WIAS Preprint No. 997, (2004)

On the Becker/Döring theory of nucleation of liquid droplets in solids



Authors

  • Dreyer, Wolfgang
  • Duderstadt, Frank

2010 Mathematics Subject Classification

  • 74A25 74A15 80A30

2008 Physics and Astronomy Classification Scheme

  • 8.60.Nh 82.20.Db 82.20.-w 61.72.Bb 61.72.Qq 64.70.Dv

Keywords

  • nucleation, kinetic of phase transition, metastability, surface stress, GaAs, elasticity

Abstract

Nucleation of liquid precipitates in semi-insulating GaAs is accompanied by deviatoric stresses resulting from the liquid/solid misfit. A competition of surface tension and stress deviators at the interface determines the nucleation barrier. The evolution of liquid precipitates in semi-insulating GaAs is due to diffusional processes in the vicinity of the droplet. The diffusion flux results from a competition of chemical and mechanical driving forces. The size distribution of the precipitates is determined by a Becker/Döring system. The study of its properties in the presence of deviatoric stresses is the subject of this study. The main tasks of this study are: (i) We propose a new Becker/Döring model that takes thermomechanical coupling into account. (ii) We compare the current model with already existing models from the literature. Irrespective of the incorporation of mechanical stresses, the various models differ by different environments where the evolution of precipitates takes place. (iii) We determine the structure of equilibrium solutions according to the Becker/Döring model, and we compare these solutions with those that result from equilibrium thermodynamics.

Appeared in

  • J. Statist. Phys., 123 (2006) pp. 55--87.

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