1.0.0 Introduction

Electrochemical noise is naturally generated during corrosion of metals, and can be easily measured by using commercially available potentiostats and zero resistance ammeters. This procedure does not introduce any perturbation to the corroding surface. The measured electrochemical noise can be then analysed to provide invaluable information on the corrosion process.

The new electrochemical noise analysis software, ECN Analysis 1.0, provides a cutting-edge tool to analyse the electrochemical noise data both by statistical methods and Fast Fourier Transform. ECN analysis 1.0 calculates the time evolution of noise resistance, low-frequency noise impedance, charge and frequency of corrosion events based on the user selected parameters (see "Selection of processing parameters").

1.1.0 Algorithms used in the software

In this section, the algorithms used in the software are described.

1.1.1 Segmentation of the Original Dataset

In order to obtain time-dependent quantities (noise impedance, noise resistance, average charge of a corrosion event, average frequency of corrosion events), the original dataset is segmented in shorter consecutive and partially overlapping datasets. The calculation of the relevant quantities is the performed iteratively using the potential and current segment as input data. In practice, at the first iteration, a segment of a number of points defined by the parameter length of FFT is extracted and used for the calculation, as described below. The results of the calculations are assigned to the time corresponding to the time of the first point of the extracted segment.The time position of the first point of the segment being extracted is represented graphically by the moving points in the screen Time Record.

Figure 1.0 Segmentation of the Original Data Set

Figure 2.0 The Calculations are performed iteratively using potential and current segments

1.1.2 Calculation of potential and current power spectral densities

At the next iteration, a segment of identical size is extracted from the time record, the calculation repeated, and the results assigned to the time value corresponding to the first point of the second extracted segment. The spacing between segment can be adjusted by modifying the overlap parameter in the preference window. For example, if a step size of 1024 is selected and an overlap of 50 % is selected, the first points of two consecutive segments is spaced of 512 points. The spacing between one segment and the following is displayed on the Parameters screen and is rounded to the higher closest integer. Any value between 1% and 99% overlap can be selected in the preferences menu.

Figure 3.0. The Time position is represented graphically by a moving point ( a diamond shape ) in the Time record.

Figure 4.0 ECN Analysis 1.0 calculates the linear trend for the potential and current segments

The segment iteratively extracted from the complete potential and current noises time records are displayed on the Processing screen. The length of the extracted segment can be adjusted between 128 and 4096 points in the preference menu by changing the Length of FFT parameter. On the same screen, the linear trend line is displayed overlapped the extracted segment. Such trend line is subtracted, to obtain the linear trend removed potential and current segment, required for FFTs.

Fig 5.0 Linear Trend Removal

Prior to performing fast fourier transform (FFT), a window is applied to the linear trend removed segments . The window type can be selected from the preference menu under “window type”. Once the segment are de-trended and windowed, the power spectral density is calculated by using FFT (single side), and displayed both in screen Processing and screen PSD.

Figure 6.0 Current Power Spectral Density and Potential Power spectral Density.

1.1.3 Calculation of noise impedance spectra

The noise impedance spectrum is calculated from power spectral densities of noise potential and noise current. The potential power spectral density is divided by the current power spectral density , and the square root of this result provides the noise impedance spectrum. This is illustrated in Figure7.0 .

Figure 7.0 Noise Impedance is calculated from Potential PSD and Current PSD.

1.1.4 Averaging of noise impedance spectra

Generally, the noise impedance spectra are relatively noisy and it is useful to average several impedance spectra to obtain a less noisy spectrum. In the screen PSD, the Averaged Impedance graph displays a moving average of a number of spectra. The number of spectra used to calculate the moving average can be selected in the preferences menu.

Figure 8.0 Noise Impedance spectra are usually noisy and averaging is required to improve readability.

1.1.5 Calculation of the low-frequency noise impedance

In order to plot the time evolution of the low-frequency noise impedance, the value of the low-frequency noise impedance at each iteration must be extracted. This is performed by averaging a given number of points at the low-frequency end of the time-averaged noise impedance spectrum. The number of points from the low frequency end of the noise impedance spectrum that are used to perform such operation can be selected in the preferences menu (Points Average for low frequency impedance). The point obtained from FFT at 0 frequency is excluded from this computation.

Figure 9.0 Calculation of low frequency noise impedance

The calculation of the average charge of a corrosion event is performed for each segment by the following equation

q = ( v VPSD * v CPSD ) / B (Equation 1.0 )

Where VPSD and CPSD are the low-frequency values of potential and current power spectral densities, and B is the Stearn-Geary coefficient. The low frequency value of the potential and current power spectral density is obtained averaging a number of points in the low-frequency end of the potential and current power spectral density spectra. The number of points for such average and the appropriate value for the Stearn-Geary coefficient can be selected in the preference window.

1.1.6 Calculation of average charge and frequency of corrosion events

Fig 10.0 The average charge of corrosion events is calculated from the low frequency values of current and potential power spectral densities .

The calculation of the frequency of corrosion events 'f' is performed for each segment by the following equation

f = ICORR / q (Equation 2.0 )

Or

f = B2 / VPSD (Equation 3.0 )

Where 'VPSD' is the low-frequency values of potential power spectral density, ICORR is the corrosion current, q is the charge and B is the Stearn-Geary coefficient. The low frequency value of the potential power spectral density is obtained averaging a number of points in the low-frequency end of the potential and current power spectral density spectra. The number of points for such average can be selected in the preference window.

1.1.7 Calculation of noise resistance

The noise resistance for each segment is calculated by taking the square root of the potential variance divided by the current variance. This is shown in both in the first and in fourth screen. The fourth screen has four quadrants showing low-frequency noise impedance, noise resistance, average charge of corrosion events and frequency of corrosion events respectively.

Fig 11.0 The fourth screen ( Resistance/Charge/Frequency ) displays noise impedance, noise resistance,average charge and

frequency of corrosion events

1.1.8 Graphical Representation of the calculation algorithm

The complete algorithm is graphically illustrated in figure 13.0 below. The steps used for the calculations of noise resistance, noise impedance, charge and frequency of corrosion events are explained in details in the previous sections.

Figure 12.0 Graphical Illustration of the calculation algorithm

1.2.0 Selection of Processing Parameters.

1.2.1 FFT Length

The 'FFT Length' parameter determines the length of each segment used to obtain all the time-dependent quantities. Longer FFT length will generate spectra extending towards lower frequencies, but the time resolution of the processed data will be reduced because more points are used to generate a single result. Ideally, to generate reliable values of charge and frequency of corrosion events, the 'FFT length' should be sufficiently long that a plateau is visible in the low-frequency end of current and potential power spectral densities spectra.

Fig 13.0 The selection of FFT length can be made in the preference menu.The default length is 1024

1.2.2 FFT Window

FFT is usually calculated for a fixed length of time record. When the signal is discontinues, the abrupt ending on both ends of the signal causes a phenomenon called 'spectral leakage '. When a signal is terminated abruptly and analysed using FFT the spectrum spreads into all the the FFT bins rather than confining into a particular FFT bin. The spectral leakage can be reduced considerably if the signal amplitude can be gradually reduced to 0 at both the ends rather than abruptly cutting the signal. This type of technique is called 'windowing'. There are different types of windowing function are generally used, the most common one is 'hanning' window.

Fig 14.0 The software supports different windowing functions for FFT . The most popular windowing function is 'hanning'.

1.2.3 Sampling Interval

The sampling interval must be set equal to the actual sampling interval used during the acquisition of noise potential and noise current. The software ignores the time column and assume that the points are equally spaced of the sampling interval selected by the user.

Fig 15.0 The user need to to enter the sampling interval manually. This should be actual value used while acquiring the noise data from a potentiostat

1.2.4 Spectra Average

The spectra average parameter determines how many impedance spectra are used to calculate the averaged impedance spectrum. A high number of spectra will generally produce a less-noisy averaged impedance spectrum and a less noisy low frequency impedance vs. time plot, but it will decrease the time resolution.

Fig 16.0 Spectra average parameter determines how many spectra are averaged.

1.2.5 Points Average for Low Frequency Limit

This parameters determines how many low-frequency points are averaged to obtain the low-frequency values of impedance, potential power spectral density and current power spectral density. If a plateau is evident in the low-frequency end of the spectra, the parameter should be set to include roughly all the points that belongs to the low-frequency plateau.

Fig 17.0 This parameter determines how many low frequency points are averaged for estimating the low-frequency impedance.

1.2.6 Stern-Geary Coefficient

It is the Stern-Geary coefficient for the material under investigation, and it is required to estimate charge and frequency of corrosion events. It must be obtained experimentally or from the literature. The value of the Stern-Geary coefficient does not affect the calculation of impedance and resistance.

Fig 18.0 The stearn-Geary coefficient of the material under investigation can be entered here

1.2.7 Skip Iterations between saved spectra

The software provides an option for the user to save the spectra periodically, which is calculated by the FFT function. The option is provided to the user at the beginning of the processing. The software will ask the user whenever the software starts a new electro chemical noise analysis. It is not always required to save the complete spectra, doing so can result in very large files. The parameter 'skip iterations between saved spectra' determines how often the complete spectra will be saved to the disk.

Fig 19.0 Before processing a file the user is asked if complete spectra are to be saved.

Fig 20.0 Saving the complete spectrum is not required always and can result in large data file.

Table below shows how a typical spectra file is organized

Nth Record |
X axis ( in log) |
potential PSD |
Current PSD |
Impedance PSD |

1126 |
-3.01029996 |
0.52261167 |
0.00000002 |
4172.30476987 |

1126 |
-2.70926996 |
0.29134762 |
0.00000001 |
4156.83706831 |

1126 |
-2.53317870 |
0.06467640 |
0.00000000 |
6102.40065220 |

1126 |
-2.40823997 |
0.03039187 |
0.00000000 |
6702.12785726 |

- |
- |
- |
- |
- |

1126 |
-0.30103000 |
0.00000009 |
0.00000000 |
8180.12650179 |

1177 |
-3.01029996 |
0.61943963 |
0.00000001 |
4172.30476987 |

1177 |
-2.70926996 |
0.30128671 |
0.00000001 |
4156.83706831 |

1177 |
-2.53317870 |
0.05226266 |
0.00000000 |
6102.40065220 |

**Note : ( Total number of values depends on FFT Length, for Ex. if FFT length is 1024 there will 1024 values for 1126th record)

1.2.8 Segment Overlap Percentage

This parameter determines the overlap between a segment extracted from the complete dataset and the following segment. High values of overlap, combined with high values of spectra average generally provide less noisy output data, but this considerably increases the computation time.

Fig 21.0 A high percentage of FFT overlap ensures less noisy output data but increases computational time.

1.2.9 Processing Speed

This parameters determines how fast the processing progress. It is useful to set the processing speed to a low value in order to follow step-by step the calculations and identify the best set of process parameters. Once the best process parameters are identified, the processing speed can be increased to maximum value to reduce computation time. The processing speed parameter does not affect the values of the results.

Fig 22.0 User can change the processing speed. The value of processing speed does not affect the results.