Schematic illustration of a nanometer-sized spherical particle on a solid substrate and its diameter of curvature D cur .
Comparisons of T m (D) functions for free-standing and graphite substrate-supported spherical Au nanoparticles between the predictions in terms of Eqs. (2)–(6) and available experimental values11,12 as well as other theoretical result.22
Comparisons of T m (D) functions for free-standing, amorphous carbon and graphite substrate-supported spherical Au nanoparticles between the predictions and available experimental values.11,12
Gibbs free energies of the solid and liquid Au for the bulk material, 4 nm amorphous carbon and graphite substrate-supported spherical nanoparticle. Note that the Gibbs free energy curves for 4 nm amorphous carbon and graphite substrate-supported nanoparticle superpose nearly. The temperature at which Gibbs free energy of the solid and liquid phase is identical is identified as the melting point.
Normalized melting point dependence on the reciprocal of free particle radius, tungsten substrate-supported Au nanoparticles radius r, and their curvature radius rcur. The present model is compared to the results of Lee et al.,20 Ding et al.,16 and Safaei,21 as well as experimental data.10 the results from Ding et al.'s model16 is found to be the same as that of a free spherical particle with the same curvature radius.
The free surface-to-volume ratio a s (θ)/v(θ) of a substrate-supported and a free spherical particle vs the contact angle θ.
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