Work functions and sublimation entropies of the elements

A phenomenological relationship between the work functions and the sublimation probabilities is shown to hold for most of the solid electron-conducting elements at the same vapor pressure. According to this relationship, the sublimation probabilityf increases exponentially with decreasing work functionW, i.e.,f∝exp(−W/W _o), whereW _o=0.60 eV. On the basis of a direct evaporation model, it follows that the work function is directly proportional to the sublimation entropy. This connection between two quantities, which seemingly refer to either electrons or atoms, respectively, is explained by expressing the sublimation entropy as the difference between the entropies of the gas and solid phases in equilibrium, and by deriving implications on the material properties contained in these individual entropies. The work function can thus be related to the second derivative of the crystal energy with respect to the atomic radius, which is corroborated by a universal relation between the work functions and the compressibilities for over 60 elements. For elements with a simple electron structure, the second derivative of the energy-atomic-radius dependence is essentially determined by a truly electronic property, namely the Fermi energy. It is shown that the Fermi energy variation is accompanied by a sufficient variation of the electron affinity in order to account for the appropriate work function change. For elements with a more complicated electron structure, a case-by-case study of the second derivative of the energy-atomic-radius dependence is required.