Theoretical Calculation of the Electronic Thermal Expansion of Simple Metals

Abstract

At low temperatures the excitation of conduction electrons in metals gives rise to an electronic contribution $\mathrm{C=\Gamma ̃T}$ to the heat capacity, and also a contribution β∝T to the thermal expansion coefficient, where T is the absolute temperature. The electronic Grüneisen parameter is $\mathrm{\gamma =V\beta B/C=(d\hspace{0.17em}}\ln \mathrm{\Gamma ̃/d\hspace{0.17em}}\ln \mathrm{V)}$ , where V and B are the crystal volume and bulk modulus, respectively, at T=0. We have used a local pseudopotential model to calculate all the contributions to Γ̃ and its volume derivative, including the electron‐phonon interactions in first‐order perturbation. The calculated γ is 1.18 for Na, 1.01 for K, and 1.63 for Al, while the measured γ is 1.8 for Al. The free electron model predicts γ=⅔. From our calculations it appears that the Umklapp interactions of electrons with transverse phonons give important contributions to Γ̃.