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On the incorporation of cubic and hexagonal interfacial energy anisotropy in phase field models using higher order tensor terms

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Title On the incorporation of cubic and hexagonal interfacial energy anisotropy in phase field models using higher order tensor terms
 
Creator NANI, ES
GURURAJAN, MP
 
Subject phase field modelling
interfacial energy anisotropy
cubic anisotropy
hexagonal anisotropy
invariant theory
MICROELASTICITY THEORY
MICROSTRUCTURE EVOLUTION
COMPUTER-SIMULATION
GRAIN-GROWTH
ALLOY
VECTOR
SYSTEM
 
Description In this paper, we show how to incorporate cubic and hexagonal anisotropies in interfacial energies in phase field models; this incorporation is achieved by including up to sixth rank tensor terms in the free energy expansion, assuming that the free energy is only a function of coarse-grained composition, its gradient, curvature and aberration. We derive the number of non-zero and independent components of these tensors. Further, by demanding that the resultant interfacial energy is positive definite for inclusion of each of the tensor terms individually, we identify the constraints imposed on the independent components of these tensors. The existing results in the invariant group theory literature can be used to simplify the process of construction of some (but not all) of the higher order tensors. Finally, we derive the relevant phase field evolution equations and describe some preliminary results from our 1D simulations.
 
Publisher TAYLOR & FRANCIS LTD
 
Date 2014-12-28T12:22:18Z
2014-12-28T12:22:18Z
2014
 
Type Article
 
Identifier PHILOSOPHICAL MAGAZINE, 94(29)3331-3352
1478-6435
1478-6443
http://dx.doi.org/10.1080/14786435.2014.958588
http://dspace.library.iitb.ac.in/jspui/handle/100/16500
 
Language English