Hello,
Here is the chemical mobility for a Fe-Cr binary alloy given by Darken's equation (Refer - Effect of applied strain on phase separation of Fe–28 at.% Cr alloy: 3D phase-field simulation):
M = (Ccr*Mfe + Cfe*Mcr)*Ccr*Cfe/Vm
1. How did the terms (Ccr*Cfe/Vm) arrive in this equation, since the inter-diffusion coefficient is just given by D = Ccr*Dfe + Cfe*Dcr?
2. What is the unit for mobility? For a mono-Vacancy mechanism, the diffusion coefficient is given by D=R*T*M. If the diffusion coefficient is given by m2/s , then can I just assume the corresponding mobility also has units in terms of m2?
It would be great if you provide any fundamental text books for understanding this.
Thank you.
Dear Viswanathan;
I would recommend you please first to consult the text book entitled "Diffusion in Solids , Chapter IV Second Edition by Paul Shewmon", before you try to connect the intrinsic mobilities with the intrinsic diffusion coefficients (equally well between the traces mobilities and diffusivities) through the thermodynamic factors, which involve chemical activities of the individual species such as Fe and Cr etc.
Dear Viswanathan,
For friction motions like diffusion, the atomic mobility M is the coefficient that relates velocity of atoms, V, to the driving force, F that causes the motion:
V [m/s] = M x F
and the atomic flux J is defined by velocity times concentration C (number per volume):
J [n/m/m/s] = V [m/s] x C [n/m/m/m] = M C F
Now you see that the unit of M depends on the unit of driving force.
If the driving force is per mole your M is D/RT and if it is per particle your M is D/kT.
Dear Viswanathan , Darken equation has nothing to do with the effect of strain on the phase separation. The residual strain energy in the matrix as well in the growing secondary phase definitely has effects on the rate of growth and on its morphology or its shape especially if the diffusivity would be anisotropic.
- Badges
- Science topic
- Similar topics
- Engineering
- Materials Engineering
- Annealing
- Metallurgy
- Metals