FindGlobalBMatrix v1¶

Summary¶

Takes multiple peak tables from different runs and refines common lattice parameters and angles.

Properties¶

Description¶

FindGlobalBMatrix refines the lattice parameters (encoded in the B matrix) across PeaksWorkspaces from multiple runs with a separate U matrix (which encodes the orientation for an identity goniometer matrix) per run. This is useful for when the goniometer matrix is inaccurate/not well known.

The quantity minimised is the average of the square of the difference in QSample between the observed peak and the peak at integer HKL (see CalculateUMatrix v1 for details). The average rather than the sum of the squared residuals is used so as not to penalise the indexing of more peaks as the UB matrix becomes more accurate.

FindGlobalBMatrix adds a different UB to each peak workspace that can be indexed - note the algorithm ensures consistent indexing across all runs (i.e. axes are not swapped or inverted). All peaks workspaces must have more then 6 peaks in (a requirement of some child algorithms used).

The algorithm proceeds in this way:

• Finds an initial UB
  • If a UB exists on any workspace the initial is the UB that indexes the most peaks.
  • Otherwise FindUBUsingLatticeParameters is run on the workspaces with the input lattice parameters until a UB is found.
• Peaks in all workspaces are indexed consistently with the initial UB
  • If a workspace has a valid UB it is transformed to preserve consistent indexing.
  • Otherwise we try to index the peaks using the initial UB and the goniometer matrix on the workspace
  • If the above doesn’t work because e.g. the goniometer matrix is inaccurate, we find a UB using FindUBUsingLatticeParameters and transform to preserve consistent indexing.
• Once peaks are indexed the optimal lattice parameters are found that minimise the average of the squared residuals in QSample across all runs.
  • The U matrix of each run is found for a given set of lattice parameters using CalculateUMatrix v1.

Useage¶

Example:

from mantid.simpleapi import *

# load empty instrument so can create a peak table
ws = LoadEmptyInstrument(InstrumentName='SXD', OutputWorkspace='empty_SXD')
axis = ws.getAxis(0)
axis.setUnit("TOF")

# create two peak tables with UB corresponding to different lattice constants, a
peaks1 = CreatePeaksWorkspace(InstrumentWorkspace=ws, NumberOfPeaks=0)
UB = np.diag([1.0/3.8, 0.25, 0.1])  # alatt = [3.8, 4, 10]
SetUB(peaks1, UB=UB)
peaks2 = CreatePeaksWorkspace(InstrumentWorkspace=ws, NumberOfPeaks=0)
UB = np.diag([1.0/4.2, 0.25, 0.1])  # alatt = [4.2, 4, 10]
SetUB(peaks2, UB=UB)
# Add some peaks
for h in range(0, 3):
    for k in range(0, 3):
        for peaks in [peaks1, peaks2]:
            pk = peaks.createPeakHKL([h, k, 4])
            peaks.addPeak(pk)

FindGlobalBMatrix(PeakWorkspaces=[peaks1, peaks2], a=4.1, b=4.2, c=10, alpha=88, beta=88, gamma=89,
                  Tolerance=0.15)

# show that both workspaces have the average of the two a lattice constants (a=4 Ang)
print(peaks1.sample().getOrientedLattice())
# lattice parameters: a = 4.00025 b = 3.98794 c = 9.99608 alpha = 89.9698 beta = 90.0829 gamma = 89.9336

print(peaks2.sample().getOrientedLattice())
# lattice parameters: a = 4.00025 b = 3.98794 c = 9.99608 alpha = 89.9698 beta = 90.0829 gamma = 89.9336

Categories: AlgorithmIndex | Diffraction\Reduction

Source¶

Python: FindGlobalBMatrix.py (last modified: 2021-08-20)