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<div itemprop="articleBody">
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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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<HR>
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<H3>compute xrd 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 xrd 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>xrd = style name of this compute command
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|
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<LI>lambda = wavelength of incident radiation (length units)
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|
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<LI>type1 type2 ... typeN = chemical symbol of each atom type (see valid options below)
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|
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<LI>zero or more keyword/value pairs may be appended
|
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|
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<LI>keyword = <I>2Theta</I> or <I>c</I> or <I>LP</I> or <I>manual</I> or <I>echo</I>
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|
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<PRE> <I>2Theta</I> 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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<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>LP</em> value = switch to apply Lorentz-polarization factor
|
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<I>LP</I> 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
|
||||
</pre></div>
|
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</div>
|
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<div class="highlight-python"><div class="highlight"><pre>fix 1 all ave/histo/weights 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/weights 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>
|
||||
<p>Define a computation that calculates x-ray diffraction intensity as described
|
||||
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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<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
|
||||
<I>echo</I> = flag to provide extra output for debugging purposes
|
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</PRE>
|
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|
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</UL>
|
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<P><B>Examples:</B>
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</P>
|
||||
<PRE>compute 1 all xrd 1.541838 Al O 2Theta 0.087 0.87 c 1 1 1 LP 1 echo
|
||||
compute 2 all xrd 1.541838 Al O 2Theta 10 100 c 0.05 0.05 0.05 LP 1 manual
|
||||
</PRE>
|
||||
<PRE>fix 1 all ave/histo/weights 1 1 1 0.087 0.87 250 c_1[1] c_1[2] mode vector file Rad2Theta.xrd
|
||||
fix 2 all ave/histo/weights 1 1 1 10 100 250 c_2[1] c_2[2] mode vector file Deg2Theta.xrd
|
||||
</PRE>
|
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<PRE>
|
||||
</PRE>
|
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<P><B>Description:</B>
|
||||
</P>
|
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<P>Define a computation that calculates x-ray 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 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,
|
||||
is computed from the structure factor, F, using the equations:</p>
|
||||
<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)
|
||||
of wavelength lambda.
|
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</P>
|
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<P>The x-ray diffraction intensity, I, at each reciprocal lattice point, k,
|
||||
is computed from the structure factor, F, using the equations:
|
||||
</P>
|
||||
<CENTER><IMG SRC = "Eqs/compute_xrd1.jpg">
|
||||
</CENTER>
|
||||
<CENTER><IMG SRC = "Eqs/compute_xrd2.jpg">
|
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</CENTER>
|
||||
<CENTER><IMG SRC = "Eqs/compute_xrd3.jpg">
|
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</CENTER>
|
||||
<CENTER><IMG SRC = "Eqs/compute_xrd4.jpg">
|
||||
</CENTER>
|
||||
<P>Here, K is the location of the reciprocal lattice node, rj is the
|
||||
position of each atom, fj are atomic scattering factors, LP is the
|
||||
Lorentz-polarization factor, and theta is the scattering angle of
|
||||
diffraction. The Lorentz-polarization factor can be turned off using
|
||||
the optional <I>LP</I> keyword.
|
||||
</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/xrd_mesh.jpg"
|
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class=""
|
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title=""
|
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data-title=""
|
||||
><img src="_images/xrd_mesh.jpg"
|
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class="align-center"
|
||||
width="25%"
|
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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.
|
||||
</P>
|
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<CENTER><A HREF = "JPG/xrd_mesh.jpg"><IMG SRC = "JPG/xrd_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
|
||||
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
|
||||
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
|
||||
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 range of
|
||||
scattering angles explored. The <em>2Theta</em> parameters allows the user
|
||||
require a periodic boundary.
|
||||
</P>
|
||||
<P>The limits of the reciprocal lattice mesh are determined by range of
|
||||
scattering angles explored. The <I>2Theta</I> parameters allows the user
|
||||
to reduce the scattering angle range to only the region of interest
|
||||
which reduces the cost of the computation.</p>
|
||||
<p>The atomic scattering factors, fj, accounts for the reduction in
|
||||
which reduces the cost of the computation.
|
||||
</P>
|
||||
<P>The atomic scattering factors, fj, accounts for the reduction in
|
||||
diffraction intensity due to Compton scattering. Compute xrd 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="#colliex"><span>(Colliex)</span></a>:</p>
|
||||
<img alt="_images/compute_xrd5.jpg" class="align-center" src="_images/compute_xrd5.jpg" />
|
||||
<p>Coefficients parameterized by <a class="reference internal" href="#peng"><span>(Peng)</span></a> are assigned for each
|
||||
atom type designating the chemical symbol and charge of each atom
|
||||
type. Valid chemical symbols for compute xrd are:</p>
|
||||
<dl class="docutils">
|
||||
<dt>H: He1-: He: Li: Li1+:</dt>
|
||||
<dd><blockquote class="first">
|
||||
<div><blockquote>
|
||||
<div><dl class="docutils">
|
||||
<dt>Be: Be2+: B: C: Cval:</dt>
|
||||
<dd>N: O: O1-: F: F1-:</dd>
|
||||
</dl>
|
||||
<p>Ne: Na: Na1+: Mg: Mg2+:
|
||||
Al: Al3+: Si: Sival: Si4+:</p>
|
||||
<blockquote>
|
||||
<div>P: S: Cl: Cl1-: Ar:
|
||||
K: Ca: Ca2+: Sc: Sc3+:</div></blockquote>
|
||||
<p>Ti: Ti2+: Ti3+: Ti4+: V:</p>
|
||||
</div></blockquote>
|
||||
<p>V2+: V3+: V5+: Cr: Cr2+:</p>
|
||||
</div></blockquote>
|
||||
<dl class="docutils">
|
||||
<dt>Cr3+: Mn: Mn2+: Mn3+: Mn4+:</dt>
|
||||
<dd>Fe: Fe2+: Fe3+: Co: Co2+:
|
||||
Co: Ni: Ni2+: Ni3+: Cu:</dd>
|
||||
</dl>
|
||||
<p>Cu1+: Cu2+: Zn: Zn2+: Ga:
|
||||
Ga3+: Ge: Ge4+: As: Se:</p>
|
||||
<blockquote>
|
||||
<div>Br: Br1-: Kr: Rb: Rb1+:
|
||||
Sr: Sr2+: Y: Y3+: Zr:</div></blockquote>
|
||||
<p>Zr4+: Nb: Nb3+: Nb5+: Mo:
|
||||
Mo3+: Mo5+: Mo6+: Tc: Ru:
|
||||
Ru3+: Ru4+: Rh: Rh3+: Rh4+:</p>
|
||||
<blockquote>
|
||||
<div>Pd: Pd2+: Pd4+: Ag: Ag1+:</div></blockquote>
|
||||
<dl class="docutils">
|
||||
<dt>Ag2+: Cd: Cd2+: In: In3+:</dt>
|
||||
<dd>Sn: Sn2+: Sn4+: Sb: Sb3+:</dd>
|
||||
<dt>Sb5+: Te: I: I1-: Xe:</dt>
|
||||
<dd>Cs: Cs1+: Ba: Ba2+: La:</dd>
|
||||
</dl>
|
||||
<p>La3+: Ce: Ce3+: Ce4+: Pr:
|
||||
Pr3+: Pr4+: Nd: Nd3+: Pm:
|
||||
Pm3+: Sm: Sm3+: Eu: Eu2+:
|
||||
Eu3+: Gd: Gd3+: Tb: Tb3+:</p>
|
||||
<blockquote>
|
||||
<div>Dy: Dy3+: Ho: Ho3+: Er:</div></blockquote>
|
||||
<p>Er3+: Tm: Tm3+: Yb: Yb2+:
|
||||
Yb3+: Lu: Lu3+: Hf: Hf4+:</p>
|
||||
<blockquote>
|
||||
<div>Ta: Ta5+: W: W6+: Re:
|
||||
Os: Os4+: Ir: Ir3+: Ir4+:
|
||||
Pt: Pt2+: Pt4+: Au: Au1+:</div></blockquote>
|
||||
<p>Au3+: Hg: Hg1+: Hg2+: Tl:
|
||||
Tl1+: Tl3+: Pb: Pb2+: Pb4+:</p>
|
||||
<blockquote>
|
||||
<div>Bi: Bi3+: Bi5+: Po: At:
|
||||
Rn: Fr: Ra: Ra2+: Ac:</div></blockquote>
|
||||
<dl class="docutils">
|
||||
<dt>Ac3+: Th: Th4+: Pa: U:</dt>
|
||||
<dd>U3+: U4+: U6+: Np: Np3+:</dd>
|
||||
</dl>
|
||||
<p class="last">Np4+: Np6+: Pu: Pu3+: Pu4+:
|
||||
Pu6+: Am: Cm: Bk: Cf:tb(c=5,s=:)</p>
|
||||
</dd>
|
||||
</dl>
|
||||
<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>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_xrd 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_ave_histo.html"><em>fix ave/histo</em></a>,
|
||||
<a class="reference internal" href="compute_saed.html"><em>compute saed</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 2Theta = 1 179 (degrees), c = 1 1 1, LP = 1,
|
||||
no manual flag, no echo flag.</p>
|
||||
<hr class="docutils" />
|
||||
<p id="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>
|
||||
</div>
|
||||
<A HREF = "#Colliex">(Colliex)</A>:
|
||||
</P>
|
||||
<CENTER><IMG SRC = "Eqs/compute_xrd5.jpg">
|
||||
</CENTER>
|
||||
<P>Coefficients parameterized by <A HREF = "#Peng">(Peng)</A> are assigned for each
|
||||
atom type designating the chemical symbol and charge of each atom
|
||||
type. Valid chemical symbols for compute xrd are:
|
||||
</P>
|
||||
<P> H: He1-: He: Li: Li1+:
|
||||
Be: Be2+: B: C: Cval:
|
||||
N: O: O1-: F: F1-:
|
||||
Ne: Na: Na1+: Mg: Mg2+:
|
||||
Al: Al3+: Si: Sival: Si4+:
|
||||
P: S: Cl: Cl1-: Ar:
|
||||
K: Ca: Ca2+: Sc: Sc3+:
|
||||
Ti: Ti2+: Ti3+: Ti4+: V:
|
||||
V2+: V3+: V5+: Cr: Cr2+:
|
||||
Cr3+: Mn: Mn2+: Mn3+: Mn4+:
|
||||
Fe: Fe2+: Fe3+: Co: Co2+:
|
||||
Co: Ni: Ni2+: Ni3+: Cu:
|
||||
Cu1+: Cu2+: Zn: Zn2+: Ga:
|
||||
Ga3+: Ge: Ge4+: As: Se:
|
||||
Br: Br1-: Kr: Rb: Rb1+:
|
||||
Sr: Sr2+: Y: Y3+: Zr:
|
||||
Zr4+: Nb: Nb3+: Nb5+: Mo:
|
||||
Mo3+: Mo5+: Mo6+: Tc: Ru:
|
||||
Ru3+: Ru4+: Rh: Rh3+: Rh4+:
|
||||
Pd: Pd2+: Pd4+: Ag: Ag1+:
|
||||
Ag2+: Cd: Cd2+: In: In3+:
|
||||
Sn: Sn2+: Sn4+: Sb: Sb3+:
|
||||
Sb5+: Te: I: I1-: Xe:
|
||||
Cs: Cs1+: Ba: Ba2+: La:
|
||||
La3+: Ce: Ce3+: Ce4+: Pr:
|
||||
Pr3+: Pr4+: Nd: Nd3+: Pm:
|
||||
Pm3+: Sm: Sm3+: Eu: Eu2+:
|
||||
Eu3+: Gd: Gd3+: Tb: Tb3+:
|
||||
Dy: Dy3+: Ho: Ho3+: Er:
|
||||
Er3+: Tm: Tm3+: Yb: Yb2+:
|
||||
Yb3+: Lu: Lu3+: Hf: Hf4+:
|
||||
Ta: Ta5+: W: W6+: Re:
|
||||
Os: Os4+: Ir: Ir3+: Ir4+:
|
||||
Pt: Pt2+: Pt4+: Au: Au1+:
|
||||
Au3+: Hg: Hg1+: Hg2+: Tl:
|
||||
Tl1+: Tl3+: Pb: Pb2+: Pb4+:
|
||||
Bi: Bi3+: Bi5+: Po: At:
|
||||
Rn: Fr: Ra: Ra2+: Ac:
|
||||
Ac3+: Th: Th4+: Pa: U:
|
||||
U3+: U4+: U6+: Np: Np3+:
|
||||
Np4+: Np6+: Pu: Pu3+: Pu4+:
|
||||
Pu6+: Am: Cm: Bk: Cf:tb(c=5,s=:)
|
||||
</P>
|
||||
<P>If the <I>echo</I> keyword is specified, compute xrd will provide extra
|
||||
reporting information to the screen.
|
||||
</P>
|
||||
<P><B>Output info:</B>
|
||||
</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 <I>2Theta</I> 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 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_xrd command does not work for triclinic cells.
|
||||
</P>
|
||||
<P><B>Related commands:</B>
|
||||
</P>
|
||||
<P><A HREF = "fix_ave_histo.html">fix ave/histo</A>,
|
||||
<A HREF = "compute_saed.html">compute saed</A>
|
||||
</P>
|
||||
<P><B>Default:</B>
|
||||
</P>
|
||||
<P>The option defaults are 2Theta = 1 179 (degrees), c = 1 1 1, LP = 1,
|
||||
no manual flag, no echo flag.
|
||||
</P>
|
||||
<HR>
|
||||
|
||||
<A NAME = "Coleman"></A>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
<footer>
|
||||
|
||||
<P><B>(Coleman)</B> Coleman, Spearot, Capolungo, MSMSE, 21, 055020
|
||||
(2013).
|
||||
</P>
|
||||
<A NAME = "Colliex"></A>
|
||||
|
||||
<hr/>
|
||||
<P><B>(Colliex)</B> Colliex et al. International Tables for Crystallography
|
||||
Volume C: Mathematical and Chemical Tables, 249-429 (2004).
|
||||
</P>
|
||||
<A NAME = "Peng"></A>
|
||||
|
||||
<div role="contentinfo">
|
||||
<p>
|
||||
© Copyright .
|
||||
</p>
|
||||
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|
||||
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|
||||
<P><B>(Peng)</B> Peng, Ren, Dudarev, Whelan, Acta Crystallogr. A, 52, 257-76
|
||||
(1996).
|
||||
</P>
|
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</HTML>
|
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|
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Reference in New Issue
Block a user