Kinetic analysis of surface reduction in transition metal oxide single crystals

Abstract

A mathematical treatment of the kinetics of metal oxide reduction is presented that is particularly applicable to single crystal substrates under conditions which promote slow, orderly removal of lattice oxygen at the crystal surface. The crystal is modeled as a semi-infinite plane with oxygen removal at the surface only and with Fickian diffusion from subsurface oxide into the depleted surface region. Removal of oxygen at the surface has been related to oxide surface concentration, as well as to oxygen vacancy concentration in an attempt to model the commonly observed induction period to reduction onset. Solutions to the models are given in closed analytic form for zeroth and first-order oxygen surface concentration dependencies and as an infinite, but converging, series in reaction time for the first and higher reaction orders. A numerical method is also used to extend the fit to longer times for which the infinite series method converges too slowly to be practically useful. As an example of the relevance of the kinetic analysis, the model is applied to data obtained on a NiO(100) substrate reduced under 1.0×10 −7 to 1.3×10 −6 Torr H 2.