On the Calculation of Lorenz Numbers for Complex Thermoelectric Materials

TL;DR

This paper presents a first-principles method for calculating Lorenz numbers in complex thermoelectric materials, emphasizing the importance of accurate band structures and scattering models to identify low Lorenz numbers that can enhance thermoelectric efficiency.

Contribution

It introduces a general computational approach for Lorenz number calculation that accounts for detailed electronic structures and scattering mechanisms, improving upon previous simplified models.

Findings

Lorenz numbers below 2(kB/q)^2 can occur in non-degenerate limits

Accurate band structures and energy-dependent scattering times are crucial

Low Lorenz numbers are linked to the shape of the transport distribution

Abstract

A first-principles informed approach to the calculation of Lorenz numbers for complex thermoelectric materials is presented and discussed. Example calculations illustrate the importance of using accurate band structures and energy-dependent scattering times. Results obtained by assuming that the scattering rate follows the density-of-states show that in the non-degenerate limit, Lorenz numbers below the commonly assumed lower limit of 2(kB/q)^2 can occur. The physical cause of low Lorenz numbers is explained by the shape of the transport distribution. The numerical and physical issues that need to be addressed in order to produce accurate calculations of the Lorenz number are identified. The results of this study provide a general method that should contribute to the interpretation of measurements of total thermal conductivity and to the search for materials with low Lorenz numbers, which may provide improved thermoelectric figures of merit, zT.