Study On Size Effects And Shape Effects Of Thermodynamic Properties Of Metallic Nanoparticles

The present work aims at developing a general model to account for size effects and shape effects of the thermodynamic properties of metallic nanoparticles. The main contents are listed in the following:(1) A new dimensionless parameter, i.e. shape factor, is proposed to account for the particle shape difference of nanoparticles, where its definition and calculation method are also shown. Furthermore, the relational expressions between particle size, shape factor, number of total atoms, number of surface atoms and specific surface area have also been derived.(2) A new lattice model of nanoparticle is proposed, where a nanoparticle is moved out from the bulk crystal and form in thermodynamic equilibrium. Based on this model, the expression for the size and shape dependent lattice parameter of nanoparticles has been derived, and the corresponding computational results are consistent with the experimental ones.(3) Based on the basic concept of cohesive energy, we have proposed that the cohesive energy of a solid equals the difference between the total surface energy of all isolated atoms of the solid and the surface energy of the solid, which leads to the surface energy model; By considering the large number of dangling bonds of the surface atoms and surface relaxation of nanoparticles, the bond model has been established. Both calculation results are consistent with the experimental values of the cohesive energy of Mo and W nanoparticles, and the results of bond model are more close to the experimental values. Furthermore, it is proved that the liquid drop model in literature is a special case of surface energy model.(4) A formula has been derived to account for the melting temperature of free surface nanoparticles based on the relationship between the cohesive energy and the melting temperature of solids. By considering the matrix effect on the bonds of the surface atoms , an expression is developed to describe the melting temperature of the nanopaticles embedded in a matrix with high melting temperature and formingcoherent interface with matrix, where the superheating of these nanoparticles has been explained. Furthermore, we have obtained the relations accounting for the size and shape dependent melting entropy and melting enthalpy of nanoparticles with free and non-free surface.(5) By considering size effects and shape effects on the melting temperature and the melting enthalpy of nanoparticles, the phase diagram of nanoparticles of binary systems is calculated, and the calculation results show that the solidus and the liquidus of phase diagram of nanopaticles are lower than that of the corresponding the bulk systems, but the amplitude of variation are similar. The present results are different from that reported in literatures, where the size effect on the melting temperature is only considered.(6) Based on the bond energy model of nanoparticles and the relationship between cohesive energy and vacancy formation energy, the expressions for the vacancy formation energy and the vacancy density of nanoparticles have been derived. It is shown that both the vacancy formation energy and the vacancy density of nanoparticles depend on the particle size and shape factor, and the particle size is the major factor affecting these two properties. If one neglects the particle shape effect on the vacancy formation energy, the error in the final results may reach 10%.(7) Based on the method of bond model, the expressions for the size dependent cohesive energy .melting temperature , melting entropy , melting enthalpy, vacancy formation energy and vacancy density of nanowires and nanofilms have been established. It is found that the ratio for the cohesive energy of spherical nanoparticle, nanowire and nanofilm in the same size is 3:2:1 when their surface relaxation is neglected, and their melting temperature, vacancy formation energy and melting entropy (in the first approximation) follow the same ratio.