Editing Equations of state for crystals of hard spheres
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A number of [[equations of state]] have been proposed for this system. The usual procedure to obtain precise equations of | 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 techniques | computer simulation]] results. | state is to fit [[Computer simulation techniques | computer simulation]] results. | ||
*Alder, Hoover and Young equation of state (Ref 1) is given by | |||
:<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) | |||
* Speedy equation of state (Ref 3) | |||
==References== | ==References== | ||
#[http://dx.doi.org/10.1063/1.1670653 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)] | |||
#[http://dx.doi.org/10.1063/1.1678576 Kenneth R. Hall "Another Hard-Sphere Equation of State", Journal of Chemical Physics '''57''' pp. 2252- (1972)] | |||
#[http://dx.doi.org/10.1088/0953-8984/10/20/006 Robin J. Speedy "Pressure and entropy of hard-sphere crystals", Journal of Physics: Condensed Matter '''10''' pp. 4387-4391 (1998)] | |||
[[category: equations of state]] | [[category: equations of state]] |