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I understand that in a crystal lattice the molecule will tend towards the structure that is the lowest in energy (fcc, hcp, ccp, etc.). How does the molecule find these lowest energy states? Is it possible for a molecule to be caught in a local minima?

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    $\begingroup$ Yes, local minima are totally possible. It happens all the time. Ever seen a diamond? That's an example. $\endgroup$ Commented Sep 19, 2018 at 16:15
  • $\begingroup$ @IvanNeretin Could you explain why a diamond is an example of a local minima? Wouldn't all of the carbons want to be as far away as possible, forming a cubic lattice where each carbon has only major interations with its 6 nearest neighbors? $\endgroup$
    – Alex Day
    Commented Sep 19, 2018 at 16:22
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    $\begingroup$ (It is 4, not 6 nearest neighbors, but that's irrelevant.) Because the global minimum is graphite, we know that for sure. $\endgroup$ Commented Sep 19, 2018 at 16:23
  • $\begingroup$ Isn't it 6 nearest neighbors in diamond? Because you have the four around the sides and then the two above and below? So you're saying that a pure carbon molecule is metastable at diamond and stable at graphite? $\endgroup$
    – Alex Day
    Commented Sep 19, 2018 at 18:04
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    $\begingroup$ No, it's 4, and they are not around the sides. A complete explanation would deserve a separate question on your part; then again, it has been asked and answered multiple times before. Carbon doesn't form molecules (except fullerenes), it's a covalent crystal. Yes, diamond is metastable at normal conditions and graphite is stable. $\endgroup$ Commented Sep 19, 2018 at 18:43

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The answer is it doesn't. The molecule transfers from state to state, whenever it can get over the excitation energy barrier between them.

Once it lands in the lowest energy state (or a relatively low one), it just has a hard time getting out again. And if the lowest energy state is on the surface of a crystal, the hole gets deeper and the walls get higher the more other molecules (or atoms) arrange themselves around it.

If the arrangement (the crystal lattice) only represents a local minimum, that's likely still quite (=meta)stable. Actually those metastable states tend to be created with a high probablility, see https://en.wikipedia.org/wiki/Polymorphism_(materials_science)#Ostwald's_rule

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