Elastic properties of multicomponent crystals in neutron stars and white dwarfs

Elastic properties play an important role in neutron stars and white dwarfs. They are crucial for modeling stellar oscillations and different processes in magnetars and in degenerate stars which enter compact binary systems. Using electrostatic energy of deformed lattices, we calculate elastic moduli of ordered binary body-centered cubic (sc2) and face-centered cubic (fc2) lattices. We use two methods to determine the effective shear modulus $\mu_{\rm eff}$. We show that $\mu_{\rm eff}$ calculated as a Voigt average agrees with the results obtained from the linear mixing rule. For the sc2 lattice, our calculations are also consistent with the results of numerical simulations of disordered binary body-centered cubic lattice.