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Chemical diffusion derivation from thermodynamic factor and self-diffusion

  1. Apr 16, 2012 #1
    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!
     
  2. jcsd
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