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There should also be terms accounting for the system making a transition from one distinct well to another. We assume that the system spends most of its time in individual wells rather than between them, in which case these terms are small (Ref.).
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Our agreement would be significantly better if we used a diamond bulk modulus and a Grüneisen parameter from experiment to fit our EOS since the thermal-expansion coefficient involves the ratio of these two quantities. Part of the discrepancy is therefore due to our adherence to the first-principles results for this study, together with the fact that our bulk modulus was taken from a fit to a wide range of volumes (rather than just in the neighborhood of V0). We feel this is of little concern, however, since thermal expansion for diamond is so small (for most materials it is an order of magnitude larger). Thus, our final EOS: E=E (V,T), P=P (V,T) should still be quite accurate.
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