# Lorenz number calculator (SPB model)

Published: 12 July 2019| Version 1 | DOI: 10.17632/frb4543dyy.1
Contributors:
Artur Kosonowski,
Taras Parashchuk

## Description

This spreadsheet allows quick calculation of the Lorenz number from Seebeck coefficient using fermi integrals and fitting of reduced Fermi energy (assuming single parabolic band model). After entering the Seebeck coefficient values this spreadsheet will automatically calculate the Lorenz number. Spreadsheet is divided into 5 parts: Step 1, Step 2, ... Step 5 so one can observe how applied methodology works in detail. Step 1 - Fermi integral values obtained from widely available tables were put into graphs and polynomials were fitted. Step 2 - Information about the assumed value of the scattering parameter. Step 3 - The relation between the Seebeck coefficient and the reduced Fermi energy was calculated, the result was put into the graph and polynomial was fitted. Step 4 - Experimental values of the Seebeck coefficient for a given temperature should be copied here (orange background). Please note that using this methodology calculated Lorenz number will be larger than 2.45·10^(-8) (V/K)^2 if the absolute value of Seebeck coefficient will be smaller than ~57 microV/K. Step 5 - Lorenz number is calculated (red background). The result is accurate for materials with scattering parameter r = -1/2 (for acoustic phonon scattering) and if the band could be described by single parabolic band model.
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