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FindMultipleUMatrices v1

Summary

Finds multiple UB matrices using lattice parameters - can be used to find UBs in the presence of mutiple domains, crystallites or in the presence of spurious peaks.

See Also

FindUBUsingLatticeParameters, CalculateUMatrix

Properties

Name	Direction	Type	Default	Description
PeaksWorkspace	Input	IPeaksWorkspace	Mandatory	A PeaksWorkspace containing the peaks to integrate.
OutputWorkspace	Output	WorkspaceGroup	Mandatory	The output peak workspaces with UBs set - 1 per UB requested.
NumberOfUBs	Input	number	1	Number of UB matrices to find.
a	Input	number	1	Lattice parameter a
b	Input	number	1	Lattice parameter b
c	Input	number	1	Lattice parameter c
alpha	Input	number	90	Lattice angle alpha (in degrees)
beta	Input	number	90	Lattice angle beta (in degrees)
gamma	Input	number	90	Lattice angle gamma (in degrees)
HKLTolerance	Input	number	0.15	Tolerance to index peaks in in H,K and L - see IndexPeaks for details.
DSpacingTolerance	Input	number	0.05	Tolerance in d-spacing used to try and index peaks
AngleTolerance	Input	number	1	Tolerance (in degrees) of angle between peaks in QLab when identifying possible pairs of HKL.
MinAngleBetweenPeaks	Input	number	2	Minimum angle in QLab (in degrees) between pairs of peaks in when calculating U matrix.
MinAngleBetweenUB	Input	number	2	Minimum angle in degrees between u and v vectors (converted from HKL to QLab) of different UB.
MinDSpacing	Input	number	0	Min d-spacing of reflections to consider.
MaxDSpacing	Input	number	0	Max d-spacing of reflections to consider.
Spacegroup	Input	string		Spacegroup Hermann–Mauguin symbol used to determine the point group of the Laue class.
MaxOrder	Input	number	0	Maximum order to apply ModVectors. Default = 0
ModVector1	Input	string	0.0,0.0,0.0	Offsets for h, k, l directions
ModVector2	Input	string	0.0,0.0,0.0	Offsets for h, k, l directions
ModVector3	Input	string	0.0,0.0,0.0	Offsets for h, k, l directions
OptimiseFoundUBs	Input	boolean	True	Optimise final UBs using all peaks indexed best by that UB.

Description

FindMultipleUMatrices will use the lattice parameters and spacegroup provided to optimise a number (NumberOfUBs) of UB matrices (B is hard-coded due to the lattice parameters provided) and returns a group of peak workspaces one for each UB, containing the peaks that are indexed most accurately by that UB.

This algorithm is useful for finding a single UB in the presence of spurious peaks, or finding multiple UBs when there are multiple domains.

The algorithm proceeds by looping over each pair of peaks in PeaksWorkspace within the d-spacing limits (MinDSpacing and MaxDSpacing), trying to index them based on their d-spacing and angle between the peaks (within tolerances given by DSpacingTolerance and AngleTolerance). It then calculates the HKL errors (difference in HKL residuals squared) for all peaks in PeaksWorkspace and identifies the UBs that index the most peaks with the highest accuracy (i.e. better than any other UB found)

Note that although the user can provide modulation vectors, these are not currently used to index pairs of peaks but are indexed by each candidate UB found and used to determine the best UBs to return.

Peaks with relatively higher d-spacing are easier to index correctly, try using a smaller number of higher d-spacing peaks to start.

Useage

Example:

from mantid.simpleapi import *
from scipy.spatial.transform import Rotation as rot

ws = LoadEmptyInstrument(InstrumentName='SXD', OutputWorkspace='empty_SXD')
axis = ws.getAxis(0)
axis.setUnit("TOF")

# create a peak tables of orthorhombic domains with lattice parameters a=4, b=5, c=10
alatt = {'a': 4, 'b': 5, 'c': 10, 'alpha': 90, 'beta': 90, 'gamma': 90}
ubs = [np.diag([1/alatt['a'], 1/alatt['b'], 1/alatt['c']])]
ubs.append(rot.from_rotvec([0,0,90], degrees=True).as_matrix()  @ ubs[0])

peaks = CreatePeaksWorkspace(InstrumentWorkspace=ws, NumberOfPeaks=0, OutputWorkspace=f"peaks")
for iub, ub in enumerate(ubs):
    SetUB(peaks, UB=ub)
    for h in range(1, 3):
        for k in range(1, 3):
            for l in range(2,4):
                pk = peaks.createPeakHKL([h, k ,l])
                if pk.getDetectorID() > 0:
                    peaks.addPeak(pk)

peaks_out = FindMultipleUMatrices(PeaksWorkspace=peaks, OutputWorkspace='peaks_out', **alatt,
                                  MinDSpacing=1.25, MaxDSpacing=3.5, Spacegroup='P m m m',
                                  NumberOfUBs=2)

for ipk, pks in enumerate(peaks_out):
    print("HKL along x-axis of QLab = ", abs(np.round(pks.sample().getOrientedLattice().getvVector())))

Output:

HKL along x-axis of QLab =  [4. 0. 0.]
HKL along x-axis of QLab =  [0. 5. 0.]

Categories: AlgorithmIndex | Diffraction\Reduction | Crystal\UBMatrix

Source

Python: FindMultipleUMatrices.py