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FindUBUsingFFT v1

Summary

Calculate the UB matrix from a peaks workspace, given min(a,b,c) and max(a,b,c).

See Also

SetUB, FindUBUsingIndexedPeaks, FindUBUsingLatticeParameters, FindUBUsingMinMaxD

Properties

Name	Direction	Type	Default	Description
PeaksWorkspace	InOut	IPeaksWorkspace	Mandatory	Input Peaks Workspace
MinD	Input	number	Mandatory	Lower Bound on Lattice Parameters a, b, c
MaxD	Input	number	Mandatory	Upper Bound on Lattice Parameters a, b, c
Tolerance	Input	number	0.15	Indexing Tolerance (0.15)
Iterations	Input	number	4	Iterations to refine UB (4)
DegreesPerStep	Input	number	1.5	The resolution of the search through possible orientations is specified by this parameter. One to two degrees per step is usually adequate.

Description

Given a set of peaks, and given a range of possible a,b,c values, this algorithm will attempt to find a UB matrix, corresponding to the Niggli reduced cell, that fits the data. The algorithm projects the peaks on many possible direction vectors and calculates a Fast Fourier Transform of the projections to identify regular patterns in the collection of peaks. Based on the calcuated FFTs, a list of directions corresponding to possible real space unit cell edge vectors is formed. The directions and lengths of the vectors in this list are optimized (using a least squares approach) to index the maximum number of peaks, after which the list is sorted in order of increasing length and duplicate vectors are removed from the list.

The algorithm then chooses three of the remaining vectors with the shortest lengths that are linearly independent, form a unit cell with at least a minimum volume and for which the corresponding UB matrix indexes at least 80% of the maximum number of indexed using any set of three vectors chosen from the list.

A UB matrix is formed using these three vectors and the resulting UB matrix is again optimized using a least squares method. Finally, starting from this matrix, a matrix corresponding to the Niggli reduced cell is calculated and returned as the UB matrix. If the specified peaks are accurate and belong to a single crystal, this method should produce the UB matrix corresponding to the Niggli reduced cell. However, other software will usually be needed to adjust this UB to match a desired conventional cell. While this algorithm will occasionally work for as few as four peaks, it works quite consistently with at least ten peaks, and in general works best with a larger number of peaks.

Usage

Example:

ws=LoadIsawPeaks("TOPAZ_3007.peaks")
print("After LoadIsawPeaks does the workspace have an orientedLattice: %s" % ws.sample().hasOrientedLattice())

FindUBUsingFFT(ws,MinD=8.0,MaxD=13.0)
print("After FindUBUsingFFT does the workspace have an orientedLattice: %s" % ws.sample().hasOrientedLattice())

print(ws.sample().getOrientedLattice().getUB())

Output:

After LoadIsawPeaks does the workspace have an orientedLattice: False
After FindUBUsingFFT does the workspace have an orientedLattice: True
[[ 0.01223576  0.00480107  0.08604016]
 [-0.11654506  0.00178069 -0.00458823]
 [-0.02737294 -0.08973552 -0.02525994]]

Categories: AlgorithmIndex | Crystal\UBMatrix

Source

C++ header: FindUBUsingFFT.h

C++ source: FindUBUsingFFT.cpp