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so what you see is only at really low
temperature
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temperature
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temperature
um is the electronic thermal expansion
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um is the electronic thermal expansion
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um is the electronic thermal expansion
important in these materials now why is
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important in these materials now why is
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important in these materials now why is
it so important here anybody know
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it's actually because the phoneon one is
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it's actually because the phoneon one is
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it's actually because the phoneon one is
really small remember this is the ratio
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really small remember this is the ratio
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really small remember this is the ratio
of the two um when you're at really low
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of the two um when you're at really low
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of the two um when you're at really low
temperature the thermal expansion is
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temperature the thermal expansion is
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temperature the thermal expansion is
very small in general and the reason is
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very small in general and the reason is
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very small in general and the reason is
you're essentially harmonic in your
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you're essentially harmonic in your
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you're essentially harmonic in your
phone on degrees of freedom so you have
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phone on degrees of freedom so you have
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phone on degrees of freedom so you have
almost no thermal expansion you know if
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almost no thermal expansion you know if
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almost no thermal expansion you know if
you have fully harmonic vibrations