Size-dependent Melting Point Of Metallic Nanocrystals

Takagi in 1954 demonstrated for the first time that ultrafine metallic particles melt below their corresponding bulk melting temperature. It is now known that the melting temperature of all low dimensional crystals, including metal, semiconductor and organic crystals, depends on their sizes. Although there are relatively extensive investigations on the size-dependent melting of nanocrystals, it has not been accompanied by the necessary investigation of the size-dependent thermodynamics of nanocrystals. Such an investigation should deepen our understanding of the size effect of melting. In particular, a complete understanding of the melting transition in nanocrystals cannot be obtained without a clear understanding of the enthalpy of melting, which is an important property of melting.Of many melting theories, Lindemann criterion which was put forward about a century is experiential and quite effective for the studying of melting behavior of maters. It has been widely used to study the melting and solidification process of crystals, noncrystals and organic materials. Experiments have shown that the melting process of nanocrystals follows Lindemann criterion as bulk crystals, it is feasible to further discuss the melting theory of nanocrystals based on the criterion in theory. In fact, the studying of melting thermodynamics of nanocrystals is to study size effect on the melting thermodynamic properties of crystals compared with bulk crystals. F. G. Shi theoretically presented a model for size-dependent melting temperature based on Lindemann criterion. The model can perfectly interpret melting behaviour of nanocrystals, it is applicable both for melting depression and for superheating. For free-standing nanocrystals, the fraction of surface atoms increases with size decreasing and the thermal vibration of surface atoms is larger than that of internal atoms, mean square displacement increases with size decreasing, thus the melting temperature decreases with size decreasing. For nanocrystals embedded in a matrix, the melting temperature will decrease when the interface between nanocrystals and matrix is incoherent. When the interface is coherent or semi-coherent, the amplitude of surface atoms is less than that of internal atoms leading to mean square displacement of nanocrystals decrease, the melting temperature increases with size decreasing. But this model has drawback for it including a undefined parameter which is obtained through experiment.A physical model for the melting entropy and melting enthalpy of metallic nanocrystals had been developed based on the above model for the size-dependent melting temperature and on Mott's expression for the vibrational entropy of melting at melting temperature. It is shown that the melting entropy of metallic nanocrystals is dominated by vibrational entropy of atoms and decreases with size decreasing. One hand, a new function of melting temperature dependent on the size is developed by deciding the parameter of previous model; these functions are very simple and free any adjustable parameter. On the other hand, the relationship between critical size and shape (dimension of crystals) of low dimensional crystals is obtained by defining critical size of different dimensional crystal which equal to the size at which a half of atoms of the particle is located on its surface. Thus above model can be applied to predict the melting behavior of different nanocrystals, for example, nanoparticles, thin films and nanowires. The model predictions for different crystals are consistent with experimental evidences. Compared with other theoretical models, both predictions are identical when the size is larger, when the size is smaller; our model gives a rather better size-dependent melting than other theoretical models do. Our model is more advantage than other models since it is simple and free any adjustable parameters which is applicable for different shape nanocrystals.The melting behavior of a particle embedded a matrix depends on the structure between the particle and the matr...