Editing Equations of state for crystals of hard spheres
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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 (face-centred cubic)== | ==Hall equation of state (face-centred cubic)== | ||
<ref>[http://dx.doi.org/10.1063/1.1678576 Kenneth R. Hall "Another Hard-Sphere Equation of State", Journal of Chemical Physics '''57''' pp. 2252-2254 (1972)]</ref> Eq. | <ref>[http://dx.doi.org/10.1063/1.1678576 Kenneth R. Hall "Another Hard-Sphere Equation of State", Journal of Chemical Physics '''57''' pp. 2252-2254 (1972)]</ref> Eq. 12: | ||
:<math> | :<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 | where | ||
:<math>\xi = \pi \sqrt{2}/6-y</math> | |||
:<math>\ | |||
==Speedy equation of state== | ==Speedy equation of state== | ||
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|- | |- | ||
| face-centred cubic || 0.5921 || 0.7072 || 0.601 | | face-centred cubic || 0.5921 || 0.7072 || 0.601 | ||
|} | |} | ||
==Almarza equation of state== | |||
For the face-centred cubic solid phase <ref>[http://dx.doi.org/10.1063/1.3133328 N. G. Almarza "A cluster algorithm for Monte Carlo simulation at constant pressure", Journal of Chemical Physics '''130''' 184106 (2009)]</ref> Eq. 19: | |||
:<math>\beta p \left(v-v_0\right) = 3 - 1.807846y + 11.56350 y^2 + 141.6000y^3 - 2609.260y^4 + 19328.09 y^5</math>, | |||
where <math> \left. v \right. </math> is the volume per particle, <math> v_0 \equiv \sigma^3/\sqrt{2} </math> is the volume per particle at close packing, | |||
and <math> y \equiv ( \beta p \sigma^3)^{-1} </math>. | |||
==References== | ==References== |