These two videos visualize the nucleation of partial dislocations in a dot-like structure {lower substrate} + {upper dot}, composed of two different materials A and B, one in the substrate, and the other one in the dot. The two materials are made of Lennard-Jones atoms with two different length parameters sigmaA and sigmaB.

The origin of the dislocation nucleation in the two videos below is very different:

1. Relaxation of different materials. In the first video the sample has non-relaxed initial conditions, since initially all the atoms are placed initially on the same lattice of material A with parameter sigmaA. Clearly the atoms of material B with parameter sigmaB will be out of equilibrium on such a lattice and large oscillations appear as soon the simulation starts, leading to the formation of temporary dislocations, eventually re-absorbed by the sample.

2. Adiabatic change. In the second video (relaxed initial conditions) all the atoms of materials A and B have the same length parameter sigmaA = sigmaB. - so in practice they are initially the same material. The sample is initially thermalized at equilibrium and only afterwards sigmaB is slowly changed, turning the dot material into an actually different material. At some point, the strain produced by the new sigmaB is so strong that dislocations are produced and the strain is released. This time the dislocations do not disappear, since they are stable, corresponding to a lower energy state. For another example of this adiabatic approach to dislocation nucleation in in mismatch heterostrucutres see the video below visualizing the dynamics of a double layer.

Visualization of the stacking faults.

The sample visible in this video is a model of double layer with periodic boundary conditions both in the x and in the y direction; instead, the z direction is the vertical direction in which one passes from material A to material B.

In this video, atoms in a regular crystal are not shown; therefore the two horizontal layers are hidden, and only a selected set of atoms is visible, namely those that do not have a regular arrangement of atoms around them because they for a crystal defect.

Initially, the two materials A and B are identical: same length parameters SA = SB as well as the other parameters of the inter-atomic potential. Then SB is slowly changed until, when reaching a critical misfit (SB* - SA)/SA, the produced strain is released trough the formation of dislocations. Such dislocations move and leave stacking faults, which are visualized by plotting only the atoms which are further from their first neighbors than the expected equilibrium constant of the lattice. By making such a selected visualization, one can follow the nucleation and subsequent growth of the stacking fault.

(The group of atoms visible on the right boundary is spurious and is an effect of boundary conditions)