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<h1>Activity 4: From single scattering to multiple scattering</h1>
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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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<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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<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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<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 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>
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<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>
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<span class="linenos">68</span>
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<span class="linenos">69</span><span class="c1"># 2. for each view in each dataset, change the scale accordingly</span>
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<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>
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<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>
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<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>
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<span class="linenos">73</span>
|
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<span class="linenos">74</span><span class="c1"># Pop up the graphical window</span>
|
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<span class="linenos">75</span><span class="n">all_data</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
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<span class="linenos">76</span><span class="c1"># You can end your script with the line below to remove the temporary</span>
|
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<span class="linenos">77</span><span class="c1"># folder needed for the calculation</span>
|
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<span class="linenos">78</span><span class="n">calc</span><span class="o">.</span><span class="n">shutdown</span><span class="p">()</span>
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