ABSTRACT

Figure 5.25 depicts the main volume changes that need to be considered for the growth of an anion-deficient oxide. Interchange of an oxygen gas atom with an oxide vacancy produces a volume change as given by:

anA = nMO - nM (5.111) where

However, since a vacancy is also expected to be involved with the reaction at this interface, the total volume change will be given by:

an = anA - ana (5.112) The values of ana are not well established, whereas those of AnA are much better known through the concept of Pilling-Bedworth ratio (Ill = nMotnM). Utilizing this, one can obtain:

(5.113)

(a)

It has been further pointed out that there exists the possibility for the stress, either originating from the growth process or deriving from external constraints,

to prevent or reduce the oxidation process. The most straightforward approach is first to establish the level of stress required to prevent the chemical process of oxidation. This is simply obtained by equating the energy obtained from stress through the volume change 40A, with the free energy released 4(;0, on oxidation:

(5.114)

to suppress further reaction. Estimates of the stresses needed to satisfy the above inequality often exceed typical material flow or fracture stresses by over two orders of magnitude. This suggests that under most experimental or engineering conditions, the direct effect of stress on the chemical process of oxidation is negligible.