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| View Original: | Hard-sphere phase diagram pressure packing fraction.svg (476x424) | |||
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| Keywords: Hard-sphere phase diagram pressure packing fraction.svg en Phase diagram of hard sphere system Solid line - stable branch dashed line - metastable branch Reduced pressure <math>\beta P\sigma 3</math> as a function of the volume fraction or packing fraction <math>\eta</math> With inverse thermal energy <math>\beta kT -1 </math> sphere diameter <math>\sigma 2R</math> packing fraction <math>\eta V_0\rho</math> volume of a single sphere <math>V_0 4\pi R 3/3 \pi\sigma 3/6</math> number density <math>\rho N/V</math> system volume <math>V</math> total particle number <math>N</math> Vertical grey lines indicate freezing <math>\eta_\mathrm f \approx 0 494</math> melting <math>\eta_\mathrm m \approx 0 545</math> random close packing <math>\eta_\mathrm rcp \approx 0 644</math> close packing <math>\eta_\mathrm cp \pi \sqrt 2 /6 \approx 0 74048</math> Reference A Mulero Theory and Simulation of Hard-Sphere Fluids and Related Systems Springer 2008 ISBN 978-3-540-78766-2 own Franzl aus tirol 2012-08-08 Thermodynamic diagrams Cc-zero | ||||
