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High-pressure effects in solids and liquids PACS 65.80.-g -Thermal properties of small particles, nanocrystals, nanotubes, and other related systems PACS 65.40.-b -Thermal properties of crystalline solids Abstract -A simple and new analytical model is proposed to explore the pressure effect on melting temperature for free-standing nanoparticles, based on the Lindemann's formula of melting and the size-dependent Grüneisen parameter. The Grüneisen parameter is a valuable quantity which can be used to set the limitations on the pressure and temperature dependence of thermal properties. The present study reveals that the Grüneisen parameter decreases with the decrement in particle size due to variation in specific heat and lattice constant. On the other hand, melting temperature shows a superheating phenomenon with an increment in pressure for an individual size of free-standing nanoparticles. Due to compression the interatomic distance decreases and there is comparatively more interaction within the atoms of nanoparticles under pressure. Compactness of nanomaterial and reduction in surface vibrations due to external pressure create favourable conditions for superheating. This model is applied to Al (37 nm), Pb (6.7 nm) and Bi (50 nm) nanometals over a range of pressure up to 1 GPa. The consistency of the calculated results with the available experimental data of melting for the above-said materials as core in a particle/matrix system by induced pressure supports the validity of the proposed model.

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