Indirect Data Analysis¶

Table of Contents

Overview
- Action Buttons
Bayesian
Elwin
- Options
MSD Fit
- Options
I(Q, t)
- Options
- Binning
I(Q, t) Fit
- Options
Conv Fit
JumpFit
- Options

Overview ¶

The Indirect Data Analysis interface is a collection of tools within MantidPlot for analysing reduced data from indirect geometry spectrometers, such as IRIS and OSIRIS.

The majority of the functions used within this interface can be used with both reduced files (_red.nxs) and workspaces (_red) created using the Indirect Data Reduction interface or using $S(Q, \omega)$ files (_sqw.nxs) and workspaces (_sqw) created using either the Indirect Data Reduction interface or taken from a bespoke algorithm or auto reduction.

Action Buttons ¶

?: Opens this help page.
Py: Exports a Python script which will replicate the processing done by the current tab.
Run: Runs the processing configured on the current tab.
Manage Directories: Opens the Manage Directories dialog allowing you to change your search directories and default save directory and enable/disable data archive search.

Bayesian ¶

There is the option to perform Bayesian data analysis on the I(Q, t) Fit ConvFit tabs on this interface by using the FABADA fitting minimizer, however in order to to use this you will need to use better starting parameters than the defaults provided by the interface.

You may also experience issues where the starting parameters may give a reliable fit on one spectra but not others, in this case the best option is to reduce the number of spectra that are fitted in one operation.

In both I(Q, t) Fit and ConvFit the following options are available when fitting using FABADA:

Output Chain: Select to enable output of the FABADA chain when using FABADA as the fitting minimizer.
Chain Length: Number of further steps carried out by fitting algorithm once parameters have converged (see ChainLength is FABADA documentation)
Convergence Criteria: The minimum variation in the cost function before the parameters are considered to have converged (see ConvergenceCriteria in FABADA documentation)
Acceptance Rate: The desired percentage acceptance of new parameters (see JumpAcceptanceRate in FABADA documentation)

Elwin ¶

Provides an interface for the ElasticWindow algorithm, with the option of selecting the range to integrate over as well as the background range. An on-screen plot is also provided.

For workspaces that have a sample log or have a sample log file available in the Mantid data search paths that contains the sample environment information the ELF workspace can also be normalised to the lowest temperature run in the range of input files.

Options ¶

Input File: Specify a range of input files that are either reduced (_red.nxs) or $S(Q, \omega)$ .
Integration Range: The energy range over which to integrate the values.
Background Subtraction: If checked a background will be calculated and subtracted from the raw data.
Background Range: The energy range over which a background is calculated which is subtracted from the raw data.
Normalise to Lowest Temp: If checked the raw files will be normalised to the run with the lowest temperature, to do this there must be a valid sample environment entry in the sample logs for each of the input files.
SE log name: The name of the sample environment log entry in the input files sample logs (defaults to sample).
SE log value: The value to be taken from the “SE log name” data series (defaults to the specified value in the intrument parameters file, and in the absence of such specification, defaults to “last value”)
Plot Result: If enabled will plot the result as a spectra plot.
Save Result: If enabled the result will be saved as a NeXus file in the default save directory.

MSD Fit ¶

../_images/Data_Analysis_tabMSD_widget.png

Given either a saved NeXus file or workspace generated using the ElWin tab, this tab fits $log(intensity)$ vs. $Q^{2}$ with a straight line for each run specified to give the Mean Square Displacement (MSD). It then plots the MSD as function of run number.

MSDFit searches for the log files named <runnumber>_sample.txt in your chosen raw file directory (the name ‘sample’ is for OSIRIS). If they exist the temperature is read and the MSD is plotted versus temperature; if they do not exist the MSD is plotted versus run number (last 3 digits).

The fitted parameters for all runs are in _msd_Table and the <u2> in _msd. To run the Sequential fit a workspace named <inst><first-run>_to_<last-run>_lnI is created of $ln(I)$ v. $Q^{2}$ for all runs. A contour or 3D plot of this may be of interest.

A sequential fit is run by clicking the Run button at the bottom of the tab, a single fit can be done using the Fit Single Spectrum button underneath the preview plot.

Options ¶

Input File: A file that has been created using the Elwin tab with an $x$ axis of $Q^2$ .
StartX & EndX: The $x$ range to perform fitting over.
Plot Spectrum: The spectrum shown in the preview plot and will be fitted by running Fit Single Spectrum.
Spectra Range: The spectra range over which to perform sequential fitting.
Plot Result: If enabled will plot the result as a spectra plot.
Save Result: If enabled the result will be saved as a NeXus file in the default save directory.

I(Q, t)¶

../_images/Data_Analysis_tabIqt_widget.png

Given sample and resolution inputs, carries out a fit as per the theory detailed in the TransformToIqt algorithm.

Options ¶

Sample: Either a reduced file (_red.nxs) or workspace (_red) or an $S(Q, \omega)$ file (_sqw.nxs) or workspace (_sqw).
Resolution: Either a resolution file (_res.nxs) or workspace (_res) or an $S(Q, \omega)$ file (_sqw.nxs) or workspace (_sqw).
ELow, EHigh: The rebiinning range.
SampleBinning: The ratio at which to decrease the number of bins by through merging of intensities from neighbouring bins.
Plot Result: If enabled will plot the result as a spectra plot.
Save Result: If enabled the result will be saved as a NeXus file in the default save directory.

Binning ¶

As a bin width that is a factor of the binning range is required for this analysis the bin width is calculated automatically based on the binning range and the number of desired bins in the output which is in turn calculated by reducing the number of sample bins by a given factor.

The calculated binning parameters are displayed alongside the binning options:

EWidth: The calculated bin width.
SampleBins: Number of bins in the sample after rebinning.
ResolutionBins: Number of bins in the resolution after rebinning, typically this should be at least 5 and a warning will be shown if it is less.

I(Q, t) Fit ¶

I(Q, t) Fit provides a simplified interface for controlling various fitting functions (see the Fit algorithm for more info). The functions are also available via the fit wizard.

Additionally, in the bottom-right of the interface there are options for doing a sequential fit. This is where the program loops through each spectrum in the input workspace, using the fitted values from the previous spectrum as input values for fitting the next. This is done by means of the PlotPeakByLogValue algorithm.

A sequential fit is run by clicking the Run button at the bottom of the tab, a single fit can be done using the Fit Single Spectrum button underneath the preview plot.

Options ¶

Input: Either a file (_iqt.nxs) or workspace (_iqt) that has been created using the Fury tab.
Fit Type: The type of fitting to perform.
Constrain Intensities: Check to ensure that the sum of the background and intensities is always equal to 1.
Constrain Beta over all Q: Check to use a multi-domain fitting function with the value of beta constrained.
Plot Guess: When checked a curve will be created on the plot window based on the bitting parameters.
Max Iterations: The maximum number of iterations that can be carried out by the fitting algorithm (automatically increased when FABADA is enabled).
StartX & EndX: The range of $x$ over which the fitting will be applied (blue lines on preview plot).
Use FABADA: Select to enable use of the FABADA minimizer when performing the fit.
Linear Background A0: The constant amplitude of the background (horizontal green line on the preview plot).
Fitting Parameters: Depending on the Fit Type the parameters shown for each of the fit functions will differ, for more information refer to the documentation pages for the fit function in question.
Plot Spectrum: The spectrum shown in the preview plot and will be fitted by running Fit Single Spectrum.
Spectra Range: The spectra range over which to perform sequential fitting.
Plot Output: Allows plotting spectra plots of fitting parameters, the options available will depend on the type of fit chosen.
Save Result: If enabled the result will be saved as a NeXus file in the default save directory.

Conv Fit ¶

Similarly to FuryFit, ConvFit provides a simplified interface for controlling various fitting functions (see the Fit algorithm for more info). The functions are also available via the fit wizard.

A sequential fit is run by clicking the Run button at the bottom of the tab, a single fit can be done using the Fit Single Spectrum button underneath the preview plot.

Fitting Model ¶

The model used to perform fitting is described in the following tree, note that everything under the Model section is optional and determined by the Fit Type and Use Delta Function options in the interface.

CompositeFunction
- LinearBackground
- Convolution
  - Resolution
  - Model (CompositeFunction)
    - DeltaFunction
    - ProductFunction (One Lorentzian)
      - Lorentzian
      - Temperature Correction
    - ProductFunction (Two Lorentzians)
      - Lorentzian
      - Temperature Correction
    - ProductFunction (InelasticDiffSphere)
      - Inelastic Diff Sphere
      - Temperature Correction
    - ProductFunction (InelasticDiffRotDiscreteCircle)
      - Inelastic Diff Rot Discrete Circle
      - Temperature Correction
    - ProductFunction (ElasticDiffSphere)
      - Elastic Diff Sphere
      - Temperature Correction
    - ProductFunction (ElasticDiffRotDiscreteCircle)
      - Elastic Diff Rot Discrete Circle
      - Temperature Correction
    - ProductFunction (StretchedExpFT)
      - StretchedExpFT
      - Temperature Correction

The Temperature Correction is a UserFunction with the formula $((x * 11.606) / T) / (1 - exp(-((x * 11.606) / T)))$ where $T$ is the temperature in Kelvin.

Options ¶

Sample: Either a reduced file (_red.nxs) or workspace (_red) or an $S(Q, \omega)$ file (_sqw.nxs) or workspace (_sqw).
Resolution: Either a resolution file (_res.nxs) or workspace (_res) or an $S(Q, \omega)$ file (_sqw.nxs) or workspace (_sqw).
Fit Type: The type of fitting to perform.
Background: Select the background type, see options below.
Plot Guess: When checked a curve will be created on the plot window based on the bitting parameters.
Max Iterations: The maximum number of iterations that can be carried out by the fitting algorithm (automatically increased when FABADA is enabled).
StartX & EndX: The range of $x$ over which the fitting will be applied (blue lines on preview plot).
Use FABADA: Select to enable use of the FABADA minimizer when performing the fit.
A0 & A1 (background): The A0 and A1 parameters as they appear in the LinearBackground fir function, depending on the Fit Type selected A1 may not be shown.
Delta Function: Enables use of a delta function.
Fitting Parameters: Depending on the Fit Type the parameters shown for each of the fit functions will differ, for more information refer to the documentation pages for the fit function in question.
Plot Spectrum: The spectrum shown in the preview plot and will be fitted by running Fit Single Spectrum.
Spectra Range: The spectra range over which to perform sequential fitting.
Plot Output: Allows plotting spectra plots of fitting parameters, the options available will depend on the type of fit chosen.
Save Result: If enabled the result will be saved as a NeXus file in the default save directory.

Background Options ¶

Fixed Flat: The A0 parameter is applied to all points in the data.
Fit Flat: Similar to Fixed Flat, however the A0 parameter is treated as an initial guess and will be included as a parameter to the LinearBackground fit function with the coefficient of the linear term fixed to 0.
Fit Linear: The A0 and A1 parameters are used as parameters to the LinearBackground fit function and the best possible fit will be used as the background.

Theory ¶

The measured data $I(Q, \omega)$ is proportional to the convolution of the scattering law $S(Q, \omega)$ with the resolution function $R(Q, \omega)$ of the spectrometer via $I(Q, \omega) = S(Q, \omega) ⊗ R(Q, \omega)$ . The traditional method of analysis has been to fit the measured $I(Q, \omega)$ with an appropriate set of functions related to the form of $S(Q, \omega)$ predicted by theory.

In quasielastic scattering the simplest form is when both the $S(Q, \omega)$ and the $R(Q, \omega)$ have the form of a Lorentzian - a situation which is almost correct for reactor based backscattering spectrometers such as IN10 & IN16 at ILL. The convolution of two Lorentzians is itself a Lorentzian so that the spectrum of the measured and resolution data can both just be fitted with Lorentzians. The broadening of the sample spectrum is then just the difference of the two widths.
The next easiest case is when both $S(Q, \omega)$ and $R(Q, \omega)$ have a simple functional form and the convolution is also a function containing the parameters of the $S(Q, \omega)$ and R(Q, omega) functions. The convoluted function may then be fitted to the data to provide the parameters. An example would be the case where the $S(Q, \omega)$ is a Lorentzian and the $R(Q, \omega)$ is a Gaussian.
For diffraction, the shape of the peak in time is a convolution of a Gaussian with a decaying exponential and this function can be used to fit the Bragg peaks.
The final case is where $R(Q, \omega)$ does not have a simple function form so that the measured data has to be convoluted numerically with the $S(Q, \omega)$ function to provide an estimate of the sample scattering. The result is least-squares fitted to the measured data to provide values for the parameters in the $S(Q, \omega)$ function.

This latter form of peak fitting is provided by SWIFT. It employs a least-squares algorithm which requires the derivatives of the fitting function with respect to its parameters in order to be faster and more efficient than those algorithms which calculate the derivatives numerically. To do this the assumption is made that the derivative of a convolution is equal to the convolution of the derivative-as the derivative and the convolution are performed over different variables (function parameters and energy transfer respectively) this should be correct. A flat background is subtracted from the resolution data before the convolution is performed.

Four types of sample function are available for $S(Q, \omega)$ :

Quasielastic: This is the most common case and applies to both translational (diffusion) and rotational modes, both of which have the form of a Lorentzian. The fitted function is a set of Lorentzians centred at the origin in energy transfer.
Elastic: Comprising a central elastic peak together with a set of quasi-elastic Lorentzians also centred at the origin. The elastic peak is taken to be the un-broadened resolution function.
Shift: A central Lorentzian with pairs of energy shifted Lorentzians. This was originally used for crystal field splitting data but more recently has been applied to quantum tunnelling peaks. The fitting function assumes that the peaks are symmetric about the origin in energy transfer both in position and width. The widths of the central and side peaks may be different.
Polymer: A single quasi-elastic peak with 3 different forms of shape. The theory behind this is described elsewhere [1,2]. Briefly, polymer theory predicts 3 forms of the $I(Q,t)$ in the form of $exp(-at2/b)$ where $b$ can be 2, 3 or 4. The Full Width Half-Maximum (FWHM) then has a Q-dependence (power law) of the form $Qb$ . The $I(Q,t)$ has been numerically Fourier transformed into $I(Q, \omega)$ and the $I(Q, \omega)$ have been fitted with functions of the form of a modified Lorentzian. These latter functions are used in the energy fitting procedures.

References:

J S Higgins, R E Ghosh, W S Howells & G Allen, JCS Faraday II 73 40 (1977)
J S Higgins, G Allen, R E Ghosh, W S Howells & B Farnoux, Chem Phys Lett 49 197 (1977)

JumpFit ¶

One of the models used to interpret diffusion is that of jump diffusion in which it is assumed that an atom remains at a given site for a time $\tau$ ; and then moves rapidly, that is, in a time negligible compared to $\tau$ ; hence ‘jump’.

Options ¶

Sample: A sample workspace created with either ConvFit or Quasi.
Fit Funcion: Selects the model to be used for fitting.
Width: Spectrum in the sample workspace to fit.
QMin & QMax: The Q range to perform fitting within.
Fitting Parameters: Provides the option to change the defautl fitting parameters passed to the chosen function.
Plot Result: Plots the result workspaces.
Save Result: Saves the result in the default save directory.

Categories: Interfaces | Indirect