PDConvertReciprocalSpace v1#

Summary#

Transforms a Workspace2D between different reciprocal space functions.

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.

\(\frac{d\sigma}{d\Omega}(Q)\) conversions are:
- To \(F(Q)\) see pystog.converter.Converter.DCS_to_F()
- To \(F_K(Q)\) see pystog.converter.Converter.DCS_to_FK()
- To \(S(Q)\) see pystog.converter.Converter.DCS_to_S()
\(S(Q)\) conversions are:
- To \(F(Q)\) see pystog.converter.Converter.S_to_F()
- To \(F_K(Q)\) see pystog.converter.Converter.S_to_FK()
- To \(\frac{d\sigma}{d\Omega}(Q)\) see pystog.converter.Converter.S_to_DCS()
\(F(Q)\) conversions are:
- To \(\frac{d\sigma}{d\Omega}(Q)\) see pystog.converter.Converter.F_to_DCS()
- To \(F_K(Q)\) see pystog.converter.Converter.F_to_FK()
- To \(S(Q)\) see pystog.converter.Converter.F_to_S()
\(F_K(Q)\) conversions are:
- To \(\frac{d\sigma}{d\Omega}(Q)\) see pystog.converter.Converter.FK_to_DCS()
- To \(F(Q)\) see pystog.converter.Converter.FK_to_F()
- To \(S(Q)\) see pystog.converter.Converter.FK_to_S()

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:

Categories: AlgorithmIndex | Diffraction\Utility

Source#

Python: PDConvertReciprocalSpace.py