Why Pitsch ?

1. Why Pitsch? July 9 2012

2. How do we end up with the Pitsch orientation relationship and two twinned variants? Follow up on compression of box in x-direction (see previous slides) Orientation Relationship [110]FCC||[112]BCC [010]FCC || [-110]BCC PitschOrientation Relationship This is the same as the Bain transformation combined with a rotation of 10.26o about the [010]FCC which is a rotation in the plane shown below. Z X

3. Compare: Deformation occuring under controlled stress (direct Bain orientation relationship) Deformation under fixed displacement in x-direction (two twinned Pitsch orientations) Can see the large difference in the shape of the boxes just after the transformation in these two cases. All of these boxes are at the same scale to show the deformation Z Starting FCC block Single {100} plane X

4. 10.26o 10.26o Other possible Bain variant You can actually see the 10.26o rotation between the perfect Bain orientation (grey points) and the one Pitsch oriented region – the other Pitsch region corresponds to a rotation of 10.26o away from the other possible Bain orientation that could have formed

5. Z 9 13 X 18 25 Following the transformation of the box where strain was controlled in the x-direction one can see that before the onset of the transformation there is a sort of “anticipatory” behaviour – the material seems to start to show some shearing on {110} planes (two of them) as shown in the top left figure. As the strain is increased, one of these variants starts to win. If you look very closely you can watch the rotation of the lattice in the two twinned variants. This occurs by a shearing in the Y-plane in what appears to be the <110> direction. In one variant the shearing is in one sense, in the other it is in the other sense. 30

6. Z X There actually appears to be two stages to the transformation – first there is the nucleation of the martensite – this appears to occur by a homogeneous shear within the material (see circled areas) – the material becomes unstable locally and transforms

7. Z X Following the initial transformation there is a sort of growth/coarsening – this seems to be controlled by interace defects

8. Z One can see that the macroscopic plane of shear seems to be rotating with strain - X

9. The shearing on {110} is not homogeneous – you see that macroscopically the “shear bands” are actually not {110} – the interfaces have steps – the “growth” of these regions occurs by a sort of ledge growth – or perhaps by a dislocation migration 5 layers 4 layers 3 layers

10. Y 2 1 X Z 3 4 5 Here you can see the interfacial defects on the interface between the “twins” (the dark blue atoms are the edge of the ledges on the interface) – you can see the high density of these defects decreases as the “twin” interface rotates – of course, if this were a real twin interface it should be coherent and there should be no defects -- thus, the interface initially contains defects which allow for thickening of the plates but as this thickening occurs and the interface plane rotates it rotates into the ideal twin position

11. Z 9 30 X From earlier, the net deformation associated with a Pitsch OR martensite variant is of the form: One can start to understand what is happening and why Pitsch forms: The material can’t perform the Bain strain homogeneously because the x-direction is not free to deform – essentially when the transformation occurs, the length in the x-direction is fixed. The two different regions start to shear in opposite senses in {110}<110> – these two shearing operations allow for the Bain strain to be accomplished without there being a change in the length of the box in the x-direction. For the particular conditions considered here we have the two variants giving the following deformation gradients: Now, you can combine these two variants to have a condition where the strain parallel to the X-direction is zero. In this case this occurs when:

12. So Why Pitsch? Pitsch is the consequence of two things: Because of the constraint in the X-direction, the stiffness of the material for shear in {110}<110> is not the same for all variants – thus, initially it is one specific {110}<110> that softens more than the others. Due to the need to maintain the strain in the X-direction, a compensating shearing on a {110}<110> system must occur. When the transformation initially occurs it forms an elastically distorted martensite – this is evidenced by the fact that the interface between the two twin orientations is not a coherent twin boundary. By glide of defects on the twin boundary plane, the lattice rotates making the interface orientation rotate into the twin orientation – thus, the Pitsch is not perfectly formed initially, it develops with a coarsening of the structure.