Cubic-to-Tetragonal Transition


The cubic-to-tetragonal transition is described by two parameters, two unequal stretches along two mutually perpendicular directions.

Some alloys undergoing this transition are

Arguably the most important martensitic transformation is the cubic to tetragonal transition in steels (Fe-C); however, this transformation is not thermoelastic, so it is not considered.

There are several possible transitions between a cubic Bravais lattice and a tetragonal Bravais lattice:

  1. simple cubic to simple tetragonal, and
  2. either body-centered cubic (BCC) or face-centered cubic (FCC) to face-centered tetragonal (FCT), which is equivalent to body-centered tetragonal (BCT).
To help in the visualization of the latter transitions, Figure 1 indicates how a FCT lattice is contained in a BCC lattice and how a BCT lattice is contained in a FCC lattice.

Figure 1: Left: FCT lattice in a BCC lattice. Right: BCT lattice in a FCC lattice.

Transformation Stretch Matrices

The transformation stretch matrices are the gradient of the deformations which take a cubic lattice into a tetragonal lattice. There are 3 such matrices, one for each variant of the martensite phase. They have components

The transformation stretches alpha and beta are proportional to alpha ~ a/ao and c/ao, where a and c are the lattice parameters of the tetragonal lattice and ao is the lattice parameter of the cubic lattice.

Microstructures for the Cubic-to-Tetragonal Transition

Here are links to various pages, where a number of different microstructures are discussed. Also contained therein is a table showing the possible microstructures for the cubic-to-tetragonal transition.


Some references are

  1. ``Fine phase mixtures as minimizers of energy.'' by John M. Ball and Richard D. James. Archive for Rational Mechanics and Analysis 100, 13 (1987).

  2. ``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).

  3. ``Wedge-like microstructure in martensites.'' by Kaushik Bhattacharya. Acta Metallurgica et Materialia 39, 2431 (1991).

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

  5. ``A microstructure of martensite which is not a minimizer of energy: the X-interface.'' by Guy Ruddock. Archive for Rational Mechanics and Analysis 127, 1 (1994).

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