Lorenz number calculator (SPB model)

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.

本电子表格可借助费米积分（Fermi integral）和约化费米能（reduced Fermi energy）拟合，基于单抛物线能带模型（single parabolic band model），从塞贝克系数（Seebeck coefficient）快速计算洛伦兹数（Lorenz number）。输入塞贝克系数数值后，该表格将自动完成洛伦兹数的计算。
本电子表格共分为5个模块：步骤1至步骤5，便于使用者详细观察所采用方法的具体运作流程。
步骤1：将从通用公开表格中获取的费米积分值绘制成图表，并拟合得到多项式表达式。
步骤2：展示所假设的散射参数（scattering parameter）相关信息。
步骤3：计算塞贝克系数与约化费米能之间的关系，将结果绘制成图表并拟合得到多项式表达式。
步骤4：将指定温度下的塞贝克系数实验值复制粘贴至橙色背景单元格中。需注意：当塞贝克系数的绝对值小于约57 μV/K时，本方法计算得到的洛伦兹数将大于2.45×10^(-8) (V/K)²。
步骤5：完成洛伦兹数的计算（结果位于红色背景单元格中）。本计算结果仅适用于散射参数r=-1/2（对应声学声子散射（acoustic phonon scattering））且能带可通过单抛物线能带模型描述的材料。