LatticeFunction¶

Description¶

After a list of Bragg reflections has been indexed, it is often necessary to refine the unit cell parameters that have been used to assign indices. LatticeFunction can be used to achieve that task with Fit v1. The function can work with a PeaksWorkspace or with a TableWorkspace that contains two columns named HKL and d (see PawleyFit v1 for specification of the table).

After setting the CrystalSystem attribute to one of the seven crystal systems, the function exposes the corresponding lattice parameters, as well as a ZeroShift. In most cases it’s recommended to fix this additional parameter as this is often taken care of in earlier steps of the data reduction.

Usage¶

The following script demonstrates how the function can be used. The algorithm PoldiCreatePeaksFromCell v1 is used to generate Bragg reflections that are expected for the crystal structure of Silicon.

import numpy as np

# Create Silicon peaks for indexing
peaks_Si = PoldiCreatePeaksFromCell(
            SpaceGroup="F d -3 m",
            a=5.4311946,
            Atoms="Si 0 0 0",
            LatticeSpacingMin=0.7)

# Fit a cubic cell, starting parameter is 5
Fit(Function="name=LatticeFunction,CrystalSystem=Cubic,a=5",
    InputWorkspace=peaks_Si,
    Ties="ZeroShift=0.0",
    CreateOutput=True,
    Output="Si",
    CostFunction="Unweighted least squares")

# Print the refined lattice parameter with error estimate
parameters = AnalysisDataService.retrieve("Si_Parameters")

a_true = 5.4311946
a = np.round(parameters.cell(0, 1), 7)
a_err = np.round(parameters.cell(0, 2), 16)

print "Refined lattice parameter: a =", a, "+/-", a_err
print "Difference from expected value: a_observed - a_expected =", np.round(a - a_true, 7)
print "Is this difference within the standard deviation?", "Yes" if np.fabs(a - a_true) <= a_err else "No"

Executing the script produces some output with information about the fit:

Refined lattice parameter: a = 5.4311946 +/- 2e-16
Difference from expected value: a_observed - a_expected = 0.0
Is this difference within the standard deviation? Yes

In addition there is also an output workspace, which contains information about the peaks used for the fit and how well the peak positions calculated from the fitted parameters match the observed positions.

Attributes (non-fitting parameters)¶

Properties (fitting parameters)¶

Categories: FitFunctions | General

Source¶

C++ source: LatticeFunction.cpp

C++ header: LatticeFunction.h