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

• Published in: Advanced materials (Weinheim) Vol. 31; no. 35; pp. e1902980 - n/a
• Main Authors: Agne, Matthias T., Voorhees, Peter W., Snyder, G. Jeffrey
• Format: Journal Article
• Language: English
• Published: Germany Wiley Subscription Services, Inc 01.08.2019; Wiley Blackwell (John Wiley & Sons)
• Subjects: Diffusivity; Enthalpy; heat capacity; Heat conductivity; Heat transfer; High temperature; Latent heat; Materials science; Order parameters; phase transition; Phase transitions; Specific heat; Thermal conductivity; Thermal diffusivity; thermal fluctuations; Thermodynamic properties; thermoelectric; Thermoelectricity; Zinc antimonides; heat capacity; thermoelectric; phase transition; thermal fluctuations; thermal conductivity; thermal diffusivity
• ISSN: 0935-9648; 1521-4095
• DOI: 10.1002/adma.201902980

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, ρcp, of the material is known. However, in the relation κ = ρcpD, there is some confusion as to what value of cp should be used in materials undergoing phase transformations. Herein, it is demonstrated that the Dulong–Petit estimate of cp 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 ρcp  =  Cpϕ  +  ΔH (∂ϕ​/​∂T)p where φ is an order parameter that describes how much latent heat responds “instantly” to temperature changes. Here, Cpφ is the intrinsic heat capacity (e.g., approximately the Dulong–Petit heat capacity at high temperature). It is shown experimentally in Zn4Sb3 that the decrease in D through the phase transition at 250 K is fully accounted for by the increase in cp, 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. Estimates of thermal conductivity from thermal diffusivity measurements are likely underestimated when latent heat contributions to the heat capacity are not considered. Latent heat effects are especially important when phase‐transformation kinetics are fast relative to the timescale of thermal transport. The importance of these effects in material measurements is highlighted, particularly for the estimation of thermoelectric efficiency.