# How to perform Strain induced properties in Quantum ESPRESSO?

I have to perform strain engineering in a material. The strain would be expansive strain and compressive strain. How do I perform those both?

I am currently using the press command for hydrostatic pressure which is giving me compression as it's reducing the cell parameters. How do I also include expansive strain? Do I have to do it manually by increasing/decreasing cell parameters?

### References:

1. Khandy, S. A.; Chai, J. Strain engineering of electronic structure, phonon, and thermoelectric properties of p-type half-Heusler semiconductor. J. Alloys Compd. 2021, 850, 156615. DOI: 10.1016/j.jallcom.2020.156615.

"Do I have to do it manually by increasing/decreasing cell parameters?"

The answer is yes, you need to change the simulation box vector based on strain.

You can use the following logic:

$$a'=a(\epsilon+I),\tag{1}$$

where $$a'$$ is the new simulation cell vector and $$a$$ is the current simulation vector. $$I$$ is the $$6\times6$$ identity matrix and $$\epsilon$$ is $$6\times6$$ strain matrix. In your case of expansion and compression: $$\epsilon_{\text{exp}}=\begin{bmatrix}1+\delta & 0 & 0\\0 & 1+\delta&0\\0 & 0 &1+\delta \end{bmatrix},\tag{2}$$ $$\epsilon_{\text{com}}=\begin{bmatrix}1-\delta & 0 & 0\\0 & 1-\delta&0\\0 & 0 &1-\delta \end{bmatrix}.\tag{3}$$

• +1. Please see the edits by Tyberius and myself, since these are recommended for future answers in order for us to maintain our very high quality standards here! Thanks for the helpful answer here :) Commented Jan 29, 2022 at 21:15
• Thank you. Here what is delta? the % up to which it should be compressed/expanded? Then it is multiplied to relaxed parameter of the material. So then I have to calculate these cell parameters to apply to get band structure, right? Commented Jan 30, 2022 at 5:08
• @epsilon02fft you are right about delta Commented Jan 30, 2022 at 14:42
• @pranavkumar So let's say my cell parameter is 5 angstrom. I am doing 3% expansion and compression. So new cell parameters would be expansion = 5(1+0.03) = 5.15 and compression = 5(1-0.03) = 4.85 respectively. Am I doing it correctly? Now i just have to use these cell parameter values to calculate (let's say) band structures and further such properties. And these will be called hydrostatic compression/expansion strain? Thank you so much pranav, this helps a lot. Commented Jan 31, 2022 at 5:36
• @epsilon02fft For cubic cell, change in lattice parameter is enough, For general system, use equation 2 and 3 Commented Jan 31, 2022 at 10:02