"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)

:line

compute saed command :h3

[Syntax:]

compute ID group-ID saed lambda type1 type2 ... typeN keyword value ... :pre

ID, group-ID are documented in "compute"_compute.html command :ulb,l
saed = style name of this compute command :l
lambda = wavelength of incident radiation (length units) :l
type1 type2 ... typeN = chemical symbol of each atom type (see valid options below) :l

zero or more keyword/value pairs may be appended :l
keyword = {Kmax} or {Zone} or {dR_Ewald} or {c} or {manual} or {echo} :l
  {Kmax} value = Maximum distance explored from reciprocal space origin 
                 (inverse length units)
  {Zone} values = z1 z2 z3
    z1,z2,z3 = Zone axis of incident radiation. If z1=z2=z3=0 all 
               reciprocal space will be meshed up to {Kmax}
  {dR_Ewald} value = Thickness of Ewald sphere slice intercepting 
                     reciprocal space (inverse length units)
  {c} values = c1 c2 c3
    c1,c2,c3 = parameters to adjust the spacing of the reciprocal 
               lattice nodes in the h, k, and l directions respectively
  {manual} = flag to use manual spacing of reciprocal lattice points   
             based on the values of the {c} parameters 
  {echo} = flag to provide extra output for debugging purposes :pre
:ule

[Examples:]

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
compute 2 all saed 0.0251 Ni Kmax 1.70 Zone 0 0 0 c 0.05 0.05 0.05 manual echo :pre

fix saed/vtk 1 1 1 c_1 file Al2O3_001.saed
fix saed/vtk 1 1 1 c_2 file Ni_000.saed :pre

[Description:]

Define a computation that calculates electron diffraction intensity as 
described in "(Coleman)"_#Coleman on a mesh of reciprocal lattice nodes 
defined by the entire simulation domain (or manually) using simulated 
radiation of wavelength lambda. 

The electron diffraction intensity I at each reciprocal lattice point 
is computed from the structure factor F using the equations:

:c,image(Eqs/compute_saed1.jpg) 
:c,image(Eqs/compute_saed2.jpg)

Here, K is the location of the reciprocal lattice node, rj is the 
position of each atom, fj are atomic scattering factors.

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.

:c,image(JPG/saed_mesh_small.jpg,JPG/saed_mesh.jpg)

For a mesh defined by the simulation domain, a rectilinear grid is
constructed with spacing {c}*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.

If the {manual} flag is included, the mesh of reciprocal lattice nodes 
will defined using the {c} 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.

The limits of the reciprocal lattice mesh are determined by the use of 
the {Kmax}, {Zone}, and {dR_Ewald} parameters.  The rectilinear mesh 
created about the origin of reciprocal space is terminated at the 
boundary of a sphere of radius {Kmax} centered at the origin.  If 
{Zone} 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, {Zone} 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 
{dR_Ewald} thick surface of the Ewald sphere.  See the example 3D 
intestiety data and the intersection of a \[010\] zone axis in the below image. 

:c,image(JPG/saed_ewald_intersect_small.jpg,JPG/saed_ewald_intersect.jpg)

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
"(Brown)"_#Brown:

:c,image(Eqs/compute_saed3.jpg)

Coefficients parameterized by "(Fox)"_#Fox are assigned for each 
atom type designating the chemical symbol and charge of each atom 
type. Valid chemical symbols for compute saed are:

         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=:)


If the {echo} keyword is specified, compute saed will provide extra 
reporting information to the screen.  

[Output info:]

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.

The vector can be accessed by any command that uses global values
from a compute as input.  See "this
section"_Section_howto.html#howto_15 for an overview of LAMMPS output
options.

All array values calculated by this compute are "intensive".  

[Restrictions:] 

The compute_saed command does not work for triclinic cells. 

[Related commands:] 

"fix saed_vtk"_fix_saed_vtk.html, "compute xrd"_compute_xrd.html

[Default:] 

The option defaults are Kmax = 1.70, Zone 1 0 0, c 1 1 1, dR_Ewald =
0.01.

:line

:link(Coleman)
[(Coleman)] Coleman, Spearot, Capolungo, MSMSE, 21, 055020
(2013).

:link(Brown)
[(Brown)] Brown et al. International Tables for Crystallography 
Volume C: Mathematical and Chemical Tables, 554-95 (2004).

:link(Fox)
[(Fox)] Fox, O'Keefe, Tabbernor, Acta Crystallogr. A, 45, 786-93
(1989).
