The `Bragg_crystal_bent` Component

Bent, 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_bent.comp supercedes Perfect_Crystal_bent.comp with major edits
and corrections.

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
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 external geometry of the crystal follows that of Elliptic_mirror.comp. I.e.
the crystal is positioned such that the a-axis of the ellipsoid is on the
z-axis, the b-axis is along the y-axis and the c is along the x-axis. The
reference point of the crystal is the ellipsoid centre, offset by one half-axis
along the y-axis. (See the component manual for Elliptic_mirror for a drawing).

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.

NOTE: elliptical coordinate code and documentation taken from
Mirror_elliptic.comp distributed in McXtrace v1.2 However, the coordinates are
rotated to be consistent with Bragg_crystal_flat.comp and Perfect_Crystal.comp.
Idealized elliptic mirror with surface ellipse and lattice ellipses
independent, to allow construction of Johansson optics, for example.

Example: Bragg_crystal_bent(length=0.05, width=0.02, V=160.1826, h=1, k=1, l=1, alpha=0)

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
x_a	m	1st short half axis (along x). Commonly set to zero, which really implies infinite value, so crystal is an elliptic cylinder.	0
y_b	m	2nd short half axis (along y), which is also the presumed near-normal direction, reflection near the y-z plane.	1.0
z_c	m	long half axis (along z). Commonly a=0. b=c, which creates a circular cylindrical surface.	1.0
lattice_x_a	m	curvature matrix for underlying lattice, for bent/ground/rebent crystals THERE HAS BEEN NO TESTING for the case in which lattice_x_a != x_a.	0
lattice_y_b	m	curvature matrix for underlying lattice, for bent/ground/rebent crystals	1.0
lattice_z_c	m	curvature matrix for underlying lattice, for bent/ground/rebent crystals	1.0
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_bent Component

Identification

Description

Input parameters

Links

The `Bragg_crystal_bent` Component