PredictPeaks v1

../_images/PredictPeaks-v1_dlg.png

PredictPeaks dialog.

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

Name Direction Type Default Description
InputWorkspace Input Workspace Mandatory An input workspace (MatrixWorkspace, MDEventWorkspace, or PeaksWorkspace) containing: - The relevant Instrument (calibrated as needed). - A sample with a UB matrix. - The goniometer rotation matrix.
WavelengthMin Input number 0.1 Minimum wavelength limit at which to start looking for single-crystal peaks.
WavelengthMax Input number 100 Maximum wavelength limit at which to stop looking for single-crystal peaks.
MinDSpacing Input number 1 Minimum d-spacing of peaks to consider. Default = 1.0
MaxDSpacing Input number 100 Maximum d-spacing of peaks to consider.
ReflectionCondition Input string Primitive Which reflection condition applies to this crystal, reducing the number of expected HKL peaks? Allowed values: [‘Primitive’, ‘C-face centred’, ‘A-face centred’, ‘B-face centred’, ‘Body centred’, ‘All-face centred’, ‘Rhombohedrally centred, obverse’, ‘Rhombohedrally centred, reverse’, ‘Hexagonally centred, reverse’]
CalculateStructureFactors Input boolean False Calculate structure factors for the predicted peaks. This option only works if the sample of the input workspace has a crystal structure assigned.
HKLPeaksWorkspace Input PeaksWorkspace   Optional: An input PeaksWorkspace with the HKL of the peaks that we should predict. The WavelengthMin/Max and Min/MaxDSpacing parameters are unused if this is specified.
RoundHKL Input boolean True When using HKLPeaksWorkspace, this will round the HKL values in the HKLPeaksWorkspace to the nearest integers if checked. Keep unchecked to use the original values
OutputWorkspace Output PeaksWorkspace   An output PeaksWorkspace.

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.

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', predicted.getNumberPeaks(), 'detectable peaks.'

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%:', 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:', len(absences)
print 'Absent HKLs:', [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 294 detectable peaks.
Maximum intensity: 6101.93
Peaks with relative intensity < 1%: 94
Number of absences: 16
Absent HKLs: [[2,0,-1], [3,0,-1], [4,0,-1], [5,0,-1], [6,0,-3], [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,-5], [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.

Using HKLPeaksWorkspace

If you specify the HKLPeaksWorkspace parameter, then the algorithm will use the list of HKL in that workspace as the starting point of HKLs, instead of doing all HKLs within range of Max/MinDSpacing and WavelengthMin/WavelengthMax.

A typical use case for this method is to use FindPeaksMD v1 followed by IndexPeaks v1 to find the HKL of each peak. The HKLs found will be floats, so specify RoundHKL=True in PredictPeaks to predict the position at the exact integer HKL. This may help locate the center of peaks.

Another way to use this algorithm is to use CreatePeaksWorkspace v1 to create a workspace with the desired number of peaks. Use python or the GUI to enter the desired HKLs. If these are fraction (e.g. magnetic peaks) then make sure RoundHKL=False.

See also

Algorithm PredictFractionalPeaks v1

Categories: Algorithms | Crystal\Peaks

Source

C++ source: PredictPeaks.cpp

C++ header: PredictPeaks.h