High-pressure elastic anisotropy and superconductivity of hafnium: A first-principles calculation*

Abstract

The elastic anisotropy and superconductivity upon hydrostatic compression of α, ω, and β Hf are investigated using first-principle methods. The results of elastic anisotropies show that they increase with increasing pressure for α and ω phases, while decrease upon compression for β phase. The calculated superconducting transition temperatures are in excellent agreement with experiments. Electron–phonon coupling constants (λ) are increasing with pressure for α and ω phases, while decreasing for β phase. For β phase, the large values of λ are mainly due to the obvious TA1 soft mode. Under further compression, the TA1 soft vibrational mode will disappear gradually.

Systematic Study on Electronic, Mechanical, and Thermal Transport Properties of Germanium Antimony Selenide Telluride Alloy by a First-Principles Approach

“…The larger Young’s modulus usually corresponds to better stiffness, showing less susceptibility to deformation, while the larger shear modulus can lead to superb resistance to shear stress. Therefore, layered Ge 2 Sb 2 Se 4 Te presents much better immunity to shear strain and deformation along the x -axis and y -axis than those along the z -axis . The Poisson’s ratio can be used to predict the character of the chemical bonding.…”

“…Therefore, layered Ge 2 Sb 2 Se 4 Te presents much better immunity to shear strain and deformation along the x-axis and y-axis than those along the z-axis. 44 The Poisson's ratio can be used to predict the character of the chemical bonding. The typical value of Poisson's ratio is about 0.5 for a pure-ionic limit, whereas it is about 0.3∼0.4 for ionic materials and 0.2∼0.3 for ioniccovalent materials, respectively.…”

Intercalation-dependent elastic properties of transition metal dichalcogenides

“…1 The degree of anisotropy can play an important role in fabrication and electrode cycling, inlfuencing plastic deformation, mircoscale cracking, and defect mobility. 3,88 We can evaluate the extent of this anisotropy using a universal elastic anisotropy index, A U , using the Voigt and Reuss moduli discussed above, 89 This takes a minimal value of zero when the single crystal is locally isotropic. Departure from this minimal value gives a measure of the single crystal anisotropy, accounting for both the shear and bulk contributions.…”

“…1 The degree of anisotropy can play an important role in fabrication and electrode cycling, inlfuencing plastic deformation, mircoscale cracking, and defect mobility. 3,88 We can evaluate the extent of this anisotropy using a universal elastic anisotropy index, A U , using the Voigt and Reuss moduli discussed above, 89…”