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to deal with vibrational entropy by |
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to deal with vibrational entropy by |
calculating the phon density of States |
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calculating the phon density of States |
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calculating the phon density of States |
um so literally you would look at the |
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um so literally you would look at the |
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um so literally you would look at the |
quantized vibrations do the statistical |
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quantized vibrations do the statistical |
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quantized vibrations do the statistical |
mechanics on them um and those of you |
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mechanics on them um and those of you |
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mechanics on them um and those of you |
whove taken 320 may have sort of |
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whove taken 320 may have sort of |
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whove taken 320 may have sort of |
remember this and calculate the free |
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remember this and calculate the free |
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remember this and calculate the free |
energy associated with these phonons and |
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energy associated with these phonons and |
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energy associated with these phonons and |
I'll say a little more about this later |
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I'll say a little more about this later |
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I'll say a little more about this later |
for example this is the phonon Spectrum |
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for example this is the phonon Spectrum |
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for example this is the phonon Spectrum |
uh for silicon um so can actually quite |
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uh for silicon um so can actually quite |
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uh for silicon um so can actually quite |
accurately calculated uh remember that |
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accurately calculated uh remember that |
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accurately calculated uh remember that |
to get the thermal expansion |
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to get the thermal expansion |
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