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<li class="toctree-l1"><a class="reference internal" href="../Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
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</ul>
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</div>
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<li class="toctree-l1"><a class="reference internal" href="../Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
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</ul>
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</div>
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<li class="toctree-l1"><a class="reference internal" href="../Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
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</ul>
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</div>
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<input checked="checked" id="sd-tab-item-0" name="sd-tab-set-0" type="radio">
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<label class="sd-tab-label" for="sd-tab-item-0">
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<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
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<p>By using the <code class="docutils literal notranslate"><span class="pre">Atoms</span></code> class of the <code class="docutils literal notranslate"><span class="pre">ase</span></code> package, try to build a O-Rh chain where atoms are 4 Å apart. Here is the begining of the script. Try to complete the line of code and view your two-atoms chain.</p>
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<p>By using the <a class="reference external" href="https://wiki.fysik.dtu.dk/ase/ase/atoms.html#ase.Atoms"><code class="docutils literal notranslate"><span class="pre">Atoms</span></code></a> class of the <code class="docutils literal notranslate"><span class="pre">ase</span></code> package, try to build a O-Rh chain where atoms are 4 Å apart. Here is the begining of the script. Try to complete the line of code and view your two-atoms chain.</p>
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<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">ase</span><span class="w"> </span><span class="kn">import</span> <span class="n">Atoms</span>
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<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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<script async="async" src="../_static/sphinx-thebe.js?v=c100c467"></script>
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<script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
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<script>const THEBE_JS_URL = "https://unpkg.com/thebe@0.8.2/lib/index.js"; const thebe_selector = ".thebe,.cell"; const thebe_selector_input = "pre"; const thebe_selector_output = ".output, .cell_output"</script>
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<script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
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<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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<script>DOCUMENTATION_OPTIONS.pagename = 'Activity04/Activity04';</script>
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<link rel="index" title="Index" href="../genindex.html" />
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<link rel="search" title="Search" href="../search.html" />
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@ -190,8 +192,6 @@
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<li class="toctree-l1"><a class="reference internal" href="../Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
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</ul>
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</div>
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</button>
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`);
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</script>
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<button class="sidebar-toggle secondary-toggle btn btn-sm" title="Toggle secondary sidebar" data-bs-placement="bottom" data-bs-toggle="tooltip">
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<span class="fa-solid fa-list"></span>
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</button>
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</div></div>
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</div>
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@ -333,6 +335,17 @@ document.write(`
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<div id="print-main-content">
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<div id="jb-print-toc">
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<div>
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<h2> Contents </h2>
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</div>
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<nav aria-label="Page">
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<ul class="visible nav section-nav flex-column">
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#polar-scans-of-ni-atomic-chains">Polar scans of Ni atomic chains</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-a-chain-of-atoms">Building a chain of atoms</a></li>
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</ul>
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</li>
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</ul>
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</nav>
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</div>
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</div>
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</div>
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@ -343,106 +356,94 @@ document.write(`
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<article class="bd-article">
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<section class="tex2jax_ignore mathjax_ignore" id="activity-4-from-single-scattering-to-multiple-scattering">
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<h1>Activity 4: From single scattering to multiple scattering<a class="headerlink" href="#activity-4-from-single-scattering-to-multiple-scattering" title="Link to this heading">#</a></h1>
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<span id="ssc2ms"></span><h1>Activity 4: From single scattering to multiple scattering<a class="headerlink" href="#activity-4-from-single-scattering-to-multiple-scattering" title="Link to this heading">#</a></h1>
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<p>In the <a class="reference internal" href="../Activity03/Activity03.html#ssc"><span class="std std-ref">previous activity</span></a>, we saw that simple single scattering calculations (SSC) can be used to simulate photodiffraction diagrams with good accuracy. The approximation works fine when the emitting atom is very close to the surface.
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However, the SSC approach is no longer suitable for deeper emitter atoms, where multiple scattering effects come into play. In this activity, we will focus on a major consequence of multiple scattering: <em>the defocusing effect</em>.</p>
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<p>The defocusing effect is presented in the <a class="reference internal" href="#ni-fig1"><span class="std std-ref">figure below</span></a> for a chain of nickel atoms. Although purely illustrative, understanding multiple scattering in atomic chains is fundamental because they are found in many situations, such as in particular directions of a crystal or in molecules of various lengths.</p>
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<figure class="align-default" id="ni-fig1">
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<a class="reference internal image-reference" href="../_images/Ni_fig1.png"><img alt="Ni chain" class="align-center" src="../_images/Ni_fig1.png" style="width: 600px;" />
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<a class="reference internal image-reference" href="../_images/defocusing_animation.gif"><img alt="defocusing effect" class="align-center" src="../_images/defocusing_animation.gif" style="width: 600px;" />
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</a>
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<figcaption>
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<p><span class="caption-number">Fig. 10 </span><span class="caption-text">Polar scan of a Ni chain of 2-5 atoms for single and mutliple (5<sup>th</sup> order) scattering.</span><a class="headerlink" href="#ni-fig1" title="Link to this image">#</a></p>
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<p><span class="caption-number">Fig. 10 </span><span class="caption-text">The defocusing effect dur to multiple scattering in an atomic chain of Ni atoms.</span><a class="headerlink" href="#ni-fig1" title="Link to this image">#</a></p>
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</figcaption>
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</figure>
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<div class="admonition seealso">
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<p>In 1989, M.-L Xu, J.J. Barton and M.A. Van Hove studied these multiple scattering effects on atomic chains (<a class="reference internal" href="#defocusing-paper"><span class="std std-ref">see their paper below</span></a>).
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In the spirit of figure 3 of their paper, we will create 3 atomic chains of Ni atoms (2, 3 and 5 atoms) tilted by 45° and we will compare the intensity of the forward scattering peak for single scattering and for full multiple scattering.</p>
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<div class="admonition seealso" id="defocusing-paper">
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<p class="admonition-title">See also</p>
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<p>based on this paper from M.-L. Xu <em>et al.</em>
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<a class="reference external" href="https://doi.org/10.1103/PhysRevB.39.8275">Phys. Rev. B <strong>39</strong> p8275 (1989)</a></p>
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</div>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="linenos"> 1</span><span class="c1"># coding: utf-8</span>
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<span class="linenos"> 2</span>
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<span class="linenos"> 3</span><span class="c1"># import all we need and start by msspec</span>
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<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>
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<span class="linenos"> 5</span>
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<span class="linenos"> 6</span><span class="c1"># we will build a simple atomic chain</span>
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<span class="linenos"> 7</span><span class="kn">from</span><span class="w"> </span><span class="nn">ase</span><span class="w"> </span><span class="kn">import</span> <span class="n">Atom</span><span class="p">,</span> <span class="n">Atoms</span>
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<span class="linenos"> 8</span>
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<span class="linenos"> 9</span><span class="c1"># we need some numpy functions</span>
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<span class="linenos">10</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="linenos">11</span>
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<span class="linenos">12</span>
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<span class="linenos">13</span><span class="n">symbol</span> <span class="o">=</span> <span class="s1">'Ni'</span> <span class="c1"># The kind of atom for the chain</span>
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<span class="linenos">14</span><span class="n">orders</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span> <span class="c1"># We will run the calculation for single scattering</span>
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<span class="linenos">15</span> <span class="c1"># and multiple scattering (5th diffusion order)</span>
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<span class="linenos">16</span><span class="n">chain_lengths</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span> <span class="c1"># We will run the calculation for differnt lengths</span>
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<span class="linenos">17</span> <span class="c1"># of the atomic chain</span>
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<span class="linenos">18</span><span class="n">a</span> <span class="o">=</span> <span class="mf">3.499</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span> <span class="c1"># The distance bewteen 2 atoms</span>
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<span class="linenos">19</span>
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<span class="linenos">20</span><span class="c1"># Define an empty variable to store all the results</span>
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<span class="linenos">21</span><span class="n">all_data</span> <span class="o">=</span> <span class="kc">None</span>
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<span class="linenos">22</span>
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<span class="linenos">23</span><span class="c1"># 2 for nested loops over the chain length and the order of diffusion</span>
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<span class="linenos">24</span><span class="k">for</span> <span class="n">chain_length</span> <span class="ow">in</span> <span class="n">chain_lengths</span><span class="p">:</span>
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<span class="linenos">25</span> <span class="k">for</span> <span class="n">order</span> <span class="ow">in</span> <span class="n">orders</span><span class="p">:</span>
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<span class="linenos">26</span> <span class="c1"># We build the atomic chain by</span>
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<span class="linenos">27</span> <span class="c1"># 1- stacking each atom one by one along the z axis</span>
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<span class="linenos">28</span> <span class="n">chain</span> <span class="o">=</span> <span class="n">Atoms</span><span class="p">([</span><span class="n">Atom</span><span class="p">(</span><span class="n">symbol</span><span class="p">,</span> <span class="n">position</span> <span class="o">=</span> <span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="n">i</span><span class="o">*</span><span class="n">a</span><span class="p">))</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span>
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<span class="linenos">29</span> <span class="nb">range</span><span class="p">(</span><span class="n">chain_length</span><span class="p">)])</span>
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<span class="linenos">30</span> <span class="c1"># 2- rotating the chain by 45 degrees with respect to the y axis</span>
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<span class="linenos">31</span> <span class="c1">#chain.rotate('y', np.radians(45.))</span>
|
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<span class="linenos">32</span> <span class="n">chain</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="mf">45.</span><span class="p">,</span> <span class="s1">'y'</span><span class="p">)</span>
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<span class="linenos">33</span> <span class="c1"># 3- setting a custom Muffin-tin radius of 1.5 angstroms for all</span>
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<span class="linenos">34</span> <span class="c1"># atoms (needed if you want to enlarge the distance between</span>
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<span class="linenos">35</span> <span class="c1"># the atoms while keeping the radius constant)</span>
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<span class="linenos">36</span> <span class="c1">#[atom.set('mt_radius', 1.5) for atom in chain]</span>
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<span class="linenos">37</span> <span class="c1"># 4- defining the absorber to be the first atom in the chain at</span>
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<span class="linenos">38</span> <span class="c1"># x = y = z = 0</span>
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<span class="linenos">39</span> <span class="n">chain</span><span class="o">.</span><span class="n">absorber</span> <span class="o">=</span> <span class="mi">0</span>
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<span class="linenos">40</span>
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<span class="linenos">41</span> <span class="c1"># We define a new PED calculator</span>
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<span class="linenos">42</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>
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<span class="linenos">43</span> <span class="n">calc</span><span class="o">.</span><span class="n">set_atoms</span><span class="p">(</span><span class="n">chain</span><span class="p">)</span>
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<span class="linenos">44</span> <span class="c1"># Here is how to tweak the scattering order</span>
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<span class="linenos">45</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">order</span>
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<span class="linenos">46</span> <span class="c1"># This line below is where we actually run the calculation</span>
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<span class="linenos">47</span> <span class="n">all_data</span> <span class="o">=</span> <span class="n">calc</span><span class="o">.</span><span class="n">get_theta_scan</span><span class="p">(</span><span class="n">level</span><span class="o">=</span><span class="s1">'3s'</span><span class="p">,</span> <span class="c1">#kinetic_energy=1000.,</span>
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<span class="linenos">48</span> <span class="n">theta</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">80.</span><span class="p">),</span> <span class="n">data</span><span class="o">=</span><span class="n">all_data</span><span class="p">)</span>
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<span class="linenos">49</span>
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<span class="linenos">50</span> <span class="c1"># OPTIONAL, to improve the display of the data we will change the dataset</span>
|
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<span class="linenos">51</span> <span class="c1"># default title as well as the plot title</span>
|
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<span class="linenos">52</span> <span class="n">t</span> <span class="o">=</span> <span class="s2">"order </span><span class="si">{:d}</span><span class="s2">, n = </span><span class="si">{:d}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">order</span><span class="p">,</span> <span class="n">chain_length</span><span class="p">)</span> <span class="c1"># A useful title</span>
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<span class="linenos">53</span> <span class="n">dset</span> <span class="o">=</span> <span class="n">all_data</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="c1"># get the last dataset</span>
|
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<span class="linenos">54</span> <span class="n">dset</span><span class="o">.</span><span class="n">title</span> <span class="o">=</span> <span class="n">t</span> <span class="c1"># change its title</span>
|
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<span class="linenos">55</span> <span class="c1"># get its last view (there is only one defined for each dataset)</span>
|
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<span class="linenos">56</span> <span class="n">v</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="o">-</span><span class="mi">1</span><span class="p">]</span>
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<span class="linenos">57</span> <span class="n">v</span><span class="o">.</span><span class="n">set_plot_options</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">t</span><span class="p">)</span> <span class="c1"># change the title of the figure</span>
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<span class="linenos">58</span>
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<span class="linenos">59</span>
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<span class="linenos">60</span>
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<span class="linenos">61</span><span class="c1"># OPTIONAL, set the same scale for all plots</span>
|
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<span class="linenos">62</span><span class="c1"># 1. iterate over all computed cross_sections to find the absolute minimum and</span>
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<span class="linenos">63</span><span class="c1"># maximum of the data</span>
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<span class="linenos">64</span><span class="n">min_cs</span> <span class="o">=</span> <span class="n">max_cs</span> <span class="o">=</span> <span class="mi">0</span>
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<span class="linenos">65</span><span class="k">for</span> <span class="n">dset</span> <span class="ow">in</span> <span class="n">all_data</span><span class="p">:</span>
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<span class="linenos">66</span> <span class="n">min_cs</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">min_cs</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">dset</span><span class="o">.</span><span class="n">cross_section</span><span class="p">))</span>
|
||||
<span class="linenos">67</span> <span class="n">max_cs</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">max_cs</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">dset</span><span class="o">.</span><span class="n">cross_section</span><span class="p">))</span>
|
||||
<span class="linenos">68</span>
|
||||
<span class="linenos">69</span><span class="c1"># 2. for each view in each dataset, change the scale accordingly</span>
|
||||
<span class="linenos">70</span><span class="k">for</span> <span class="n">dset</span> <span class="ow">in</span> <span class="n">all_data</span><span class="p">:</span>
|
||||
<span class="linenos">71</span> <span class="n">v</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="o">-</span><span class="mi">1</span><span class="p">]</span>
|
||||
<span class="linenos">72</span> <span class="n">v</span><span class="o">.</span><span class="n">set_plot_options</span><span class="p">(</span><span class="n">ylim</span><span class="o">=</span><span class="p">[</span><span class="n">min_cs</span><span class="p">,</span> <span class="n">max_cs</span><span class="p">])</span>
|
||||
<span class="linenos">73</span>
|
||||
<span class="linenos">74</span><span class="c1"># Pop up the graphical window</span>
|
||||
<span class="linenos">75</span><span class="n">all_data</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
|
||||
<span class="linenos">76</span><span class="c1"># You can end your script with the line below to remove the temporary</span>
|
||||
<span class="linenos">77</span><span class="c1"># folder needed for the calculation</span>
|
||||
<span class="linenos">78</span><span class="n">calc</span><span class="o">.</span><span class="n">shutdown</span><span class="p">()</span>
|
||||
<section id="polar-scans-of-ni-atomic-chains">
|
||||
<h2>Polar scans of Ni atomic chains<a class="headerlink" href="#polar-scans-of-ni-atomic-chains" title="Link to this heading">#</a></h2>
|
||||
<section id="building-a-chain-of-atoms">
|
||||
<h3>Building a chain of atoms<a class="headerlink" href="#building-a-chain-of-atoms" title="Link to this heading">#</a></h3>
|
||||
<p>Start by creating a simple chain of 2 Ni atoms: an emitter and a scatterer in the [101] direction.</p>
|
||||
<div class="admonition tip">
|
||||
<p class="admonition-title">Tip</p>
|
||||
<p>Nickel is <em>fcc</em> with lattice parameter <span class="math notranslate nohighlight">\(a\)</span>=3.499 Å. Use the <a class="reference external" href="https://wiki.fysik.dtu.dk/ase/ase/atoms.html#ase.Atoms"><code class="docutils literal notranslate"><span class="pre">Atoms</span></code></a> class of <code class="docutils literal notranslate"><span class="pre">ase</span></code> like in the <a class="reference internal" href="../Activity03/Activity03.html#ssc"><span class="std std-ref">previous activity</span></a>…</p>
|
||||
<div class="dropdown admonition">
|
||||
<p class="admonition-title">if you need help to start…</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></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">ase</span><span class="w"> </span><span class="kn">import</span> <span class="n">Atoms</span>
|
||||
|
||||
<span class="n">symbol</span> <span class="o">=</span> <span class="o">...</span> <span class="c1"># The kind of atom for the chain</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="o">...</span> <span class="c1"># The distance bewteen 2 atoms</span>
|
||||
<span class="c1"># in [101] direction</span>
|
||||
|
||||
<span class="n">chain</span> <span class="o">=</span> <span class="n">Atoms</span><span class="p">(</span><span class="o">...</span><span class="p">,</span> <span class="n">positions</span><span class="o">=</span><span class="p">[</span><span class="o">...</span><span class="p">])</span>
|
||||
<span class="n">chain</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="o">...</span><span class="p">)</span>
|
||||
<span class="n">chain</span><span class="o">.</span><span class="n">edit</span><span class="p">()</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="docutils">
|
||||
</div>
|
||||
<div class="dropdown admonition">
|
||||
<p class="admonition-title"><em>Solution…</em></p>
|
||||
<p>Building the 2-atoms chain</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">msspec.calculator</span><span class="w"> </span><span class="kn">import</span> <span class="n">MSSPEC</span>
|
||||
<span class="linenos"> 2</span><span class="kn">from</span><span class="w"> </span><span class="nn">ase</span><span class="w"> </span><span class="kn">import</span> <span class="n">Atoms</span>
|
||||
<span class="linenos"> 3</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"> 4</span>
|
||||
<span class="linenos"> 5</span><span class="n">symbol</span> <span class="o">=</span> <span class="s1">'Ni'</span> <span class="c1"># The kind of atom for the chain</span>
|
||||
<span class="linenos"> 6</span><span class="n">a</span> <span class="o">=</span> <span class="mf">3.499</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span> <span class="c1"># The distance bewteen 2 atoms</span>
|
||||
<span class="linenos"> 7</span> <span class="c1"># in [101] direction</span>
|
||||
<span class="linenos"> 8</span>
|
||||
<span class="linenos"> 9</span><span class="n">chain</span> <span class="o">=</span> <span class="n">Atoms</span><span class="p">(</span><span class="n">symbol</span><span class="o">*</span><span class="mi">2</span><span class="p">,</span> <span class="n">positions</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="mi">0</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="n">a</span><span class="p">)])</span>
|
||||
<span class="linenos">10</span><span class="n">chain</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="mi">45</span><span class="p">,</span> <span class="s1">'y'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<figure class="align-default" id="ni-fig2">
|
||||
<a class="reference internal image-reference" href="../_images/Ni_2atomsSSC.png"><img alt="Ni 2 atoms" class="align-center" src="../_images/Ni_2atomsSSC.png" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 11 </span><span class="caption-text">Polar scan of a Ni(3s) chain of 2 atoms for single scattering.</span><a class="headerlink" href="#ni-fig2" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
</div>
|
||||
<div class="sd-tab-set docutils">
|
||||
<input checked="checked" id="sd-tab-item-0" name="sd-tab-set-0" type="radio">
|
||||
<label class="sd-tab-label" for="sd-tab-item-0">
|
||||
<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
|
||||
<p>Some questions to answer</p>
|
||||
<p>Create an <code class="docutils literal notranslate"><span class="pre">MSSPEC</span></code> calculator with <code class="docutils literal notranslate"><span class="pre">expansion</span></code> algortithm and set the <code class="docutils literal notranslate"><span class="pre">scattering_order</span></code>=1 to compute a polar scan of the Ni(3s) in single scattering. How is varying the height of the peak at 45° (along the chain) if you increase the number of atoms in the chain ?</p>
|
||||
<p>Repeat the same experiment with <code class="docutils literal notranslate"><span class="pre">inversion</span></code> algorithm for having the full multiple scattering result. What do you observe ?</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="dropdown admonition">
|
||||
<p class="admonition-title"><em>Solution…</em></p>
|
||||
<p>The peak at 45° is increasing with the number of atoms in the chain for SSC. We observe defocusing of this peak for full multiple scattering calculations (MSC). For the 2-atoms chain, both SSC and MSC give the same result owing to the fact that the emitter has only one scatterer atom and that kinetic energy is high enough to cancel out all backscattering.</p>
|
||||
<figure class="align-default" id="ni-figx">
|
||||
<a class="reference internal image-reference" href="../_images/Ni_SSCvsMI.jpg"><img alt="Ni chain" class="align-center" src="../_images/Ni_SSCvsMI.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 12 </span><span class="caption-text">Polar scan of a Ni chain of 2-5 atoms for single and full mutliple scattering.</span><a class="headerlink" href="#ni-figx" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<script type="text/x-thebe-config">
|
||||
|
|
@ -500,6 +501,24 @@ document.write(`
|
|||
|
||||
|
||||
|
||||
<div class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
|
||||
|
||||
|
||||
<div class="sidebar-secondary-item">
|
||||
<div class="page-toc tocsection onthispage">
|
||||
<i class="fa-solid fa-list"></i> Contents
|
||||
</div>
|
||||
<nav class="bd-toc-nav page-toc">
|
||||
<ul class="visible nav section-nav flex-column">
|
||||
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#polar-scans-of-ni-atomic-chains">Polar scans of Ni atomic chains</a><ul class="nav section-nav flex-column">
|
||||
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#building-a-chain-of-atoms">Building a chain of atoms</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</nav></div>
|
||||
|
||||
</div></div>
|
||||
|
||||
|
||||
</div>
|
||||
<footer class="bd-footer-content">
|
||||
|
|
|
|||
|
|
@ -192,8 +192,6 @@
|
|||
<li class="toctree-l1"><a class="reference internal" href="../Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
|
@ -422,7 +420,7 @@ document.write(`
|
|||
<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>
|
||||
<p><span class="caption-number">Fig. 13 </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">
|
||||
|
|
@ -1050,7 +1048,7 @@ What do you conclude about the value of the <code class="docutils literal notran
|
|||
<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>
|
||||
<p><span class="caption-number">Fig. 14 </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>
|
||||
|
|
@ -1060,7 +1058,7 @@ What do you conclude about the value of the <code class="docutils literal notran
|
|||
<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>
|
||||
<p><span class="caption-number">Fig. 15 </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.
|
||||
|
|
|
|||
|
|
@ -192,8 +192,6 @@
|
|||
<li class="toctree-l1"><a class="reference internal" href="../Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
|
@ -391,7 +389,7 @@ document.write(`
|
|||
<a class="reference internal image-reference" href="../_images/msd.jpg"><img alt="Cu MSD" class="align-center" src="../_images/msd.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 14 </span><span class="caption-text">Variation of MSD for copper versus temperature using equation <a class="reference internal" href="#equation-eq-debye">(2)</a></span><a class="headerlink" href="#msd-fig" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 16 </span><span class="caption-text">Variation of MSD for copper versus temperature using equation <a class="reference internal" href="#equation-eq-debye">(2)</a></span><a class="headerlink" href="#msd-fig" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<div class="sd-tab-set docutils">
|
||||
|
|
@ -664,7 +662,7 @@ complete the hilighted lines in the following script to compute the anisotropy o
|
|||
<a class="reference internal image-reference" href="../_images/anisotropies.png"><img alt="anisotropies" class="align-center" src="../_images/anisotropies.png" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 15 </span><span class="caption-text">Variation of anisotropy as a function of temperature and polar angle for Cu(2p).</span><a class="headerlink" href="#anisotropy-fig" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 17 </span><span class="caption-text">Variation of anisotropy as a function of temperature and polar angle for Cu(2p).</span><a class="headerlink" href="#anisotropy-fig" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<p>The anisotropy decreases when the temperature is increased due to the increased disorder in the structure coming from thermal agitation. This variation in anisotropy is more pronounced for grazing incidence angles since surface atoms are expected to vibrate more than bulk ones and the expected mean depth of no-loss emission is <span class="math notranslate nohighlight">\(\sim 1\)</span> atomic layer at <span class="math notranslate nohighlight">\(\theta = 83°\)</span> and 3-4 layers at <span class="math notranslate nohighlight">\(\theta = 45°\)</span> as estimated by <span class="math notranslate nohighlight">\(\Lambda_e\sin\theta\)</span> (where <span class="math notranslate nohighlight">\(\Lambda_e\)</span> is the photoelectron mean free path at 560 eV).</p>
|
||||
|
|
|
|||
|
|
@ -192,8 +192,6 @@
|
|||
<li class="toctree-l1"><a class="reference internal" href="../Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
|
@ -392,7 +390,7 @@ document.write(`
|
|||
<a class="reference internal image-reference" href="../_images/fig1.jpg"><img alt="path filtering" class="align-center" src="../_images/fig1.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 16 </span><span class="caption-text">The time for computing all scattering path for increasing cluster size and scattering order (up to 6<sup>th</sup> order with 739 atoms. (One path is assumed to be calculated within 1 µs)</span><a class="headerlink" href="#nbpaths-fig" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 18 </span><span class="caption-text">The time for computing all scattering path for increasing cluster size and scattering order (up to 6<sup>th</sup> order with 739 atoms. (One path is assumed to be calculated within 1 µs)</span><a class="headerlink" href="#nbpaths-fig" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
</div>
|
||||
|
|
@ -412,7 +410,7 @@ document.write(`
|
|||
<a class="reference internal image-reference" href="../_images/filters.jpg"><img alt="path filtering" class="align-center" src="../_images/filters.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 17 </span><span class="caption-text">Some examples of scattering paths with <code class="docutils literal notranslate"><span class="pre">forward_scattering</span></code>, <code class="docutils literal notranslate"><span class="pre">backward_scattering</span></code> and <code class="docutils literal notranslate"><span class="pre">distance</span></code> filters selected. The accepted forward angle is 45°, the accepted backscattering angle is 20° and the threshold distance is <span class="math notranslate nohighlight">\(6a_0\)</span> where <span class="math notranslate nohighlight">\(a_0\)</span> is the lattice parameter. Note that the yellow path is rejected but if the <code class="docutils literal notranslate"><span class="pre">off_cone_events</span></code> option is set to a value > 1, then it could have been accepted.</span><a class="headerlink" href="#filters-fig" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 19 </span><span class="caption-text">Some examples of scattering paths with <code class="docutils literal notranslate"><span class="pre">forward_scattering</span></code>, <code class="docutils literal notranslate"><span class="pre">backward_scattering</span></code> and <code class="docutils literal notranslate"><span class="pre">distance</span></code> filters selected. The accepted forward angle is 45°, the accepted backscattering angle is 20° and the threshold distance is <span class="math notranslate nohighlight">\(6a_0\)</span> where <span class="math notranslate nohighlight">\(a_0\)</span> is the lattice parameter. Note that the yellow path is rejected but if the <code class="docutils literal notranslate"><span class="pre">off_cone_events</span></code> option is set to a value > 1, then it could have been accepted.</span><a class="headerlink" href="#filters-fig" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
</section>
|
||||
|
|
@ -502,7 +500,7 @@ document.write(`
|
|||
<a class="reference internal image-reference" href="../_images/results.png"><img alt="Si polar scan" class="align-center" src="../_images/results.png" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 18 </span><span class="caption-text">Si(2p) polar scan (contribution of an emitter in the 4<sup>th</sup> plane with all 7 114 945 scattering paths taken into account (orange curve), and for only 1525 filtered paths (blue curve).</span><a class="headerlink" href="#si-fig" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 20 </span><span class="caption-text">Si(2p) polar scan (contribution of an emitter in the 4<sup>th</sup> plane with all 7 114 945 scattering paths taken into account (orange curve), and for only 1525 filtered paths (blue curve).</span><a class="headerlink" href="#si-fig" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="linenos"> 1</span><span class="c1"># coding: utf8</span>
|
||||
|
|
|
|||
|
|
@ -192,8 +192,6 @@
|
|||
<li class="toctree-l1 current active"><a class="current reference internal" href="#">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
|
@ -373,25 +371,25 @@ This is the key to computing the total photodiffraction signal of a <em>substrat
|
|||
<a class="reference internal image-reference" href="../_images/AlN-fig1.jpg"><img alt="AlN crystal direction" class="align-center" src="../_images/AlN-fig1.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 19 </span><span class="caption-text">AlN hexagonal lattice. Left) N polarity with nitrogen terminated surface and AlN<sub>4</sub> tetrahedrons pointing downward. Right) Al polarity with aluminium terminated surface and AlN<sub>4</sub> tetrahedrons pointing upward</span><a class="headerlink" href="#aln-fig1" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 21 </span><span class="caption-text">AlN hexagonal lattice. Left) N polarity with nitrogen terminated surface and AlN<sub>4</sub> tetrahedrons pointing downward. Right) Al polarity with aluminium terminated surface and AlN<sub>4</sub> tetrahedrons pointing upward</span><a class="headerlink" href="#aln-fig1" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<p>The AlN(0001) and (00.-1) faces share the same crystallograpphic symmetry and the Al and N atoms have the same geometrical surrounding differing only in the exchange of Al and N atoms (<a class="reference internal" href="#aln-fig2"><span class="std std-numref">Fig. 20</span></a>).</p>
|
||||
<p>The AlN(0001) and (00.-1) faces share the same crystallograpphic symmetry and the Al and N atoms have the same geometrical surrounding differing only in the exchange of Al and N atoms (<a class="reference internal" href="#aln-fig2"><span class="std std-numref">Fig. 22</span></a>).</p>
|
||||
<p>It is thus expected that Al(2p) and N(1s) XPD patterns exhibit almost the same features with only small differences due to the contrast between Al and N scattering amplitudes.</p>
|
||||
<figure class="align-default" id="aln-fig2">
|
||||
<a class="reference internal image-reference" href="../_images/AlN-fig2.jpg"><img alt="AlN crystal direction" class="align-center" src="../_images/AlN-fig2.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 20 </span><span class="caption-text">Side views of N- or Al- terminated surfaces showing nearest neighbours main polar crystallographic directions. The inset shows the experimental Al(2p)/N(1s) ratio versus polar angle for both AlN polarities (taken from <a class="reference internal" href="#aln-paper">Lebedev <em>et al.</em></a>).</span><a class="headerlink" href="#aln-fig2" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 22 </span><span class="caption-text">Side views of N- or Al- terminated surfaces showing nearest neighbours main polar crystallographic directions. The inset shows the experimental Al(2p)/N(1s) ratio versus polar angle for both AlN polarities (taken from <a class="reference internal" href="#aln-paper">Lebedev <em>et al.</em></a>).</span><a class="headerlink" href="#aln-fig2" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<p>The strongest differences in photoemission intensities suitable for a quick and unambiguous determination of polarity were found in the (10-10) azimuthal plane at <strong>32°</strong> and <strong>59°</strong> (polar scans in the inset of <a class="reference internal" href="#aln-fig2"><span class="std std-numref">Fig. 20</span></a>).</p>
|
||||
<p>The strongest differences in photoemission intensities suitable for a quick and unambiguous determination of polarity were found in the (10-10) azimuthal plane at <strong>32°</strong> and <strong>59°</strong> (polar scans in the inset of <a class="reference internal" href="#aln-fig2"><span class="std std-numref">Fig. 22</span></a>).</p>
|
||||
<p>These are the directions of short neighbor distances between the atoms of the same element (32°) and between Al and N atoms (58.5°), respectively.</p>
|
||||
<div class="sd-tab-set docutils">
|
||||
<input checked="checked" id="sd-tab-item-0" name="sd-tab-set-0" type="radio">
|
||||
<label class="sd-tab-label" for="sd-tab-item-0">
|
||||
<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
|
||||
<p>Using the crystal view in <a class="reference internal" href="#aln-fig1"><span class="std std-numref">Fig. 19</span></a> and assuming that we want to compute Al(2p) and N(1s) intensities for emitters located in 3 different planes to get a <em>substrate</em> signal. How many clusters do we need to build ?</p>
|
||||
<p>Using the crystal view in <a class="reference internal" href="#aln-fig1"><span class="std std-numref">Fig. 21</span></a> and assuming that we want to compute Al(2p) and N(1s) intensities for emitters located in 3 different planes to get a <em>substrate</em> signal. How many clusters do we need to build ?</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="toggle docutils container">
|
||||
|
|
@ -399,7 +397,7 @@ This is the key to computing the total photodiffraction signal of a <em>substrat
|
|||
<a class="reference internal image-reference" href="../_images/AlN-fig3.jpg"><img alt="AlN number of clusters" class="align-center" src="../_images/AlN-fig3.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 21 </span><span class="caption-text">Number of different clusters to build for Al(2p) and N(1s) in 3 planes</span><a class="headerlink" href="#aln-fig3" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 23 </span><span class="caption-text">Number of different clusters to build for Al(2p) and N(1s) in 3 planes</span><a class="headerlink" href="#aln-fig3" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
</div>
|
||||
|
|
@ -409,7 +407,7 @@ This is the key to computing the total photodiffraction signal of a <em>substrat
|
|||
<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>Download <a class="reference download internal" download="" href="../_downloads/0e4320262cbcdc4d473d0b9d43e0f7e9/AlN.py"><span class="xref download myst">this script</span></a> and fill in the lines indicated by the comments “FILL HERE”. Run the calculation and check that you are reproducing polar scan of <a class="reference internal" href="#aln-fig2"><span class="std std-numref">Fig. 20</span></a>.</p>
|
||||
<p>Download <a class="reference download internal" download="" href="../_downloads/0e4320262cbcdc4d473d0b9d43e0f7e9/AlN.py"><span class="xref download myst">this script</span></a> and fill in the lines indicated by the comments “FILL HERE”. Run the calculation and check that you are reproducing polar scan of <a class="reference internal" href="#aln-fig2"><span class="std std-numref">Fig. 22</span></a>.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="toggle docutils container">
|
||||
|
|
@ -417,17 +415,17 @@ This is the key to computing the total photodiffraction signal of a <em>substrat
|
|||
<a class="reference internal image-reference" href="../_images/AlN-fig4.png"><img alt="AlN results" class="align-center" src="../_images/AlN-fig4.png" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 22 </span><span class="caption-text">Polar scans in the (10-10) azimuthal plane of AlN for Al polarity (left) and N polarity (right)</span><a class="headerlink" href="#aln-fig4" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 24 </span><span class="caption-text">Polar scans in the (10-10) azimuthal plane of AlN for Al polarity (left) and N polarity (right)</span><a class="headerlink" href="#aln-fig4" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<figure class="align-default" id="aln-fig5">
|
||||
<a class="reference internal image-reference" href="../_images/AlN-fig5.jpg"><img alt="AlN results" class="align-center" src="../_images/AlN-fig5.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 23 </span><span class="caption-text">Al(2p)/N(1s) intensity ratio for both polarities</span><a class="headerlink" href="#aln-fig5" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 25 </span><span class="caption-text">Al(2p)/N(1s) intensity ratio for both polarities</span><a class="headerlink" href="#aln-fig5" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<p>As can be seen in <a class="reference internal" href="#aln-fig5"><span class="std std-numref">Fig. 23</span></a>, the peaks at 32° and 58.5° are well reproduced by the calculation for an Al polarity. Some discreapancies arise between the experimental work and this simulation especially for large polar angles. This may be due to a too small cluster in diameter for the deeper emitters.</p>
|
||||
<p>As can be seen in <a class="reference internal" href="#aln-fig5"><span class="std std-numref">Fig. 25</span></a>, the peaks at 32° and 58.5° are well reproduced by the calculation for an Al polarity. Some discreapancies arise between the experimental work and this simulation especially for large polar angles. This may be due to a too small cluster in diameter for the deeper emitters.</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>
|
||||
<span class="linenos"> 2</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"> 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="p">,</span> <span class="n">XRaySource</span>
|
||||
|
|
|
|||
|
|
@ -192,8 +192,6 @@
|
|||
<li class="toctree-l1"><a class="reference internal" href="../Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
|
||||
<li class="toctree-l1 current active"><a class="current reference internal" href="#">Activity 9: Comparing simulation and experiment with R-factors</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
|
@ -371,7 +369,7 @@ document.write(`
|
|||
<a class="reference internal image-reference" href="../_images/COFe_fig1.jpg"><img alt="" class="align-center" src="../_images/COFe_fig1.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 24 </span><span class="caption-text">Small cluster used for SSC calculations (left) and (right) Normalized polar scan of the C(1s) at 1202 eV for [100] and [1-10] azimths.</span><a class="headerlink" href="#cofe-fig1" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 26 </span><span class="caption-text">Small cluster used for SSC calculations (left) and (right) Normalized polar scan of the C(1s) at 1202 eV for [100] and [1-10] azimths.</span><a class="headerlink" href="#cofe-fig1" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<div class="sd-tab-set docutils">
|
||||
|
|
@ -379,13 +377,13 @@ document.write(`
|
|||
<label class="sd-tab-label" for="sd-tab-item-0">
|
||||
<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
|
||||
<p>Download <a class="reference download internal" download="" href="../_downloads/179b010d01a3689041dba01413ac667b/COFe.py"><span class="xref download myst">this script</span></a> and write the body of the function <code class="docutils literal notranslate"><span class="pre">create_cluster</span></code>. The function should return a
|
||||
small cluster of 5 Fe atoms with the CO molecule adsorbed like in figure <a class="reference internal" href="#cofe-fig2"><span class="std std-numref">Fig. 25</span></a> below. The function
|
||||
small cluster of 5 Fe atoms with the CO molecule adsorbed like in figure <a class="reference internal" href="#cofe-fig2"><span class="std std-numref">Fig. 27</span></a> below. The function
|
||||
will accept 4 keyword arguments to control the adsorption geometry.</p>
|
||||
<figure class="align-default" id="cofe-fig2">
|
||||
<a class="reference internal image-reference" href="../_images/COFe_fig2.jpg"><img alt="CO-Fe adsorption geometry" class="align-center" src="../_images/COFe_fig2.jpg" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 25 </span><span class="caption-text">Adsorption geometry of carbon monoxide on Fe(001).</span><a class="headerlink" href="#cofe-fig2" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 27 </span><span class="caption-text">Adsorption geometry of carbon monoxide on Fe(001).</span><a class="headerlink" href="#cofe-fig2" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<div class="admonition note">
|
||||
|
|
@ -473,7 +471,7 @@ Finally there is the <em>Main part</em> that is built in two sections:</p>
|
|||
<a class="reference internal image-reference" href="../_images/Comparison.png"><img alt="R-Factor result" class="align-center" src="../_images/Comparison.png" style="width: 600px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 26 </span><span class="caption-text">Best polar scan according to R-Factor analysis.</span><a class="headerlink" href="#cofe-comparison" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 28 </span><span class="caption-text">Best polar scan according to R-Factor analysis.</span><a class="headerlink" href="#cofe-comparison" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
</div>
|
||||
|
|
@ -482,7 +480,7 @@ Finally there is the <em>Main part</em> that is built in two sections:</p>
|
|||
<a class="reference internal image-reference" href="../_images/formula.jpg"><img alt="R-Factor result" class="align-center" src="../_images/formula.jpg" style="width: 800px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 27 </span><span class="caption-text">The 12 R-Factors used in MsSpec. The Pendry’s R-Factor is n°11.</span><a class="headerlink" href="#rfactors-formula" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 29 </span><span class="caption-text">The 12 R-Factors used in MsSpec. The Pendry’s R-Factor is n°11.</span><a class="headerlink" href="#rfactors-formula" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<div class="sd-tab-set docutils">
|
||||
|
|
@ -499,7 +497,7 @@ Finally there is the <em>Main part</em> that is built in two sections:</p>
|
|||
<a class="reference internal image-reference" href="../_images/results1.png"><img alt="results" class="align-center" src="../_images/results1.png" style="width: 800px;" />
|
||||
</a>
|
||||
<figcaption>
|
||||
<p><span class="caption-number">Fig. 28 </span><span class="caption-text">The number of R-Factors for which the parameter set (in abscissa) gives the best agreement.</span><a class="headerlink" href="#results" title="Link to this image">#</a></p>
|
||||
<p><span class="caption-number">Fig. 30 </span><span class="caption-text">The number of R-Factors for which the parameter set (in abscissa) gives the best agreement.</span><a class="headerlink" href="#results" title="Link to this image">#</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
</div>
|
||||
|
|
|
|||
|
|
@ -408,7 +408,6 @@ can be changed).</p>
|
|||
<p>In the paper discussed in <a class="reference internal" href="../Activity09/Activity09.html#rfactor"><span class="std std-ref">Activity 9: Comparing simulation and experiment with R-factors</span></a>, experimental values of the anisotropy suggest an adsorption height between 0.2 and 0.6 Å. Modify the script to add another sweep for variying the adsorption height of the CO molecule.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="toggle docutils container">
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="linenos">63</span><span class="c1"># 1) Multiprocess calculations </span>
|
||||
<span class="linenos">64</span><span class="n">theta</span> <span class="o">=</span> <span class="n">Sweep</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="s1">'theta'</span><span class="p">,</span> <span class="n">comments</span><span class="o">=</span><span class="s2">"The molecule tilt angle"</span><span class="p">,</span>
|
||||
<span class="linenos">65</span> <span class="n">start</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">stop</span><span class="o">=</span><span class="mi">60</span><span class="p">,</span> <span class="n">step</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">unit</span><span class="o">=</span><span class="s1">'degree'</span><span class="p">)</span>
|
||||
|
|
@ -435,6 +434,21 @@ can be changed).</p>
|
|||
<span class="linenos">86</span><span class="n">results</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">parameters</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="s1">'output'</span><span class="p">),</span> <span class="p">(</span><span class="n">df</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</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">1</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="cell tag_answer tag_hide docutils container">
|
||||
<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">IPython.display</span><span class="w"> </span><span class="kn">import</span> <span class="n">Markdown</span>
|
||||
|
||||
<span class="n">Markdown</span><span class="p">(</span><span class="s2">"""</span>
|
||||
|
||||
<span class="s2">Hello world</span>
|
||||
|
||||
<span class="s2">"""</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<p>Hello world</p>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
|
|
|
|||
|
|
@ -60,8 +60,6 @@
|
|||
<script>DOCUMENTATION_OPTIONS.pagename = 'Activity11/Activity11';</script>
|
||||
<link rel="index" title="Index" href="../genindex.html" />
|
||||
<link rel="search" title="Search" href="../search.html" />
|
||||
<link rel="next" title="Final word" href="../backmatter.html" />
|
||||
<link rel="prev" title="Activity 10: Parallelization and multi-processing in MsSpec" href="../Activity10/Activity10.html" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
||||
<meta name="docsearch:language" content="en"/>
|
||||
</head>
|
||||
|
|
@ -124,6 +122,8 @@
|
|||
|
||||
|
||||
|
||||
|
||||
|
||||
<div class="bd-sidebar-primary bd-sidebar">
|
||||
|
||||
|
||||
|
|
@ -179,7 +179,7 @@
|
|||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<ul class="current nav bd-sidenav">
|
||||
<ul class="nav bd-sidenav">
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity01/Activity01.html">Activity 1: Getting started</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity02/Activity02.html">Activity 2: Setting up the “experiment”</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity03/Activity03.html">Activity 3: Adsorbates and the single scattering approach</a></li>
|
||||
|
|
@ -190,8 +190,6 @@
|
|||
<li class="toctree-l1"><a class="reference internal" href="../Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
|
||||
<li class="toctree-l1 current active"><a class="current reference internal" href="#">Activity 11: Spectral radius and convergence</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../backmatter.html">Final word</a></li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
|
@ -376,24 +374,6 @@ document.write(`
|
|||
<footer class="prev-next-footer d-print-none">
|
||||
|
||||
<div class="prev-next-area">
|
||||
<a class="left-prev"
|
||||
href="../Activity10/Activity10.html"
|
||||
title="previous page">
|
||||
<i class="fa-solid fa-angle-left"></i>
|
||||
<div class="prev-next-info">
|
||||
<p class="prev-next-subtitle">previous</p>
|
||||
<p class="prev-next-title">Activity 10: Parallelization and multi-processing in MsSpec</p>
|
||||
</div>
|
||||
</a>
|
||||
<a class="right-next"
|
||||
href="../backmatter.html"
|
||||
title="next page">
|
||||
<div class="prev-next-info">
|
||||
<p class="prev-next-subtitle">next</p>
|
||||
<p class="prev-next-title">Final word</p>
|
||||
</div>
|
||||
<i class="fa-solid fa-angle-right"></i>
|
||||
</a>
|
||||
</div>
|
||||
</footer>
|
||||
|
||||
|
|
|
|||
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|
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|
|
@ -62,7 +62,7 @@
|
|||
"::::{tab-set}\n",
|
||||
"\n",
|
||||
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
|
||||
"By using the `Atoms` class of the `ase` package, try to build a O-Rh chain where atoms are 4 Å apart. Here is the begining of the script. Try to complete the line of code and view your two-atoms chain.\n",
|
||||
"By using the [`Atoms`](https://wiki.fysik.dtu.dk/ase/ase/atoms.html#ase.Atoms) class of the `ase` package, try to build a O-Rh chain where atoms are 4 Å apart. Here is the begining of the script. Try to complete the line of code and view your two-atoms chain.\n",
|
||||
"\n",
|
||||
"```python\n",
|
||||
"from ase import Atoms\n",
|
||||
|
|
@ -409,7 +409,7 @@
|
|||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.11.13"
|
||||
"version": "3.11.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -11,7 +11,13 @@
|
|||
"tags": []
|
||||
},
|
||||
"source": [
|
||||
"# Activity 4: From single scattering to multiple scattering"
|
||||
"(ssc2ms)=\n",
|
||||
"# Activity 4: From single scattering to multiple scattering\n",
|
||||
"\n",
|
||||
"In the [previous activity](ssc), we saw that simple single scattering calculations (SSC) can be used to simulate photodiffraction diagrams with good accuracy. The approximation works fine when the emitting atom is very close to the surface.\n",
|
||||
"However, the SSC approach is no longer suitable for deeper emitter atoms, where multiple scattering effects come into play. In this activity, we will focus on a major consequence of multiple scattering: *the defocusing effect*.\n",
|
||||
"\n",
|
||||
"The defocusing effect is presented in the [figure below](Ni-fig1) for a chain of nickel atoms. Although purely illustrative, understanding multiple scattering in atomic chains is fundamental because they are found in many situations, such as in particular directions of a crystal or in molecules of various lengths."
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -26,17 +32,27 @@
|
|||
},
|
||||
"source": [
|
||||
":::{figure-md} Ni-fig1\n",
|
||||
"<img src=\"Ni_fig1.png\" alt=\"Ni chain\" width=\"600px\" align=\"center\">\n",
|
||||
"<img src=\"defocusing_animation.gif\" alt=\"defocusing effect\" width=\"600px\" align=\"center\">\n",
|
||||
"\n",
|
||||
"Polar scan of a Ni chain of 2-5 atoms for single and mutliple (5{sup}`th` order) scattering.\n",
|
||||
"The defocusing effect dur to multiple scattering in an atomic chain of Ni atoms.\n",
|
||||
":::"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "b1b4c789-e62c-40cc-92a3-053e6a90d315",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"In 1989, M.-L Xu, J.J. Barton and M.A. Van Hove studied these multiple scattering effects on atomic chains ([see their paper below](defocusing-paper)).\n",
|
||||
"In the spirit of figure 3 of their paper, we will create 3 atomic chains of Ni atoms (2, 3 and 5 atoms) tilted by 45° and we will compare the intensity of the forward scattering peak for single scattering and for full multiple scattering."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "4988e7d3-2ba3-470f-9676-8116348c30a1",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"(defocusing-paper)=\n",
|
||||
":::{seealso}\n",
|
||||
"based on this paper from M.-L. Xu *et al.*\n",
|
||||
"[Phys. Rev. B **39** p8275 (1989)](https://doi.org/10.1103/PhysRevB.39.8275) \n",
|
||||
|
|
@ -45,27 +61,97 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "b2aa92f1-3170-47f6-87c2-e7abffcbdb12",
|
||||
"id": "011ef23b-5a76-410d-8d44-1c4a899e2a23",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
":::{literalinclude} Ni_chain.py\n",
|
||||
":lineno-match:\n",
|
||||
"## Polar scans of Ni atomic chains\n",
|
||||
"\n",
|
||||
"### Building a chain of atoms\n",
|
||||
"\n",
|
||||
"Start by creating a simple chain of 2 Ni atoms: an emitter and a scatterer in the [101] direction.\n",
|
||||
"\n",
|
||||
":::{tip}\n",
|
||||
"Nickel is *fcc* with lattice parameter $a$=3.499 Å. Use the [`Atoms`](https://wiki.fysik.dtu.dk/ase/ase/atoms.html#ase.Atoms) class of `ase` like in the [previous activity](ssc)...\n",
|
||||
"\n",
|
||||
":::{admonition} if you need help to start...\n",
|
||||
":class: dropdown\n",
|
||||
"\n",
|
||||
":::{code} python\n",
|
||||
"from msspec.calculator import MSSPEC\n",
|
||||
"from ase import Atoms\n",
|
||||
"\n",
|
||||
"symbol = ... # The kind of atom for the chain\n",
|
||||
"a = ... # The distance bewteen 2 atoms\n",
|
||||
" # in [101] direction\n",
|
||||
"\n",
|
||||
"chain = Atoms(..., positions=[...])\n",
|
||||
"chain.rotate(...)\n",
|
||||
"chain.edit()\n",
|
||||
":::\n",
|
||||
"\n",
|
||||
":::\n",
|
||||
"\n",
|
||||
":::"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "bbd682d1-d142-4ac5-872d-0b57f3deecb9",
|
||||
"id": "3ed73f46-c12f-452f-a584-00d142f2e133",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"```{admonition} *Solution...*\n",
|
||||
":class: tip\n",
|
||||
":class: dropdown\n",
|
||||
"Building the 2-atoms chain\n",
|
||||
"\n",
|
||||
":::{literalinclude} Ni_chain1.py\n",
|
||||
":linenos: true\n",
|
||||
":lines: 1-10\n",
|
||||
":::\n",
|
||||
"\n",
|
||||
":::{figure-md} Ni-fig2\n",
|
||||
"<img src=\"Ni_2atomsSSC.png\" alt=\"Ni 2 atoms\" width=\"600px\" align=\"center\">\n",
|
||||
"\n",
|
||||
"Polar scan of a Ni(3s) chain of 2 atoms for single scattering.\n",
|
||||
":::\n",
|
||||
"```"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "5c57f951-bfa7-435e-8e74-b3de11909768",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"::::{tab-set}\n",
|
||||
"\n",
|
||||
":::{tab-item} <i class=\"fa-solid fa-circle-question\"></i> Quiz\n",
|
||||
"Some questions to answer\n",
|
||||
"Create an `MSSPEC` calculator with `expansion` algortithm and set the `scattering_order`=1 to compute a polar scan of the Ni(3s) in single scattering. How is varying the height of the peak at 45° (along the chain) if you increase the number of atoms in the chain ?\n",
|
||||
"\n",
|
||||
"Repeat the same experiment with `inversion` algorithm for having the full multiple scattering result. What do you observe ?\n",
|
||||
":::\n",
|
||||
"\n",
|
||||
"::::"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "626708d9-c421-4bf0-bd70-f32113360f9c",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"```{admonition} *Solution...*\n",
|
||||
":class: tip\n",
|
||||
":class: dropdown\n",
|
||||
"\n",
|
||||
"The peak at 45° is increasing with the number of atoms in the chain for SSC. We observe defocusing of this peak for full multiple scattering calculations (MSC). For the 2-atoms chain, both SSC and MSC give the same result owing to the fact that the emitter has only one scatterer atom and that kinetic energy is high enough to cancel out all backscattering.\n",
|
||||
"\n",
|
||||
":::{figure-md} Ni-figX\n",
|
||||
"<img src=\"Ni_SSCvsMI.jpg\" alt=\"Ni chain\" width=\"600px\" align=\"center\">\n",
|
||||
"\n",
|
||||
"Polar scan of a Ni chain of 2-5 atoms for single and full mutliple scattering.\n",
|
||||
":::\n",
|
||||
"\n",
|
||||
"```"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
|
|
@ -84,7 +170,7 @@
|
|||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.11.13"
|
||||
"version": "3.11.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -878,7 +878,7 @@
|
|||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.11.13"
|
||||
"version": "3.11.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -67,20 +67,46 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "0a1fabce-c42d-4cb4-9720-bcd21ff0cd09",
|
||||
"metadata": {},
|
||||
"id": "3833a4c3-2d47-49e8-b78d-5c97dad47716",
|
||||
"metadata": {
|
||||
"editable": true,
|
||||
"slideshow": {
|
||||
"slide_type": ""
|
||||
},
|
||||
"tags": []
|
||||
},
|
||||
"source": [
|
||||
"```{toggle}\n",
|
||||
"\n",
|
||||
":::{literalinclude} COFe_mp_completed.py\n",
|
||||
":lineno-start: 63\n",
|
||||
":linenos: true\n",
|
||||
":lines: 63-86\n",
|
||||
":emphasize-lines: 6,7, 9,10, 18\n",
|
||||
":::\n",
|
||||
":::"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "1b25de5e-4402-4746-8082-9f7d8362b3f6",
|
||||
"metadata": {
|
||||
"editable": true,
|
||||
"slideshow": {
|
||||
"slide_type": ""
|
||||
},
|
||||
"tags": [
|
||||
"answer",
|
||||
"hide"
|
||||
]
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from IPython.display import Markdown\n",
|
||||
"\n",
|
||||
"Markdown(\"\"\"\n",
|
||||
"\n",
|
||||
"```"
|
||||
"Hello world\n",
|
||||
"\n",
|
||||
"\"\"\")"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
|
|||
|
|
@ -60,7 +60,6 @@
|
|||
<script>DOCUMENTATION_OPTIONS.pagename = 'backmatter';</script>
|
||||
<link rel="index" title="Index" href="genindex.html" />
|
||||
<link rel="search" title="Search" href="search.html" />
|
||||
<link rel="prev" title="Activity 11: Spectral radius and convergence" href="Activity11/Activity11.html" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
||||
<meta name="docsearch:language" content="en"/>
|
||||
</head>
|
||||
|
|
@ -123,6 +122,8 @@
|
|||
|
||||
|
||||
|
||||
|
||||
|
||||
<div class="bd-sidebar-primary bd-sidebar">
|
||||
|
||||
|
||||
|
|
@ -178,7 +179,7 @@
|
|||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<ul class="current nav bd-sidenav">
|
||||
<ul class="nav bd-sidenav">
|
||||
<li class="toctree-l1"><a class="reference internal" href="Activity01/Activity01.html">Activity 1: Getting started</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="Activity02/Activity02.html">Activity 2: Setting up the “experiment”</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="Activity03/Activity03.html">Activity 3: Adsorbates and the single scattering approach</a></li>
|
||||
|
|
@ -189,8 +190,6 @@
|
|||
<li class="toctree-l1"><a class="reference internal" href="Activity08/Activity08.html">Activity 8: Inequivalent emitters and the XPD of a substrate</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="Activity09/Activity09.html">Activity 9: Comparing simulation and experiment with R-factors</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="Activity10/Activity10.html">Activity 10: Parallelization and multi-processing in MsSpec</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="Activity11/Activity11.html">Activity 11: Spectral radius and convergence</a></li>
|
||||
<li class="toctree-l1 current active"><a class="current reference internal" href="#">Final word</a></li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
|
@ -396,15 +395,6 @@ document.write(`
|
|||
<footer class="prev-next-footer d-print-none">
|
||||
|
||||
<div class="prev-next-area">
|
||||
<a class="left-prev"
|
||||
href="Activity11/Activity11.html"
|
||||
title="previous page">
|
||||
<i class="fa-solid fa-angle-left"></i>
|
||||
<div class="prev-next-info">
|
||||
<p class="prev-next-subtitle">previous</p>
|
||||
<p class="prev-next-title">Activity 11: Spectral radius and convergence</p>
|
||||
</div>
|
||||
</a>
|
||||
</div>
|
||||
</footer>
|
||||
|
||||
|
|
|
|||
Binary file not shown.
|
|
@ -27,19 +27,15 @@ nbclient.exceptions.CellExecutionError: An error occurred while executing the fo
|
|||
------------------
|
||||
```{toggle}
|
||||
|
||||
:::{literalinclude} COFe_mp_completed.py
|
||||
:lineno-start: 63
|
||||
:::{literalinclude} Ni_chain1.py
|
||||
:lines: 1-9
|
||||
:linenos: true
|
||||
:lines: 63-86
|
||||
:emphasize-lines: 6,7, 9,10, 18
|
||||
:::
|
||||
|
||||
|
||||
```
|
||||
------------------
|
||||
|
||||
|
||||
[36mCell[39m[36m [39m[32mIn[2][39m[32m, line 1[39m
|
||||
[36mCell[39m[36m [39m[32mIn[1][39m[32m, line 1[39m
|
||||
[31m [39m[31m```{toggle}[39m
|
||||
^
|
||||
[31mSyntaxError[39m[31m:[39m invalid syntax
|
||||
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Reference in New Issue