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34          <span>Home</span></a></h1>
35        <h2 class="heading"><span>2.2.2. Dab</span></h2>
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38     
39        <p>
40        «&#160;&#160;<a href="broad_peak.html">2.2.1. Broad peak</a>
41        &#160;&#160;::&#160;&#160;
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44        <a href="gaussian_peak.html">2.2.3. Gaussian peak</a>&#160;&#160;»
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48      <div class="content">
49       
50       
51  <div class="section" id="dab">
52<span id="id1"></span><h1>2.2.2. Dab<a class="headerlink" href="#dab" title="Permalink to this headline">¶</a></h1>
53<p>DAB (Debye Anderson Brumberger) Model</p>
54<table border="1" class="docutils">
55<colgroup>
56<col width="21%" />
57<col width="38%" />
58<col width="15%" />
59<col width="27%" />
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>length</td>
80<td>correlation length</td>
81<td>Å</td>
82<td>50</td>
83</tr>
84</tbody>
85</table>
86<p>The returned value is scaled to units of cm<sup>-1</sup>.</p>
87<p>Scattering model class for the DAB (Debye Anderson Brumberger) Model</p>
88<div class="section" id="definition">
89<h2>2.2.2.1. Definition<a class="headerlink" href="#definition" title="Permalink to this headline">¶</a></h2>
90<p>Calculates the scattering from a randomly distributed, two-phase system based on
91the Debye-Anderson-Brumberger (DAB) model for such systems. The two-phase system
92is characterized by a single length scale, the correlation length, which is a
93measure of the average spacing between regions of phase 1 and phase 2. <strong>The
94model also assumes smooth interfaces between the phases</strong> and hence exhibits
95Porod behavior (I ~ <em>q</em><sup>-4</sup>) at large <em>q</em> (<em>QL</em> &gt;&gt; 1).</p>
96<p>The DAB model is ostensibly a development of the earlier Debye-Bueche model.</p>
97<p><em>Definition</em></p>
98<div class="math">
99\[I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q \cdot L)^2)^2} + \text{background}\]</div>
100<p>where scale is</p>
101<div class="math">
102\[\text{scale} = 8 \pi \phi (1-\phi)(\Delta \rho)^2\]</div>
103<p>and the parameter <em>L</em> is the correlation length.</p>
104<p>For 2D data: The 2D scattering intensity is calculated in the same way as 1D,
105where the <em>q</em> vector is defined as</p>
106<div class="math">
107\[q = \sqrt{q_x^2 + q_y^2}\]</div>
108<table border="1" class="docutils">
109<colgroup>
110<col width="40%" />
111<col width="23%" />
112<col width="37%" />
113</colgroup>
114<thead valign="bottom">
115<tr class="row-odd"><th class="head">Parameter name</th>
116<th class="head">Units</th>
117<th class="head">Default value</th>
118</tr>
119</thead>
120<tbody valign="top">
121<tr class="row-even"><td>scale</td>
122<td>None</td>
123<td>1.0</td>
124</tr>
125<tr class="row-odd"><td>corr length L</td>
126<td>Å</td>
127<td>50.0</td>
128</tr>
129<tr class="row-even"><td>background</td>
130<td>cm<sup>-1</sup></td>
131<td>0.0</td>
132</tr>
133</tbody>
134</table>
135<div class="figure">
136<img alt="../_images/dab_1d.jpg" src="../_images/dab_1d.jpg" />
137<p class="caption">Figure 1: 1D plot using the default values (w/200 data point).</p>
138</div>
139</div>
140<div class="section" id="reference">
141<h2>2.2.2.2. Reference<a class="headerlink" href="#reference" title="Permalink to this headline">¶</a></h2>
142<p>P Debye, H R Anderson, H Brumberger, <em>Scattering by an Inhomogeneous Solid. II.
143The Correlation Function and its Application</em>, <em>J. Appl. Phys.</em>, 28(6) (1957) 679</p>
144<p>P Debye, A M Bueche, <em>Scattering by an Inhomogeneous Solid</em>, <em>J. Appl. Phys.</em>,
14520 (1949) 518</p>
146<p><em>2013/09/09 - Description reviewed by King, S and Parker, P.</em></p>
147</div>
148</div>
149
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