Phase Transformation Contributions to Heat Capacity and Impact on Thermal Diffusivity, Thermal Conductivity, and Thermoelectric Performance
Abstract
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 pφ 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 Kmore »
- Authors:
-
- Department of Materials Science and Engineering Northwestern University Evanston IL 60208
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1530905
- Grant/Contract Number:
- DE‐SC0001299/DE‐FG02‐09ER46577
- Resource Type:
- Publisher's Accepted Manuscript
- Journal Name:
- Advanced Materials
- Additional Journal Information:
- Journal Name: Advanced Materials Journal Volume: 31 Journal Issue: 35; Journal ID: ISSN 0935-9648
- Publisher:
- Wiley Blackwell (John Wiley & Sons)
- Country of Publication:
- Germany
- Language:
- English
Citation Formats
Agne, Matthias T., Voorhees, Peter W., and Snyder, G. Jeffrey. Phase Transformation Contributions to Heat Capacity and Impact on Thermal Diffusivity, Thermal Conductivity, and Thermoelectric Performance. Germany: N. p., 2019.
Web. doi:10.1002/adma.201902980.
Agne, Matthias T., Voorhees, Peter W., & Snyder, G. Jeffrey. Phase Transformation Contributions to Heat Capacity and Impact on Thermal Diffusivity, Thermal Conductivity, and Thermoelectric Performance. Germany. https://doi.org/10.1002/adma.201902980
Agne, Matthias T., Voorhees, Peter W., and Snyder, G. Jeffrey. Wed .
"Phase Transformation Contributions to Heat Capacity and Impact on Thermal Diffusivity, Thermal Conductivity, and Thermoelectric Performance". Germany. https://doi.org/10.1002/adma.201902980.
@article{osti_1530905,
title = {Phase Transformation Contributions to Heat Capacity and Impact on Thermal Diffusivity, Thermal Conductivity, and Thermoelectric Performance},
author = {Agne, Matthias T. and Voorhees, Peter W. and Snyder, G. Jeffrey},
abstractNote = {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 pφ 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 .},
doi = {10.1002/adma.201902980},
journal = {Advanced Materials},
number = 35,
volume = 31,
place = {Germany},
year = {2019},
month = {7}
}
https://doi.org/10.1002/adma.201902980
Web of Science
Works referenced in this record:
Is Cu 3 SbSe 3 a promising thermoelectric material?
journal, January 2015
- Wei, Tian-Ran; Wu, Chao-Feng; Sun, Wei
- RSC Advances, Vol. 5, Issue 53
Transport Properties of Bulk Thermoelectrics: An International Round-Robin Study, Part II: Thermal Diffusivity, Specific Heat, and Thermal Conductivity
journal, March 2013
- Wang, Hsin; Porter, Wallace D.; Böttner, Harald
- Journal of Electronic Materials, Vol. 42, Issue 6
Order–Disorder Transition in AgCrSe 2 : a New Route to Efficient Thermoelectrics
journal, May 2011
- Gascoin, Franck; Maignan, Antoine
- Chemistry of Materials, Vol. 23, Issue 10
Towards the high-throughput synthesis of bulk materials: thermoelectric PbTe–PbSe–SnTe–SnSe alloys
journal, January 2019
- Ortiz, Brenden R.; Adamczyk, Jesse M.; Gordiz, Kiarash
- Molecular Systems Design & Engineering, Vol. 4, Issue 2
Thermoelectric properties of p-type polycrystalline SnSe doped with Ag
journal, January 2014
- Chen, Cheng-Lung; Wang, Heng; Chen, Yang-Yuan
- Journal of Materials Chemistry A, Vol. 2, Issue 29, p. 11171-11176
Phase separation as a key to a thermoelectric high efficiency
journal, January 2013
- Schwall, Michael; Balke, Benjamin
- Phys. Chem. Chem. Phys., Vol. 15, Issue 6
State of the art Ag50-Sb Se50-Te alloys: Their high zT values, microstructures and related phase equilibria
journal, July 2015
- Wu, Hsin-jay; Lan, Tian-Wey; Chen, Sinn-wen
- Acta Materialia, Vol. 93
Thermophysical Properties of Solid Phase Zirconium at High Temperatures
journal, July 2006
- Milošević, N. D.; Maglić, K. D.
- International Journal of Thermophysics, Vol. 27, Issue 4
Complex thermoelectric materials
journal, February 2008
- Snyder, G. Jeffrey; Toberer, Eric S.
- Nature Materials, Vol. 7, Issue 2, p. 105-114
Phase Transitions of Thermoelectric TAGS-85
journal, November 2017
- Kumar, Anil; Vermeulen, Paul A.; Kooi, Bart J.
- Inorganic Chemistry, Vol. 56, Issue 24
Enhancing p-Type Thermoelectric Performances of Polycrystalline SnSe via Tuning Phase Transition Temperature
journal, July 2017
- Lee, Yong Kyu; Ahn, Kyunghan; Cha, Joonil
- Journal of the American Chemical Society, Vol. 139, Issue 31
Measuring thermoelectric transport properties of materials
journal, January 2015
- Borup, Kasper A.; de Boor, Johannes; Wang, Heng
- Energy & Environmental Science, Vol. 8, Issue 2
Lower limit to the thermal conductivity of disordered crystals
journal, September 1992
- Cahill, David G.; Watson, S. K.; Pohl, R. O.
- Physical Review B, Vol. 46, Issue 10, p. 6131-6140
Multi-scale architectured thermoelectric materials in the Mg2(Si,Sn) system
journal, March 2016
- Gorsse, S.; Vivès, S.; Bellanger, P.
- Materials Letters, Vol. 166
Charge-Compensated Compound Defects in Ga-containing Thermoelectric Skutterudites
journal, February 2013
- Qiu, Yuting; Xi, Lili; Shi, Xun
- Advanced Functional Materials, Vol. 23, Issue 25
High ZT in p-Type (PbTe) 1–2 x (PbSe) x (PbS) x Thermoelectric Materials
journal, February 2014
- Korkosz, Rachel J.; Chasapis, Thomas C.; Lo, Shih-han
- Journal of the American Chemical Society, Vol. 136, Issue 8
Phonon anharmonicity and negative thermal expansion in SnSe
journal, August 2016
- Bansal, Dipanshu; Hong, Jiawang; Li, Chen W.
- Physical Review B, Vol. 94, Issue 5
Thermal Conductivity during Phase Transitions
journal, December 2018
- Chen, Hongyi; Yue, Zhongmou; Ren, Dudi
- Advanced Materials
Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals
journal, April 2014
- Zhao, Li-Dong; Lo, Shih-Han; Zhang, Yongsheng
- Nature, Vol. 508, Issue 7496, p. 373-377
A Phenomenological Model of Unconventional Heat Transport Induced by Phase Transition in Cu2−xSe
journal, December 2018
- Vasilevskiy, D.; Masut, R. A.; Turenne, S.
- Journal of Electronic Materials, Vol. 48, Issue 4
Advanced two-channel ac calorimeter for simultaneous measurements of complex heat capacity and complex thermal conductivity
journal, June 2003
- Minakov, A. A.; Adamovsky, S. A.; Schick, C.
- Thermochimica Acta, Vol. 403, Issue 1
Reduced thermal conductivity in Pb-alloyed AgSbTe2 thermoelectric materials
journal, October 2012
- Wu, Hsin-jay; Chen, Sinn-wen; Ikeda, Teruyuki
- Acta Materialia, Vol. 60, Issue 17
High performance thermoelectric materials and devices based on GeTe
journal, January 2016
- Perumal, Suresh; Roychowdhury, Subhajit; Biswas, Kanishka
- Journal of Materials Chemistry C, Vol. 4, Issue 32
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
- Xiao, Yu; Wu, Haijun; Wang, Dongyang
- Advanced Energy Materials, Vol. 9, Issue 17
The thermoelectric performance of anisotropic SnSe doped with Na
journal, January 2016
- Leng, Hua-Qian; Zhou, Min; Zhao, Jie
- RSC Advances, Vol. 6, Issue 11
Elastic properties, thermal stability, and thermodynamic parameters of MoAlB
journal, April 2017
- Kota, Sankalp; Agne, Matthias; Zapata-Solvas, Eugenio
- Physical Review B, Vol. 95, Issue 14
Self-Tuning the Carrier Concentration of PbTe/Ag2Te Composites with Excess Ag for High Thermoelectric Performance
journal, February 2011
- Pei, Yanzhong; May, Andrew F.; Snyder, G. Jeffrey
- Advanced Energy Materials, Vol. 1, Issue 2
Thermoelectric Figure-of-Merit of Fully Dense Single-Crystalline SnSe
journal, March 2019
- Wei, Pai-Chun; Bhattacharya, Sriparna; Liu, Yu-Fei
- ACS Omega, Vol. 4, Issue 3
Assessment of the thermoelectric performance of polycrystalline p-type SnSe
journal, May 2014
- Sassi, S.; Candolfi, C.; Vaney, J.-B.
- Applied Physics Letters, Vol. 104, Issue 21, Article No. 212105
Low-Temperature Structural Transitions in the Phonon-Glass Thermoelectric Material β-Zn 4 Sb 3 : Ordering of Zn Interstitials and Defects
journal, February 2007
- Nylén, Johanna; Lidin, Sven; Andersson, Magnus
- Chemistry of Materials, Vol. 19, Issue 4
Characterization of Lorenz number with Seebeck coefficient measurement
journal, April 2015
- Kim, Hyun-Sik; Gibbs, Zachary M.; Tang, Yinglu
- APL Materials, Vol. 3, Issue 4
Minimum thermal conductivity in the context of diffuson -mediated thermal transport
journal, January 2018
- Agne, Matthias T.; Hanus, Riley; Snyder, G. Jeffrey
- Energy & Environmental Science, Vol. 11, Issue 3
Phase transition enhanced thermoelectric figure-of-merit in copper chalcogenides
journal, November 2013
- Brown, David R.; Day, Tristan; Borup, Kasper A.
- APL Materials, Vol. 1, Issue 5
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
- Samanta, Manisha; Biswas, Kanishka
- Journal of the American Chemical Society, Vol. 139, Issue 27
Impact of Ni content on the thermoelectric properties of half-Heusler TiNiSn
journal, January 2018
- Tang, Yinglu; Li, Xiaoshuang; Martin, Lukas H. J.
- Energy & Environmental Science, Vol. 11, Issue 2
Phase diagram investigation and proposition of a thermodynamic evaluation of the Tin-Selenium system
journal, January 1996
- Feutelais, Y.; Majid, M.; Legendre, B.
- Journal of Phase Equilibria, Vol. 17, Issue 1
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
- Vasilevskiy, D.; Keshavarz, M. K.; Simard, J. -M.
- Journal of Electronic Materials, Vol. 47, Issue 6
3D charge and 2D phonon transports leading to high out-of-plane ZT in n-type SnSe crystals
journal, May 2018
- Chang, Cheng; Wu, Minghui; He, Dongsheng
- Science, Vol. 360, Issue 6390
Peierls distortion as a route to high thermoelectric performance in In4Se3-δ crystals
journal, June 2009
- Rhyee, Jong-Soo; Lee, Kyu Hyoung; Lee, Sang Mock
- Nature, Vol. 459, Issue 7249
Relating phase transition heat capacity to thermal conductivity and effusivity in Cu 2 Se
journal, July 2016
- Brown, David R.; Heijl, Richard; Borup, Kasper A.
- physica status solidi (RRL) - Rapid Research Letters, Vol. 10, Issue 8
Comparative Study of the Thermoelectric Properties of Amorphous Zn 41 Sb 59 and Crystalline Zn 4 Sb 3
journal, January 2009
- Wu, Yang; Nylén, Johanna; Naseyowma, Craig
- Chemistry of Materials, Vol. 21, Issue 1
Apparent critical phenomena in the superionic phase transition of Cu 2- x Se
journal, January 2016
- Kang, Stephen Dongmin; Danilkin, Sergey A.; Aydemir, Umut
- New Journal of Physics, Vol. 18, Issue 1
Temperature dependent solubility of Yb in Yb–CoSb3 skutterudite and its effect on preparation, optimization and lifetime of thermoelectrics
journal, March 2015
- Tang, Yinglu; Chen, Sinn-wen; Snyder, G. Jeffrey
- Journal of Materiomics, Vol. 1, Issue 1
Ultrahigh Thermoelectric Performance by Electron and Phonon Critical Scattering in Cu 2 Se 1-x I x
journal, September 2013
- Liu, Huili; Yuan, Xun; Lu, Ping
- Advanced Materials, Vol. 25, Issue 45
Effect of disorder on the thermal transport and elastic properties in thermoelectric
journal, October 2006
- Bhattacharya, S.; Hermann, R. P.; Keppens, V.
- Physical Review B, Vol. 74, Issue 13
The updated Zn–Sb phase diagram. How to make pure Zn 13 Sb 10 (“Zn 4 Sb 3 ”).
journal, January 2018
- Lo, Chun-Wan Timothy; Svitlyk, Volodymyr; Chernyshov, Dmitry
- Dalton Transactions, Vol. 47, Issue 33
Chemical composition tuning in quaternary p-type Pb-chalcogenides – a promising strategy for enhanced thermoelectric performance
journal, January 2014
- Yamini, Sima Aminorroaya; Wang, Heng; Gibbs, Zachary M.
- Phys. Chem. Chem. Phys., Vol. 16, Issue 5
Recent Developments in Experimental Methods for Heat-Capacity Measurements
journal, January 1976
- Takashi, Yoichi
- Pure and Applied Chemistry, Vol. 47, Issue 4
Nanoscale Behavior and Manipulation of the Phase Transition in Single-Crystal Cu 2 Se
journal, November 2018
- Chen, Lu; Liu, Jun; Jiang, Chao
- Advanced Materials, Vol. 31, Issue 4
Reactivity, stability and thermoelectric properties of n-Bi2Te3 doped with different copper amounts
journal, October 2014
- Lognoné, Quentin; Gascoin, Franck
- Journal of Alloys and Compounds, Vol. 610
Enhanced thermoelectric performance in the very low thermal conductivity Ag 2 Se 0.5 Te 0.5
journal, September 2013
- Drymiotis, Fivos; Day, Tristan W.; Brown, David R.
- Applied Physics Letters, Vol. 103, Issue 14
Broad temperature plateau for high ZTs in heavily doped p-type SnSe single crystals
journal, January 2016
- Peng, Kunling; Lu, Xu; Zhan, Heng
- Energy & Environmental Science, Vol. 9, Issue 2
Heat capacity of Mg3Sb2, Mg3Bi2, and their alloys at high temperature
journal, August 2018
- Agne, Matthias T.; Imasato, Kazuki; Anand, Shashwat
- Materials Today Physics, Vol. 6
New insight into InSb-based thermoelectric materials: from a divorced eutectic design to a remarkably high thermoelectric performance
journal, January 2017
- Cheng, Yudong; Yang, Junyou; Jiang, Qinghui
- Journal of Materials Chemistry A, Vol. 5, Issue 10
Studies on Thermoelectric Properties of n-type Polycrystalline SnSe 1- x S x by Iodine Doping
journal, April 2015
- Zhang, Qian; Chere, Eyob Kebede; Sun, Jingying
- Advanced Energy Materials, Vol. 5, Issue 12
Ultrahigh power factor and thermoelectric performance in hole-doped single-crystal SnSe
journal, November 2015
- Zhao, L.-D.; Tan, G.; Hao, S.
- Science, Vol. 351, Issue 6269, p. 141-144
Rational design of p-type thermoelectric PbTe: temperature dependent sodium solubility
journal, January 2013
- Yamini, Sima Aminorroaya; Ikeda, Teruyuki; Lalonde, Aaron
- Journal of Materials Chemistry A, Vol. 1, Issue 31