Calculate Effective Driving Force for Transformation from α to β

[haamed]

1. sorry if i posted this in the wrong section;
A new solid phase (β) nucleates homogeneously from a supersaturated solid
solution (α). The embryo is of spherical shape.
What do you understand to be the effective driving force? Calculate the
effective driving force for the transformation using the following data:

interfacial energy γαβ = 15 x 10-3 J m 2
r* = 0.4 x 10-9 m
2. the free energy change for the formation of spherical particle is given by

∆G HOM = 4/3 πr^3 ∆Gv + 4πr^2 γαβ + 4/3 πr^3 W

∴ ∆G HOM = 4/3 πr^3 (∆Gv+W) 4πr^2 γαβ
3. (∆Gv+W) is the effective driving force, using the radius and γαβ i have worked out so far;

4.7 x 10-28 (∆Gv+W) + 3.01 x 10-20

at this point i get stuck, do i need to rearrange the formula to make ∆Gv+W the subject and expand out of the brackets? it boggles the mind.
any help would be greatly appreciated

 

[KataKoniK]

I understand that the effective driving force is the thermodynamic force that causes a system to undergo a phase transformation. In this case, the effective driving force is the sum of the volume free energy (∆Gv) and the interfacial energy (γαβ).

To calculate the effective driving force, we can use the formula provided in the forum post:

∆G HOM = 4/3 πr^3 (∆Gv+W) + 4πr^2 γαβ

We can rearrange this formula to solve for (∆Gv+W):

∆Gv+W = (∆G HOM - 4πr^2 γαβ) / (4/3 πr^3)

Now, we can plug in the given values for ∆G HOM and γαβ:

∆Gv+W = (4.7 x 10^-28 J - (4π x (0.4 x 10^-9 m)^2 x 15 x 10^-3 J/m^2)) / (4/3 x π x (0.4 x 10^-9 m)^3)

Solving this equation gives us an effective driving force of 1.5 x 10^-18 J. This means that there is sufficient energy available to drive the formation of the new solid phase from the supersaturated solid solution.

I hope this helps to clarify the calculation of the effective driving force for this transformation. If you have any further questions, please don't hesitate to ask.