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Abstract:
The subject of this lecture is an application of the phase-field concept to solid-solid phase
transformations in single-component systems. The first attempt to use the phase-field ideas for
analysis of the structure and mobility of an interface at structural transformations has been done
in sixties [1]. The movement of interface through the Paires’s barier was considered for
explanation of its temperature dependence. Later, the ideas of phase-field were employed for
development of the non-classical theory of nucleation in solid and theory of martensitic
transformations [2]. The analysis of the interface structure demonstrates its close similarity
with domain walls in ferromagnetics. Another aspect of this similarity is that both interfaces
are the sources of long-range fields (elastic and magnetic (or electrostatic in ferroelectrics)).
The minimization of the energy of these long-range fields leads to the formation of an equilibrium
domain structure. Among the three basic types of domains in solids, magnetic, electric and elastic,
the last is the most universal, because all phase transformations in solids are accompanied by the
change of the crystalline lattice (self-strain) [3]. The successful description of elastic domain
structures arising at different solid-solid phase transformations has been obtained by the
phase-field modeling last decade [4,5]. I present as an example the results of our recent studies
of domain structure in constrained (epitaxial) layers [6]. Comparing to experimental observations
shows that the phase-field modeling of time-dependent domain evolution is an effective tool for
study of equilibrium or near-equilibrium domain structures, which are determined by the interactions
of domains through the long-range fields. However, it is necessary to take into account that the
elastic fields are determined by incompatibility between phases or domains and not depend on fine
structure of interfaces. Thus, the interface energy and mobility are parameters of phase-field
calculations rather than their results. Therefore the question, if the variational procedure
used for obtaining the equilibrium domain structures adequately describes a real kinetics of
transformations, requires a special discussion.
1. A.L.Roitburd, Kristallografiya, 7, 291 (1962) (in Russian)
2.A.L.Roitburd in “Solid State Physics”, eds. H.Ehrenreich, F.Seitz and D.Turnbull, vol.33, Academic Press, New York, 1978, p. 317.
3. A.L.Roitburd, Sov.Phys.-Solid State, 10, 2870 (1969).
4. see works of A. G. Khachaturyan and his school (L.-Q.Chen, Y.Wang et.al )
5. T.Lookman et al, Phys.Rev.B, 67, 24114 (2003)
6. J.Slutsker, A.Artemev and A.L.Roytburd, J. Appl.Phys. 91, 9049 (2002); Acta Mat. to be published.
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