Wagner oxidation in the nonisothermal regime
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Daniel A. Jelski Department of Chemistry, State University of New York, College at Fredonia, Fredonia, New York 14063
Imre Hevesi Department of Experimental Physics, JozsefAttila University, H-6720 Szeged, Hungary
Thomas F. George Departments of Chemistry and Physics, Washington State University, Pullman, Washington 99164-1046 (Received 21 August 1992; accepted 30 December 1992)
A computational model for laser-induced Wagner oxidation processes on a vanadium metal surface is described and compared with the experiment. It is found that for thin oxide layers, the oxide is nearly transparent and the metal temperature rapidly increases. For thicker layers, the oxide is nearly opaque and the metal temperature slowly decreases. The Wagner rate law is found to hold for thicker oxide layers, but not at the beginning of the process.
During Wagner oxidation 1 the rate of oxidation is diffusion limited, and thus the rate will increase as a function of temperature, but decrease as a function of oxide layer thickness. In the isothermal limit (in this paper isothermal means V r = 0 with no restriction on dT/dt), the well-known equation obtains, d0_ dt
(1)
where 0 is the oxide thickness and yo is the oxide ion rate constant, which depends on the temperature and the concentration differences. Wagner processes are supposed to occur for oxidation thicknesses greater than about 0.1 ix. Essential to the derivation of Eq. (1) is the isothermal condition, perfectly reasonable under slow, ovenlike heating conditions, but possibly inappropriate when the primary heat source is a laser. The question asked in this paper, therefore, is to what extent the traditional Wagner oxidation law applies to laser-induced oxidation. We present a numerical simulation of the oxidation process retaining the basic Wagner premise, i.e., that the process is diffusion limited. The relevant experimental data have been previously reported.2 It is clear that the rate constant, JQ, is a function of temperature. This is most obvious at phase changes since diffusion through a liquid will be faster than diffusion through a solid. But it is true at other times as well, since the rate of diffusion of oxide ions through the solid will depend primarily on the number of defects in the solid. Hence y0 will depend exponentially on temperature, and J. Mater. Res., Vol. 8, No. 5, May 1993
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from our experiments, we find that (2)
70 =
where (for V/V 2 O 5 systems between 300 and 1700 K) d = 1.1 X 10^ 10 m 2 /s and 0 = 3.3 X 10" 3 K" 1 . A second way in which oxidation will depend on temperature is the variation in the absorption coefficient.3 We have attempted to find empirical parameters that would model the isothermal process for oxide deposition at various temperatures, using data for T(t) and dT(t)/dt. The isothermal absorptivity can be determined from the different rates of heating and cooling at the same temperature by
f
dT
dT "^heating
^'cooling
5
= 5.15 X 10~ r • 0.12,
(3)
where A(T) is the absorpti
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