12 - Electrons: the free electron model

Summary

Introduction

In the last two chapters we explored the behavior of phonons in a crystal. There we saw how these discrete, quantized pieces of propagating energy contributed to both the specific heat and thermal conductivity of the solid. Here we turn our attention to crystalline metals whose metallic bonding results in the formation of a sea of mobile electrons present within the crystal. Like phonons, these mobile electrons carry around energy and consequently contribute to the specific heat. But they also carry around charge and so contribute also to the electrical conductivity of the metal.

In this chapter, we begin with a simplistic model of the mobile electrons as quantum mechanical waves trapped within an infinite square well potential. This model is known as the free electron model because the interaction of the electron with the ion cores of the metal lattice is disregarded. The electron is only trapped by the confines of the crystal itself. Although this simple model is unable to capture all the experimental features of conduction in metals, it readily accounts for the smallness of the electron contribution to the specific heat and does provide a simple interpretation of such electron emission phenomena as the photoelectric effect.