The `Bragg_crystal` Component

Perfect, reflecting crystal with common cubic structures (diamond, fcc, or bcc, and others if symmetry form factor multipliers provided explicitly)

Identification

Site:
Author: Marcus H Mendenhall, NIST
Origin: NIST, Gaithersburg, MD, USA
Date: December 1, 2016

Description

Bragg_crystal.comp supercedes Perfect_Crystal.comp with major edits and corrections.

Reads atomic formfactors from a data input file.

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, with its normam pointing in
the positve Y-direction. The angle between the Bragg planes and the crystal
surface is alpha

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.

Changelog:
- Off-axis rays fixed June 2015 so axial divergence corrections are right
- Inclusion of polarization and temperature dependence (via Debye-Waller factor), June-September 2015
- Errors in complex arithmetic in DarwinReflectivity2 corrected, September 2015, MHM
- Symmetries for form factors corrected 20150924
- Rotation code updated to use exact DarwinReflectivity Theta0, Thetah so answer is right even if alpha != 0. 20151009 MHM
- Results for (1,1,1) etc. with complex form factor made to agree with XOP. December 1st, 2016

Notation follows Tadashi Matsushita and Hiro-O Hashizume, X-RAY MONOCHROMATORS.
Handbook on Synchrotron Radiation,North-Holland Publishing Company, 1:263–274, 1983.

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.

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

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	AA^3	unit cell volume	160.1826
form_factors			"FormFactors.txt"
material		Si, Ge (maybe also GaAs?)	"Si.txt"
alpha	rad	asymmetry angle (alpha=0 for symmetric reflection, ie the Bragg planes are parallel to the crystal surface)	0.0
R0		Reflectivity. Overrides the computed Darwin reflectivity. Probably only useful for debugging.	0
debye_waller_B	AA^2	Debye-Waller temperature factor, M=B(sin(theta)/lambda)^2(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,	1
h		Miller index of reflection	1
k		Miller index of reflection	1
l		Miller index of reflection	1
structure_factor_scale_r			0.0
structure_factor_scale_i			0.0

AT (	,	,		) RELATIVE
ROTATED (	,	,		) RELATIVE

McXtrace - An X-ray ray-trace simulation package

The Bragg_crystal Component

Identification

Description

Input parameters

Links

The `Bragg_crystal` Component