PredictPeaks v1¶

Summary¶

Using a known crystal lattice and UB matrix, predict where single crystal peaks should be found in detector/TOF space. Creates a PeaksWorkspace containing the peaks at the expected positions.

Properties¶

Description¶

This algorithm will predict the position of single-crystal diffraction peaks (both in detector position/TOF and Q-space) and create an output PeaksWorkspace containing the result when OutputType is set to Peak, otherwise a LeanElasticPeaksWorkspace will be created that only has the Q-space positions.

This algorithm uses the InputWorkspace to determine the instrument in use, as well as the UB matrix and Unit Cell of the sample used. You can use the CopySample v1 algorithm (with CopyLattice=1) to copy a UB matrix from a PeaksWorkspace to another workspace.

The algorithm operates by calculating the scattering direction (given the UB matrix) for a particular HKL, and determining whether that hits a detector. The Max/MinDSpacing parameters are used to determine what HKL’s to try.

The parameters of WavelengthMin/WavelengthMax also limit the peaks attempted to those that can be detected/produced by your instrument.

Furthermore it’s possible to calculate structure factors for the predicted peaks by activating the CalculateStructureFactors-option. For this to work the sample needs to have a crystal structure stored, which can currently be achieved as in the following example:

from mantid.geometry import CrystalStructure
import numpy as np

# Generate a workspace with an instrument definition
ws = CreateSimulationWorkspace(Instrument='WISH',
                               BinParams='0,10000,20000',
                               UnitX='TOF')

# Set a random UB, in this case for an orthorhombic structure
SetUB(ws, a=5.5, b=6.5, c=8.1, u='12,1,1', v='0,4,9')

# Set an arbitrary crystal structure with 2 atoms and some
# systematic absences due to space group Pbca
cs = CrystalStructure('5.5 6.5 8.1', 'P b c a',
                      """Ni 0.232 0.114 0.543 1.0 0.00843;
                         Al 0.434 0.041 0.854 1.0 0.01120""")
ws.sample().setCrystalStructure(cs)

predicted = PredictPeaks(InputWorkspace=ws,
                         CalculateStructureFactors=True,
                         MinDSpacing=0.5,
                         WavelengthMin=0.9, WavelengthMax=6.0)

print('There are {} detectable peaks.'.format(predicted.getNumberPeaks()))

intensities = np.array(predicted.column('Intens'))
maxIntensity = np.max(intensities)
relativeIntensities = intensities / maxIntensity

print('Maximum intensity: {0:.2f}'.format(maxIntensity))
print('Peaks with relative intensity < 1%: {}'.format(len([x for x in relativeIntensities if x < 0.01])))

absences = [i for i, x in enumerate(intensities) if x < 1e-9]
print('Number of absences: {}'.format(len(absences)))
print('Absent HKLs: {}'.format([predicted.getPeak(i).getHKL() for i in absences]))

The script provides some information about the predicted peaks and their structure factors. Additionally it prints out the HKL of peaks with predicted structure factor very close to 0, which are absent:

There are 295 detectable peaks.
Maximum intensity: 6101.93
Peaks with relative intensity < 1%: 94
Number of absences: 16
Absent HKLs: [[2,0,-1], [6,0,-3], [10,0,-5], [3,0,-1], [4,0,-1], [5,0,-1], [6,0,-1], [7,0,-3], [7,0,-1], [8,0,-3], [8,0,-1], [9,-1,0], [9,0,-3], [9,0,-1], [10,0,-3], [10,0,-1]]

All absent HKLs have the form H0L with odd L. This fits with the reflection conditions given for \(Pbca\) in the International Tables for Crystallography A.

Please note that the calculated structure factors are currently not corrected for any instrument effects, so depending on instrument geometry and other factors (detector efficiency etc.) measured intensities will deviate from these values. They can however provide an estimate for which reflections might be especially strong or weak.

Source¶

C++ header: PredictPeaks.h (last modified: 2021-04-05)

C++ source: PredictPeaks.cpp (last modified: 2021-04-07)