Edge Fitting Analysis using EXAFSPAK: A Tutorial

Ingrid J. Pickering
December 2, 2001
Stanford Synchrotron Radiation Laboratory

Edge Fitting Analysis - How It Works

X-ray absorption spectroscopy probes all occurrences of a specific element in a sample, irrespective of the state (aqueous, crystalline, dissolved gas, etc.). The near-edge region (also known as XANES - X-ray absorption near-edge spectrum) is especially sensitive to the local structural and electronic environment of the element. Each type of chemical species can be thought of as having its own specific fingerprint, and the spectrum of a mixture of two or more chemical species of an element will quantitatively reflect the abundance of those species in the sample being measured. Hence, under favorable conditions, it is possible to use the edge to quantitatively analyze the different chemical forms present.

In order to do this, we need to record the spectra of a series of standard compounds which are candidates for what is in the unknown. These should be as similar as possible to what is there; for example, differences are found between crystalline solid and aqueous solution of the same compound, and between different allotropes of an element. Hence, the reliability of the results will strongly reflect the appropriateness of the standards used. Care should also be taken that the standards are collected under the same conditions as the sample, e.g. same energy resolution and conditions of calibration, as these may bias the results.

Having acquired a library of standard spectra, selected spectra are used in a least-squares fitting procedure to simulate the spectrum of the unknown. Once a "good" fit is achieved, the percentage contribution of a standard spectrum to the fit is considered to be equivalent to the percentage of the element present in that form.

The method works best for a small number of chemical components whose spectra are substantially different. It cannot be used to distinguish or quantitate between very similar spectra. Although it can work on relatively low elemental abundances, it cannot detect a trace of one chemical form of the element in presence of a large excess of another form of the same element.

Summary of Analysis

Analysis is carried out using the EXAFSPAK programs, which are written by Graham George of SSRL.

1. View the raw data (MVIEW)

Check the integrity of the raw data, including:

2. Calibrate individual sweeps (MCALIB)

Find the calibration point for each sweep and write to a file.

3. Generate averaged data (MAVE)

Specify sweeps and channels to average, shift each spectrum and form the total average.

4. Subtract backgrounds and normalize (PROCESS)

Generate an edge file for plotting and fitting, including:

5. Carry out edge fitting analysis (DATFIT)

Fit the unknown spectrum to a linear combination of library spectra.

A "How-To" Guide

The following is a tutorial of how to progress from XAS-Collect raw data files to an edge fitting analysis using the EXAFSPAK programs. It is written specifically for multi-element array detectors. For modification of the procedure for other detector configurations, click here.

1. View the raw data (MVIEW)

MVIEW is used to check the integrity of the raw data. Generally we collect two or more sweeps of each sample. Each successive sweep should be a reproducible copy of the first one, and each contains data from multiple detector channels. When examining the data, we are looking for a variety of problems, including bad channels, bad sweeps and distortions. For more information on the origin of problems, see Possible Problems with Data in the Detailed Description section. While there are many ways of examining the raw data, a couple are shown here and more plotting examples are listed below in the Detailed Description section.

Suppose we have five sweeps of data, collected using a multi-element detector:

MYSAMPLE_037.001
MYSAMPLE_037.002
MYSAMPLE_037.003
MYSAMPLE_038.001
MYSAMPLE_038.002
To examine individual fluorescence (FF) channels in a single sweep of 30-element data (NUM=7-19 for 13-element detector):
MVIEW/NUM=10-39/DEN=4 MYSAMPLE_037.001
For sum of fluorescence channels in all sweeps of 30-element data (NUM=7-19 for 13-element detector):
MVIEW/NUM=10-39/DEN=4/SUM MYSAMPLE_037.00*,MYSAMPLE_038.00*

2. Calibrate individual sweeps (MCALIB)

Ideally we calibrate each individual sweep using an "internal reference", a "foil" (or other standard material) set between the ion chambers I0 and I1. This is necessary because small changes in the experiment, such as shifts in beam position, changes in ring current or variations in detuning mean that the energy calibration changes slightly with time. For each data sweep we measure the transmittance spectrum of the foil and during analysis we use MCALIB to graphically determine the observed calibration point, generally the first inflection point. This is compared with a tabulated value, and the experimental data is shifted accordingly.
MCALIB/ELEM=AS/OUT=MYSAMPLE.CAL MYSAMPLE_037.001
By default the program uses log(I1/I2), and the smoothed first derivative. It also assumes a K-edge ( /EDGE=L3 will use the L3 edge). You will see a plot of the foil spectrum, the smoothed first derivative, and vertical lines marking peaks in the latter. If needed, use the left/right arrows to move the highlighted peak, but usually the strongest inflection is also the desired first inflection (an exception: for Mo K-edge, the strongest is the second, so need to move to the first). When the desired peak is highlighted, hit return to exit and write the calibration point to the specified file, in this example MYSAMPLE.CAL. Then repeat with each of the sweeps for this sample:
MCALIB/ELEM=AS/OUT=MYSAMPLE.CAL MYSAMPLE_037.002
MCALIB/ELEM=AS/OUT=MYSAMPLE.CAL MYSAMPLE_037.003
MCALIB/ELEM=AS/OUT=MYSAMPLE.CAL MYSAMPLE_038.001
MCALIB/ELEM=AS/OUT=MYSAMPLE.CAL MYSAMPLE_038.002
When done, MYSAMPLE.CAL will have a list of filenames, each energy calibration point, as well as the element and tabulated calibration point.

3. Generate averaged data (MAVE)

Next, we use MAVE to sum all the "good" channels and average over the "good" sweeps, apply the energy calibration and write the resulting averaged data file. MAVE is an interactive program - generally use defaults unless indicated below. For help in choosing array positions for other configurations, see here. In this example, we use the file MYSAMPLE.CAL generated by MCALIB and write the binary averaged file MYSAMPLE.AVE.
MAVE/OUT=MYSAMPLE.AVE/MCALIB=MYSAMPLE.CAL

   5 Files found :
   1    MYSAMPLE_037.001
   2    MYSAMPLE_037.002
   3    MYSAMPLE_037.003
   4    MYSAMPLE_038.001
   5    MYSAMPLE_038.002

Do you want to remove files from this list? [y/n] [N] : (use this to remove a file if needed)
Do you want to change file weights? [y/n] [N] :
Enter array position for eV  [3] :
Enter array position for rtc [1] :
Enter array position range for numerator   [7, 19] : 10,39 (7,19 for 13-element; 10,39 for 30-element)
Enter array position range for denominator [4, 4] :
 Do you want to take logs? [y/n] [N] :
 Do you want to change array position weights? [y/n] [N] : (use to remove a channel from all sweeps)
 Do you want to perform deadtime corrections? [y/n] [Y] :n
Statistical weights :
Enter 1 to calculate, 2 to use weights from file, 3 for unit weights [2] :
Do you want to exclude specific array positions? [y/n] [N] :(use to exclude channels in single sweeps)
Recalibration ...
Do you want to shift individual spectra? [y/n] [N] :     (see * below)
Enter apparent eV0, true eV0 [11865.5, 11867.0] :
Enter d-space, steps per degree [1.92016, 100000.] :
Enter Za, E0 [33.0000, 11885.0] :
My sample info
 File MYSAMPLE_037.001
 ...

* If the calibration points found are very similar, answer N. This will average all the sweeps and shift by the mean calibration difference. As this does not require interpolation of the data, this is preferable. However, if the calibration point is varying significantly (e.g. >0.3 eV for As or Se), averaging the data this way would broaden the spectral features. Therefore, in this case shift the spectra individually.

4. Subtract backgrounds and normalize (PROCESS)

Before we can compare and fit the edge spectra, we need to subtract pre-edge background and also to normalize the data using the program PROCESS. PROCESS is a menu-driven program which is started using:
PROCESS MYSAMPLE
The program automatically looks for the .AVE file.
The background from the array detectors typically decays from highest intensity at the lowest energy and is due to the tail of the scatter peak impinging on the window which is set around the fluorescence peak. We model it using a Gaussian, with some manually adjustable parameters. In doing so, we attempt to achieve:

Background subtraction

In PROCESS use menu option (1) to view the raw data then proceed to the background subtraction, using defaults unless otherwise indicated:
 Press 1 to subtract baseline file :
 Press 1 to plot baseline subtraction :
 Press 1 to subtract pre-edge :1
 Press 1 for polynomial pre-edge fit, 2 for Gaussian, 3 for erf function :2
Enter eV(low), eV(high) [0.0, 11840.0] :,11820                            (a)
Enter energy eV for middle of SCA window [10543.0] :
Enter window width, detector resoln. (eV) [750.000, 250.000] : ,700       (b)
Enter scaling factors a, b (y=a*y+b) [5.62004, .290140] :
 Press 1 to plot pre-edge result :1
(a) The eV(high) value should be below the onset of the edge. If the edge is strong, this value may need to be decreased from the default value.
(b) Change the second number ("detector resoln.") primarily to adjust the background until it looks good (flat and zero). A good starting value for Se and As is 700, but it may vary depending on the specific setup and the nature and strength of the sample. If the pre-edge looks "arched", increase this number, and vice versa.

To "try again" with different numbers, type Ctrl-Z and choose the baseline/pre-edge option (2) from the main menu.

For very weak samples (the scatter tail is by far the dominant feature, spectrum appears very noisy), the background is much more difficult tofit. Some suggestions to make it work:

Fitting the spline

Once a good background is achieved, we proceed to calculate the spline. This is a stiff function fitted through the oscillatory part of the spectrum above the edge, which will be used to normalize the spectrum. Either proceed on from the background subtraction or choose option (3) from the main menu.
 Press 1 to subtract Spline :1
Do you wish to reset to defaults? [y/n] [Y] :      (2nd or more type Y here)
Enter Spline eV(low) & eV(high) [11885.0, 12033.0] :
Enter order of Spline & No. of ranges [4, 3] :2 2     (use 2,2 for short edge range)
Enter k-weighting for spline [4] :
Enter 1 to use Victoreen [1] :
Enter 1 for k-spaced spline points [0] :
 Enter  1 Spline Points
Spline Point  0  [11885.0] :
Spline Point  1  [11959.0] :
Spline Point  2  [12033.0] :
Enter symbol for element [AS] :
Enter edge (K, L1,..) [K] :
Enter Victoreen Coefficients Cvic,Dvic [262.000, 95.4000] :
Enter Edge jump u0 for ratio (0 = auto) [0.0] :
Enter eV to calc. u0 [11905.0] :              (the spline value at this eV is used to normalize)
 Using calculated value for u0 (  0.22633    )
 final falloff was 0.97
 Press 1 to plot spline removal :
 Press 1 to plot spline removal + Victoreen :1
If the background has been well computed, then the spline (green) and the Victoreen (red) should overlay (for high energies, see above). If not, use Ctrl-Z to return to the background subtraction and tweak the "detector resoln." (increase if spline is sloping down too much to high energy, and vice versa). However, only change if the pre-edge remains visually flat.

Saving the changes

You should save the background-subtracted data and the spline parameters to the .AVE file. Note that the original, unprocessed data is also maintained in the same file, so if you change your mind you can return to PROCESS at a later date and recalculate the background. USe Ctrl-Z to return to the main menu, then (6) for file input/output, (1) to write .AVE file (use the same name), and (5) to return.

Writing the .EDG file

From the main menu, (7) for utilities, (1) to calculate deriv. etc, (1) to reset (use the defaults columns [1,6], which are energy and pre-edge subtracted data). If desired, use (2) to clip data. Then, select (3) to normalize and do not use the maximum but select the default value under "Enter y to normalize" - this is the value of the spline at the energy specified above. Then (8) to write the .EDG file, return and exit the program.

The .EDG file is an ASCII file which can be plotted using the EXAFSPAK program MULDAT or alternatively exported to another graph-plotting program.

5. Carry out edge fitting analysis (DATFIT)

First we need to create a library file for DATFIT. This is a text file listing the filenames of the standard compounds to be used in the fit. It can list more than will be used - we will get to pick the ones we want later. Traditionally this has extension .HLD, e.g. DATFIT_AS.HLD, and should include the locations of the standard files (if they are in a different directory to the unknown).
e.g. filename: DATFIT_AS.HLD
ARSENATE-AQ.EDG
ARSENITE-AQ.EDG
ASGS3.EDG
AS-ELEM.EDG
Launch DATFIT using
DATFIT DATFIT_AS.HLD
and select 1 to read in data.
Enter name of file to be fitted [ ] :MYSAMPLE.EDG
Enter col. nos for x,y [1, 2] :
Clip data - enter min. and max. x-values [2460.00, 2490.00] : 11840,11940
Enter parameter filename [ ] :MYSAMPLE.PAR
Enter No. of components for fit [4] :3
Component  1 - Select file by number [1] :
Enter col. nos for x,y [1, 2] :
...
It is a good idea to keep the fit range ("Clip data") fairly broad. For Se use 12600,12750.
Then choose option 2 to carry out the fit. The results of the fit are also written automatically to the text file DATFIT.LIS.
Component  1 - Enter initial fraction, eV shift [0.0, 0.0] : 0.2
              Enter 1 to fix fraction, eV shift [0, 1] :
...
Enter max. no of iterations [5000] :

Fit complete
( Info =  6 )
File MYSAMPLE.EDG                                   Edge
Energy range (eV) :   11840.0     -   11940.0
 #   Fraction       e.s.d.       eV-shift       e.s.d.     i i File
 1  0.257040      0.996237E-03  0.000000E+00  0.000000E+00 0 1 [-]ARSENATE-AQ.EDG
 2  0.101991      0.183439E-02  0.000000E+00  0.000000E+00 0 1 [-]ARSENITE-AQ.EDG
 3  0.637315      0.165220E-02  0.000000E+00  0.000000E+00 0 1 [-]ASGS3.EDG

     No. of function evals :      15
     No. of variables      :       3
     No. of data points    :     335
                  Residual :  0.117783E-03
                  Total    :  0.996346
                  D ratio  :   30.5793
 

E.s.d. - the estimated standard deviation derived from the diagonal elements of the variance-covariance matrix. Often we quote three times the e.s.d., which is the 99% confidence limit. Note that this is a measure of the precision of the parameter in the fit but not its accuracy. The accuracy of the result will be somewhat poorer and depends, in particular, on the appropriateness of the standards and the quality of the data.

Residual - the mean sum of squares of the differences between observed and calculated normalized intensities, S(Iobs-Icalc)2/N, where Iobsand Icalc are the observed and calculated normalized intensities, respectively, and the summation is over N data points. The smaller the residual the better the fit for a given unknown spectrum. Note that noise contributes to the residual so a noisy spectrum will always have a bigger residual than a clean one.

Total - the sum of the fractions, which ideally should be unity. Deviation from this indicates either that the spectra have not been normalized in the same way or that the standards used in the fit are not properly representative of the components of the sample.

D ratio - do not use.

Some suggestions:

Plotting - option 3. The following is an example of the plot of a fit using option 3 and 3 for fit + components. These plots are useful for diagnosing the fitting analysis; for plots for presentation purposes, see below.

Output - option 4. Two files can be written:

Enter filename for output [ ] : MYSAMPLE.OUT
Enter parameter filename [MYSAMPLE.PAR] :
The parameter file holds information on the component number, fractions and eV shifts (if any) for use in future fits.

The output file is a text file of various spectra. This can be used, together with the original .EDG file, to produce a custom plot in MULDAT. Alternatively, these files can be exported to another graph-plotting program. For a 3-component fit the columns are as follows:

1   - energy
2   - calculated fit spectrum
3-5 - spectra of components 1-3, with eV shifts (if any) applied but not scaled. (i.e. to generate a fit plot, scale these components by the respective fractions obtained).
6   - residual spectrum

What is a good fit?

What do the results mean?

Rarely can we say from the edge alone that we have unambiguously identified a specific species. More usually we can say that we have identified a type of species. For example, the identification of As(GS)3 in a fit is representative of As(III) with three RS- ligands, rather than glutathione specifically. Complementary analyses might assist in determining the likely precise nature of the ligands.

Modifications for different detector configurations.

Program Fluorescence using Lytle detector Transmittance Reference foil transmittance
MVIEW MVIEW/NUM=7/DEN=4 MVIEW/NUM=4/DEN=5/TAKE MVIEW/NUM=5/DEN=6/TAKE
MAVE numerator: [7,7] numerator: [4,4]
denominator: [5,5]
takelogs: Y		 numerator: [5,5]
denominator: [6,6]
takelogs: Y
PROCESS Polynomial background, order -1 or -2*. Polynomial background, order -1 or -2*. Polynomial background, order -1 or -2*.

*Adjust range and order to make a flat pre-edge and a coincident spline.

Detailed Description of Programs

MVIEW

Usage:    mview FILES [OPTIONS]
Options can be denoted by "-option" or "/option"
 

MVIEW options

MVIEW options

Default

Comments
/help none Displays all options for this program.

Data Manipulation:
/numerator=<arg> /num=7-19 Specify array of numerator channels. Can use range (e.g. 10-39), or pick (e.g. 12;13;14-17)
See table below for channel positions for different detector configurations.
/denominator=<arg> /den=4 Specify denominator channel(s). Generally den=4 for I0. Use den=1 to divide by count time only.
/takelog do not take log Take the logarithm of the specified (num/den).
/sumdata plot individual traces Sum all specified numerator channels.
/normalize do not normalize Normalize to the maximum intensity in each trace.
/abscissa=<arg> /abs=3 Specify abscissa (x-axis) channel. Energy is abs=3. Use 
abs=index to plot vs. point number.

Plot Style:
/xminimum=<arg>
/xmaximum=<arg>		 extent of data Specify plot range for x-axis.
/yminimum=<arg>
/ymaximum=<arg>		 extent of data Specify plot range for y-axis.
/cursors no cursors Invoke cursors to find position, mark or zoom (cursors can also be called by typing c with plot displayed)
/highlight no highlight Highlights (in yellow) single channel while remainder are in blue. Press space bar to cycle between channels.
/colours=<arg> default colour map Specify colours for plotting.
/points[=<arg>] no points Specify style of plot points. (0=single pixel, 1=squares, 2=triangles, etc)
/noline plot line Do not plot line (useful if plotting points).

Output:
/route=<arg> /route=TT: Specify plot to file (route=filename) or to screen (default, route=TT:).
/device=<arg> /device=10 Specify plot device type (10=x-windows, 2=regis, 8=postscript, 9=encapsulated postscript).
/xwindows=<arg> /xwindows=on Specify whether x-windows is used or not.
/write[=<arg>] do not write After plotting to screen, output to ascii file(s).

Keystroke files:
/logfile[=<arg>] none Record keystroke file (default logfile is MVIEW.LOG)
/recover[=<arg>] none Replay keystroke file (default logfile is MVIEW.LOG).
/dumb none No output to screen while replaying keystroke file (useful for file generation alone). 

 
 

MVIEW channel specification

Plot type

Specification
Incident intensity, I0 /num=4/den=1
Sample transmittance, log(I0/I1) /num=4/den=5/take
Foil transmittance, log(I1/I2) /num=5/den=6/take
13-element fluorescence /num=7-19
30-element fluorescence  /num=10-39
13-element incoming countrates (ICRs/I0) /num=20-32
30-element incoming countrates (ICRs/I0) /num=40-69

 
 

Possible Problems with Data
Nature of problem Description Possible fix at beamline Fix during data analysis
Monochromator crystal glitch Sharp peaks or dips, in all channels and all sweeps, caused by Bragg diffraction of the monochromator "stealing" intensity from main beam Try detuning more None
Windowing problem with single channel Single channel output has no edge jump (all sweeps) while others do. Window for this channel is not correct. Check windowing Exclude channel
Electronic problem with single channel Single channel is zero or has abnormally high noise (some or all sweeps) for a variety of possible reasons. Ask for help Exclude channel
Sample diffraction peaks Spikes or dips in individual channels, reproducible sweep to sweep. ICR channels have many extraneous peaks. This can occur if a composite sample has crystalline particles (e.g. a soil) or if a solution sample is frozen too slowly and forms ice crystals. If frozen solution, flash freeze or use glassing agent (e.g. glycerol). If peaks not too large, reduce total count rate. If visible in FF channels, exclude channel
Sample changing in beam Systematic change in edge shape from sweep to sweep, most likely caused by beam damage (or possibly reaction with air, etc.) To minimize photon damage, lower temperature (use lHe cryostat), and/or scan more quickly Use only 1st sweep (but may have already changed)
Beam motion Excursion in all channels of single sweep. Also present in I0. None (restart sweep) Exclude sweep
Short sweep MVIEW plot all bunched up in one corner. Run was terminated in middle of sweep. None (don't stop run in middle of sweep) Exclude short sweep from MVIEW plot
Countrates too high ICR maximum countrate above ~150k cps (for dilute) or 100k cps (for concentrated). Spectral features may appear "squashed" due to deadtiming. Move detector back Check transmittance data
Sample too concentrated Self-absorption means that fluorescence signal from a concentrated sample is distorted, irrespective of sample. If this is a standard solution, check the dilution. 5-10 mM is a good range for fluorescence. Transmittance data may be usable

More MVIEW examples

To examine specific fluorescence (FF) channels in a single sweep:
MVIEW/NUM=10-12;14;16;17-19/DEN=4 MYSAMPLE_037.001
For all individual fluorescence channels in all sweeps:
MVIEW/NUM=10-39/DEN=4 MYSAMPLE_037.00*,MYSAMPLE_038.00*
To examine individual total incoming countrate (ICR) channels in a single sweep of 30-element data (NUM=20-32 for 13-element detector), useful if looking for sample diffraction:
MVIEW/NUM=40-69/DEN=4 MYSAMPLE_037.001
To check actual countrates (ICRs) for a single sweep of 30-element data (NUM=20-32 for 13-element detector):
MVIEW/NUM=40-69/DEN=1 MYSAMPLE_037.001
To plot incident intensity I0 for all sweeps:
MVIEW/NUM=4/DEN=1 MYSAMPLE_037.00*

Acknowledgments

SSRL is funded by the Department of Energy, Offices of Basic Energy Sciences and Biological and Environmental Research; the National Institutes of Health, National Center for Research Resources, Biomedical Technology Program, and the National Institute of General Medical Sciences.