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γ-plot (Surface Energy)

Drag points to adjust surface energies

γ = 0.5γ = 1.0γ = 1.5[10][11][01][1̄1][1̄0][1̄1̄][01̄][11̄]

Equilibrium Crystal Shape

Intersection of half-planes

(1̄1)(01)(11)(10)(11̄)(01̄)(1̄1̄)(1̄0)

Drag the points in the γ-plot to adjust surface energies!

The Wulff construction:

  • Each surface energy γ defines a half-plane at distance γ from origin
  • The equilibrium shape is the intersection of all half-planes
  • Lower energy surfaces (closer to origin) create larger facets
  • High energy surfaces may not appear if neighbors have lower energy
  • The shape is always convex and minimizes total surface energy