## Perfect Crystal

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

Ju-Wei Wang 1I
Posts: 31
Joined: Fri Sep 29, 2017 7:05 am

### Perfect Crystal

During lecture, we talked about perfect crystals, which I don't really understand. Can someone explain what that is, i.e. what conditions make them a perfect crystal?

Samantha Joseph 1F
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### Re: Perfect Crystal

A perfect crystal is just an ideal substance where there is no thermal or positional disorder (as justified by S->0 and T->0), but the main purpose of defining a "perfect crystal" is to create a scale of measuring entropy for realistic substances.

skalvakota2H
Posts: 52
Joined: Sat Jul 22, 2017 3:01 am

### Re: Perfect Crystal

A perfect crystal is a substance in which all the molecules are lined up perfectly, so there are no planar imperfections. Nothing within the crystal is moving, so the arrangement cannot be altered. This implies that at ground state, a perfect crystal would have a degeneracy of 1, or W=1; subsequently the entropy is zero.

Michelle Lee 2E
Posts: 64
Joined: Thu Jul 27, 2017 3:01 am

### Re: Perfect Crystal

In friday's lecture, Dr. Lavelle's powerpoint said "if a system can be prepared in only one way, then S=KblnW=0".
What did he mean by prepared in only one way?
I'm not completely sure what he meant by this line and how it relates to the equation.

Matthew 1C
Posts: 47
Joined: Fri Sep 29, 2017 7:06 am

### Re: Perfect Crystal

Michelle Lee 2E wrote:In friday's lecture, Dr. Lavelle's powerpoint said "if a system can be prepared in only one way, then S=KblnW=0".
What did he mean by prepared in only one way?
I'm not completely sure what he meant by this line and how it relates to the equation.

When it says something can only be prepared in one way, that means the degeneracy, or W in the equation, equals one. When plugging in W=1 into the equation, you get ln1, which equals 0, so therefore S=0.

Posts: 51
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### Re: Perfect Crystal

Moreover, it means that we can pinpoint exactly where the particles are within an object which we have never been able to do before.

Dang Lam
Posts: 55
Joined: Thu Jul 27, 2017 3:01 am

### Re: Perfect Crystal

Can someone explain why entropy of a "perfect crystal" is 0 (S=0)?

Max Mazo 2C
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Joined: Fri Sep 29, 2017 7:06 am

### Re: Perfect Crystal

Dang Lam wrote:Can someone explain why entropy of a "perfect crystal" is 0 (S=0)?

At 0K there is no movement of atoms so there is only one possible state for each molecule in a crystal, so it is perfectly ordered and we can know the exact position of everything. Since there is only one possible state, degeneracy is 1, so S = Kb ln(1) = 0

Mary Becerra 2D
Posts: 53
Joined: Fri Sep 29, 2017 7:06 am

### Re: Perfect Crystal

The perfect crystal is related to the third law of thermodynamics which is about systems in equilibrium at absolute zero (0 Kelvin). It states that the entropy of a perfect crystal at absolute zero is exactly equal to zero.

Amy Zheng 2l
Posts: 57
Joined: Fri Sep 29, 2017 7:04 am

### Re: Perfect Crystal

basically entropy=0 in a perfect crystal because they must be in perfect order

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