Nanoparticle Melting — 3D Lattice (Gibbs–Thomson)

Material

Nanocrystal

Radius r 6.0 nm

Temperature T 1200 K

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Bulk T_m

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T_m(r)

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Depression ΔT_m

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Liquid shell / R

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Phase

Solid

How the lattice responds

Every sphere here is one atom, placed on a real lattice sized to the particle's radius. The Gibbs–Thomson equation sets the size-depressed melting point T_m(r); as T climbs toward it, a quasi-liquid skin nucleates at the outer, least-coordinated shell and thickens inward, its boundary drawn as a translucent sphere. At T = T_m(r) the skin has consumed the whole lattice and every atom goes liquid at once.

T_m(r) = T_m,bulk · [1 − 4·σ_sl / (ΔH_f·ρ_s·r)]
liquid volume fraction f(T) rises from 0 to 1 as T → T_m(r)⁻
shell boundary radius: r_shell = R · (1 − f)^(1/3)

Radius r — sets both the physical T_m(r) depression and how many atoms fit the rendered lattice (drag to see it visibly shrink/grow).
Temperature T — drive it past T_m(r) and the shell sweeps to the core in real time.
Drag to orbit the crystal; smaller particles show a proportionally thicker premelting skin at the same reduced temperature — a direct, size-dependent consequence of the same equation.

Real-world relevance: this quasi-liquid-skin picture (Pawlow, later refined by Buffat & Borel for gold nanoparticles) is the accepted microscopic mechanism behind nanoscale melting-point depression, and explains why nanoparticle catalysts and solder can sinter or liquefy at temperatures a bulk phase diagram would never predict.

Crystalline solid Premelting skin Liquid

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Nanoparticle Melting — 3D Lattice Simulator