Shape evolution and splitting of a single coherent particle

J. D. Zhang, D. Y. Li, Long-qing Chen

Research output: Contribution to journalConference articlepeer-review

7 Scopus citations


The morphology and its evolution of a single coherent precipitate was investigated using the Cahn-Hilliard equation and Khachaturyan's continuum elasticity theory for solid solutions. A cubic solid solution with negative elastic anisotropy and isotropic interfacial energy was considered. The lattice mismatch between the precipitate and the matrix was assumed to be purely dilatational and its compositional dependence obeys the Vegard's law. Both two- and three-dimensional systems were studied. The Cahn-Hilliard equation was numerically solved using a semi-implicit Fourier-spectral method. It was demonstrated that, with increasing elastic energy contribution, the equilibrium shape of a coherent particle gradually changes from a circle to a square in two dimensions, and from a sphere to a cube in three dimensions, and the composition profile becomes increasingly inhomogeneous within the precipitate with the minimum at the center of the particle, consistent with previous theoretical studies and experimental observations. It was also shown that, with sufficiently large elastic strain energy contribution, a coherent particle may split to four particles from a square, or eight particles from a sphere, during its evolution to equilibrium. For both two and three dimensions, the splitting starts by nucleating the matrix phase at the center of the particle.

Original languageEnglish (US)
Pages (from-to)243-248
Number of pages6
JournalMaterials Research Society Symposium - Proceedings
StatePublished - Jan 1 1998
EventProceedings of the 1997 MRS Fall Symposium - Boston, MA, USA
Duration: Nov 30 1997Dec 4 1997

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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