Heriot-Watt Mathematics Report Series
HWM98-74, 22 Jan 1999
Modelling of phase separation in alloys with coherent elastic misfit
P Fratzl, O Penrose and J L Lebowitz
Elastic interactions arising from a difference of lattice spacing
between two coherent phases can have a strong influence on the
phase separation (coarsening behaviour) of alloys.
If the elastic moduli are different in the two phases, the elastic
interactions may accelerate, slow down or even stop the
phase separation process. If the material is elastically anisotropic,
the precipitates can be shaped like plates or needles instead of
spheres and can form regular precipitate superlattices.
Tensions or compressions applied externally to the specimen
may have a strong effect on the shapes and arrangement of the precipitates.
In this paper, we review the main theoretical approaches that
have been used to model these effects and we relate them to experimental
observations. The theoretical approaches considered are
(i) `macroscopic' models treating the two phases as elastic
media separated by a sharp interface (ii) `mesoscopic' models
in which the concentration varies continuously across the
interface (iii) `microscopic' models which use the positions
of individual atoms.
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