Hard Sphere Phase Diagram
φ < 0.494: fluid
0.494 < φ < 0.545: coexistence
φ > 0.545: FCC crystal
φ_rcp = 0.637 (random close pack)
φ_fcc = 0.740 (close pack)
Asakura-Oosawa
Depletion force: entropic,
U_dep ≈ −n_p·kT·V_overlap
Bragg: λ = 2d·sin(θ)
d = a/√(h²+k²+l²)
φ < 0.494: fluid
0.494 < φ < 0.545: coexistence
φ > 0.545: FCC crystal
φ_rcp = 0.637 (random close pack)
φ_fcc = 0.740 (close pack)
Asakura-Oosawa
Depletion force: entropic,
U_dep ≈ −n_p·kT·V_overlap
Bragg: λ = 2d·sin(θ)
d = a/√(h²+k²+l²)