Summary of previous studies about the estimation the corrosion rate using electrochemical techniques.
An attempt was made to estimate the corrosion rate of AZ31 and AZ61 magnesium alloys immersed in 0.6 M NaCl during long‐term exposure using electrochemical impedance spectroscopy (EIS). The EIS results were compared with the corrosion rate independently assessed by the hydrogen evolution test. A correlation was established between the integration of the polarization resistance (Rp) and charge transfer resistance (Rt) over time, as evaluated by EIS and hydrogen gas measurements. Regardless of the immersion time, a strong link was found between the Rt and Rp values determined by EIS. This relation seems to depend on the composition of the alloy. The influence of immersion time on the estimated corrosion rate reliability was investigated. The typical deviations of the measurement methods are apparently decreasing upon prolonging the immersion time. No significant errors were obtained in the measurement of the corrosion rate when using Rt or Rp determined by EIS with their corresponding “apparent” Stern‐Geary coefficient values compared with the real values determined by gravimetric measurements.
- weight loss
- electrochemical impedance spectroscopy
- corrosion rate
- hydrogen evolution
Mg‐Al alloys have aroused great scientific and technological interest in recent decades. From a practical point of view, their high strength‐weight ratio makes them ideal alloys for automotive, aerospace and electronics applications, where weight reduction is of significant concern . The usage of magnesium alloys in automotive applications can significantly contribute to greater fuel savings and environmental conservation . Also, magnesium and its alloys have been investigated recently by many authors as a suitable biodegradable biomaterial . However, their corrosion performance at the current stage of development is still not good enough for increasingly diverse their practical applications . Given the growing use of Mg alloys as structural alloys, an accurate assessment of corrosion is imperative and the unambiguous determination of electrode kinetics in the case of Mg electrodes is essential .
Electrochemical impedance spectroscopy (EIS) has been shown in innumerable studies to be an efficient and accurate tool for investigating the nature of surface films and the associated corrosion mechanisms of metals and alloys . The most outstanding and well‐known advantages of EIS are that it allows continuous monitoring of the corrosion with measurements of the instantaneous corrosion rate. Such measurements of the corrosion rate require only minor disturbance in the system because a very small AC signal is applied . The use of electrochemical impedance spectroscopy (EIS) to assess electrochemical corrosion behavior of magnesium and its alloys is of great technical relevance. Since stationary values take significant time to become established, it should be noted that short‐term measurements may give rise to misleading comparisons of corrodibility of the magnesium alloys . As James et al.  noted, EIS is an ideal method for monitoring the long‐term corrosion behavior and ranking the corrosion protective ability of Mg and its alloys. The term “long term” is used to distinguish it from the standard electrochemical corrosion studies, which are performed within the first 1 or 2 h .
Many Mg corrosion studies assign the first capacitive semicircle, appearing at high frequencies, to the charge transfer reaction of Mg‐Al alloys with a partial protective oxide/hydroxide layer formed as the corrosion product in the test solution [6, 9–14]. The charge transfer resistance Rt is determined by the diameter of this capacitive loops [15–20]. The corrosion rate of freely corroding metal in the absence of coverage effects is inversely proportional to polarization resistance as described by the Stern‐Geary relationship [21, 22]:
where B is the Stern‐Geary constant and can be determined using anodic (βa) and cathodic (βc) Tafel slopes  (B = (1/2.303) × (βa.βc/(βa+βc)).
The determination of the anodic Tafel slope is not trivial because the magnesium electrode can sustain very high anodic current with minimal anodic polarization, accompanied by substantial hydrogen evolution and local alkalinization, producing a large Ohmic drop in the proximity of the electrode surface . Anodic potentiodynamic polarization of Mg and Mg alloys initially exhibits a very low apparent Tafel slope, representative of an ideally non‐polarizable electrode behavior, followed by the bending of the curve [22, 24–26].
In our previous studies [15, 19, 20], due to the uncertainty in the βa values from the polarization curves commented above [22, 24–26], it was decided to use the constant B estimated empirically from the correlation between electrochemical and gravimetric measurements . Previous investigation  yielded B values of around 65 mV for the AZ31 alloy and of around 120 mV for the AZ61 alloy. Cumulative weight loss after an extended period of time was determined by the integration of the weight changes for individual exposure periods. In this way, the average corrosion rates of the specimens after 14 days of exposure to the 0.6 M NaCl solution were obtained from EIS, which were similar to that determined from hydrogen evolution and gravimetric measurements .
Recently, King et al.  and Bland et al.  have shown that the determination of polarization resistance, Rp, at the zero frequency limit as evaluated from analysis of impedance data, provided excellent correlation between the volume of hydrogen collected and mass loss, for both commercially pure Mg and the AZ31 alloy. King et al.  critically address previous studies which have utilized the impedance behavior of magnesium and which claim electrochemical tests may underestimate the corrosion rate of Mg; in most cases by a factor of 2 or more, while attempting to use a charge transfer resistance at intermediate frequencies and do not account for the electrochemically justified inductive behavior. Later, Curioni et al.  have revealed that the reciprocal of the values of resistance estimated by EIS is linearly correlated with the corrosion current measured by hydrogen collection. The experimentally measured proportionality constant provides an “apparent” Stern‐Geary coefficient that can be used to evaluate the corrosion current from EIS data .
In these studies [22, 24, 25], impedance measurements were taken during free corrosion while monitoring in real time the amount of hydrogen evolved from the corroding electrodes to obtain instantaneous values of corrosion current of pure magnesium and the AZ31 alloy in NaCl solutions. As Curioni et al.  commented, the lack of reproducibility of the corrosion current is due to statistical variation in the corrosion process, but the combined measurement of the corrosion rate by impedance spectroscopy and hydrogen evolution is reliable. From a practical viewpoint, however, the possibilities of obtaining “apparent” Stern‐Geary coefficients from the relationship between independent hydrogen evolution and electrochemical impedance spectroscopy measurements are of interest since the experimentation is easy to replicate and to implement; although long exposure times may be involved, the relatively simple procedure reduces the propensity to introduce systematic errors.
The effect of exposure time to the corrosive solution is important since there are frequent cases in which the corrosion rate of Mg tends to change significantly with the immersion time [8, 29–34]. Typically, the initial corrosion rate is less, and then the corrosion rate accelerates to a steady state [35–38]. Due to the high protective nature of the pre‐existing native oxide film formed on the polished surfaces of some magnesium alloys, significant fractions of uncorroded silvery regions can be found even after 24 h immersion in 3.5% NaCl aqueous solution [29, 32]. Bland et al.  noted that because of the rapid corrosion rates normally observed for the Mg system, the Tafel characteristics can change dramatically between a short‐ and long‐term test. Hsieh et al.  examined the relationship between weight loss (WL) measurements and polarization resistance measurements of corrosion in metals and metal alloys (mild steel, aluminum, copper, and cupronickel) commonly used in industrial cooling systems. The experimentally measured proportionality constant B', based on the correlation between electrochemically and gravimetric measured corrosion rates, changes with the exposure time until steady state is reached, which may take up to 3 days. At longer immersion times (>3 days), the B’ value begins to stabilize and changes little with the corrosivity of water. For this reason, long‐term exposure to saline aqueous solutions was selected (AZ31 specimen after 4 days and AZ61 specimen after 14 days of testing) for the measurement of an “apparent” Stern‐Geary coefficient for these alloys. The purpose of this study is to report new results within a broader study carried out on the factors affecting the estimation of the corrosion rate in magnesium alloys by EIS . The ultimate aim is to expand our overall understanding of such phenomena and improve the reliability of the experimental results by devising better study designs.
|Authors||Work title||Main aspects||Reference|
|Makar L, Kruger J||Corrosion Studies of Rapidly Solidified Magnesium Alloys||The charge transfer resistance could be used to accurately measure the corrosion rates of magnesium alloys.|||
|Kirkland NT, Birbilis|
N, Staiger MP
|Assessing the corrosion of biodegradable magnesium implants: A critical review of current methodologies and their limitations||EIS also does not directly yield a corrosion rate of magnesium implants.|||
|Pebere N, Riera C, Dabosi F||Investigation of magnesium corrosion in aerated sodium sulfate solution by electro-|
chemical impedance spectroscopy
|The electrochemical determination of the corrosion rate are in agreement with those obtained by atomic absorption spectroscopy.|||
|Liu M, Schmutz P, Uggowitzer PJ, Song GL, Atrens A||The influence of yttrium (Y)|
on the corrosion of Mg‐Y binary alloys
|The corrosion rate evaluated by electrochemical impedance spectroscopy was somewhat smaller than that evaluated from H evolution.|||
|King AD, Birbilis N, Scully JR||Accurate electrochemical measurement of magnesium corrosion rates; a combined impedance, mass‐loss and hydrogen collection study||The determination corrosion rate from EIS polarization resistance correlated to the mass loss and volume of hydrogen collected.|||
|Qiao ZX, Shi ZM, Hort N, Abidin NIZ, Atrens A||Corrosion behaviour of a nominally high purity Mg ingot produced by permanent mould direct chill casting||The corrosion rate measured using electrochemical techniques was consistently lower than that measured independently by weight loss or hydrogen evolution.|||
|Bland LG, King AD, Birbilis N, Scully JR.||Assessing the corrosion of commercially pure magnesium and commercial AZ31B by electrochemical impedance, mass‐loss, hydrogen collection, and inductively coupled plasma optical emission spectrometry solution analysis||The integration of the polarization resistance over time, as evaluated from EIS provided correlation to the cumulative mass loss, ICP‐OES solution analysis, and volume of hydrogen collected for commercially pure Mg and for AZ31.|||
|Shkirskiy V, King AD, Gharbi O, Volovitch P, Scully JR, Ogle K, Birbilis N.||Revisiting the electrochemical impedance spectroscopy of magnesium with online inductively coupled plasma atomic emission|
|In real time, electrochemical impedance spectroscopy (EIS) was coupled with online atomic emission spectroelectrochemistry (AESEC) to simultaneously measure Mg corrosion.|||
|Curioni M, Scenini F, Monetta T, Bellucci F||Correlation between electrochemical impedance measurements and corrosion rate of magnesium investigated by real‐time hydrogen measurement and optical imaging||A very good correlation between values of resistances estimated by EIS and corrosion currents obtained from real‐time hydrogen measurement was found.|||
|Shi ZM, Cao FY, Song GL, Atrens A||Low apparent valence of Mg during corrosion||The values of the corrosion evaluated|
from EIS data were typically not good
measurements of the corrosion
rate of Mg as measured
by weight loss.
|Atrens A, Song GL,|
Cao F, Shi Z,
|Advances in Mg corrosion and research suggestions||The reliability of corrosion rate obtained by EIS is questionable.|||
|Shi ZM, Liu M,|
|Measurement of the corrosion|
rate of magnesium alloys using
|In principle, the electrochemical measurement hypothesis for Mg can be disproved.|||
|Cao FY, Shi ZM, Hofstetter J,|
Song GL, Liu M,
|Corrosion of ultra‐high‐purity Mg in 3.5% NaCl solution saturated with Mg(OH)(2)||The amount of dissolution under|
electrochemical control was a small amount of
the total dissolution.
|Atrens A, Song GL,|
Liu M, Shi Z, Cao F, Dargusch MS
|Review of recent developments in the field of magnesium corrosion||Good values of the Tafel slopes are needed to|
EIS measurements of the corrosion rate.
|Evolution of hydrogen at dissolving magnesium surfaces||Cathodic reaction of magnesium is enhanced during dissolution|||
2. Materials and methods
AZ31 and AZ61 magnesium alloys manufactured under wrought conditions with the chemical composition indicated in Table 2 (as detailed by the manufacturer, Magnesium Elektron Company) were used in the present study. Samples were cut into test strips, 2 ×2 cm squares with a thickness of 0.3 cm and then mechanically dry grounded successively with finer and finer abrasive paper up to P2000 SiC grit papers and polished to produce a uniformly flat surface with mirror‐like reflectivity. All samples were rinsed in distilled water and dried in air stream as the final step.
The corrosion rate of magnesium alloys was calculated from the volume of collected hydrogen during the corrosion test. Specimens were immersed in a beaker containing 700 ml of 0.6 M NaCl. The beaker was covered with an inverted funnel, and the released gas was collected in a graduated burette. All experiments were conducted at room temperature. The hydrogen evolution was measured for 4 days in the case of the AZ31 specimen and for 14 days in the case of the AZ61 specimen. Three replicated specimens were tested to confirm reproducibility of the results. Also, the corrosion rates were determined from the weight loss of the tested specimens, after removing all the corrosion products from the sample surface using chromic acid (200 g L-1 CrO3 + 10 g L-1 AgNO3).
Electrochemical experiments were performed using an AUTOLAB PGSTAT30, with a frequency response analyzer. EIS scans were acquired from 100 kHz to 0.005 Hz with 5 points per decade and an AC amplitude of ±10 mV. A three electrode configuration was used in which the sample was the working electrode, a graphite rod was the counter electrode, and an Ag/AgCl (Sat.) electrode was the reference electrode. The tested specimens exposed an area of 9.0 cm2 to the 0.6 M NaCl solution. Measurements were performed in triplicate to ensure the reproducibility of the results. ZView software was used for equivalent circuit fitting to the impedance plots obtained in these experiments .
3. Results and discussion
3.1. Influence of the immersion time on the error margin of the hydrogen evolution and electrochemical impedance measurements in 0.6 M NaCl solution
Figure 1 compares the time evolution of the corrosion current measured by the hydrogen collection method of tested materials immersed in 0.6 M NaCl solution. The corrosion current for the AZ31 alloy initially increased slowly during the first day of immersion, after which it increased approximately linearly with the immersion time. This can be attributed to an incubation period in which the initial surface films were partially protective and break down, leading to the steady state corrosion indicated by the later linear trend . The AZ31 alloy was completely dissolved after 4 days of immersion. In contrast, for the AZ61 alloy (Figure 1b), the corrosion current measured by the hydrogen evolution was relatively small for the whole immersion duration (14 days). This difference may be due to the strong protective effect of the oxide film that forms spontaneously on the polished AZ61 alloy surface, much more perfect and protective than the film on the AZ31 alloy [29, 31, 49]. The absence of significant variations in the corrosion current measured by the hydrogen evolution for the AZ61 alloy (Figure 1b) indicates the presence of a very protective film in this case.
Figure 1 also presents the error bars, which indicate the data variability, as deduced from three parallel measurements. It is interesting to note that the error tends to decrease quickly with immersion time. The observed variations in the error bars‐time behavior are attributed to a larger quantity of evolved volume of hydrogen with increasing immersion time, which improves the scale‐reading precision . On the other hand, hydrogen gas is very soluble in aqueous environments [22, 51], so it is likely that some H2 was lost by dissolution in the first stages of experimentation .
The Nyquist diagrams (Figure 2) obtained for the AZ31 and AZ61 specimens immersed in 0.6 M NaCl show the presence of a capacitive loop at high frequencies (HF) and an inductive loop at low frequencies (LF). Figure 3 shows the representative impedance spectra of the tested specimens in term of Bode plots.
The impedance spectra fitted with the equivalent circuit, as shown in Figure 4, were reported by King et al. . Rs represents the electrolyte resistances, C1 and C2 are associated with the oxide/hydroxide layers capacitance and the double layer capacitance at the metal/electrolyte interface, respectively. R1 is related to the initial metallic corrosion step, and R2 represents the discharge of the intermediate adsorbed species formed in the initial step [53, 54]. Finally, L accounts for the variation in the extension of active anodic regions during the sinusoidal polarization, and R3 represents the resistances associated with local environmental changes (precipitation of gels, presence of bubbles) nearby the anodic and cathodic regions . In full compliance with the suggestions of King et al. , for the analysis of EIS data, in this work, we have included capacitors in the place of constant phase element (CPE) for the representation of the capacitive elements.
The Nyquist and Bode plots in Figure 5 include the measured data along with a fit employing the equivalent circuit proposed and validated by King et al . Generally, the simulated and experimental impedance spectra were closely similar, and the center of the Nyquist plots does not appear depressed, which is a near ideal capacitive behavior [22, 26]. Polarization resistance (Rp) can profile the corrosion rate with time . According to King et al. , the Rp can be evaluated as the zero frequency impedance (f → 0) at -Z″ = 0 . On the other hand, Rt is defined as the value corresponding to Z' when −Z″ = 0, which is commonly obtained at intermediate frequencies . The Rp [22, 26] and Rt values have been determined using the following equations derived from the equivalent circuit:
The quantitative results from spectra fitting are given in Tables 3 and 4, in which the data represent the mean values for the three parallel measurements, and the standard deviation suggests the reproducibility of the EIS measurements.
|1 h||5 ± 0.2||0.09 ± 0.03||3 ± 1||0.64 ± 0.15||0.50 ± 0.18||0.41 ± 0.17||0.25 ± 0.09||0.75 ± 0.18||0.13 ± 0.05|
|4 h||13 ± 6||0.09 ± 0.02||15 ± 12||0.27 ± 0.09||0.26 ± 0.06||0.29 ± 0.12||0.15 ± 0.02||0.37 ± 0.10||0.25 ± 0.01|
|7 h||16 ± 1||0.12 ± 0.05||20 ± 5||0.31 ± 0.08||0.61 ± 0.19||0.42 ± 0.22||0.21 ± 0.09||0.43 ± 0.13||0.24 ± 0.00|
|1 day||20 ± 2||0.11 ± 0.02||26 ± 5||0.28 ± 0.10||1.26 ± 0.34||0.19 ± 0.04||0.13 ± 0.03||0.39 ± 0.12||0.25 ± 0.01|
|2 days||28 ± 2||0.07 ± 0.01||31 ± 6||0.13 ± 0.04||0.61 ± 0.19||0.07 ± 0.01||0.05 ± 0.01||0.20 ± 0.05||0.32 ± 0.01|
|3 days||25 ± 2||0.08 ± 0.01||45 ± 3||0.11 ± 0.02||0.82 ± 0.10||0.14 ± 0.01||0.08 ± 0.01||0.20 ± 0.03||0.37 ± 0.01|
|4 days||24 ± 1||0.08 ± 0.01||41 ± 2||0.09 ± 0.01||0.77 ± 0.14||0.14 ± 0.02||0.08 ± 0.01||0.18 ± 0.02||0.40 ± 0.01|
|1 h||4.18 ± 0.06||1.38 ± 0.02||4.08 ± 0.68||2.16 ± 0.49||43.43 ± 5.63||8.82 ± 1.70||2.53 ± 0.88||3.55 ± 1.82||0.028 ± 0.024|
|4 h||3.66 ± 0.16||1.25 ± 0.01||2.85 ± 0.08||3.39 ± 0.25||22.58 ± 0.41||16.63 ± 1.94||3.62 ± 0.95||4.64 ± 1.10||0.037 ± 0.005|
|1 day||3.18 ± 0.05||1.21 ± 0.18||2.25 ± 0.36||4.45 ± 1.32||34.60 ± 5.79||22.72 ± 0.34||4.51 ± 0.72||5.66 ± 1.15||0.034 ± 0.001|
|2 days||3.20 ± 0.17||1.67 ± 0.18||2.48 ± 0.09||4.31 ± 0.43||61.21 ± 0.54||22.04 ± 1.82||4.70 ± 0.46||5.98 ± 0.61||0.034 ± 0.003|
|3 days||2.94 ± 0.07||1.02 ± 0.36||2.30 ± 0.60||3.97 ± 0.83||51.80 ± 5.30||18.94 ± 5.40||3.86 ± 0.41||4.92 ± 0.45||0.032 ± 0.003|
|4 days||3.06 ± 0.04||1.00 ± 0.06||2.20 ± 0.32||3.54 ± 0.59||33.05 ± 2.70||10.66 ± 3.26||3.17 ± 0.55||4.55 ± 0.53||0.030 ± 0.002|
|7 days||3.03 ± 0.36||0.59 ± 0.21||2.24 ± 0.64||2.96 ± 0.15||31.05 ± 5.96||9.77 ± 0.39||2.60 ± 0.22||3.55 ± 0.36||0.029 ± 0.001|
|8 days||2.70 ± 0.19||0.33 ± 0.01||2.21 ± 0.17||3.34 ± 0.15||32.45 ± 2.08||8.87 ± 2.39||2.53 ± 0.19||3.68 ± 0.39||0.030 ± 0.000|
|9 days||2.91 ± 0.31||0.33 ± 0.03||2.34 ± 0.14||3.32 ± 0.19||29.91 ± 3.20||10.16 ± 1.11||2.68 ± 0.04||3.65 ± 0.22||0.030 ± 0.000|
|10 days||2.94 ± 0.17||0.37 ± 0.16||2.43 ± 0.13||3.53 ± 0.44||25.83 ± 3.79||9.81 ± 0.93||2.65 ± 0.41||3.90 ± 0.25||0.031 ± 0.000|
|11 days||3.18 ± 0.38||0.42 ± 0.17||2.50 ± 0.08||3.06 ± 0.02||39.67 ± 4.70||7.81 ± 1.29||2.39 ± 0.08||3.47 ± 0.18||0.031 ± 0.000|
|14 days||3.18 ± 0.35||0.51 ± 0.11||3.09 ± 0.01||3.10 ± 0.30||33.26 ± 2.43||8.43 ± 0.08||2.53 ± 0.11||3.11 ± 0.23||0.033 ± 0.000|
The evolution of resistance (Rp and Rt) values as a function of immersion time in 0.6 M NaCl solution is presented in Figure 6. After the first day of immersion test, the EIS data for the AZ31 specimen, illustrated in Figure 6a and c indicate that the resistance (Rp and Rt) values decreased markedly, approximately consistent with the linear increase in the corrosion current measured by the hydrogen collection presented in Figure 1, suggesting that the corrosion product layer formed on this alloy in 0.6 M NaCl is not particularly protective. In contrast, it is interesting to note that there is little effect or a moderate increase observed in the case of the AZ61 specimen over the 14 days immersion time (Figure 6b and d) in comparison to the high resistance (Rp and Rt) values obtained after 1h of immersion. During the first 2 days of immersion, the AZ61 specimens present a slight increase in the resistance (Rp and Rt) values (Figure 6b and d), which may be attributed to the growth of partially protective corrosion product film on the surface [30, 57]. According to a previous study , filiform corrosion was initiated almost immediately on the magnesium specimens after immersion, and the population of filaments expanded in less than 1 day across the entire exposed surface.
The standard deviations of the average resistance (Rp and Rt) values decrease quickly and strongly with the immersion time indicating the formation of an homogeneous corrosion layer, as it can be seen in Figure 6. Curioni et al.  observed significant variations in the values of impedance measured under similar conditions attributed to the statistical nature of the corrosion process and to the relatively small electrode size. Because EIS measurements in this study were made with a large (9.0 cm2) exposed area, it is reasonable to assume that the stochastic nature of the filament formation and growth processes initiated immediately after immersion and expanded in less than 1 day across the entire exposed surface, Samaniego et al.  contributed to this initial increase in the deviation of the resistance values. Increasing immersion time showed a decrease in the deviation of the resistance values, probably due to the formation of a uniform corrosion layer on the surface.
3.2. Low‐frequency inductive behaviors
As already commented, the impedance diagrams in this study are characterized by a capacitive loop at HF followed by a well‐marked inductive loop at LF. Numerous examples of such inductive loops can be found in the literature. An inductive effect may be explained by different reasons. In the corrosion of magnesium and its alloys, the low‐frequency inductive loop in the Nyquist plot has been interpreted as a manifestation of localized corrosion damage of the magnesium substrate [58–67], produced by the relaxation of adsorbed species such as Mg(OH)ads+ or Mg(OH)2 [9, 35, 68–73], to the formation and precipitation of a salt film [74, 75], to the incorporation of elements with properties of a semiconductor in the passive films  or most recently with accelerated anodic dissolution [22, 77]. However, the species responsible for the inductive response are yet to be determined , and the physical interpretation of inductive behavior associated with electrochemical processes is non‐trivial, and that is probably the reason why this inductive behavior is often neglected .
The notable size of the inductive loops in this work may be seen in Figure 2. If the loop size is expressed as the diameter of the semicircle that fits it, and δ is the ratio between the diameters of the inductive and capacitive loops, δ values of the order of 0.6–0.7 have been obtained throughout exposure with the AZ31 alloy but decrease significantly with alloy AZ61 approximately to 0.2–0.3. Our previous EIS data of the specimens corroded under experimental conditions similar to those in this work have produced similar Nyquist plots [8, 15, 27, 28, 29, 49]. Asmussen et al.  suggested that the change in EIS behavior seems to be related somehow, with the alloy microstructure and subsequent distribution of the alloying elements, especially Al. According to Song et al. , the inductive points could be associated with the corrosion of the α phase while the inert β phase normally shows a capacitive spectrum . Figure 7 gives the microstructures of the AZ31 and AZ61 magnesium alloys. In the case of AZ61, the electrochemical signals from small amounts of β‐phase (Mg17Al12), which is formed at the grain boundaries (Figure 7b) may modify the α phase formation . In contrast, it can be found that the alloying element Al in the AZ31 alloy completely dissolved into the Mg matrix and no precipitation of the β‐phase is observed (Figure 7a).
Figure 8 illustrates the relationship between the Rp values and the Rt values obtained from impedance measurements. It is evident that a linear relationship between Rp and Rt values was observed for the two alloys. The absence of significant modifications in the shape of the impedance diagrams throughout the test (Figure 2) may explain the high correlation between measured Rp and Rt values. As it has been suggested by Curioni , the values of charge transfer resistance (RCT) and corrosion product resistance (RCP) indirectly determine the value of adsorption resistance (RA), and therefore also the zero frequency resistance.
3.3. “Apparent” Stern and Geary values obtained from the correlation between independent EIS and hydrogen evolution measurements
King et al.  and Bland et al.  have shown that the integration of the corrosion current density over the exposure period via Eq. (4), and conversion of the volume of H2 gas evolved to a corresponding anodic charge () via the ideal gas law and Faraday's Law, all resulted in anodic charge estimations that are similar in value .
where is the corrosion current density obtained from hydrogen measurement, icorr is the corrosion current density obtained via Eq (1), B is the Stern‐Geary coefficient, and R is the value of resistance obtained from fitting of the EIS spectra. In our previous studies  and , we have also observed high degree of similarity between the amounts of corroded metal determined by hydrogen evolution, gravimetric, and electrochemical measurements.
Under the assumption that B does not change with time for a metal or a metal alloy in a certain aqueous solution , one can obtain
where B′ is the “apparent” Stern‐Geary coefficient.
The averages and standard deviations of charge values obtained from hydrogen evolution measurements as a function of time‐integrated reciprocal of the polarization resistance Rp or charge transfer resistance Rt values determined by EIS from 1 h and a maximum of 4 days immersion for the AZ31 alloy and 14 days immersion for the AZ61 alloy were used in this study to determine B’ values. The results are shown in Figures 9 and 10. These figures show that for each alloy immersed in 0.6 M NaCl, charge values from hydrogen evolution measurements and time‐integrated reciprocal of the polarization or charge transfer values were approximately proportional. Consequently, the value of B' for that particular system can be directly estimated from the graphs of Figures 9 and 10 by considering the slope of the fitting lines [24, 39]. A very good correlation between Rp or Rt values estimated by EIS and corrosion currents obtained from independent hydrogen measurements was found. Due to the direct dependence of both resistance values commented above and shown in Figure 8, the points in the plots for the determination of the “apparent” Stern‐Geary coefficient appear similarly scattered (Figures 9 and 10).
Clearly, depending on the resistance and the alloy selected for the calculation, the “apparent” Stern‐Geary coefficient is different; 93 or 32 mV for the AZ31 alloy if the charge transfer resistance or the polarization resistance is used and a value of around 126 mV or around 90 mV for the AZ61 alloy if the charge transfer resistance or the polarization resistance is used, respectively. These values are significantly lower compared to the “apparent” Stern‐Geary values of 223 mV for the Rt and 116 mV for the Rp previously obtained by Curioni  for pure magnesium.
In the case of the AZ31 specimen, the “apparent” Stern‐Geary coefficient obtained when the polarization resistance is used is significantly lower (approximately by a factor of 3) compared to when the values of the charge transfer resistance are used (Figure 8), while in the case of AZ61 specimen (Figure 9), little effect or a moderate decrease in the “apparent” Stern‐Geary coefficient is observed. This behavior tends to suggest that the differences between the “apparent” Stern‐Geary coefficients obtained from the polarization resistance and charge transfer resistance are dependent on the different sizes of the inductive loops in the impedance diagrams of the studied alloys (Figure 2).
A compilation of values of B quoted in the literature of AZ31 and AZ61 alloys arranged by determination method, test solution, time of exposure, author and reference is given in Table 5. Quoted B values obtained from Tafel determination method were 5–37 mV for the AZ31 alloy [22, 27, 44, 61, 80–86]. In the literature for AZ61, the B values are quoted ranging from 21 to 52 mV [27, 87–91]. The calculated B’ value of 31 mV for the Rp for the AZ31 alloy is consistent with B values calculated by Bland et al. , Cao et al. , and Shi et al.  (Table 5). On the other hand, the B' values of around 118 mV for the AZ61 alloy if the charge transfer resistance is similar to that previously obtained by empirical estimation, from electrochemical and gravimetric measurements  (Table 5).
|Alloy||B determination method||Immersion time||B (mV)||NaCl|
|AZ31B||Tafel extrapolation method||60 min||7.0||0.6 M||Tekin et al.|||
|AZ31||Fitting software||48 h||10.1||0.6 M||Lim et al.|||
|AZ31||Tafel extrapolation method||1800 sg||13.4||0.6 M||Li et al.|||
|AZ31 Mg alloy||Tafel extrapolation method||16.2||0.6 M||Shen et al.|||
|Bare AZ31 Mg alloy||Tafel extrapolation method||an initial delay of 5 min||16.5||0.6 M||Einkhah et al.|||
|AZ31 alloy||Fitting software||30 min of exposure.||17.4||0.6 M||Singh et al.|||
|AZ31||Fitting software||20.8||0.6 M||Zhang et al|||
|AZ31||Tafel assumption||24 h||31.1||0.6 M saturated with Mg(OH)2||Cao et al.|||
|AZ31||Tafel assumption||24 h||36||0.6 M||King et al.|||
|AZ31||Tafel assumption||24 h||36.8||0.6 M saturated with Mg(OH)2||Shi et al.|||
|AZ31||Empirical estimation from electrochemical and gravimetric measurements||10 d||65||0.6 M||Feliu et al.|||
|Mg6Al||LEV method from polarization curves||for 1 day||21.2||0.6 M saturated with Mg(OH)2||Cao et al.|||
|Untreated AZ60||Fitting software||21.5||0.6 M||Su et al.|||
|AZ61 magnesium alloy||30 min immersion||24.2||0.6 M||Rajabalizadeh and Seifzadeh|||
|AZ61 magnesium alloy||30 min immersion||35.5||0.6 M||Seifzadeh, and Rajabalizadeh|||
|LEV method||10 d||38.6||0.6 M saturated with Mg(OH)2||Cao et al.|||
|LEV method||10 d||46.1||0.6 M saturated with Mg(OH)2||Cao et al.|||
|As‐cast Mg6Al02||LEV method||10 d||46.7||0.6 M saturated with Mg(OH)2||Cao et al.|||
|As‐cast Mg6Al01||LEV method||10 d||52.4||0.6 M saturated with Mg(OH)2||Cao et al.|||
|AZ61||Empirical estimation from electrochemical and gravimetric measurements||10 d||120||0.6 M NaCl||Feliu et al.|||
3.4. Estimation of the corrosion rate from EIS measurements
In Figure 11, the variations in EIS‐estimated corrosion rate using Eq. (4) and the “apparent” B’ values obtained in this study with immersion time are compared with the corrosion rate as determined from hydrogen collection. A decrease in the differences between the corrosion rate values derived from impedance measurements and those derived from the hydrogen evolution rate occurs with increasing exposure time. As commented previously, this might be associated with the transformation of an air formed film to the steady corrosion layer for Mg specimens exposed to saline solutions and the lower hydrogen evolution rates at the beginning of the immersion tests.
Finally, Figure 12 compares long‐term cumulative corrosion rates determined by mass loss, measurement of the H2 evolved over the entire testing period and integration of the current density (icorr) versus time data determined by the temporal evolution of Rp and Rt over time. All resulted in corrosion rate estimations that are similar in value for each alloy. This corroborating outcome is similar to that from King et al.  and Bland et al. , indicating that the comparison of unique methods not only provides good comparison for the corrosion rate of magnesium alloys but validates the electrochemical approach as a standalone method.
In this research, it has been investigated the possible relationships between independent hydrogen evolution and electrochemical impedance spectroscopy measurements during long‐term exposure of AZ31 and AZ61 magnesium alloys in 0.6 M NaCl.
Linear relationships with high correlation coefficients have been obtained between time‐integrated polarization resistance Rp or charge transfer resistance Rt values determined by EIS and hydrogen evolution measurements.
The changes of Rt values with the immersion time have shown a direct and close relationship with the changes of Rp values determined by EIS, being the relationship characteristic of the microstructure of the alloy.
With immersion time, the system becomes more stable and the reproducibility of the EIS data appears to be improved. Also, the average error for hydrogen measurements after prolonged periods of exposure is usually smaller.
In this investigation, an empirical determination of the “apparent” Stern‐Geary coefficient from the correlation between electrochemical and hydrogen measurements has yielded values of around 118 mV for the AZ61 alloy if the charge transfer resistance is used and of around 83 mV if the polarization resistance is used and values of around 97 mV for the AZ31 alloy if the charge transfer resistance is used and of around 31 mV if the polarization resistance is used.
No significant errors are obtained in the measurement of the corrosion rate when using Rt or Rp with their corresponding “apparent” Stern‐Geary coefficient values.
The authors gratefully acknowledge the financial support provided by the Ministry of Economy and Competitiveness of Spain (MAT 2009‐13530, MAT2012‐30854, and MAT2015‐65445‐C2‐1‐R) to carry out the present study, and Prof. S. Feliu is duly acknowledged for fruitful discussions in the frame of this work.