The Physics of Metals and Metallography

, Volume 117, Issue 8, pp 749–755 | Cite as

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

  • V. M. SamsonovEmail author
  • S. A. Vasilyev
  • A. G. Bembel
Theory of Metals


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 λ0 = 2σ sl v s . If we go from the reduced radius of the particle R/δ to the redefined reduced radius R/r 1 or R/d, where r 1 is the radius of the first coordination shell and dr 1 is the effective atomic diameter, then the simplex δ/r 1 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.


metallic nanoclusters melting point thermodynamic similarity 


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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • V. M. Samsonov
    • 1
    Email author
  • S. A. Vasilyev
    • 1
  • A. G. Bembel
    • 1
  1. 1.Tver State UniversityTver’Russia

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