All about twining…..now in detail Twin planes Habit planes Martensite
Review There are only two planes that are neither extended, nor compressed when the lattice flips over. Others planes get compressed or stretched - handy for phase transformations in which lattice constant has to change => more later
The k 1 and k 2 planes in Prof. Bakers lecture notes in the model of Haasen. The Haasen picture gives you the deformation of any other plane. In particular, it allows you to find the plane with a (pre-specified) compression or extension From Lecture 16
Objective of twinning geometry theory Regular twins The objective is to find the planes, directions, rotations that will result in a twin such that the unit cell remains the same. Martensitic Transformation Here, the unit cell changes. This makes above search more complicated because now we have to find the twinning operation that transforms fcc iron into distorted bcc.
Twinning geometry is the shear direction. lies in the k 1 or twin plane. is not the shear direction. is the intersection of the k 2 plane with the shear plane, see next page
The shear plane is perpendicular on the twinning plane
The basic problem in (simple) twining is to find 3 non-coplanar vectors (I.e. defining a volume a x b x c) that do not change when twining is performed. If those vectors coincide with the unit cell, the unit cell will survive the shear unchanged.
One way of doing this Put two axis of the unit cell into the twinning plane. Search for a third axis of the unit cell such that it is parallel to Because makes equal angles with any arbitrary vector lying in the twinning plane k 1 the unit cell shall survive the twinning unscathed !
Twins of the first kind You can look in the following way: The lattice was rotated 180 o around the pole of k 1 The lattice planes are flipped over by a shear angle 2 (mirrored at the plane contain the pole of k 1 and the 2 rotation axis ) and then mirrored at the shear plane. Shear plane it’s intersect
Twins of the second kind: The reverse of above is to put two axis of the unit cell into k 2 and the third axis as a “rational” direction in the twinning plane. You can look at this as The lattice plane were rotated 180 degree around the shear direction n 1 The lattice were mirrored at plane k 1 and the mirrored again at the shear plane
In the stereographic projection, this goes like this Trace of K 1 plane before being flipped over Trace of K 1 plane after being flipped over Flip angle 2 Mirror plane for “flip over” K 1
Second order twin is a twin within an other twin Typically the result of consecutive twinning on different lattice planes
Example A CZ Silicon crystals containing 3 twin boundaries Two are first order. One is second order.
T1 are first order coherent twins, twin plane (111), shear direction  Starting at T1 the crystal twins once to H, than again with a coherent twin to T2. This leaves a second order 221/221 twin boundary between T2 and T1 Second order twin
HW 17-1 Show the twinning operation on the preceding page on a stereographic projection
Martensitic transformation Goes by nucleation and growth. But - it proceeds via the movement of screw dislocations that set up periodic shear displacements. So it’s not like an interface between two phases. The composition is the same and the lattice is a distorted fcc lattice that has been sheared
The interface is made up of screw dislocation. Every 6th or so lattice plane contains a screw. The boundary can move with the speed of dislocations. Dislocations speed has an upper limit similar to the speed of sound
Layer by layer transformation => the pole mechanism (Lecture 16) can account for this
Stress field Two surface scratches Martensite Plate Sheared scratch A surface step forms in the posterior crack. The morphology, not accidentally, is similar to that of “super screw” dislocation
HW 17-2 If the martensite plate would be twice as thick, the surface step would - pick one Remain the same Increase its height (z displacement) by 1.412 Increase its height (z displacement) by 1.73 Double it’s height None of above Optional: One sentence explaining your choice
Morphology Martensite. The fine striations are twins in the martensite
Origins of twins in martensite a => b is the martensite transformation (shear transform) that changes the lattice In a matrix, this sets up too much stress due to geometric incompatibility. To restore the original shape the martensite plate twins internally without changing the lattice further. Do not confuse this subsequent shear deformation with the original martensite formation !
The martensite plate in 3-D. Every 6 th atomic plane is a screw dislocation of the type shown before. The screws are negative on top and positive on the bottom. The boundary between the plate and the matrix is the “habit” plane. Since the twining that makes martensite goes along with a change of the unit cell it’s not a simple low index plane
Martensite starts forming at M s. When reheated there is a large hysteresis before austenite begins to form at A s The hysteresis is due to the deformation energy stored and removed. Suspected equilibrium line between austenite and martensite in Fe-Ni alloys. The higher the Ni, the lower the T required to generate martensite.
Martensite crystallography a) Bain transformation (starting from representing fcc as tetragonal with c/a = 1.412 see lecture 16) The Bain transformation puts the C atom at the right place but can’t predict any habit plane (we would need one unchanged principle strain and one large and one smaller) More importantly, it does not include the subsequent twinning within the martensite which reduces the strain energy and effectively, rotates the
For MS&E students How the Baines Cell by compression and extension can be formed by pure shear. I don’t want to resurrect Mohr’s circle and transformation of coordinate sytems, so I will leave it there
If only part of the matrix transforms, we have a tremendous compatibility problem. We need to rotate back by twining inside the martensite. The volume percent twinned, x is an adjustable parameter A vector r in the austenite becomes the vector r’ in martensite. S => shear matrix, R => rotation matrix, B => Bain Matrix. Requesting to be unchanged yield the habit plane
The theory fits the experiment very well Normal of habit plane, orientation relationship, shear direction, shear angle are all predicted with little error
Nucleation of Martensite preformed nuclei in austenite likely arrangement of screw dislocation similar to those shown (parallel screws near each other) for the austenite/martensite boundary Driven by the shear Only activation is that to move the dislocations (Peierls) Stops when the boundary dislocations run into other dislocations and make sessile arrangements, or by other martensite plates