Derived crystal structure of martensitic materials by solid–solid phase transformation

Karami, Mostafa; Tamura, Nobumichi; Yang, Yong; Chen, Xian

doi:10.1107/s2053273320006087

Title: Derived crystal structure of martensitic materials by solid–solid phase transformation

Journal Article · Tue Jun 30 00:00:00 EDT 2020 · Acta Crystallographica. Section A, Foundations and Advances (Online)

DOI:https://doi.org/10.1107/s2053273320006087· OSTI ID:1775392

Karami, Mostafa ^[1]; Tamura, Nobumichi ^[2]; Yang, Yong ^[3];

^[1]

Hong Kong Univ. of Science and Technology (Hong Kong)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Advanced Light Source (ALS)
City Univ. of Hong Kong (Hong Kong)

A mathematical description of crystal structure is proposed consisting of two parts: the underlying translational periodicity and the distinct atomic positions up to the symmetry operations in the unit cell, consistent with the International Tables for Crystallography. By the Cauchy–Born hypothesis, such a description can be integrated with the theory of continuum mechanics to calculate a derived crystal structure produced by solid–solid phase transformation. In addition, the expressions for the orientation relationship between the parent lattice and the derived lattice are generalized. Additionally, the derived structure rationalizes the lattice parameters and the general equivalent atomic positions that assist the indexing process of X-ray diffraction analysis for low-symmetry martensitic materials undergoing phase transformation. The analysis is demonstrated in a CuAlMn shape memory alloy. From its austenite phase (L2₁ face-centered cubic structure), it is identified that the derived martensitic structure has orthorhombic symmetry Pmmn with the derived lattice parameters a_d = 4.36491, b_d = 5.40865 and c_d = 4.2402 Å, by which the complicated X-ray Laue diffraction pattern can be well indexed, and the orientation relationship can be verified.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Hong Kong Research Grants Council; Engineering and Physical Sciences Research Council (EPSRC); City University of Hong Kong

Grant/Contract Number:: AC02-05CH11231; 16207017; 1620101; EP/R014604/1; 9610391

OSTI ID:: 1775392

Journal Information:: Acta Crystallographica. Section A, Foundations and Advances (Online), Vol. 76, Issue 4; ISSN 2053-2733

Publisher:: International Union of CrystallographyCopyright Statement

Country of Publication:: United States

Language:: English

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