Chemical diffusion derivation from thermodynamic factor and self-diffusion

DiffusConfuse

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= X_AD_B+X_BD_A

meaning the chemical diffusion of B is:

DC_B=X_AD_B=X_ADT_B(1+∂lnγ/dlnX_B)

and the chemical potential of B is:

μ_A=μ⁰_0.5B2+RTlnγ_Bx_B=μ⁰_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(pB₂)/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!