= Solution
Prepare size-characterized gold-particle ensembles, heat them on a calibrated in-situ <electron diffraction> stage, and follow the loss of sharp fcc <diffraction> features and appearance of liquid-like diffuse scattering. Measure the <particle size distribution> rather than treating a polydisperse ensemble as one diameter. Temperature-dependent weakening of a <diffraction> peak alone is insufficient: thermal vibrations, particle motion, coalescence, evaporation and beam damage can also reduce intensity. Low-dose repeats, heating/cooling runs, size checks before and after heating, a bulk-like reference and support-dependent controls help distinguish <melting> from those effects. <Electron diffraction> measurements on <gold> particles down to about 2 nm are a classic demonstration.<Size effect on the melting temperature of gold particles by Ph. Buffat and J-P. Borel>[Physical Review A 13 (1976), pp. 2287–2298, abstract: scanning diffraction and size-distribution analysis]{ref}
The physical origin is the large interface contribution to <free energy> at small radius. A curved solid–liquid interface raises the solid's <thermodynamic equilibrium> <chemical potential> relative to the flat-interface case, so coexistence occurs below the bulk <melting> <temperature>. Reduced coordination and surface disorder provide a microscopic interpretation, but the quantitative continuum relation is a <free energy> balance, not simply a claim that every surface atom has a universal lower <melting> point.
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