Schottky Emission as a Rate-Limiting Factor in Thermal Oxidation of Metals

Abstract

Wagner 1 based a theory for the formation of coherent oxide (and other tarnish) layers on metals on the hypothesis that particle transport through the layer occurs by the separate diffusion of ions and electrons by lattice-defect mechanisms, the driving force being the electrochemical potential gradient in the layer. The formation rate was considered to be limited by either ions or electrons, depending upon which had the smaller partial conductivity since equal magnitude charge currents were assumed. This model has been verified for a number of tarnishing processes, 1 one example apparently being very thick copper-oxide films (1.25 xl0~2 cm) formed during the high-temperature oxidation of copper. 2 Equal charge concentra-p. 109. 10 G. Dolling and R. A. Cowley, Proc. Phys. Soc. (London) ^8, 463 (1966); G. Dolling, private communication. u The Ge frequency-distribution function given in Ref. 10 is for 90°K. Following a suggestion of Dolling (private communication) based on the work of B. N. Brockhouse and B. A. Dasannacharya [Solid State Commun. 1. , 205 (1963)], the distribution at 300°K was obtained from the one at 90°K by multiplying all vibrational frequencies by 0.983. 12

True diffusion current of substrate ions as the rate-controlling factor of surface film growth

“…1 and equation (3), v ( t ) - for films "not too thin". The deviation of function (7) from the solution of equation (4) is 2 1 . 7 % for w 5 0.1 and t 2 2:/(144 w2 D).…”

The High Temperature Oxidation Behavior of Mg–Gd–Y–Zr Alloy

“…A model explaining the limiting thickness behavior was first proposed by Mott [20] and Cabrera [21] and further developed by Fromhold and Cook (FC theory) [22][23][24]. The model is based on the assumption that no net electric charge is transported through the oxide.…”

Oxidation of epitaxial Nb(110) films on a-plane sapphire substrates: An x-ray study

“…Subsequent annealing of 20 min at 950 8C ensures an additional smoothening of the surface and the interface. The data could be fitted by a theoretical expression for thermoemission limited oxide growth derived from Fromhold [11]. Out-ofplane XRD measurements after taking the samples out of the UHV into air (at RT) are shown in Fig.…”