Derived Crystal Structure of Martensitic Materials by Solid-Solid Phase Transformation

TL;DR

This paper develops a mathematical framework for deriving crystal structures of martensitic materials during phase transformations, aiding in X-ray analysis and understanding of low-symmetry phases.

Contribution

It introduces a continuum mechanics-based method to calculate derived crystal structures and generalizes orientation relationships for martensitic transformations.

Findings

Derived structure for CuAlMn alloy identified as orthorhombic Pmmm

Lattice parameters for the derived martensitic phase determined

X-ray diffraction pattern indexing verified with the derived structure

Abstract

We propose a mathematical description of crystal structure: underlying translational periodicity together with the distinct atomic positions up to the symmetry operations in the unit cell. It is consistent with the international table of 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, we generalize the expressions for orientation relationship between the parent lattice and the derived lattice. 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 (L2_1 face-centered cubic structure), we identify that the derived martensitic structure has the orthorhombic symmetry Pmmm with derived lattice parameters a_dv = 4.36491 \AA, b_dv = 5.40865 \AA and c_dv = 4.2402 \AA, by which the complicated X-ray Laue diffraction pattern can be well indexed, and the orientation relationship can be verified.