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<h1>Activity 2: Setting up the “experiment”</h1>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sb-induced-smooth-growth-of-ag-on-ag-111-example">Sb-induced smooth growth of Ag on Ag(111) example</a><ul class="nav section-nav flex-column">
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<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#building-the-cluster">Building the cluster</a></li>
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<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#compute-an-azimuthal-scan">Compute an azimuthal scan</a></li>
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<section class="tex2jax_ignore mathjax_ignore" id="activity-2-setting-up-the-experiment">
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<h1>Activity 2: Setting up the “experiment”<a class="headerlink" href="#activity-2-setting-up-the-experiment" title="Link to this heading">#</a></h1>
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<p>To model a spectroscopy experiment, some parameters need to be correctly defined. In MsSpec, parameters are grouped in different categories (<code class="docutils literal notranslate"><span class="pre">detector_parameters</span></code>, <code class="docutils literal notranslate"><span class="pre">source_parameters</span></code>, <code class="docutils literal notranslate"><span class="pre">calculation_parameters</span></code>…). Each category is an attribute of your calculator object and contains different parameters.
|
||
For example, to define the angle of the incoming light with respect to the sample normal direction, you will use</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># (assuming your calculator variable is calc)</span>
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<span class="c1"># e.g: Incoming X-Ray light is 30° from the sample normal</span>
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<span class="n">calc</span><span class="o">.</span><span class="n">source_parameters</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="mi">30</span>
|
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</pre></div>
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</div>
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<section id="sb-induced-smooth-growth-of-ag-on-ag-111-example">
|
||
<h2>Sb-induced smooth growth of Ag on Ag(111) example<a class="headerlink" href="#sb-induced-smooth-growth-of-ag-on-ag-111-example" title="Link to this heading">#</a></h2>
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<p>To see how some parameters - not related to the cluster shape - may change the results, we will look at the effect of two parameters:</p>
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||
<ol class="arabic simple">
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<li><p>The source direction</p></li>
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<li><p>The inner potential of the sample</p></li>
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</ol>
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<p>The inner potential is material specific. It will add to the photoelectron kinetic energy inside the material. When the photoelectron escapes the sample, this internal potential is missing and this will create an energy step that will act as a refraction for the photoelectron intensity. The effect will be significant for large polar angles and for small kinetic energy of the photoelectron.</p>
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<p>Let’s look at the effect of those parameters on the following example.
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The idea is to use low energy photoelectron diffraction to see the substitution of Ag by Sb atoms on the surface plane.</p>
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<div class="admonition seealso">
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<p class="admonition-title">See also</p>
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<p>based on this paper from H. Cruguel <em>et al.</em> <a class="reference external" href="https://doi.org/10.1103/PhysRevB.55.R16061">Phys. Rev. B <strong>55</strong> R16061</a></p>
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</div>
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<section id="building-the-cluster">
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<h3>Building the cluster<a class="headerlink" href="#building-the-cluster" title="Link to this heading">#</a></h3>
|
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<p>Let’s start by building the cluster</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">bulk</span>
|
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<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>
|
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<span class="linenos"> 3</span>
|
||
<span class="linenos"> 4</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"> 5</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="p">,</span> <span class="n">cut_plane</span>
|
||
<span class="linenos"> 6</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>
|
||
<span class="linenos"> 7</span><span class="kn">from</span><span class="w"> </span><span class="nn">matplotlib</span><span class="w"> </span><span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
|
||
<span class="linenos"> 8</span>
|
||
<span class="linenos"> 9</span><span class="c1"># Create the silver cell</span>
|
||
<span class="linenos">10</span><span class="n">Ag</span> <span class="o">=</span> <span class="n">bulk</span><span class="p">(</span><span class="s1">'Ag'</span><span class="p">,</span> <span class="n">cubic</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<span class="linenos">11</span><span class="c1"># Orientate the cell in the [111] direction</span>
|
||
<span class="linenos">12</span><span class="n">Ag</span><span class="o">.</span><span class="n">rotate</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="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</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">13</span><span class="c1"># Align the azimuth to match experimental reference</span>
|
||
<span class="linenos">14</span><span class="n">Ag</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="mi">15</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">15</span>
|
||
<span class="linenos">16</span><span class="c1"># Create a cluster</span>
|
||
<span class="linenos">17</span><span class="n">cluster</span> <span class="o">=</span> <span class="n">hemispherical_cluster</span><span class="p">(</span><span class="n">Ag</span><span class="p">,</span> <span class="n">diameter</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">emitter_plane</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
<span class="linenos">18</span><span class="n">cluster</span> <span class="o">=</span> <span class="n">cut_plane</span><span class="p">(</span><span class="n">cluster</span><span class="p">,</span> <span class="n">z</span><span class="o">=-</span><span class="mf">4.8</span><span class="p">)</span>
|
||
<span class="linenos">19</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">20</span><span class="n">cluster</span><span class="p">[</span><span class="n">cluster</span><span class="o">.</span><span class="n">emitter</span><span class="p">]</span><span class="o">.</span><span class="n">symbol</span> <span class="o">=</span> <span class="s1">'Sb'</span>
|
||
</pre></div>
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||
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<section id="compute-an-azimuthal-scan">
|
||
<h3>Compute an azimuthal scan<a class="headerlink" href="#compute-an-azimuthal-scan" title="Link to this heading">#</a></h3>
|
||
<p>Now create a calculator and configure experimental parameters</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="linenos">25</span>
|
||
<span class="linenos">26</span><span class="c1"># Define parameters</span>
|
||
<span class="hll"><span class="linenos">27</span><span class="n">calc</span><span class="o">.</span><span class="n">source_parameters</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="mi">0</span>
|
||
</span><span class="linenos">28</span><span class="n">calc</span><span class="o">.</span><span class="n">source_parameters</span><span class="o">.</span><span class="n">phi</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<span class="linenos">29</span>
|
||
<span class="linenos">30</span><span class="n">calc</span><span class="o">.</span><span class="n">detector_parameters</span><span class="o">.</span><span class="n">angular_acceptance</span> <span class="o">=</span> <span class="mi">1</span>
|
||
<span class="linenos">31</span><span class="n">calc</span><span class="o">.</span><span class="n">detector_parameters</span><span class="o">.</span><span class="n">average_sampling</span> <span class="o">=</span> <span class="s1">'low'</span>
|
||
<span class="linenos">32</span>
|
||
<span class="hll"><span class="linenos">33</span><span class="n">calc</span><span class="o">.</span><span class="n">muffintin_parameters</span><span class="o">.</span><span class="n">interstitial_potential</span> <span class="o">=</span> <span class="mi">0</span>
|
||
</span><span class="linenos">34</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>Finally, add those lines to compute the <span class="math notranslate nohighlight">\(\phi\)</span>-scan (in orange) and compare it to the experimental data (in blue).</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="linenos">34</span>
|
||
<span class="linenos">35</span><span class="c1"># Compute an azimuthal scan</span>
|
||
<span class="linenos">36</span><span class="n">data</span> <span class="o">=</span> <span class="n">calc</span><span class="o">.</span><span class="n">get_phi_scan</span><span class="p">(</span><span class="n">level</span><span class="o">=</span><span class="s1">'4d'</span><span class="p">,</span> <span class="n">theta</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">phi</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">240</span><span class="p">,</span><span class="mi">121</span><span class="p">),</span> <span class="n">kinetic_energy</span><span class="o">=</span><span class="mi">45</span><span class="p">)</span>
|
||
<span class="linenos">37</span>
|
||
<span class="linenos">38</span><span class="c1"># Normalize data between [0,1] (to ease comparison with experimental data)</span>
|
||
<span class="linenos">39</span><span class="n">dset</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
<span class="linenos">40</span><span class="n">dset</span><span class="o">.</span><span class="n">cross_section</span> <span class="o">-=</span> <span class="n">dset</span><span class="o">.</span><span class="n">cross_section</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
|
||
<span class="linenos">41</span><span class="n">dset</span><span class="o">.</span><span class="n">cross_section</span> <span class="o">/=</span> <span class="n">dset</span><span class="o">.</span><span class="n">cross_section</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
|
||
<span class="linenos">42</span>
|
||
<span class="linenos">43</span><span class="c1"># Add experimental data points in the dataset</span>
|
||
<span class="linenos">44</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">loadtxt</span><span class="p">(</span><span class="s1">'data.txt'</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
|
||
<span class="linenos">45</span><span class="n">dset</span><span class="o">.</span><span class="n">add_columns</span><span class="p">(</span><span class="n">experiment</span><span class="o">=</span><span class="n">y</span><span class="p">)</span>
|
||
<span class="linenos">46</span>
|
||
<span class="linenos">47</span><span class="c1"># Add points to view</span>
|
||
<span class="linenos">48</span><span class="n">view</span> <span class="o">=</span> <span class="n">dset</span><span class="o">.</span><span class="n">views</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
<span class="linenos">49</span><span class="n">view</span><span class="o">.</span><span class="n">select</span><span class="p">(</span><span class="s1">'phi'</span><span class="p">,</span> <span class="s1">'experiment'</span><span class="p">,</span> <span class="n">legend</span><span class="o">=</span><span class="s1">'Exp. data'</span><span class="p">)</span>
|
||
<span class="linenos">50</span>
|
||
<span class="linenos">51</span><span class="c1"># Popup GUI</span>
|
||
<span class="linenos">52</span><span class="n">data</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
|
||
<span class="linenos">53</span>
|
||
<span class="linenos">54</span><span class="c1"># Remove temp. files</span>
|
||
<span class="linenos">55</span><span class="n">calc</span><span class="o">.</span><span class="n">shutdown</span><span class="p">()</span>
|
||
</pre></div>
|
||
</div>
|
||
<figure class="align-default" id="sbag-fig1">
|
||
<a class="reference internal image-reference" href="../_images/fig11.png"><img alt="../_images/fig11.png" class="align-center" src="../_images/fig11.png" style="width: 600px;" />
|
||
</a>
|
||
<figcaption>
|
||
<p><span class="caption-number">Fig. 4 </span><span class="caption-text">Azimuthal (<span class="math notranslate nohighlight">\(\phi\)</span>) scan for Sb(4d) emitter in the top layer of Ag(111) at 45 eV kinetic energy.</span><a class="headerlink" href="#sbag-fig1" title="Link to this image">#</a></p>
|
||
</figcaption>
|
||
</figure>
|
||
<p>The agreement is not satisfactory although most of the features may be identified.</p>
|
||
<div class="sd-tab-set docutils">
|
||
<input checked="checked" id="sd-tab-item-0" name="sd-tab-set-0" type="radio">
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||
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|
||
<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
|
||
<p>Try to change the source direction and the inner potential of Ag to better match the experiment…</p>
|
||
<div class="admonition note">
|
||
<p class="admonition-title">Note</p>
|
||
<p>The cluster is smaller than it should for size convergence, but the calculation would take too much memory for this example</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="toggle docutils container">
|
||
<figure class="align-default" id="sbag-fig2">
|
||
<a class="reference internal image-reference" href="../_images/fig21.png"><img alt="../_images/fig21.png" class="align-center" src="../_images/fig21.png" style="width: 600px;" />
|
||
</a>
|
||
<figcaption>
|
||
<p><span class="caption-number">Fig. 5 </span><span class="caption-text">Azimuthal (<span class="math notranslate nohighlight">\(\phi\)</span>) scan for Sb(4d) emitter in the top layer of Ag(111) at 45 eV kinetic energy, with <code class="docutils literal notranslate"><span class="pre">muffintin_parameters.interstitial_potential</span></code> = 10.2 and <code class="docutils literal notranslate"><span class="pre">source_parameters.theta</span></code> = 22.5</span><a class="headerlink" href="#sbag-fig2" title="Link to this image">#</a></p>
|
||
</figcaption>
|
||
</figure>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Source geometry (the former SA73 beamline of the LURE synchrotron)</span>
|
||
<span class="c1"># given in ref 6 of the paper...</span>
|
||
<span class="n">calc</span><span class="o">.</span><span class="n">source_parameters</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="mf">22.5</span>
|
||
<span class="c1"># Inner potential is generally between 10 and 20 eV for most metrials</span>
|
||
<span class="n">calc</span><span class="o">.</span><span class="n">muffintin_parameters</span><span class="o">.</span><span class="n">inner_potential</span> <span class="o">=</span> <span class="mf">10.2</span>
|
||
</pre></div>
|
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sb-induced-smooth-growth-of-ag-on-ag-111-example">Sb-induced smooth growth of Ag on Ag(111) example</a><ul class="nav section-nav flex-column">
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<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#building-the-cluster">Building the cluster</a></li>
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<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#compute-an-azimuthal-scan">Compute an azimuthal scan</a></li>
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