Anton–Schmidt equation of state

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 the equation of 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]

The equation of state has been used in cosmological contexts to describe the dark energy dynamics.[6] However its use has been recently criticized since it appears disfavored than simpler equations of state adopted for the same purpose.[7]

See also

References

  1. 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.
  2. 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
  3. Jund, Philippe, et al., Physical properties of thermoelectric zinc antimonide using first-principles calculations., Physical Review B 85.22 (2012) arXiv:1207.1670.
  4. Atomic Simulation Environment documentation of the Technical University of Denmark, Department of Physics
  5. Gilgamesh chemical software documentation of the Department of Chemical Engineering of Carnegie Mellon University "7.2. Equations of State — Gilgamesh documentation v0.01 documentation". Archived from the original on 2014-04-14. Retrieved 2014-05-30.
  6. Salvatore Capozziello, Rocco D'Agostino, Orlando Luongo, Cosmic acceleration from a single fluid description, Physics of the Dark Universe 20 (2018) 1-12, arXiv:1712.04317.
  7. Kuantay Boshkayev, Talgar Konysbayev, Orlando Luongo, Marco Muccino, Francesco Pace, Testing generalized logotropic models with cosmic growth, Physical Review D 104 (2021) 2, 023520, arXiv:2103.07252.
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