1. Visualization of Dislocations in a 3-D Nanoindentation Simulation
Aree Witoelar
Computational Physics
Rijksuniversiteit Groningen

2. Outline Dislocations Simple dislocations
Stacking faults, partial dislocations
Nanoindentation Simulation
Results
Summary

3. Introduction Imperfections in crystals are: point defects,
line defects (dislocations),
planar defects and
volume defects.
Dislocations can be analyzed by atomic simulations, for example a nanoindentation simulation.

4. What are Dislocations?
Dislocations are one-dimensional line defects in crystals.
Example: edge dislocation and screw dislocation on SC.
Slip
The Burgers vector determines the direction of a dislocation and its magnitude. We make a circuit by jumping from atom to atom. A closing failure of the circuit defines the Burgers vector.
Edge dislocation: an extra half plane of atom is inserted
Screw dislocation: atoms go around in a ramp
H. Föll, Defects in Crystal,

5. Close-Packed Lattices
Close-packed lattices are comprised of layers of close-packed planes of atoms.
FCC: ABCABCABC…
HCP: ABABAB…
Stacking fault examples:
ABCABCABC  ABCABCBABC…
ABCABCABC  ABCACABC…
H. Föll, Defects in Crystal,

6. Stacking Faults
A stacking fault occurs when there is a mismatch of close-packed planes.
ABCABC  ABCBABC…
Perfect dislocations may disassociate into stacking faults as it has lower energy.
DISLOCATION
Partial Dislocation
Stacking fault examples:
ABCABCABC  ABCABCBABC…
ABCABCABC  ABCACABC… C A B

7. Nanoindentation Simulation
A 3-D nanoindentation experiment is simulated using Molecular Dynamics.
A spherical indenter is pushed down into the system gradually.
The position of each atom in the system are recorded at given times.

8. Molecular Dynamics
The position and momentum of each atom are calculated at each time step.
Equations of motion using Verlet algorithm:
Atom-atom potential and atom-indenter potential

9. Potential Models Potential models:
Lennard-Jones (LJ) : two-body potential.
rij = distance between two atoms
Lennard-Jones Spline (LJS): adds a term to soften discontinuity.
Embedded Atom Method (EAM): embedded in an “electron sea”
χ = vacancy formation energy/cohesive energy, ε = potential well depth, σ = distance of zero potential. rij = distance between two atoms, rc = cut-off radius, d = dimensionality

10. Visualization of Dislocations
Detect dislocations using coordinate number C (number of nearest neighbors).
On a perfect crystal:
SC: 6 nearest-neighbors
FCC: 12 nearest-neighbors
Atoms with wrong C  dislocated atoms!

11. Simple Dislocations in SC
We make a perfect SC crystal and adjust the positions to make simple dislocations analytically.
Edge dislocation
Screw dislocation
Top view
Dislocation
U = displacement
Dislocation
Extra half-plane

12. Dislocations in a Nanoindentation Simulation
We simulate FCC-type iron (Fe)
± atoms in a box
Lennard-Jones potential between atoms
Side and bottom boundaries are fixed, top surface is free
The indenter is pushed into the system (loading) and then pulled out (unloading).
Only atoms with C ≠ 12 (dislocated) and surface atoms will be shown.

13. Loading Yellow = surface atoms Black = dislocated bulk atoms Indenter
Blue = dislocated surface atoms
Indenter
17Å
68Å
Atoms are dislocated because of stress.
Dislocated atoms form into loops.
100Å
100Å

14. Dislocation Loops Loops indicate stacking faults.
Partial dislocations are the edges of the stacking fault.
Partial dislocation
Stacking fault
Dislocation loops by Kelchner1
1. C. L. Kelchner et al., Phys. Rev. B 58, 11085–11088 (1998)

15. Dislocation Loops Propagation
LJ, -2.0Å
Loop
LJ, -3.1Å
Loop
Loops may appear or disappear during loading.
Loops can move away or towards the indenter tip.
Loops always connect to the surface or other dislocations.
LJ, -8.4Å
Loop grows
LJ, -14Å
New loop

16. Unloading Yellow = surface atoms Black = dislocated bulk atoms
Blue = dislocated surface atoms
Some dislocated atoms remain after unloading.

17. Dislocation Loops Loops to the surface can travel as a unit.
Stacking fault
“Hillock” (bump on surface)
Glides away as a unit
Simulation by Rodriguez1
The effect of the size of the indenter is not straightforward. Large-indenter dislocation structure is less sharp and more delocalized J. Knap, M. Ortiz, Effect of Indenter Radius Size on Au(001) Nanoindentation, Phys. Rev. Letter Vol 90 Num 22
Dislocations
1. Rodriguez et al, Phys. Rev. Letters Vol. 88 Num.3, (2002)

18. Slip Direction
Hillock
Top view
Experiment1
Slip in direction
Close-packed planes slip along <110> directions  shortest dislocation on FCC
1. Rodriguez et al, Phys. Rev. Letters Vol. 88 Num.3, (2002)

19. Comparing LJ and LJS-EAM
We compare simulations with the same parameters, but two different potentials: LJ and LJS-EAM potentials.

20. Comparing LJ and LJS-EAM
The two simulation create different patterns of dislocated atoms.
Lennard-Jones
LJ, -0.9Å
LJ, -8.4Å
LJ, -20.0Å
Lennard-Jones Spline with Embedded Atom Method
LJS-EAM, -0.9Å
LJS-EAM, -8.4Å
LJS-EAM, -20.0Å

21. Comparing LJ and LJS-EAM
Less atoms jump out of the surface in LJS-EAM
 LJS-EAM has additional forces to keep the atoms in the system.
Deeper dislocation loops in LJS-EAM.
 More atoms creates higher stress, causing dislocations.
LJ, -20.0Å
LJS-EAM, -20.0Å

22. Summary We have shown simple dislocations on a SC crystal.
Dislocation loops are seen in the nanoindentation simulation, indicating stacking faults.
The loops always reach the surface or other dislocations.
Small bumps on the surface (“hillocks”) are created along the <110> directions.
Dislocation loops in LJS-EAM go deeper into the system than in LJ.

23. Credits Dr. K. Michielsen Prof. Dr. H. de Raedt
RUG Computational Physics Group

24. The End