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Nucleation Barriers for the Cubic‐to‐Tetragonal Phase Transformation
Author(s) -
Knüpfer Hans,
Kohn Robert V.,
Otto Felix
Publication year - 2013
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21448
Subject(s) - tetragonal crystal system , martensite , austenite , scaling , nucleation , elastic energy , phase (matter) , transformation (genetics) , elasticity (physics) , mathematics , condensed matter physics , materials science , thermodynamics , geometry , physics , metallurgy , chemistry , microstructure , composite material , quantum mechanics , biochemistry , gene
We are interested in the phase transformation from austenite to martensite. This transformation is typically accompanied by the generation and growth of small inclusions of martensite. We consider a model from geometrically linear elasticity with sharp energy penalization for phase boundaries. Focusing on a cubic‐to‐tetragonal phase transformation, we show that the minimal energy for an inclusion of martensite scales like $\max \{ V^{2/3}, V^{9/11} \}$ in terms of the volume V . Moreover, our arguments illustrate the importance of self‐accommodation for achieving the minimal scaling of the energy. The analysis is based on Fourier representation of the elastic energy. © 2012 Wiley Periodicals, Inc.