592 lines
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592 lines
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<div class="section" id="compute-xrd-command">
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<span id="index-0"></span><h1>compute xrd command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">compute</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">xrd</span> <span class="k">lambda</span> <span class="n">type1</span> <span class="n">type2</span> <span class="o">...</span> <span class="n">typeN</span> <span class="n">keyword</span> <span class="n">value</span> <span class="o">...</span>
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</pre></div>
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</div>
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<ul class="simple">
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<li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> command</li>
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<li>xrd = style name of this compute command</li>
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<li>lambda = wavelength of incident radiation (length units)</li>
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<li>type1 type2 ... typeN = chemical symbol of each atom type (see valid options below)</li>
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<li>zero or more keyword/value pairs may be appended</li>
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<li>keyword = <em>2Theta</em> or <em>c</em> or <em>LP</em> or <em>manual</em> or <em>echo</em></li>
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</ul>
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<pre class="literal-block">
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<em>2Theta</em> values = Min2Theta Max2Theta
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Min2Theta,Max2Theta = minimum and maximum 2 theta range to explore
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(radians or degrees)
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<em>c</em> values = c1 c2 c3
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c1,c2,c3 = parameters to adjust the spacing of the reciprocal
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lattice nodes in the h, k, and l directions respectively
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<em>LP</em> value = switch to apply Lorentz-polarization factor
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0/1 = off/on
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<em>manual</em> = flag to use manual spacing of reciprocal lattice points
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based on the values of the <em>c</em> parameters
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<em>echo</em> = flag to provide extra output for debugging purposes
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</pre>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">compute</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">xrd</span> <span class="mf">1.541838</span> <span class="n">Al</span> <span class="n">O</span> <span class="mi">2</span><span class="n">Theta</span> <span class="mf">0.087</span> <span class="mf">0.87</span> <span class="n">c</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="n">LP</span> <span class="mi">1</span> <span class="n">echo</span>
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<span class="n">compute</span> <span class="mi">2</span> <span class="nb">all</span> <span class="n">xrd</span> <span class="mf">1.541838</span> <span class="n">Al</span> <span class="n">O</span> <span class="mi">2</span><span class="n">Theta</span> <span class="mi">10</span> <span class="mi">100</span> <span class="n">c</span> <span class="mf">0.05</span> <span class="mf">0.05</span> <span class="mf">0.05</span> <span class="n">LP</span> <span class="mi">1</span> <span class="n">manual</span>
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</pre></div>
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</div>
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<pre class="literal-block">
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fix 1 all ave/histo/weight 1 1 1 0.087 0.87 250 c_1[1] c_1[2] mode vector file Rad2Theta.xrd
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fix 2 all ave/histo/weight 1 1 1 10 100 250 c_2[1] c_2[2] mode vector file Deg2Theta.xrd
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</pre>
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</div>
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<div class="section" id="description">
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<h2>Description</h2>
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<p>Define a computation that calculates x-ray diffraction intensity as described
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in <a class="reference internal" href="#xrd-coleman"><span class="std std-ref">(Coleman)</span></a> on a mesh of reciprocal lattice nodes defined
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by the entire simulation domain (or manually) using a simulated radiation
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of wavelength lambda.</p>
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<p>The x-ray diffraction intensity, I, at each reciprocal lattice point, k,
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is computed from the structure factor, F, using the equations:</p>
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<img alt="_images/compute_xrd1.jpg" class="align-center" src="_images/compute_xrd1.jpg" />
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<img alt="_images/compute_xrd2.jpg" class="align-center" src="_images/compute_xrd2.jpg" />
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<img alt="_images/compute_xrd3.jpg" class="align-center" src="_images/compute_xrd3.jpg" />
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<img alt="_images/compute_xrd4.jpg" class="align-center" src="_images/compute_xrd4.jpg" />
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<p>Here, K is the location of the reciprocal lattice node, rj is the
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position of each atom, fj are atomic scattering factors, LP is the
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Lorentz-polarization factor, and theta is the scattering angle of
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diffraction. The Lorentz-polarization factor can be turned off using
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the optional <em>LP</em> keyword.</p>
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<p>Diffraction intensities are calculated on a three-dimensional mesh of
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reciprocal lattice nodes. The mesh spacing is defined either (a)
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by the entire simulation domain or (b) manually using selected values as
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shown in the 2D diagram below.</p>
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<a class=""
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data-lightbox="group-default"
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href="_images/xrd_mesh.jpg"
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title=""
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data-title=""
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><img src="_images/xrd_mesh.jpg"
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class="align-center"
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width="25%"
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height="auto"
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alt=""/>
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</a><p>For a mesh defined by the simulation domain, a rectilinear grid is
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constructed with spacing <em>c</em>*inv(A) along each reciprocal lattice
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axis. Where A are the vectors corresponding to the edges of the
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simulation cell. If one or two directions has non-periodic boundary
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conditions, then the spacing in these directions is defined from the
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average of the (inversed) box lengths with periodic boundary conditions.
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Meshes defined by the simulation domain must contain at least one periodic
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boundary.</p>
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<p>If the <em>manual</em> flag is included, the mesh of reciprocal lattice nodes
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will defined using the <em>c</em> values for the spacing along each
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reciprocal lattice axis. Note that manual mapping of the reciprocal
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space mesh is good for comparing diffraction results from multiple
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simulations; however it can reduce the likelihood that Bragg
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reflections will be satisfied unless small spacing parameters (< 0.05
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Angstrom^(-1)) are implemented. Meshes with manual spacing do not
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require a periodic boundary.</p>
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<p>The limits of the reciprocal lattice mesh are determined by range of
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scattering angles explored. The <em>2Theta</em> parameters allows the user
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to reduce the scattering angle range to only the region of interest
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which reduces the cost of the computation.</p>
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<p>The atomic scattering factors, fj, accounts for the reduction in
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diffraction intensity due to Compton scattering. Compute xrd uses
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analytical approximations of the atomic scattering factors that vary
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for each atom type (type1 type2 ... typeN) and angle of diffraction.
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The analytic approximation is computed using the formula
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<a class="reference internal" href="#colliex"><span class="std std-ref">(Colliex)</span></a>:</p>
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<img alt="_images/compute_xrd5.jpg" class="align-center" src="_images/compute_xrd5.jpg" />
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<p>Coefficients parameterized by <a class="reference internal" href="#peng"><span class="std std-ref">(Peng)</span></a> are assigned for each
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atom type designating the chemical symbol and charge of each atom
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type. Valid chemical symbols for compute xrd are:</p>
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<table border="1" class="docutils">
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<colgroup>
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<col width="19%" />
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<col width="19%" />
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<col width="19%" />
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<col width="23%" />
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<col width="19%" />
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</colgroup>
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<tbody valign="top">
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<tr class="row-odd"><td>H</td>
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<td>He1-</td>
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<td>He</td>
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<td>Li</td>
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<td>Li1+</td>
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</tr>
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<tr class="row-even"><td>Be</td>
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<td>Be2+</td>
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<td>B</td>
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<td>C</td>
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<td>Cval</td>
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</tr>
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<tr class="row-odd"><td>N</td>
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<td>O</td>
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<td>O1-</td>
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<td>F</td>
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<td>F1-</td>
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</tr>
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<tr class="row-even"><td>Ne</td>
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<td>Na</td>
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<td>Na1+</td>
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<td>Mg</td>
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<td>Mg2+</td>
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</tr>
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<tr class="row-odd"><td>Al</td>
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<td>Al3+</td>
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<td>Si</td>
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<td>Sival</td>
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<td>Si4+</td>
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</tr>
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<tr class="row-even"><td>P</td>
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<td>S</td>
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<td>Cl</td>
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<td>Cl1-</td>
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<td>Ar</td>
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</tr>
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<tr class="row-odd"><td>K</td>
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<td>Ca</td>
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<td>Ca2+</td>
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<td>Sc</td>
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<td>Sc3+</td>
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</tr>
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<tr class="row-even"><td>Ti</td>
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<td>Ti2+</td>
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<td>Ti3+</td>
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<td>Ti4+</td>
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<td>V</td>
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</tr>
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<tr class="row-odd"><td>V2+</td>
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<td>V3+</td>
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<td>V5+</td>
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<td>Cr</td>
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<td>Cr2+</td>
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</tr>
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<tr class="row-even"><td>Cr3+</td>
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<td>Mn</td>
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<td>Mn2+</td>
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<td>Mn3+</td>
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<td>Mn4+</td>
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</tr>
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<tr class="row-odd"><td>Fe</td>
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<td>Fe2+</td>
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<td>Fe3+</td>
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<td>Co</td>
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<td>Co2+</td>
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</tr>
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<tr class="row-even"><td>Co</td>
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<td>Ni</td>
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<td>Ni2+</td>
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<td>Ni3+</td>
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<td>Cu</td>
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</tr>
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<tr class="row-odd"><td>Cu1+</td>
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<td>Cu2+</td>
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<td>Zn</td>
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<td>Zn2+</td>
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<td>Ga</td>
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</tr>
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<tr class="row-even"><td>Ga3+</td>
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<td>Ge</td>
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<td>Ge4+</td>
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<td>As</td>
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<td>Se</td>
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</tr>
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<tr class="row-odd"><td>Br</td>
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<td>Br1-</td>
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<td>Kr</td>
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<td>Rb</td>
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<td>Rb1+</td>
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</tr>
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<tr class="row-even"><td>Sr</td>
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<td>Sr2+</td>
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<td>Y</td>
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<td>Y3+</td>
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<td>Zr</td>
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</tr>
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<tr class="row-odd"><td>Zr4+</td>
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<td>Nb</td>
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<td>Nb3+</td>
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<td>Nb5+</td>
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<td>Mo</td>
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</tr>
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<tr class="row-even"><td>Mo3+</td>
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<td>Mo5+</td>
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<td>Mo6+</td>
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<td>Tc</td>
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<td>Ru</td>
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</tr>
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<tr class="row-odd"><td>Ru3+</td>
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<td>Ru4+</td>
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<td>Rh</td>
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<td>Rh3+</td>
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<td>Rh4+</td>
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</tr>
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<tr class="row-even"><td>Pd</td>
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<td>Pd2+</td>
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<td>Pd4+</td>
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<td>Ag</td>
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<td>Ag1+</td>
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</tr>
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<tr class="row-odd"><td>Ag2+</td>
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<td>Cd</td>
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<td>Cd2+</td>
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<td>In</td>
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<td>In3+</td>
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</tr>
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<tr class="row-even"><td>Sn</td>
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<td>Sn2+</td>
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<td>Sn4+</td>
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<td>Sb</td>
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<td>Sb3+</td>
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</tr>
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<tr class="row-odd"><td>Sb5+</td>
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<td>Te</td>
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<td>I</td>
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<td>I1-</td>
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<td>Xe</td>
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</tr>
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<tr class="row-even"><td>Cs</td>
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<td>Cs1+</td>
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<td>Ba</td>
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<td>Ba2+</td>
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<td>La</td>
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</tr>
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<tr class="row-odd"><td>La3+</td>
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<td>Ce</td>
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<td>Ce3+</td>
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<td>Ce4+</td>
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<td>Pr</td>
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</tr>
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<tr class="row-even"><td>Pr3+</td>
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<td>Pr4+</td>
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<td>Nd</td>
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<td>Nd3+</td>
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<td>Pm</td>
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</tr>
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<tr class="row-odd"><td>Pm3+</td>
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<td>Sm</td>
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<td>Sm3+</td>
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<td>Eu</td>
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<td>Eu2+</td>
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</tr>
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<tr class="row-even"><td>Eu3+</td>
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<td>Gd</td>
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<td>Gd3+</td>
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<td>Tb</td>
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<td>Tb3+</td>
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</tr>
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<tr class="row-odd"><td>Dy</td>
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<td>Dy3+</td>
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<td>Ho</td>
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<td>Ho3+</td>
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<td>Er</td>
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</tr>
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<tr class="row-even"><td>Er3+</td>
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<td>Tm</td>
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<td>Tm3+</td>
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<td>Yb</td>
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<td>Yb2+</td>
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</tr>
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<tr class="row-odd"><td>Yb3+</td>
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<td>Lu</td>
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<td>Lu3+</td>
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<td>Hf</td>
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<td>Hf4+</td>
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</tr>
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<tr class="row-even"><td>Ta</td>
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<td>Ta5+</td>
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<td>W</td>
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<td>W6+</td>
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<td>Re</td>
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</tr>
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<tr class="row-odd"><td>Os</td>
|
|
<td>Os4+</td>
|
|
<td>Ir</td>
|
|
<td>Ir3+</td>
|
|
<td>Ir4+</td>
|
|
</tr>
|
|
<tr class="row-even"><td>Pt</td>
|
|
<td>Pt2+</td>
|
|
<td>Pt4+</td>
|
|
<td>Au</td>
|
|
<td>Au1+</td>
|
|
</tr>
|
|
<tr class="row-odd"><td>Au3+</td>
|
|
<td>Hg</td>
|
|
<td>Hg1+</td>
|
|
<td>Hg2+</td>
|
|
<td>Tl</td>
|
|
</tr>
|
|
<tr class="row-even"><td>Tl1+</td>
|
|
<td>Tl3+</td>
|
|
<td>Pb</td>
|
|
<td>Pb2+</td>
|
|
<td>Pb4+</td>
|
|
</tr>
|
|
<tr class="row-odd"><td>Bi</td>
|
|
<td>Bi3+</td>
|
|
<td>Bi5+</td>
|
|
<td>Po</td>
|
|
<td>At</td>
|
|
</tr>
|
|
<tr class="row-even"><td>Rn</td>
|
|
<td>Fr</td>
|
|
<td>Ra</td>
|
|
<td>Ra2+</td>
|
|
<td>Ac</td>
|
|
</tr>
|
|
<tr class="row-odd"><td>Ac3+</td>
|
|
<td>Th</td>
|
|
<td>Th4+</td>
|
|
<td>Pa</td>
|
|
<td>U</td>
|
|
</tr>
|
|
<tr class="row-even"><td>U3+</td>
|
|
<td>U4+</td>
|
|
<td>U6+</td>
|
|
<td>Np</td>
|
|
<td>Np3+</td>
|
|
</tr>
|
|
<tr class="row-odd"><td>Np4+</td>
|
|
<td>Np6+</td>
|
|
<td>Pu</td>
|
|
<td>Pu3+</td>
|
|
<td>Pu4+</td>
|
|
</tr>
|
|
<tr class="row-even"><td>Pu6+</td>
|
|
<td>Am</td>
|
|
<td>Cm</td>
|
|
<td>Bk</td>
|
|
<td>Cf</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<p>If the <em>echo</em> keyword is specified, compute xrd will provide extra
|
|
reporting information to the screen.</p>
|
|
<p><strong>Output info:</strong></p>
|
|
<p>This compute calculates a global array. The number of rows in the
|
|
array is the number of reciprocal lattice nodes that are explored
|
|
which by the mesh. The global array has 2 columns.</p>
|
|
<p>The first column contains the diffraction angle in the units (radians
|
|
or degrees) provided with the <em>2Theta</em> values. The second column contains
|
|
the computed diffraction intensities as described above.</p>
|
|
<p>The array can be accessed by any command that uses global values from
|
|
a compute as input. See <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">this section</span></a>
|
|
for an overview of LAMMPS output options.</p>
|
|
<p>All array values calculated by this compute are “intensive”.</p>
|
|
</div>
|
|
<div class="section" id="restrictions">
|
|
<h2>Restrictions</h2>
|
|
<p>This compute is part of the USER-DIFFRACTION package. It is only
|
|
enabled if LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
|
|
<p>The compute_xrd command does not work for triclinic cells.</p>
|
|
</div>
|
|
<div class="section" id="related-commands">
|
|
<h2>Related commands</h2>
|
|
<p><a class="reference internal" href="fix_ave_histo.html"><span class="doc">fix ave/histo</span></a>,
|
|
<a class="reference internal" href="compute_saed.html"><span class="doc">compute saed</span></a></p>
|
|
</div>
|
|
<div class="section" id="default">
|
|
<h2>Default</h2>
|
|
<p>The option defaults are 2Theta = 1 179 (degrees), c = 1 1 1, LP = 1,
|
|
no manual flag, no echo flag.</p>
|
|
<hr class="docutils" />
|
|
<p id="xrd-coleman"><strong>(Coleman)</strong> Coleman, Spearot, Capolungo, MSMSE, 21, 055020
|
|
(2013).</p>
|
|
<p id="colliex"><strong>(Colliex)</strong> Colliex et al. International Tables for Crystallography
|
|
Volume C: Mathematical and Chemical Tables, 249-429 (2004).</p>
|
|
<p id="peng"><strong>(Peng)</strong> Peng, Ren, Dudarev, Whelan, Acta Crystallogr. A, 52, 257-76
|
|
(1996).</p>
|
|
</div>
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