PDFFourierTransform v1¶

PDFFourierTransform dialog.

Table of Contents

Summary
Properties
Description
References
Output Options
Usage
Source

Summary ¶

Fourier transform from S(Q) to G(r), which is paired distribution function (PDF). G(r) will be stored in another named workspace.

Properties ¶

Name	Direction	Type	Default	Description
InputWorkspace	Input	MatrixWorkspace	Mandatory	S(Q), S(Q)-1, or Q[S(Q)-1]
OutputWorkspace	Output	MatrixWorkspace	Mandatory	Result paired-distribution function
InputSofQType	Input	string	S(Q)	To identify whether input function. Allowed values: [‘S(Q)’, ‘S(Q)-1’, ‘Q[S(Q)-1]’]
Qmin	Input	number	Optional	Minimum Q in S(Q) to calculate in Fourier transform (optional).
Qmax	Input	number	Optional	Maximum Q in S(Q) to calculate in Fourier transform. (optional)
Filter	Input	boolean	False	Set to apply Lorch function filter to the input
PDFType	Input	string	G(r)	Type of output PDF including G(r). Allowed values: [‘G(r)’, ‘g(r)’, ‘RDF(r)’]
DeltaR	Input	number	Optional	Step size of r of G(r) to calculate. Default = $\frac{\pi}{Q_{max}}$ .
Rmax	Input	number	20	Maximum r for G(r) to calculate.
rho0	Input	number	Optional	Average number density used for g(r) and RDF(r) conversions (optional)

The algorithm transforms a single spectrum workspace containing spectral density $S(Q)$ , $S(Q)-1$ , or $Q[S(Q)-1]$ (as a fuction of MomentumTransfer or dSpacing units ) to a PDF (pair distribution function) as described below.

The input Workspace spectrum should be in the Q-space (MomentumTransfer) units . (d-spacing is not supported any more. Contact development team to fix that and enable dSpacing again)

References ¶

B. H. Toby and T. Egami, Accuracy of Pair Distribution Functions Analysis Appliced to Crystalline and Non-Crystalline Materials, Acta Cryst. (1992) A 48, 336-346 doi: 10.1107/S0108767391011327
B.H. Toby and S. Billinge, Determination of Standard uncertainities in fits to pair distribution functions Acta Cryst. (2004) A 60, 315-317] doi: 10.1107/S0108767304011754

Output Options ¶

G(r)¶

$G(r) = 4\pi r[\rho(r)-\rho_0] = \frac{2}{\pi} \int_{0}^{\infty} Q[S(Q)-1]\sin(Qr)dQ$

and in this algorithm, it is implemented as

$G(r) = \frac{2}{\pi} \sum_{Q_{min}}^{Q_{max}} Q[S(Q)-1]\sin(Qr) M(Q,Q_{max}) \Delta Q$

where $M(Q,Q_{max})$ is an optional filter function. If Filter property is set (true) then

$M(Q,Q_{max}) = \frac{\sin(\pi Q/Q_{max})}{\pi Q/Q_{max}}$

otherwise

$M(Q,Q_{max}) = 1\,$

g(r)¶

$G(r) = 4 \pi \rho_0 r [g(r)-1]$

transforms to

$g(r) = \frac{G(r)}{4 \pi \rho_0 r} + 1$

RDF(r)¶

$RDF(r) = 4 \pi \rho_0 r^2 g(r)$

transforms to

$RDF(r) = r G(r) + 4 \pi \rho_0 r^2$

Note: All output forms except $G(r)$ are calculated by transforming $G(r)$ .

Usage ¶

Example - PDF transformation examples:

# Simulates Load of a workspace with all necessary parameters
import numpy as np;
xx = np.array(range(0,100))*0.1
yy = np.exp(-(2.0 * xx)**2)
ws = CreateWorkspace(DataX=xx, DataY=yy, UnitX='MomentumTransfer')
Rt = PDFFourierTransform(ws, InputSofQType='S(Q)', PDFType='g(r)')

# Look at sample results:
print('part of S(Q) and its correlation function')
for i in range(10):
   print('! {0:4.2f} ! {1:5f} ! {2:f} ! {3:5f} !'.format(xx[i], yy[i], Rt.readX(0)[i], Rt.readY(0)[i]))

Output:

part of S(Q) and its correlation function
! 0.00 ! 1.000000 ! 0.317333 ! -3.977330 !
! 0.10 ! 0.960789 ! 0.634665 ! 2.247452 !
! 0.20 ! 0.852144 ! 0.951998 ! 0.449677 !
! 0.30 ! 0.697676 ! 1.269330 ! 1.313403 !
! 0.40 ! 0.527292 ! 1.586663 ! 0.803594 !
! 0.50 ! 0.367879 ! 1.903996 ! 1.140167 !
! 0.60 ! 0.236928 ! 2.221328 ! 0.900836 !
! 0.70 ! 0.140858 ! 2.538661 ! 1.079278 !
! 0.80 ! 0.077305 ! 2.855993 ! 0.940616 !
! 0.90 ! 0.039164 ! 3.173326 ! 1.050882 !

Categories: Algorithms | Diffraction\Utility

Source ¶

C++ source: PDFFourierTransform.cpp (last modified: 2016-10-24)

C++ header: PDFFourierTransform.h (last modified: 2016-10-10)