Stability of a uniform composition

Following the pioneering work of Cahn (1961), the Helmholtz free energy at fixed temperature of a solid solution occupying region R is given as a functional of composition xz, t) by 

In discussing epitaxial systems in preceding chapters, the quantity represented by ei was customarily denoted by Cm. 

the time rate of change of free energy of the material in R that arises from time dependence of composition at any point in R is examined. Differentiation of (9.89) with respect to time for a fixed material volume R with bounding surface S, followed by application of the divergence theorem to the result, yields 

The factor dR is the rate of change of volume of material B in dR. It follows that the quantity in square brackets in the integral over R in (9.91) is the generalized force that is work-conjugate to this local volume change. This field thus represents the local chemical potential of material B in the solution, 

Consider an elastic material subjected to an equi-biaxial state of stress, characteristic of a uniform epitaxial thin film coherently bonded to a substrate in the presence of lattice mismatch. This is the state of stress that develops in the film when the alloy with spatially uniform compo- 

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Compositional variations in solid solutions 9.6.2 Stability of a uniform composition... 

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