A sample for magnon or phonon scattering based on numerical cross sections
Author: Daniel Lomholt Christensen and Kim Lefmann
Origin: NBI
Date: 22.06.23
Single-cylinder shape. Absorption included. No multiple scattering. No incoherent scattering emitted. No attenuation from coherent scattering. No Bragg scattering. Any crystal system: the unit cell is given either by its lengths and angles (a, b, c, aa, bb, cc) or by its real-space lattice vectors (ax ... cz).
Algorithm: 0. Always perform the scattering if possible (otherwise ABSORB) 1. Choose a dispersion mode, a scattering point and a direction within a focusing solid angle 2. Calculate the zeros of (E_i-E_f-hbar omega(kappa)) as a function of k_f 3. Choose one value of k_f (always at least one is possible!) 4. Perform the correct weight transformation
Dispersion files: folder_path holds one file per dispersion mode. Each file has the columns
h k l E I
on a regular grid covering one unit cell in reciprocal lattice units: h, k, l are the coordinates of q along the reciprocal lattice vectors a*, b*, c*, h = a.q/(2 pi) and so on. For a cell with 90 degree angles and no vectors given, a*, b*, c* lie along the sample x, y, z axes, as a, b, c do in SpinWave_BCO and Phonon_simple. E [meV] is the mode energy and I [barn/sr per unit cell of the given lattice] is the partial differential scattering cross section of the mode, as the factor in front of the delta function: d2sigma/dOmega dE_f = (k_f/k_i) * DW * I(q) * n_B * delta(hbar omega - E(q)). The component adds k_f/k_i, the Debye-Waller factor DW and the Bose factor n_B = n(omega) + 1 for neutron energy loss and n(omega) for energy gain, so I should not include them. I is looked up at the scattering vector folded into the unit cell.
Weight: p *= exp(-mu l) * dOmega * l_full * m * n_modes * rho_cell
* (k_f/k_i) * DW * I(q) * n_B * |dE_f/d(E(q) - |E_i - E_f|)|
with l the path length in the sample, dOmega the focusing solid angle, l_full the path length without scattering, m the number of final velocities found, n_modes the number of dispersion files and rho_cell the density of unit cells.
Parameters in boldface are required; the others are optional.
|
Name |
Unit |
Description |
Default |
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radius |
m |
Outer radius of sample in (x,z) plane. |
|
|
yheight |
m |
Height of sample in y direction. |
|
|
sigma_abs |
barns |
Absorption cross section at 2200 m/s per unit cell. |
|
|
sigma_inc |
barns |
Incoherent scattering cross section per unit cell. |
|
|
a |
Å |
Lattice constant, length of the a vector. |
0 |
|
b |
Å |
Lattice constant, length of the b vector. |
0 |
|
c |
Å |
Lattice constant, length of the c vector. |
0 |
|
DW |
1 |
Debye-Waller factor. |
|
|
T |
K |
Temperature. |
|
|
aa |
deg |
Angle alpha between b and c. |
90 |
|
bb |
deg |
Angle beta between a and c. |
90 |
|
cc |
deg |
Angle gamma between a and b with lengths and angles, a lies along x, b in the x-y plane and c completes a right handed set. With 90 degree angles, a, b, c lie along x, y, z. |
90 |
|
ax |
Å |
x component of the real-space lattice vector a. If any of ax ... cz is non-zero, the vectors are used as given in the component frame and a, b, c, aa, bb, cc are ignored. |
0 |
|
ay |
Å |
y component of a. |
0 |
|
az |
Å |
z component of a. |
0 |
|
bx |
Å |
x component of b. |
0 |
|
by |
Å |
y component of b. |
0 |
|
bz |
Å |
z component of b. |
0 |
|
cx |
Å |
x component of c. |
0 |
|
cy |
Å |
y component of c. |
0 |
|
cz |
Å |
z component of c. |
0 |
|
folder_path |
|
Folder with one dispersion file per mode, see above. |
|
|
target_x |
m |
position of target to focus at . Transverse coordinate. |
0 |
|
target_y |
m |
position of target to focus at. Vertical coordinate. |
0 |
|
target_z |
m |
position of target to focus at. Straight ahead. |
0 |
|
target_index |
1 |
relative index of component to focus at, e.g. next is +1. |
0 |
|
focus_r |
m |
Radius of sphere containing target. |
0 |
|
focus_xw |
m |
horiz. dimension of a rectangular area. |
0 |
|
focus_yh |
m |
vert. dimension of a rectangular area. |
0 |
|
focus_aw |
deg |
horiz. angular dimension of a rectangular area. |
0 |
|
focus_ah |
deg |
vert. angular dimension of a rectangular area. |
0 |
|
e_steps_low |
1 |
Number of intervals the final velocity is searched in for roots on the energy loss side of the elastic line. |
100 |
|
e_steps_high |
1 |
Number of intervals on the energy gain side. Each interval holds at most one root, so two roots closer than an interval are missed: increase these for steep or crossing modes. |
100 |
|
verbose |
1 |
Prints information about the component if set to 1. |
0 |
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Component source code found in file Dispersion_relation.comp.
The test instrument Test_Dispersion_relation_TAS.instr.