QENS DATA ANALYSIS - ku

QENS DATA ANALYSIS Workbook, 1st Edition This workbook is designed to instruct those neutron users new to the Quasi-Elastic Neutron Scattering technique about basic QENS data reduction. The learning approach adopted is guided analysis of real data to illustrate some of the challenges posed by actual problems and datasets. The worked examples chosen also illustrate the kind of information one can extract from a QENS experiment once data reduction is complete and analysis begins. The reduction and analysis process is specifically underpinned by the Mantid package. Mark Telling NBIAW, November 2014

Introduction To QENS Data

Reduction And Analysis

QENS DATA ANALYSIS

Mark Telling NBIAW, 10-14th November 2014 1

Introduction

This workbook is designed to instruct those neutron users new to the Quasi-Elastic Neutron

Scattering technique about basic QENS data reduction. The learning approach adopted is

guided analysis of real data to illustrate the challenges posed by actual problems and

datasets. The worked examples chosen (translational diffusion of water molecules and side

group rotation in peptides) also illustrate the kind of information one can extract from a

QENS experiment once data reduction is complete and analysis begins. The reduction and

analysis process is specifically underpinned by the Mantid package. Comments and

suggestions about this workbook are most welcome and should be sent to:

[email protected]

All the data files referred to in this workbook can be downloaded as a .zip file from:

www.isis.stfc.ac.uk/groups/muons/downloads/downloads4612.html

under Related Links

The Mantid project provides a framework that supports high-performance computing and

visualization of scientific data. Mantid has been created to manipulate and analyse neutron

and muon data, but could be applied to many other techniques. The framework is open

source and supported on multiple target platforms (Windows, Linux, Mac). Tailor made

data reduction and analysis procedures can be formulated using Python scripting. However,

this tutorial focuses on the reduction and analysis of QENS data collected from any neutron

instrument via a Graphical User Interface (GUI). This interface has been specifically designed

to guide the user through the data reduction and analysis procedure.

NB: All procedures have been tested using the Windows 7 installation and Mantid 3.2

mailto:[email protected]

http://www.isis.stfc.ac.uk/groups/muons/downloads/downloads4612.html



QENS DATA ANALYSIS


Mantid can be downloaded from, download.mantidproject.org For reliability choose the

‘Latest Stable Build’. However, as the interface is developing rapidly, the ‘Nightly

Development Build’ may contain additional features and bug fixes that are useful for data

analysis. The page, www.mantidproject.org/Main_Page contains a wealth of information

and supplementary information regarding the Mantid project and its functionality.

http://download.mantidproject.org/

http://www.mantidproject.org/Main_Page



QENS DATA ANALYSIS


Getting Started

To launch the main Mantid interface type: MantidPlot (Unix) or click on the Windows

desktop icon

The worked examples presented in this workbook will use two dedicated GUI’s. These are

launched by following: Interfaces > Indirect > Convert To Energy or Interfaces > Indirect >

Indirect Data Analysis from the tool bar at the top of the main MantidPlot window. Before

starting you should ensure that Mantid is configured for your needs. In particular you should

add paths to directories which contain the worked example data. To do this, click on File >

Manage User Directories. The window below will appear. Data can be added as a path by

browsing or typing the directory name in the field below Data Search Directories and then

clicking Add Directory. Once a path has been added, data stored in that location can be

accessed simply by entering the run number.

The Manage User Directories window



QENS DATA ANALYSIS


Basic Mantid Data Manipulation

This section explains:

the concept of workspaces

how to export data

how to use QtiPlot fitting

how to overlay data

I. Workspaces

Mantid utilises workspaces to hold data. These come in several forms, but the most

common is the Matrix Workspace which represents XYE data for one, or several, spectra.

The data contained in a workspace can viewed as a matrix or as a table, and graphed in

many ways including line graphs, contour plots and 3D graphs. Interaction with workspaces

is typically through a Graphical User interface. Matrix Workspaces are typically created by

executing one of Mantid's 'Load' algorithms or are the output of algorithms which take a

Matrix Workspace as input. In addition to data, workspaces hold a workspace history which

lists the algorithms that have been applied to the data.

Two types of workspace are listed in the Workspace List pane in the figure below

NB: In the following discussion workspace IRIS00057252 has been created by loading raw

data file via the LOAD button at the top of the Workspaces window and

IRS57252_graphite002_red has been created using the Interfaces > Indirect > Convert To

Energy GUI. These two methods of loading data will be discussed later

http://www.mantidproject.org/MatrixWorkspace

http://www.mantidproject.org/index.php?title=WorkspaceHistory&action=edit&redlink=1



QENS DATA ANALYSIS


The workspace list window

a) Workspace: IRIS00057252

Workspace, IRIS00057252, holds within it raw neutron counts / s for each individual IRIS

detector. To examine the data collected in a single detector, right click on workspace

IRIS00057252 and select Plot Spectrum. The following input fields appear.

Raw data plotting options



QENS DATA ANALYSIS


On IRIS, as way of example, there are 114 detectors hence ID numbers: 1-114 (1,2 = neutron

monitors, 3-53 = graphite analyser detectors, 54 - 107 = mica analyser detectors, 107 - 114 =

diffraction detectors). Enter a detector (ID) number and click OK to plot the associated raw

data. The raw counts / s for detector 5 are shown below. Alternatively, entering '5,10,20'

plots spectra 5,10 and 20 on one graph

Raw data (counts / s) collected in IRIS

detector no. 5 (left) and in detectors 5,10,20 (right)

NB: Click on the small arrows beside the workspace name to expand the entry and see

specific workspace information.

b) Workspace: IRS57252_graphite002_red

Contains corrected or _REDuced data converted from counts/s to counts/energy transfer.

Workspace IRS57252_graphite002_red contains only 10 spectra/histograms since the raw

data in workspace IRIS00057252 has been reduced and corrected such that a) only

detectors viewing the graphite analyser are included (i.e. 3 to 53) in the analysis and b) the

raw counts in every 5 detectors have been added together to give 10 output spectra.



QENS DATA ANALYSIS


II. Exporting Data

To export the data contained within any listed workspace click on the Algorithms tab at the

bottom of the workspace list pane. The options shown below should appear. Select

SaveAscii from the dropdown menu (beside Execute) and click Execute.

The SaveAscii Input Dialog box should appear. Select a directory (for the written data file)

and specify a file name. The workspace to be exported can be selected from the dropdown

list next to InputWorkspace. The user can also, for example, define which workspace spectra

i.e. indices (Min and Max) to export, choose the type of data separator used in the file (CSV

is usually a reliable option), add comments and decide whether to WriteXError.

The Algorithms options



QENS DATA ANALYSIS


The SaveAscii dialog box

III. QtiPlot

Enabling QtiPlot allows data sets and workspaces to be analysed using a suite of inbuilt

Origin fitting algorithms. To enable QtiPlot follow View > Preferences > Fitting. The following

window should appear. Select Enable QtiPlot Fitting

The Choose Default Settings window



QENS DATA ANALYSIS


When QtiPlot fitting has been enabled, and a data file has been plotted, Analysis appears in

the list of options above the main MantidPlot window toolbar.

Tool bar options at the top of MantidPlot. Analysis appears when QtiPlot is enabled

The fitting options found under Analysis are shown below

The QtiPlot analysis options



QENS DATA ANALYSIS


IV Overlaying Data

To overlay data, select the plot window in which you wish to compare data. Right click on

the plot window and select Add/Remove Curve. A list of available data sets will appear. As

an example, in the figure below we have the option of adding the data contained in the

workspaces IRIS_57252_H20_290K_002-sp-10 and IRIS_57252_H20_290K_002-sp-20 to the

plot window of IRIS_57252_H20_290K_002-5. To do so, first select the two spectra in the

left hand pane and then click the ‘right’ pointing arrow. Reversing this process removes data

from a plot window.

Add / Remove Curves options window

The plot style (line, scatter, line + scatter etc) of the added data set can be selected using

the New Curves Style drop down menu at the top of the Add/Remove Curve window.



QENS DATA ANALYSIS


Example One: translational diffusion

Aims

To reduce and correct (using Mantid’s in-built analytical and numerical integration

algorithms) QENS data collected from water (H2O @ 290 K)

To perform line width analysis and determine the diffusion coefficient of H20 at 290K

To compare the result with literature

To consider the limitations imposed by the experimental data on the analysis

Data files

File Name Sample Proton Current

___________________________________________________________________

IRIS_57242_H20_280K_002 Water 280 K 300.0 uamps




IRIS_57081_Van_RT_002 Van Cylinder 300.0 uamps

IRIS_56068_Empty_Annular_RT_002 Empty Annular Can 300.0 uamps



QENS DATA ANALYSIS


Task One: optimal sample thickness

To minimise multiple scattering effects (and hence complex correction procedures which

will not be discussed here) a sample’s thickness should be limited such that it scatters only

10 – 15 % of the incident beam. For more info about multiple scattering see: Bée M., Quasi-

Elastic Neutron Scattering, 1988, Adam Hilger, Chapter 4, p 107)

Using the Beer-Lambert relation below, calculate the optimal thickness of a water sample

Itrans = Iincidentexp(-nt)

n = number density

= total scattering cross section / formula unit

t = sample thickness

1. Calculate the thickness of the water sample

Task Two: Detector efficiency correction file

Different detectors will have slightly different efficiencies. The result is an observable

fluctuation in measured neutron intensity across a detector bank. Ideally, a wholly elastic

scattering sample should have the same measured intensity in all detectors. To correct for

such discrepancy, data is collected from a sample that only scatters neutrons elastically;

usually a thin walled vanadium cylinder ( ~ 10% scatterer). This measurement should be

performed before the actual experiment begins and then used to create a detector

calibration file that is applied to all subsequent measurements during analysis.



QENS DATA ANALYSIS


To create a detector calibration file using Mantid:

1. Launch the GUI: Interfaces > Indirect > Convert To Energy

2. Select the correct spectrometer

3. Click on the tab ‘Calibration’

4. Browse for the Vanadium Cylinder data file and Open

5. Select Create RES File (default limits are loaded but ensure Start/End < 0.5)

6. The calibration algorithm works by subtracting a background level and

integrating over the elastic peak for each of detector. The resulting integrals, or

areas, are then compared and a correction factor generated.

7. To see the resulting detector calibration and RES files

instrument’Run_No’_AnalyserReflection_calib

instrument’Run_No’_AnalyserReflection_res

check ‘Plot result’and Save Result and then Run Calibration

The IRIS57081_graphite002_calib file



QENS DATA ANALYSIS


Q. How might the calibration plot differ if you created a detector calibration file

using data collected from a 2mm thick flat vanadium plate oriented at 90o to the

incident beam?

A note on ‘Create Res File’: Choosing this option creates a workspace labelled

‘Instrument’Run_No’_AnalyserReflection_res’ which will be used later for QENS line width

analysis. The algorithm takes the experimental vanadium calibration data in each detector,

efficiency corrects the raw counts and sums all the spectra. The result / output is a single

high statistic instrument resolution file.

Q. What are the possible assumptions / limitations imposed by creating a RES file in

this manner?

Task Three: Applying the detector efficiency correction file to the data

1. Select tab Energy Transfer

2. Load data file ‘IRIS_57246_H20_290K_002’ in Run Files input field

3. Load the detector calibration file and check ‘Use Calib File’

4. In ‘Mapping’ select ‘individual’ – the mapping option allows you to define how

you group the detectors. The option ‘individual’ treats all 51 IRIS spectra

individually (surprise surprise!)

5. Select ‘contour’ from the ‘Plot Output’ options

6. Click ‘Run Energy Transfer’ and the contour plot below should appear (a new

workspace with detector efficiency corrected H20 290K data in it should appear

with the name ‘****_red’)

7. Reduced the empty sample can data (56068) in the same way



QENS DATA ANALYSIS


Efficiency corrected data : individual spectra : IRIS57246_graphite002_red

Tip: to visualise a workspace in 3D double click on the workspace name and the option ‘3D

plot’ will appear in the main taskbar

Q. How could you test that the detector efficiency corrections were being applied

correctly? Try it!

Task Four: Absorption corrections and empty can subtraction

The main correction to be applied to neutron scattering data is that for neutron absorption

both in the sample and its container, when present. For flat plate geometry, theses

corrections can be analytical and have been discussed, for example, by Carlile [C J Carlile,

Rutherford Laboratory report, RL-74-103 (1974)]. The situation for cylindrical geometry is

more complex and requires numerical integration. These techniques are well known, used in

liquid and amorphous diffraction and are described in the ATLAS manual [A K Soper, W S

Howells & A C Hannon, RAL Report RAL-89-046 (1989) H H Paalman & C J Pings, J Appl Phys



QENS DATA ANALYSIS


33 2635 (1962)]. The routines used here have been developed from the corrections

programs in the ATLAS suite and take into account the wavelength variation of both the

absorption and the scattering cross-sections for the inelastic flight paths.The application of

theoretical absorption corrections to experimental data is a 2-stage process.

Stage 1: Generate correction files based on user input sample and sample-can geometry

and composition information:

1. Launch the ‘Indirect Data Analysis’GUI

2. Click on ‘Calculate Corrections’

3. Input type ‘File’ and select detector efficiency corrected H20 file

4. Select ‘Use Can’ – this option will incorporate the effect of scattering from the

aluminium sample can. Deselect if you just want to treat the sample

5. The water data was collected using an aluminium annular can. Enter the 3 radii

and step size (see For Reference below). NB: The calculation cuts the cylinder

into several annuli where step-size is the radial increment. There are a minimum

number of annuli, n, required for reliable results (20) where n is determined

from n = (r2-r1)/step. If n < 20 then an error will occur. The smaller the step the

better the result but computing time increases.

6. Calculate number density and absorption / scattering cross sections for sample

and sample can. Enter calculated parameters. Number density in atoms/Å3.

NB In is possible to generate cross section information by entering the samples chemical

formula. For example, H2O is entered: H2-O but check the values generated in the Result Log

7. Select Plot Output ‘wavelength’, tick Save Result and click Run

8. Workspace ‘****_cyl_Abs’ should be created. This work space contains neutron

scattering and absorption data for both sample and sample-can as a function of

wavelength.



QENS DATA ANALYSIS


Stage 2: Apply correction file to experimental data and subtract scattering intensity from

empty sample-cell

1. Select tab ‘Apply Corrections’

2. Tick all relevant check boxes:

a. Tick ‘Use Corrections’ to apply the ‘****_cyl_Abs’ correction file to the data

b. Tick ‘Use Can’ to subtract empty sample-can scattering intensity

c. Tick ‘Scale Can By’ if exact number densities / neutron scattering properties

are unknown. The Scale value will adjust the intensity of the empty cell data

to avoid over correction (which may result in an inverted peak at E = 0)

3. Enter empty sample-can file or select workspace

4. Select ‘Plot Contributions’ to see relative intensities and Plot Output > contour

5. Select ‘Save Result’ and click ‘Run’

6. Two new workspaces are created. Depending on the level of correction

performed the workspaces will have different labels. For fully corrected data (i.e

absorption and empty cell subtraction) the extensions will be:

‘****_correct_RunNo_rqw’,

‘****_correct_RunNo_red’

‘****_correct_RunNo_result’

NB: For just empty can subtracted data ‘correct’ will be replaced by ‘subtract’

For Reference:

Aluminium has a Face Centre Cubic crystal structure with a lattice constant of

4.0495 Å and a density of 2.7 gcm-3



QENS DATA ANALYSIS


Total scattering and absorption cross sections can be found at:

http://www.ncnr.nist.gov/resources/n-lengths/

For annular geometry enter values of r1, r2 and r3 where:

r1 = inner sample radius

r2 = outer sample radius

r3 = outer sample radius + (2 x can wall thickness)

For the sample can use:

Inner sample radius = 1cm

Sample thickness = use calculated value from Task One

Sample can wall thickness = 0.06cm

Beam width = 2 cm

Task Five: Line-width analysis in energy

There are several approaches to QENS line width analysis; the method chosen is really a

matter of personal preference and can include basic least squares fitting or Bayesian

probability (D.Sivia, Physica B, 202, 332, 1994). Here we will use the former, and the ConvFit

option, to convolve N lorentzian functions with the instrument resolution file (and a

background if necessary) to get the best fit to the experimental data.

To perform line width analysis:

http://www.ncnr.nist.gov/resources/n-lengths/



QENS DATA ANALYSIS


1. In the Indirect Data Analysis GUI click on ConvFit

2. Select your corrected water data file

3. Select the _res file create in Task Two

4. Select Fit Type – One Lorentzian

Q. Do you need a background term? Include one for the purpose of this

demonstration

5. Adjust your starting parameters - fitting range (blue lines), background level etc.

If you want to Fix a parameter for all fits, right click on the Property name and

select Fix

6. Manually adjusting the red lines allows you to ‘guess’ a starting line width and

amplitude for your fit. To activate them, and visualise the effect of

broadening/narrowing the lorentzian, click Plot Guess – you can also adjust the

parameters of the lorentzian by using the Lorentzian 1 or 2 Property box

7. Select Plot Output (Single Run) and click ‘Run’ – this will plot the fit for just one

spectrum in a new plot window with the residual; the spectrum shown being

determined by the value in the first Spectra Range input field. Suggestion:

choose spectrum 10

8. If the resulting fit is poor adjust your fit parameters accordingly

9. When satisfied with the fit of one spectrum select the complete spectral range

for fitting, Plot Output : FWHM, check Save Result and click Run Sequential Fit

10. A plot of line width vs. Q will appear. The plot data (data, fits, result, residual) for

a sequential 1L fit will be written to workspace:

‘*****_graphite002_conv_1LFitL_’start’_to_’end’_Workspace’

11. All fit parameters will be written to table

‘*****_graphite002_conv_1LFitL_0_to_50_Parameters’



QENS DATA ANALYSIS


12. Graphs of line width and amplitude will be written to

‘*****_graphite002_conv_1LFitL_0_to_50_Results

Q. From a data analysis point of view, what are the limitations of the data that has

been collected?

Q. From an experimental point of view, what could you do to improve the results of

your analysis?

Task Six: Fitting

By modelling the Q dependence of the QENS line width, diffusion coefficients, residence

times and jump lengths associated with diffusive motions of molecules can be extracted.

Several models are proposed in the literature and each considers deviations from the

continuous diffusion model, or Fick’s Law, for specific environments when the mechanism of

the diffusion needs to be considered at smaller and smaller length scales i.e. larger and

larger Q. For a comprehensive overview see Bée M., Quasi-Elastic Neutron Scattering, 1988,

Adam Hilger, Chapter 5, p 148. As way of examples,

Model Function

________________________________________________________________

Fick’s law 6

))((22

2 QlDQQhwhm

The Chudley-Elliot Jump diffusion model (1961)

Ql

QlQhwhm

)sin(1

1))((



QENS DATA ANALYSIS


Diffusive modes in water:

i) Singwi and Sjölander (1960)

o

o

o DQ

lRDQQhwhm

2

1222

1

)exp(1

1))((

ii) Teixeira (1985) o

av

o

lD

DQ

DQQhwhm

6;

1))((

2

2

2

Use the Teixeira model, fit your line width data and extract root mean jump length, L =

<l2>0.5, the residence time, o , and ultimately the translational diffusion constant, D.

To code and fit a function in Mantid:

1. Click on the plot of line width vs. Q

2. Click on Analysis in the main Mantid window tool bar

3. Select Fit Wizard

4. Select Category > User defined

5. Enter a name for your new function

6. Enter the equation into the blank input field. For example, y=mx+c might be

coded:

Name: Linear Fit

Parameters: m, c

Entry on equation field: (m*x)+c

7. Save the file and click on Fit to launch the Fit Wizard dialogue box

8. Click Fit



QENS DATA ANALYSIS


Q. How do your values compare with values reported in the literature?

Q. A single lorentzian (and background) fit to S(Q,) is a greatly oversimplified

description of the water diffusion problem. Why? What does such a simple model

neglect?

Suggestions: Further Analysis

Process the 280, 300 and 310K data sets and extract mean squared jump lengths

and residence times. Do the results follow the trends presented in the Teixeira

paper?

Create a plot to compare of line width vs. Q vs. temperature and associated fits.



QENS DATA ANALYSIS


Example Two: localised diffusion

While QENS line width analysis can tell us a lot about the motion, or diffusive properties, of

molecules the Q dependence of the intensity of only those neutrons scattered elastically

(i.e. the intensity at E = 0) also contains a wealth of information; from the geometry of a

localised motion to transition temperatures. For more detailed information about the

science driving the following worked analysis please see:

pubs.rsc.org/en/content/articlelanding/2011/sm/c1sm05603d

Aims

To reduce and correct elastic incoherent scattering data collected as a function of

temperature from the lyophilised protein, apoferritin.

To identify transition temperatures via analysis of the elastic scattering intensity

To investigate the effect of hydration upon the protein via analysis of the mean

squared displacement

To investigate the Q-dependence of the line width associated with a localised mode

To determine the elastic incoherent structure factor (EISF) associated with the

dynamic process



QENS DATA ANALYSIS


Data files

File Name Temp Sample Start Temp / Increment Proton Current

___________________________________________________________________________

IRS38113 10 K Dry Apo 300.1

IRS38114 to IRS38156 Dry Apo Start Temp 15K T=5K 30.1

IRS38157 300 K Dry Apo 1687.9

IRS56016 290K Empty Flat Plate Cell 526.1

OSI65560 5K Hydrated Apo h=0.14 65

OSI65562 to OSI65608 Hydrated Apo h=0.14 Start Temp 10 K T=10K 65

OSI65610 to OSI65636 Hydrated Apo h=0.14 Start Temp 245 K T=5K 65

OSI73075 4K Empty Flat Plate Cell 65

OSI65437 10K Hydrated Apo h=0.31 80

OSI65439 to OSI65495 Hydrated Apo h=0.31 Start Temp 20 K T=10K 65.1

OSI73075 4K Empty Flat Plate Cell 160.1

Task One: Detector efficiency correction file

1. Taking the DRY (aka LYOPHILISED) PROTEIN data only! Follow the procedure set

out in Example 1: Task 2. However, this time create a detector efficiency file

from the sample itself measured at low temperature.

NB: This approach should ONLY be used if the temperature of the sample is low enough that

you are sure that ALL scattering is elastic! The advantage of this approach, however, is that



QENS DATA ANALYSIS


you have a direct measure of absorption effects from both sample and sample can as well as

correction for the orientation of the sample can should a flat plate cell be used.

Q. What might be the disadvantages of this method when creating a RES file from

experimental flat sample-can data?

Task Two: Applying the detector efficiency correction file to the data

1. Create a suitable detector mapping file (****.map) to process individual

detectors BUT such that the ‘dead’ detectors seen in the efficiency plot are

removed from all subsequent analysis. A mapping file should have the following

structure:

3 ; number of spectra to be created

1 ; spectrum 1

13 ; number of detectors to be added

3 4 5 6 7 8 9 10 11 12 13 14 15 ; detector nos

2 ; spectrum 2

5

16 17 18 19 20

3

5

21 22 23 24 25

The mapping file above will create 3 spectra. These spectra will be the sum of

counts in detectors 3-15, 16-20 and 21-25



QENS DATA ANALYSIS


3. Check that the mapping file is applied correctly

4. Apply the detector efficiency correction and mapping file to all the lyophilised

data in the Data Files list above so you have a _red file for 38113 > 38157 and

also for the empty cell

Task Three: Empty sample can subtraction

1. Follow the procedure set out in Stage 2, Example 1: Task 4 to subtract the empty

cell from all detector efficiency corrected data files

Task Four: Analysis of the elastic scattering intensity

Since energy must be conserved during the scattering process, any onset of QENS

broadening must result in an associated decrease in elastic scattering intensity. Monitoring

the elastic scattering intensity, I(Q,T, ≈ 0), as a function of temperature and momentum

transfer therefore allows ‘transition’ temperatures to be identified. To analyse the intensity

of the elastic peak from our lyophilised protein:

1. Select the Indirect Data Analysis GUI

2. Click on the Elwin tab

3. Select the ‘_subtract_’ data files which correspond to temperatures 15K to 290K

4. The blue lines show the range over which integration of the elastic line will be

performed

Q. Does this range seem suitable? Remember ONLY neutrons scattered

elastically should be included in the analysis



QENS DATA ANALYSIS


7. Check Save Result and click Run

8. Three workspaces are written:

‘Inst’First Run No’_AnalyserReflection_to_’Last Run No’_eq1’ = intensity vs. Q

vs. temp

‘Inst’First Run No’_ AnalyserReflection _to_’Last Run No’_eq2’ = ln(intensity)

vs. Q2 vs. temp (for mean squared displacement analysis)

‘Inst’First Run No’_ AnalyserReflection _to_’Last Run No’_elf’ = intensity vs.

Q vs. temp

NB: if only one data file is processed using ELWIN the output workspaces will be named

‘inst’Run No’_ AnalyserReflection _eq'N'’ and ‘inst’Run No’_ AnalyserReflection _elf’

NB: depending on when a data file was collected, the x-axis in the .elf workspace will be

either the last 3 digits of the run number (i.e. 38113 > 113) OR the temperature associated

with the measurement. Sample temps will be used if the raw data file has a temperature log

associated with it. For example, when loading 38113, Elwin looks for SE Log Name: sample.

However, this log name does not exist in the raw data log information (right click on the

irs38113_graphite002_red and open Sample Logs) In contrast, irs27252_graphite002_red

does contain a temperature log Name called sample

9. Select the ‘_elf’ file > right click > Plot Spectrum With Errors > enter 3 spectrum

values of your choice (suggestion: 10,30,40) and click OK. Alternatively, plot the

‘_elf’ file in 3D

Q. What do you notice? Is the elastic intensity constant as a function of run

number?

Q. Is the data too ‘noisy’? If so, how could you reduce the ‘noise’?



QENS DATA ANALYSIS


Task Five: Mean square displacement, <r(T)2>, analysis

The mean square displacement, <r(T)2>, of atoms in a material can be extracted from elastic

neutron scattering intensities, I(Q,T, ≈ 0), by fitting,

))(3

1exp()0,,()0,,( 22 TrQTQITQSinc (1)

Strictly speaking, this form is valid for harmonic oscillations or equivalent atoms. Any

deviation from harmonic behaviour is noted as the activation of an-harmonic behaviour.

Experimentally, harmonic to an-harmonic behaviour is usually identified by an inflexion in

the temperature dependence of <r(T)2>. Equation (1) is only valid in the low-Q regime.

However, <r(T)2> still proves itself to be a useful tool for relative changes in <r(T)2> as a

function of, for example, hydration level, temperature and / or sample.

3exp

22 rQFit



QENS DATA ANALYSIS


To extract <r(T)2> from the elastic scattering created in Task Four:

1. Select tab MSD Fit

2. Browse for and load the ‘_eq2’ file

3. Select one of the higher temperature spectra to display using Plot Spectrum

(suggestion : 30)

4. Eq (1) above will be fitted to data points delineated by the blue lines.

Q. Does the fit range in Q look suitable? If not, adjust the range by modifying StartX

and EndX in the MSD tab Property field or drag the blue lines on the plot

5. Check Plot Result and Save Result

6. Click on Run to fit the data on screen OR Run Sequential to fit all temperatures

7. The fit of Eqn (1) to the data on screen is shown

8. Three workspaces are created:

Inst’First Run No’_graphite002_to_’Last Run No’_msd_Workspaces – contains

individual workspaces with raw data, associated fits and residuals

Inst’First Run No’_graphite002_to_’Last Run No’_msd – contains the initial

amplitude (A0) and gradient (A1) vs run no/temp

Inst’First Run No’_graphite002_to_’Last Run No’_msd_Parameters – table of

A0 and A1 vs run number / temperature

16. To see <r2> vs. temperature - right click on ‘Inst’First Run

No’_graphite002_to_’Last Run No’_msd’ and select Plot Spectrum With Errors.

Right click on the plot window that appear, select Add/Remove Curve and

remove workspace ‘_a0’



QENS DATA ANALYSIS


Q. Is there a change in the slope of <r(T)2>? If so, does it broadly correspond with

the temperature at which the elastic intensity starts to decrease?

NB: if no temperature information is included in the output files then the temps will have to

be entered manually by viewing the table in workspace Inst’First Run

No’_graphite002_to_’Last Run No’_msd_Parametersand changing the x-axis values

Task Six: <r(T)2> and the effect of hydration

1. Now repeat the data reduction, ELWIN and MSD Fit analysis detailed above

using the hydrated protein data sets. Plot the resulting <r(T)2> from the

hydrated materials on top of the lyophilised protein response.

Q. What do you notice?

Q. Should you actually compare the three experimental data sets?

Q. If so, what is this result telling you about the protein?

Task Seven: Line width analysis in time

Experimentally, the measured scattering function, Smeasinc(Q,), is a convolution of Sinc(Q,)

and the resolution function of the neutron instrument, R(Q,). For spectrometers operating

in Q- space, Smeasinc(Q,w) = Sinc(Q,) ⓧ R(Q,). In its simplest form the instrument

resolution approximates to a Gaussian or Lorentzian function of finite width, res (usually

quoted as full width at half maximum). As we saw in Example 1, using either a measured or

theoretical R(Q,), least squares fitting or Bayesian analysis routines can be used to isolate

the intensities and widths of the spectral contributions to Sinc(Q,). Here, however, we will



QENS DATA ANALYSIS


adopt an analysis method which relies on the Fourier transform of the measured scattering

function.

The merits of fitting in the time regime are discussed in V. Arrighi, J. S. Higgins, A. N. Burgess

and W. S. Howells, Macromolecules, 1995, 28, 4622–4630. Using Fast Fourier Transform

(FFT) methods, the measured QENS and resolution spectra are converted to the time

domain. Deconvolution of R(Q,) and Smeasinc(Q,), is achieved by simply dividing the Fourier

response of the sample by that of the resolution. The result is the time-dependent

intermediate scattering function, I(Q,t). In the simplest case, a single relaxation process will

manifest itself in the time domain as a simple exponential, I(Q,t) = Ao(Q) + [1 -

Ao(Q)]exp((t/). Here, is the relaxation time and Ao(Q) is the Elastic Incoherent Structure

Factor (EISF). A system that exhibits a distribution of relaxation rates, however, may be

better described using the Kohlrausch–Williams–Watt (KWW), or stretched exponential,

form i.e. I(Q,t) = Ao(Q) + [1 - Ao(Q)]exp(-(t/KWW))

It should be noted that here KWW is an effective relaxation time which is dependent upon

both T and , or more correctly the temperature dependence of the spectral shape of the

distribution. Non-exponential behaviour is immediately apparent should the stretching

parameter fall below unity. Another advantage of converting S(Q,) to I(Q,t) is for direct

comparison with data collected using NSE. Such comparison can allow relaxation

phenomena to be followed out to much longer time scales and thus modelled with much

greater certainty; at least at certain momentum transfer vectors.

In this task we will look to analyse data taken at 300K in the time domain. Analysis is a 2

stage process i.e. first we FFT the spectra, changing energy to time, and then we fit.



QENS DATA ANALYSIS


Stage 1:

1. Using the Convert To Energy GUI, reduce data file 38157 (lyophilised protein,

300K) such that a) run 38113 (lyophilised protein, 10K) is used to create the

detector efficiency file and b) a suitable mapping file is produced that collates

every 5 detectors.

2. Reduce the empty sample-can data and the base temp sample file as above

3. Using the Indirect Data Analysis GUI, subtract the empty sample-cell data from

both reduced sample files

4. Select Indirect Data Analysis > Fury

5. Browsed for the 300K '_subtract_' data file and Plot Input

7. For Resolution, browse for the 10K '_subtract_' data file

8. Adjust Elow, Ehigh and Ewidth to be -0.5, 0.01 and 0.5 respectively

9. Check Save Result and click Run

10. The resulting workspace from Fury analysis is named 'inst'Run

No'_AnalyserReflection_iqt'

I(Q,t) data for spectra 1,4,7, 10 from IRS38157_graphite002_iqt



QENS DATA ANALYSIS


Stage 2:

There are several options to fit I(Q,t) curves a) the FuryFit GUI, b) creating a user defined fit

function in Fit Wizard or c) using an external program such as DAVE

FuryFit: The following details how to perform I(Q,t) analysis using the FuryFit GUI – a GUI

very similar in operation to the ConvFit analysis tool described earlier.

1. Select File or workspace IRS38157_graphite002_iqt. A plot of the data in

spectrum ‘N’ will appear (default for ‘N’ is spectrum 0). Select spectrum 5

2. Select Fit Type: 1 Stretched Exponential

3. Click Constrain Intensities to insure that the sum of the initial amplitudes of all

individual fit components is 1

4. Define the range of the fit by either entering values in the StartX / End X fields or

dragging the blue lines on the plot

5. Define the background level by either entering values in the LinearBackground

field or by dragging the green base line up to the required level

6. Selecting Plot Guess automatically adds a ‘fit’ to the data based only the initial

values associated with each fit function Property.

7. Once initial values are set, click Run to fit the spectrum displayed in the GUI only

NB Selecting Plot Output launches a new window (when Run is pressed) showing the single

fit, data and residuals in greater detail and only over the x and y fit range entered

8. Function parameters can be fixed by right clicking on the parameter name and

selecting Fix. Fixed parameters are un-fixed by following the same procedure



QENS DATA ANALYSIS


9. Once happy with the fit of a single spectrum, select which fit parameter to plot

(e.g. tau, intensity or beta), select Save Result and click Run Sequential Fit to

analyse all the spectra

10. Three workspaces are created:

Inst’Run No’_graphite002_fury_1S_s0_to_9_Result – contains fit parameter

values for all spectra in WORKSPACE form which can be plotted individually

Inst’Run No’_graphite002_fury_1S_s0_to_9_Parameters – contains fit

parameter values for all spectra in TABLE form

Inst’Run No’_graphite002_fury_1S_s0_to_9_Workspace – contains data (ID

0), fits (ID 1) and residuals (ID 2) for each spectrum. Expand the workspace

(click on the side arrow) to see individual spectrum workspaces. To create the

multi-plot below, select four workspaces > right click > Plot Spectrum > enter,

0-1 (for data and fit only)

I(Q,t) data and sequential fits for spectra 1,4,7, 10 from IRS38157_graphite002_iqt



QENS DATA ANALYSIS


11. Examine the fits and fit parameters. Are they reasonable? Are any fit parametrs

constant (within error) as a function of Q? Could any be fixed at a single value to

reduce uncertainty in the other parameters?

NB If beta is constant, within error, then it can be constrained at a mean value by either a)

FIXING the parameter OR b) clicking Constrain Beta Over All Q. The latter creates the output

files detailed above BUT with the additional description _1Smult

12. Analyse the I(Q,t) data using FuryFit and ensure you can broadly replicate the

plots in the reference SoftMatter paper.

NB: for consistency with the data in the SoftMatter paper fix beta at 0.64

Fit Wizard: Analysis can also be performed using the Fit Wizard GUI described earlier. As

such only additional information required to analyse the data will be given below.

1. Using irs38157_graphite002_iqt, create a plot showing all I(Q,t) curves > right

click, Plot Spectrum, enter spectrum ID numbers : 1-10. Adjust axis values to: x =

0 to 0.1. y = 0.82 to 1.02

2. Click on the graph that appears and select Main Menu > Analysis > Fit Wizard

3. Create and save a new User function with the form : (1-A)*exp(-(x/t)^B))+A

4. Select Fit With Selected User Function and click Fit >>

5. In Custom Output >> click One Table For All Fits, click Parameter Table and then

<< Fit. A new table named Parameters should appear

6. Select Curve ***-sp-1, change fit range to x = 0 to 0.1 and click Fit. The fit

parameters should be appended to the Parameter table

7. Repeat for Curves ****-sp-2 to ****-sp-10

8. Manipulate the fit parameters and plot the Parameter table values to replicate

the plots in the reference SoftMatter paper



QENS DATA ANALYSIS


DAVE: For completeness, the following details how to perform I(Q,t) analysis using the very

versatile IDL based package, DAVE, which can be downloaded

here:www.ncnr.nist.gov/dave/ Taking a ‘monkey-see-monkey-do’ approach to speed up

analysis…

1 In Mantid, click on the Algorithms tab

2 In the Execute input field, type SaveDaveGrp and click Execute

3 A new dialogue box will appear which will allow us to convert the Mantid

'inst'Run No'_AnalyserReflection_iqt' file into a format DAVE can read. Select the

relevant '_iqt' file, check ToMicroEv and enter a filename for the written dataset

4 Click Run

5 Launch DAVE by typing Dave

6 In the DAVE Gui > File > Preferences : Set Data And Working Directory

7 Load your I(Q,t) file by following: Data Input/Output > Read Dataset From > ASCII

8 Click on OK when the Specify Axes Labels For Data window appears

9 Data Input/Output > Write Dataset As > DAVE - a file with the extension .dave is

created in your working directory

10 Analysis > 1D Peak Fitting (PAN). The PAN GUI will launch and the data in the

.dave file should be visible in the plot window

11 In the PAN GUI, define the fit range by following File > Preferences and check /

enter the following:



QENS DATA ANALYSIS


9. Click Accept and the Dismiss

10. To write a function: Select Function > Userfunction. Create a simple exponential

decay function. Save your expression

Q. Do you need to add a background to your equation? What does any background

(or asymptotic I(Q,t) level) intensity tell you?

11. Click Accept > enter suitable start values > click Apply And Dismiss

12. Click Fit Current Group

Q. Does a simple exponential provide a suitable description of the data? Note: linear

axes can be deceptive! Examine the data with logx and logy axes by following

Plot_Options > XLog and YLog. Focus the plot range by following File >

Preferences. Suggestion: x = 0.01 to 0.1 and y = 0.87 to 1.0

13. Click Fit All Groups and examine the goodness of fit at different Q values.

14. Click Clear All Curves and create a new stretched exponential function. Refit the

data



QENS DATA ANALYSIS


Q. Is the stretched exponential description more appropriate? What does the

stretched exponential form tell you about the internal mobility of the protein?

15. To examine the resulting fit parameters click > Plot Fit Parameter and select the

parameter to view. For example, for the simple exponential model Parameter #0

will probably be the background level and Parameter #1 will probably be the

decay time,

Q. Compared to the water example would you say that the relaxation rate, , is Q

dependent?

Q. What does a Q independent relaxation rate suggest about the motion being

probed?

Q. To improve the fit / reduce errors could you ‘fix’ one of the parameters in your

model? Refit the data with or fixed. To perform a new fit, first click on Clear

All Curves and then follow the procedure above

Task Eight: Fitting the Elastic Incoherent Structure Factor (EISF)

The EISF, Ao(Q), provides information about the geometry of a particular localised motion

and can be extracted from I(Q,t) if the decay curve reaches a ‘plateau’ at 'long' decay times.

From the I(Q,t) analysis above, the Q dependence of the background level gives reasonable

access to the EISF; or, in the case of a partially mobile sample as is the case here, an

‘effective’ structure factor.

The theoretical Q dependence of elastic scattering intensity has been computed for many

different types of localised motions. For a comprehensive list see Bée M., Quasi-Elastic

Neutron Scattering, 1988, Adam Hilger, Chapter 6, p 200). As examples:



QENS DATA ANALYSIS


Ao,CH3(Q) = 1/3[1 + 2jo(Qr√3)] the theoretical EISF expected for a proton undergoing

a localised 3-fold jump rotation. r = 1.032 Angstrom

and jo is the zero-order Bessel function.

Ao,jump(Q) = 1/2[1+jo(Qd)] the theoretical EISF response predicted for protons

undergoing 2-site jumps of distance, d

Ao,diff(Q) = |(3j1(Qr))/Qr|2 the theoretical EISF response predicted for protons

diffusing on a sphere of radius, r,

Use the equations above to model the EISF response generated from your I(Q,t) analysis.

NB: when fitting the model EISF functions remember that your experimental EISF is in fact

an ‘effective’ EISF since only a certain percentage of the sample is actually ‘mobile’ – the

theoretical EISF functions assume the entire ‘sample’ is mobile! The theoretical expressions

therefore have to be ‘modified’ to reflect this :

1. From your Mantid I(Q,t) FuryFit analysis, plot the Q-dependence of your

background parameter

2. Fit the data using FitWIzard and the three EISF expressions above; suitably

modified to describe an ‘effective’ EISF

Q. Which of the three models provide the best description of the experimental data?

Q. From your fits, what percentage of the protons in the material is mobile?

Q. What would you need to do to truly ascertain the model which best describes the

experimental data?



QENS DATA ANALYSIS


Suggestions: Further Analysis

By modelling the temperature dependence of for the lyophilised material,

determine a mean activation energy, Ea, ave, for the protein dynamics observed.

How does this compare to Ea, ave determined from other dry proteins?



QENS DATA ANALYSIS


Example Three: Dental Cements

Right....now we have all the tools to explore QENS data we will focus on data collected from

dental cements; data which is so far is unanalysed and the 'result' unknown. The rational

behind this work is given in the proposal (raw data directory) submitted to gain access to

beam time on the IRIS instrument. Use the various data analysis methods explored in

Examples One and Two to gain insight into the role of water in the solidification of dental

cements. Don’t forget to make use of advice from all the experimental team!

Data Files

File Name Temp Description

___________________________________________________________________________

54638-40 2 K 28 day old HEMA cement

54635-36 310 K

54641-54698 15 – 300 K Elastic Window Scan Data

54435, 54498, 54499 310 K Liquid POLY

54436, 54497 300 K

54437, 54438 10 K

54439 - 54496 15 – 300 K Elastic Window Scan Data

53593 310 K Liquid HEMA

53594 300 K

53595 + 53596 10 K

53583 290 K Vanadium

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