Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

Abstract

Using density-functional perturbation theory and the Grüneisen formalism, we directly calculate the linear thermal expansion coefficients (TECs) of a hexagonal bulk system MoS2 in the crystallographic a and c directions. The TEC calculation depends critically on the evaluation of a temperature-dependent quantity Ii(T ), which is the integral of the product of heat capacity and Γi(ν), of frequency ν and strain type i, where Γi(ν) is the phonon density of states weighted by the Grüneisen parameters. We show that to determine the linear TECs we may use minimally two uniaxial strains in the z direction, and either the x or y direction. However, a uniaxial strain in either the x or y direction drastically reduces the symmetry of the crystal from a hexagonal one to a base-centered orthorhombic one. We propose to use an efficient and accurate symmetry-preserving biaxial strain in the xy plane to derive the same result for Γ(ν). We highlight that the Grüneisen parameter associated with a biaxial strain may not be the same as the average of Grüneisen parameters associated with two separate uniaxial strains in the x and y directions due to possible preservation of degeneracies of the phonon modes under a biaxial deformation. Large anisotropy of TECs is observed where the linear TEC in the c direction is about 1.8 times larger than that in the a or b direction at high temperatures. Our theoretical TEC results are compared with experiment. The symmetry-preserving approach adopted here may be applied to a broad class of two lattice-parameter systems such as hexagonal, trigonal, and tetragonal systems, which allows many complicated systems to be treated on a first-principles level.

Raman Fingerprint of Pressure-Induced Phase Transitions in TiS3 Nanoribbons: Implications for Thermal Measurements under Extreme Stress Conditions

“…GPa 37 , and considering our experimental mode Grüneisen parameters, the linear thermal expansion along the c-axis at 300 K is estimated as  = 1.321  10 -6 K -1 , which is found to be of the same order of magnitude as the one reported in MoS2 53 .…”

Thermal Expansion Coefficient of Monolayer Molybdenum Disulfide Using Micro-Raman Spectroscopy

“…(2) Most 2D materials are optically transparent, which makes it difficult to measure the TEC using conventional optical approaches. 15 Accordingly, current understanding of the TEC for 2D materials relies on either pure theoretical calculations 16,17 or more recently, combining experimental characterization (such as electron energy-loss (EEL) spectroscopy 18 ) with first-principle modeling which still depends on the choice of ab initio simulation methods. 12,[16][17][18] In addition, Bao et al characterized the TEC of a graphene membrane using scanning electron microscope, which utilized graphene's negative TEC to create a sagging membrane on a trench and finite element simulation to estimate the TEC of the trench.…”

“…15 Accordingly, current understanding of the TEC for 2D materials relies on either pure theoretical calculations 16,17 or more recently, combining experimental characterization (such as electron energy-loss (EEL) spectroscopy 18 ) with first-principle modeling which still depends on the choice of ab initio simulation methods. 12,[16][17][18] In addition, Bao et al characterized the TEC of a graphene membrane using scanning electron microscope, which utilized graphene's negative TEC to create a sagging membrane on a trench and finite element simulation to estimate the TEC of the trench. 19 In this work, we propose a method that experimentally determines the TEC for 2D materials in which the only necessary input is the lattice symmetry group.…”

“…[6][7][8] Many theoretical results of MoS 2 are also available to validate our approach. 16,17 We theoretically analyzed a temperature and stress dependent Raman spectrum of monolayer MoS 2 through the phonon deformation potential and group theory, which describes the effect of substrates on the supported 2D flakes. This unified theoretical framework was then used to decouple the thermal stress, in-plane and out-of-plane thermal expansion effect and guide the TEC measurement.…”

Phonon scattering processes in molybdenum disulfide

“…14,29,30 However, in 2H- MoS 2 , the thermal expansion coefficient was reported to be 10 À5 to 10 À6 in magnitudes. 31 The small thermal expansion coefficient brings about little contribution to the change in the frequency and thus can be neglected. The observed change in Raman spectra with temperature is mainly governed by the anharmonic potential.…”