Complex Martensitic Microstructures in Ti76Nb22Al2
Abstract
We analyze the unusual microstructure resulting from the cubic to orthorhombic phase transformation in the shape-memory alloy Ti76Nb22Al2. This seems to represent an approximate experimental realization of a deformation having a finite number of incompatible deformation gradients, which has been known to exist only as a theoretical possibility. Because the middle eigenvalue γ of the transformation strain is very close to 1, the phase transformation in this alloy takes place via nucleation of exact austenite-martensite interfaces rather than, as usual for other alloys, by classical austenite-martensite interfaces separating the austenite from a finely-twinned laminate of martensite. According to the moving mask approximation of Della Porta this leads to the question whether a microstructure can be formed from the set H of the twelve matrices Vi on the martensite energy wells that are rank-one connected to the identity, even though these matrices are mutually incompatible. We show that when γ=1 and the transformation is volume preserving, such a microstructure is possible that does not deform the grain boundary. This is a consequence of H forming a degenerate T12 configuration in the sense of Kirchheim. In fact there are such microstructures supported on just 8 of the 12 matrices in H. However there is no deformation satisfying the same boundary condition whose gradient belongs to H almost everywhere. An additional prediction, confirmed experimentally, is that the macroscopic deformation gradient equals the identity everywhere. We also analyse the approximate compatibility of the Vi. Although mutually incompatible, they are nearly compatible, with some pairs much more nearly compatible than others, these pairs corresponding to interfaces that are more frequently observed.
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BibTeX
@misc{ball2026complex,
title = {{Complex Martensitic Microstructures in $\rm Ti_76\rm Nb_22\rm Al_2$}},
author = {John M. Ball and Francesco Della Porta and Tomonari Inamura},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06383},
eprint = {2611.06383},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06383},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complex Martensitic Microstructures in Ti_76Nb_22Al_2
AU - John M. Ball
AU - Francesco Della Porta
AU - Tomonari Inamura
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06383
UR - https://arxiv.org/abs/2611.06383
AB - We analyze the unusual microstructure resulting from the cubic to orthorhombic phase transformation in the shape-memory alloy Ti_76Nb_22Al_2. This seems to represent an approximate experimental realization of a deformation having a finite number of incompatible deformation gradients, which has been known to exist only as a theoretical possibility. Because the middle eigenvalue γ of the transformation strain is very close to 1, the phase transformation in this alloy takes place via nucleation of exact austenite-martensite interfaces rather than, as usual for other alloys, by classical austenite-martensite interfaces separating the austenite from a finely-twinned laminate of martensite. According to the moving mask approximation of Della Porta this leads to the question whether a microstructure can be formed from the set H of the twelve matrices V_i on the martensite energy wells that are rank-one connected to the identity, even though these matrices are mutually incompatible. We show that when γ=1 and the transformation is volume preserving, such a microstructure is possible that does not deform the grain boundary. This is a consequence of H forming a degenerate T_12 configuration in the sense of Kirchheim. In fact there are such microstructures supported on just 8 of the 12 matrices in H. However there is no deformation satisfying the same boundary condition whose gradient belongs to H almost everywhere. An additional prediction, confirmed experimentally, is that the macroscopic deformation gradient equals the identity everywhere. We also analyse the approximate compatibility of the V_i. Although mutually incompatible, they are nearly compatible, with some pairs much more nearly compatible than others, these pairs corresponding to interfaces that are more frequently observed.
ER -