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 (MX 2 , X = S, Se, and Te). The strength of 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 two-fold lattice dimensionality renders the bending ZA mode having parabolic dispersion and negative Grüneisen constant (γ). While nonorthogonal bonds lead to inter-direction vibrational hybridizations, which increases γ ZA , but decreases γ T A and γ LA . The minima of γ T A and γ LA decrease with decreasing bond strength, and become negative in MTe 2 . MX 2 always has a negative thermal expansion at low temperatures (T< 50K), 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 MX 2 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.

Tunable Negative Thermal Expansion in Layered Perovskites from Quasi-Two-Dimensional Vibrations

“…1, left panel): The lowest acoustic branch along the Γ-X path (i.e., [ξ, 0, 0] path, ξ ∈ [0, 1 2 ]) exhibits a quadratic dispersion. Similar quadratic acoustic modes are ubiquitous in 2D materials [16,17], which have an important phonon mode with largely Z character that is referred to as the ZA mode. The ZA mode in such 2D materials resembles a bending vibration on a contin-uum membrane or guitar string, and tensile strain can stiffen this bending vibration [9,16], resulting in a negative Grüneisen parameter (γ − ) of the ZA mode that is responsible for the NTE reported in 2D materials.…”

“…In this Letter, we propose and computationally demonstrate a quasi-two dimensional (quasi-2D) mechanism for NTE in layered RP oxides, utilizing our recently implemented self-consistent quasiharmonic approximation (SC-QHA) method to treat the lattice anharmonicity within a density functional theory (DFT) framework. In the prototypical layered ferroelectric, Ca 3 Ti 2 O 7 (CTO), we discover a quasi-2D vibrational mode in the polar phase by discerning an acoustic branch with a quadratic dispersion, which appears in the intensely studied 2D materials, e.g., graphene and MoS 2 [16,17]. The quasi-2D vibration resembles the bending vibration on a 2D membrane; we show this feature results in various extraordinary membrane effects in CTO, including negative mode Grüneisen parameters (γ − ) and the enlargement of γ − by hydrostatic pressure.…”

“…2(a,c)]. Such positive sign and large value of γ + at the Γ point both originate from the softness (low ν) of the quadratic ZA mode: Indeed, first there is a stretching of the weak interlayer bonds induced by the ZA mode, and it has been found that bond stretching has a positive contribution to γ [9,17], which becomes important when the ZA mode is soft enough and results in a positive γ despite a quasi-2D quadratic phonon mode dispersion being retained; second, a soft mode always has a high sensitivity to an external perturbation, e.g., volume compression explored below, resulting in the large value of γ + (ZA). Along the Γ-S path (S: [ Along the Γ-X path, ν(ZA) increases and approaches other acoustic and optical modes at higher frequencies [ Fig.…”

“…2(d) and (e), respectively. In contrast to the ZA mode in 2D materials, which have large negative γ (i.e., γ − ) at the Γ point [16,17], the quasi-2D ZA mode in CTO exhibits a large positive γ (γ + ) at the Γ point, and a γ + → γ − transition only occurs when approaching the X point [ Fig. 2(a,c)].…”

“…Guided by this understanding, we calculated the properties of Ca 3 Zr 2 O 7 and Sr 3 Zr 2 O 7 which exhibit the same polar Cmc2 1 phase [5] and find larger quasi-2D NTEs appearing at lower pressures [ Fig. 4(d,e)], because the metal-oxygen bond weakening from Zr and Sr substitutions promotes quasi-2D NTE [17,22]. Additional lattice dynamical and thermodynamic properties are provided in Ref.…”