Demixing Under Non-Hydrostatic Stress

Let us investigate the steady state behavior of multicomponent crystals exposed to uniform but non-hydrostatic stresses. We first introduce some ideas on the thermodynamics of such solids (which will be discussed in more detail in Chapter 14). Solid state galvanic cells can be used to perform the appropriate experiments. 

Gibbs [J.W. Gibbs (1878)] showed that a non-hydrostatically stressed solid surrounded (Fig. 8-7) by a fluid (in which it is soluble) is entirely determined by the nature and state of the solid through the relation 

The surrounding fluid (Fig. 8-7) serves two purposes 1) it transmits the pressure to stress-load the surface and 2) it allows the surface to equilibrate chemically and thus provides juL in Eqn. (8.61) with physical meaning. Ideally, the Gibbs fluid has a vanishing buffer capacity for the solid so that after a change in an, the fluid becomes resaturated with respect to the solid before a noticeable amount of the solid or its surface dissolves. The key to verify Gibbs relation for solids under non-hydrostatic stress is therefore the existence of such an idealized fluid. 

Solid electrolytes may have the requisite properties of a Gibbs fluid [W. Durham, H. Schmalzried (1987)] if 1) their conducting ion corresponds to an atomic component of the solid under stress and 2) they exhibit significant mechanical strength. Topical stress energy densities correspond to electrical potentials in the millivolt range. In order to establish them, only a small fraction of a surface monolayer of the electrolyte needs to dissolve during its equilibration with the stressed solid and 

If we identify jy in Eqn. (8.66) with j° in Eqn. (8.3), we can use Eqn. (8.3) to calculate the (steady state) demixing when a stress driven vacancy flux flows across the solid solution (A,B)0. At a fixed oxygen potential, we obtain from the steady state condition 

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