# about the influence of the periodic boundary on the strain relaxation

Dear all,

I want to calculate the strain distribution in the epitaxial film. In real experiment, if epitaxial film grows on the different substrate with different lattice constant , there will be strain in the epitaxial film because of the lattice mismatch. In my model, I put epitaxial film on the substrate and set the x and y direction in periodic boundary. Using compute stress to calculate the strain, But I found the strain value is not that obvious. How can I test whether the boundary is really connected? Or are there other reason for me not to obtain the strain distribution like in real experiments.

Many thanks,

Xiaojing

Dear all,

I want to calculate the strain distribution in the epitaxial film. In real experiment, if epitaxial film

Strain can be directly and precisely calculated by the lattice constants of the two slabs? Why the need to estimate it with a simulation?

grows on the different substrate with different lattice constant , there will be strain in the epitaxial film because of the lattice mismatch. In my model, I put epitaxial film on the substrate and set the x and y

X and Y do not mean anything if we do not know which direction the mismatched interface normal is.

direction in periodic boundary. Using compute stress to calculate the strain, But I found the strain value

How exactly do you calculate the “strain” by using a “compute stress” command? I believe the correct word here is “strained induced stress”? Is it not?

Also, how do you verify the boundary condition with stress calculations? Using computed stress commands, putting how exactly you used them aside, does not tell you anything for definite if there is something wrong with the boundary. Contradictory to your expectations, I would think the PBC is not correct if you obtain a huge stress, and the PBC is probably right with non-obvious stress.

To verify the PBC across the two lateral directions, try visualize the atoms, bond lengths, coordinations numbers, etc. You may also use compute rdf to compute the radial distribution functions of the two slabs and see if there is any unusual peaks.

is not that obvious. How can I test whether the boundary is really connected? Or are there other reason for me not to obtain the strain distribution like in real experiments.

Lastly, please note that empirical potentials are not guaranteed to reproduce experiments. The functional form may not be flexible enough to describe all possible conditions, the parameter set may not be transferrable enough to be applied to all problems, and the training/fitting procedure may not be accurate enough. So without deeper understanding of the potential and its capability/limitation, it is bad to say “why can’t I obtain XXX like in real experiments.”

Ray.

Many thanks for reply me.

Strain can be directly and precisely calculated by the lattice constants of the two slabs? Why the need to estimate it with a simulation
–> How can I estimated it? could you give me the formula? there are many simulations to obtain the stain by simulations,pls see the attachment file.

X and Y do not mean anything if we do not know which direction the mismatched interface normal is —> The normal direction of the mismatched interface is Z

How exactly do you calculate the “strain” by using a “compute stress” command? I believe the correct word here is “strained induced stress”? Is it not?
–> Yes!

Also, how do you verify the boundary condition with stress calculations? Using computed stress commands, putting how exactly you used them aside, does not tell you anything for definite if there is something wrong with the boundary. Contradictory to your expectations, I would think the PBC is not correct if you obtain a huge stress, and the PBC is probably right with non-obvious stress.
–> It is the point I want to make clear. For my understanding if there is no periodic boundary , then the strain will relax, because there is space for atoms to relax in x and y direction (if the normal direction of the mismatched interface is Z), is that right? so I think if you want to obtain

！WebbFinal.pdf (1.36 MB)

Strain can be directly and precisely calculated by the lattice constants of the two slabs? Why the need to estimate it with a simulation?
–> I want to calculate the stress distribution, so if the strain can be calulated, how to obtain the stress distribution?

Many thanks
XJ

Many thanks for reply me.

Strain can be directly and precisely calculated by the lattice constants of the two slabs? Why the need to estimate it with a simulation

–> How can I estimated it? could you give me the formula? there are many simulations to obtain the

The formula for calculating strain is: “strain = (L-L0)/L0”.

stain by simulations,pls see the attachment file.

Obviously you have confused with the terms “stress” and “strain”. The attached paper talked about measuring stress and stress field, not strain.

[…]

Also, how do you verify the boundary condition with stress calculations? Using computed stress commands, putting how exactly you used them aside, does not tell you anything for definite if there is something wrong with the boundary. Contradictory to your expectations, I would think the PBC is not correct if you obtain a huge stress, and the PBC is probably right with non-obvious stress.

–> It is the point I want to make clear. For my understanding if there is no periodic boundary , then the strain will relax, because there is space for atoms to relax in x and y direction (if the normal direction of the mismatched interface is Z), is that right? so I think if you want to obtain

There is periodic boundary if the boundary is set to p p p - simple as that.

Now if the PBC is incorrect, atoms will relax, but only to a certain point. If the PBC is so wrong that the atoms have nowhere else to go, the energy and forces are going to remain high. Worse case, you will see lost atoms.

–> I want to calculate the stress distribution, so if the strain can be calulated, how to obtain the stress distribution?

If you have strain, stress can be evaluated by simple energy-volume (or named energy-lattice constant, force-volume, stress-strain) curves. Also, what distribution? Distribution of stress on the interface along one of the lateral directions? Or distribution across the interface along the plane normal? Use fix ave/spatial or similar commands, or simply post-process the dump file and bin the atomic forces.

Ray