Equations of state for crystals of hard spheres
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The stable phase of the hard sphere model at high densities is thought to have a face-centered cubic structure. A number of equations of state have been proposed for this system. The usual procedure to obtain precise equations of state is to fit computer simulation results.
Alder, Hoover and Young equation of state (face-centred cubic solid)[edit]
where where is the volume at close packing, is the pressure, is the temperature and is the Boltzmann constant.
Almarza equation of state[edit]
For the face-centred cubic solid phase [2] (Eq. 19):
- ,
where is the volume per particle, is the volume per particle at close packing, and ; with being the hard sphere diameter.
Hall equation of state (face-centred cubic)[edit]
[3] Eq. 13:
where
Speedy equation of state[edit]
([4], Eq. 2)
where
and (Table 1)
Crystal structure hexagonal close packed 0.5935 0.7080 0.601 face-centred cubic 0.5921 0.7072 0.601 face-centred cubic [5] 0.620735 0.708194 0.591663
References[edit]
- ↑ B. J. Alder, W. G. Hoover, and D. A. Young "Studies in Molecular Dynamics. V. High-Density Equation of State and Entropy for Hard Disks and Spheres", Journal of Chemical Physics 49 pp 3688-3696 (1968)
- ↑ N. G. Almarza "A cluster algorithm for Monte Carlo simulation at constant pressure", Journal of Chemical Physics 130 184106 (2009)
- ↑ Kenneth R. Hall "Another Hard-Sphere Equation of State", Journal of Chemical Physics 57 pp. 2252-2254 (1972)
- ↑ Robin J. Speedy "Pressure and entropy of hard-sphere crystals", Journal of Physics: Condensed Matter 10 pp. 4387-4391 (1998)
- ↑ Marcus N. Bannerman, Leo Lue, and Leslie V. Woodcock "Thermodynamic pressures for hard spheres and closed-virial equation-of-state", Journal of Chemical Physics 132 084507 (2010)