# compute saed command

## Syntax

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

-   ID, group-ID are documented in [compute](compute) command

-   saed = style name of this compute command

-   lambda = wavelength of incident radiation (length units)

-   type1 type2 \... typeN = chemical symbol of each atom type (see
    valid options below)

-   zero or more keyword/value pairs may be appended

-   keyword = *Kmax* or *Zone* or *dR_Ewald* or *c* or *manual* or
    *echo*

        *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

## Examples

``` LAMMPS
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

fix 1 all saed/vtk 1 1 1 c_1 file Al2O3_001.saed
fix 2 all saed/vtk 1 1 1 c_2 file Ni_000.saed
```

## Description

Define a computation that calculates electron diffraction intensity as
described in [(Coleman)](saed-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:

$$\begin{aligned}
I = & \frac{F^{*}F}{N} \\
F(\mathbf{k}) = & \sum_{j=1}^{N}f_j(\theta)exp(2\pi i \mathbf{k} \cdot \mathbf{r}_j)
\end{aligned}$$

Here, K is the location of the reciprocal lattice node, $r_j$ is the
position of each atom, $f_j$ 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.

![image](img/saed_mesh.jpg){.align-center}

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 ($<0.05~\AA^-1$) 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 $z3=\ell$ (in a global sense) 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
intensity data and the intersection of a \[010\] zone axis in the below
image.

![image](img/saed_ewald_intersect.jpg){.align-center}

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):

$$f_j\left ( \frac{sin(\theta)}{\lambda} \right )=\sum_{i}^{5}
a_i exp\left ( -b_i \frac{sin^{2}(\theta)}{\lambda^{2}} \right )$$

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:

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 the [Howto output](Howto_output) doc page for an
overview of LAMMPS output options.

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

## Restrictions

This compute is part of the DIFFRACTION package. It is only enabled if
LAMMPS was built with that package. See the [Build
package](Build_package) page for more info.

The compute_saed command does not work for triclinic cells.

## Related commands

[fix saed_vtk](fix_saed_vtk), [compute xrd](compute_xrd)

## Default

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

------------------------------------------------------------------------

::: {#saed-Coleman}
**(Coleman)** Coleman, Spearot, Capolungo, MSMSE, 21, 055020 (2013).
:::

::: {#Brown}
**(Brown)** Brown et al. International Tables for Crystallography Volume
C: Mathematical and Chemical Tables, 554-95 (2004).
:::

::: {#Fox}
**(Fox)** Fox, O\'Keefe, Tabbernor, Acta Crystallogr. A, 45, 786-93
(1989).
:::