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In this section, we will study the phenomenological theory of martensite transformation which

Â explains the mechanism of displacive transformation.

Â While considering what we observe in the displacive transformation and the nature of the structural

Â change between FCC to BCC structure we encounter several difficulties.

Â In this section, at first, we will think about those kinds of difficulties in relating observing

Â the shape deformation and the actual deformation converting FCC lattice into BCC structure.

Â Then we will see how the theory of martensite transformation reconciles the discrepancy

Â between them.

Â As I mentioned, the shape deformation of the transformation has a character of invariant

Â plane deformation which looks like a kind of shear deformation.

Â Then the simplest way to explain the shape deformation is regarding it as a successive

Â slip parallel to the habit plane.

Â However, the observation on the microstructure tell us that the habit plane is not the slip

Â plane of austenite and observed indices of habit plane is not rational numbers.

Â Moreover it is clear that the simple shear deformation cannot convert the FCC lattice

Â into the BCC structure.

Â It implies that even though the observed shape deformation looks like a simple shear deformation,

Â the actual deformation which convert the FCC lattice to BCC during displacive transformation

Â should have more complicated nature.

Â Indeed there are many ways to convert FCC structure into BCC by applying deformation.

Â This figure illustrate one example.

Â Here the broken line indicate the lattice structure of FCC.

Â Within the FCC lattice, we can identify a potential unit cell as indicated in this red

Â lines which can be converted into BCC structure by applying proper deformation.

Â Among numerous ways which can convert the FCC lattice into the BCC structure, the deformation

Â suggested by Bain is known to involve the smallest principal strain.

Â This is a basic concept of Bain deformation.

Â Here the broken line again indicate the lattice of FCC structure.

Â In a similar way to the previous case, we can determine a unit cell which can be converted

Â into BCC lattice by proper deformation.

Â What Bain suggest is the unit cell given by this blue lines.

Â Actually this unit cell is body centered tetragonal lattice, BCT lattice.

Â And you can understand that by applying the compressive stress along the vertical axis

Â and tensile deformation along these two axes this BCT lattice can be converted into BCC

Â structure.

Â The Bain Deformation is energetically most favorable way for structural change from FCC

Â to BCC lattice because it requires the minimum deformation.

Â But the Bain deformation is not the invariant plane deformation which is observed during

Â the displacive transformation.

Â To understand it, let's consider a sphere having FCC structure then applying Bain deformation

Â to sphere by compressing the sphere along this vertical direction and stretching it

Â along the other two axis.

Â It will deform this blue sphere into this red oblate spheroid.

Â When we think about any vectors connecting the origin of the sphere and the surface,

Â for instant OA, all the vectors in the oblate are distorted after the Bain deformation as

Â shown in OAâ€™,

Â It indicates that the Bain deformation is not Invariant plane deformation.

Â However after the Bain deformation we can find one set of vectors of which direction

Â is changed but the length is not changed.

Â That is the vector OA' in this figure which was OA vector before the deformation.

Â Then combining the Bain deformation and rigid body rotation makes us to leave one vector

Â of which lengths and direction are not changed as shown in this figure.

Â You can see that the vector OA and OA' is the same after the combined deformation of

Â Bain deformation and the rigid body rotation.

Â Since the application of rigid body rotation does not change the crystal structure, so

Â the combination of the Bain deformation and rigid body rotation still converts FCC structure

Â into the BCC structure.

Â It means that the Bain deformation is not invariant plane deformation by itself but,

Â by combining with the rigid body rotation, we can make the deformation leave one line

Â unchanged after the deformation, having the character of the invariant line deformation.

Â Now we have the combination of Bain deformation and rigid body rotation which converts the

Â FCC lattice into BCC structure with minimum principal strain.

Â But there is still difficulty in relating the deformation to the shape deformation of

Â the displacive transformation.

Â It is because the combination of Bain deformation and rigid body rotation is invariant line

Â deformation but the observed shape deformation is invariant plane deformation.

Â In other word, the Bain deformation and rigid body rotation leaves only one set of undistorted

Â line after the deformation which is not consistent with the observation of shape deformation

Â indicating the presence of undistorted plane after the deformation.

Â To reconcile the discrepancy between the deformation converting FCC to BCC lattice and the actual

Â observation of shape deformation, the theory of martensite transformation proposed subsidiary

Â deformation which is called lattice invariant shear.

Â The concept of lattice invariant shear start with the fact that the combination of two

Â invariant plane deformation, generate one invariant line deformation where the invariant

Â line is the intersection of two invariant plane as shown in this figure..

Â Then in the reverse way, any invariant line deformation can be factorized into two invariant

Â plane deformation as long as the invariant planes contain the Invariant line.

Â Now recalling the combination of Bain deformation and the rigid body rotation makes the invariant

Â line deformation, the deformation converting FCC lattice to BCC structure can be factorized

Â into two invariant plane deformation.

Â Then if we determine the second invariant plane deformation so that we can make the

Â first invariant plane deformation correspond to the observed shape deformation, then the

Â cancellation of shape change associated with the second invariant plane deformation by

Â lattice in invariant shear will give the final lattice change of FCC to BCC with observed

Â shape change..

Â It implies that the application of above lattice invariant shear combined with Bain deformation

Â and rigid body rotation will correspond to the observed shape deformation which converts

Â the FCC lattice to BCC structure.

Â It is noted that the conversion of FCC to BCC structure is done by the Bain deformation

Â and rigid body rotation.

Â And the lattice invariant shear only changes the shape of product phase not affecting the

Â crystal structure.

Â The lattice invariant shear not affecting the crystal structure can be done either slip

Â or twinning.

Â This figure schematically shows how the lattice invariant shear by slip or twinning makes

Â the invariant line deformation into macroscopically invariant plane deformation.

Â The theory of martensite transformation also explains why the indices of habit plane are

Â not rational numbers.

Â As you can see in this figure, the habit plane is merely the boundary of twinned or slip

Â region by lattice invariant shear.

Â Therefore, it does not necessarily correspond to a specific crystallographic planes and

Â thus does not have rational indices.

Â Actually, this phenomenological theory of martensite transformation was firstly developed

Â in 1950s without detailed knowledge on the microstructure generated by the displaced

Â transformation.

Â Later, the development of advanced characterization tools such as transmission electron microscope

Â makes it possible to observe the dislocation substructures like these fine twins in the

Â martensite plate, which is well consistent with a theory.

Â