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Volumn 78, Issue 2, 2008, Pages

First-principles multiphase equation of state of carbon under extreme conditions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 46749128171     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.024101     Document Type: Article
Times cited : (82)

References (56)
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    • At very high temperatures (many times Tmelt), ion kinetic energy dominates over interion potential energy and the system behaves like an ideal gas with E∼ 3 2 kB T. This is taken into account in our plasma-based model.
    • At very high temperatures (many times Tmelt), ion kinetic energy dominates over interion potential energy and the system behaves like an ideal gas with E∼ 3 2 kB T. This is taken into account in our plasma-based model.
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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.
    • 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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    • Uncertainty of this magnitude is to be expected from the prediction of melting temperatures using DFT-based methods.
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    • We determined the solid and liquid Hugoniots of Fig. 14 by taking the initial density to be that of experiment at ambient conditions (P=0, T=300 K). Since the ambient density of our EOS model is slightly shifted from this (due to the GGA-DFT error), our starting pressure is nonzero (∼12 GPa). Alternatively, we could have chosen the same experimental starting density but required P=0. This would have shifted the curves in temperature. If we use this prescription, the resulting solid and liquid Hugoniots are shifted up in pressure (relative to those displayed) by roughly 20 GPa near shock-melting. This is a very small shift compared to the theory-experiment liquid Hugoniot disagreement we discuss here.
    • We determined the solid and liquid Hugoniots of Fig. 14 by taking the initial density to be that of experiment at ambient conditions (P=0, T=300 K). Since the ambient density of our EOS model is slightly shifted from this (due to the GGA-DFT error), our starting pressure is nonzero (∼12 GPa). Alternatively, we could have chosen the same experimental starting density but required P=0. This would have shifted the curves in temperature. If we use this prescription, the resulting solid and liquid Hugoniots are shifted up in pressure (relative to those displayed) by roughly 20 GPa near shock-melting. This is a very small shift compared to the theory-experiment liquid Hugoniot disagreement we discuss here.
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