Equilibrium Cosine Law and Scattering Symmetry at the Gas–Surface Interface

Earlier derivations of the equilibrium cosine scattering law at the gas–surface interface based on the second law of thermodynamics and on the principle of detailed balance are shown to be inconclusive. Presented is a derivation involving time reversal invariance, along with an assumption of a canonical distribution of states in the solid, which results in a reciprocity relationship for the surface scattering cross section that yields the cosine law at equilibrium. A symmetry property for the scattered particle flux results from the reciprocity relationship, and molecular beam data are shown to exhibit the indicated symmetry. An application of this previously unrecognized symmetry permits the prediction of the scattered particle flux distribution for an arbitrary angle of incidence from experimental data reported for a limited number of incident angles.