Roles of Mass, Structure, and Bond Strength in the Phonon Properties and Lattice Anharmonicity of Single-Layer Mo and W Dichalcogenides

Abstract

A hierarchical first-principles study has been performed to reveal the roles of mass, structure, and atomic bond strength in phonon spectra, phonon anharmonicity, thermal expansion, and thermomechanics of single-layer Mo and W dichalcogenides (MX2, X = S, Se, and Te). The strength of the M–X bond is determined by the competition between ionicity and covalency and increases (decreases) with increasing the cation (anion) nucleon number. The total mass and cation–anion mass ratio isotopically influence phonon frequencies. The twofold lattice dimensionality renders the bending ZA mode with parabolic dispersion and negative Grüneisen constant (γ). While nonorthogonal bonds lead to interdirection vibrational hybridizations, which increases γZA but decreases γTA and γLA. The minima of γTA and γLA decrease with decreasing bond strength and become negative in MTe2. MX2 always has a negative thermal expansion at low temperatures (T < 50 K) due to the advanced excitation of those low negative-γ ZA modes. At higher temperatures, the excitation of other positive-γ modes results in positive thermal expansion. Additionally, thermal expansion is determined jointly by lattice stiffness, phonon excitation, and phonon anharmonicity. The contributions of these involved factors are quantitatively disentangled here, and their relationships with mass, structure, and bond strength are revealed. The softening of the bulk modulus of MX2 under heating is mainly caused by thermal expansion, which is partially canceled by the stiffening effect from phonon excitation. Both bulk modulus and its thermal softening rate decrease with anion nucleon number, due to the decrease in bond strength and bond-strength anharmonicity, respectively.