Determination of the stretch tensor for structural transformations

Xian Chen, Yintao Song, Nobumichi Tamura, Richard D. James

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41 Scopus citations


Structural transformations in crystalline solids are increasingly the basis of the functional behavior of materials. Recently, in diverse alloy systems, both low hysteresis and reversibility of phase transformations have been linked to the satisfaction of the nongeneric conditions of compatibility between phases. According to the Cauchy–Born rule, these conditions are expressed as properties of transformation stretch tensor. The transformation stretch tensor is difficult to measure directly due to the lack of knowledge about the exact transforming pathway during the structural change, and the complicating effects of microstructure. In this paper we give a rigorous algorithmic approach for determining the transformation stretch tensor from X-ray measurements of structure and lattice parameters. For some traditional and emerging phase transformations, the results given by the algorithm suggest unexpected transformation mechanisms.

Original languageEnglish (US)
Pages (from-to)34-43
Number of pages10
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Aug 1 2016

Bibliographical note

Funding Information:
We thank Liping Liu, Robert Kohn, Kaushik Bhattacharya, Anton Mühlemann and Konstantinos Koumatos for helpful discussions during the preparation of this work. X.C., Y.S., and R.D.J. acknowledge the support of the MURI Project Managing the Mosaic of Microstructure ( FA9550-12-1-0458 , administered by AFOSR), NSF-PIRE ( OISE-0967140 ), ONR ( N00014-14-1-0714 ) and AFOSR FA9550-15-1-0207 . The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract no. DE-AC02-05CH11231 . X.S. and N.T. would like to thank Alastair McDowell and Scott DiMaggio for their assistance on the technical design and construction of the sample heating stage.

Publisher Copyright:
© 2016 Elsevier Ltd


  • Crystallography
  • Geometrically nonlinear theory of martensite
  • Lattice Correspondence
  • Phase transformation


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