SUMMARY
The complete set of independent second- and third-order elastic constants of rare-earth hexaborides LaB 6 and CeB 6 are determined by the combination method of first-principles calculations and homogeneous deformation theory. The ground-state lattice parameters, second-order elastic constants, and bulk modulus are in reasonable agreement with the available experimental data. The third-order elastic constant of longitudinal mode C 111 has a larger absolute value than other shear modes, showing the contribution to lattice vibrations from longitudinal modes to be greater. The pressure derivatives of the second-order elastic constants related to the third-order elastic constants are calculated to be positive for the two hexaborides, which are consistent with those of their polycrystalline bulk modulus and shear modulus. Furthermore, the effect of pressure on the structural stability, mechanical property, and elastic anisotropy of the two hexaborides are investigated, showing a reduction in mechanical stability and an increase in ductility and anisotropy with increasing pressure.