Variants of Martensite

The transformations under consideration are all symmetry lowering; that is, the lattice of the austenite has higher symmetry than the lattice of the martensite. Consequently, there are multiple configurations of the martensite lattice, and these are called variants.

For example, the cubic to tetragonal transition in 2-dimensions has two variants as depicted in Figure 1 below.

Figure 1: Left is a 2-dimensional cubic lattice, and at the right are the two variants of a 2-dimensional tetragonal lattice.

To find all of the variants:

Possible symmetry lowering transformations between Bravais lattices are given in the table below, where the hexagonal and triclinic lattices are not included.

Symmetry Lowering Transitions

Parent Product Number of Variants, n
cubic tetragonal 3
cubic trigonal 4
cubic orthorhombic 6
cubic monoclinic 12
tetragonal orthorhombic 2
tetragonal monoclinic 4
orthorhombic monoclinic 2
trigonal monoclinic 3

In the table above, the first column is the crystal structure of the parent phase; the second lists the crystal structure of the product phase; and the last column gives the number of variants of the product phase.

Once all of the variants are known, then the energy functional and its energy wells can be constructed for the material.


Some references are

  1. ``Proposed experimental tests of a theory of fine microstructure and the two-well problem.'' by John M. Ball and Richard D. James. Philosophical Transactions of the Royal Society of London A 338, 389 (1992).

  2. `Symmetry and microstructure in martensites.'' by Kevin F. Hane and Thomas W. Shield. Philosophical Magazine A, 78, 1512 (1998).

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