Parameter-free model to estimate thermal conductivity in nanostructured materials

Abstract

Achieving low thermal conductivity and good electrical properties is a crucial condition for thermal energy harvesting materials. Nanostructuring offers a very powerful tool to address both requirements: in nanostructured materials, boundaries preferentially scatter phonons compared to electrons. The computational screening for low-thermal-conductivity nanostructures is typically limited to materials with simple crystal structures, such as silicon, because of the complexity arising from modeling branch- and wave-vector-dependent nanoscale heat transport. The phonon mean-free-path (MFP) dependent Boltzmann transport equation (MFP-BTE) approach is a model that overcomes this limitation. To illustrate this, we analyze thermal transport in 75 nanoporous half-Heusler compounds for different pore sizes. Our calculations demonstrate that, in most cases, the optimization of thermal transport in nanostructures should take into account both bulk thermal properties and geometry-dependent size effects, two aspects that are typically engineered separately. To enable efficient calculations within this paradigm we derive a model, based on the ``gray'' formulation of the BTE, that can decouple the influence of the geometry and the material on the effective thermal conductivity with relatively little loss in accuracy compared to the MFP-BTE. Our study motivates the need for a holistic approach to engineering thermal transport and provides a method for high-throughput low-thermal conductivity materials discovery.