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Chemical diffusion derivation from thermodynamic factor and self-diffusion

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DiffusConfuse
#1
Apr16-12, 01:18 AM
P: 22
I am working through a paper in which the chemical diffusion coefficient is related to the self-diffusion (or tracer) through the following derivation, on which I am a little hung up.

AB2 metal.

Overall diffusion D= XADB+XBDA

meaning the chemical diffusion of B is:

DCB=XADB=XADTB(1+∂lnγ/dlnXB)

and the chemical potential of B is:

μA00.5B2+RTlnγBxB00.5B2+RTlnp0.5B2

finally the mole fractions of XB and XA vary accordingly:

XB = (2+x)/(3+x)

XA = 1/(3+x)

and then DCB is:

DCB=DTB(2+x/2) ∂ln(pB2)/dx

I am confused as to where the (2+x)/2 term comes from.

I believe it is from the mole fraction XA in the overall diffusion equation combined with a derivation including the mole fraction XB from the chemical potential, but can't work it out exactly.

Thank you in advance for any clarification on this topic!
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