Based on: Perfect_crystal.comp written by Anette Vickery, Andrea Prodi, Erik Knudsen
Perfect, reflecting crystal with common cubic structures (diamond, fcc, or bcc, and others if symmetry form factor multipliers provided explicitly)

Identification

Author: Marcus H Mendenhall, NIST

Origin: NIST, Gaithersburg, MD, USA

Date: December 1, 2016

Version: 2.1

Description

Bragg_crystal.comp supercedes Perfect_Crystal.comp with major edits and corrections.
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 crystal code reflects ray in an ideal geometry, does not include surface imperfections or mosaicity
The crystal planes from which the reflection is made must lie in the X-Z plane on the unbent crystal rotated
by an angle alpha about the x axis with respect to the crystal surface.
The crystal is positioned such that the long axis of the crystal surface coincides with
z-axis. The angle between the Bragg planes and the crystal surface is alpha
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
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:
December 1, 2016: results for (1,1,1) etc. with complex form factor made to agree with XOP
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.

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

maybe also GaAs?

[ ] Si, Ge

"Si.txt"

alpha

rad

asymmetry angle (alpha=0 for symmetric reflection, ie the Bragg planes are parallel to the crystal surface)
alpha is defined so that positive alpha reduces the Bragg angle to the plane i.e. alpha=Thetain grazes the planes.
if alpha!=0, one should restrict to rays which have small kx values, since otherwise the alpha rotation is not
around the diffraction axis.

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,
2 => Mx_crystal_diamond: diamond
3 => Mx_crystal_fcc: fcc
4 => Mx_crystal_fcc: bcc