Equations of state for crystals of hard spheres: Difference between revisions
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Carl McBride (talk | contribs) (Added Alder, Hoover and Young equation of state) |
Carl McBride (talk | contribs) (Added Hall equation of state) |
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:<math>\frac{pV}{Nk_BT} = \frac{3}{\alpha} + 2.56 + 0.56 \alpha + O(\alpha^2).</math> | :<math>\frac{pV}{Nk_BT} = \frac{3}{\alpha} + 2.56 + 0.56 \alpha + O(\alpha^2).</math> | ||
where <math>\alpha = (V-V_0)/V_0</math> where <math>V_0</math> is the volume at close packing, <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>k_B</math> is the [[Boltzmann constant]]. | where <math>\alpha = (V-V_0)/V_0</math> where <math>V_0</math> is the volume at close packing, <math>p</math> is the [[pressure]], <math>T</math> is the [[temperature]] and <math>k_B</math> is the [[Boltzmann constant]]. | ||
* Hall equation of state (Ref 2) | * Hall equation of state (Ref 2) Eq. 12: | ||
:<math>Z_{\mathrm{solid}}= \frac{1+y+y^2-0.67825y^3-y^4-0.5y^5-6.028e^{\xi(7.9-3.9\xi)}y^6}{1-3y+3y^2-1.04305y^3}</math> | |||
where | |||
:<math>\xi = \pi \sqrt{2}/6-y</math> | |||
* Speedy equation of state (Ref 3) | * Speedy equation of state (Ref 3) | ||
==References== | ==References== |
Revision as of 15:10, 12 December 2008
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 (Ref 1) is given by
where where is the volume at close packing, is the pressure, is the temperature and is the Boltzmann constant.
- Hall equation of state (Ref 2) Eq. 12:
where
- Speedy equation of state (Ref 3)
References
- 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- (1968)
- Kenneth R. Hall "Another Hard-Sphere Equation of State", Journal of Chemical Physics 57 pp. 2252- (1972)
- Robin J. Speedy "Pressure and entropy of hard-sphere crystals", Journal of Physics: Condensed Matter 10 pp. 4387-4391 (1998)