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The phonon thermal contribution to the melting temperature of nano-particlesis inspected. Unlike in periodic boundary condition, under a general boundarycondition the integration volume of low energy phonon for a nano-particle ismore complex. We estimate the size-dependent melting temperature through thephase shift of the low energy phonon mode acquired by its scattering onboundary surface. A nano-particle can have either a rising or a decreasingmelting temperature due to the boundary condition effect, and we found that anupper melting temperature bound exists for a nano-particle in variousenvironments. Moreover, the melting temperature under a fixed boundarycondition sets this upper bound.

Can nano-particle stand above the melting temperature of its fixed surface partner?