Variation in electron work function with temperature and its effect on the Young's modulus of metals

TL;DR

This paper proposes a model linking the electron work function of metals to temperature and demonstrates its application in understanding how Young's modulus varies with temperature, aligning well with experimental data.

Contribution

A simple temperature-dependent model of the electron work function is introduced, connecting electronic properties to mechanical behavior in metals.

Findings

The model accurately predicts the temperature dependence of Young's modulus.

The work function decreases with temperature following the proposed quadratic relation.

The relationship aligns with experimental observations across different metals.

Abstract

Properties of metals are fundamentally determined by their electron behavior, which is largely reflected by the electron work function ($\varphi $). Recent studies have demonstrated that many properties of metallic materials are directly related to $\varphi $, which may provide a simple but fundamental parameter for material design. Since material properties are affected by temperature, in this article a simple model is proposed to correlate the work function with temperature, expressed as $\varphi (T)=\varphi_{0} -\gamma \frac{(k_{B} T)^{2}}{\varphi_{0}} $, where $\gamma $ varies with the crystal structure. This $\varphi $-T relationship helps determine and understand the dependence of metal properties on temperature on a feasible electronic base. As a sample application, the established relationship is applied to determine the dependence of Young's modulus of metals on temperature. The proposed relationship is consistent with experimental observations.