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<div itemprop="articleBody">
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<div class="section" id="compute-saed-command">
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<span id="index-0"></span><h1>compute saed command<a class="headerlink" href="#compute-saed-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 saed 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>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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<HR>
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<H3>compute saed command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>compute ID group-ID saed lambda type1 type2 ... typeN keyword value ...
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
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<LI>saed = style name of this compute command
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<LI>lambda = wavelength of incident radiation (length units)
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<LI>type1 type2 ... typeN = chemical symbol of each atom type (see valid options below)
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<LI>zero or more keyword/value pairs may be appended
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<LI>keyword = <I>Kmax</I> or <I>Zone</I> or <I>dR_Ewald</I> or <I>c</I> or <I>manual</I> or <I>echo</I>
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<PRE> <I>Kmax</I> 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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<I>Zone</I> 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 <I>Kmax</I>
|
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<I>dR_Ewald</I> 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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<I>c</I> 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<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 saed 0.0251 Al O Kmax 1.70 Zone 0 0 1 dR_Ewald 0.01 c 0.5 0.5 0.5
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compute 2 all saed 0.0251 Ni Kmax 1.70 Zone 0 0 0 c 0.05 0.05 0.05 manual echo
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</pre></div>
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</div>
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<div class="highlight-python"><div class="highlight"><pre>fix saed/vtk 1 1 1 c_1 file Al2O3_001.saed
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fix saed/vtk 1 1 1 c_2 file Ni_000.saed
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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 electron diffraction intensity as
|
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described in <a class="reference internal" href="fix_saed_vtk.html#coleman"><span>(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>
|
||||
<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" />
|
||||
<p>Here, K is the location of the reciprocal lattice node, rj is the
|
||||
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
|
||||
<I>manual</I> = flag to use manual spacing of reciprocal lattice points
|
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based on the values of the <I>c</I> parameters
|
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<I>echo</I> = flag to provide extra output for debugging purposes
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</PRE>
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>compute 1 all saed 0.0251 Al O Kmax 1.70 Zone 0 0 1 dR_Ewald 0.01 c 0.5 0.5 0.5
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compute 2 all saed 0.0251 Ni Kmax 1.70 Zone 0 0 0 c 0.05 0.05 0.05 manual echo
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</PRE>
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<PRE>fix saed/vtk 1 1 1 c_1 file Al2O3_001.saed
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fix saed/vtk 1 1 1 c_2 file Ni_000.saed
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</PRE>
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<P><B>Description:</B>
|
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</P>
|
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<P>Define a computation that calculates electron diffraction intensity as
|
||||
described in <A HREF = "#Coleman">(Coleman)</A> on a mesh of reciprocal lattice nodes
|
||||
defined by the entire simulation domain (or manually) using simulated
|
||||
radiation of wavelength lambda.
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</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:
|
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</P>
|
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<CENTER><IMG SRC = "Eqs/compute_saed1.jpg">
|
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</CENTER>
|
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<CENTER><IMG SRC = "Eqs/compute_saed2.jpg">
|
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</CENTER>
|
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<P>Here, K is the location of the reciprocal lattice node, rj is the
|
||||
position of each atom, fj are atomic scattering factors.
|
||||
</P>
|
||||
<P>Diffraction intensities are calculated on a three-dimensional mesh of
|
||||
reciprocal lattice nodes. The mesh spacing is defined either (a) by
|
||||
the entire simulation domain or (b) manually using selected values as
|
||||
shown in the 2D diagram below.</p>
|
||||
<a data-lightbox="group-default"
|
||||
href="_images/saed_mesh.jpg"
|
||||
class=""
|
||||
title=""
|
||||
data-title=""
|
||||
><img src="_images/saed_mesh.jpg"
|
||||
class="align-center"
|
||||
width="25%"
|
||||
height="auto"
|
||||
alt=""/>
|
||||
</a><p>For a mesh defined by the simulation domain, a rectilinear grid is
|
||||
constructed with spacing <a href="#id1"><span class="problematic" id="id2">*</span></a>c**inv(A) along each reciprocal lattice
|
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shown in the 2D diagram below.
|
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</P>
|
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<CENTER><A HREF = "JPG/saed_mesh.jpg"><IMG SRC = "JPG/saed_mesh_small.jpg"></A>
|
||||
</CENTER>
|
||||
<P>For a mesh defined by the simulation domain, a rectilinear grid is
|
||||
constructed with spacing <I>c</I>*inv(A) along each reciprocal lattice
|
||||
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
|
||||
conditions, then the spacing in these directions is defined from the
|
||||
average of the (inversed) box lengths with periodic boundary conditions.
|
||||
Meshes defined by the simulation domain must contain at least one periodic
|
||||
boundary.</p>
|
||||
<p>If the <em>manual</em> flag is included, the mesh of reciprocal lattice nodes
|
||||
will defined using the <em>c</em> values for the spacing along each reciprocal
|
||||
lattice axis. Note that manual mapping of the reciprocal space mesh is
|
||||
good for comparing diffraction results from multiple simulations; however
|
||||
it can reduce the likelihood that Bragg reflections will be satisfied
|
||||
unless small spacing parameters <0.05 Angstrom^(-1) are implemented.
|
||||
Meshes with manual spacing do not require a periodic boundary.</p>
|
||||
<p>The limits of the reciprocal lattice mesh are determined by the use of
|
||||
the <em>Kmax</em>, <em>Zone</em>, and <em>dR_Ewald</em> parameters. The rectilinear mesh
|
||||
created about the origin of reciprocal space is terminated at the
|
||||
boundary of a sphere of radius <em>Kmax</em> centered at the origin. If
|
||||
<em>Zone</em> parameters z1=z2=z3=0 are used, diffraction intensities are
|
||||
computed throughout the entire spherical volume - note this can greatly
|
||||
increase the cost of computation. Otherwise, <em>Zone</em> parameters will
|
||||
denote the z1=h, z2=k, and z3=l (in a global since) zone axis of an
|
||||
intersecting Ewald sphere. Diffraction intensities will only be
|
||||
computed at the intersection of the reciprocal lattice mesh and a
|
||||
<em>dR_Ewald</em> thick surface of the Ewald sphere. See the example 3D
|
||||
intestiety data and the intersection of a [010] zone axis in the below image.</p>
|
||||
<a data-lightbox="group-default"
|
||||
href="_images/saed_ewald_intersect.jpg"
|
||||
class=""
|
||||
title=""
|
||||
data-title=""
|
||||
><img src="_images/saed_ewald_intersect.jpg"
|
||||
class="align-center"
|
||||
width="25%"
|
||||
height="auto"
|
||||
alt=""/>
|
||||
</a><p>The atomic scattering factors, fj, accounts for the reduction in
|
||||
diffraction intensity due to Compton scattering. Compute saed uses
|
||||
analytical approximations of the atomic scattering factors that vary
|
||||
for each atom type (type1 type2 ... typeN) and angle of diffraction.
|
||||
boundary.
|
||||
</P>
|
||||
<P>If the <I>manual</I> flag is included, the mesh of reciprocal lattice nodes
|
||||
will defined using the <I>c</I> values for the spacing along each reciprocal
|
||||
lattice axis. Note that manual mapping of the reciprocal space mesh is
|
||||
good for comparing diffraction results from multiple simulations; however
|
||||
it can reduce the likelihood that Bragg reflections will be satisfied
|
||||
unless small spacing parameters <0.05 Angstrom^(-1) are implemented.
|
||||
Meshes with manual spacing do not require a periodic boundary.
|
||||
</P>
|
||||
<P>The limits of the reciprocal lattice mesh are determined by the use of
|
||||
the <I>Kmax</I>, <I>Zone</I>, and <I>dR_Ewald</I> parameters. The rectilinear mesh
|
||||
created about the origin of reciprocal space is terminated at the
|
||||
boundary of a sphere of radius <I>Kmax</I> centered at the origin. If
|
||||
<I>Zone</I> parameters z1=z2=z3=0 are used, diffraction intensities are
|
||||
computed throughout the entire spherical volume - note this can greatly
|
||||
increase the cost of computation. Otherwise, <I>Zone</I> parameters will
|
||||
denote the z1=h, z2=k, and z3=l (in a global since) zone axis of an
|
||||
intersecting Ewald sphere. Diffraction intensities will only be
|
||||
computed at the intersection of the reciprocal lattice mesh and a
|
||||
<I>dR_Ewald</I> thick surface of the Ewald sphere. See the example 3D
|
||||
intestiety data and the intersection of a [010] zone axis in the below image.
|
||||
</P>
|
||||
<CENTER><A HREF = "JPG/saed_ewald_intersect.jpg"><IMG SRC = "JPG/saed_ewald_intersect_small.jpg"></A>
|
||||
</CENTER>
|
||||
<P>The atomic scattering factors, fj, accounts for the reduction in
|
||||
diffraction intensity due to Compton scattering. Compute saed uses
|
||||
analytical approximations of the atomic scattering factors that vary
|
||||
for each atom type (type1 type2 ... typeN) and angle of diffraction.
|
||||
The analytic approximation is computed using the formula
|
||||
<a class="reference internal" href="#brown"><span>(Brown)</span></a>:</p>
|
||||
<img alt="_images/compute_saed3.jpg" class="align-center" src="_images/compute_saed3.jpg" />
|
||||
<p>Coefficients parameterized by <a class="reference internal" href="#fox"><span>(Fox)</span></a> are assigned for each
|
||||
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>
|
||||
<dd><blockquote class="first">
|
||||
<div>C: N: O: F: Ne:</div></blockquote>
|
||||
<dl class="docutils">
|
||||
<dt>Na: Mg: Al: Si: P:</dt>
|
||||
<dd>S: Cl: Ar: K: Ca:</dd>
|
||||
</dl>
|
||||
<p class="last">Sc: Ti: V: Cr: Mn:
|
||||
Fe: Co: Ni: Cu: Zn:
|
||||
Ga: Ge: As: Se: Br:
|
||||
Kr: Rb: Sr: Y: Zr:
|
||||
Nb: Mo: Tc: Ru: Rh:
|
||||
Pd: Ag: Cd: In: Sn:
|
||||
Sb: Te: I: Xe: Cs:
|
||||
Ba: La: Ce: Pr: Nd:
|
||||
Pm: Sm: Eu: Gd: Tb:
|
||||
Dy: Ho: Er: Tm: Yb:
|
||||
Lu: Hf: Ta: W: Re:
|
||||
Os: Ir: Pt: Au: Hg:
|
||||
Tl: Pb: Bi: Po: At:
|
||||
Rn: Fr: Ra: Ac: Th:
|
||||
Pa: U: Np: Pu: Am:
|
||||
Cm: Bk: Cf:tb(c=5,s=:)</p>
|
||||
</dd>
|
||||
</dl>
|
||||
<p>If the <em>echo</em> keyword is specified, compute saed will provide extra
|
||||
reporting information to the screen.</p>
|
||||
<p><strong>Output info:</strong></p>
|
||||
<p>This compute calculates a global vector. The length of the vector is
|
||||
the number of reciprocal lattice nodes that are explored by the mesh.
|
||||
The entries of the global vector are the computed diffraction
|
||||
intensities as described above.</p>
|
||||
<p>The vector 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>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<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
|
||||
<p>The compute_saed command does not work for triclinic cells.</p>
|
||||
</div>
|
||||
<div class="section" id="related-commands">
|
||||
<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
|
||||
<p><a class="reference internal" href="fix_saed_vtk.html"><em>fix saed_vtk</em></a>, <a class="reference internal" href="compute_xrd.html"><em>compute xrd</em></a></p>
|
||||
</div>
|
||||
<div class="section" id="default">
|
||||
<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
|
||||
<p>The option defaults are Kmax = 1.70, Zone 1 0 0, c 1 1 1, dR_Ewald =
|
||||
0.01.</p>
|
||||
<hr class="docutils" />
|
||||
<p id="coleman"><strong>(Coleman)</strong> Coleman, Spearot, Capolungo, MSMSE, 21, 055020
|
||||
(2013).</p>
|
||||
<p id="brown"><strong>(Brown)</strong> Brown et al. International Tables for Crystallography
|
||||
Volume C: Mathematical and Chemical Tables, 554-95 (2004).</p>
|
||||
<p id="fox"><strong>(Fox)</strong> Fox, O’Keefe, Tabbernor, Acta Crystallogr. A, 45, 786-93
|
||||
(1989).</p>
|
||||
</div>
|
||||
</div>
|
||||
<A HREF = "#Brown">(Brown)</A>:
|
||||
</P>
|
||||
<CENTER><IMG SRC = "Eqs/compute_saed3.jpg">
|
||||
</CENTER>
|
||||
<P>Coefficients parameterized by <A HREF = "#Fox">(Fox)</A> are assigned for each
|
||||
atom type designating the chemical symbol and charge of each atom
|
||||
type. Valid chemical symbols for compute saed are:
|
||||
</P>
|
||||
<P> H: He: Li: Be: B:
|
||||
C: N: O: F: Ne:
|
||||
Na: Mg: Al: Si: P:
|
||||
S: Cl: Ar: K: Ca:
|
||||
Sc: Ti: V: Cr: Mn:
|
||||
Fe: Co: Ni: Cu: Zn:
|
||||
Ga: Ge: As: Se: Br:
|
||||
Kr: Rb: Sr: Y: Zr:
|
||||
Nb: Mo: Tc: Ru: Rh:
|
||||
Pd: Ag: Cd: In: Sn:
|
||||
Sb: Te: I: Xe: Cs:
|
||||
Ba: La: Ce: Pr: Nd:
|
||||
Pm: Sm: Eu: Gd: Tb:
|
||||
Dy: Ho: Er: Tm: Yb:
|
||||
Lu: Hf: Ta: W: Re:
|
||||
Os: Ir: Pt: Au: Hg:
|
||||
Tl: Pb: Bi: Po: At:
|
||||
Rn: Fr: Ra: Ac: Th:
|
||||
Pa: U: Np: Pu: Am:
|
||||
Cm: Bk: Cf:tb(c=5,s=:)
|
||||
</P>
|
||||
<P>If the <I>echo</I> keyword is specified, compute saed will provide extra
|
||||
reporting information to the screen.
|
||||
</P>
|
||||
<P><B>Output info:</B>
|
||||
</P>
|
||||
<P>This compute calculates a global vector. The length of the vector is
|
||||
the number of reciprocal lattice nodes that are explored by the mesh.
|
||||
The entries of the global vector are the computed diffraction
|
||||
intensities as described above.
|
||||
</P>
|
||||
<P>The vector can be accessed by any command that uses global values
|
||||
from a compute as input. See <A HREF = "Section_howto.html#howto_15">this
|
||||
section</A> for an overview of LAMMPS output
|
||||
options.
|
||||
</P>
|
||||
<P>All array values calculated by this compute are "intensive".
|
||||
</P>
|
||||
<P><B>Restrictions:</B>
|
||||
</P>
|
||||
<P>The compute_saed command does not work for triclinic cells.
|
||||
</P>
|
||||
<P><B>Related commands:</B>
|
||||
</P>
|
||||
<P><A HREF = "fix_saed_vtk.html">fix saed_vtk</A>, <A HREF = "compute_xrd.html">compute xrd</A>
|
||||
</P>
|
||||
<P><B>Default:</B>
|
||||
</P>
|
||||
<P>The option defaults are Kmax = 1.70, Zone 1 0 0, c 1 1 1, dR_Ewald =
|
||||
0.01.
|
||||
</P>
|
||||
<HR>
|
||||
|
||||
<A NAME = "Coleman"></A>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
<footer>
|
||||
|
||||
<P><B>(Coleman)</B> Coleman, Spearot, Capolungo, MSMSE, 21, 055020
|
||||
(2013).
|
||||
</P>
|
||||
<A NAME = "Brown"></A>
|
||||
|
||||
<hr/>
|
||||
<P><B>(Brown)</B> Brown et al. International Tables for Crystallography
|
||||
Volume C: Mathematical and Chemical Tables, 554-95 (2004).
|
||||
</P>
|
||||
<A NAME = "Fox"></A>
|
||||
|
||||
<div role="contentinfo">
|
||||
<p>
|
||||
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|
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|
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||||
<P><B>(Fox)</B> Fox, O'Keefe, Tabbernor, Acta Crystallogr. A, 45, 786-93
|
||||
(1989).
|
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Block a user