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1 | .. _hardsphere: |
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2 | |
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3 | Hardsphere |
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4 | ======================================================= |
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5 | |
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6 | Hard sphere structure factor, with Percus-Yevick closure |
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7 | |
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8 | ============= =============================== ======= ============= |
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9 | Parameter Description Units Default value |
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10 | ============= =============================== ======= ============= |
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11 | scale Source intensity None 1 |
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12 | background Source background |cm^-1| 0 |
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13 | effect_radius effective radius of hard sphere |Ang| 50 |
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14 | volfraction volume fraction of hard spheres None 0.2 |
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15 | ============= =============================== ======= ============= |
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16 | |
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17 | The returned value is scaled to units of |cm^-1|. |
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18 | |
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19 | Calculate the interparticle structure factor for monodisperse |
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20 | spherical particles interacting through hard sphere (excluded volume) |
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21 | interactions. |
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22 | |
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23 | The calculation uses the Percus-Yevick closure where the interparticle |
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24 | potential is |
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25 | |
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26 | .. math: |
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27 | |
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28 | U(r) = \begin{cases} |
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29 | \infty & r < 2R \\ |
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30 | 0 & r \geq 2R |
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31 | \end{cases} |
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32 | |
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33 | where *r* is the distance from the center of the sphere of a radius *R*. |
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34 | |
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35 | For a 2D plot, the wave transfer is defined as |
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36 | |
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37 | .. math:: |
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38 | |
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39 | q = \sqrt{q_x^2 + q_y^2} |
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40 | |
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41 | |
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42 | .. image:: img/HardSphere_1d.jpg |
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43 | |
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44 | *Figure. 1D plot using the default values (in linear scale).* |
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45 | |
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46 | REFERENCE |
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47 | |
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48 | J K Percus, J Yevick, *J. Phys. Rev.*, 110, (1958) 1 |
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49 | |
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