Phase ordering kinetics of second-phase formation near an edge dislocation

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Phase ordering kinetics of second-phase formation near an edge dislocation

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Publication Article, peer reviewed scientific
Title Phase ordering kinetics of second-phase formation near an edge dislocation
Author(s) Bjerkén, Christina ; Massih, Ali R.
Date 2014
English abstract
The time-dependent Ginzburg-Landau (TDGL) equation for a single component non-conservative structural order parameter is used to study the spatio-temporal evolution of a second phase in the vicinity of an edge dislocation in an elastic crystalline solid. A symmetric Landau potential of sixth-order is employed. Dislocation field and elasticity modify the second-order and fourth-order coefficients of the Landau polynomial, respectively, where the former makes the coefficient singular at the origin. The TDGL equation is solved numerically using a finite volume method, where a wide range of parameter sets is explored. Computations are made for temperatures both above and below the transition temperature of a defect-free crystal Tc0. In both cases, the effects of the elastic properties of the solid and the strength of interaction between the order parameter and the displacement field are examined. If the system is quenched below Tc0, a steady state is first reached on the compressive side of the dislocation. On the tensile side, the growth is held back. The effect of thermal noise term in the TDGL equation is studied. We find that if the dislocation is introduced above Tc0, thermal noise supports the nucleation of the second phase, and a steady state will be attained earlier than if the thermal noise was absent. For a dislocation-free solid, we have compared our numerical computations for a mean-field (spatially averaged) order parameter versus time with the late time growth of the ensemble-averaged order parameter, calculated analytically, and find that both results follow upper asymptotes of sigmoid curves.
DOI http://dx.doi.org/10.1080/14786435.2013.858193 (link to publisher's fulltext)
Publisher Taylor & Francis
Host/Issue Philosophical Magazine;6
Volume 94
ISSN 1478-6435
Pages 569-593
Language eng (iso)
Subject(s) heterogeneous nucleation
phase ordering
edge dislocation
Ginzburg-Landau theory
phase-field method
Sciences
Research Subject Categories::NATURAL SCIENCES
Handle http://hdl.handle.net/2043/16920 (link to this page)

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