Size dependence of the melting temperature of metallic nanoclusters from the viewpoint of the thermodynamic theory of similarity

Abstract

The generalized Thomson formula Tm = Tm(∞)(1-δ)R for the melting point of small objects Tm has been analyzed from the viewpoint of the thermodynamic theory of similarity, where R is the radius of the particle and Tm(∞) is the melting point of the corresponding large crystal. According to this formula, the parameter δ corresponds to the value of the radius of the Tm(R-1) particle obtained by the linear extrapolation of the dependence to the melting point of the particle equal to 0 K. It has been shown that δ = αδ0, where α is the factor of the asphericity of the particle (shape factor). In turn, the redefined characteristic length δ0 is expressed through the interphase tension σsl at the boundary of the crystal with its own melt, the specific volume of the solid phase vs and the macroscopic value of the heat of fusion λ∞:δ0 = 2σslvs/λ∞. If we go from the reduced radius of the particle R/δ to the redefined reduced radius R/r1 or R/d, where r1 is the radius of the first coordination shell and d ≈r1 is the effective atomic diameter, then the simplex δ/r1 or δ/d will play the role of the characteristic criterion of thermodynamic similarity. At a given value of α, this role will be played by the simplex Estimates of the parameters δ0 and δ0/d have been carried out for ten metals with different lattice types. It has been shown that the values of the characteristic length δ0 are close to 1 nm and that the simplex δ0/d is close to unity. In turn, the calculated values of the parameter δ agree on the order of magnitude with existing experimental data.