Lattice energies and polarizabilities of lanthanide gallium garnets (Ln3Ga5O12)

Lattice energies ΔLHθ of lanthanide gallium garnets Ln3Ga5O12 (Ln = Nd–Lu) have been determined from the Born–Haber thermochemical cycle and compared with those previously obtained by atomistic simulations in the Born model or calculated by an empirical equation. The Born–Haber cycle yields the lowest values among the three methods. Molar polarizations Pm of Ln3Ga5O12 have been calculated by the Debye equation. It has been found that the partial derivative (∂ΔLHθ/∂Pm) corresponds by magnitude to the shear moduli of these crystals.

► The lattice energies ΔLHθ of Ln3Ga5O12 are determined by the Born–Haber cycle.
► The Born–Haber cycle yields the lowest values among three applied methods.
► Molar polarizations Pm of Ln3Ga5O12 have been calculated by the Debye equation.
► The derivative (∂ΔLHθ/∂Pm) corresponds to the shear moduli of these crystals.