Anton–Schmidt equation of state
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The Anton–Schmidt equation is an empirical equation of state for crystalline solids, e.g. for pure metals or intermetallic compounds.[1] Quantum mechanical investigations of intermetallic compounds show that the dependency of the pressure under isotropic deformation can be described empirically by
- .
Integration of leads to equation of the state for the total energy. The energy required to compress a solid to volume is
which gives
- .
The fitting parameters and are related to material properties, where
- is the bulk modulus at equilibrium volume .
- correlates with the Grüneisen parameter .[2][3]
However, the fitting parameter does not reproduce the total energy of the free atoms.[4]
The total energy equation is used to determine elastic and thermal material constants in quantum chemical simulation packages.[4][5]
See also[]
- Murnaghan equation of state
- Rose–Vinet equation of state
- Birch–Murnaghan equation of state
References[]
- ^ Mayer, B.; Anton, H.; Bott, E.; Methfessel, M.; Sticht, J.; Harris, J.; Schmidt, P.C. (2003). "Ab-initio calculation of the elastic constants and thermal expansion coefficients of Laves phases". Intermetallics. 11 (1): 23–32. doi:10.1016/S0966-9795(02)00127-9. ISSN 0966-9795.
- ^ Otero-de-la-Roza, et al., Gibbs2: A new version of the quasi-harmonic model code. Computer Physics Communications 182.8 (2011): 1708-1720. doi:10.1016/j.cpc.2011.04.016
- ^ Jund, Philippe, et al., Physical properties of thermoelectric zinc antimonide using first-principles calculations., Physical Review B 85.22 (2012) arXiv:1207.1670.
- ^ a b Atomic Simulation Environment documentation of the Technical University of Denmark, Department of Physics [1]
- ^ Gilgamesh chemical software documentation of the Department of Chemical Engineering of Carnegie Mellon University "Archived copy". Archived from the original on 2014-04-14. Retrieved 2014-05-30.
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: CS1 maint: archived copy as title (link)
Categories:
- Solid mechanics
- Equations of state