## This content will become publicly available on February 8, 2020

## Lorenz number in relation to estimates based on the Seebeck coefficient

## Abstract

Separation of thermal conductivity (k) into its electronic, lattice and other parts is of great importance in understanding heat transport. Commonly, the Wiedemanne–Franz relation is used to obtain the electronic thermal conductivity based on the electrical conductivity and a Lorenz number that is either set to the standard value for metals or using an approximate formula based on the Seebeck coefficient. We used the Boltzmann transport theory to test this formula for realistic electronic structures of thermoelectrics in different scattering regimes. Here, we find that this expression can give values of the Lorenz number that differ infstantially from Boltzmann theory for the range of doping levels important in thermoelectrics. This happens for materials with complex non-parabolic band structures, which are common in high performance thermoelectrics. The results imply that caution should be exercised in the use of this formula in thermoelectrics and other materials that may have complex electronic structures.

- Authors:

- Univ. of Missouri, Columbia, MO (United States). Dept. of Physics and Astronomy

- Publication Date:

- Research Org.:
- Univ. of Missouri, Columbia, MO (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

- OSTI Identifier:
- 1497393

- Grant/Contract Number:
- SC0019114

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Materials Today Physics

- Additional Journal Information:
- Journal Volume: 8; Journal Issue: C; Journal ID: ISSN 2542-5293

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 30 DIRECT ENERGY CONVERSION; Thermoelectric; Thermal Conductivity; Electronic thermal conductivity; Lorenz number; Boltzmann transport theory; First principles calculations

### Citation Formats

```
Putatunda, A., and Singh, D. J. Lorenz number in relation to estimates based on the Seebeck coefficient. United States: N. p., 2019.
Web. doi:10.1016/j.mtphys.2019.01.001.
```

```
Putatunda, A., & Singh, D. J. Lorenz number in relation to estimates based on the Seebeck coefficient. United States. doi:10.1016/j.mtphys.2019.01.001.
```

```
Putatunda, A., and Singh, D. J. Fri .
"Lorenz number in relation to estimates based on the Seebeck coefficient". United States. doi:10.1016/j.mtphys.2019.01.001.
```

```
@article{osti_1497393,
```

title = {Lorenz number in relation to estimates based on the Seebeck coefficient},

author = {Putatunda, A. and Singh, D. J.},

abstractNote = {Separation of thermal conductivity (k) into its electronic, lattice and other parts is of great importance in understanding heat transport. Commonly, the Wiedemanne–Franz relation is used to obtain the electronic thermal conductivity based on the electrical conductivity and a Lorenz number that is either set to the standard value for metals or using an approximate formula based on the Seebeck coefficient. We used the Boltzmann transport theory to test this formula for realistic electronic structures of thermoelectrics in different scattering regimes. Here, we find that this expression can give values of the Lorenz number that differ infstantially from Boltzmann theory for the range of doping levels important in thermoelectrics. This happens for materials with complex non-parabolic band structures, which are common in high performance thermoelectrics. The results imply that caution should be exercised in the use of this formula in thermoelectrics and other materials that may have complex electronic structures.},

doi = {10.1016/j.mtphys.2019.01.001},

journal = {Materials Today Physics},

number = C,

volume = 8,

place = {United States},

year = {2019},

month = {2}

}