Vapor—Solid Interactions and the Effusion Oven. I. The Total Effusion Current through a Cylindrical Orifice

Abstract

Until recently, all treatments of molecular flow in and from an effusion cell have been based upon the ``diffuse reflection'' vapor—solid collision model of Clausing. Winterbottom and Hirth have pointed out the inadequacy of a collision process that assumes the diffuse emission of an impingent vapor molecule from the point of its incidence and have treated the oven with a more realistic collision process that assumes the adsorption of the vapor molecule following a surface collision. The treatment presented here modifies the model developed by Winterbottom and Hirth to include the influence of the mobility of the adpopulation on the inside walls of the oven. The results of the analysis of the total effusion current from a cylindrical orifice agree qualitatively with those of the earlier treatment in predicting an appreciable surface-diffusion contribution for certain orifice geometries when the vapor—solid interactions are typical of chemisorption. Quantitatively, however, the analysis deviates significantly from the earlier predictions and indicates the necessity of considering the adpopulation on the walls within the cell. Numerical solutions for the total effusion current under steady-state conditions are presented and compared with the predictions of earlier models and with some recent effusion measurements. New definitions for the Clausing transmission probability and an effusion coefficient are presented to remove the ambiguities that exist in the older versions for the model of effusion considered here. The results show that the Clausing model, where there is a zero time of stay in the adsorbed state, is just a limiting case of the more general model considered in which the effusion current and its spatial distribution are material-, pressure-, and geometry-dependent.