Chemical diffusion derivation from thermodynamic factor and self-diffusion

  • #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!
 

Answers and Replies

Related Threads on Chemical diffusion derivation from thermodynamic factor and self-diffusion

  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
1
Views
996
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
1
Views
4K
  • Last Post
2
Replies
29
Views
3K
  • Last Post
Replies
2
Views
802
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
977
  • Last Post
Replies
12
Views
9K
Top