4.2

Theory of Le Bail Fit

To overcome some of the problems of the Pawley method as experienced at the time, Armel le Bail took a wholly different approach to the extraction of the peak intensities from the powder profile. The method uses a two-step cyclic process. As with the Pawley method, the instrument geometry parameters and peak profile parameters are fitted by a standard least-squares methods. However, the intensities of the individual peaks are not treated as least-squares parameters and are never refined.

Le Bail Fit Algorithms Suite

The purpose to develop Le Bail fit algorithm in Mantid is to calibrate powder diffractometer instrument profile parameters. LeBailFit itself cannot solve the problem. Thus a set of algorithms have been implemented to work with LeBailFit.

  • LeBailFit
  • CreateLeBailFitInput reads and parses Fullprof’s reflection (.hkl) file, which contains list of reflections’ miller indexes and resolution (.irf) file for starting values of peak profile parameters.
  • ProcessBackground is designed to process background to some extent, such as create a data workspace containing background points selected according to users input. Then some simple Fit will give a good starting point of background parameters. This is needed because LeBailFit does not have background fitting included.
  • UpdatePeakParameterTableValue allows users to update the values in peak profile parameter table workspace to specify the parameter to fit, modify its starting value or value boundary, and etc.
  • SaveFullprofResolution
  • FitPowderDiffPeaks
  • RefinePowderInstrumentParameters

The refinement result of LeBailFit can be saved to Fullprof .irf file by SaveFullprofResolution from the output peak profile parameter table workspace.

If the starting values of instrument geometry parameters, such as Dtt1, Dtt1t, Dtt2t, Zero, Zerot, are off too much, calling LeBailFit even in Monte Carlo mode with large number of Monte Carlo cycles may not render an acceptable solution. FitPowderDiffPeaks and RefinePowderInstrumentParameters are designed to refine those geometry parameters in this case. These 2 algorithms will fit each peak individually and refine geometry parameters against peaks’ centre in d-spacing vs. TOF, respectively.

Sample script which illustrates the steps of the Le-Bailfit method

The data for this script are present in the system tests directory.

# Load data
LoadAscii(Filename=r'PG3_11485-1.dat',OutputWorkspace='PG3_11485',Unit='TOF')

# Create input workspaces for Le Bail fit
CreateLeBailFitInput(ReflectionsFile=r'LB4844b1.hkl',
        FullprofParameterFile=r'2011B_HR60b1.irf',
        LatticeConstant='4.1568899999999998',
        InstrumentParameterWorkspace='Bank1InstrumentParameterTable1',
        BraggPeakParameterWorkspace='BraggPeakParameterTable1')

# Initial Le Bail fit in calculation mode to see how far the starting parameters are off
LeBailFit(InputWorkspace='PG3_11485',
        OutputWorkspace='PG3_11485_Calculated_0',
        InputParameterWorkspace='Bank1InstrumentParameterTable1',
        OutputParameterWorkspace='TempTable',
        InputHKLWorkspace='BraggPeakParameterTable1',
        OutputPeaksWorkspace='BraggPeakParameterTable2',
        Function='Calculation',
        BackgroundType='Chebyshev',
        BackgroundParameters='0,0,0',   # No background at first
        UseInputPeakHeights='0',
        PeakRadius='8',
        Minimizer='Levenberg-Marquardt')

# Fit the instrumental geometry-related parameters.  Dtt1, Dtt1t, Dtt2, Zero, Zerot,
# Step 1: Fit single diffraction peaks
FitPowderDiffPeaks(InputWorkspace='PG3_11485',
        OutputWorkspace='Bank1FittedPeaks',
        BraggPeakParameterWorkspace='BraggPeakParameterTable2',
        InstrumentParameterWorkspace='Bank1InstrumentParameterTable1',
        OutputBraggPeakParameterWorkspace='BraggPeakParameterTable2_0',
        OutputBraggPeakParameterDataWorkspace='BraggPeakParameterTable2_P',
        OutputZscoreWorkspace='BraggPeakParameterTable2_Zscore',
        MinTOF='15000',MaxTOF='49387',UseGivenPeakCentreTOF='0',
        MinimumPeakHeight='0.29999999999999999',
        PeaksCorrelated='1',
        MinimumHKL='12,12,12',
        RightMostPeakHKL='2,0,0',
        RightMostPeakLeftBound='46000',
        RightMostPeakRightBound='48000')

# Step 2: Refine geometry-related parameters.  Dtt1, Dtt1t, Dtt2, Zero, Zerot,
RefinePowderInstrumentParameters(InputPeakPositionWorkspace='BraggPeakParameterTable2_P',
        OutputPeakPositionWorkspace='PG3_11485_PeakPositions',
        InputInstrumentParameterWorkspace='Bank1InstrumentParameterTable1',
        OutputInstrumentParameterWorkspace='Bank1InstrumentParameterTable1_01',
        RefinementAlgorithm='OneStepFit')

# Create a workspace containing background of diffraction data to fit background polynomial
ProcessBackground(InputWorkspace='PG3_11485',
        OutputWorkspace='PG3_11485_Background',
        Options='SelectBackgroundPoints',
        LowerBound='5053',
        UpperBound='49387',
        BackgroundPoints='5243,8910,11165,12153,13731,15060,16511,17767,19650,21874,23167,24519,36000,44282,49000',
        NoiseTolerance='0.10000000000000001')

# Fit background function
Fit(Function='name=Polynomial,n=6,A0=0.558765,A1=-3.36699e-05,A2=-9.89997e-10,A3=2.29598e-13,A4=-1.07727e-17,A5=2.10058e-22,A6=-1.49446e-27',
        InputWorkspace='PG3_11485_Background',
        MaxIterations='1000',
        Minimizer='Levenberg-MarquardtMD',
        CreateOutput='1',
        Output='PG3_11485_Background',
        StartX='5053',EndX='49387')

# Use LeBailFit to calculate the diffraction pattern to see whether the refined geometry-related parameters are good as starting value
LeBailFit(InputWorkspace='PG3_11485',
        OutputWorkspace='CalculatedPattern0',
        InputParameterWorkspace='Bank1InstrumentParameterTable1_01',
        OutputParameterWorkspace='Bank1InstrumentParameterTable1_0',
        InputHKLWorkspace='BraggPeakParameterTable1',
        OutputPeaksWorkspace='BraggPeakParameterTable2_0',
        Function='Calculation',
        BackgroundParametersWorkspace='PG3_11485_Background_Parameters',
        UseInputPeakHeights='0',PeakRadius='8',Minimizer='Levenberg-Marquardt')

# Use LeBailFit to refine POWGEN's instrument profile parameters by Monte Carlo algorithm
LeBailFit(InputWorkspace='PG3_11485',
        OutputWorkspace='PG3_11485_MC_1000',
        InputParameterWorkspace='Bank1InstrumentParameterTable1_0',
        OutputParameterWorkspace='Bank1InstrumentParameterTable_MC',
        InputHKLWorkspace='BraggPeakParameterTable1',
        OutputPeaksWorkspace='BraggPeakParameterTable3',
        FitRegion='5053,49387',
        Function='MonteCarlo',
        BackgroundParametersWorkspace='PG3_11485_Background_Parameters',
        UseInputPeakHeights='0',
        PeakRadius='8',
        Minimizer='Levenberg-Marquardt',
        Damping='0.90000000000000002',
        NumberMinimizeSteps='1000',
        FitGeometryParameter='1',
        RandomSeed='1000',
        AnnealingTemperature='10',
        DrunkenWalk='1')