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

Matthias T. Agne*, Peter W Voorhees, Gerald Jeffrey Snyder

*Corresponding author for this work

Research output: Contribution to journalArticle

5 Scopus citations


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 pc p = C + ∆H (∂φ/ ∂T )p where φ is an order parameter that describes how much latent heat responds “instantly” to temperature changes. Here, C 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.

Original languageEnglish (US)
Article number1902980
JournalAdvanced Materials
Issue number35
StatePublished - Jan 1 2019



  • heat capacity
  • phase transition
  • thermal conductivity
  • thermal diffusivity
  • thermal fluctuations
  • thermoelectric

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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