\(\renewcommand\AA{\unicode{x212B}}\)

FitPowderDiffPeaks v1¶

FitPowderDiffPeaks dialog.

Table of Contents

Summary
- See Also
Properties
Description
Peak Fitting Algorithms
Use Cases
- Use case 1: robust fitting
- Use Case 2: Fitting Peak Parameters From Scratch
How to use algorithm with other algorithms
- Example of Working With Other Algorithms
Usage
Source

Summary ¶

Fit peaks in powder diffraction pattern.

Properties ¶

Name	Direction	Type	Default	Description
InputWorkspace	Input	MatrixWorkspace	Mandatory	Input workspace for data (diffraction pattern).
OutputWorkspace	Output	Workspace2D		Output Workspace2D for the fitted peaks.
BraggPeakParameterWorkspace	Input	TableWorkspace	Mandatory	TableWorkspace containg all peaks’ parameters.
InstrumentParameterWorkspace	InOut	TableWorkspace	Mandatory	TableWorkspace containg instrument’s parameters.
OutputBraggPeakParameterWorkspace	Output	TableWorkspace		Output TableWorkspace containing the fitted peak parameters for each peak.
OutputBraggPeakParameterDataWorkspace	Output	Workspace2D		Output Workspace2D containing fitted peak parameters for further refinement.
OutputZscoreWorkspace	Output	TableWorkspace		Output TableWorkspace containing the Zscore of the fitted peak parameters.
WorkspaceIndex	Input	number	0	Worskpace index for the data to refine against.
MinTOF	Input	number	Optional	Minimum TOF to fit peaks.
MaxTOF	Input	number	Optional	Maximum TOF to fit peaks.
FittingMode	Input	string	Robust	Fitting mode such that user can determinewhether the input parameters are trustful or not. Allowed values: [‘Robust’, ‘Confident’]
UseGivenPeakCentreTOF	Input	boolean	True	Use each Bragg peak’s centre in TOF given in BraggPeakParameterWorkspace.Otherwise, calculate each peak’s centre from d-spacing.
PeakParametersStartingValueFrom	Input	string	(HKL) & Calculation	Choice of how to generate starting values of Bragg peak profile parmeters. Allowed values: [‘(HKL) & Calculation’, ‘From Bragg Peak Table’]
MinimumPeakHeight	Input	number	0.2	Minimum peak height (with background removed) Any peak whose maximum height under this value will be treated as zero intensity.
PeaksCorrelated	Input	boolean	False	Flag for fact that all peaks’ corresponding profile parameters are correlated by an analytical function
MinimumHKL	Input	int list		Miller index of the left most peak (peak with minimum d-spacing) to be fitted.
NumberPeaksToFitBelowLowLimit	Input	number	0	Number of peaks to fit with d-spacing value less than specified minimum.
RightMostPeakHKL	Input	int list		Miller index of the right most peak. It is only required and used in RobustFit mode.
RightMostPeakLeftBound	Input	number	Optional	Left bound of the right most peak. Used in RobustFit mode.
RightMostPeakRightBound	Input	number	Optional	Right bound of the right most peak. Used in RobustFit mode.
FitCompositePeakBackground	Input	boolean	True	Flag to do fit to both peak and background in a composite function as last fit step.

Description ¶

This algorithm fits a certain set of single diffraction peaks in a powder diffraction pattern.

The assumption is that all the peaks in the diffraction patter can be described by a single peak type. A specific peak parameter will have its values plotted by an analytical function among all the peaks.

It serves as the first step to fit/refine instrumental parameters that will be introduced in Le Bail fit. The second step is realized by algorithm RefinePowderInstrumentParameters.

Peak Fitting Algorithms ¶

Peak Fitting Mode ¶

Fitting mode determines the approach (or algorithm) to fit diffraction peaks. 2 modes are supported:

Confident: User is confident on the input peak parameters. Thus the fitting will be a one-step minimizer by Levenberg-Marquardt.
Robust: The given starting values of peak parameters may be too far away from true values. A trial-and-error approach is used.

Starting Values of Peaks’ Parameters ¶

“(HKL) & Calculation”: the starting values are calculated from each peak’s miller index and thermal neutron peak profile formula;
“From Bragg Peak Table”: the starting values come from the Bragg Peak Parameter table.

Peak-fitting sequence ¶

Peaks are fitted from high d-spacing, i.e., lowest possible Miller index, to low d-spacing values. If MinimumHKL is specified, then peak will be fitted from maximum d-spacing/TOF, to the peak with Miller index as MinimumHKL.

Correlated peak profile parameters ¶

If peaks profile parameters are correlated by analytical functions, then the starting values of one peak will be the fitted peak profile parameters of its right neighbour.

Use Cases ¶

Several use cases are listed below about how to use this algorithm.

Use case 1: robust fitting ¶

User wants to use the starting values of peaks parameters from input thermal neutron peak parameters such as Alph0, Alph1, and etc;
User specifies the right most peak range and its Miller index;
“FitPowderDiffPeaks” calculates Alpha, Beta and Sigma for each peak from parameter values from InstrumentParameterTable;
“FitPowderDiffPeaks” fits peak parameters of each peak from high TOF to low TOF.

Use Case 2: Fitting Peak Parameters From Scratch ¶

This is the extreme case such that

Input instrumental geometry parameters, including Dtt1, Dtt1t, Dtt2t, Zero, Zerot, Tcross and Width, have roughly-guessed values;
There is no pre-knowledge for each peak’s peak parameters, including Alpha, Beta, and Sigma.

How to use algorithm with other algorithms ¶

This algorithm is designed to work with other algorithms to do Le Bail fit. The introduction can be found in the wiki page of LeBailFit v1.

Example of Working With Other Algorithms ¶

FitPowderDiffPeaks is designed to work with other algorithms, such RefinePowderInstrumentParameters, and LeBailFit. See Le Bail *fit concept page for full list of such algorithms.

A common scenario is that the starting values of instrumental geometry related parameters (Dtt1, Dtt1t, and etc) are enough far from the real values.

“FitPowderDiffPeaks” fits the single peaks from high TOF region in robust mode;
“RefinePowderInstrumentParameters” refines the instrumental geometry related parameters by using the d-TOF function;
Repeat step 1 and 2 for more single peaks incrementally. The predicted peak positions are more accurate in this step.

Usage ¶

Example - Fit diffraction peaks by single peak fitting:

# Load reduced powder diffraction data
LoadAscii(Filename='PG3_11487-3.dat',
      OutputWorkspace='PG3_11487', Unit='TOF')

# Create table workspaces used by Le Bail fit algorithms
CreateLeBailFitInput(ReflectionsFile='LB4854b3.hkl', FullprofParameterFile='2011B_HR60b3.irf',
      Bank=3, LatticeConstant=4.1568899999999998, InstrumentParameterWorkspace='Bank3InstrumentParameterTable1',
      BraggPeakParameterWorkspace='BraggPeakParameterTable1')

# Fit background of the powder diffraction data
ProcessBackground(InputWorkspace='PG3_11487', OutputWorkspace='PG3_11487_Background', Options='SelectBackgroundPoints',
      LowerBound=10080, UpperBound=72000, SelectionMode='FitGivenDataPoints',
      BackgroundPoints='10082,10591,11154,12615,13690,13715,15073,16893,17764,19628,21318,24192,35350,44212,50900,60000,69900,79000',
      NoiseTolerance=0.10000000000000001, UserBackgroundWorkspace='dummy0', OutputBackgroundParameterWorkspace='dummy1')

Fit(Function='name=Polynomial,n=6,A0=0.473391,A1=-3.8911e-05,A2=1.7206e-09,A3=-3.21291e-14,A4=9.31264e-20,A5=3.90465e-24,A6=-3.28688e-29',
      InputWorkspace='PG3_11487_Background', MaxIterations=1000, OutputStatus='success',
      OutputChi2overDoF=2.0078239589764837, Minimizer='Levenberg-MarquardtMD', CreateOutput=True,
      Output='PG3_11487_Background', StartX=10080, EndX=72000,
      OutputNormalisedCovarianceMatrix='PG3_11487_Background_NormalisedCovarianceMatrix',
      OutputParameters='PG3_11487_Background_Parameters', OutputWorkspace='PG3_11487_Background_Workspace', Version=1)

# Fit individual peaks in the diffraction pattern
FitPowderDiffPeaks(InputWorkspace='PG3_11487', OutputWorkspace='Bank3FittedPeaks',
      BraggPeakParameterWorkspace='BraggPeakParameterTable1',
      InstrumentParameterWorkspace='Bank3InstrumentParameterTable1',
      OutputBraggPeakParameterWorkspace='BraggPeakParameterTable2_0',
      OutputBraggPeakParameterDataWorkspace='BraggPeakParameterTable2_P',
      OutputZscoreWorkspace='BraggPeakParameterTable2_Zscore',
      MinTOF=16866, MaxTOF=70000, UseGivenPeakCentreTOF=False, MinimumPeakHeight=0.29999999999999999,
      PeaksCorrelated=True, MinimumHKL='12,12,12', RightMostPeakHKL='1,1,0', RightMostPeakLeftBound=65800, RightMostPeakRightBound=67000)

# Print result
resultws = mtd["BraggPeakParameterTable2_P"]
for i in range(10):
    print("Peak @ d = {:.5f}, TOF_0 = {:.5f}, A = {:.5f}, B = {:.5f}, Sigma = {:.5f}".
          format(resultws.readX(0)[i], resultws.readY(0)[i], resultws.readY(1)[i], resultws.readY(2)[i], resultws.readY(3)[i]))

Output:

GeneraateHKL? =  False
Peak @ d = 0.75894, TOF_0 = 17142.23075, A = 0.15403, B = 0.10084, Sigma = 6.03789
Peak @ d = 0.77192, TOF_0 = 17435.01857, A = 0.16520, B = 0.10221, Sigma = 6.63462
Peak @ d = 0.79999, TOF_0 = 18069.21642, A = 0.15039, B = 0.09358, Sigma = 6.41801
Peak @ d = 0.81523, TOF_0 = 18413.34201, A = 0.14661, B = 0.09132, Sigma = 6.67055
Peak @ d = 0.83138, TOF_0 = 18778.30857, A = 0.13545, B = 0.09075, Sigma = 6.44981
Peak @ d = 0.84852, TOF_0 = 19164.95217, A = 0.14572, B = 0.08599, Sigma = 7.30674
Peak @ d = 0.88625, TOF_0 = 20017.59170, A = 0.12676, B = 0.08361, Sigma = 7.24717
Peak @ d = 0.90711, TOF_0 = 20488.70341, A = 0.12200, B = 0.08131, Sigma = 7.27715
Peak @ d = 0.92951, TOF_0 = 20994.85671, A = 0.12909, B = 0.08600, Sigma = 8.46692
Peak @ d = 0.95366, TOF_0 = 21540.74042, A = 0.10656, B = 0.07592, Sigma = 7.61463

Categories: AlgorithmIndex | Diffraction\Fitting

Source ¶

C++ header: FitPowderDiffPeaks.h (last modified: 2020-03-25)

C++ source: FitPowderDiffPeaks.cpp (last modified: 2020-04-07)