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Chemical diffusion derivation from thermodynamic factor and selfdiffusion 
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#1
Apr1612, 01:18 AM

P: 22

I am working through a paper in which the chemical diffusion coefficient is related to the selfdiffusion (or tracer) through the following derivation, on which I am a little hung up.
AB_{2} metal. Overall diffusion D= X_{A}D_{B}+X_{B}D_{A} meaning the chemical diffusion of B is: DC_{B}=X_{A}D_{B}=X_{A}DT_{B}(1+∂lnγ/dlnX_{B}) and the chemical potential of B is: μ_{A}=μ^{0}_{0.5B2}+RTlnγ_{B}x_{B}=μ^{0}_{0.5B2}+RTlnp^{0.5}_{B2} finally the mole fractions of X_{B} and X_{A} vary accordingly: X_{B} = (2+x)/(3+x) X_{A} = 1/(3+x) and then DC_{B} is: DC_{B}=DT_{B}(2+x/2) ∂ln(pB_{2})/dx I am confused as to where the (2+x)/2 term comes from. I believe it is from the mole fraction X_{A} in the overall diffusion equation combined with a derivation including the mole fraction X_{B} 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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