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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_start.html">2. Getting Started</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_commands.html">3. Commands</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_accelerate.html">5. Accelerating LAMMPS performance</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_howto.html">6. How-to discussions</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_example.html">7. Example problems</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_perf.html">8. Performance & scalability</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_python.html">11. Python interface to LAMMPS</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_errors.html">12. Errors</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_history.html">13. Future and history</a></li>
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<li>compute saed command</li>
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<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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<div class="section" id="compute-saed-command">
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<span id="index-0"></span><h1>compute saed 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">saed</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>saed = 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>Kmax</em> or <em>Zone</em> or <em>dR_Ewald</em> or <em>c</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>Kmax</em> value = Maximum distance explored from reciprocal space origin
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(inverse length units)
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<em>Zone</em> values = z1 z2 z3
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z1,z2,z3 = Zone axis of incident radiation. If z1=z2=z3=0 all
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reciprocal space will be meshed up to <em>Kmax</em>
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<em>dR_Ewald</em> value = Thickness of Ewald sphere slice intercepting
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reciprocal space (inverse length units)
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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>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">saed</span> <span class="mf">0.0251</span> <span class="n">Al</span> <span class="n">O</span> <span class="n">Kmax</span> <span class="mf">1.70</span> <span class="n">Zone</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="n">dR_Ewald</span> <span class="mf">0.01</span> <span class="n">c</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span>
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<span class="n">compute</span> <span class="mi">2</span> <span class="nb">all</span> <span class="n">saed</span> <span class="mf">0.0251</span> <span class="n">Ni</span> <span class="n">Kmax</span> <span class="mf">1.70</span> <span class="n">Zone</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">0</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">manual</span> <span class="n">echo</span>
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</pre></div>
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</div>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">saed</span><span class="o">/</span><span class="n">vtk</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="n">c_1</span> <span class="n">file</span> <span class="n">Al2O3_001</span><span class="o">.</span><span class="n">saed</span>
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<span class="n">fix</span> <span class="n">saed</span><span class="o">/</span><span class="n">vtk</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="n">c_2</span> <span class="n">file</span> <span class="n">Ni_000</span><span class="o">.</span><span class="n">saed</span>
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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</h2>
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<p>Define a computation that calculates electron diffraction intensity as
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described in <a class="reference internal" href="#saed-coleman"><span class="std std-ref">(Coleman)</span></a> on a mesh of reciprocal lattice nodes
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defined by the entire simulation domain (or manually) using simulated
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radiation of wavelength lambda.</p>
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<p>The electron diffraction intensity I at each reciprocal lattice point
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is computed from the structure factor F using the equations:</p>
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<img alt="_images/compute_saed1.jpg" class="align-center" src="_images/compute_saed1.jpg" />
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<img alt="_images/compute_saed2.jpg" class="align-center" src="_images/compute_saed2.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.</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) by
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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/saed_mesh.jpg"
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title=""
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data-title=""
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><img src="_images/saed_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><a href="#id1"><span class="problematic" id="id2">*</span></a>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 reciprocal
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lattice axis. Note that manual mapping of the reciprocal space mesh is
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good for comparing diffraction results from multiple simulations; however
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it can reduce the likelihood that Bragg reflections will be satisfied
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unless small spacing parameters <0.05 Angstrom^(-1) are implemented.
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Meshes with manual spacing do not require a periodic boundary.</p>
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<p>The limits of the reciprocal lattice mesh are determined by the use of
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the <em>Kmax</em>, <em>Zone</em>, and <em>dR_Ewald</em> parameters. The rectilinear mesh
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created about the origin of reciprocal space is terminated at the
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boundary of a sphere of radius <em>Kmax</em> centered at the origin. If
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<em>Zone</em> parameters z1=z2=z3=0 are used, diffraction intensities are
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computed throughout the entire spherical volume - note this can
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greatly increase the cost of computation. Otherwise, <em>Zone</em>
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parameters will denote the z1=h, z2=k, and z3=l (in a global since)
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zone axis of an intersecting Ewald sphere. Diffraction intensities
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will only be computed at the intersection of the reciprocal lattice
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mesh and a <em>dR_Ewald</em> thick surface of the Ewald sphere. See the
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example 3D intestiety data and the intersection of a [010] zone axis
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in the below image.</p>
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<a class=""
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data-lightbox="group-default"
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href="_images/saed_ewald_intersect.jpg"
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title=""
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data-title=""
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><img src="_images/saed_ewald_intersect.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>The atomic scattering factors, fj, accounts for the reduction in
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diffraction intensity due to Compton scattering. Compute saed 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="#brown"><span class="std std-ref">(Brown)</span></a>:</p>
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<img alt="_images/compute_saed3.jpg" class="align-center" src="_images/compute_saed3.jpg" />
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<p>Coefficients parameterized by <a class="reference internal" href="#fox"><span class="std std-ref">(Fox)</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 saed are:</p>
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<dl class="docutils">
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<dt>H: He: Li: Be: B:</dt>
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<dd><blockquote class="first">
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<div>C: N: O: F: Ne:</div></blockquote>
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<dl class="docutils">
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<dt>Na: Mg: Al: Si: P:</dt>
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<dd>S: Cl: Ar: K: Ca:</dd>
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</dl>
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<p class="last">Sc: Ti: V: Cr: Mn:
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Fe: Co: Ni: Cu: Zn:
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Ga: Ge: As: Se: Br:
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Kr: Rb: Sr: Y: Zr:
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Nb: Mo: Tc: Ru: Rh:
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Pd: Ag: Cd: In: Sn:
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Sb: Te: I: Xe: Cs:
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Ba: La: Ce: Pr: Nd:
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Pm: Sm: Eu: Gd: Tb:
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Dy: Ho: Er: Tm: Yb:
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Lu: Hf: Ta: W: Re:
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Os: Ir: Pt: Au: Hg:
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Tl: Pb: Bi: Po: At:
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Rn: Fr: Ra: Ac: Th:
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Pa: U: Np: Pu: Am:
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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 saed 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 vector. The length of the vector is
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the number of reciprocal lattice nodes that are explored by the mesh.
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The entries of the global vector are the computed diffraction
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intensities as described above.</p>
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<p>The vector can be accessed by any command that uses global values
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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
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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</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 class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
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<p>The compute_saed 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</h2>
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<p><a class="reference internal" href="fix_saed_vtk.html"><span class="doc">fix saed_vtk</span></a>, <a class="reference internal" href="compute_xrd.html"><span class="doc">compute xrd</span></a></p>
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</div>
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<div class="section" id="default">
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<h2>Default</h2>
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<p>The option defaults are Kmax = 1.70, Zone 1 0 0, c 1 1 1, dR_Ewald =
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0.01.</p>
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<hr class="docutils" />
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<p id="saed-coleman"><strong>(Coleman)</strong> Coleman, Spearot, Capolungo, MSMSE, 21, 055020
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(2013).</p>
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<p id="brown"><strong>(Brown)</strong> Brown et al. International Tables for Crystallography
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Volume C: Mathematical and Chemical Tables, 554-95 (2004).</p>
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<p id="fox"><strong>(Fox)</strong> Fox, O’Keefe, Tabbernor, Acta Crystallogr. A, 45, 786-93
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(1989).</p>
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