The Anton–Schmidt equation is an empirical equation of state for crystalline solids, e.g. for pure metals or intermetallic compounds. 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 .Otero-de-la-Roza, et al., Gibbs2: A new version of the quasi-harmonic model code. Computer Physics Communications 182.8 (2011): 1708-1720. Jund, Philippe, et al., Physical properties of thermoelectric zinc antimonide using first-principles calculations., Physical Review B 85.22 (2012) .
However, the fitting parameter does not reproduce the total energy of the free atoms.Atomic Simulation Environment documentation of the Technical University of Denmark, Department of Physics
The total energy equation is used to determine elastic and thermal material constants in quantum chemical simulation packages.Gilgamesh chemical software documentation of the Department of Chemical Engineering of Carnegie Mellon University
The equation of state has been used in cosmological contexts to describe the dark energy dynamics.Salvatore Capozziello, Rocco D'Agostino, Orlando Luongo, Cosmic acceleration from a single fluid description, Physics of the Dark Universe 20 (2018) 1-12, . However its use has been recently criticized since it appears disfavored than simpler equations of state adopted for the same purpose.Kuantay Boshkayev, Talgar Konysbayev, Orlando Luongo, Marco Muccino, Francesco Pace, Testing generalized logotropic models with cosmic growth, Physical Review D 104 (2021) 2, 023520, .
See also
Murnaghan equation of state Rose–Vinet equation of state Birch–Murnaghan equation of state
References