Atomsk

The Swiss-army knife of atomic simulations

Tutorial: Screw Dislocation in Aluminium

This tutorial explains how to construct a 1/2[110] screw dislocation in aluminium. It is recommended to be familiar with the theory of dislocations in order to follow the steps below.

1. Crystallographic orientation of the system

As in the case of the edge dislocation, we need a supercell with the appropriate crystal orientation that will later allow to introduce the screw dislocation. However, to keep the geometry of the system identical (i.e. dislocation line along Z), we cannot use the same orientation as for the edge dislocation. Here the Burgers vector of the screw dislocation is aligned with the dislocation line, so we need Z=[110]. The slip plane is still normal to the Y axis, i.e. Y=[111]. As a result we have X=[112]. Let us construct this supercell:

atomsk --create fcc 4.046 Al orient [1-12] [-111] [110] -duplicate 40 20 1 Al_supercell.xsf

2. Introduce a screw dislocation

Similarly to the edge dislocation, the screw dislocation can be introduced with Atomsk by using the option "-dislocation" with the parameter "screw":

atomsk Al_supercell.xsf -dislocation 0.51*box 0.501*box screw Z Y 2.860954 Al_screw.xsf cfg

Note that for a screw dislocation, the Poisson ratio is omitted (contrary to edge dislocations where it was mandatory).

Atomsk computes the theoretical stress components (from elasticity theory), which can be visualized with Atomeye. For instance the image below shows the stress component σxz:

When introducing screw dislocations, the number of atoms remains constant. Due to the displacements of atoms, the periodicity of the lattice is lost along both the X and Y directions. The periodicity remains along the Z direction though.

3. Deal with boundary conditions

It is possible to recover the periodicity of the lattice along the direction of glide (i.e. along the X direction in the current example). Indeed, at the edge of the supercell, atoms are displaced along Z by +b/2 above the glide plane, and -b/2 below the glide plane. Therefore, adding a Z component equal to b/2 to the first supercell vector restores the periodicity along the glide direction. This can easily be done manually in the final file, at the condition that it contains atom positions in Cartesian coordinates, like XCrySDen XSF files or LAMMPS data files (and not reduced coordinates, like e.g. CFG files). For instance, in a XSF file, modify the third value in the first vector (here displayed in bold characters):

Al_screw.xsf

# Fcc Al oriented X=[1-12] Y=[-111] Z=[110].
CRYSTAL
PRIMVEC
198.21270999 0.00000000 1.43047700
0.00000000 140.15755135 0.00000000
0.00000000 0.00000000 2.86095404
CONVVEC
198.21270999 0.00000000 1.43047700
0.00000000 140.15755135 0.00000000
0.00000000 0.00000000 2.86095404
PRIMCOORD
(...)

Beware that, depending on the file format, the value may have to be modified at different places. Please refer to the documentation of the simulation or visualization code that you are using.

4. Construct a quadrupole of dislocations

Sometimes, it is preferrable to construct a dipole, or a quadrupole of dislocations. This can be achieved with Atomsk, simply by calling the option "-dislocation" several times. Each time it is called, a new dislocation is introduced in the system.

Let us construct a quadrupole of screw dislocations in an aluminium system:

atomsk --create fcc 4.046 Al orient [1-12] [-111] [110] \
-duplicate 40 30 1 \
-dislocation 0.251*box 0.251*box screw Z Y 2.860954 \
-dislocation 0.751*box 0.251*box screw Z Y -2.860954 \
-dislocation 0.251*box 0.751*box screw Z Y -2.860954 \
-dislocation 0.751*box 0.751*box screw Z Y 2.860954 \
Al_quadrupole.cfg

As before, we create a unit cell of aluminium with the mode "--create", and duplicate it to form a supercell. Then, the four dislocations are introduced: two with positive Burgers vectors at the reduced coordinates (0.25,0.25) and (0.75,0.75), and two with negative Burgers vectors at (0.75,0.25) and (0.25,0.75). Again, each coordinate is shifted by a small amount (0.001) to avoid placing the dislocations at the exact location of an atom.

When introducing several dislocations, their contributions to the stress components are added. As before, it is possible to visualize it. For instance the σxz component looks like the following:

This time, at the border of the supercell, the displacements due to the four dislocations cancel out (because the sum of their Burgers vectors is naught). Therefore, the boundary conditions are 3-D periodic.

5. Further comments

As for the edge dislocation, it is important to note that the screw dislocations constructed with the method above are not relaxed nor optimized. They correspond, at best, to the displacement fields predicted by the elastic theory of dislocations. However, in order to find the actual atomic configuration of the dislocation, the system needs to be optimized (e.g. by performing ab initio or atomistic simulations).

By default the option "-dislocation" uses the displacement fields of isotropic elasticity. This is justified in the case of aluminium because it is an isotropic material. In materials that are highly anisotropic, it is recommended to use the anisotropic elasticity to introduce dislocations, as explained in the following tutorial.