frequency-dependent, complex-valued proportionality factor, ΔE/ΔI, between the applied potential or current and the response current or potential in an electrochemical cell Note 1 to ent
Simple corroding system
Simple corrosion systems, characterized by uniform corrosion on a homogeneous surface and controlled by charge transfer, can be represented by a basic equivalent circuit For effective electrochemical impedance spectroscopy (EIS) analysis of corroding metals, it is essential that the system remains stable during measurements to maintain a steady-state condition Corrosion occurs at the metal/solution interface through anodic and cathodic reactions.
A simple corroding system in an electrolyte is represented by an anodic and cathodic reaction:
Cathode: Me 2n+ + ne - → Me 2 where n is the number of electrons e - ;
Metal 1 has less nobility than metal 2.
The equivalent circuit of the metal/solution interface includes a polarization resistance (R_p), also known as charge transfer resistance (R_ct), in parallel with an electric double-layer capacitance (C_dl), which is connected in series with a solution resistance (R_s).
A metal sample in immersion forms an electric double layer at its interface, which is represented by a capacitance in electrochemical impedance spectroscopy (EIS) However, this capacitance does not reflect a true capacitive value, leading to the use of a constant phase element (CPE) to account for deviations The CPE and polarization resistance (R p) may not solely indicate corrosion resistance but can also represent the overall electrical resistance and dielectric properties of passive film oxides The growth of a passive film is influenced by the transport of cations, anions, or their vacancies through the oxide film Defects like pores, channels, or cracks in the passive film can allow electrolyte penetration, compromising its resistance Additionally, the surface oxide film may display capacitive behavior due to the dielectric nature of the oxide.
The Constant Phase Element (CPE) is essential for modeling the behavior of an electrical double layer, acting as an imperfect capacitor The impedance of a CPE is expressed as \( \frac{1}{Z_{CPE}} = Q^\circ (j\omega)^n \), where \( Q^\circ \) represents the constant related to the electric double-layer capacitance The exponent \( n \) varies between 0 and 1, indicating the degree of imperfection in the capacitor's behavior.
Figure 1 — Schematic representation of a metal in solution and the equivalent circuit representing the metal/solution interface
C dl double layer capacitance 2 metal
The capacitance of the double layer, \$C_{dl}\$, for a corroding metal typically correlates with the actual surface area of the working electrode When the anodic and cathodic reactions are governed by the charge transfer step near the corrosion potential, the current through the working electrode, \$I_w\$, can be expressed by Formula (1).
I cor is the corrosion current; β a and β c are Tafel constants (V/decade) in anodic and cathodic regions, respectively.
The R p and I cor have the following relation:
The value of K is dependent upon the type of specimen material and the environment, and the I cor can be obtained from R p theoretically.
In cases where the Nyquist plot shows a depressed semicircle indicating an inaccurate capacitance, a constant phase element (CPE) should be used in the equivalent circuit instead of the double layer capacitance (C dl) The characteristics of the CPE are detailed in Annex B It is important to note that the theoretical relationship in Formula (3) may not apply to corrosion systems involving a CPE, as other electrochemical reactions beyond simple metallic corrosion could be present Therefore, it is advisable to utilize the correlation between R p values and I cor values obtained from weight-loss measurements to determine K values.
Presentation of impedance by a complex number
The impedance Z is represented by the complex number with real part Z′ and imaginary part Z″.
The relation of Z′ and Z″ on the complex plane is depicted in Figure 2 The magnitude impedance, |Z|, and phase shift φ (in degrees) or θ (in radians) of Z are related by
The phase angle of vector Z is presented in φ (degrees) on the complex plane, as in Figure 2.
Figure 2 — Impedance Z presented on the complex plane
Impedance spectra of circuit elements
The impedance spectra of circuit elements, including resistors (R) and capacitors (C), as well as their combinations, can be effectively illustrated using Bode and Nyquist plots Figure 3 displays the Bode plots for the impedance spectra of each individual circuit element and their combinations.
The impedance of a resistor \( R \) is defined by the formula \( Z = R \) Throughout the entire frequency range, the magnitude \( |Z| \) remains constant at \( R \), while the phase shift \( \phi \) is consistently zero, as illustrated in Figure 3 a).
The impedance of a capacitor \( C \) is given by the formula \( Z = \frac{1}{j\omega C} \) As the frequency \( f \) increases, the magnitude of \( \log |Z| \) decreases with a slope of -1, following the relationship \( \log |Z| = -\log f - \log (2\omega C) \) For a capacitor, the phase shift \( \phi \) is -90°, and at \( f = \frac{1}{2\omega} \) (Hertz), the value of \( \log |Z| \) equals \( \log (1/C) \), as illustrated in Figure 3 b).
4.3.4 For a serial RC circuit, the magnitude of log |Z| decreases with the increase in log f, and the slope is
In the low frequency range, the impedance phase angle (\( \phi \)) is -90° due to the condition \( R \ll \frac{1}{\omega C} \) Conversely, in the high frequency range, the phase angle becomes 0° as \( R \gg \frac{1}{\omega C} \), resulting in a constant magnitude of log |Z| This behavior is illustrated in Figure 3 c).
In a parallel RC circuit, the logarithm of the impedance magnitude, log |Z|, remains constant at low frequencies, where the phase angle φ is 0° due to the condition R ≪ 1/ωC, indicating that current primarily flows through the resistor As the frequency increases, log |Z| decreases with a slope of -1, and the phase angle φ shifts to -90° at high frequencies, where R ≫ 1/ωC, indicating that current predominantly flows through the capacitor.
Figure 3 — Circuit elements and their Bode plots
Presentation of a simple corroding system
The Bode plot for the equivalent circuit for a simple corrosion system in Figure 4 a) is shown in Figure 4 b)
In the low frequency range, the logarithm of impedance (\$ \log |Z| \$) remains constant at approximately \$ R_s + R_p \$ with a phase angle (\$ \phi \$) of 0°, due to the dominance of the capacitive reactance (\$ 1/\omega C \$) As frequency increases into the middle range, \$ \log |Z| \$ decreases with a slope of -1, reflecting the condition where resistance (\$ R \$) significantly exceeds \$ 1/\omega C \$, influenced by high capacitance and frequency In the high frequency range, \$ \log |Z| \$ approaches \$ R_s \$ with a phase angle of 0°, as the capacitive reactance becomes negligible.
The magnitude of real and imaginary parts of Z for an equivalent circuit in Figure 4 a) is given by Formula (8):
The Nyquist plot for the equivalent circuit depicted in Figure 4 a) is illustrated in Figure 4 c), where the impedance locus forms a semicircle with a diameter of \( R_p \) The low and high frequency limits on the real axis converge to \( R_s + R_p \) and \( R_s \), respectively Additionally, the frequency at the peak of the semicircle, denoted as \( f_{max} \), is related to the time constant \( R_p C_{dl} \) by the equation \( f_{max} = R C_1 \).
2π p dl (10) a) log f log ( R p+ R s) log l Z l log ( 1/ C dl) log R s slope = -1
Figure 4 — A simple corroding system: a) equivalent circuit, b) the Bode plot, and c) the Nyquist plot
General
The measurement system consists of an electrochemical cell connected to instrumentation and software for the characterization of materials using precision electrical measurement techniques.
NOTE 1 Guidance is given in ISO 17474.
In electrochemical impedance spectroscopy, the measurement procedure involves capturing the frequency spectrum with logarithmic data point spacing To ensure adequate data resolution, it is recommended to collect at least 5 data points per decade of frequency This minimum resolution is essential for accurate equivalent circuit modeling of the experimental data.
The perturbation amplitude refers to the potential sine wave applied via the potentiostat as a polarization voltage to the working electrode, typically measured in millivolts Keeping this amplitude as low as possible minimizes electrode perturbation, which is crucial to avoid permanent changes to the electrode surface caused by excessive polarization during measurements.
It should be applied within the linear response window of the electrode Due to this small polarization, the resulting currents will also be very small.
The EIS system must accurately measure and extract the values of resistors and capacitors in the dummy cell, as detailed in Annex A The discrepancies between the fitted values of the electronic components and their actual values should remain within the accuracy limits of the components used Significant errors in these values may suggest issues with the EIS system or improper system operation.
NOTE 2 Guidance is given in ISO 16773-2.
The potentiostat utilized for applying the potential signal from an AC generator to the Frequency Response Analyzer (FRA) must maintain the electrode potential within ±1 mV of a predetermined value It should provide voltage outputs relative to ground for both potential and current, ensuring adequate bandwidth to minimize phase shift up to at least 100,000 Hz Additionally, the terminals designed to measure the potential difference between the working and reference electrodes must possess a high input impedance, approximately 10^{11} Ω.
10 14 Ω to minimize current drawn from the system during measurement The sensitivity of current- measurement should have maximum error of less than 0,5 %.
Test cell
The cell must be made from non-corrosive and non-deteriorating materials to prevent contamination of the solution Additionally, it should be designed to be leak-proof to maintain the integrity of the sample's geometrical surface over time.
The cell design must accommodate essential components such as the working electrode, reference electrode, counter electrode, thermometer for temperature control, and gas inlet/outlet tubes to adjust oxygen levels When utilizing inert gases, a gas scrubber is necessary It is crucial to address the potential formation of crevices between the cell and the test material, especially when the test solution contains halides For accurate corrosion measurements of material properties, a crevice-free setup or cell is highly recommended.
The test cell must be sufficiently spacious to accommodate the electrolyte, working electrode, reference electrode, and counter electrode It should feature gas inlet and outlet ports, as well as a port for a temperature-measuring device Additionally, the construction material of the test cell must be inert under the testing conditions To prevent contamination of the working electrode by reaction products from the counter electrode, it is advisable to separate the counter electrode from the main cell using a fritted disc.
A reference electrode can be directly inserted into the main cell if there is no risk of contamination or damage from a corrosive electrolyte To prevent mutual contamination, a double-junction reference electrode is recommended Alternatively, the reference electrode can be placed in a separate chamber and connected to the main cell via a salt bridge It is important that the tip of the capillary probe, known as the Luggin capillary, is positioned at least twice the diameter of the tip away from the working electrode.
Electrode holder
To ensure accurate measurements, the counter and working electrodes must be securely mounted without interference from the holder or mounting materials It is crucial to take special precautions to avoid crevice attack in specific applications.
Electrode material
Inert materials can be utilized for the counter electrode, which may be designed as a sheet, rod, or gauze supported by a glass frame, with the test specimen positioned centrally The counter electrode's area must be at least equal to that of the working electrode While graphite is a viable option for the counter electrode, precautions should be taken to prevent contamination, and desorption of retained species in the graphite may be required before use.
Electrolyte
For accurate measurements, the resistance of the test solution must be significantly lower than the impedance of the system being investigated It is essential to use a conductive electrolyte that effectively represents the measured system, rather than merely reflecting the resistance of the solution itself.
The specimen must be thoroughly cleaned, degreased, rinsed, and dried While a mill-finished surface is acceptable, a specific surface finish may be required based on the application, ideally with a well-defined texture Generally, an R a value of less than 1 μm is recommended to minimize the risk of increased reactions in grooves caused by grinding.
The time between grinding and immersion significantly affects the measured impedance values This elapsed time should be standardized for specific tests, with a minimum of 1 day recommended, as surface-film thickness shows little variation after 24 hours Additionally, specimens must be cleaned and degreased using alcohol or acetone and stored in a desiccated cabinet.
The solutions shall be prepared from analytical reagent-grade chemicals and high-purity water (with a conductivity less than 1 μS ã cm), unless testing takes place in the actual service fluid.
In addition to the confidence tests described in ISO 16773-2 and ISO 16773-3, Annex A provides a procedure for check of the overall experimental arrangement The dummy cell is mounted separately.
To ensure accurate validation, measure the potential difference between the reference electrode and two validation electrodes, which must be traceable to the standard hydrogen electrode and exclusively used for validation purposes If the potential difference exceeds 3 mV, the test electrode should be discarded.
9.2 Measure the exposed surface area of the specimen.
9.3 Assemble the cell with the counter electrode, reference electrode, and Luggin capillary.
9.4 Prepare the test solution in sufficient amount to be added to the electrochemical cell.
In electrochemical testing, the procedure for mounting the sample varies based on the cell type For a crevice-free flush port cell, the test sample should be mounted prior to adding the test solution Conversely, in a standard electrochemical glass cell with a lid, the test solution can be introduced before the sample is mounted.
9.6 Add the test solution to the cell.
To achieve equilibrium during gas purging, the solution must be purged with the appropriate gas for at least 60 minutes For testing in aerated solutions, it is essential to use either an air pump or a cylinder of compressed air to maintain consistent conditions.
To achieve precise temperature control within ±1 °C, utilize temperature sensors or a double-wall electrochemical cell with water bath circulation Another effective method is to immerse the exterior of the test cell in a temperature-controlled water bath or employ other suitable techniques.
9.9 Adjust the Luggin probe tip so that it is at a distance from the working electrode of about, but not closer than, 2 times the diameter of the tip.
To accurately assess the corrosion potential of the working electrode, it is essential to record the open-circuit potential over time following immersion The duration of exposure at open circuit before polarization varies based on the experiment's objectives In certain cases, allowing the open-circuit potential to stabilize is beneficial; otherwise, a minimum exposure period of 60 minutes is recommended.
Conduct the impedance experiment at either the corrosion potential (\$E_{cor}\$) or the polarized potential, based on the test's objective Ensure that the amplitude of the superimposed AC potential ranges from 5 mV to an appropriate level for accurate measurements.
10 mV The frequency is scanned logarithmically between a minimum 10 000 Hz (10 kHz) and, typically, 0,01 Hz (10 mHz).
Impedance data are primarily displayed using Bode plots or Nyquist diagrams, which facilitate visual comparisons of various treatments or exposure tests These diagrams are effective for monitoring corrosion and passivity By analyzing impedance measurements over time, one can observe changes in the passive oxide film or the onset of corrosive reactions, rather than focusing solely on the evaluation of the equivalent circuit.
Electrochemical impedance data can be effectively analyzed by fitting it to an equivalent circuit, where the electrical elements such as resistors, capacitors, and inductors correspond to the physical characteristics of the corroding or passive metal To ensure the reliability of the measurements, the Kramers-Kronig (K-K) test is employed to verify the linearity and stability of the system over time during spectral uptake However, if the system experiences changes, such as temperature fluctuations or non-equilibrium states, the K-K test may yield inconclusive results.
Electrochemical impedance spectra in real corrosion systems are often more complex than those outlined in this Technical Report, making the interpretation and identification of various chemical and corrosion processes challenging.
Active dissolution, such as the corrosion of passive metals in sulfuric acid and sodium chloride, involves both adsorption and desorption reactions alongside corrosion processes These reactions can lead to the introduction of inductive loops in the spectral analysis.
Real part (Ωcm 2 ) Real part (Ωcm 2 )
Figure 5 — Measured electrode impedance of Fe17Cr in 0,5 M H 2 SO 4 with addition of chloride [13]
To effectively interpret data, it is essential to establish equivalent circuit models based on electrochemical principles This approach allows for the extraction of meaningful parameters, ensuring that the model's adequacy is clearly demonstrated.
Revisions of this Technical Report aim to broaden the scope to encompass more complex corrosion systems, as simple models often fall short The literature includes examples of interpreting intricate corrosion phenomena, such as the impedance associated with pitting processes in aluminium-based materials A proposed electrochemical circuit model for these pitting processes is documented, along with an EIS analysis and an equivalent circuit example for an aluminium alloy experiencing pitting corrosion in a chloride solution, as illustrated in Figure 6.