Steady demixing profile

Equation (8.10) can be further simplified by the Gibbs-Duhem equation for the solid solution (A, B)0. As a result, the differential equation for the steady slate demixing profile is found to be... 

Figure 8-3. a) Experimental and calculated demixing profiles for (Mg.Co)O under steady state conditions in an oxygen potential gradient (t = 126 h at T = I439°C p /p 0 = 3) and b) its steady state reaction path. 

In concluding, let us comment on the time needed to attain the steady state after establishing the surface activities. Two transient processes having different relaxation times occur I) the steady state vacancy concentration profile builds up and 2) the component demixing profile builds up until eventually the system becomes truly stationary. Even if the vacancies have attained a (quasi-) steady state, their drift flux is not stationary until the demixing profile has also reached its steady state. This time dependence of the vacancy drift is responsible for the difficulties that arise when the transient transport problem must be solved explicitly, see, for example, [G. Petot-Er-vas, et al. (1992)]. 

Eqn. (8.6) describes the steady state concentration profile of an (A, B) alloy which has been exposed to the stationary vacancy flux j°. The result is particularly simple if the mobilities, b are independent of composition, that is, if P = constant. From Eqn. (8.6), we infer that, depending on the ratio of the mobilities P, demixing can occur in two directions (either A or B can concentrate at the surface acting as the vacancy source). The demixing strength is proportional toy°-(l-p)/RT, and thus directly proportional to the vacancy flux density j°, and to the reciprocal of the absolute temperature, 1/71 For p = 1, there is no demixing. 

Figure 8-11. Results of a demixing experiment for (Mn,Fe)On. a) Theoretical steady state concentration profile and b) phase sequence photograph. p Q = 3.3xlO 6bar p o = 4,6x 10 bar T = 120O°C sp = spinel (Fe,Mn)304, w = wiistite (Fe, Mnjo [Y. Ueshima, et at. (1989)].

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