Shape evolution and splitting of a single coherent particle

Book · Thu Dec 31 04:00:00 EST 1998

OSTI ID:323468

Zhang, J D; Li, D Y; Chen, L Q ^[1]

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1. Pennsylvania State Univ., University Park, PA (United States). Dept. of Materials Science and Engineering

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.

• Sponsoring Organization: Office of Naval Research, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• OSTI ID: 323468
• Report Number(s): CONF-971201--
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
COMPUTERIZED SIMULATION
CONCENTRATION RATIO
MATHEMATICAL MODELS
MORPHOLOGY
PARTICLE SIZE
PARTICLES
SHAPE
SOLID SOLUTIONS
THEORETICAL DATA