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I'm going through the quaternary phase field example and having some
difficulty understanding the calculation of standard potentials. If
I understand correctly, "standard" potentials denoted by o are the
for reference states of the pure component, and the
composition-dependent potential for the component in solution is
obtained by mu = mu^o + R*T*ln(C/rho) I can follow the manipulations of equations in the example and can see how the relevant quantity ends up being only the difference between standard potentials of the solid and liquid phases after taking the derivatives  which is just named Cj.standardPotential in the code. But I don't understand how you "cook" these standard potentials: for Cj in interstitials + substitutionals + [solvent]: ... Cj.standardPotential = R * T * (numerix.log(Cj.L/rhoL) ... - numerix.log(Cj.S/rhoS)) Since this is the difference between the solid and liquid potentials, any terms common to both would have disappeared and we should be left with the remaining terms unique to each phase. But if these are indeed "standard" potentials for the solid and liquid, it seems like none of them should include R*T*ln(C/p) terms in the first place? So I don't see how this _expression_ is obtained (or why the solid term is being subtracted from the liquid term rather than vice versa). Could anyone elaborate a bit on this part? Thanks, Adam |
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