Phase Transformation Contributions to Heat Capacity and Impact on Thermal Diffusivity, Thermal Conductivity, and Thermoelectric Performance.

Abstract

The accurate characterization of thermal conductivity κ, particularly at high temperature, is of paramount importance to many materials, thermoelectrics in particular. The ease and access of thermal diffusivity D measurements allows for the calculation of κ when the volumetric heat capacity, ρc_p , of the material is known. However, in the relation κ = ρc_p D, there is some confusion as to what value of c_p should be used in materials undergoing phase transformations. Herein, it is demonstrated that the Dulong-Petit estimate of c_p at high temperature is not appropriate for materials having phase transformations with kinetic timescales relevant to thermal transport. In these materials, there is an additional capacity to store heat in the material through the enthalpy of transformation ΔH. This can be described using a generalized model for the total heat capacity for a material [Formula: see text] where φ is an order parameter that describes how much latent heat responds "instantly" to temperature changes. Here, C_pφ is the intrinsic heat capacity (e.g., approximately the Dulong-Petit heat capacity at high temperature). It is shown experimentally in Zn₄ Sb₃ that the decrease in D through the phase transition at 250 K is fully accounted for by the increase in c_p , while κ changes smoothly through the phase transition. Consequently, reports of κ dropping near phase transitions in widely studied materials such as PbTe and SnSe have likely overlooked the effects of excess heat capacity and overestimated the thermoelectric efficiency, zT.