Quantitative analysis of compatible microstructure by electron backscatter diffraction

Michael Chapman, Marc De Graef, Richard D. James, Xian Chen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We propose a scheme for assigning the martensite variant using electron backscatter diffraction in a martensite material that undergoes a solid-solid phase transformation. Based on the solutions of the crystallographic equations of martensite, we provide an algorithm to assign martensite variants to a particular microscopic region, and to check the elastic compatibility of the microstructure corresponding to low hysteresis and high reversibility in shape memory alloys. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Original languageEnglish (US)
Article number379
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2201
StatePublished - Jul 12 2021

Bibliographical note

Funding Information:
Data accessibility. This article has no additional data. Competing interests. We declare we have no competing interests. Funding. This work was supported by: EPSRC grant no. EP/R014604/1 and RGC grant nos. 16201019 and 16207017 and CRF grant no. C6016-20G-C. Acknowledgements. X.C., M.C., M.D.G. and R.D.J. acknowledge the financial support of MURI Project No. FA9550-12-1-0458 (administered by AFOSR). X.C. acknowledges the financial support of the HK Research Grants Council under grant nos. 16201019 and 16207017 and CRF grant no. C6016-20G-C. The authors X.C. and R.D.J. would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme: DNM The mathematical design of new materials. R.D.J. and M.D.G. have also benefited from the support of a Vannevar Bush Faculty Fellowship.

Publisher Copyright:
© 2021 The Author(s).


  • Compatibility
  • Electron backscatter diffraction
  • Martensite
  • Microstructure


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