Crystal Grain Boundaries

Read-Shockley energy formula — misorientation & dislocation structure

Grain Parameters

Theory

Read-Shockley formula:
E(θ) = E₀ θ(A − ln θ)

E₀ = μb/4π(1−ν)
A = 1 + ln(b/2πr₀)

Dislocation spacing:
D = b/θ (Frank's rule)

High-angle: θ > θ_c ≈ 15°
E ≈ const (disloc. cores overlap)
θ: --° | D: -- nm
E(θ): -- mJ/m²
Type: --