Framan 4.9
User Manual
for
Frequency Response Analysis (FRA)
for Windows
version 4.9
Eco Chemie B.V.
P.O. Box 85163
3508 AD Utrecht
The Netherlands
 Copyright 2007 Eco Chemie
Table of contents
3
1. PRINCIPLES OF OPERATION ......................................................................................................5
1.1 Preface ................................................................................................................................................5
1.2 The concept.........................................................................................................................................5
1.3 The instrument and hardware description...........................................................................................7
2. GETTING STARTED WITH FRA ................................................................................................11
2.1 Recording an Impedance spectrum...................................................................................................12
2.2 Manual control..................................................................................................................................13
2.3 Data manipulation with FRADEMO ................................................................................................14
2.4 Measuring double layer capacitance as a function of potential. .......................................................16
3. THE FRA WINDOWS .....................................................................................................................19
3.1 FRA Manager window .....................................................................................................................19
File menu ........................................................................................................................................19
Method............................................................................................................................................22
Utilities ...........................................................................................................................................23
Options ...........................................................................................................................................25
Project ............................................................................................................................................26
Window ...........................................................................................................................................30
Help ................................................................................................................................................30
Tool bar ..........................................................................................................................................30
3.2 Status bar ..........................................................................................................................................31
3.3 Autolab manual control window.......................................................................................................31
Current range .................................................................................................................................31
Settings ...........................................................................................................................................32
Noise meters ...................................................................................................................................32
Potential .........................................................................................................................................33
iR-compensation (not yet possible).................................................................................................33
3.4 FRA Settings window.......................................................................................................................33
3.5 FRA manual control window............................................................................................................34
3.6 Data presentation window ................................................................................................................35
Copy................................................................................................................................................36
File..................................................................................................................................................36
Save work data................................................................................................................................36
Merge..............................................................................................................................................36
View ................................................................................................................................................36
Plot .................................................................................................................................................40
Analysis...........................................................................................................................................43
Edit data .........................................................................................................................................45
Editing graphical items and viewing data ......................................................................................47
3.7 Edit procedure window.....................................................................................................................49
Pre-treatment..................................................................................................................................50
Edit frequencies ..............................................................................................................................50
3.8 Analysis results window ...................................................................................................................51
4. MEASUREMENTS ..........................................................................................................................53
4.1 Advice on measurements ..................................................................................................................53
4.2 Internal / External measurements .....................................................................................................53
4.3 Time, potential and current measurements .......................................................................................53
4.4 Time scan..........................................................................................................................................53
4.5 Single and Multiple Sine-waves .......................................................................................................54
4.6 The measurement sequence ..............................................................................................................54
4.7 Technical background.......................................................................................................................55
4.8 Measurements using an Automatic mercury drop electrode.............................................................57
4.9 Sequence of measurements in case of synchronised measurements .................................................57
4.10 Measurements at open circuit potential ..........................................................................................58
APPENDIX I FRA DATA FILES .......................................................................................................59
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APPENDIX II BANDWIDTH AND GAINS ......................................................................................61
APPENDIX III DEFINITION OF PROCEDURE PARAMETERS ...............................................63
APPENDIX IV COMBINATION OF GPES AND FRA...................................................................67
APPENDIX V NOISE CONSIDERATIONS .....................................................................................69
APPENDIX VI SPECIFICATIONS ...................................................................................................71
Hardware specifications.................................................................................................................72
Software specifications ...................................................................................................................73
APPENDIX VII THEORETICAL CONSIDERATIONS ON THE PERFORMANCE OF FRA
INSTRUMENT .....................................................................................................................................75
Effect of integration time on noise rejection...................................................................................75
Effect of noise on impedance measurements ..................................................................................76
Effect of non-stationary dc-current.................................................................................................77
Effect of measurement resolution ...................................................................................................78
APPENDIX VIII FIT AND SIMULATION.......................................................................................79
Circuit description code (cdc) ........................................................................................................79
File menu ........................................................................................................................................80
Edit menu........................................................................................................................................81
Options menu..................................................................................................................................81
Using fit and simulation..................................................................................................................83
APPENDIX IX KRAMERS-KRONIG TEST....................................................................................87
The Kramers-Kronig test ................................................................................................................87
Using the Kramers-Kronig test.......................................................................................................89
APPENDIX X HYDRODYNAMIC IMPEDANCE MEASUREMENTS........................................91
INDEX ...................................................................................................................................................93
Chapter 1
Principles of operation
1. Principles of operation
1.1 Preface
Autolab and the Frequency Response Analysis system software (FRA) provide fully
computer controlled electrochemical impedance spectroscopy.
This powerful technique can be used in the study of, for example, electrode kinetics,
electro deposition, corrosion, and membranes.
The instrument is controlled by a personal computer. The Autolab configurations
supported by FRA are:
•
Autolab with potentiostat/galvanostat PGSTAT10 and FRA modules
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Autolab with potentiostat/galvanostat PGSTAT12 and FRA modules
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Autolab with potentiostat/galvanostat PGSTAT20 and FRA modules
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Autolab with potentiostat/galvanostat PGSTAT30 and FRA modules
•
Autolab with potentiostat/galvanostat PGSTAT100 and FRA modules.
The FRA combines the measurement of data and its subsequent analysis. The
"Installation and Diagnostics" guide describes its installation.
The user should be familiar with MS-Windows.
The FRA program consists of two distinct parts, i.e.:
•
The user-interface, graphics and data-analysis software.
•
The routines that perform all the communication with the Autolab instrument.
Familiarisation with FRA is best obtained by experimenting. The on-line help within
the program provides most of the required help, which may be necessary to perform
the measurements and the data analysis.
This manual concentrates more on explaining the general concepts and backgrounds
than on guiding the user through the program. Moreover, this manual tries to explain
the possibilities of FRA. Please keep this manual together with the "Installation and
Diagnostics" guide. The latter guide explains the installation.
1.2 The concept
The FRA screen consists of several windows: one for manual control over the
potentiostat/galvanostat, one for data presentation and manipulation, one for entering
the experiment parameters, one for viewing the FRA settings, and one for controlling
the FRA modules. Surrounding windows, menu options, and tool bars give extra
facilities like cell-diagnosis, accessory control, Autolab configuration, access, and
data transfer to programs like Excel and MS-Word.
The MS-Windows related terminology used in this manual is in agreement with the
standard as described in the book "The GUI Guide - international terminology for
Windows Interface" (Microsoft Press, Washington ISBN 1-55615-538-7).
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The following mouse conventions are used:
•
Quickly pressing and releasing the mouse button is called "clicking". A click of
the left mouse button on a menu option, a button, an input item on the screen,
etcetera will result in an action.
•
Clicking and holding down the left mouse button is called "dragging" and is used
for several purposes. You can focus on an item on the screen without an action.
You can drag a window when the mouse pointer is in its title bar. It can be used to
shrink or to enlarge a window when the mouse pointer is on the border of a
window. Finally, you can drag a scroll bar, a slider, or a zoom-panel.
•
A double-click of the left mouse button is used to perform particular actions.
Except for the standard uses in window actions, it is used to edit the graph in the
Data presentation window.
•
A click of the right mouse button is used to open a zoom panel in the Data
presentation window, or to shrink or enlarge the Graphics panel in the Print menu
window. This panel appears after selecting Print from the File option in the FRA
Manager window
The following keyboard functions are supported:
•
RETURN/ENTER key:
jump to next data input field;
select menu option; or
click button with focus.
•
left and right arrow key:
move cursor in data input field.
•
up and down arrow:
move up and down in a menu.
•
ALT:
puts focus on the menu bar of the window with the focus;
typing a subsequent underlined character will move the cursor to the
corresponding menu item; and
a RETURN/ENTER will select the menu item.
•
ESC: aborts the execution of the measurement procedure.
•
F1: access Help.
•
F4: plot rescale.
•
F5: starts the execution of the measurement procedure.
•
F6 and shift F6: change focus to the next window.
Chapter 1
Principles of operation
7
This manual does not describe the background of electrochemical impedance
spectroscopy. We would like to refer to some excellent textbooks:
•
C.M.A. Brett and A.M.O. Oliveira Brett,
Electrochemistry
Oxford science publications ISBN 0-19-855388-9
•
Allen J. Bard and Larry R. Faulkner,
Electrochemical Methods: Fundamentals and Applications
J. Wiley & Sons ISBN 0-471-05542-5
•
R. Greef, R. Peat, L.M. Peter, D. Pletcher and J. Robinson,
Instrumental Methods in Electrochemistry
Ellis Horwood Limited ISBN 0-13-472093-8.
•
John R. Scully, David C. Silverman and Martin W. Kendig,
Electrochemical Impedance: Analysis and Interpretation
STP 1188 ASTM ISBN 0-8031-1861-9
1.3 The instrument and hardware description
The FRA-hardware consists of a digital signal generator (DSG), a signal conditioning
unit (SCU), and a fast analog to digital converter with two channels (ADC).
The DSG consists of a large digital memory, which is loaded with the digital
representation of the applied signal and a fast settling 16-bit digital to analog
converter. A multiplying digital to analog converter controls the signal amplitude.
This architecture ensures accurate signal generation.
The time dependent potential and current signals from the potentiostat are filtered and
amplified by the SCU and recorded by means of the ADC. The acquired signals are
stored in the digital memory on the ADC board. This digital memory allows time
domain averaging of up to 4096 repetitive measurement cycles.
Each cycle can consist of 4096 points. This feature provides high accuracy and
reproducibility. Since a cycle can consist of 4096 points and a measurement can
consist of 4096 repetitive cycles, a single impedance measurement can take 4096 x
4096 AD-conversions for each channel.
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Fig. 1 Scheme of the FRA instrument
RAM
16 bit
DAC
12 bit
mDAC
dc - input
FILTER
ac - input
PGSTAT
CLOCK
SCU
RAM
12 bit
ADC
12 bit
ADC
FILTERS
AMPLIFIERS
i - output
E -output
The analysis of the time-domain measurements is done by means of the 'Fast Fourier
Transform' method. Both the potential signal e(t) and current signal i(t) are
transformed to E(f), I(f) and their complex conjugated E°(f) and I°(f).
The cell impedance Z is calculated from the equation:
Z=( E(f) E°(f) )/( I(f) E°(f) )
The older FRA-module allows measurements in the range of 0.1 mHz to 50 kHz. The
newer FRA2-module allows measurements in the range of 0.01 mHz to 1 Mhz. The
module can be used in two different modes:
•
single sine, i.e. a signal with a single frequency is applied,
•
multiple sines, i.e. a signal with more than one frequency is applied.
The 'single sine' mode offers highest accuracy at higher frequencies, e.g. higher than
50 Hz. However, at low frequencies, the time of measurement of a complete
frequency scan can cause a problem. The 'multiple sines' mode provides the
opportunity of measuring 5 frequencies within one decade or even 15 frequencies
within two decades in a single measurement cycle. This method saves a lot of time,
thus allowing the measurement of more reliable impedance data in case the behaviour
of the electrochemical cell is time dependent.
Each of the two parts, FRA-DSG and FRA-ADC, consists of two boards.
The 64 kB RAM of the digital signal generator (DSG), is loaded from the computer.
While loading, the LED marked 'load DSG' is on. The memory is loaded with the
digital representation of the signal to be applied. The 16-bits words are loaded from
the hard disk drive.
The 12 bit multiplying DAC is used to control the amplitude of the output signal of the
DSG. The maximum amplitude of the DSG peak to peak equals 3.5 V (FRA2) or 10 V
(FRA). This mDAC makes it possible to set the output of the DSG with a resolution of
1 in 4096. Since the signal is divided by ten inside the potentiostat/galvanostat, the
Chapter 1
Principles of operation
9
maximum amplitude peak to peak equals 0.35 V (FRA2) or 1 V (FRA). The resolution
of the applied signal is better than 0.1 mV..
The output of the DSG is available at the BNC plug 'dsg out' or 'signal out'. As long as
the contents of the RAM are used to set the 16 bit DAC, the LED 'signal on' will be
on.
The output signals of the potentiostat, I (current output) and E (potential output), are
filtered and amplified.
The two identical amplifiers have software programmable gains of 1, 2, 4, 8, 16, 32,
64, 128, 256, and 512. The filter is a programmable 8th order Butterworth low-pass
filter.
The two-channel simultaneous-sample-and-hold analog to digital converters are 12
bits wide. The maximum conversion rate is 200 kHz for the older FRA and 800 kHz
for the current FRA2. The results of the conversions are stored in two memories each
with 4096 words of 24-bits wide. Thus each memory location can contain the sum of
up to 4096 conversions.
The DSG and the ADC's are synchronised by using one clock crystal for both
modules.
Chapter 2
Getting started with FRA
11
2. Getting started with FRA
Connect the dummy cell box, which is delivered with Autolab. The red lead should be
connected to WE(c). Switch the instrument on.
To start the program, double-click the FRA icon in the program manager. The factory
default windows of FRA appear.
Fig. 2 Factory default layout of the FRA windows
The screen consists of the following parts:
•
The FRA Manager window with a title bar and a tool bar.
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The Manual control window. This window is used to control all
potentiostat/galvanostat settings.
•
The Edit procedure window. This window is used to modify experimental
parameters. When using FRA for the first time the default parameters are the
"factory" settings. Changed parameters are saved automatically at exit and appear
as default parameters on the next occasion.
•
The Data presentation window. This window gives a graphical display of the
measured data and provides the entries to analyse and modify the data.
•
The Status window. This window is used to start and stop a measurement
procedure and to display system messages.
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These windows are explained in detail in the next chapter. The rest of this chapter is
used to walk through a number of examples that come with the FRA program. These
examples give you an idea of the possibilities of the program. Please follow the
instruction per example in detail. It is assumed that you have experience with the
GPES program. Otherwise, please first read the chapter "Getting started with GPES"
of the corresponding manual.
2.1 Recording an Impedance spectrum
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Click the Method option in the upper left corner of the screen.
Click Potentiostatic.
Click Single potential.
Click File option in the upper left corner of the screen.
Click Open procedure...
Type \Autolab\testdata\fratest.pfr. Press ENTER.
Click View on the Data presentation window.
Click Z" versus Z'.
Click the upper right button of the Z" versus Z' window.
Click the upper right button of the Data presentation window.
Connect the dummy cell. The red lead should be connected to WE(c).
Click the Start button in the lower left corner of the screen.
Click during the measurements on the Plot option of the Data presentation
window.
Click Automatic. The graph rescales.
Click during the measurements on both greenish toolbar buttons. They allow you
to inspect the ac sine waves and their frequency spectrum.
After the measurement a semi-circle is displayed.
Chapter 2
Getting started with FRA
13
Fig. 3 Semi-circle in impedance plot
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Click View again. Select Y" versus Y'. Now the admittance plot appears
Click Window on the Data presentation window. Select the Tile option. Now the
impedance and admittance plot are both presented.
Close the Admittance plot window.
Click Window on the Frequency response
2.2 Manual control
1
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Connect the dummy cell. The red lead should be connected to WE(c).
Click Window on the Frequency Response Analyser manager window. Select FRA
manual control and FRA settings.
Click the green led of the 1 mA current range. Make sure that the check box of 1
mA is checked.
Apply 1 V by moving the slider in the potential panel.
Click the Cell on. The current should be about 0.91 mA.
Click the 1 kHz button of the Range panel in the FRA manual control window.
Apply an amplitude of 0.01 V rms by moving the slider in the Amplitude panel.
Click the Measure button on the FRA manual control window. Inspect all the data
presented on the active windows.
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Fig. 4 FRA manual control
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Click the greenish buttons on the toolbar to activate Oscilloscope windows.
Click the Stop button on the FRA manual control window.
Change the frequency to a lower value using the slider in the Frequency panel.
Click Measure again.
At the end click Stop and close the FRA manual control window.
2.3 Data manipulation with FRADEMO
1
2
3
4
5
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7
Click the File option in the upper left corner of the screen.
Click Load data
Type \AUTOLAB\testdata\frademo.dfr. Press ENTER.
Click the upper right button of the Data presentation window. The Data
presentation window will fill almost the whole screen.
Click the View option. Select Z" versus Z'.
Click now the upper right button of the Z" versus Z' window. The Z" versus Z' plot
will now fill almost the whole screen. It is also possible to drag the borders of the
window in such a way that the window is maximised or that the window looks like
a square. Now you should see a semi-circle which, at the right side, becomes a
straight rising line.
Click Analysis on the Data presentation window. Select the Linear regression
option.
Chapter 2
Getting started with FRA
15
Fig. 5 Straight line analysis
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Mark two points on the straight line part of the impedance plot by clicking them.
After a data point has been clicked, the frequency at which the data point is
measured is displayed in red in the top of the Z" versus Z 'window.
Click OK on the Marker window.
A slope of nearly 1.00 should be printed in the Linear regression window.
Otherwise click the Set line option in this window to try it again.
Click Close on the Linear regression window
Click Window on the Frequency Response Analyser manager window. Select the
Analysis results option to obtain a printed copy of the results.
Close the Analysis results window.
Click Analysis on the Data presentation window and select the option Find circle.
Mark three points on the semi-circle part of the impedance spectrum and
subsequently click OK on the Marker window. The results are displayed in the
Find circle window. Click Cancel to stop or Find circle to try again.
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Click Edit data and select Correct for Ohmic drop. Type a value of 74 on the
displayed window and click OK. Now the so called electrode impedance is
displayed.
Fig. 6 Semi-circle analysis
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Close the Z" versus Z' window.
Click Plot and select Change axis text.
Change for the Z" versus Z' plot the Horizontal-axis and Main vertical axis text so
that they indicate that electrode impedance is shown.
Click View and select the Z" versus Z'. Now the axis text has been changed.
If the precision of the axis annotation is not sufficient, double-click the axis
annotation and specify a new value for the precision and click OK.
2.4 Measuring double layer capacitance as a function of potential.
1
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3
4
5
Click Window. Select the Tile option.
Click Method on the Title bar and select Potentiostatic: Potential scan.
Specify the next values in the Edit procedure screen:
Start potential (V): 0 V
End potential (V): -1 V
Step potential (V): 0.02 V
Connect the working electrode lead to WE(d).
Click 'Edit frequencies' in the Edit procedure screen.
Chapter 2
Getting started with FRA
17
Specify:
Begin frequency: 1000 Hz
End frequency: 100
Number of frequencies: 3
Amplitude: .005 V
Select a logarithmic frequency distribution.
6
Fig. 7 Double layer capacitance measurements
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Click Calculate and then OK.
Select View in the Data presentation window. Click Potential scan plot and Cs vs
E.
Click the upper right button of the Cs versus E window as well as of the Data
presentation window.
Click Start and wait until the measurement is ready. During the measurement the
plot can be re-scaled by pressing F4.
Select View and click Potential scan plot.
Click Select frequency and click in the part 'Frequencies not displayed' those
frequencies to be shown and click the upper button to bring the selected frequency
to the part 'Frequencies selected'. Now click the OK button. The selected
frequencies are shown on the screen.
Click Edit data: Change all points. Select Cs/F and specify a value of 2.
Click the Multiply button. All capacitance values of the black coloured points are
multiplied now. This option can be used to correct for the surface area. Click
Close.
Select Plot and click Resume as well as Automatic. Now the original measured
data are shown again.
Select View again followed by clicking Potential scan plot and Y"/w versus E plot.
Select Window in the Data presentation window and click Tile. The two plots are
shown now.
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Double-click the upper left button of the Y"/w versus E plot. This time the screen
only shows the capacitance plot.
Select File from the upper left corner and select Save data as. Enter a filename and
make sure that the Directory is \Autolab\DATA and press OK.
Now select File again and click Convert to ASCII. Select the data file created
above and click Convert. Select the required file format and click Convert again.
The data are stored as an ASCII file with the specified format. (For explanation of
File extensions, see Appendix 1). If a potential scan is loaded, a potential value
should be selected before the file can be converted. For each potential, a file is
created with an extension as explained in Appendix 1.
Click in the upper left corner of the screen and exit the Frequency Response
Analyser program.
Chapter 3
The FRA windows
19
3. The FRA windows
3.1 FRA Manager window
The title bar of the FRA Manager window contains several options, i.e. File, Method,
Utilities, Project, Window, Help.
File menu
This menu contains options that are usually present in Windows programs.
Fig. 8 The File menu
Open procedure
A procedure is a file containing all the experiment parameters. It contains
measurement parameters, potentiostat/galvanostat settings, and graphics display
values. The extension of the file, which is mentioned in the "File name" field, should
not be changed.
The directory in which the procedure file is stored, is called the procedure directory.
When the directory in the Open procedure window is changed and a procedure file is
successfully loaded from this new directory, this new directory becomes the new
default procedure directory.
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It is also possible to load procedure files from the DOS version of FRA. If this is
required, click the "List Files of Type" drop down button and select the proper option.
Save procedure
This option will save a procedure under its current name in the procedure directory.
Save procedure as
The Save procedure option allows storage of a procedure on disk in the procedure
directory with a different name as the current one. Please use the default file extension
as mentioned in "File name" field or omit the extension. In the latter case the correct
extension will be added.
Print
The Print menu window appears. The Print select panel makes it possible to choose
between the print-out of the measured data, the experiment parameters, or a dump of
the data presentation window. The type of data or the window can be selected from a
neighbouring window. The Print Preview button allows you to preview the print-out of
data.
Print setup...
This option gives access to the standard window for printer setup and control.
Load data
The Load data option allows load of previously measured data from disk. It is also
possible to load data files from the DOS version of FRA. If this is required click the
"List Files of Type" drop down button and select the proper option.
Save data
Store the most recent measured data under the current procedure name on disk. The
data are stored in the so-called data directory, together with the corresponding
procedure parameters.
Save data as
The Save data as option is similar to the previous option, but the name of the file
name containing the data can be specified.
Convert to ASCII
This option allows conversion of the FRA data files to readable ASCII files.
These files can be read by any spreadsheet program, but also by third party data
analysis programs.
Chapter 3
The FRA windows
21
Fig. 8a Convert data
First a FRA output data file has to be selected. After clicking on a file in the list box
some file info is given. To proceed the ‘Convert’ button has to be clicked.
Subsequently, the following columned ASCII or text files can be created:
- Frequency value, Z’ and Z” value, time of measurement, Edc and Idc at the time of
measurement
- Frequency value, Y’ and Y” value, serial capacitance value, time of measurement,
Edc and Idc at the time of measurement.
- Potential value (or current value), Z’ and Z” value, time of measurement, Edc and
Idc at the time of measurement.
- Potential value (or current value), Y’ and Y” value, serial capacitance value, time of
measurement, Edc and Idc at the time of measurement.
The tm, Edc and Idc can be left out of the file by unchecking the ‘Include tm, Edc and
Idc’ check box.
Depending on the type, the required ASCII file format, one or more frequency,
potential or current value has to selected from the list box. For each frequency,
potential or current a file is created. The name of the file is the same as the data file
name. The files are stored in the same directory as the data file resides. The extension
depends on the type of file (see Appendix).
A special type is the Mott-Schottky-file. It contains a matrix of values for (ωZ”)2values for all frequencies and potentials. The extension of this file is .MOT. Please
note that data sets created before FRA version 2.4 will not contain any data for time,
Idc and Edc.
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Load calibration file
This option allows to change the calibration values to optimise performance for
specific FRA2 modules. This option is useful when different Autolab instruments are
connected to a single computer.
Since the calibration files are instrument dependent, they should be kept together. The
indicated number when starting up the FRA software should match the serial number
on the instrument. If one exchanges instruments on one computer, the “Load
calibration file” can be used to adjust the calibration file to the new situation. Please
note that the new calibration file does not have to be in the Autolab root folder.
It is advisable to be cautious with this command and only use it for the situation
described above. If you keep the computer and instrument as a pair after the initial
software installation, this option may never be necessary.
Delete files
This option allows deletion of procedures and measured data files. The File window
only shows the procedure files. A selected procedure will be deleted from disk
together with corresponding data files. A delete action cannot be undone.
Exit
The FRA window will be closed and the program is exited. The program settings are
stored on disk.
Method
The type of measurement can be selected with the Method menu. The experiment
parameters in the Edit procedure window will change depending on the selected
type of measurement.
The following methods are available:
Potentiostatic single potential
A frequency scan is measured at a single dc-potential value.
Potentiostatic potential scan
A frequency scan is measured at a set of dc-potentials.
Potentiostatic time scan
A frequency scan is made at a fixed potential at regular time intervals.
Galvanostatic single current
A frequency scan is measured at a single dc-current value.
Galvanostatic current scan
A frequency scan is measured at a set of dc-current values.
Galvanostatic time scan
A frequency scan is made at a fixed current at regular time intervals.
Chapter 3
The FRA windows
23
Utilities
The Utilities menu allows the user to select electrode control, burette control, RDE
control and sleep mode.
Electrode control
The Electrode control option allows the user to operate a static mercury drop electrode
which is connected via an IME-interface to the Autolab. The stirrer can be switched
on and off, the purge valve can be opened and closed, and a mercury drop can be
created.
The Reset button will reset the digital I/O port of the Autolab instrument. The Purge
and Stirrer will be switched off. This option is not accessible when no static mercury
drop electrode is connected to the Autolab.
Burette control
The burette control option allows the user to control motorburettes connected to
Autolab via the DIO48 module. Consult the "Installation and Diagnostics" guide
about the type of burettes that can be connected. First click the Setup button. Then
select the burette.
The displayed Burette setup window gives the possibility to define the connected
burette. Please consult the manual of your burette for the parameters.
The ‘Maximum time to check for Ready’ is the maximum time for the software
waiting to receive a "ready" signal from the burette.
The DIO port used is shown on your Autolab front.
The Dose button will dose the amount specified above. The dosed volume is
displayed.
The Dose on button will dose with the speed displayed above.
The Reset button will give a ‘reset’-command to the burette and sets the dosed
volume to zero.
RDE-control
In order to control an external Rotating Disk Electrode (RDE), an option is available
in the Utilities menu of the GPES manager. In the hardware configuration an external
RDE should be specified. After selecting the RDE control item the following window
appears:
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Fig. 9 The RDE control window
With the scroll bar it is possible to control the rotation speed of the RDE. You can
also enter the number of rotations per second by changing the r.p.m. edit field or enter
the rotation speed in rad per second in the rad/s edit field.
After pressing the Setup button the RDE setup window appears:
Fig. 10 The RDE setup window
In this screen you can configure the RDE.
Chapter 3
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25
MUX control
The channel number of the SCNR16A, SCNR8A or MULTI4 module can be selected
manually by the operator before starting the measurement procedure:
1. Open the MUX control dialog by selecting MUX control from the Utility menu.
The dialog screen shown in the figure below will pop up.
2. Enable the checkbox “Use Multiplexer Module”.
3. Choose the desired channel.
4. Pressing <Apply> or closing the dialog screen will set the selected channel.
5. The active channel number will be indicated in the Manual control window.
Fig. 11 The MUX control window
If you want to return to direct connections, you can disable the “Use Multiplexer
Module” checkbox.
Options
Several options for data presentation can be specified:
Rescale after measurement: perform autoscale and replot data when measurement
has finished.
Rescale during measurement: rescale and replot when necessary, also during the
measurement.
Procedure name in Data presentation: displays filename and path of the result file in
graph.
Trigger
Under this item the option Trigger is present. After selecting this option the following
window appears. In this window the trigger pulse can be configured.
After enabling the trigger pulse option, the 'Start' button has to be clicked. The
program will go through pretreatment and equilibration and will then wait for the
trigger-signal.
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pretreatment…. equilibration
Version 4.9
measurement
end of measurement
high
low
Fig. 11a The Trigger option window
Project
The Project option allows the execution of a large number of electrochemical
experiments unattended. A project encompasses a number of tasks which have to be
executed sequentially.
Sometimes this is called batch mode processing. A measurement procedure is
normally activated by clicking the Start button in the lower left corner. It is also
possible to start a procedure by creating and subsequently executing a project.
A project can be created by selecting the Project edit option. First you have to indicate
whether a new project should be made (New option) or an existing project file should
Chapter 3
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27
be opened (Open option). An example of a project is delivered with the FRA2
program in the testdata directory.
After editing a Project it can be stored on disk under its current name (Save option) or
under a new name (Save as option).
When Edit is selected the Edit project window appears with two options on the main
menu bar. The Check option checks whether there are syntax errors in the project
commands. The Edit option provides the standard Cut, Copy, and Paste option.
Below you will find the Project script language definitions and rules.
Project command rules
•
•
•
•
•
•
Both upper and lower case characters can be used in command lines.
Space characters are ignored.
If during the execution an error occurs the project continues with the next line.
An error message will be printed in the Results window.
One line per command.
The following commands are allowed:
; <string>
rem <string>
Procedure!Open("<filename>")
Procedure!Start
Procedure!SaveAs(“<filename>”)
Dataset!Open("<filename>")
Dataset!SaveAs("<filename>")
Dataset!AutoNum = <n>
Dataset!AutoReplace
("<string>")
:
:
:
:
:
comment
comment
open a procedure file
start the execution of the procedure
save a procedure file
: open a previously measured data file
: save the measured data
: enable auto-numbered files names,
starting with number <n>
: specify the string which should be
: replaced by a number in the
<filename> for auto-numbered files.
System!Run("<filename>")
System!Beep
: execute an other program.
: give a beep
Print!Procedure
: make a hardcopy of the experiment
parameter
: print a hardcopy of the plot of Z"
versus Z'
: print a hardcopy of the plot of Y"
versus Y'
: print a hardcopy of the Bode plot
: print a hardcopy of the measured data
Print!PLOTZZ
Print!PLOTYY
Print!PLOTBODE
Print!DATA
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Utility!Channel = <n>
Utility!NextChannel
Version 4.9
: sets the active channel to <n>. The
MUX will be automatically enabled
when necessary.
: increase the active channel number
with one. If the channel is not
available, the active channel number
is set to 1.
Please note:
The last 2 commands are available in the GPES and FRA programs. However, for
FRA projects that are called from within GPES projects, all channel switching
commands in the FRA project scripts are ignored. In such cases, the GPES project
will have exclusive control over the channel selection.
Utility!Delay = <n>
Repeat (<n>)
EndRepeat
Message ("string")
ForAllChannels("<filename>")
: hold the project for <n> seconds.
: With these commands you can repeat
an enclosed sequence of instructions
multiple times. You can nest loops
maximal 5 times.
: Give a message and wait for click on
OK
: executes the active measurement
procedure for all available MUXchannels and store the results in the
<filename> adding 3 characters to the
filename as channel number counter,
for example: fname001, fname002,
etc. .
DIO!SetMode("<Connector>",
"<Port>","<Mode>") : set the mode of a port of the DIO.
DIO!SetBit("<Connector>","<Port>",
"<n>","<Bit>")
: set a single pin of the DIO on or off.
DIO!SetByte("<Connector>","<Port>"
,"<n>")
: set a port of the DIO to the specified
value.
DIO!WaitBit("<Connector>","<Port>",
"<n>","<Bit>")
: wait until a single pin of the DIO is
set on or off.
DIO!WaitByte("<Connector>","<Port>",
"<n>")
: wait until a port of the DIO is set to
the specified value.
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29
Burette!DoseVolume (<Burette number>
,<Dose volume>) : dose a specified volume to the
specified burette.
Burette!Fill (<Burette number>)
: Fill the burette.
Burette!Flush (<Burette number>
,<Number of flushes>) : flush the burette.
Burette!Reset (<Burette number>)
: Will give a 'reset'-command to the
burette.
<string>
<filename>
: line of text
: a filename without extension, but including a directory name
A special case occurs when the measurements are done with respect to the open
circuit potential. Normally the user is asked to click the Accept button, but in
automatic mode the program continues by itself.
Project wizard
The Project wizard provides an easy way of editing and/or defining a project. This
option allows the user to pick project command lines from a list of all commands,
insert them in a project and define the parameters. The window below gives a project
Wizard overview.
Fig. 12 An example of a project inside the Project wizard
Every project command can be inserted in the project, deleted or moved to another
place. A short description of the command is given in the information and syntax box.
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Using the parameter button one can define the parameters that belong to that specific
command.
Project example
Example 1 Record frequency scan on all available MUX-channels.
This example script will record a frequency scan on all available MUX-channels, and
store the results automatically as “fra scanner test_001”, “fra scanner test_002”, etc.
until the last available channel is reached:
Procedure!Open("c:\autolab\testdata\fratest")
ForAllChannels("c:\autolab\data\fra scanner test_")
Window
The Window option allows selection of windows which should be shown on the
screen. The Tile option gives the default partitioning of the screen.
The Close all option will delete all the FRA windows except for the status bar and the
FRA Manager window.
Help
The Help option is the top entry point in the help structure. For most topics on the
screen Help is available. By pressing F1 the specific information about the part of the
screen on which has been focused is given.
Tool bar
The tool bar contains a list of buttons, the current electrochemical method, and the
name of the current measurement procedure.
The buttons give short cuts to various menu options which are frequently used. Place
the mouse pointer on top of a button. Its meaning will appear in yellow, if pressing the
button is allowed.
The two greenish buttons require some extra explanation. They can be pressed during
impedance measurements. They allow the user to inspect the ac potential and ac
current signal in real time domain and in the frequency domain. When one or both
buttons are pressed monitor plots appear. The vertical axis in the time domain plot
represents the potential or current as a percentage of the full input range.
The vertical axis in the frequency domain plot is an arbitrary log scale of the amplitude
of the ac signals.
This plot can be used in order to check whether second harmonic effects occur. In case
of a single sine signal and low frequency (< 200 Hz) the applied sine wave has the
index n=1. At higher frequencies, the index of the applied signal is equal to the
number of sines present within a single cycle. When the multiple sine mode is used,
Chapter 3
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31
the number of applied frequencies is equal to 5 or 15. The frequency domain clearly
shows high amplitudes for the applied frequencies.
The horizontal axis is an arbitrary time scale.
3.2 Status bar
The lowest part of the screen is reserved for the status bar. The Start button starts the
execution of a measurement procedure. After clicking this button, other buttons
appear which make it possible to advance to a next stage or to abort a measurement
procedure. The Status and Message panel give important control information. A
measurement can be temporarily suspended by pressing the <Hold> button. More
information on the sequence of events after starting the measurements is given in a
separate chapter.
3.3 Autolab manual control window
The Manual control window gives full control over the potentiostat/galvanostat of the
Autolab instrument.
Note, that some of the presented Autolab settings are part of the measurement
procedure. The Manual control window consists of several panels.
Fig. 13 Autolab manual control window
Current range
In the Current range panel the green 'LED' indicates the actual current range. A mark
in the neighbouring check box indicates whether the current range can be selected.
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Only a joined column of selectable current ranges is allowed. The software always
checks whether the row is closed. If a range separated from another range is checked,
the intermediate ranges are checked automatically. When a check box is clicked
again, the check disappears. The allowed current ranges are stored on disk as part of
the procedure. The highest applicable current range for autoranging during
potentiostatic measurements: the advised highest current range depends on the lowest
measured impedance of the cell. In general the lowest measured impedance must be
higher than 0.2/(current range), e.g. 20 ohm with a current range of 10 mA. In normal
application the highest current range can be 1 A with the PGSTAT20/30, 100mA with
PGSTAT12/100 or 10 mA with the PGSTAT10.
Settings
With the buttons in the settings panel the PGSTAT can be controlled.
The text on the button represents the current situation. The following buttons might
appear (depending on the type of potentiostat/galvanostat):
Cell on/off: allows to switch cell on or off. In the ‘off’ position the connection of the
potentiostat with the potentiostat/galvanostat is broken, so no current can flow
between the counter and working electrode.
High Sens off/on: This button has limited functionality in the FRA-software. With
High Sens on the displayed value of the dc current is improved with a factor of 10
compared to High Sens off. However, in most cases the button position is not relevant
.
High Stability/High Speed: in High stability mode the PGSTAT is less susceptible to
oscillations but its bandwidth is narrower.
It is advised to switch the potentiostat into ‘High stability’ mode before the
measurements start in case you work with an electrochemical cell with a high
capacitive load, i.e. in most cases a high electrode surface area. High stability mode
offers the potentiostat a better protection for oscillation. Oscillations of the
potentiostat might destroy your electrode.
If the applied frequency is too high for high stability the program will automatically
switch the potentiostat into High speed mode.
Potentiostat/Galvanostat: allows to switch from potentiostatic to galvanostatic. It is
highly recommended to switch the cell off before switching from one mode to
another. In case of Potentiostatic control, the output of the DAC module corresponds
to an applied potential level. In case of galvanostatic control, an output of the DAC
module corresponds to an applied current.
iR-compensation on/off: Switches iR-compensation ‘on’ or ‘off’. For impedance
measurements iR-compensation should be switched off, therefore this button cannot
be clicked in the FRA-program.
Noise meters
The noise levels for current and potential signals are visualised by 2 noise meters at
the signal panels. When these VU-meters are active, the first green LED or a grey
background is shown.
The VU-meter for the current signal is only active when the cell is switched on. The
VU meter for the potential signal is also active when the cell is switched off i.e. no
Chapter 3
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33
current can flow. During the execution of the procedure (except for pre-treatment
stage) the VU-meters are inactive.
In case more than 4 LED's of the VU-meter are on, it is advised to take precautions.
You can select a higher current range or minimise the noise of your electrochemical
cell. High voltage noise levels are often caused by the reference electrode.
Potential
The Potential panel contains a slider and a text box. With these tools the applied
potential can be specified. The slider box can be dragged to change the value. A click
on the arrows and slider bar changes the value by a distinct increment. The increment
is different for the arrows and for the bar.
In the two panels below the measured current, potential and time can be displayed,
depending on the option button selected.
iR-compensation (not yet possible)
The iR-compensation panel appears only when the Autolab is equipped with a
PGSTAT12/20/30/100 potentiostat/galvanostat. In order to perform iR-compensation
the iR-compensation button on the Settings panel should be switched to "iR-comp.
on". Subsequently the ohmic resistance can be specified by using the slider or by
typing in the textbox. Note that when the iR-compensation is switched on, automatic
current ranging is no longer possible. The only checked current range box becomes
the actual current range.
3.4 FRA Settings window
The parameters printed in this window give information about the measurements.
In the ‘Offset potential/current’ panel the values with which the potential and current
are compensated to remove the DC component from the signal. Also the amplitude of
the AC-signal is given.
In the Results panel the applied frequency (or base frequencies in case a multi-sine is
used as modulation), the measured impedance and phase-shift are displayed.
In the Resolution panel the resolution of the actual measurement of the AC-current
and -potential are displayed, the maximum value is 100%. A low resolution (say
<0.5%) yields a poor accuracy of the results .
The resolution of the measurement depends on the applied current range and the gains
of the amplifier. In case the resolution is too low and the gain of the amplifier is at its
maximum, a lower current range can be used. However, the applicable lowest current
range depends on the applied frequency, since the bandwidth decreases with lower
current ranges. If the resolution is 100%, the measurement is done in an (almost)
overload situation. The highest allowed current range has to be increased. See the
Autolab manual control window.
The Gain panel indicates the gains which are used to amplify the I and E signal. The
maximum gain is 128.
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3.5 FRA manual control window
The FRA manual control window makes it possible to apply an ac signal to the
electrochemical cell. It consists of several panels.
In the range panel a frequency range can be selected. With the Frequency and
Amplitude panel below, the frequency and amplitude of the ac-signal can be selected.
Both panels contain a slider and a text box. The slider box can be dragged to change
the value. A click on the arrows or on the slider bar itself changes the value by a
distinct increment. The increment is different for the arrows and for the bar. The
input fields below determine how the measurements are done. They require some
extra explanation.
The integration time
The minimum period during which the signals are measured. The longer this period,
the more accurate the result will be. The minimum time of measurement is equal to
one cycle of the (in case of multi-sine lowest) frequency. Thus, if the cycle time is
longer than the sampling time, the sampling time will automatically set to the time of
one cycle. A generally suitable value equals one second. If the time to measure the
minimum number of cycles (see below) is larger than the specified integration time,
the actual integration time will be determined by the minimum number of cycles.
The minimum number of cycles to integrate
The minimum number of ac signal periods during which the signals are measured.
The more periods, the more accurate the result will be. One cycle is the minimum.
Number of cycles to reach steady state
The period between applying the ac-signal and start of the measurements. This time
is often needed to measure stationary state behaviour. A standard value can be 10.
Maximum time to reach steady state
The maximum time between applying the ac-signal and the measurements. When the
applied frequency is low, the time of the specified number of cycles to reach steady
state, can be too high. As soon as the previous criterion or this criterion is found to be
true, the measurement starts.
With a minimum fraction of cycle
In case the ‘Maximum time to reach steady state’ is shorter than the time equivalent
to the duration of the ‘minimum fraction of cycle’, the latter value is used to wait for
steady state.
Chapter 3
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35
The effective time to wait for steady state now depends on four parameters:
- f (frequency)
- Number of cycles to reach steady state: ncycles
- Maximum time to reach steady state: tmax
- with a minimum fraction of a cycle: Xfraction
The time to wait for steady state twait is:
twait = ncycles / f
if twait ≥ tmax then twait = tmax
if twait ≥ tmax then if twait < Xfraction / f then twait = Xfraction / f
These parameters are also stored as part of the measurement procedure, so they might
change when a procedure is loaded from disk.
In the panel below the results of the measurement can be observed after the Measure
button has been clicked.
It is advised that during the 'manual' impedance measurements, the FRA Settings
window is opened as well via the Window menu on the FRA manager window.
Use external inputs
When this box is checked, the FRA2 module does not determine the impedance by
measuring the current and potential signals from the potentiostat/galvanostat. Instead,
the signals applied to the BNC connectors X and Y are measured. It is possible that
X or Y is connected to the BNC connector Eout or Iout respectively at the rear of the
Autolab instrument (see also Appendix XI on Hydrodynamic Impedance
Measurements).
3.6 Data presentation window
The Data presentation window serves several functions:
display of data
•
data analysis
•
data manipulation
•
communication with other programs like Paintbrush, Excel or MS-Word.
The window consists of a menu bar, a graphical display, and a message line.
As mentioned earlier the measured data are kept in a shared data memory block with
the data acquisition software. During the measurement the measured data points are
also copied to the memory block of the Data presentation window. After the
measurements the data in this memory block can be modified by options in the Data
presentation window. However, it is always possible to resume the measured data.
Note that the save options of the File menu of the FRA Manager window always save
the measured data. The data, which can be modified in the Data presentation window,
are called work data and can be stored from the File menu of the Data presentation
window in a work data file. This file cannot be distinguished from the files with
measured data. Both types of files have the same format and layout.
On the message line at the bottom of the graphical display important text about the
required user actions during analysis of editing data appears. If no message is
displayed, the currently measured potential and current are displayed.
•
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Copy
The Copy option allows to copy the graph to clipboard or to dump the graph in a
bitmap file (.BMP) or a Windows meta file (.WMF). These files can be read by
programs like Paintbrush, Excel, or MS-Word. These programs allow editing of the
graphs. Please note that the size of the axis annotations etc. in the meta file depend on
the size of the Data presentation window. Moreover, the sizes in the meta file may be
somewhat different from what is displayed in the Data presentation window.
The best way to copy the graph to MS-Word is to make a .WMF file using the Copy
to option. The best result is obtained by doing this from a maximised Data
presentation window. By default FRA only draws dots. It is sometimes better to draw
lines. This can be achieved by double-clicking the data points in the graph. For further
information, see the paragraph on Editing graphical items.
File
The File option allows saving the data presented in the Data presentation window and
allows merging of previously measured data with the current data.
Save work data
Allows saving of edited or merged data as previously discussed.
Merge
This option allows merging of two frequency scans at single potential or current.
The merged scans can subsequently be stored on disk using the "Save work data"
option. However, conflicts may occur in the procedure parameters of the two merged
data files. The procedure parameters of the already loaded data are dominant. This
option is useful to obtain a full frequency scan from two or more separately measured
scans. For example, in order to save time, the low frequency part of a scan is
measured using the multi-sine mode and the high frequency part is measured using
the single-sine mode. After a subsequent merge a full scan is obtained.
View
The View option makes it possible to inspect one or more graphical presentations of
the measured impedance data. A maximum of 4 plot windows can be opened at the
same time.
When the measurements are performed at one single potential or current a selection
can be made from the following items:
Z" versus Z'
Draw a plot of the quadrature impedance versus in-phase impedance.
Y" versus Y'
Draw a plot of the quadrature admittance versus in-phase admittance.
Bode plot
Draw a plot of the logarithm of the impedance and the phase angle versus the
logarithm of the frequency.
Chapter 3
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37
Z', Z" versus f
Draw in-phase and quadrature impedance versus the frequency.
Z versus√ω
Draw in-phase and quadrature impedance versus square root of 2πf.
Z versus 1/√ω
Draw in-phase and quadrature impedance versus one over square root of 2πf.
Y versus √ω)
Draw in-phase and quadrature admittance versus square root of 2πf.
Y versus 1/√ω
Draw in-phase and quadrature admittance versus one over square root of 2πf.
Y"/ω versus Y'/ω
Draw quadrature admittance over 2πf versus in-phase admittance over 2πf.
Epsilon plot
Draw quadrature versus in-phase permittivity, after specifying the geometric
capacitance being the capacitance of the empty cell. The permittivity is defined as
epsilon = Y/iωC = epsilon' + i*epsilon''.
Z' versus ωZ"
Draw in-phase versus 2πf times quadrature impedance.
Z' versus Z"/ω
Draw in-phase versus quadrature impedance over 2πf.
ωZ'versus ωZ"
Draw 2πf times in-phase versus 2πf times quadrature impedance.
Select potential or currents
When a potential or current scan has been performed, the option 'Select potential' or
'Select current can be chosen. A window appears from which one or more potentials
or currents can be selected or deselected.
The frequency scans measured at the selected potentials or currents will be shown.
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Fig. 14 Select potentials window
The data measured at the selected potentials or currents are plotted in different
colours in one or more of the plot available types. The potential or current values at
which the frequency scans are displayed, are shown in a drop down menu in the upper
left corner of each graphical window. The value selected from the drop down menu is
the so called work data set. All Edit and Analysis action are performed on this data
set.
A maximum of four plot types can be displayed at the same time. Each plot in a
separate window.
In case a potential or current scan has been performed one or more of the following
potential scan plots can also be selected:
Z' versus E
Draw a plot of the in-phase impedance versus the potential (or current).
Z" versus E
Draw a plot of the quadrature impedance versus the potential (or current).
Y' versus E
Draw a plot of the in-phase admittance versus the potential (or current).
Y" versus E
Draw a plot of the quadrature admittance versus the potential (or current).
Cs versus E
Draw a plot of the substituted serial capacitance versus the potential (or current).
ωZ' versus E
Draw a plot of the in-phase impedance * 2πf versus the potential (or current).
Chapter 3
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39
ωZ" versus E
Draw a plot of the quadrature impedance * 2πf versus the potential (or current).
Mott-Schottky
Two types of Mott-Schottky plots are available:
Rs-Cs: the experimental capacitance is calculated from a Rs-Cs circuit in series.
Rs-Cp/Rp: the capacitance is calculated assuming that a resistance Rs is in series with
a capacitor Cp.
Select frequency
The impedance/admittance plots can be drawn at one or more frequencies.
A window appears from which one or more frequencies can be selected or deselected.
The potential scans measured at the frequencies will be shown.
The data measured at the selected frequencies are plotted in different colours in one
or more of the plot available types. The frequency values at which the frequency
scans are displayed, are shown in a drop down menu in the upper left corner of each
graphical window. The value selected from the drop down menu is the so called work
data set. All Edit and Analysis action are performed on this data set.
A maximum of four plot types can be displayed at the same time. Each plot in a
separate window.
When a time scan has been performed one or more of the following time scan plots
can be selected:
Z' versus t
Draw a plot of the in-phase impedance versus time.
Z" versus t
Draw a plot of the quadrature impedance versus time.
Y' versus t
Draw a plot of the in-phase admittance versus time.
Y" versus t
Draw a plot of the quadrature admittance versus time.
Cs versus t
Draw a plot of the substituted serial capacitance versus time.
ωZ' versus t
Draw a plot of the in-phase impedance * 2πf versus time.
ωZ" versus t
Draw a plot of the quadrature impedance * 2πf versus time.
Z’, Z” versus t
Draw in-phase and quadrature impedance versus time.
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Z, Phi versus t
Draw impedance and Phase shift versus time.
Y’, Y” versus t
Draw in-phase and quadrature admittance as a function of time.
A maximum of four plot types can be displayed at the same time. Each plot in a
separate window.
Plot
The Plot option contains all kind of possibilities to manipulate the graph like plot
refresh, automatic scaling, zooming, or display of a previously measured signal.
Sometimes, not all options are selectable because they are not applicable or intervene
with current active data analysis options. Also when the execution of a procedure is
going on, not all options are selectable.
Some sub-options require explanation.
Automatic
The plot will be scaled automatically. Some plots i.e. Z" versus Z' and Y" versus Y'
will be scaled in such a way that both axes have a similar division, so that a semicircle can be displayed correctly.
Resume
The Resume option makes a fresh copy of the measured data into the Data
presentation window.
Zoom
Clicking the Zoom option has the same effect as pressing the right mouse button.
When this option is activated a magnifying glass appears. When subsequently the left
mouse button is clicked and held down, a Zoom window can be created.
Set window
This option allows to select part of the data set for further editing of data or data
analysis. Only the selected range of data-points remains visible on the plot. The
removal will be done in all loaded plots. With the Resume option on the Plot menu
the originally measured data will be reloaded. The Save work data option on the File
menu can be used to save the selection of the data set.
Load overlay file
This option allows the making of an overlay of one or more previously measured data
sets. The overlay data will appear in all open graphs. The legends of these overlay
files are selectable with the overlay legends dropdown box. This dropdown box
overrules the standard dropdown box where the different
potentials/currents/frequencies are shown. A maximum of 5 overlays can be made. In
case the overlay file contains a potential or current scan, a window appears to select a
potential, current or frequency value, depending on the active plot type,. After
clicking the Resume option (see above) the overlays will disappear.
Chapter 3
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41
Enter text
When this option is clicked the “Additional text” appears in the top left corner of the
graph. This text can be dragged over the graph. After double-clicking the field, the
text itself as well as the format can be modified. The first text line of the Paste buffer
can be inserted on the text field as well. Thus a line of text from the Analysis results
window can be copied to the Paste buffer and subsequently inserted there. Please note
that the text cannot be stored.
Change axis text
A window appears in which the axis description of all plot types can be edited.
After clicking OK, all future plots will appear with the updated axis text.
The modified axis description will be stored on disk when the FRA program has been
exited in a regular way. This options offers also the possibility to specify an Isotropic
plot. The plot will be shown isotropic the next time you open the plot.
Fig. 14a Change axis text window
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Fig 14b. Example of an Isotropic Z’, Z’’ plot
Save graphical settings
The presentation of the graphs is determined by many parameters like the marker type
of each displayed data set, the format of the axis indices, the colours, etc. All these
parameters can be modified (see below). The modified settings can be saved by
selecting this option. Only one set of graphics parameters can be saved, so any new
plot type subsequently created will use the newly saved graphical settings as default.
The graphical settings are stored on disk when the program is exited in a regular way.
Default graphical settings
All parameters which determine the presentation of the graph will be set to their
default i.e. as they were when the graphical settings were saved the last time.
Chapter 3
The FRA windows
43
Fig. 15 Two potential scan plots
Analysis
The analysis menu has four options. Selection of these options opens a specific
window to perform the operation and to display the results. The results are printed in
the Analysis results window as well. This window can be made visible from the
Window option on the FRA manager menu bar.
Linear regression
The Linear regression option makes it possible to fit a straight line through a part of
the measured curve. When the option is selected, two windows appear. One is the
Linear regression window and the other is the Markers window. When the begin and
end point of the line have been marked on the measured curve and the OK button on
the Markers window has been clicked, a line is drawn in such a way that the sum of
squares of the differences between measured data points and calculated line is
minimum. The slope of the line (dY/dX), the intercepts i.e. Y(at X=0) and X(at Y=0),
and several other helpful data are given. More lines can be fitted when the Set line
button is clicked.
In case the plot type is such that a left as well as a right hand Y-axis is displayed, an
extra panel is added to the Linear regression window where the user can select on
which data the linear regression should take place.
Find Circle
The Find circle option makes it possible to fit a semi-circle through a part of the
measured curve. When the option is selected, two windows appear. One is the Find
circle window and the other is the Markers window. When the begin, centre, and end
point of the circle have been marked on the measured curve and OK is clicked on the
Markers window, a semi-circle is drawn through the marked points. The slope of the
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line (dY/dX), the intercepts i.e. Y(at X=0) and X(at Y=0), and several other helpful
data. More semi-circles can be drawn when the Find circle button is clicked.
If the Find circle option is not appropriate for a certain plot type, it can not be
selected.
For the plot type Z" vs Z', the program calculates the values of Rs, Rp and CPE
assuming an equivalent circuit with a CPE parallel to a resistance Rp and a resistor in
series with this combination. The impedance of the CPE is Z = 1/(iωCPE)n
Fig. 16 The Rs-Rp//CPE equivalent circuit
Rp
Rs
CPE
For the plot Y" vs Y', the program calculates the values of Rs, Rp and r
where r is the radius of the semi-circle.
Find minimum and maximum
The Find minimum and maximum option shows the minimum and maximum Yvalue(s) with their corresponding X-values.
Interpolate
The Interpolate option allows to calculate one or more X-values or Y-values which
correspond to a given value on the axis. A linear interpolation is used to calculate
intermediate values.
Data info
this option sets a marker in the presently loaded curve and gives the corresponding
frequency and X,Y values.
The Kramers-Kronig (K-K) test
This test can be used to check whether the measured data comply with the
assumptions of Kramers-Kronig transformation. These assumptions are: (1) the
response is only related to the excitation signal, (2) the response is linear (or the
perturbation is small, e.g. <10 mV, for non-linear systems), (3) the system does not
change with time and (4) the system is finite for all values of ω, including zero and
infinity. If the investigated system changes with time due to e.g. ageing, temperature
change, non-equilibrium initial state etc., the test fails. Failure of K-K test usually
means that no good fit can be obtained using the equivalent circuits method. This
option is based on the work of Dr. B.A. Boukamp as published in J. Electrochem.
Soc., Vol 142, 6 (June 1995) and coded in the program RCNTRANS by the same
author.
Please refer to the Appendix for more information about this option.
Chapter 3
The FRA windows
45
Fit and Simulation
This option allows you to simulate responses of equivalent circuit and to fit the circuit
parameters to the measured data, using the non-linear least squares method. The
equivalent circuits can be defined by the user (using Circuit Description Code). It is
possible to define elements with fixed values as well as constraints for values of fitted
parameters. This option is based on the work of Dr. B.A. Boukamp as first published
in Solid State Ionics, 20 (1986) 31-44 and coded in the program EQUIVCRT by the
same author.
Please refer to the Appendix for more information about this option.
Edit data
Change all points
All the data displayed in the focused plot window can be changed; however, the
change only effects the displayed data, not the work data. This means that the
changed data cannot be saved and also newly created plots will be based on the
unchanged work data.
Correct for ohmic drop
All data points can be changed using this option. A value for either Z’, Z’’ or the
potential, current or time can be given. Subsequently all loaded plots will be updated
with newly calculated values. With the Resume option of the Plot menu the originally
measured data will be reloaded. The Save work data option of the File menu can be
used to save the modified data set.
Delete points
An option is available to remove points from the plot. This option can be used to
remove spikes from the measured data. The removal will be activated in all loaded
plots. With the Resume option from the Plot menu the original data set will be plots.
The Save work data option from the File menu can be used to save the adjusted dataset.
Element subtraction
The influence of a circuit elements can be subtracted from the measured data. This
can simplify the analysis of the data. All elements which can be used in the Fit and
simulation option can also be subtracted. The element can either be subtracted from
impedance data or from admittance data. The impedance data should be used in case
the element is supposed to be in series with the remaining circuit; the admittance data
should be used if the element is parallel with the remaining circuit.
A description of the available circuit elements can be found in the appendix on Fit and
simulation.
Dispersion functions for elements
The table below defines the dispersion functions for the elements in both impedance
and admittance representation (ω = 2πf).
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CDC
element
impedance
admittance
R
resistance
R
1R
R
C
capacitance
− j ( ωC )
jωC
C
L
inductance
jωL
− j ( ωL)
L
W
Warburg
impedance
1 / Y0 jw
Y0 jω
Y0
Q
constant phase
element
( Y jω)
( Y jω)
Y0 , n
T
hyperbolic
tangent element
(Y
jω
)
−1
hyperbolic
cotangent
element
(Y
jω
)
−1
Gerischer
impedance
(Y )
O
G
(
)
−n
0
0
0
0
−1
parameters
n
0
(
) (Y
jω tanh B jω
(
) (Y
jω coth B jω
coth B jω
tanh B jω
Ka + jω
0
0
)
(
)
Y0 , B
)
(
)
Y0 , B
Y0 Ka + jω
Y0 , Ka
(Please note that the definition of the Q element differs from the EQUIVCRT program
Chapter 3
The FRA windows
47
fig. 16b The marked points have been removed from the data-set
Editing graphical items and viewing data
Except for the available options, items of the graph can be edited by double-clicking
them. The following items can be double-clicked:
•
the axis labels
•
the axis itself
•
the axis description
•
the plot title and subtitle
•
the data.
Colours, sizes, marker types, text, formats, axis position: all these things can be
changed. Please take some care with changes in Colours. E.g. do not make the data
colour the same as its background colour.
By double-clicking the data points a window appears, which among the standard
graphical operations also gives the possibility to view the data values itself and to edit
them. Moreover, the data can be copied to clipboard and subsequently be entered into
e.g. a spreadsheet program. The format of the data is similar to the format of the axis
labels.
Double-clicking the axis itself allows scaling and positioning of the axis and selection
of the axis function. Data can be displayed, among others, as linear inverse, 10log,
natural log, square root, inverse square root. Except for the linear and 10log, the value
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of the presented data is modified in real. So all subsequent operations are really
performed on e.g. the square root of the data.
In case of the 10log, not the values but the axis is changed to a logarithmic axis.
Sometimes it is necessary to perform automatic scaling after changing the axis, press
F4.
Double clicking the axis labels allows specification of the format of the axis labels. It
is very important that the correct precision of the labels is specified.
When the button "| 1 |" in the upper right corner is clicked, the Graph parameter
window appears. This window allows modification of the relative scale parameters of
the so called graph and plotting area, and their background colours.
All changes made to colour and sizes are stored in the default graphics display file.
Other changes are kept in the procedure file.
Fig. 17 Window which appears after double clicking horizontal axis
Chapter 3
The FRA windows
Fig. 18 Window which appears after double clicking the axis labels
Fig. 19 Window which appears after double clicking the data
3.7 Edit procedure window
The edit procedure window consists of two pages. On page 1 the most common
parameters can be specified. Page 2 contains the other parameters.
The parameters are divided in several sections i.e. pre-treatment, measurement,
potential, comment, title, and subtitle. A full list of the definition is found in the
appendix.
The FRA data can be saved directly to disk while the measurement is in progress by
specifying a direct output name. The data will be written with the extension ".DFR".
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This option is useful for long duration scans and prevents data loss due to a failure of
the power supply. If no path is included, the default data directory is used.
Please note that next to the parameter in this window, the current ranges of the
Autolab manual control window and the four parameters of the FRA manual control
window will be stored as part of the procedure as well and will influence the
measurements.
Pre-treatment
The pre-treatment facility allows conditioning of the electrochemical cell at specified
potentials or currents, during a specified time. This pre-treatment can be performed
before each applied ac frequency or before each new applied dc potential or current.
If this facility is not to be used, specify all times as zero.
Edit frequencies
The frequencies can be edited from a separate window which can be opened by
clicking on Edit frequency option just below the top window bar.
The frequencies to be applied can be calculated according to the parameters in the
Parameter panel.
The exact applied frequencies and their amplitude can be changed in the second input
screen.
A complete frequency scan can be divided in up to five sub-scans.
This facility makes it possible to measure for instance from 50 kHz down up to 10 Hz
with an amplitude of 0.005 V first and after that from 10 Hz down to 1 mHz at 0.05
V.
Begin and end frequency : The (sub-)scan is performed from the begin to the end
frequency. It is strongly advised to perform a frequency scan from high to low
frequencies. The frequency limits are 50 kHz down to 0.1 mHz (FRA) or 1 MHz
down to 0.01 mHz (FRA2).
Number of points: The number of frequencies in the (sub-)scan.
Frequency distribution : The distribution of the frequencies from the begin to the end
frequency can be either linear, square root-linear, or logarithmic.
The amplitude (rms value) of the ac signal. In case of potentiostatic measurements, a
general applicable value equals 0.01 V. The value should be so low that non-linear
effects are avoided. Amplitude limits are normally 0.0002 V and 0.35 V.
In case of galvanostatic measurements, the ac current amplitude should cause a
potential response at which, again, no second harmonic effects are found. However
some specific measurements, e.g. in case of very high impedance’s, require increased
ac signals.
Chapter 3
The FRA windows
51
In case it is unknown at which amplitudes non-linear effects occur, some
measurements can be performed, while monitoring the frequency domain plot. Nonlinear effects will give higher amplitudes at frequencies higher than the applied
frequencies. The software provides the button ‘Show/hide FFT spectrum’ in order to
monitor the amplitude as a function of frequency.
Fig. 20 Edit frequency window
3.8 Analysis results window
The Analysis option of the Data presentation window allows the making of an
analysis of the data. In some cases the results are displayed in a special window which
differs per analysis technique. In all cases an analysis report is printed in the Analysis
results window.
The Analysis results window contains all the results of the analysis of the data. Only
when the FRA Manager window is closed, the Analysis results window is cleared.
The File option of this window allows the user to clear, save, or print the content of
the window. The Edit option allows the user to remove (Cut) the selected part of the
text. Text can be selected by keeping the left mouse button pressed and moving it over
the window. The Copy option copies the content of the window to the paste buffer.
The Paste option will include text from the paste buffer.
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It is possible to copy the analysis results to the data presentation graph in this manner.
Fig. 21 Analysis results window
Chapter 4
Measurements
53
4. Measurements
4.1 Advice on measurements
It is advised to switch the potentiostat into ‘High stability’ mode before the
measurements start in case you work with an electrochemical cell with a high
capacitive load, i.e. in most cases a high electrode surface area. High stability mode
offers the potentiostat a better protection for oscillation. Oscillations of the
potentiostat might destroy your electrode.
If the applied frequency is too high for high stability the program will automatically
switch the potentiostat into High speed mode.
It is better to start with higher frequencies and then go to lower frequencies. It can
save time. The FRA module will settle at the first applied frequency. At very low
frequencies this might take quite a long time.
4.2 Internal / External measurements
The FRA2-modules allow doing impedance measurements by passing the built-in
potentiostat/galvanostat. The external inputs X and Y can be seen on the front of the
module. The program supports recording the impedance with respect to an external
applied ac-signal instead of the applied ac-potential. For this purpose the applied acsignal should be connected from an external source to the X-input. Furthermore, the
checkbox ‘Use external inputs’ should be clicked on the FRA manual control window.
Now the current response with respect to this external source is measured. The current
signal from the rear of the Autolab instrument (connector Iout) should be connected to
‘Y’ using a BNC cable. This software option is only available for instruments
delivered after September 1997. Please consult Eco Chemie in case of problems.
4.3 Time, potential and current measurements
After each impedance measurement the time, dc-current and dc-potential are
recorded. The time is recorded from the start of the equilibration stage.
4.4 Time scan
It is possible to perform frequency scan of impedance measurements at a specified
interval time at a fixed potential or current.
For this purpose the Method menu on the FRA-manager window contains the option
‘Time scan’ for both the potentiostatic as well as the galvanostatic mode.
The minimum interval time is at least two seconds, but will depend on factors like the
number of frequencies to be measured, the frequency itself, the ‘minimum cycles to
integrate’ and the ‘maximum time to reach steady state’ (see the FRA manual control
window). In case the interval time exceeds the specified value, a message will be
given but the measurements will continue.
The time at which a measurement is done is stored in memory for every single
frequency, but on the graphical window the whole frequency scan is plotted at the
time at which the latest frequency in the scan is measured.
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The time at which each single frequency is measured can be viewed in ASCII-files
which can be created. (See the paragraph on ‘Convert to ASCII')
4.5 Single and Multiple Sine-waves
The applied AC perturbation on top of a DC potential or current can either be a single
sine, a superposition of five carefully selected sines of different frequencies over one
decade or fifteen sines over three decades of frequencies. It is advised for common
use to choose the single sine wave as perturbation, because it gives the best signal to
noise ratio. The multi-sine capabilities can be of use in two particular cases:
- to save time in the low frequency region.
- to record a frequency spectrum at an unstable electrode surface
The multiple sine mode can only be used in a limited frequency range. The maximum
base frequency for the five sine perturbation is 3120 Hz and for fifteen sine
perturbation is 312 Hz.
In both cases the maximum upper frequency is about 31200 Hz.
4.6 The measurement sequence
The execution of the measurement procedure is conducted through several stages:
1
2
3
4
5
6
7
8
The memory of the DSG is loaded using one of the signal files from disk,
containing the proper ac-signal, but is not switched on yet.
A new drop signal is generated if the hardware configuration shows the presence
of a mercury drop electrode (see Hardware configuration program).
The pre-treatment starts if one or more conditioning times are unequal to zero and
the pre-treatment has to be performed before every frequency.
The dc-potential or dc-current is applied and the filter is set to the proper cut-off
frequency. The ac-signal is applied. The timer is set to the equilibration time and
waits until the timer is ready. If the measurement is synchronised, the timer is set
to the equilibration time minus 1 second, but the program continues without
waiting for end of timer.
The gains of both amplifiers are set. The current range is set. In case of the first
measurement, the 'Highest current range'. In all other cases according to
calculated optimal current range, depending on last measured results. If the
measurement is synchronised, the program holds until end of timer is found. Now
the timer is set to one second.
At higher frequencies (higher than the minimum frequency for autoranging, see
Appendix I), the gains of both channels are increased until an overload is found
and then decreased with a factor of 2. At lower frequencies, the gains are set
according to the previous measurement.
If the measurement is synchronised, the program waits for end of timer and waits
the specified time, needed to reach steady state of the ac-response.
The measurement is performed and results are calculated. If an overload is found,
the gains and if necessary the current range are corrected and measurement is
repeated at step 2. If the resolution of the measurement is too poor, the
measurement is repeated if a more optimal setting is possible.
Chapter 4
9
10
Measurements
55
The impedance is calculated. If the applied current range does not match the
measured impedance, the new 'best' current range is determined and if applicable,
the measurement is performed again from step 2.
The results are graphically displayed.
The pre-treatment as well as the measurements can be aborted by clicking the Abort
button or by pressing the <ESC> key. If the FRA-settings window is opened, it will
show whether the measurements are done properly. If the greenish button on the tool
bar is clicked, the monitor plots appear. They also give an indication about the quality
of the measurement. The results of the measurements are plotted in the data
presentation window. When no plot is loaded, the measurements will automatically be
presented in a Z” versus Z’ plot. See the View option on the data presentation window
for other plot types.
After the measurement the data are now always sorted on frequency. Data files
measured with older versions of the FRA software (version 2.1) are not sorted.
A sorted data-set can be obtained after saving a loaded data file, using the option
“Save work data” from the Data presentation window.
4.7 Technical background
This paragraph explains step by step the measurement sequence which is conducted
during the execution of a procedure. However, more dedicated this time towards the
software and hardware internals.
1.
Load the memory (RAM) of the digital signal generator (DSG).
The data to fill the memory of the DSG is read from the disk. On the disk several
files, each representing a specific signal type, must be present in the signal
directory:
- W_SIN01.F01 (FRA) or W_SGNL01.F12 and .F22 (FRA2)
: a single sine
- W_SIN02.F01 (FRA) or W_SGNL05.F12 and .F22
: five superimposed sine waves
- W_SIN03.F01 (FRA) or W)_SGNL15.F12 and .F22 (FRA2)
: fifteen superimposed sine waves.
The datafile contains 16384 (FRA) or 32728 (FRA2) words of 16 bits wide,
representing the specified signal. The content of this file is downloaded in the
memory of the DSG. The 16 bit DAC is set with a maximum frequency of 3.23
MHz (FRA) or 32 MHz (FRA2). The number of points or DA conversions per
sine wave depends on the frequency. With the FRA module, a single sine is
generated with 16384 points when the frequency is below 197 Hz. When the
frequency is below 976 Hz, the FRA2 generates it with 32768 points.
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2.
The amplitude of the signal is controlled by setting the 12 bit multiplying DAC,
providing a amplitude setting with a resolution of 1 in 4096. The output of the
DSG is filtered with a RC-filter.
3.
If the measurements have to be performed by using the autoranging facility, the
optimal current range is set, according to the specified input parameters. The
selected current range during autoranging depends on the value of the impedance
Z. The measured value at the selected current must be between
FACTOR1/(current range) and FACTOR2/(current range). The default values for
FACTOR1 and FACTOR2 are 0.2 and 5. Thus a current range of 1 mA is
selected for impedance’s between 200 ohm and 5000 ohm. The selected current
range depends on the applied frequency. This is due to the fact that lower current
ranges have a lower bandwidth (See Appendix).
4.
The filter is set to a cut-off frequency of the frequency to be measured multiplied
by a user-specified factor. In case a multiple sine is applied, the cut-off frequency
equals the highest frequency to be measured multiplied by this user-specified
multiplication factor. However, the highest cut-off frequency is limited to 140
kHz (FRA) or 160 kHz (FRA2). However, with the FRA2 modules a fixed filter
is used when the applied frequency is higher than 19 kHz. The lowest applied
cut-off frequency is limited by software. The default frequency limit is 10 Hz. A
cut-off frequency close to the applied frequency (factor for filter frequency close
to unity), cause significant attenuation of the signal as well as a severe phase
shift. Since both filters do not exactly match, a systematic error will be found. A
reasonable minimum value for this filter factor is 32.
5.
The conversion rate of the two simultaneous sampling ADC's is set. This is done
by using the same crystal as used for the 16 bit DAC, and by dividing its
frequency by an integer number.
The default number of points for one cycle of ADC's equals 1024. For lower
frequencies the FRA2 also measures 2048 or 4096 points per sine wave. At
frequencies higher than 200 Hz (FRA) or 488 Hz (FRA2) more than one sine
wave is measured with 1024 points. The oscilloscope windows will show more
than one sine wave.
Each memory location is 24 bits wide. Since the ADC's are 12 bits, the maximum
number of conversions per memory location equals 4096. Thus, a frequency of
for instance 200 Hz is sampled with 200 kHz conversion rate. Measurement of
one cycle takes 1/200 s = 0.005 s. Up to 4096 cycles can be measured and
averaged. The maximum time of measurement or integration time equals
1/200 Hz x 4096 = 20 s.
When the frequency of the applied sine wave is so low that the time between two
samples of the ADC allows more than one conversion per point, multiple
conversions are added within the same memory location. So, the conversion rate
of the ADC is always as high as possible, in order to perform as many
measurements as possible. The actual integration will never be shorter than the
specified integration time, and the time needed to complete the specified
minimum number of integration cycles (see FRA manual control window).
Chapter 4
Measurements
57
During conversions, the software checks the overload indicators. As soon as an
overload is detected, the measurement is aborted, the gain of the corresponding
amplifier is lowered, and the measurement is performed again.
6.
After completing the measurement, the data from the memory of the two ADC's
are read by the computer. A Fast Fourier Transform method is applied to
calculate the frequency spectra of both potential and current. These spectra are
used to calculate the in-phase and quadrature components of the impedance.
The software allows the user to view the data read from the memory; the 'time
domain plot' as well as the FFT processed signal; the 'frequency domain plot'.
For more information about the basics of the approach of this instrument, see:
R.J. Schwall, A.M. Bond, R.J. Loyd, J.G. Larsen and D.E. Smith, Analytical
Chemistry, Vol. 49, no.12, October 1977, p.1797-1805 and p.1805-1812.
4.8 Measurements using an Automatic mercury drop electrode
The Autolab instrument supports several mercury drop electrode configurations. The
IME or IME663 interface for mercury drop electrode provides an interface. The FRA
measurements can be done at a static as well as at a mercury drop electrode.
A new drop is created when "New drop" has been checked on page 2 of the Edit
procedure window and the presence of an automatic electrode is indicated in the
hardware configuration. In the sequence of events a new drop is created, just after the
first conditioning potential, or current stage has finished (if any):
•
•
•
In the Edit screen called 'Pre-treatment', 'Yes' is specified behind 'New drop'.
'Second conditioning time' is greater than zero. This means that a new drop is
created at this 'Second conditioning potential', after which the specified
conditioning time is included.
If 'Repeat pre-treatment before every frequency' is 'Yes' then every measurement
is performed at a new drop. In case it is 'No', but 'Yes' is specified for 'Repeat pretreatment before every potential', a new drop is created for each frequency scan at
a new dc-potential or dc-current.
4.9 Sequence of measurements in case of synchronised measurements
The sequence of measurements in case of synchronised measurements is as follows:
1. If the duration of the first conditioning potential or current is larger than zero, the
first conditioning potential or current is applied.
2. If 'New drop' is checked on Page 2 of the Edit procedure window, New drop
signals are generated.
3. If the duration of the second conditioning potential or current is larger than zero,
the second conditioning potential or current is applied.
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4. If the duration of the third conditioning potential or current is larger than zero, the
third conditioning potential or current is applied.
5. The measurement potential or current is applied.
6. The equilibration period starts with the ac-signal applied and the instrument
settings are controlled.
7. Immediately perform the measurements without controlling the settings. This
assures accurate timed or synchronised measurements, after applying the dcpotential or current.
8. If the measurement is incorrect i.e. an overload occurred or less accurate
measurements were recorded, the measurement sequence is repeated.
9. Depending on whether a repeat of the pre-treatment is required, the program
continues with point 1 or 5.
4.10 Measurements at open circuit potential
In case the frequency scan is to be measured at open circuit potential (OCP), the
equilibration stage is to be used to apply a potential where the measured current is as
low as possible.
The OCP, measured with the cell switched off, is applied at the start of the
equilibration stage. During this stage, the potential is continuously adjusted to a value
where the current is minimal.
In case the pre-treatment is repeated before each frequency, the applied potential may
vary from frequency to frequency. This feature is enabled with the option Repeat pretreatment before every scan or frequency.
The algorithm that minimises the current is as follows:
Ecoarse = 1.5 (in mV)
Efine = .15
(in mV)
Ncount = 15
Number of times Efine is used before return to Ecoarse
E = EOCP (first measured Open circuit potential)
Estep = Ecoarse
Read Current
PreviousCurrent = Current
iTel = 0
Repeat
E = E + Estep
Apply E
Read Current
if Sign (Current) <> Sign (PreviousCurrent) then Estep = Efine
if Estep = Efine then iTel = iTel + 1
if iTel > Ncount then iTel = 0: Estep = Ecoarse
PreviousCurrent = Current
Until Equilibration Stage is finished
Appendix I
FRA Data Files
Appendix I FRA Data Files
The following types of files are used by FRA
File
Description
Directory
*.PFR
directory
*.DFR
*.FMA
*.TXT
*.P??
Experiment parameters
Default procedure
Default data directory
Default data directory
Default data directory
*.MOT
Measured data
Project
Analysis results
Frequency, Z' and Z"/
File format for EQUIVCRT program
(?? = potential no.)
Frequency, Y' and Y"
(?? = potential no.)
Potential, Z' and Z"
(?? = frequency no.)
Potential, Y', Y" and Cs
(?? = frequency no.)
Mott Schottky data
SYSDEF40.INP
SYSDEF40.TXT
System definition parameters
Description of SYSDEF40.INP
Autolab directory
Autolab directory
W_SIN*.*
W_SGNL*.*
Signal file for DSG (FRA)
Signal file for DSG (FRA2)
Signals directory
Signals directory
FRA.INI
FRA2CAL.INI
FRA user settings
FRA2 calibration data
Autolab directory
Autolab directory
*.C??
*.F??
*.E??
Default data directory
Default data directory
Default data directory
Default data directory
Default data directory
59
Appendix II
Bandwidth and Gains
61
Appendix II Bandwidth and Gains
The bandwidth of the current follower depends on which current range is used. In the
system definition the highest applicable frequency for each current range is specified.
When the autoranging facility is used, i.e. more than one current range is enabled in
the Manual control window.
The optimal current range is determined by:
•
the dc current, the current should be given an analog output signal within the
linear range of the current to voltage converter (± 5 V),
•
the cell impedance, the ac output signal should have an amplitude high enough to
be measured accurately, but should also be within the linear range,
•
the applied frequency, the frequency must be lower than the specified maximum
frequency, so within the bandwidth of the current range.
The system default maximum frequency is 15Hz for the 100nA scale, 150Hz for the
1µA, 1500Hz for the 10µA and 10.000Hz for the 100µA. Higher current ranges are
not frequency limited. In case you want to change them, please contact Eco Chemie.
However, please note that they have been carefully chosen and wrong values can
deteriorate measurements.
The allowed gains of the amplifiers are also in the system definition file.
Possible values of the gains range from 0 (gain=1) to 9 (gain=512). The system
default for the maximum gain is 128 for all current ranges.
The minimum gain is 8 for all current ranges, except for the highest current range for
which the gain is set to 1.
Appendix III
Definition of procedure parameters
63
Appendix III Definition of procedure parameters
A.C. mode:
This is the most important measurement parameter. It determines whether the applied
ac-signal is a sine with one frequency or whether it is a signal composed of 5 sines
over one decade or 15 sines over two decades of frequencies. The multi-sine option is
suitable for low frequencies, when the measurement time should be as short as
possible.
Base frequency:
The lowest applied frequency in case the multi-sine mode is used. The applied signal
is a super imposition the specified base frequency and 4 or 14 higher harmonics.
Cell off after measurement:
When a measurement is completed, the cell can either be switched off or left switched
on at a potential or current specified as standby potential.
Comments:
A panel to type in several lines of text.
Current range:
Current range to be used for galvanostatic experiments.
Define potentials w.r.t. OCP:
The potential values specified under ‘Potential’ on page 1 are applied with respect to
the open circuit potential which is measured before the impedance measurements are
started. If the measurements have to be done at the open circuit potential, the value to
be specified is 0.000V. Note that the potentials given under pre-treatment and as
stand-by potential are not applied versus the open circuit potential.
Duration of measurement:
The total time the execution of the measurement should last, including the
equilibration time, in case a potentiostatic or galvanostatic time scan is made.
Enable internal ac-input of PGSTAT
Enable internal ac-input of PGSTAT:
If external inputs are used, the DSG signal is also applied to the PGSTAT.
End potential or current:
The last potential or current of a potential or current scan. This input is only requested
for the potential scan method.
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Equilibration threshold level:
If enabled, the Equilibration stage will be aborted after reaching this specified current.
The measurements will start as soon as this threshold is exceeded. This option is not
available for galvanostatic measurements.
Equilibration time:
Time between applying the dc-potential or dc-current and actual impedance
measurement. In case of synchronised measurements, the minimum time is 1 s.
First, second and third conditioning potential or current:
Before the actual ac-impedance measurement, a conditioning potential or current can
be applied. When the duration is set to zero, the stage is discarded.
Interval time:
The time between frequency scans of impedance measurements in case a
potentiostatic or galvanostatic time scan is made.
The minimum interval time is at least two seconds, but will depend on the ‘minimum
cycles to integrate’ and the ‘maximum time to reach steady state’ (see the FRA
manual control window). If the interval time is exceeded, a message will be given, but
the measurements will continue.
New drop:
If checked, a new mercury drop is created immediately after applying the first
conditioning potential. This option is only applicable if an Automatic electrode is
selected in the AUTOLAB hardware configuration program. Consult the proper
Appendix in case a mercury drop electrode is applied.
Potential or current:
Potential or current at which the measurement has to be performed. This input is only
requested for the single potential or current method.
Repeat pre-treatment before every:
The drop down menu appears from which the options 'no', 'frequency' and 'freq. scan'
can be selected. The latter option only appears in case potential or current scan is
made. 'no' means that the pre-treatment only takes place before the measurements.
Standby potential or current:
The potential or current applied as soon as the measurements have been performed.
Start potential or current:
The first potential or current of a potential or current scan. This input is only
requested for the potential scan method.
Step potential or current:
The potential or current increment between two successive measurements. This input
is only requested for the potential scan method.
Appendix III
Definition of procedure parameters
Stirrer on during conditioning:
Switch on the stirrer during the different conditioning stages.
Synchronised measurement:
If checked, the impedance measurement is performed after a waiting period equal to
the 'Equilibration time'. This allows measurement at a fixed time after applying the
dc-potential or dc-current.
For more information, please read the chapter about the measurement sequence.
Stop equilibrium at threshold
Enable the option to abort the equilibration stage when the Equilibrium threshold
level is reached.
Time to wait for OCP:
The time you want to wait for acceptance of the Open Circuit Potential. If this time
has expired the program will continue using the OCP measured at that time. If this
parameter is 0(zero), the program will not continue, unless the 'Accept' button is
pressed. If 0(zero) is specified in a procedure that is used in a project, the program
will wait for 1 second and will use the OCP measured at that moment.
Title and Subtitle:
Two lines of text to describe the experiment. These lines are the same as the ones
displayed above the plot.
65
Appendix IV
Combination of GPES and FRA
67
Appendix IV Combination of GPES and FRA
The FRA and GPES programs can be used at the same time. Moreover a FRA project
file can be executed from GPES. The command FRA!Start(<"filename">) is available
for this purpose.
However, in general it is important to note that both programs share the Autolab
instrument and the graphics part of the software. Moreover, both programs require a
considerable amount of the system resources. This means that when both programs
are active, hardly any system resources are left.
Practical rules are:
•
The computer should be equipped with 32 MB RAM
•
It is not possible that both programs measure and control the Autolab instrument
•
Before the FRA program starts measuring, the ‘sleep mode’ in GPES is
automatically switched on. This means that the GPES screen is no longer updated.
•
Do not use function keys when both programs are active, because they will cause
actions in both programs.
•
When a measurement procedure is being executed, user interaction with the
programs should be avoided.
•
Apart from GPES and FRA no other application should be active.
Appendix V
Noise considerations
Appendix V Noise considerations
Some rules for preventing excessive noise are:
•
Do not use unshielded cables and connections.
•
Place the electrochemical cell as far as possible from electrical appliances.
•
Place the cell inside a faraday cage.
•
The Differential Electrometer Amplifier increases the noise. Do not use it if it is
not required, i.e. a two or three (and not four) electrode cell is used and the dccurrent does not exceed approximately 10 to 50 mA.
•
Use the high stability mode where possible.
69
Appendix VI
Specifications
71
Appendix VI Specifications
µAutolab
type III /FRA2
Autolab with
PGSTAT12
Autolab with
PGSTAT302N
Autolab with
PGSTAT100
maximum output current
maximum output voltage
± 80 mA
± 12 V
± 250 mA
± 12 V
±2A
± 30 V
± 250 mA
± 100 V
potentiostat
galvanostat
yes
yes
yes
yes
yes
yes
yes
yes
potential range
applied potential accuracy
±5V
± 0.2% of setting
2 mV
150 µV
300 or 30 µV
± 10 V
± 0.2% of setting
2 mV
150 µV
300 or 30 µV
± 10 V
± 0.2% of setting
2 mV
150 µV
300 or 30 µV
± 10 V
± 0.2% of setting
2 mV
150 µV
300 or 30 µV
10 nA to 10 mA in
seven ranges
10 nA to 100 mA
in eight ranges
10 nA to 1 A
in nine ranges
10 nA to 100 mA
in eight ranges
± 0.2% of current
and ± 0.2% of
current range
0.015% of current
range
0.0003% of current
range
± 0.2% of current
and ± 0.2% of
current range
0.015% of current
range
0.0003% of current
range
± 0.2% of current
and ± 0.2% of
current range
0.015% of current
range
0.0003% of current
range
± 0.2% of current
and ± 0.2% of
current range
0.015% of current
range
0.0003% of current
range
30 fA
500 kHz
1 µs
30 fA
500 kHz
< 500 ns
30 fA
500 kHz
< 500 ns
input impedance of
electrometer
input bias current @25°C
bandwidth of electrometer
IR-compensation
high speed/
high stability
> 100 GΩ//< 8 pF
high speed/
high stability
> 100 GΩ//< 8 pF
30 fA
>1 MHz
< 250 ns
(with external source)
high speed/
high stability
> 1 TΩ//< 8 pF
< 1 pA
> 4 MHz
n.a.
- resolution
n.a.
< 1 pA
> 4 MHz
depending on selected
range: 0Ω-200Ω at
100 mA range to 0Ω200 MΩ at 10 nA
range, current
interrupt and positive
feedback available
0.025%
< 1 pA
> 4 MHz
depending on selected
range: 0Ω-20Ω at 1 A
range to 0Ω-200 MΩ
at 10 nA range,
current interrupt and
positive feedback
available
0.025%
< 1 pA
> 4 MHz
depending on selected
range: 0Ω-200Ω at
100 mA range to 0Ω200 MΩ at 10 nA
range, current
interrupt and positive
feedback available
0.025%
four electrode control
front panel meter
no
no
yes
potential and current
yes
potential and current
yes
potential and current
Analog outputs (BNC
connector)
control voltage input
multichannel option
potential and
current
no
no
potential, current and
optionally charge
yes
multipleWE option
potential, current and
optionally charge
yes
multipleWE option
potential, current and
optionally charge
yes
no
applied potential resolution
measured potential resolution
current ranges
applied and measured
current accuracy
applied current resolution
measured current
resolution
- at current range
of 10 nA
potentiostat bandwidth (1)
- potentiostat risetime/falltime
(1 V step, 10-90%) (1)
potentiostat modes
high speed/
high stability
> 100 GΩ//< 8 pF
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Version 4.9
µAutolab
type III /FRA2
Autolab with
PGSTAT12
Autolab with
PGSTAT302N
Autolab with
PGSTAT100
booster option
no
no
yes
analog integrator
- time constants
yes
10 and 100 ms,
1 and 10 s
optionally available
10 and 100 ms,
1 and 10 s
optionally available
10 and 100 ms,
1 and 10 s
on request BSTR10A
only
optionally available
10 and 100 ms,
1 and 10 s
interfacing
A/D converter
USB
16-bit with software
programmable gains
of 1, 10 and 100
USB
16-bit with software
programmable gains
of 1, 10 and 100
USB
16-bit with software
programmable gains
of 1, 10 and 100
USB
16-bit with software
programmable gains
of 1, 10 and 100
auxiliary input channels
D/A converter
1
16-bit
three channels
1
48
2
16-bit, four channels
(optionally eight)
1
48
2
16-bit, four channels
(optionally eight)
1
48
2
16-bit, four channels
(optionally eight)
1
48
26 x 26 x 10 cm³
4.2kg / FRA2
144 W
100-240 V, 50/60 Hz
52 x 42 x 17 cm³
18 kg
247 W
100-240 V, 50/60 Hz
51.5 x 41.6 x 16 cm³
18 kg
247 W
100-240 V, 50/60 Hz
52 x 42 x 17 cm³
21 kg
300 W
100-240 V, 50/60 Hz
auxiliary output channel
digital I/O lines
(W x D x H)
weight
power requirements
Notes:
(1) Measured at 1 mA current range, 1 kOhm impedance, high speed mode when applicable.
All specifications at 25°C.
Hardware specifications
FRA modules
•
frequency range
•
applied amplitude
•
•
•
•
resolution of DSG
output impedance of DSG
resolution of dual channel ADC
ADC input ranges
FRA2 module
•
frequency range
•
applied amplitude
•
•
•
•
resolution of DSG
output impedance of DSG
resolution of dual channel ADC
ADC input ranges
0.1 mHz to 50 kHz
0.2 mV to 0.35 V(rms) with steps
of 0.1 mV (potentiostatic mode)
0.0002 to 0.35 with steps of 0.0001 times applied
current range (galvanostatic mode)
1 in 65536 (16 bits)
50 Ohm
1 in 4096 (12 bits)
0.01 V to 5 V
(10 ranges, software programmable)
10 µHz to 1 MHz
0.2 mV to 0.35 V(rms) with steps
of 0.1 mV (potentiostatic mode)
0.0002 to 0.35 with steps of 0.0001 times applied
current range (galvanostatic mode)
1 in 65536 (16 bits)
50 Ohm
1 in 4096 (12 bits)
0.01 V to 5 V
(10 ranges, software programmable)
Appendix VI
Specifications
Software specifications
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
maximum number of frequencies * maximum
number of dc-potentials or dc-currents
measurement modes
automatic current ranging
1st, 2nd and 3rd conditioning time
1st, 2nd and 3rd conditioning potential
or conditioning current
wait time before measurement
stand-by potential
stand-by current
potential scan measurement
initial and final potential
current scan measurement
initial and final current
20000 (not checked)
single sine
5 superimposed sines
(within one decade)
15 superimposed sines
(within two decades)
optional mode
0 - 30000 s
± 10 V
± 1 A (PGSTAT12/20/30/100) or
± 50 mA (PGSTAT10)
0 - 30000 s
± 10 V
± 1 A (PGSTAT12/20/30/100) or
± 50 mA (PGSTAT10)
±5V
± 1 A (PGSTAT12/20/30/100) or
± 50 mA (PGSTAT10)
time scan measurement
end time
interval time
integration time
minimum number of cycles to be integrated
minimum number of cycles to reach steady state
maximum time to reach steady state
With a minimum fraction of cycle
1 - 30000 s
1 - 30000 s
0.1 - 10000 s
1 - 16
0 - 30000
0 - 30000 s
0 - 10
repeat prepolarisation before each frequency scan
repeat prepolarisation before each frequency
synchronised measurement
cell off after measurement
potentials with respect to open circuit potential
Y/N
Y/N
Y/N
Y/N
Y/N
73
Appendix VII
Theoretical considerations on the performance of FRA instrument
75
Appendix VII Theoretical considerations on the performance
of FRA instrument
The performance of the FRA impedance analyser depends partly on the construction
principles and partly on the setup parameters, i.e. the integration time, the number of
integration cycles and the time to reach steady state. These parameters can be
specified on the FRA manual control window.
In this appendix it is investigated how the measurement results depend on these
parameters. Moreover, this appendix can be used to compare the measurement
principle of the FRA with other impedance analysers.
All the data presented in this appendix result from numerical simulation.
Effect of integration time on noise rejection
The effect of integration time on noise rejection is determined by numerical
simulation. The transfer function of the FRA module as a function of the frequency,
normalised with respect to e.g. 1000Hz, for a different number of integrated cycles
has been calculated. The transfer function is calculated by performing Fast Fourier
Transformation on the signal generated with frequency f. The amplitude found at
frequency f0 gives the transfer function. Frequency f0 is in fact the frequency at which
the impedance should be measured. The transfer function shows the theoretical noise
rejection ability.
Fig.22 Transfer function of the FRA module as a function of the normalised frequency
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The transfer function, i.e. the impedance normalised with respect to f = f0, is
calculated for a different number of integration cycles. In case of e.g. 100 Hz, an
integration time of 0.01 s gives one integration cycle. The default integration time of 1
s gives 100 integration cycles.
The transfer function resembles the calculated curve for a different FRA instrument
based on correlation with synchronous reference signals (Ref. Impedance
Spectroscopy by J. Ross Macdonald (Ed.), Wiley, New York, 1987).
Conclusion:
It is clearly shown that a larger number of integration cycles, and thus a longer
integration time, significantly improves noise rejection.
Effect of noise on impedance measurements
The effect of noise on impedance measurements can also be simulated. This is done
by adding noise with frequency f to a signal of interest at frequency f0. The
calculations are done using a sine wave for the potential and the current. Both have
the same amplitude and frequency f0. A sine wave with the same amplitude but
different frequency f is superimposed on the potential and current perturbations.
The simulation is performed assuming a current range of 1 mA. The perfect
impedance should therefore be 1.000 kOhm and the phase shift 0. When the frequency
of the noise is f0 as well, the amplitude of the current signal will be doubled. This
yields an impedance of 500 ohm.
Fig. 23 Effect of 'noise' with frequency f on the impedance measured at frequency f0. The
'noise' amplitude is equal to the amplitude of the frequency of interest f
Conclusion:
A longer integration time will improve the result of the measurements.
Appendix VII
Theoretical considerations on the performance of FRA instrument
77
Effect of non-stationary dc-current
Impedance measurements with a non-stationary dc-current are simulated by
performing FFT calculations on a pure sine wave for the potential and sine wave with
super-imposed dc-slope for the current.
The error in the calculated impedance Z as a function of the dc-component of the
current has been investigated. In the simulation calculation it is assumed that the
current range is 1 mA and the 'real' impedance is 1.000 ohm.
Fig. 24 Effect of non-stationary dc-current on calculated impedance
x is the relative change in dc-current, x= 0 corresponds to a perfect stationary current,
for x= 1 the change in dc-level is equal to the peak amplitude after exactly one period
of the sine.
It shows that significant errors are found at low values of x. A small dc-ramp will give
a significant error.
Conclusion:
Impedance measurements should be done under stationary conditions.
The dc-current for potentiostatic measurements should be constant and for
galvanostatic measurements the dc-potential should not vary.
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Effect of measurement resolution
The amplitude of the measured potential and current signals depends on the output of
the potentiostat/galvanostat. The current range determines the amplitude for the
current signal. The setting of the amplifiers of the FRA also determines the amplitude
of the final measurement. The recorded amplitudes are shown in the 'FRA control’
window, as well as in the 'Oscilloscope' windows. The maximum resolution is 100 %,
however, a much lower amplitude is often found.
The effect of varying amplitude or resolution of the current signal on the calculated
impedance has been investigated.
Fig. 25 Percentage error in the impedance as a function of the resolution of the current
measurement. The resolution is given in percentage.
The curve is valid for a resolution of the potential of 50 %, normally found at an
amplitude of 15 mV (rms). A resolution of 0.5 % is observed for a measurement of an
impedance of 100.000 ohm, when the current range is 1 mA.
Conclusion:
A minimum resolution of 0.5% is required if the maximum impedance error should be
better than 1%. A higher accuracy than 0.2% requires a minimum resolution of 1%.
Appendix VIII
Fit and Simulation
79
Appendix VIII Fit and Simulation
The Fit and Simulation option in the program allows you to simulate responses of
equivalent circuit and to fit the circuit parameters to the measured data, using the nonlinear least squares method. The equivalent circuits can be defined by the user (using
Circuit Description Code). It is possible to define elements with fixed values as well
as constraints for values of fitted parameters. This option is based on the work of Dr.
B.A. Boukamp as first published in Solid State Ionics, 20 (1986) 31-44 and coded in
the program EQUIVCRT by the same author.
Circuit description code (cdc)
This is a code used for defining equivalent circuits. It consists of letters representing
circuit elements and round and square brackets representing parallel or serial
arrangement of elements. The table below shows the meaning of the letters:
letter
R
C
L
W
element
resistance
capacitance
inductance
Warburg impedance
letter
Q
T
O
G
element
constant phase element (CPE)
hyperbolic tangent element
hyperbolic cotangent element
Gerischer impedance
Square brackets mean that the elements enclosed in the brackets are arranged in
series. Elements enclosed in round brackets are arranged in parallel. In order to
simplify the notation it is assumed, that if CDC starts with letter instead of a bracket,
the elements are arranged in series. Therefore, [R(CW)] and R(CW) are equivalent.
A number of examples of CDC together with the corresponding equivalent circuits are
shown:
RCL
(RCL)
R(RQ)
R(C[RW])
R(C[R(C[RW])])Q
Dispersion functions for elements
The table below defines the dispersion functions for the elements in both impedance
and admittance representation (ω = 2πf).
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User Manual
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CDC
element
impedance
admittance
R
resistance
R
1R
R
C
capacitance
− j ( ωC )
jωC
C
L
inductance
jω L
− j ( ωL)
L
W
Warburg
impedance
1 / Y0 jω
Y0 jω
Y0
Q
constant phase
element
1 / (Y0 jω )
(Y0 jω ) n
Y0 , n
T
hyperbolic
tangent element
(Y
O
G
hyperbolic
cotangent
element
Gerischer
impedance
(
)
n
) (Y
(Y jω ) tanh( B jω ) (Y
jω
0
)
−1
(
coth B jω
(Y )
0
−1
Ka + jω
)
(
)
Y0 , B
)
(
)
Y0 , B
0
jω tanh B jω
0
jω coth B jω
−1
0
parameters
Y0 Ka + jω
Y0 , Ka
(Please note that the definition of the Q element differs from the EQUIVCRT program
of Dr. B.A. Boukamp)
Fit and simulation window
When the Fit and Simulation window is opened, the settings are similar to the
previously closed window. The window has a number of drop-down menus and a
panel for equivalent circuit description (CDC) located at the top. A list of parameters
of CDC elements and a panel for parameter editing are located at the middle of the
window. The Fit panel and buttons for starting and stopping fit and simulation are
located at the bottom of the window. The functions of these components are described
below.
File menu
Load circuit
Loads the previously saved user-defined equivalent circuit from the disk.
Save circuit
Saves the currently used equivalent circuit to the disk.,
Copy to work data
The most recent calculated data, which result either from a simulation or from the fit,
are turned into the so-called ‘work data’ and thus remain available after closing the Fit
and simulation window. Normally, the fitted and simulated data sets are erased. The
work data can be stored on disk using the File option on the Data presentation
window.
Appendix VIII
Fit and Simulation
81
Close
Closes the window and returns the focus back to the Data presentation window. The
simulated and fitted data sets are lost, unless Copy to work data is used. Results of
fitting are printed in the Analysis results window.
Edit menu
Circuit Description
Opens a window for entering or editing the Circuit Description Code (CDC). The
CDC can be modified and also standard circuits can be inserted using the "Insert
circuit" command in the toolbar. If the code contains syntax errors (like bracket
mismatch), it will not be accepted. The Help button displays a list of available
elements and shows examples of circuits and their CDC's.
Fit control parameters
Opens a window in which fitting-related parameters, like convergence criteria,
iteration limit and the type of fit can be set:
- Maximum change in χ2 (scaled): this is one of the convergence criteria. Fitting will
not be finished until the absolute change in the chi-square parameter (including
weight factors) will be lower than this value. The default value is 0.001.
- Maximum number of iterations: fitting will always stop if this number is exceeded.
The default is 50.
- Number of iterations per fitting step: the fitting step, finished by displaying a new
data set and update of the parameter set on the screen, can consist of a single or
multiple iterations. This option is useful if the program is running on a relatively slow
computer because update of the screen takes some time, so increasing the number of
iterations per fitting step can result in a slight improvement of fitting speed.
- Maximum number of iterations giving no improvement: if during the fit there is no
change in the specified number of consecutive iterations χ2 value and other
convergence criteria are still not satisfied, the program stops with an appropriate
warning. It usually suggests that the model is not appropriate - no further
improvement can be obtained while the χ2 value is still too high. The recommended
action is to change the CDC or - if the fitted curve differs very much from the
examined data set - to try other starting values for fitted parameters.
- Use weighted fit: if this box is checked, each point is multiplied with a weight factor
equal to the inverse of the square of the impedance modules,
i.e. w=1/((Z')2 +( Z")2). If this box is empty, weight factors for all points are equal to
the inverse of square root of mean impedance modules.
It is important to note that in addition to the explicit convergence criteria (i.e., max.
change in χ2) there is an implicit criterion that the change in the parameter value
during one iteration should not exceed 0.5%.
Options menu
The following items are available in this menu:
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Select frequencies
Using this option one can select the frequencies used in simulation or fitting.
Use constraints
The fitting procedure uses internal (default) constraints for maximum and minimum
values of parameters. If these limits should be changed, the Use constraints option
should be activated. The limits can then be set manually in the parameter editing panel
in the middle part of the Fit and Simulation window.
Show covariance matrix
This option displays a covariance matrix after a successful fit has been completed. In
the covariance matrix the diagonal elements are unity, and off-diagonal terms are a
measure of covariance (interdependence) of the parameters. In general, the offdiagonal values should be small compared to diagonal elements. If large off-diagonal
elements are present, it suggests that the parameter corresponding to the row is not
independent from the parameter corresponding to the column in the matrix. Fitting
does not give correct results if parameters are not independent.
The absolute value of elements of the covariance matrix depend on the way the
weighing factors are defined.
Show residual plot
Displays residual plot (i.e., difference between the fitted and the measured data) for
both real and the imaginary part of impedance/admittance.
Circuit description panel
This panel displays the current Circuit Description Code (CDC). Each circuit element
consist of a character describing its type, and a digit to distinguish between elements
of the same type. To enter a new CDC or to modify the existing one, it is necessary to
click the panel, to use Circuit description option of the Edit menu, or to press controlC. The Edit circuit description window appears, which allows to modify the CDC, or
paste one of standard CDC. In this sub-window only letters, standing for elements,
and the brackets should be entered - the digits are added automatically when the subwindow is closed. The Help button gives an overview of the codes and bracket uses.
The Insert circuit menu at the top of the sub-window allows you to insert complete
circuits.
List of CDC parameters
The list at the middle part of the Fit and Simulation window shows symbols of
elements (as in the CDC string above), accompanied by current values of their
parameters, the error estimate (appears after the successful fit) and the information
whether the parameter is fitted or kept fixed. When CDC is modified, the values of
element parameters are defaults used as start values.
If an element from the list is selected, its parameters and settings can be edited in the
parameter editing panel directly below the element list.
Panel for parameters editing
In this panel the full description of the element selected in the list above is available
and can be edited. The values of parameters can be changed, and the parameter can be
made fitable or fixed. If the ‘Use constraints’ option (Option menu) is selected, the
Appendix VIII
Fit and Simulation
83
limiting values for the parameters can be adjusted (otherwise, internal defaults for
maximal and minimal values are used).
Fit panel
This panel allows to choose whether fitting and simulation should use impedance or
admittance representation of the data. In the lower part of the panel the status of
fitting is displayed (iteration number, fit finish, error indication) together with the
value of χ2.
Fit/Simulation switch
Using this switch one can choose between the fitting function and the simulation
function. When simulation is chosen, the buttons Simulate and Close will appear.
When fitting is chosen, three buttons are available: Fit, Stop Fit and Close.
Using fit and simulation
Fitting of equivalent circuit to the measured data
1. Load data.
2. Choose Fit and Simulation from Analysis menu (Data presentation window).
3. Make sure that the switch Fit/Simulation (bottom part of the window) is in Fit
position.
4. Load a previously saved Circuit Description Code (Load circuit option from File
menu, Fit and Simulation window) or click the Circuit Description panel to open a
sub-window to enter the CDC manually.
5. Either type in the circuit code, or insert one of the standard predefined circuits. The
predefined circuit is inserted at the cursor position, so they can be combined with
user-defined circuits.
6. Press OK in the sub-window to return to the Fit and Simulation window. The CDC
is now displayed in the Circuit description panel, each element having an ordinal
number added to the element's symbol.
7. Select elements (one by one) in the element list below the Circuit description
panel. Enter the starting value of the parameter (or leave the default) and choose
whether the parameter should be fitted or not. If special constraints for element
values are necessary, change the minimum and maximum allowed values of
parameters (this may require selecting option Use constraints from Option menu
located in Fit and Simulation window).
8. Choose whether the fitting should take place in impedance or admittance
representation. Element parameters are defined independently of the actual
representation used.
9. Press the Fit button.
10.If the fit is not satisfactory, press the Fit button again (you can also increase the
maximum number of iterations selecting Fit control parameters in Edit menu of Fit
and Simulation window) in order to continue with fitting.
11.You may wish to change the fit settings (Edit menu, Fit and Simulation window) to
fine-tune the fitting process. Or select points for fit (Select frequencies in Option
menu, Fit and Simulation window).
12.Fit results are automatically copied to Analysis window.
13.Should an error message appear, consult the section on error conditions.
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14.If the fit is finished, you may want to save the used CDC. To do this, use the ‘Save
circuit’ option from the File menu (Fit and Simulation window)
15.If you want to use or save fitted data set, choose the option Copy to work data (File
menu, Fit and Simulation window) to replace the actual data set with the fitted
data.
16.Finish fitting by pressing Close button.
Simulation of equivalent circuit response
1. Load the data file FRADEMO from the \AUTOLAB\TESTDATA directory
2. Choose Fit and Simulation from Analysis menu (Data presentation window).
3. Make sure that the switch Fit/Simulation (bottom part of the window) is in
Simulation position.
4. Open the File menu on the Fit and Simulation window. Load the Circuit
Description Code file FRADEMO from the \AUTOLAB\TESTDATA directory.
This circuit will fit rather well.
5. Click the Circuit Description panel to open a sub-window to enter the CDC
manually.
6. Either type in the circuit code, or insert one of standard predefined circuits. The
predefined circuit is inserted at the cursor position, so they can be combined with
user-defined circuits.
7. Press OK in the sub-window to return to the Fit and Simulation window. The CDC
is now displayed in the Circuit description panel, each element having an ordinal
number added to the element's symbol.
8. Select elements (one by one) in the element list appearing below the Circuit
description panel. Enter the value of the parameter.
9. Choose whether the simulation should take place in impedance or admittance
representation (the displayed result is always in the same representation as the
displayed data set). Element parameters are defined independently of the actual
representation used.
10.Press Simulate button.
11.If the simulation is finished, you may want to save the used CDC. To do this, use
option Save circuit option from File menu (Fit and Simulation window)
12.If you want to use or save simulation results, choose option Copy to work data
(File menu, Fit and Simulation window) to replace the actual data set with the
simulated data.
13.Finish simulation by pressing Close button.
Fit and simulation error messages
error -1: "xxxx"
Internal error of the fit and simulation module. String "xxxx" contains specific
information about the problem. Please report “xxxx” and the circumstances under
which this error appeared.
error 1: Not enough memory
There is not enough memory to carry out fit or simulation. Try to free some memory
by closing other applications.
Appendix VIII
Fit and Simulation
85
error 2: Overflow in numerical calculations
Value of parameters are so large or so small that overflow appears in numerical
calculations. Check the values of element parameters and change them (or use
constraints) to more moderate values.
error 51: GAUSSJ: Singular Matrix-1
Two or more parameters are dependent or nearly dependent. This error can also
happen if some parameters have extreme values. Consider use of another CDC,
change parameters to more moderated values or use constraints.
error 51: GAUSSJ: Singular Matrix-2
Two or more parameters are dependent or nearly dependent. This error can also occur
if some parameters have extreme values. Consider using another CDC, change
parameters to more moderated values or use constraints.
error 60: error in CDC
The entered CDC is not correct.
Appendix IX
Kramers-Kronig test
87
Appendix IX Kramers-Kronig test
The Kramers-Kronig test
The Kramers-Kronig (K-K) test can be used to check whether the measured system is
stable in time and linear. Stability and linearity are a prerequisite for fitting equivalent
circuits. If the system changes in time the data points measured on the beginning of
the experiment do not agree with those measured at the end of the experiment.
Stability problems are most likely to be observed in low frequency range.
In fact, the K-K test checks whether the measured data comply with the assumptions
of Kramers-Kronig transformation. These assumptions are: (1) the response is only
related to the excitation signal, (2) the response is linear (or the perturbation is small,
e.g. <10 mV, for non-linear systems), (3) the system does not change with time and
(4) the system is finite for all values of ω, including zero and infinity. If the
investigated system changes with time due to e.g. ageing, temperature change, nonequilibrium initial state etc., the test fails.
The idea of K-K test is based on fitting a special model circuit (which always satisfies
K-K assumptions) to the measured data points. If the measured data set can be
represented with this circuit, then the data set should also satisfy Kramers-Kronig
assumptions. The special circuit used in the test is a series of RC circuits (for
impedance representation) or a ladder of serial RC arrangements (for admittance
representation). These circuits are shown below:
C
R
circuit for impedance representation
R
circuit for admittance representation
C
L
L
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By default, the number of RC circuits or RC serial arrangements is equal to the
number of data points. If there is a chance that the measured signal was very noisy,
the number of circuits may be reduced to avoid overfitting and - consequently including the noise in the model.
The ‘Tau-range factor’ is a special parameter which is default set to 1. It is related to
the distribution of RC-times in the circuits, which are kept fixed during the fit. In the
‘K-K’ fit is only done on the R-value of each RC-circuit. The parameter should not be
modified unless the theory, as fully described in the article by
B.A. Boukamp, J. Electrochem. Soc. 142, 1885 (1995), is understood.
The result of the test is the value of pseudo χ2, the sum of squares of the relative
residuals. In each case the χ2 for the real and the imaginary part is reported (overall χ2
is a sum of real and imaginary χ2). Large χ2 value means bad fit, small value - good
fit. What is actually large and small depends on the number and the value of data
points. As a rule of thumb, values lower than 10-6 usually mean an excellent fit,
reasonable between 10-5 and 10-6 , marginal between 10-4 and 10-5 and bad for even
higher values. Moreover, the residuals should be small and randomly distributed
around zero.
The test can be carried out on real part, imaginary part or both part of
admittance/impedance (complex fit). In the case of fit on one part only, the second
part of the measured data set is generated using Kramers-Kronig transformation (on
the assumption that the system obeys K-K criteria) and then χ2 for the second part is
computed.
Definitions of pseudo χ2
[Z re,i − Z re(ω i)] +[Z im,i − Z im(ω i)]
2
χ
N
2= ∑
ps
i =1
2
Z (ω i )
[Z re,i − Z re(ω i)]
2
2
χ
N
re
2=∑
i =1
Z (ω i )
2
[Z im,i − Z im(ω i)]
2
χ
N
im
2=∑
i =1
Z (ω i )
2
Zre,i and Zim,i are the experimental data.
Zre(ωi) and Zim(ωi) are the fitted, calculated values.
In addition to χ2, the serial or parallel (depending on representation) R, L and C
values are computed (see circuits). These values do not have any special meaning and
they simply belong to the set of results of K-K test. In particular, they should not be
associated with any serial or parallel elements present in the system or its equivalent
circuit representation.
The detailed discussion of the Kramers-Kronig test, the theory underlying the choice
of parameters, and a refined interpretation of the outcomes can be found in the
previously mentioned article of Dr. B.A. Boukamp. It is advised to read this article
before this option is used.
Appendix IX
Kramers-Kronig test
89
Using the Kramers-Kronig test
1. Load the data file FRADEMO from the \AUTOLAB\TESTDATA directory.
2. From the Analysis menu (Data presentation window) select Kramers-Kronig test.
3. Choose whether impedance or admittance representation of the tested data should
be used.
4. Modify the number of subcircuits if necessary (default number of subcircuits is
equal to the number of data points).
5. If necessary, change the number of frequencies per decade using the extension
factor (default=1, i.e., the number of frequencies per decade is the same as in the
measured data).
6. Choose the type of the test: complex, real or imaginary.
7. Press Start test button.
8. To leave the window, press Close button.
Appendix X
Hydrodynamic Impedance Measurements
91
Appendix X Hydrodynamic Impedance Measurements
Autolab instruments equipped with the FRA2 module can be used for hydrodynamic
impedance measurements.
The required external connections to the BNC connectors at the front panel of the
FRA2 module are:
- 'signal out' to the input of the controller of the rotating disk electrode (RDE)
- 'Y' to the output of the controller of the RDE
- 'X' to the current output marked ‘Iout’ at the rear of Autolab
These connections have to be made using shielded BNC cables.
The 'signal out' of the FRA2 module is used to modulate the rotational speed of the
RDE.
The impedance analyser part of the FRA2 measures the signal from the RDE
controller and the current intensity from the potentiostat/galvanostat.
When signals coming from the X and Y external inputs on the front panel have to be
measured, this can be specified in the FRA manual control window. The check box
'Use external inputs' in this window must be checked.
The message 'External inputs are used!' appears after the START button has been
pressed.
Appendix X
Index
93
Index
A
ADC...................................................................................................................................... 7, 8, 9, 56, 57
Analysis results.......................................................................................................................................51
Automatic mercury drop electrode .........................................................................................................57
axis annotation........................................................................................................................................36
axis description .......................................................................................................................................47
axis labels .........................................................................................................................................47, 48
axis text.............................................................................................................................................16, 41
B
Batch mode .............................................................................................................................................26
BMP........................................................................................................................................................36
Burette control ........................................................................................................................................23
C
calibration file.........................................................................................................................................22
circle ...........................................................................................................................................15, 43, 44
click ..........................................................................................................................................................6
colours ..............................................................................................................................................47, 48
Computer ..................................................................................................................................................5
concept......................................................................................................................................................5
configuration.............................................................................................................................................5
Convert .............................................................................................................................................18, 20
copy ........................................................................................................................................................36
Copy ...........................................................................................................................................27, 36, 51
current range ................................................................................................. 31, 32, 33, 54, 55, 56, 61, 63
Cut ..........................................................................................................................................................27
D
Delete files..............................................................................................................................................22
double-click ..............................................................................................................................................6
DSG ...................................................................................................................................... 7, 8, 9, 55, 56
E
Edit frequencies ......................................................................................................................................50
Edit procedure.........................................................................................................................................11
Electrode control.....................................................................................................................................23
Exit .........................................................................................................................................................22
F
F1..............................................................................................................................................................6
F4..............................................................................................................................................................6
F5..............................................................................................................................................................6
F6..............................................................................................................................................................6
file...............................................................................................................................................36, 40, 61
File menu ..........................................................................................................................................19, 35
frequency distribution.......................................................................................................................17, 50
G
galvanostat..........................................................................................................................................5, 11
Galvanostatic current scan......................................................................................................................22
Galvanostatic single current ...................................................................................................................22
graphical items........................................................................................................................................47
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graphical settings ....................................................................................................................................42
graphics............................................................................................................................... 5, 6, 19, 42, 48
H
hardware description.................................................................................................................................7
help .................................................................................................................................................5, 6, 30
I
impedance spectrum .........................................................................................................................12, 15
instrument .................................................................................................................................................7
iR-compensation.....................................................................................................................................33
Isotropic plot...........................................................................................................................................41
L
linear regression..........................................................................................................................14, 15, 43
Load data ................................................................................................................................................20
M
Manual control............................................................................................................ 5, 11, 13, 14, 31, 34
merge ......................................................................................................................................................36
Method............................................................................................................ 8, 12, 16, 22, 30, 57, 63, 64
mouse........................................................................................................................................................6
MS-Windows............................................................................................................................................5
MS-Word ......................................................................................................................................5, 35, 36
MULTI4 .................................................................................................................................................25
multi-sine ..........................................................................................................................................36, 63
MUX control...........................................................................................................................................25
O
Ohmic drop.......................................................................................................................................16, 45
Open procedure.......................................................................................................................................19
Oscilloscope windows ............................................................................................................................14
P
Paste........................................................................................................................................................27
Plot........................................................................................................................................ 12, 16, 17, 40
plot title...................................................................................................................................................47
potential .............................................................. 16, 17, 22, 30, 33, 35, 37, 38, 39, 40, 50, 54, 57, 63, 64
potentiostat ...................................................................................................................................5, 11, 19
Potentiostatic potential scan ...................................................................................................................22
Potentiostatic single potential .................................................................................................................22
Preface ......................................................................................................................................................5
pre-treatment............................................................................................................. 50, 54, 55, 57, 58, 64
Print ....................................................................................................................................................6, 20
Print setup... ............................................................................................................................................20
Project.........................................................................................................................................26, 27, 30
Project wizard .........................................................................................................................................29
R
resolution ............................................................................................................................ 8, 9, 33, 54, 56
Resume ...................................................................................................................................................40
S
Save data.................................................................................................................................................20
Save procedure .......................................................................................................................................20
Save procedure as ...................................................................................................................................20
Save work data........................................................................................................................................36
SCNR16A...............................................................................................................................................25
Appendix X
Index
95
SCNR8A.................................................................................................................................................25
Select frequency ...............................................................................................................................17, 39
Select potential c.q. currents ...................................................................................................................37
semi-circle ................................................................................................................ 12, 14, 15, 40, 43, 44
sequence ...........................................................................................................................................54, 57
settings........................................................................................................................ 5, 33, 35, 42, 55, 58
single-sine...............................................................................................................................................36
Status bar ................................................................................................................................................31
subtitle ....................................................................................................................................................47
synchronized measurements .......................................................................................................57, 58, 64
T
Technical background.............................................................................................................................55
textbooks...................................................................................................................................................7
tool bar....................................................................................................................................5, 11, 30, 55
trigger .....................................................................................................................................................25
types of files............................................................................................................................................59
U
Utilities ...................................................................................................................................................23
V
View .......................................................................................................................................................36
viewing data............................................................................................................................................47
W
WMF.......................................................................................................................................................36
Z
zoom ...................................................................................................................................................6, 40
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