Stability of a Perfect Crystal
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Stability of a Perfect Crystal
Say you have a perfect crystal cooled down to 0 Kelvin. I understand that S=0 at this point since there is no atomic movement or vibration and that U=0 since there is no heat or work to supply internal energy. As I understand, the Entropy Maximization Principle implies that since S=0, the system is unstable since the entropy is not at its maximum. However, from what I understand, the Energy Minimization Principle implies that since U=0, the system is actually stable since the internal energy is at its minimum. I remember reading in the notes that entropy "overrides" what statements pertaining to energy have to say about the system. From that reasoning, is it correct to say that the system is unstable? Can you also say that the system is unstable because the chances of a system being in such a state is extremely low?
Re: Stability of a Perfect Crystal
In my opinion it would be very stable, since at absolute zero the atoms can't move or have energy.
Re: Stability of a Perfect Crystal
But what about the fact that entropy is zero as well at that point; wouldn't that imply that there's instability?
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Re: Stability of a Perfect Crystal
Good thought process. We define a perfect crystal as having 0 entropy. As we add defects to the lattice, the system has more possible arrangements and has higher entropy, so in a sense it is unstable. However, these defects are higher in energy--imagine a salt crystal where you are missing one sodium ion. As the temperature increases, those states are accessible and entropy will win. But at 0 K, the most energetically stable configuration is the perfect crystal (assuming no degeneracy).
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