Abstract
This work describes the logarithmic term in the size-dependent melting temperature of nanoparticles. The Lindemann melting criterion and the thermal phonon contribution are intended primarily as a clear approach for our study of melting temperature. The ratio of the melting temperature (Tmn) of a nanoparticle to the bulk melting temperature (Tmb) is numerically evaluated up to the order of the inverse of the size L of a nanoparticle: Tmn/Tmb = 1 – A/L. We show that the coefficient A is not a constant but has a logarithmic part. The logarithmic term is the dominate term in the factor A(L). Our investigation suggests the behavior of the size-dependent melting is Tmn/Tmb = 1 – (B + C ln L)/(L – 2ls) where B and C are constant factors and ls is the number dimension of the surface layers reconstructed or premelted. The results present a challenge to reach a higher resolution in future thermal experiments in order to distinguish ln L/L behavior from the previously accepted pure 1/L behavior.
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