Thermodynamic analysis and modification of Gibbs–Thomson equation for melting point depression of me

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Abnormal melting point depression of metal nanoparticles often occurs in heterogeneous catalytic reac-tions, which leads to a reduction in the stability of reactive nanoclusters. To study this abnormal phe-nomenon, the original and surface-energy modified Gibbs–Thomson equations were analyzed in this work and further modified by considering the effect of the substrate. The results revealed that the original Gibbs–Thomson equation was not suitable for the particles with radii smaller than 10 nm. Moreover, the performance of the surface-energy modified Gibbs–Thomson equation was improved, and the deviation was reduced to (-350-100) K, although further modification of the equation by considering the interfa-cial effect was necessary for the small particles (r < 5 nm). The new model with the interfacial effect improved the model performance with a deviation of approximately-50 to 20 K, where the interfacial effect can be predicted quantitatively from the thermodynamic properties of the metal and substrate. Additionally, the micro-wetting parameterαw can be used to qualitatively study the overall impact of the substrate on the melting point depression.
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