The Work Function for Electrons in Metals

A well-known property of metals is their ability to carry an electrical current by means of the movement of the electronic cloud associated with the metal atoms. Most metals are solids at room temperature and only a few, such as mercury, are liquid. Because of their importance in the design of electrochemical cells, their electronic properties are considered here in some detail. 

The work function is defined as the minimum work required to withdraw an electron from a metal under the conditions that the metallic phase bears no net charge. On the basis of the earlier discussion, one may write 

When the electrochemical approach to describing the work function (equation (8.5.1)) is compared to the physical approach (equation (8.5.3)), the following relationships are obtained. The chemical potential of the electron is related to bulk properties so that 

In the same way, the surface potential energy is related to the surface potential 

In order to determine the electronic work function the metal must be ultrapure with no contamination on the surface. The biggest problem in this regard is the fact that most metals have a surface oxide layer under ambient conditions. A clean metallic surface can be formed by sputtering the metal in a vacuum chamber, and techniques are available for growing thin metal films of known crystallographic orientation. Otherwise, the metal surface may be cleaned by positive ion bombardment techniques at very low pressures. Values of the electronic work function for polycrystalline metal surfaces are summarized in table 8.2. The lowest 

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