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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
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<div class="section" id="compute-xrd-command">
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<span id="index-0"></span><h1>compute xrd command<a class="headerlink" href="#compute-xrd-command" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="syntax">
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<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>compute ID group-ID xrd lambda type1 type2 ... typeN keyword value ...
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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"><em>compute</em></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<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>compute 1 all xrd 1.541838 Al O 2Theta 0.087 0.87 c 1 1 1 LP 1 echo
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compute 2 all xrd 1.541838 Al O 2Theta 10 100 c 0.05 0.05 0.05 LP 1 manual
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</pre></div>
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</div>
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<div class="highlight-python"><div class="highlight"><pre>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></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></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="fix_saed_vtk.html#coleman"><span>(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 data-lightbox="group-default"
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href="_images/xrd_mesh.jpg"
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class=""
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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 <a href="#id1"><span class="problematic" id="id2">*</span></a>c**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>(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>(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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<dl class="docutils">
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<dt>H: He1-: He: Li: Li1+:</dt>
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<dd><blockquote class="first">
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<div><blockquote>
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<div><dl class="docutils">
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<dt>Be: Be2+: B: C: Cval:</dt>
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<dd>N: O: O1-: F: F1-:</dd>
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</dl>
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<p>Ne: Na: Na1+: Mg: Mg2+:
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Al: Al3+: Si: Sival: Si4+:</p>
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<blockquote>
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<div>P: S: Cl: Cl1-: Ar:
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K: Ca: Ca2+: Sc: Sc3+:</div></blockquote>
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<p>Ti: Ti2+: Ti3+: Ti4+: V:</p>
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</div></blockquote>
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<p>V2+: V3+: V5+: Cr: Cr2+:</p>
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</div></blockquote>
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<dl class="docutils">
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<dt>Cr3+: Mn: Mn2+: Mn3+: Mn4+:</dt>
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<dd>Fe: Fe2+: Fe3+: Co: Co2+:
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Co: Ni: Ni2+: Ni3+: Cu:</dd>
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</dl>
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<p>Cu1+: Cu2+: Zn: Zn2+: Ga:
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Ga3+: Ge: Ge4+: As: Se:</p>
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<blockquote>
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<div>Br: Br1-: Kr: Rb: Rb1+:
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Sr: Sr2+: Y: Y3+: Zr:</div></blockquote>
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<p>Zr4+: Nb: Nb3+: Nb5+: Mo:
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Mo3+: Mo5+: Mo6+: Tc: Ru:
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Ru3+: Ru4+: Rh: Rh3+: Rh4+:</p>
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<blockquote>
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<div>Pd: Pd2+: Pd4+: Ag: Ag1+:</div></blockquote>
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<dl class="docutils">
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<dt>Ag2+: Cd: Cd2+: In: In3+:</dt>
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<dd>Sn: Sn2+: Sn4+: Sb: Sb3+:</dd>
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<dt>Sb5+: Te: I: I1-: Xe:</dt>
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<dd>Cs: Cs1+: Ba: Ba2+: La:</dd>
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</dl>
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<p>La3+: Ce: Ce3+: Ce4+: Pr:
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Pr3+: Pr4+: Nd: Nd3+: Pm:
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Pm3+: Sm: Sm3+: Eu: Eu2+:
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Eu3+: Gd: Gd3+: Tb: Tb3+:</p>
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<blockquote>
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<div>Dy: Dy3+: Ho: Ho3+: Er:</div></blockquote>
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<p>Er3+: Tm: Tm3+: Yb: Yb2+:
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Yb3+: Lu: Lu3+: Hf: Hf4+:</p>
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<blockquote>
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<div>Ta: Ta5+: W: W6+: Re:
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Os: Os4+: Ir: Ir3+: Ir4+:
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Pt: Pt2+: Pt4+: Au: Au1+:</div></blockquote>
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<p>Au3+: Hg: Hg1+: Hg2+: Tl:
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Tl1+: Tl3+: Pb: Pb2+: Pb4+:</p>
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<blockquote>
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<div>Bi: Bi3+: Bi5+: Po: At:
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Rn: Fr: Ra: Ra2+: Ac:</div></blockquote>
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<dl class="docutils">
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<dt>Ac3+: Th: Th4+: Pa: U:</dt>
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<dd>U3+: U4+: U6+: Np: Np3+:</dd>
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</dl>
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<p class="last">Np4+: Np6+: Pu: Pu3+: Pu4+:
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Pu6+: Am: Cm: Bk: Cf:tb(c=5,s=:)</p>
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</dd>
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</dl>
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<p>If the <em>echo</em> keyword is specified, compute xrd will provide extra
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reporting information to the screen.</p>
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<p><strong>Output info:</strong></p>
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<p>This compute calculates a global array. The number of rows in the
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array is the number of reciprocal lattice nodes that are explored
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which by the mesh. The global array has 2 columns.</p>
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<p>The first column contains the diffraction angle in the units (radians
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or degrees) provided with the <em>2Theta</em> values. The second column contains
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the computed diffraction intensities as described above.</p>
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<p>The array can be accessed by any command that uses global values from
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a compute as input. See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a>
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for an overview of LAMMPS output options.</p>
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<p>All array values calculated by this compute are “intensive”.</p>
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</div>
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<div class="section" id="restrictions">
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<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
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<p>This compute is part of the USER-DIFFRACTION package. It is only
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enabled if LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
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<p>The compute_xrd command does not work for triclinic cells.</p>
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</div>
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<div class="section" id="related-commands">
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<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
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<p><a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>,
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<a class="reference internal" href="compute_saed.html"><em>compute saed</em></a></p>
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</div>
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<div class="section" id="default">
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<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
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<p>The option defaults are 2Theta = 1 179 (degrees), c = 1 1 1, LP = 1,
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no manual flag, no echo flag.</p>
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<hr class="docutils" />
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<p id="coleman"><strong>(Coleman)</strong> Coleman, Spearot, Capolungo, MSMSE, 21, 055020
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(2013).</p>
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<p id="colliex"><strong>(Colliex)</strong> Colliex et al. International Tables for Crystallography
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Volume C: Mathematical and Chemical Tables, 249-429 (2004).</p>
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<p id="peng"><strong>(Peng)</strong> Peng, Ren, Dudarev, Whelan, Acta Crystallogr. A, 52, 257-76
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(1996).</p>
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