Diffusion Potential for Transformation

The local diffusion potential for a transformation, 4 (r), at a time t = t0, can be determined from the rate of change of total free energy, f, with respect to its current order-parameter field, f (r,t0). At time t = ta, the total free energy is 

6 Some readers will recognize this development as the calculus of variations [7]. A functional is a function of a function in this case, T takes the function (r,t0) and maps it to a scalar value that is numerically equal to the total free energy of the system. 

Therefore, if the order parameter changes by a small amount 5 = 8t, the change in total free energy is the sum of local changes  

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