Adiabatic and Non-Adiabatic Contributions to the Free Energy from the Electron-Phonon Interaction for Na, K, Al, and Pb

Abstract

We calculate the adiabatic contributions to the free energy due to the electron--phonon interaction at intermediate temperatures, $0⩽k_{B}T<{\epsilon }_F$ for the elemental metals Na, K, Al, and Pb. Using our previously published results for the nonadiabatic contributions we show that the adiabatic contribution, which is proportional to $T^2$ at low temperatures and goes as $T^3$ at high temperatures, dominates the nonadiabatic contribution for temperatures above a cross--over temperature, $T_c$, which is between 0.5 and 0.8 $T_m$, where $T_m$ is the melting temperature of the metal. The nonadiabatic contribution falls as $T^{-1}$ for temperatures roughly above the average phonon frequency.

Updated version

References in corpus (1)

• Non--Adiabatic Contributions to the Free Energy from the Electron--Phonon Interaction for Na, K, Al, and Pb

Cited by in corpus (4)

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