Heterogeneous recombination of atoms. Theory of the Smith-Linnett method

A general differential equation has been derived which describes the concentration of atoms diffusing and recombining in a cylindrical tube. It is shown that the previously published equations are particular cases of that equation. The boundary conditions have also been generalized. In the case of the Smith–Linnett method the simplifications of the general equation, leading to the one-dimensional linear equation, are the cause of a systematic error in calculation of the recombination coefficient. This error is considerable for very active and slightly active surfaces. In the case of recombination of atomic hydrogen, the error due to omission of the homogeneous reaction in the analysis of experimental data is negligibly small when the pressure is lower than 0.1 Torr and the concentration of atoms is lower than 10 %.The atomic hydrogen recombination coefficient γ has been calculated for nickel films and for Pyrex on the basis of the one-dimensional linear equation and on the basis of the model proposed in the present work. It was found that the two methods of calculation differ by 3–6 % in the case of surfaces having the high activity (γ over 10–2) and by 30–40 % in the case of surfaces having low activity (γ below 10–4). Both methods give approximately the same fit to the experimental data.