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

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.