Elastic constants, Poisson ratios, and the elastic anisotropy of VN(001), (011), and (111) epitaxial layers grown by reactive magnetron sputter deposition

Elastic constants are determined for single-crystal stoichiometric NaCl-structure VN(001), VN(011), and VN(111) epitaxial layers grown by magnetically unbalanced reactive magnetron sputter deposition on 001-, 011-, and 111-oriented MgO substrates at 430 °C. The relaxed lattice parameter a _o = 0.4134 ± 0.0004 nm, obtained from high-resolution reciprocal space maps, and the mass density ρ = 6.1 g/cm³, determined from the combination of Rutherford backscattering spectroscopy and film thickness measurements, of the VN layers are both in good agreement with reported values for bulk crystals. Sub-picosecond ultrasonic optical pump/probe techniques are used to generate and detect VN longitudinal sound waves with measured velocities v₀₀₁ = 9.8 ± 0.3, v₀₁₁ = 9.1 ± 0.3, and v₁₁₁ = 9.1 ± 0.3 km/s. The VN c₁₁ elastic constant is determined from the sound wave velocity measurements as 585 ± 30 GPa; the c₄₄ elastic constant, 126 ± 3 GPa, is obtained from surface acoustic wave measurements. From the combination of c ₁₁, c₄₄, v_hkl, and ρ we obtain the VN c₁₂ elastic constant 178 ± 33 GPa, the VN elastic anisotropy A = 0.62, the isotropic Poisson ratio ν = 0.29, and the anisotropic Poisson ratios ν₀₀₁ = 0.23, ν₀₁₁ = 0.30, and ν₁₁₁ = 0.29.