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PDConvertReciprocalSpace v1

Summary

Transforms a Workspace2D between different reciprocal space functions.

See Also

PDConvertRealSpace

Properties

Name

Direction

Type

Default

Description

InputWorkspace

Input

MatrixWorkspace

Mandatory

Input workspace with units of momentum transfer

From

Input

string

S(Q)

Function type in the input workspace. Allowed values: [‘S(Q)’, ‘F(Q)’, ‘FK(Q)’, ‘DCS(Q)’]

To

Input

string

S(Q)

Function type in the output workspace. Allowed values: [‘S(Q)’, ‘F(Q)’, ‘FK(Q)’, ‘DCS(Q)’]

OutputWorkspace

Output

Workspace

Mandatory

Output workspace

Description

The neutron diffraction is measuring the differential scattering cross section (DCS(Q) in the algorithm)

(1)\[\frac{d\sigma}{d\Omega} = \frac{N}{\phi d\Omega}\]

Here the \(N\) is the number of scattered neutrons in unit time in a solid angle \(d\Omega\), and \(\phi\) is the incident neutron flux. The algorithm supports the following conversions:

(2)\[S(Q) = \frac{1}{N_{s} \langle b_{coh} \rangle^2}\frac{d\sigma}{d\Omega}(Q) - \frac{\langle b_{tot}^2 \rangle - \langle b_{coh} \rangle^2}{\langle b_{coh} \rangle^2}\]
(3)\[F(Q) = Q [S(Q) - 1]\]
(4)\[F_K(Q) = \langle b_{coh} \rangle^2 [S(Q) - 1] = \frac{\langle b_{coh} \rangle^2}{Q} F(Q)\]

where \(N_s\) is the number of scatters in the sample and both \(\langle b_{tot}^2 \rangle\) and \(\langle b_{coh} \rangle^2\) are defined in the Materials concept page.

NOTE: This algorithm requires that SetSampleMaterial v1 is called prior in order to determine the \(\langle b_{tot}^2 \rangle\) and \(\langle b_{coh} \rangle^2\) terms.

PyStoG

This algorithm uses the external project PyStoG and specifically uses the pystog.converter.Converter object. To modify the underlying algorithms, the following functions are used for the conversions.

Usage

import wget
import numpy as np
import matplotlib.pyplot as plt
from mantid.simpleapi import CreateWorkspace, SetSampleMaterial, PDConvertReciprocalSpace
from mantid import plots

# Grab the reciprocal data for argon
url = "https://raw.githubusercontent.com/marshallmcdonnell/pystog/master/tests/test_data/argon.reciprocal_space.dat"
filename = wget.download(url)
q, sq, fq_, fk_, dcs_ = np.loadtxt(filename, skiprows=2, unpack=True)

# Convert S(Q) to Mantid wksp
s_of_q = CreateWorkspace(DataX=q, DataY=sq,
                       UnitX="MomentumTransfer",
                       Distribution=True)
SetSampleMaterial(InputWorkspace=s_of_q, ChemicalFormula='Ar')
f_of_q=PDConvertReciprocalSpace(InputWorkspace=s_of_q, From='S(Q)', To='F(Q)')
fk_of_q=PDConvertReciprocalSpace(InputWorkspace=s_of_q, From='S(Q)', To='FK(Q)')
dcs_of_q=PDConvertReciprocalSpace(InputWorkspace=s_of_q, From='S(Q)', To='DCS(Q)')

fig, ax = plt.subplots(subplot_kw={'projection':'mantid'})
ax.plot(s_of_q,'k-', label='$S(Q)$')
ax.plot(f_of_q,'r-', label='$F(Q)$')
ax.plot(fk_of_q,'b-', label='$F_K(Q)$')
ax.plot(dcs_of_q,'g-', label=r'$d\sigma / d\Omega(Q)$')
ax.legend() # show the legend
fig.show()

The output should look like:

../_images/PDConvertReciprocalSpace.png

Categories: AlgorithmIndex | Diffraction\Utility

Source

Python: PDConvertReciprocalSpace.py