## Austenite Single Variant of Martensite Microstructure

At the critical temperature , both of the phases can coexist in a specimen forming an austenite martensite microstructure. The simplest austenite martensite microstructure is a homogeneous region of the austenite phase coexisting with a homogeneous region of a single variant of the martensite phase. Such a deformation is depicted in Figure 1 below.

Figure 1: Austenite single variant of martensite microstructure

The compatibility equation for this microstructure with the variant Ui can be written as

The unknowns in the equation above are the rotation , the shape strain , and the habit plane normal . Further, this equation is called the habit plane equation. The shape strain gives the magnitude and sense of the transformation; while, the habit plane is the interface between the two phases. In general, the shape strain does not lie in the habit plane, and therefore, the transformation involves both shear and dilatation.

Solutions exists to the habit plane equation if and only if the matrix Ui has an eigenvalue less than one, an eigenvalue equal to one, and an eigenvalue greater than one. This requires special lattice parameters. In any event, at most two solutions can exist to the habit plane equation.

In addition, if solutions exist to the habit plane equation, then they can in general be divided into two sets of symmetry related solutions. The number of solutions in each set is of course the same as the number of martensite variants.

Some of the austenite single variant of martensite microstructures which are possible for the different transitions as listed in the table below.

#### Austenite Single Variant of Martensite Microstructures

Transition Number Observed Comment
Cubic-to-Trigonal 0 No only with =90 degrees, trivial
Cubic-to-Tetragonal 3 No with =1 only
Cubic-to-Orthorhombic 12 Ti-Ta, Ti-Ni-Cu with =1
" 12 No with =1
Cubic-to-Monoclinic 0 No not possible with the lattice parameters of Ti-Ni

In the table above, the first column is the transition; the second lists the number of unique microstructures which can be formed using all of the martensite variants; the third column indicates if the microstructure is observed; and the last column contains some comments.

Another austenite martensite microstructure has twinned martensite and austenite coexisting.