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

CalculatePlaczekSelfScattering v1

CalculatePlaczekSelfScattering dialog.

Summary

Calculates the Placzek self scattering correction of an incident spectrum

See Also

FitIncidentSpectrum

Properties

Name	Direction	Type	Default	Description
InputWorkspace	Input	MatrixWorkspace	Mandatory	Raw diffraction data workspace for associated correction to be calculated for. Workspace must have instrument and sample data.
IncidentSpectra	Input	MatrixWorkspace	Mandatory	Workspace of fitted incident spectrum with it’s first derivative. Must be in units of Wavelength.
OutputWorkspace	Output	MatrixWorkspace	Mandatory	Workspace with the Self scattering correction, in the same unit as the InputWorkspace.
CrystalDensity	Input	number	Optional	The crystalographic density of the sample material.
ScaleByPackingFraction	Input	boolean	True	Scale the correction value by packing fraction.

Description

This algorithm takes an incident spectrum function and it’s derivative, along with the workspace containing spectrum info and calculates the time-of-flight Placzek scattering correction from the workspaces material sample and detector info. [1] [2] [3] For obtaining the incident spectrum from a measurement (ie beam monitors or calibrant sample), the FitIncidentSpectrum can provide the necessary inputs.

Usage

Example: calculate Placzek self scattering correction using a sample detector setup [4]

from mantid.simpleapi import *
import matplotlib.pyplot as plt
import numpy as np

# Create the workspace to hold the already corrected incident spectrum
incident_wksp_name = 'incident_spectrum_wksp'
binning_incident = "0.1,0.02,5.0"
binning_for_calc = "0.2,0.02,4.0"
binning_for_fit = "0.15,0.02,4.5"
incident_wksp = CreateSampleWorkspace(
    OutputWorkspace=incident_wksp_name,
    NumBanks=10,
    XMin=0.1,
    XMax=5.0,
    BinWidth=0.002,
    Xunit='Wavelength')
incident_wksp = ConvertToPointData(InputWorkspace=incident_wksp)

# Spectrum function given in Milder et al. Eq (5)
def incident_spectrum(wavelengths, phi_max, phi_epi, alpha, lambda_1, lambda_2,
                     lamda_t):
    delta_term = 1. / (1. + np.exp((wavelengths - lambda_1) / lambda_2))
    term_1 = phi_max * (
        lambda_t**4. / wavelengths**5.) * np.exp(-(lambda_t / wavelengths)**2.)
    term_2 = phi_epi * delta_term / (wavelengths**(1 + 2 * alpha))
    return term_1 + term_2

# Variables for polyethlyene moderator at 300K
phi_max = 6324
phi_epi = 786
alpha = 0.099
lambda_1 = 0.67143
lambda_2 = 0.06075
lambda_t = 1.58

# Add the incident spectrum to the workspace
corrected_spectrum = incident_spectrum(
    incident_wksp.readX(0), phi_max, phi_epi, alpha, lambda_1, lambda_2, lambda_t)
incident_wksp.setY(0, corrected_spectrum)

incident_spectrum = FitIncidentSpectrum(
    InputWorkspace='incident_wksp',
    OutputWorkspace='fit_wksp',
    BinningForCalc=binning_for_calc,
    BinningForFit=binning_for_fit)
SetSampleMaterial(
    InputWorkspace='incident_wksp',
    ChemicalFormula='Co')
CalculatePlaczekSelfScattering(
    InputWorkspace='incident_wksp',
    IncidentSpecta='fit_wksp',
    OutputWorkspace='placzek_scattering',
    Version=1)

References

[1]

7. Placzek, (1952), The Scattering of Neutrons by Systems of Heavy Nuclei, Physical Review, Volume 86, Page 377-388 doi: 10.1103/PhysRev.86.377

[2]

J.G. Powles, (1973), The analysis of a time-of-flight neutron diffractometer for amorphous materials: the structure of a molecule in a liquid, Molecular Physics, Volume 26, Issue 6, Page 1325-1350, doi: 10.1080/00268977300102521

[3]

Howe, McGreevy, and Howells, J., (1989), The analysis of liquid structure data from time-of-flight neutron diffractometry,Journal of Physics: Condensed Matter, Volume 1, Issue 22, pp. 3433-3451, doi: 10.1088/0953-8984/1/22/005

[4]

4. 6. 18. Mildner, B. C. Boland, R. N. Sinclair, C. G. Windsor, L. J. Bunce, and J. H. Clarke (1977) A Cooled Polyethylene Moderator on a Pulsed Neutron Source, Nuclear Instruments and Methods 152 437-446 doi: 10.1016/0029-554X(78)90043-5

Categories: AlgorithmIndex | CorrectionFunctions

Source

C++ header: CalculatePlaczekSelfScattering.h

C++ source: CalculatePlaczekSelfScattering.cpp