Small crystals melt at a lower temperature than large crystals do, and a liquid phase exists at the grain junctions of a crystal. Accordingly, the amount of liquid present in a finely dispersed crystalline solid has been calculated when its whole particles melt, according to the Gibbs-Thomson equation, and when melting occurs within the solid, that is at their grain junctions. The fraction of the solid that pre-melts increases with increasing temperature. Hence, the experimentally determined enthalpy, entropy, volume, heat capacity and expansivity of a finely dispersed solid are higher than those of a massive solid for two reasons: firstly the pre-melting that involves latent heat; secondly the presence of a pure liquid phase, for which the quantities have a higher value than for the solid. The increase in the thermodynamic functions has been formulated for a fine powder and an emulsion and elaborated for finely dispersed gold particles. It is shown that, as a consequence of the temperature-dependent phase equilibrium, the heat capacity and thermal expansivity of a finely dispersed solid will increase with increasing amount of heat input used for measuring it, and it will vary with both the mean particle size and its distribution. Other consequences of the pre-melting have been described. The rise in heat capacity observed for a polycrystalline solid approaching its melting point may not be entirely due to the presumed softening of phonons and increase in the vacancy concentration. The formalism applies also to a solid-solid phase transformation in which the intergranular phase is seen as the high-energy solid phase. The apparent superheating of solids that float on their melt is discussed in terms of a solid-liquid-vapour phase equilibrium at a negative pressure. [References: 40]
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