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<h1>Activity 5: Multiple scattering in the forward scattering regime</h1>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ped-of-the-1t-tise2-surface">PED of the 1T-TiSe<sub>2</sub> surface</a><ul class="nav section-nav flex-column">
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<section class="tex2jax_ignore mathjax_ignore" id="activity-5-multiple-scattering-in-the-forward-scattering-regime">
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<span id="forward-scattering"></span><h1>Activity 5: Multiple scattering in the forward scattering regime<a class="headerlink" href="#activity-5-multiple-scattering-in-the-forward-scattering-regime" title="Link to this heading">#</a></h1>
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<p>In photoelectron diffraction, it is well known that for high photoelectron kinetic energy (typically > 900 eV), the scattering factor is strongly peaked in the forward direction. It means that photoelectrons are almost not deviated after a scattering event.</p>
|
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<p>Peaks of intentisity are then usually observed for dense atomic directions of the sample. This is the <strong>forward scattering approximation</strong>.</p>
|
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<p>For such high kinetic energy, multiple scattering is needed to accurately describe the measured intensity, but the matrix inversion algorithm cannot be used since the memory needed for storing the matrix itself would be generally too large. The matrix will contain
|
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<span class="math notranslate nohighlight">\((N \times (L_{max}+1)^2)^2\)</span> elements of complex type with double precision (64 bits) where <span class="math notranslate nohighlight">\(N\)</span> is the number of atoms and <span class="math notranslate nohighlight">\(L_{max}\)</span> is the number of spherical harmonics used to expand the electron wave around each atomic center. As the kinetic energy increases, the mean free path (MFP) of the photoelectron is larger and the number of atoms in the cluster has to be greater. Lmax also increases with the kinetic energy.</p>
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<p>Try to evaluate how much memory you would need for this matrix for a hemispherical cluster of copper 15 angströms thick (1 MFP) for <span class="math notranslate nohighlight">\(L_{max} = 25\)</span> ?</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
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<span class="c1"># lattice constant of fcc copper</span>
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<span class="n">a</span> <span class="o">=</span> <span class="mf">3.6</span>
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<span class="c1"># radius of the cluster</span>
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<span class="n">r</span> <span class="o">=</span> <span class="mi">15</span>
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<span class="c1"># volume of the cluster</span>
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<span class="n">V</span> <span class="o">=</span> <span class="mf">.5</span> <span class="o">*</span> <span class="p">(</span><span class="mi">4</span><span class="o">/</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">r</span><span class="o">**</span><span class="mi">3</span>
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<span class="c1"># volume of the cell</span>
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<span class="n">v</span> <span class="o">=</span> <span class="n">a</span><span class="o">**</span><span class="mi">3</span>
|
||
<span class="c1"># number of atoms in the unit cell</span>
|
||
<span class="n">n</span> <span class="o">=</span> <span class="mi">4</span>
|
||
<span class="c1"># number of atoms in the cluster</span>
|
||
<span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">V</span><span class="o">/</span><span class="n">v</span> <span class="o">*</span> <span class="n">n</span><span class="p">)</span>
|
||
|
||
<span class="n">Lmax</span> <span class="o">=</span> <span class="mi">25</span>
|
||
<span class="n">M</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span> <span class="o">*</span> <span class="p">(</span><span class="n">Lmax</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">64</span> <span class="o">/</span> <span class="mi">8</span>
|
||
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">N</span><span class="si">:</span><span class="s2">d</span><span class="si">}</span><span class="s2"> atoms, </span><span class="si">{</span><span class="n">M</span><span class="o">/</span><span class="mf">1e12</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2"> TB"</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
<div class="cell_output docutils container">
|
||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>606 atoms, 2.685 TB
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</details>
|
||
</div>
|
||
<p>This is too much memory. We will use another algorithm available in MsSpec: The <em>Rehr-Albers series expansion</em>. We already used that algorithm in activity 3 for the single scattering approach. But this time, we will explore a bit more the effect of the scattering order > 1</p>
|
||
<section id="ped-of-the-1t-tise2-surface">
|
||
<h2>PED of the 1T-TiSe<sub>2</sub> surface<a class="headerlink" href="#ped-of-the-1t-tise2-surface" title="Link to this heading">#</a></h2>
|
||
<p>Let us try to model the Ti2p XPD pattern of the transition metal dichalcogenide 1T-TiSe<sub>2</sub>.</p>
|
||
<div class="admonition seealso">
|
||
<p class="admonition-title">See also</p>
|
||
<p>based on this paper from M.V. Kuznetsov <em>et al.</em>
|
||
<a class="reference external" href="https://doi.org/10.1016/j.susc.2012.06.008">Surf. Sci. <strong>606</strong> p1760–70 (2012)</a></p>
|
||
</div>
|
||
<section id="creating-the-tise2-cluster">
|
||
<h3>Creating the TiSe<sub>2</sub> cluster<a class="headerlink" href="#creating-the-tise2-cluster" title="Link to this heading">#</a></h3>
|
||
<p>Start by creating a small cluster of 1T-TiSe<sub>2</sub> using the <code class="docutils literal notranslate"><span class="pre">mx2</span></code> function of <code class="docutils literal notranslate"><span class="pre">ase.build</span></code> and the <code class="docutils literal notranslate"><span class="pre">hemispherical_cluster</span></code> function of <code class="docutils literal notranslate"><span class="pre">msspec.utils</span></code>.</p>
|
||
<figure class="align-default" id="tise2-fig">
|
||
<a class="reference internal image-reference" href="../_images/TiSe2_cell.jpg"><img alt="TiSe2" class="align-center" src="../_images/TiSe2_cell.jpg" style="width: 300px;" />
|
||
</a>
|
||
<figcaption>
|
||
<p><span class="caption-number">Fig. 11 </span><span class="caption-text">Structure of 1T-TiSe<sub>2</sub> (<span class="math notranslate nohighlight">\(a_0=b_0=3.535\)</span> Å, <span class="math notranslate nohighlight">\(c_0=6.004\)</span> Å, <span class="math notranslate nohighlight">\(d=3.450\)</span> Å, <span class="math notranslate nohighlight">\(D=2.554\)</span> Å)</span><a class="headerlink" href="#tise2-fig" title="Link to this image">#</a></p>
|
||
</figcaption>
|
||
</figure>
|
||
<div class="sd-tab-set docutils">
|
||
<input checked="checked" id="sd-tab-item-1" name="sd-tab-set-1" type="radio">
|
||
<label class="sd-tab-label" for="sd-tab-item-1">
|
||
<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
|
||
<p>Complete the code snipet provided below to create a small TiSe<sub>2</sub> cluster with Ti emitter in the 2<sup>nd</sup> plane:</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="linenos"> 1</span><span class="kn">from</span><span class="w"> </span><span class="nn">ase.build</span><span class="w"> </span><span class="kn">import</span> <span class="n">mx2</span>
|
||
<span class="linenos"> 2</span><span class="kn">from</span><span class="w"> </span><span class="nn">ase.visualize</span><span class="w"> </span><span class="kn">import</span> <span class="n">view</span>
|
||
<span class="linenos"> 3</span><span class="kn">from</span><span class="w"> </span><span class="nn">msspec.calculator</span><span class="w"> </span><span class="kn">import</span> <span class="n">MSSPEC</span>
|
||
<span class="linenos"> 4</span><span class="kn">from</span><span class="w"> </span><span class="nn">msspec.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">hemispherical_cluster</span><span class="p">,</span> <span class="n">get_atom_index</span>
|
||
<span class="linenos"> 5</span>
|
||
<span class="linenos"> 6</span><span class="c1"># Some usefull constants (a, c, d, D) for defining the structure</span>
|
||
<span class="linenos"> 7</span><span class="n">a</span><span class="o">=...</span>
|
||
<span class="linenos"> 8</span>
|
||
<span class="linenos"> 9</span><span class="c1"># Create the TiSe2 trilayer</span>
|
||
<span class="linenos">10</span><span class="c1"># use ase help for this function</span>
|
||
<span class="linenos">11</span><span class="n">TiSe2</span> <span class="o">=</span> <span class="n">mx2</span><span class="p">(</span><span class="n">formula</span><span class="o">=...</span><span class="p">)</span>
|
||
<span class="linenos">12</span>
|
||
<span class="linenos">13</span><span class="c1"># The preious cell is 2D, let's define the c-axis to take into account </span>
|
||
<span class="linenos">14</span><span class="c1"># the Van der Waals gap between trilayers</span>
|
||
<span class="linenos">15</span><span class="n">TiSe2</span><span class="o">.</span><span class="n">cell</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">...</span><span class="p">]</span>
|
||
<span class="linenos">16</span>
|
||
<span class="linenos">17</span><span class="c1"># To be aligned like in the paper</span>
|
||
<span class="linenos">18</span><span class="n">TiSe2</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="mi">60</span><span class="p">,</span> <span class="s1">'z'</span><span class="p">,</span> <span class="n">rotate_cell</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="linenos">19</span>
|
||
<span class="linenos">20</span><span class="c1"># Since the material is multi-elements, "tag" each inequivalent atom </span>
|
||
<span class="linenos">21</span><span class="c1"># of the unit cell with a number. The "Ti" atom is tagged 0 and "Se" </span>
|
||
<span class="linenos">22</span><span class="c1"># atoms are 1 and 2.</span>
|
||
<span class="linenos">23</span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">):</span>
|
||
<span class="linenos">24</span> <span class="n">TiSe2</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">tag</span> <span class="o">=</span> <span class="n">i</span>
|
||
<span class="linenos">25</span>
|
||
<span class="linenos">26</span><span class="n">cluster</span> <span class="o">=</span> <span class="n">hemispherical_cluster</span><span class="p">(</span><span class="n">TiSe2</span><span class="p">,</span> <span class="n">emitter_tag</span><span class="o">=...</span><span class="p">,</span> <span class="n">emitter_plane</span><span class="o">=...</span><span class="p">,</span> <span class="n">planes</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
|
||
<span class="linenos">27</span><span class="n">cluster</span><span class="o">.</span><span class="n">emitter</span> <span class="o">=</span> <span class="n">get_atom_index</span><span class="p">(</span><span class="n">cluster</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||
<span class="linenos">28</span>
|
||
<span class="linenos">29</span><span class="n">view</span><span class="p">(</span><span class="n">cluster</span><span class="p">)</span>
|
||
<span class="linenos">30</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="cell tag_hide-cell docutils container">
|
||
<details class="hide above-input">
|
||
<summary aria-label="Toggle hidden content">
|
||
<span class="collapsed">Show code cell content</span>
|
||
<span class="expanded">Hide code cell content</span>
|
||
</summary>
|
||
<div class="cell_input docutils container">
|
||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">ase.build</span><span class="w"> </span><span class="kn">import</span> <span class="n">mx2</span>
|
||
<span class="kn">from</span><span class="w"> </span><span class="nn">ase.visualize</span><span class="w"> </span><span class="kn">import</span> <span class="n">view</span>
|
||
<span class="kn">from</span><span class="w"> </span><span class="nn">msspec.calculator</span><span class="w"> </span><span class="kn">import</span> <span class="n">MSSPEC</span>
|
||
<span class="kn">from</span><span class="w"> </span><span class="nn">msspec.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">hemispherical_cluster</span><span class="p">,</span> <span class="n">get_atom_index</span>
|
||
|
||
<span class="c1"># Some usefull constants (a, c, d, D) for defining the structure</span>
|
||
<span class="n">a</span><span class="o">=</span><span class="mf">3.535</span><span class="p">;</span><span class="n">c</span><span class="o">=</span><span class="mf">6.004</span><span class="p">;</span><span class="n">d</span><span class="o">=</span><span class="mf">3.450</span><span class="p">;</span><span class="n">D</span><span class="o">=</span><span class="mf">2.554</span>
|
||
|
||
<span class="c1"># Create the TiSe2 trilayer</span>
|
||
<span class="c1"># use ase help for this function</span>
|
||
<span class="n">TiSe2</span> <span class="o">=</span> <span class="n">mx2</span><span class="p">(</span><span class="n">formula</span><span class="o">=</span><span class="s1">'TiSe2'</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s1">'1T'</span><span class="p">,</span> <span class="n">a</span><span class="o">=</span><span class="n">a</span><span class="p">,</span> <span class="n">thickness</span><span class="o">=</span><span class="n">d</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">vacuum</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span>
|
||
|
||
<span class="c1"># The preious cell is 2D, let's define the c-axis to take into account </span>
|
||
<span class="c1"># the Van der Waals gap between trilayers</span>
|
||
<span class="n">TiSe2</span><span class="o">.</span><span class="n">cell</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span>
|
||
|
||
<span class="c1"># To be aligned like in the paper</span>
|
||
<span class="n">TiSe2</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="mi">60</span><span class="p">,</span> <span class="s1">'z'</span><span class="p">,</span> <span class="n">rotate_cell</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
|
||
<span class="c1"># Since the material is multi-elements, "tag" each inequivalent atom </span>
|
||
<span class="c1"># of the unit cell with a number. The "Ti" atom is tagged 0 and "Se" </span>
|
||
<span class="c1"># atoms are 1 and 2.</span>
|
||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">):</span>
|
||
<span class="n">TiSe2</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">tag</span> <span class="o">=</span> <span class="n">i</span>
|
||
|
||
<span class="n">cluster</span> <span class="o">=</span> <span class="n">hemispherical_cluster</span><span class="p">(</span><span class="n">TiSe2</span><span class="p">,</span> <span class="n">emitter_tag</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">emitter_plane</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">planes</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
|
||
<span class="n">cluster</span><span class="o">.</span><span class="n">emitter</span> <span class="o">=</span> <span class="n">get_atom_index</span><span class="p">(</span><span class="n">cluster</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
</div>
|
||
</details>
|
||
</div>
|
||
<div class="cell tag_remove-input docutils container">
|
||
<div class="cell_output docutils container">
|
||
<div class="output text_html"><html>
|
||
<head>
|
||
<title>ASE atomic visualization</title>
|
||
<link rel="stylesheet" type="text/css" href="https://www.x3dom.org/release/x3dom.css"></link>
|
||
<script type="text/javascript" src="https://www.x3dom.org/release/x3dom.js"></script>
|
||
</head>
|
||
<body>
|
||
<X3D width="400px"; height="300px";>
|
||
|
||
<!--Inserting Generated X3D Scene-->
|
||
<scene>
|
||
<viewpoint position="0 0 28.28000000000003">
|
||
<group/>
|
||
</viewpoint>
|
||
<transform translation="-0.8837500000000003 -2.220446049250313e-16 -3.002">
|
||
<group>
|
||
<group>
|
||
<transform translation="0 0 0">
|
||
<shape>
|
||
<appearance>
|
||
<material diffuseColor="0 0 0"/>
|
||
</appearance>
|
||
<lineset vertexCount="5">
|
||
<coordinate point="0 0 0 1.7675000000000005 3.0613998023779905 0.0 -1.7674999999999996 3.061399802377991 0.0 -3.535 4.440892098500626e-16 0.0 0 0 0"/>
|
||
</lineset>
|
||
</shape>
|
||
</transform>
|
||
<transform translation="0.0 0.0 6.004">
|
||
<shape>
|
||
<appearance>
|
||
<material diffuseColor="0 0 0"/>
|
||
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||
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||
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|
||
</lineset>
|
||
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|
||
</transform>
|
||
<transform translation="0 0 0">
|
||
<shape>
|
||
<appearance>
|
||
<material diffuseColor="0 0 0"/>
|
||
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|
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|
||
<coordinate point="0 0 0 1.7675000000000005 3.0613998023779905 0.0 1.7675000000000005 3.0613998023779905 6.004 0.0 0.0 6.004 0 0 0"/>
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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||
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|
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|
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<material diffuseColor="0.749 0.761 0.78"/>
|
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|
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|
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|
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|
||
<transform translation="3.5349999999999966 -4.0818664031706575 1.724999999999999">
|
||
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|
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|
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<material diffuseColor="1.0 0.631 0.0"/>
|
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|
||
<sphere radius="1.2"/>
|
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|
||
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|
||
<transform translation="1.767499999999984 -5.102333003963317 -1.7249999999999894">
|
||
<shape>
|
||
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|
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<material diffuseColor="1.0 0.631 0.0"/>
|
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|
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<sphere radius="1.2"/>
|
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|
||
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|
||
<transform translation="0.0 -4.0818664031706575 -4.279000000000005">
|
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|
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|
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<material diffuseColor="1.0 0.631 0.0"/>
|
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|
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|
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|
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|
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<transform translation="0.0 -6.122799604755983 4.6629367034256575e-15">
|
||
<shape>
|
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<appearance>
|
||
<material diffuseColor="0.749 0.761 0.78"/>
|
||
</appearance>
|
||
<sphere radius="1.6"/>
|
||
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|
||
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|
||
<transform translation="0.0 -4.0818664031706575 1.724999999999999">
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||
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|
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|
||
<transform translation="-1.7675000000000125 -5.102333003963317 -1.7249999999999894">
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<material diffuseColor="1.0 0.631 0.0"/>
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</appearance>
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<sphere radius="1.2"/>
|
||
</shape>
|
||
</transform>
|
||
<transform translation="-3.5349999999999966 -6.122799604755983 4.6629367034256575e-15">
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||
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|
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</div>
|
||
</section>
|
||
<section id="effect-of-the-scattering-order">
|
||
<h3>Effect of the scattering order<a class="headerlink" href="#effect-of-the-scattering-order" title="Link to this heading">#</a></h3>
|
||
<p>Use the line belows to create a calculator and compute a <span class="math notranslate nohighlight">\(\theta\)</span>-<span class="math notranslate nohighlight">\(\phi\)</span> scan of the Ti(2p)</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Create a calculator with Rehr-Albers series expansion algorithm</span>
|
||
<span class="n">calc</span> <span class="o">=</span> <span class="n">MSSPEC</span><span class="p">(</span><span class="n">spectroscopy</span><span class="o">=</span><span class="s1">'PED'</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s1">'expansion'</span><span class="p">)</span>
|
||
<span class="n">calc</span><span class="o">.</span><span class="n">set_atoms</span><span class="p">(</span><span class="n">cluster</span><span class="p">)</span>
|
||
|
||
<span class="n">data</span> <span class="o">=</span> <span class="kc">None</span>
|
||
<span class="k">for</span> <span class="n">ndif</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">):</span>
|
||
<span class="n">calc</span><span class="o">.</span><span class="n">calculation_parameters</span><span class="o">.</span><span class="n">scattering_order</span> <span class="o">=</span> <span class="n">ndif</span>
|
||
<span class="n">data</span> <span class="o">=</span> <span class="n">calc</span><span class="o">.</span><span class="n">get_theta_phi_scan</span><span class="p">(</span><span class="n">level</span><span class="o">=</span><span class="s1">'2p'</span><span class="p">,</span> <span class="n">kinetic_energy</span><span class="o">=</span><span class="mi">1030</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="n">data</span><span class="p">)</span>
|
||
|
||
<span class="n">data</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
<div class="sd-tab-set docutils">
|
||
<input checked="checked" id="sd-tab-item-2" name="sd-tab-set-2" type="radio">
|
||
<label class="sd-tab-label" for="sd-tab-item-2">
|
||
<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
|
||
<p>Compute a scan for an emitter in the first trilayer and in the second trilayer for scattering orders from 1 (single scattering) to 3 in order to complete the figure below.
|
||
What do you conclude about the value of the <code class="docutils literal notranslate"><span class="pre">calc.calculation_parameters.scattering_order</span></code> ?</p>
|
||
<figure class="align-default" id="results-fig">
|
||
<a class="reference internal image-reference" href="../_images/results.jpg"><img alt="../_images/results.jpg" class="align-center" src="../_images/results.jpg" style="width: 400px;" />
|
||
</a>
|
||
<figcaption>
|
||
<p><span class="caption-number">Fig. 12 </span><span class="caption-text"><span class="math notranslate nohighlight">\(\theta\)</span>-<span class="math notranslate nohighlight">\(\phi\)</span> scan of Ti(2p) at 1030 eV kinetic energy for an emitter in the first trilayer (left column) and in the second trilayer (right column). Each row correspond to a growing value for the <code class="docutils literal notranslate"><span class="pre">calc.calculation_parameters.scattering_order</span></code> parameter (from 1 to 5).</span><a class="headerlink" href="#results-fig" title="Link to this image">#</a></p>
|
||
</figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
<div class="toggle docutils container">
|
||
<figure class="align-default" id="results-completed-fig">
|
||
<a class="reference internal image-reference" href="../_images/results_completed.jpg"><img alt="../_images/results_completed.jpg" class="align-center" src="../_images/results_completed.jpg" style="width: 400px;" />
|
||
</a>
|
||
<figcaption>
|
||
<p><span class="caption-number">Fig. 13 </span><span class="caption-text"><span class="math notranslate nohighlight">\(\theta\)</span>-<span class="math notranslate nohighlight">\(\phi\)</span> scan of Ti(2p) at 1030 eV kinetic energy for an emitter in the first trilayer (left column) and in the second trilayer (right column). Each row correspond to a growing value for the <code class="docutils literal notranslate"><span class="pre">calc.calculation_parameters.scattering_order</span></code> parameter (from 1 to 5).</span><a class="headerlink" href="#results-completed-fig" title="Link to this image">#</a></p>
|
||
</figcaption>
|
||
</figure>
|
||
<p>The deeper the emitter, the greater the scattering order should be for the intensity to converge.
|
||
Typically, in the forward scattering regime, the scattering order corresponds to the number of planes above the emitter.</p>
|
||
</div>
|
||
</section>
|
||
</section>
|
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