- Q: I'm not familiar with crystal structures (fcc, bcc, lattice constants, etc.) How can I learn more?
- A: Start by checking out http://en.wikipedia.org/wiki/Face-centered_cubic and following the links you find there. For a great reference for any basic materials science concept, see Callister, "Materials Science and Engineering: An Introduction."
- Q: What's the deal with periodicity?
- A: In most calculations you'll do, your structures are not isolated in space. Instead, they're automatically replicated in all directions infinitely! Thus, when you model Au, you provide the positions of just 4 atoms (the conventional fcc cell), but you get the properties of bulk Au (an infinite crystal). This periodicity means you have to take some care to model any non-3D periodic effects, like vacancies and surfaces.
- Q: What does it mean to ensure that a calculation is converged?
- A: In computational work, calculations must be converged with respect to both physical properties (e.g., the number of Au layers included in a surface slab) and numerical issues (e.g., k-point sampling of the Brillouin zone--this will arise later). A converged calculation is one whose result does not change as a particular input is changed. For example, in the Au vacancy calculation, we converge with respect to supercell size. Obviously, a single Au conventional fcc cell (4 atoms) with an Au atom missing is not representative of an isolated vacancy; we've removed 25% of all the atoms! Thus, we make our simulation cell bigger and bigger in the x, y, and z directions until the vacancy energy we calculate stops changing. We would not expect to see any difference between a vacancy calculation where 1 in 500,000 Au atoms is missing, and one in which 1 in 1,000,000 atoms is missing. That means, in effect, the vacancy is not "feeling" the effects of its periodic neighbors.
- Q: Do I need to repeat vacancy supercell calculations after re-inserting the missing atom?
- A: Many people have been doing this but it's actually not necessary! You already have your cohesive energy from the earlier problem in which you found the equilibrium lattice constant. There's no difference in per-atom energy between a perfect 4-atom Au unit cell and a perfect 4000-atom Au supercell.
- Q: How do I calculate a vacancy formation energy?
- A: The formula provided on the homework has been confusing to some people. Here's a simpler way to look at it:
The key is that you need the same number of atoms in the two quantities you're subtracting!