The derivation of a new expression for the free area function for translation of absorbed particles in the study of the surface physics of thermionic diode electrodes. A relatively new theory involves direct energy conversion through utilization of thermionic emission of electrons from a hot metal. This Memorandum studies the surface effects that control emission rates in a totally different way. Using a digital computer, the surface migrations of particles absorbed on a surface are simulated. The simulation incorporates relevant geometrical and energetic considerations as realistically as possible, and calculates the free area for translation by a Monte Carlo process. When the resulting expression for free area is used in calculations, a substantial improvement can be seen in the agreement between predicted and measured emission rates. 89 pp. Ref.