Lattice model calculation of the strain energy density and other properties of crystalline LiCoO2

The strain energy densities for various crystalline planes of ${\mathrm{LiCoO}}_{\mathrm{2}}$ were calculated from the stiffness tensors obtained from lattice model calculations using the program GULP. In addition to Coulomb and Buckingham potentials, it was necessary to include shell models for the oxygen and cobalt ions in order to obtain acceptable agreement between the observed and calculated structural parameters and high frequency dielectric constant. The strain energy densities $u$ due to differential thermal expansion were calculated using the theoretical stiffness tensors and estimated values for the thermal expansion coefficients of ${\mathrm{LiCoO}}_{\mathrm{2}}.$ For a temperature change of 675 $°\mathrm{C},$ these ranged from 0.5 to ${\text{1.3×10}}^8\hspace{0.17em}{\mathrm{erg/cm}}^{\mathrm{3}}$ or 5 to $\text{13\hspace{0.17em}}{\mathrm{J/m}}^{\mathrm{2}}$ for 1-μm-thick films on alumina substrates. In particular, the energies for the (003), (101), and (104) planes were ordered as $\text{u(003)≫u(104)>u(101).}$ This suggests that the strong (101) preferred orientation of ${\mathrm{LiCoO}}_{\mathrm{2}}$ films $\text{(⩾1\hspace{0.17em}μ}\mathrm{m}$ thick) is due to the tendency to minimize volume strain energy that arises from differential thermal expansion between the film and the substrate. Additional properties obtained from the GULP calculations include the free energy, heat capacity, and the $\text{k=0}$ vibrational modes.