effective shear moduli for deformations orthogonal to the stretch direction have been calculated. It is possible that the epitaxial crystallization in compact stars results in a formation of large-scale crystallites or, at least, in growth of the whole crystallization front perpendicular to particular crystallographic planes. For fc structure growth orthogonal to the $\left\{111\right\}$ planes, we expect that, at any density, $\sim 5\%$ ($\sim 0.5\%$) of crystallite height is occupied by layers one (two) orders of magnitude weaker than the bulk of the crystallite. This may be important for realistic modeling of crustquakes on neutron stars.