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step 3: position optimization

A system in classical mechanics reaches its equilibrium if all excess energy has been dissipated via friction. A similar reasoning can be applied to atoms in unit cells, to find the equilibrium positions of all atoms.

Take the best unit cell for our Fe-Al crystal you found so far (lowest-energy volume, lowest-energy b/a-ratio), and calculate the forces on the atoms (see the hands-on explanations for this week in the “let’s play” section; medium precision is sufficient, expect 2-3 minutes). Are these forces in agreement with what you expected from the symmetry consideration on the previous page? Now go on to optimize the positions until the forces are zero (see the “let’s play” section, medium precision, expect about 15 minutes). Do the atoms move in agreement with the initial force? What are the final positions of the atoms? How far away are these from the initial positions? How much did the energy change between the initial and final positions?

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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