Nucleation barriers for the cubic-to-tetragonal phase transformation

Hans Knüpfer, Robert V. Kohn, and Felix Otto

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Submission date: 14. Jun. 2011
Pages: 36
published in: Communications on pure and applied mathematics, 66 (2013) 6, p. 867-904 
DOI number (of the published article): 10.1002/cpa.21448
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Abstract:

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 role of self-accommodation to achieve the minimal scaling of the energy. The analysis is based on Fourier representation of the elastic energy.