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34          <span>Home</span></a></h1>
35        <h2 class="heading"><span>2.3.1. Hardsphere</span></h2>
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40        «&#160;&#160;<a href="../ref/models/structure-factor.html">2.3. Structure Factors</a>
41        &#160;&#160;::&#160;&#160;
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52<span id="id1"></span><h1>2.3.1. Hardsphere<a class="headerlink" href="#hardsphere" title="Permalink to this headline">¶</a></h1>
53<p>Hard sphere structure factor, with Percus-Yevick closure</p>
54<table border="1" class="docutils">
55<colgroup>
56<col width="20%" />
57<col width="48%" />
58<col width="11%" />
59<col width="20%" />
60</colgroup>
61<thead valign="bottom">
62<tr class="row-odd"><th class="head">Parameter</th>
63<th class="head">Description</th>
64<th class="head">Units</th>
65<th class="head">Default value</th>
66</tr>
67</thead>
68<tbody valign="top">
69<tr class="row-even"><td>scale</td>
70<td>Source intensity</td>
71<td>None</td>
72<td>1</td>
73</tr>
74<tr class="row-odd"><td>background</td>
75<td>Source background</td>
76<td>cm<sup>-1</sup></td>
77<td>0</td>
78</tr>
79<tr class="row-even"><td>effect_radius</td>
80<td>effective radius of hard sphere</td>
81<td>Å</td>
82<td>50</td>
83</tr>
84<tr class="row-odd"><td>volfraction</td>
85<td>volume fraction of hard spheres</td>
86<td>None</td>
87<td>0.2</td>
88</tr>
89</tbody>
90</table>
91<p>The returned value is scaled to units of cm<sup>-1</sup>.</p>
92<p>Calculate the interparticle structure factor for monodisperse
93spherical particles interacting through hard sphere (excluded volume)
94interactions.</p>
95<p>The calculation uses the Percus-Yevick closure where the interparticle
96potential is</p>
97<p>where <em>r</em> is the distance from the center of the sphere of a radius <em>R</em>.</p>
98<p>For a 2D plot, the wave transfer is defined as</p>
99<div class="math">
100\[q = \sqrt{q_x^2 + q_y^2}\]</div>
101<img alt="../_images/HardSphere_1d.jpg" src="../_images/HardSphere_1d.jpg" />
102<p><em>Figure. 1D plot using the default values (in linear scale).</em></p>
103<p>REFERENCE</p>
104<p>J K Percus, J Yevick, <em>J. Phys. Rev.</em>, 110, (1958) 1</p>
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112        «&#160;&#160;<a href="../ref/models/structure-factor.html">2.3. Structure Factors</a>
113        &#160;&#160;::&#160;&#160;
114        <a class="uplink" href="../index.html">Contents</a>
115        &#160;&#160;::&#160;&#160;
116        <a href="stickyhardsphere.html">2.3.2. Stickyhardsphere</a>&#160;&#160;»
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