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

Abstract

The generalized Thomson formula T_m = T_m^(∞)(1-δ)R for the melting point of small objects T_m has been analyzed from the viewpoint of the thermodynamic theory of similarity, where R is the radius of the particle and T_m^(∞) 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 T_m(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 σ_sl at the boundary of the crystal with its own melt, the specific volume of the solid phase v_s and the macroscopic value of the heat of fusion λ_∞:δ₀ = 2σ_slv_s/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.