\(\renewcommand\AA{\unicode{x212B}}\)

PDConvertRealSpace v1

Summary

Transforms a Workspace2D between different real space functions.

See Also

PDConvertReciprocalSpace

Properties

Name

Direction

Type

Default

Description

InputWorkspace

Input

MatrixWorkspace

Mandatory

Input workspace. The units are assumed to be distance

From

Input

string

G(r)

Function type in the input workspace. Allowed values: [‘G(r)’, ‘GK(r)’, ‘g(r)’]

To

Input

string

G(r)

Function type in the output workspace. Allowed values: [‘G(r)’, ‘GK(r)’, ‘g(r)’]

OutputWorkspace

Output

Workspace

Mandatory

Output workspace

Description

The neutron diffraction is measuring the differential scattering cross section. This can be converted to the structure factor \(S(Q)\). Using the PDFFourierTransform algorithm, one can obtain the pair distribution function, \(G(r)\):

(1)\[G(r)=\frac{2}{\pi}\int_0^\infty Q[S(Q)-1]\sin(Qr) dQ\]

One can transform between this quantity and \(GK(r)\) or \(g(r)\) using:

(2)\[GK(r)=\frac{\langle b_{coh} \rangle^2}{4\pi r\rho_0}G(r)\]
(3)\[g(r)=\frac{G(r)}{4\pi r\rho_0}+1\]

where \(\rho_0\) is the sample number density and \(\langle b_{coh} \rangle^2\) is defined in the Materials concept page.

NOTE: This algorithm requires that SetSampleMaterial v1 is called prior in order to determine the \(\rho_0\) 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
# Grab the real data for argon
url = "https://raw.githubusercontent.com/marshallmcdonnell/pystog/master/tests/test_data/argon.real_space.dat"
filename = wget.download(url)
r, gofr, GofR_, GKofR_ = np.loadtxt(filename, skiprows=2, unpack=True)

# Convert gofr to Mantid wksp
g_of_r = CreateWorkspace(DataX=r, DataY=gofr,
                         UnitX="Angstrom",
                         Distribution=True)
SetSampleMaterial(InputWorkspace=g_of_r, ChemicalFormula='Ar')
bigG_of_r=PDConvertRealSpace(InputWorkspace=g_of_r, From='g(r)', To='G(r)')
GK_of_r=PDConvertRealSpace(InputWorkspace=g_of_r, From='g(r)', To='GK(r)')

fig, ax = plt.subplots(subplot_kw={'projection':'mantid'})
ax.plot(g_of_r,'k-', label='$g(r)$')
ax.plot(bigG_of_r,'r-', label='$G(r)$')
ax.plot(GK_of_r,'b-', label='$G_K(r)$')
ax.legend() # show the legend
ax.set_xlabel(r'$r(\AA)$')
fig.show()

The output should look like:

../_images/PDConvertRealSpace.png

Categories: AlgorithmIndex | Diffraction\Utility

Source

Python: PDConvertRealSpace.py