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12.3 The Bragg_crystal_BC McXtrace Component
Perfect, reflecting crystal with common cubic structures (diamond, fcc, or bcc, and others if symmetry form factor multipliers provided explicitly)
Identification
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Author: Marcus H Mendenhall, NIST <marcus.mendenhall@nist.gov>
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Origin: NIST
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Date: May, 2017
Description
Bragg_crystal_BC.comp is intended to supercede Bragg_Crystal.comp.
For details see: The optics of focusing bent-crystal monochromators on X-ray powder diffractometers with application to lattice parameter determination and microstructure analysis, Marcus H. Mendenhall, David Black and James P. Cline, J. Appl. Cryst. (2019). 52, https://doi.org/10.1107/S1600576719010951
Reads atomic formfactors from a data input file. The Bragg_Crystal code reflects ray in an ideal geometry, does not include surface imperfections or mosaicity
The crystal code reflects ray in an ideal geometry, i.e. does not include surface imperfections or mosaicity. The crystal planes from which the reflection is made lies in the X-Z plane on the unbent crystal rotated by an angle alpha about the Y axis with respect to the crystal surface.
The crystal itself is set in the X-Z plane positioned such that the long axis of the crystal surface coincides with the Z-axis, withs normal pointing in the poisitivce Y-direction.
N.B. The component does not work for rays hitting the back of the monochromator.
Bragg_crystal_BC.comp is written by Marcus H. Mendenhall, NIST, Gaithersburg, MD, USA It is based on the full vector math and exact solution of the dispersion relation in Batterman and Cole, Reviews of Modern Physics 36 number 3, page 681, July 1964
This code has been validated against both experimental data (2 channel-cut 3-bounce Si 440 crystals together in non-dispersive mode, at Cu kalpha) and against theoretical rocking rocking curves from XOP for Si220 at Sc kalpha and Si440 at Cu kalpha.
Non-copyright notice: Contributed by the National Institute of Standards and Technology; not subject to copyright in the United States. This is not an official contribution, in that the results are in no way certified by NIST.
Example: Bragg_crystal_BC( length=0.05, width=0.02, V=160.1826, h=1, k=1, l=1, alphay=1)
Input parameters
Parameters in boldface are required; the others are optional.
|
Name |
Unit |
Description |
Default |
|
|
|||
|
length |
m |
z depth (length) of the crystal. |
0.05 |
|
width |
m |
x width of the crystal. |
0.02 |
|
V |
Å\(^{3}\) |
unit cell volume |
160.1826 |
|
form_factors |
str |
Data file with atomic form factors |
”FormFactors.txt” |
|
material |
|
Si, Ge (maybe also GaAs?) |
”Si.txt” |
|
alphax |
1 |
x-component of the normal (unit vector) to the crystal planes. The crystal surface itself has normal [0,1,0]. |
0.0 |
|
alphay |
1 |
y-component of the normal (unit vector) to the crystal planes. |
1.0 |
|
alphaz |
1 |
z-component of the normal (unit vector) to the crystal planes. |
0.0 |
|
R0 |
|
Reflectivity. Overrides the computed Darwin reflectivity. Probably only useful for debugging. |
0 |
|
debye_waller_B |
Å\(^{2}\) |
Debye-Waller temperature factor, M=B*(sin(theta)/lambda)ˆ2*(2/3), default=silicon at room temp. |
0.4632 |
|
crystal_type |
|
1 => Mx_crystal_explicit: provide explicit real and imaginary form factor multipliers structure_factor_scale_r, structure_factor_scale_i; 2 => Mx_crystal_diamond: diamond; 3 => Mx_crystal_fcc: fcc; 4 => Mx_crystal_fcc: bcc |
1 |
|
h |
|
Miller index of reflection |
1 |
|
k |
|
Miller index of reflection |
1 |
|
l |
|
Miller index of reflection |
1 |
|
structure_factor_scale_r |
1 |
real part of complex explicit override of structure factor multiplier for crystal structure if Bragg_crystal_explicit |
0.0 |
|
structure_factor_scale_i |
1 |
imaginary part of complex explicit override of structure factor multiplier for crystal structure if Bragg_crystal_explicit |
0.0 |
|
verbose |
|
if non-zero: Output more information (warnings and messages) to the console. |
0 |
|
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Links
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Component source code found in file Bragg_crystal_BC.comp.
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material datafile obtained from http://physics.nist.gov/cgi-bin/ffast/ffast.pl
