DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Journal Article · · Advanced Materials

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 Δ H . This can be described using a generalized model for the total heat capacity for a material 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 Zn 4 Sb 3 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 .

Sponsoring Organization:
USDOE
Grant/Contract Number:
DE‐SC0001299/DE‐FG02‐09ER46577
OSTI ID:
1530905
Journal Information:
Advanced Materials, Journal Name: Advanced Materials Vol. 31 Journal Issue: 35; ISSN 0935-9648
Publisher:
Wiley Blackwell (John Wiley & Sons)Copyright Statement
Country of Publication:
Germany
Language:
English

References (57)

Is Cu 3 SbSe 3 a promising thermoelectric material? journal January 2015
Transport Properties of Bulk Thermoelectrics: An International Round-Robin Study, Part II: Thermal Diffusivity, Specific Heat, and Thermal Conductivity journal March 2013
Order–Disorder Transition in AgCrSe 2 : a New Route to Efficient Thermoelectrics journal May 2011
Towards the high-throughput synthesis of bulk materials: thermoelectric PbTe–PbSe–SnTe–SnSe alloys journal January 2019
Thermoelectric properties of p-type polycrystalline SnSe doped with Ag journal January 2014
Phase separation as a key to a thermoelectric high efficiency journal January 2013
State of the art Ag50-Sb Se50-Te alloys: Their high zT values, microstructures and related phase equilibria journal July 2015
Thermophysical Properties of Solid Phase Zirconium at High Temperatures journal July 2006
Complex thermoelectric materials journal February 2008
Phase Transitions of Thermoelectric TAGS-85 journal November 2017
Enhancing p-Type Thermoelectric Performances of Polycrystalline SnSe via Tuning Phase Transition Temperature journal July 2017
Measuring thermoelectric transport properties of materials journal January 2015
Lower limit to the thermal conductivity of disordered crystals journal September 1992
Multi-scale architectured thermoelectric materials in the Mg2(Si,Sn) system journal March 2016
Charge-Compensated Compound Defects in Ga-containing Thermoelectric Skutterudites journal February 2013
High ZT in p-Type (PbTe) 1–2 x (PbSe) x (PbS) x Thermoelectric Materials journal February 2014
Phonon anharmonicity and negative thermal expansion in SnSe journal August 2016
Thermal Conductivity during Phase Transitions journal December 2018
Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals journal April 2014
A Phenomenological Model of Unconventional Heat Transport Induced by Phase Transition in Cu2−xSe journal December 2018
Advanced two-channel ac calorimeter for simultaneous measurements of complex heat capacity and complex thermal conductivity journal June 2003
Reduced thermal conductivity in Pb-alloyed AgSbTe2 thermoelectric materials journal October 2012
High performance thermoelectric materials and devices based on GeTe journal January 2016
Amphoteric Indium Enables Carrier Engineering to Enhance the Power Factor and Thermoelectric Performance in n ‐Type Ag n Pb 100 In n Te 100+2 n (LIST) journal March 2019
The thermoelectric performance of anisotropic SnSe doped with Na journal January 2016
Elastic properties, thermal stability, and thermodynamic parameters of MoAlB journal April 2017
Self-Tuning the Carrier Concentration of PbTe/Ag2Te Composites with Excess Ag for High Thermoelectric Performance journal February 2011
Thermoelectric Figure-of-Merit of Fully Dense Single-Crystalline SnSe journal March 2019
Assessment of the thermoelectric performance of polycrystalline p-type SnSe journal May 2014
Low-Temperature Structural Transitions in the Phonon-Glass Thermoelectric Material β-Zn 4 Sb 3 :  Ordering of Zn Interstitials and Defects journal February 2007
Characterization of Lorenz number with Seebeck coefficient measurement journal April 2015
Minimum thermal conductivity in the context of diffuson -mediated thermal transport journal January 2018
Phase transition enhanced thermoelectric figure-of-merit in copper chalcogenides journal November 2013
Low Thermal Conductivity and High Thermoelectric Performance in (GeTe) 1–2 x (GeSe) x (GeS) x : Competition between Solid Solution and Phase Separation journal June 2017
Impact of Ni content on the thermoelectric properties of half-Heusler TiNiSn journal January 2018
Phase diagram investigation and proposition of a thermodynamic evaluation of the Tin-Selenium system journal January 1996
Assessing the Thermal Conductivity of Cu2−xSe Alloys Undergoing a Phase Transition via the Simultaneous Measurement of Thermoelectric Parameters by a Harman-Based Setup journal January 2018
3D charge and 2D phonon transports leading to high out-of-plane ZT in n-type SnSe crystals journal May 2018
Peierls distortion as a route to high thermoelectric performance in In4Se3-δ crystals journal June 2009
Relating phase transition heat capacity to thermal conductivity and effusivity in Cu 2 Se journal July 2016
Comparative Study of the Thermoelectric Properties of Amorphous Zn 41 Sb 59 and Crystalline Zn 4 Sb 3 journal January 2009
Apparent critical phenomena in the superionic phase transition of Cu 2- x Se journal January 2016
Temperature dependent solubility of Yb in Yb–CoSb3 skutterudite and its effect on preparation, optimization and lifetime of thermoelectrics journal March 2015
Ultrahigh Thermoelectric Performance by Electron and Phonon Critical Scattering in Cu 2 Se 1-x I x journal September 2013
Effect of disorder on the thermal transport and elastic properties in thermoelectric Zn 4 Sb 3 journal October 2006
The updated Zn–Sb phase diagram. How to make pure Zn 13 Sb 10 (“Zn 4 Sb 3 ”). journal January 2018
Chemical composition tuning in quaternary p-type Pb-chalcogenides – a promising strategy for enhanced thermoelectric performance journal January 2014
Recent Developments in Experimental Methods for Heat-Capacity Measurements journal January 1976
Nanoscale Behavior and Manipulation of the Phase Transition in Single-Crystal Cu 2 Se journal November 2018
Reactivity, stability and thermoelectric properties of n-Bi2Te3 doped with different copper amounts journal October 2014
Enhanced thermoelectric performance in the very low thermal conductivity Ag 2 Se 0.5 Te 0.5 journal September 2013
Broad temperature plateau for high ZTs in heavily doped p-type SnSe single crystals journal January 2016
Heat capacity of Mg3Sb2, Mg3Bi2, and their alloys at high temperature journal August 2018
New insight into InSb-based thermoelectric materials: from a divorced eutectic design to a remarkably high thermoelectric performance journal January 2017
Studies on Thermoelectric Properties of n-type Polycrystalline SnSe 1- x S x by Iodine Doping journal April 2015
Ultrahigh power factor and thermoelectric performance in hole-doped single-crystal SnSe journal November 2015
Rational design of p-type thermoelectric PbTe: temperature dependent sodium solubility journal January 2013