Kinetics and Microstructural Control

· The volume and surface contributions to the Gibbs function of the nucleus are shown as a function of nucleus radius.
· The critical radius is r^*, and ΔG* is the Gibbs function "barrier" to homogeneous nucleation. This activation energy must be provided from the thermal fluctuations of the lattice.
· The critical radius, r^*, corresponds to the maximum of ΔG_Total: d( ΔG_Total )/dr = 0; i.e. r^* = -(2 γ_αβ / ΔG_V ).
· Substituting r^* into the total Gibbs function expression gives:
ΔG^* = (16π γ³_αβ / 3ΔG_V²).

From: Barrrett, Nix & Tetelman,
"The Principles of Engineering Materials,"
Prentice Hall (1973)