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A lot of times, in my materials classes, metal atoms' behavior during deformation is described like a bunch of stacked balls. In my introduction to material class, our professors explained that metals want to form the most packed structure possible. But then why do other structures, like BCC exist? why don't they all form FCC structures?

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...and the reason you get more complicated potentials is that p, d, and f orbitals are not spherically symmetric but have lobes sticking out at specific angles.

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If you only consider an isotropic interaction such as the classic 6-12 potential $$ V(r) = V_0 (\frac{1}{(r/a)^{12}} - \frac{2}{(r/a)^6}) $$ then indeed you would always get the same crystal structure (in 2d this corresponds to a triangular lattice). But in materials we generally have more complicated potentials that include directional inter-atomic interactions. If you take the potential $V(r) = V_0 (\frac{1}{(r/a)^{12}} - \frac{1+\cos{4\theta}}{(r/a)^6})$ then you can check that you won't have a triangular lattice but instead a square lattice.

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