Summary of Martensite Creation: Box with Fixed Cylinder

1. Summary of Martensite Creation: Box with Fixed Cylinder July 1, 2012

2. Simulation Setup: Uniaxial Compression • Simulations performed with large box: 22 x 22 x 11 nm (432,000 atoms) – orientation X||[100], Y||[010] • Prismatic box (shearing allowed) • Perform NPT simulations controlling pressure along the Y and Z directions (and XY,YZ,XZ) to be zero (temperature fixed to be 1 K) • Compress parallel to the X-direction using “fix deform” – scale X length by 0.9 by the end of simulation • Run MD simulations for 100,000 timesteps • This part is exactly the same as what was done in “compress box” simulations • Differenece: A cylinder 1 nm in diameter parallel to the Z-direction was created. These atoms where fixed so that they did not deform during the simulation. Atoms were fixed using setforce to zero forces. Also, NPT conditions where only applied to the non-fixed atoms • GOAL: To induce the transformation at a point of stress/strain concentration then allow the martensite to grow into the surrounding matrix

3. Y X Z 22 nm 7.4 nm 22 nm Left: Simulation box showing cylinder of “fixed” atoms – these atoms were rigid throughout the deformation – zero velocity and zero force on these atoms Right: Simulation box showing potential energy of atoms after 10,000 timesteps. You can see the effect of the stress concentration at the cylnider interface

4. ex = -2.92% ex = -3.32% ex = -2.12% ex = -3.42% ex = -3.52% ex = -3.62% Strain (deformation gradient) in the X-direction. Dark red is zero strain and dark blue is ~ -10% strain. The rigid atoms are not shown since they have exactly zero strain. The strains noted in text are the macroscopic imposed strain in the x-direction

5. Same condition as bottom left (-3.42% imposed strain in x-direction) showing the local strain (deformation gradient) at two locations close to the rigid cylinder JXX = 0.93138132 JYY = 1.03445832 JZZ = 1.01256351 JXY = -0.02395536 JYX = 0.02972693 AllotherJij = 0 JXX = 0.862 JYY = 1.063 JZZ = 1.012 JIJ = 0

6. ex = -3.42% ex = -3.52% ex = -3.62% Coord. Name 8 LightSteelBlue 9 magenta 10 LimeGreen 11 MediumVioletRed 12 LightGoldenrod Top row: Strain in X direction (as from the previous slide) Bottom row: Coordination number – the onset of transformation appears to coincide with reaching a critical strain in the x-direction – this occurs at the top and bottom of the cylinder in the x-direction

7. Interesting that it seems that the whole system has to come nearly to the point of instability before the local transformation can occur

8. ex = -3.52% ex = -3.62% ex = -3.72% ex = -3.82% ex = -4.12% Boxes showing only the BCC coordinated atoms as a function of macroscopically imposed strain.

9. Z X Different 2-dimensional slices showing the complexity of the structure of the BCC phase as it forms. One can see different variants within the bands. Y X

10. Final BCC Structure The final structure after the box contains 4 variants of the BCC phase (2 pairs of twin related variants) Variants 1,2 are twin related as are variants 3,4 However, variants 1 and 3 and 2 and 4 are also related as will be seen on the next two slides Variant 1 Variant 4 Variant 2 Variant 3

11. Variant 4 Variant 2 JXX = 0.784 JYY = 1.075 JZZ = 1.074 JXY = -0.003 JYX = 0.006 JXZ = 0.140 JZX = -0.175 JYZ = -0.012 JZY = 0.001 JXX = 1.079 JYY = 1.108 JZZ = 0.760 JXY = 0.057 JYX = -0.017 JXZ = 0.202 JZX = -0.159 JYZ = -0.022 JZY 0.006 Z Note that variant 2 and variant 4 both have large negative Jzx X

12. Variant 1 Variant 3 JXX = 1.083 JYY = 1.085 JZZ = 0.782 JXY = 0.010 JYX = -0.003 JXZ = -0.194 JZX = 0.122 JYZ = 0.000 JZY = 0.000 JXX = 0.804 JYY = 1.056 JZZ = 1.099 JXY = 0.001JYX = 0.002 JXZ = -0.122 JZX = 0.181 JYZ = -0.002 JZY = -0.014 Z Note that variant 1 and variant 3 both have large positive JXZ X

13. Variant 3 Variant 4 Variant 2 Variant 1 JXX = 0.784 JYY = 1.075 JZZ = 1.074 JXY = -0.003 JYX = 0.006 JXZ = 0.140 JZX = -0.175 JYZ = -0.012 JZY = 0.001 JXX = 1.083 JYY = 1.085 JZZ = 0.782 JXY = 0.010 JYX = -0.003 JXZ = -0.194 JZX = 0.122 JYZ = 0.000 JZY = 0.000 JXX = 1.079 JYY = 1.108 JZZ = 0.760 JXY = 0.057 JYX = -0.017 JXZ = 0.202 JZX = -0.159 JYZ = -0.022 JZY 0.006 JXX = 0.804 JYY = 1.056 JZZ = 1.099 JXY = 0.001JYX = 0.002 JXZ = -0.122 JZX = 0.181 JYZ = -0.002 JZY = -0.014 NOTE: The above deformation gradients have been taken from single atoms within the bands and therefore are not the average – these are close to the avereage (based on a quick survey) but expect there to be some “noise” in the actual values.

14. Orientation Relationships: As before, the orientation relationships are Pitsch – here we see the orientations of the 4 variants [100] [110] [110] [110] [100] [110] [100] [100] [100] [100] [110]FCC || [112]BCC [110]FCC || [112]BCC [110]FCC || [111]BCC [110]FCC || [111]BCC

15. Summary: • Transformation still appears to occur when a critical value of strain in a [100] is reached, however, it seems that the local stress concentration is not enough to have the transformation proceed – need to globally reach the point of instability. • As with simulations with no rigid cylinder, the observed orientation relationship is Pitsch, though here we have 4 not 2 variants – likely this is due to the symmetry of the simulation (stress field caused by cylinder). • Does this mean that locally meeting the instability condition is not enough for the transformation to occur and that the condition always has to be met globally? Unlikely – is the present simulation too over-constrained?