# Theory of metal surface field evaporation

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## Description

This work addresses the effects of intense positive electric fields applied to two metal surfaces. In particular, the outward shifting of the surface layer in response to the fields, the redistribution of electronic charge within the metal initiated by the fields, and prediction of the minimum field strength which will produce evaporation of the surface monolayer of positive charge and attendant electrons are investigated Density functional theory, a powerful method of treating the inhomogeneous electron gas, is the theoretical approach taken in this work. Its utility and success within the local density approximation have been proven for many systems, diverse in size and nature, including the metal surface. By positioning the surface monolayer at a particular separation measured along the surface normal and calculating the surface energy from the semi-self-consistent electronic density generated via the Schrodinger equation with a one-electron effective potential, and repeating the procedure for other separations, an energy-displacement curve for a particular applied field can be mapped. A minimum in the curve for fields less than the least required for field evaporation locates the equilibrium position of the surface layer. The minimum will just disappear for the critical field. In this way, the critical field for the uniform positive-background-charge metal, herein named sodium-jellium (NaJ), is found to be 1.8 V/(ANGSTROM); that for Al (lll) is found to be 4.5 V/(ANGSTROM) The zero-field energies for both metals are found to map onto a curve obtained from a universal binding energy expression. This expression, which scales according to two parameters which can be related to known empirical quantities, is extended by a simple method to predict the critical fields for surface layer evaporation of a range of metals. Comparison is made of the predicted values with experimentally available critical fields for field evaporating atoms/ions singly from rounded metallic samples. The predicted values are higher than experiment by less than a factor of two. A discussion of the results is included