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

p(V)=-\beta \left({\frac {V}{V_{0}}}\right)^{n}\ln \left({\frac {V}{V_{0}}}\right)

Integration of $p(V)$ leads to equation of the state for the total energy. The energy $E$ required to compress a solid to volume $V$ is

E(V)=-\int _{V}^{\infty }p(V^{\prime })dV^{\prime }

which gives

E(V)={\frac {\beta V_{0}}{n+1}}\left({\frac {V}{V_{0}}}\right)^{n+1}\left[\ln \left({\frac {V}{V_{0}}}\right)-{\frac {1}{n+1}}\right]-E_{\infty }

The fitting parameters $\beta ,n$ and $V_0$ are related to material properties, where

\beta

is the bulk modulus

K_{0}

at equilibrium volume

V_0

n

correlates with the Grüneisen parameter

n = -\frac{1}{6} - \gamma_G

.^[2]^[3]

However, the fitting parameter $E_\infty$ 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]

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) .
1 2 Atomic Simulation Environment documentation of the Technical University of Denmark, Department of Physics
↑ 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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Anton-Schmidt equation of state

See also

References