# This file is part of xrayutilities.
#
# xrayutilities is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, see <http://www.gnu.org/licenses/>.
#
# Copyright (C) 2019-2020 Dominik Kriegner <dominik.kriegner@gmail.com>
import math
import numpy
[docs]
def mosaic_analytic(qx, qz, RL, RV, Delta, hx, hz, shape):
"""
simulation of the coplanar reciprocal space map of a single mosaic layer
using a simple analytic approximation
Parameters
----------
qx : array-like
vector of the qx values (offset from the Bragg peak)
qz : array-like
vector of the qz values (offset from the Bragg peak)
RL : float
lateral block radius in angstrom
RV : float
vertical block radius in angstrom
Delta : float
root mean square misorientation of the grains in degree
hx : float
lateral component of the diffraction vector
hz : float
vertical component of the diffraction vector
shape : float
shape factor (1..Gaussian)
Returns
-------
array-like
2D array with calculated intensities
"""
QX, QZ = numpy.meshgrid(qx, qz)
QX = QX.T
QZ = QZ.T
DD = numpy.radians(Delta)
tmp = 6 + DD**2 * ((hz * RL) ** 2 + (hx * RV) ** 2)
F = (
(
(DD * RL * RV) ** 2 * (QZ * hz + QX * hx) ** 2
+ 6 * ((RL * QX) ** 2 + (RV * QZ) ** 2)
)
/ 4
/ tmp
)
return (
math.pi
* math.sqrt(6)
* RL
* RV
/ math.sqrt(tmp)
* numpy.exp(-(F**shape))
)