Unusual elasticity of monoclinic $β−Ga2O3$

This paper determines all the 13 elastic constants C_ij of monoclinic β-Ga₂O₃, which has never been achieved since the discovery of this crystal about 100 years ago. We used resonant ultrasound spectroscopy with laser-Doppler interferometry, where the resonant-mode identification was unambiguously made by comparing measured and calculated displacement distributions on the vibrating specimen surface. Using more than 110 resonance frequencies, we inversely determined the C_ij: C₁₁ = 242.8 ± 2.9, C₂₂ = 343.8 ± 3.8, C₃₃ = 347.4 ± 2.5, C₄₄ = 47.8 ± 0.2, C₅₅ = 88.6 ± 0.5, C₆₆ = 104.0 ± 0.5, C₁₂ = 128 ± 0.1, C₁₃ = 160 ± 1.5, C₂₃ = 70.9 ± 2.1, C₁₅ = –1.62 ± 0.05, C₂₅ = 0.36 ± 0.01, C₃₅ = 0.97 ± 0.03, and C₄₆ = 5.59 ± 0.69 GPa. We also performed a density-functional-theory calculation and found that the local density approximation yields both the lattice parameters and C_ij closer to the measurements than the generalized gradient approximation. Strong elastic-stiffness anisotropy is found in the diagonal elastic constants: C₁₁ is smaller than C₂₂ and C₃₃ by ∼30%, and the difference between C₄₄ and C₆₆ exceeds 50%. Our measurements also reveal anomalous Poisson's ratios: ν₂₁ and ν₃₁ exceed 0.5, and ν₂₃ and ν₃₂ are almost zero. We explain these unusual elastic properties with the truss-like deformation of the tetrahedra-octahedra network and confirm this view with the ab- initio calculation.