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bulk modulus and pressure

The bulk modulus (inverse compressibility) is an important elastic modulus. And pressure is one of the common external perturbations we can apply on a crystal. How can we get these from DFT?

Before tackling the next Fe-Al calculations, it is worthwhile to read through the two example documents on geometry optimization in the “let’s play” section of the course. This will show you how to make this task with your preferred DFT code.

For your report on the Fe-Al crystal: estimate which pressure is required to obtain the smallest of the 5 volumes you calculated (this can be done manually, on the E(V)-graph). If your DFT code has a fitting tool for an equation of state (like the ev.x tool in Quantum Espresso, the eosfit tool in WIEN2k, …), then determine the bulk modulus based on the 5 data points you have. Such a fit will also determine the optimal volume you determined yourself on the previous page.

If your DFT code can calculate a stress tensor, you might be inclined to look at that quantity to find out which pressure is required to reach the smallest of your five volumes. Don’t do that yet, for these two reasons: (1) for a numerically precise stress tensor calculation, a high precision is required, and (2) our hypothetical crystal is so far subject to a weird anisotropic pressure – we will need optimize it further, first.

Please indicate in the form hereafter whether or not you could make this task successfully.

If you ran into a difficulty that you cannot solve, please report it in the forum hereunder. If you ran into a difficulty that you could solve, please share the solution with us too — it may help others. Feel free to post any other comment or thought about this exercise. And if you can answer questions posted by fellow students, please help them out.

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