Origins of thermal conductivity changes in strained crystals

Abstract

The strain-dependent phonon properties and thermal conductivities of a soft system [Lennard-Jones (LJ) argon] and a stiff system (silicon modeled using first-principles calculations) are predicted using lattice dynamics calculations and the Boltzmann transport equation. As is commonly assumed for materials under isotropic strain, the thermal conductivity of LJ argon decreases monotonically as the system moves from compression into tension. The reduction in thermal conductivity is attributed to decreases in both the phonon lifetimes and group velocities. The thermal conductivity of silicon, however, is constant in compression and only begins to decrease once the system is put in tension. The silicon lifetimes show an anomalous behavior, whereby they increase as the system moves from compression into tension, which is explained by examining the potential energy surface felt by an atom. The results emphasize the need to separately consider the harmonic and anharmonic effects of strain on material stiffness, phonon properties, and thermal conductivity.

Effect of exchange–correlation on first-principles-driven lattice thermal conductivity predictions of crystalline silicon

“…Parrish et al [9] predicted a thermal conductivity of 151 W/m K using an iterative solution of the BTE, the LDA XC based NC pseudopotential, and a 80 Ry planewave energy cutoff with a 6 Â 6 Â 6 electronic wavevector grid. This value is an overestimate of our converged value by 5% due to an insufficient electronic wavevector grid.…”

“…DFT-driven calculations have been successfully used to predict the experimentally-measured thermal conductivities of materials ranging from simple semiconductors such as silicon [2] and diamond [5] to compound semiconductors [4], graphene [6], and SiGe alloys [3]. DFT-driven calculations have also been used to study the effects of strain and isotopes on the thermal conductivity of semiconductors [7][8][9] and to predict the thermal conductivity of novel two-dimensional materials [6,10,11].…”

Resolving anomalous strain effects on two-dimensional phonon flows: The cases of graphene, boron nitride, and planar superlattices

“…Nevertheless, as the strain increases, the nature of the flow changes from ballistic-dominant towards diffusive-dominant. Although it is difficult to determine the precise physical mechanism underpinning the decrease of Kn, it is feasible that it arises from the softening of bonds when tensile strain is applied (discussed later), which can introduce inter-phonon scattering and reduce mean free paths 12,24 .…”

“…[10][11] Conventional wisdom based on what is known about bulk 3D materials supports the idea that in general tensile strains soften phonon modes, depress group velocities, and decrease relaxation times. 12 Additionally, even before strain is imposed, decomposition of κ into modal contributions suggests that the ZA modes contribute to (and may even be dominant contributors to) κ. However many of these studies have been carried out for single, finite-sized samples and the length-dependence of the reported trends is not clear.…”

The origin of the distinction between microscopic formulas for stress and Cauchy stress

“…12 It is a measure of the intensity of internal forces, has a clear physical origin, is the actual physical quantity measured in experiments, and is applicable on all scales. Atomistic stress formulas, on the other hand, were derived from classical or quantum mechanics as a function of the forces and positions of atoms, and is what have been used in ab initio calculations 13 as an intrinsic property of the quantummechanical ground state of matter, or in classical molecular dynamics or coarse-grained atomistic simulations to predict strength 14 , fracture toughness 15,16 , hardness 17 , or to quantify the effect of local stress on ferroelectricity 18 , thermal conductivity 19,20 , phase transition 21,22 , etc. There are numerous computational efforts that have attempted to understand the difference between various atomistic formulas for local stress and that between atomistic stress and Cauchy stress 8-11, 19, 23-25 .…”