# Science at the triple point between mathematics, mechanics and materials science

## Publication 8

### Nucleation barriers for the cubic-to-tetragonal phase transformation

##### Authors:

Hans Knupfer
Bonn University

Robert V Kohn
Courant Institute of Mathematical Sciences
New York University

Felix Otto
Max Planck Institute for Mathematics in the Sciences (MIS) in Leipzig

##### Abstract:
We are interested in the phase transformation from austenite to marten- site. 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.
##### Get the paper in its entirety
tetragonal-as-submitted.pdf

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