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

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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

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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 22 nm22 nm 22 nm 7.4 nm Z Y X

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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 x = -2.12% x = -3.32% x = -2.92% x = -3.42% x = -3.62% x = -3.52%

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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 J XX = 0.862 J YY = 1.063 J ZZ = 1.012 J IJ = 0 J XX = 0.93138132 J YY = 1.03445832 J ZZ = 1.01256351 J XY = -0.02395536 J YX = 0.02972693 All other J ij = 0

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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 Coord. Name 8 LightSteelBlue 9 magenta 10 LimeGreen 11 MediumVioletRed 12 LightGoldenrod x = -3.42% x = -3.62% x = -3.52%

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

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

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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. Z X Y X

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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 Final BCC Structure Variant 1 Variant 2 Variant 3 Variant 4

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J XX = 0.784 J YY = 1.075 J ZZ = 1.074 J XY = -0.003 J YX = 0.006 J XZ = 0.140 J ZX = -0.175 J YZ = -0.012 J ZY = 0.001 J XX = 1.079 J YY = 1.108 J ZZ = 0.760 J XY = 0.057 J YX = -0.017 J XZ = 0.202 J ZX = -0.159 J YZ = -0.022 J ZY 0.006 Z X Variant 2 Variant 4 Note that variant 2 and variant 4 both have large negative J zx

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J XX = 1.083 J YY = 1.085 J ZZ = 0.782 J XY = 0.010 J YX = -0.003 J XZ = -0.194 J ZX = 0.122 J YZ = 0.000 J ZY = 0.000 J XX = 0.804 J YY = 1.056 J ZZ = 1.099 J XY = 0.001 J YX = 0.002 J XZ = -0.122 J ZX = 0.181 J YZ = -0.002 J ZY = -0.014 Z X Variant 1 Variant 3 Note that variant 1 and variant 3 both have large positive J XZ

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J XX = 1.083 J YY = 1.085 J ZZ = 0.782 J XY = 0.010 J YX = -0.003 J XZ = -0.194 J ZX = 0.122 J YZ = 0.000 J ZY = 0.000 J XX = 0.804 J YY = 1.056 J ZZ = 1.099 J XY = 0.001 J YX = 0.002 J XZ = -0.122 J ZX = 0.181 J YZ = -0.002 J ZY = -0.014 Variant 1 Variant 3 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. J XX = 1.079 J YY = 1.108 J ZZ = 0.760 J XY = 0.057 J YX = -0.017 J XZ = 0.202 J ZX = -0.159 J YZ = -0.022 J ZY 0.006 Variant 2 J XX = 0.784 J YY = 1.075 J ZZ = 1.074 J XY = -0.003 J YX = 0.006 J XZ = 0.140 J ZX = -0.175 J YZ = -0.012 J ZY = 0.001 Variant 4

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

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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?

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