Crystal orientation and electrochemical corrosion of polycrystalline Mg

Corrosion Science 63 (2012) 100–112

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Crystal orientation and electrochemical corrosion of polycrystalline Mg Guang-Ling Song a,⇑, Zhenqing Xu b a b

Chemical Sciences and Materials Systems, GM Global R&D, Mail Code 480-106-224, 30500 Mound Road, Warren, MI 48090, USA MEDA Engineering and Technical Services, LLC, 17515 W 9 Mile Road, STE 1075, Southfield, MI 48075, USA

a r t i c l e

i n f o

Article history: Received 9 April 2012 Accepted 26 May 2012 Available online 7 June 2012 Keywords: A. Magnesium B. EIS C. Passive film

a b s t r a c t In this study, scanning Kelvin probe, in situ scanning vibrating electrode technique and micro-electrochemical electrolyte cell are employed to investigate the corrosion of polycrystalline pure Mg. It is found that differently oriented Mg grains have different electrochemical activities and corrosion behavior. The grain with a basal orientation is more stable and corrosion resistant, exhibiting a more positive corrosion potential, lower anodic polarization current density, larger impedance, and thinner surface film than the grain with a non-basal orientation. A corrosion model is proposed to explain the differences in electrochemical corrosion performance between these grains. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Magnesium (Mg) and Mg alloys are attractive engineering materials in industry because of their low density, high strength-weight ratio and great castability [1–5]. However, practical applications of Mg alloys are limited due to their poor corrosion resistance [6–14]. Various metallurgical factors, including the impurity level [15], the continuity and amount of second phase [16], the microstructure and the crystal orientation of a Mg alloy [17–19], can significantly influence the corrosion behavior. In an alloy, the matrix phase is always a critical constituent which determines the basic corrosion performance of this alloy. It is important to investigate the corrosion behavior of the matrix phase in order to comprehensively understand the alloy corrosion mechanism. A study on pure Mg is the first step in revealing the corrosion of Mg alloys. A densely packed crystallographic plane normally has a higher atomic coordination, tighter atomic bond, and thus a lower dissolution tendency than a loosely packed crystallographic plane [20– 22]. This theory can be applied to pure Mg. Liu et al. [23] reported that in 0.1 N HCl pure Mg grains with (0 0 0 1) orientation were dissolved slower than those with other orientations. This grain orientation dependent corrosion phenomenon has recently been observed on AZ31 Mg alloy as well; grains with different crystallographic orientations in the alloy exhibit different electrochemical and corrosion behavior [24]. However, Liu et al. [23] only reported corrosion depth results without electrochemical data as supporting evidence, and the measurements were conducted in an acidic solution to which practical ⇑ Corresponding author. Tel.: +1 248 807 4451; fax: +1 586 986 9260. E-mail address: [email protected] (G.-L. Song). 0010-938X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.corsci.2012.05.019

Mg alloy parts are unlikely to be exposed. Although Song et al. [24] studied the electrochemical behavior of differently oriented AZ31 Mg alloy surfaces in a dilute neutral sodium chloride solution, the results only represented the average performance of many fine grains, rather than the electrochemistry or corrosion behavior of a single grain with a defined crystal orientation. Therefore, there is a need for an insight into the electrochemistry of individual grains, which will provide essential information for a more comprehensive and fundamental understanding of the corrosion of polycrystalline pure Mg and its alloys. In natural environments there is always a surface film developed on Mg and its alloys [25]. The film can normally affect their electrochemical corrosion behavior [26]. Currently, studies on the surface films on differently oriented grains are very limited [27– 29]. For example, Schmutz et al. [27] reported a beautiful filiform corrosion pattern on Mg grain surfaces in a chromate and chloride containing solution. They found that the corrosion was limited to planes near {0 0 0 1} orientations and propagated in prismatic directions. This finding was further confirmed by McCall et al. [28] with direct polarization curve measurements on Mg grain  0Þ and ð1 1 2  0Þ, and was also supported by surfaces (0 0 0 1), ð1 0 1 Lillard et al.’s simulation analysis [29]. All these studies have undoubtedly thrown light on the understanding of the corrosion behavior of crystal Mg surfaces in chromate and chloride containing solutions. However, chromate is currently being prohibited in many applications. It is unlikely for Mg or its alloy parts to be exposed to such a toxic medium in a natural environment. Therefore, the reported results [27–29] obtained from that chromate containing solution may not be representative of the electrochemical corrosion behavior of Mg in a typical service environment. To better understand the effect of a naturally formed surface film on corrosion performance of polycrystalline pure Mg, it is essential and

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important to investigate the corrosion of individual Mg grains with different orientations in solutions that can represent natural environments. In this study, a polycrystalline pure Mg coupon is immersed in a neutral 0.01 M NaCl solution and a Mg(OH)2 saturated alkaline solution. The NaCl solution to a great extent simulates ocean fog, seawater splash and deicer mixed water spray. Saturated Mg(OH)2 represents Mg alloy surfaces in a wet environment where Mg(OH)2 deposits can be quickly formed. These two selected solutions stand for many service environments of a Mg alloy part in industrial applications. 2. Experimental 2.1. Solution and sample preparation The solutions used in this study included saturated Mg(OH)2 and 0.01 M NaCl made of analytical grade chemicals and deionized water. A 1 M NaOH solution was also used in some experiments for comparison purposes. A high purity Mg (Al < 0.01 wt.%; Cu < 0.01 wt.%; Fe < 0.03 wt.%; Mn < 0.002 wt.%, Ni < 0.01 wt.%, Si < 0.01 wt.%; Zn < 0.01 wt.%) coupon cut from an Mg ingot was used. It was mounted in epoxy resin and mechanically ground using SiC paper and then polished with a sequence of 9, 3, and 1 lm oil-based diamond suspensions, followed by fine-polishing using a liquid made of 1/3 part of 0.02 lm colloidal silica, 1/3 part of ethanol, and 1/3 part of ethylene glycol. The sample was abraded and polished again after each experiment. 2.2. AC EIS and polarization curve measurements on individual grains To obtain the polarization curve and AC Electrochemical Impedance Spectroscopy (EIS) results of individual grains, a special electrolyte cell was built using a plastic syringe (the metal needle had been removed). Fig. 1 shows the schematic drawing of the experimental setup. The inner diameter of the syringe tip was 1 mm, so that in each electrochemical measurement only one grain was exposed to the solution in the syringe as a working electrode. A platinum wire was used as a reference electrode in the cell. The whole surface of the wire was covered with a corrosion resistant paint except its tip (uncovered). A platinum mesh was used as a counter electrode in the syringe. These three electrodes were connected to a PAR273 potentiostat, respectively. The Mg sample was held at its open-circuit potential (OCP) for 5 min before measurement. Potentiodynamic polarization curves were recorded at a potential scanning rate of 0.1 mV/s from 0.1 V to +0.1 V vs. OCP. The AC impedance measurements were performed using that potentiostat and a frequency analyzer at frequencies ranging from 17,777 to

101

0.1 Hz. The amplitude of the sinusoidal potential signals was 5 mV with respect to the OCP. 2.3. SKP and SVP measurements Scanning Kelvin Probe (SKP) and Scanning Vibrating Probe (SVP) measurements were carried out in air at relative humidity around 25% and room temperature 24 °C using an electrochemical workstation Uniscan M370. The relative Volta potential values were recorded using a tungsten probe with a tip diameter of 500 lm. The vibrating amplitude and frequency of the tungsten probe were 30 lm and 80 Hz, respectively. The distance between the tip and the sample was kept constantly at 100 lm. Before measurements, SKP probe was calibrated using a standard Zn-Steel reference sample provided by the instrument manufactory. The open-circuit potentials of the Mg sample relative to a standard Ag/AgCl reference electrode in the 1 M NaOH, saturated Mg(OH)2 and 0.01 M NaCl solutions were also measured for SKP reading calibration. The corrosion processes on the Mg coupon were in situ monitored by SVP in the Mg(OH)2 saturated and 0.01 M NaCl solutions, respectively. The vibrating probe consisted of a platinum coated tip (5–50 lm in diameter) that was placed above the Mg sample surface at a height of about 100 lm. The vibrating amplitude and frequency of the SVP probe were 30 lm and 80 Hz, respectively. Peakto-peak voltage signal was recorded. The Mg(OH)2 and NaCl solutions were measured to have conductivities 0.36 and 0.96 mS/cm, respectively, with which the measured peak-to-peak voltages were converted to current densities. A relatively negative current density in SVP mapping should represent an anodic site, whereas a relatively positive current density normally stands for a cathodic point. 2.4. Surface analyses After immersion, X-ray photoelectron spectroscopy (XPS) was carried out on selected spots using a PHI Quantera SXM Scanning X-ray Microprobe System. Surface survey spectra were measured and depth profiles of C, O and Mg were acquired by sputtering. As a standard practice in XPS studies, the C1s line corresponding to the C–C bond in the measured XPS spectra was used as a reference for calibration. Electron Probe Microanalysis (EPMA) was conducted to identify surface elements after immersion. Measurement was performed using a Cameca Instruments Inc., Model SX 100. Electron beam conditions were typically 15 kV and 80 nA. Mg, O and Cl were included in the X-ray mapping. 2.5. Crystal orientation detection The texture of the Mg sample was determined using the electron backscatter diffraction (EBSD) technique. To obtain a high quality EBSD image, 2–4 s etching was conducted using a solution made of 60 mL ethanol, 20 mL distilled water, 15 mL acetic acid and 5 mL nitric acid after mechanical grinding and polishing as described earlier. EBSD results were collected using a TSL high speed Hikari camera attached to a Leo 1455 SEM operating at a voltage of 20 kV and a working distance of 18 mm. EBSD Data were analyzed using the TSL software version 5.2. 3. Results and discussion 3.1. Optical surface morphology

Fig. 1. Schematic illustration of the set-up used in electrochemical characterization of Mg grains.

The metallographic photo of the Mg specimen surface is shown in Fig. 2(a). The dark and bright regions of the Mg surface appear to be

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slightly different in textures. Particularly, the twins shown in different areas have different directions. According to these visible differences, the Mg surface can be divided into the following areas: B, C, D, E and G (see Fig. 2(b)). Areas D and G in relatively dark color appear to be much different from the other relatively bright areas (B, C and E) under the microscope. The difference in reflectivity and texture in these areas indicate that areas B, C, D, E and G may correspond to different grains, and the electrochemical behavior and corrosion performance may vary from area to area on the Mg surface.

feature for spot u in the NaCl solution is that its low frequency characteristic becomes an inductive loop. These results imply that the electrochemical process on spot / has a similar mechanism in both solutions, whereas the electrochemical mechanism at spot u is different. Moreover, the smaller diameters of the EIS loops in the NaCl solution suggest that the electrochemical processes are faster if chlorides are present, which is consistent with the polarization curve results (Fig. 3). The EIS results confirm that spot / is more corrosion resistant than spot u in both solutions, suggesting that the dark region should be electrochemically more stable than the bright region on the Mg coupon surface.

3.2. Electrochemical characterization 3.3. Corrosion behavior Two spots / and u (see Fig. 2(b)) were selected from areas D and E as representatives of the dark and bright regions for electrochemical characterization. Potentiodynamic polarization curves and AC EIS spectra were repeatedly conducted using the specially designed electrolyte cell (see Fig. 1) on these two spots in Mg(OH)2 saturated solution and 0.01 M NaCl solution, respectively. Their typical results are presented in Figs. 3 and 4. In the Mg(OH)2 saturated solution and 0.01 M NaCl solution, the open-circuit potentials or corrosion potentials of spot / are about 60 mV more positive than those of spot u; spot / has much lower anodic polarization current densities than spot u (see Fig. 3). These results suggest that spot / is more anodically stable or more corrosion resistant than spot u. Their polarization current densities are lower in the Mg(OH)2 saturated solution (Fig. 3(a)) than in the 0.01 M NaCl solution (Fig. 3(b)), particularly for spot u, because of the well known fact that NaCl is more corrosive than Mg(OH)2. In NaCl, the polarization curve of spot u near the corrosion potential appears to fluctuate more than that of spot /, indicating that severe corrosion may occur on this spot around its corrosion potential. Fig. 4(a) shows that Nyquist EIS spectra of spots / and u have two capacitive loops in the Mg(OH)2 solution. Their diameters for spot / are larger than those for u. This signifies that the electrochemical process is slower at spot / than that at u, which is consistent with the prediction based on the polarization curve measurements (Fig. 3(a)). In 0.01 M NaCl (see Fig. 4(b)), spot / still has two capacitive loops similar to its spectrum in the Mg(OH)2 saturated solution, but their diameters are smaller. A noticeable EIS

(a)

(b)

Fig. 2. (a) Optical microscopic image and (b) areas of the Mg coupon surface and selected typical spots for electrochemical characterization.

In the Mg(OH)2 solution, during 60 min immersion, no visible surface change was observed by naked eye. The SVP mapping results are presented in Fig. 5. The initial SVP map (see Fig. 5(a)) shows that cathodic activity is mainly distributed in areas B and D where a large fraction of surface area exhibits relatively positive current densities; area E is basically an anodic site. After 60 min, the anodic and cathodic contrast diminishes and the surface becomes relatively uniform in terms of the SVP signal (Fig. 5(b)). It seems that those positive current density zones slightly spread out to area G. E is still a major anodic area relative to other areas. These SVP maps indicate that the left hand side of the Mg sample should be more stable than the right. It is noted that current differences over the whole Mg surface are not significant and getting smaller with immersion time according to Fig. 5. This means that although the electrochemical corrosion activity over the Mg surface is not uniform, the difference between anodic and cathodic sites is not significant, which may not be enough to initiate localized corrosion damage. In other words, immersion in the Mg(OH)2 solution makes the surface more uniform in electrochemistry, which can be confirmed by surface morphology observation after immersion later. Mg tends to corrode faster in a chloride containing solution. A small amount of dissolved chloride salt in water can lead to localized corrosion [6,30]. Therefore, in the 0.01 M NaCl solution, hydrogen evolution from the sample surface was observed. After several minutes of immersion, a small dark point appeared in area E next to the boundary of area C, accompanied by a rising stream of gas bubbles. This dark point then spread out toward left, and then gradually became a large dark rough corrosion damaged area. The whole 3 h corrosion initiation and propagation process was in situ monitored by SVP and is shown in Fig. 6(a)–(c). The anodic dissolution, which is indicated by a significantly negative current density zone in the SVP mapping, originates from the boundary of area E next to area C. The local anodic activity or pitting corrosion spreads out. After 60 min immersion (Fig. 6(b)) the corrosion develops into area C. At 180 min, the actively corroding spot as marked by the blue color moves to areas B and C, while the earlier corroded area left in area E becomes cathodic with relatively positive SVP current density readings (Fig. 6(c)). Commonly the formation of hydrogen bubbles during the SVP scan can more or less affect the quality of the measurement, because it modifies the fluidodynamic conditions of the solvated ions in correspondence of the metal surface. However, in this study the hydrogen evolution was from corroding areas where the potentials or current densities are much more negative than an uncorroded region. Compared with the difference between corroding and uncorroded areas, the hydrogen evolution influence is relatively small. Therefore, a corroding location can still be roughly indicated by SVP mapping, although it is only a blur in the map. Compared with the corrosion in the Mg(OH)2 solution, the SVP maps obtained in the 0.01 M NaCl solution have relatively large current density difference between anodic and cathodic zones, and the distribution of the anodic activity is much more localized.

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(a)

103

(b)

Fig. 3. Polarization curves measured from spots u and / in areas D and E as representatives of the dark and bright regions of the surface of the Mg coupon immersed in (a) Mg(OH)2 saturated solution and (b) 0.01 M NaCl solution, respectively.

(a) (a)

(b)

(b)

Fig. 4. Impedance spectra measured from spots u and / in areas D and E as representatives of the dark and bright regions of the surface of the Mg coupon immersed in (a) Mg(OH)2 saturated solution and (b) 0.01 M NaCl solution, respectively.

This implies that localized corrosion damage occurred on the Mg surface in the NaCl solution. Moreover, there is an interesting phenomenon that the anodically active site becomes cathodic after the active corrosion develops. This is typically a filiform corrosion characteristic and will be further discussed later. The above in situ corrosion monitoring has clearly indicated that the Mg surface has very different electrochemical corrosion performance in different areas in the Mg(OH)2 and NaCl solutions. Different corrosion behavior will result in different corrosion morphologies and surface characteristics. 3.4. Corroded Mg surface The Mg(OH)2 saturated solution has a pH value around 10.5. Although it is not very corrosive to Mg, a certain degree of Mg dissolution in this solution is unavoidable. It was observed under microscope that a non-uniform cloudy white color was built up on the entire Mg surface (Fig. 7(a)). After that, the surface is no longer smooth or shining as its original state. The grain texture, area boundary and twin features become very blurred. This is obviously a result of dissolution of Mg and building up of corrosion products on the surface. A comparison of this metallographic photo

Fig. 5. SVP maps of the Mg coupon obtained at (a) 0 min and (b) 60 min after immersion in the Mg(OH)2 saturated solution.

with the SVP map (Fig. 5) reveals that that the corroded surface or corrosion product pattern (Fig. 7(a)) does not follow the anodic and cathodic activity zones. It is quite interesting that this optically visible color pattern (Fig. 7(a)) still roughly matches the division of areas B, C, D, E and G, indicating that the surface films deposited on these different areas may be slightly different in some aspects. The inheritance of substrate area division after immersion in Mg(OH)2 could result from different electrochemical activities of Mg in these areas. The surface film formation is to some extent affected by the Mg substrate. Fig. 7(b) shows the SKP mapping of this Mg specimen after immersion in the saturated Mg(OH)2 solution. The positive SKP voltages are mainly distributed in areas B, D and G. The most negative potentials are in area C and then area E. If this map (Fig. 7(b) is compared with the metallographic photo (Fig. 7(a)), one will see that the SKP pattern does not have distinct boundaries between those areas. It appears that SKP picks up some information differ-

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Fig. 7. (a) Optical microscopic image and (b) SKP map of the Mg coupon after 2 h immersion in the Mg(OH)2 saturated solution.

Fig. 6. SVP maps of the Mg coupon obtained at (a) 0 min, (b) 60 min and (c) 180 min after immersion in 0.01 M NaCl.

ent from an optical microscope. This indicates that the optical characteristics of a surface film cannot reflect the influence of this surface film on Volta potential or work function of Mg. Nevertheless, the SKP mapping (Fig. 7(b)) to some degree corresponds to the anodic–cathodic pattern in the SVP mapping (Fig. 5); the left part of the Mg surface is slightly more noble than the right part. An important implication of this rough correlation between SVP and SKP is that SKP may be used to characterize the corrosion activity of the Mg surface. Similar results were obtained for the Mg coupon after 180 min immersion in 0.01 M NaCl. Fig. 8(a) shows an optical microscopic photograph of the corroded Mg sample. It can be seen that a large surface fraction of areas C and E and a small area in B have been corroded, whereas areas D and G are not attacked. Corrosion can also be found along the boundaries between C and D. This corresponds very well with the development of corrosion from area E to C and finally B as demonstrated in Fig. 6. Therefore, Fig. 8(a) is actually a piece of direct evidence supporting that different areas of the Mg sample have different electrochemical activities in the NaCl solution as illustrated by the in situ SVP mapping (Fig. 6). In the non-corrosion zones, the Mg surface has completely lost its original grain texture, area boundaries and twin features. This is because there is uniform dissolution or corrosion product building up, which conceals the original surface morphology. The SKP mapping of the corroded Mg surface after immersion in the NaCl solution is shown in Fig. 8(b). Again, the corroded zone in

Fig. 8. (a) Optical microscopic image and (b) SKP map of the Mg coupon after 180 min immersion in the 0.01 M NaCl solution.

areas E, C and B (Fig. 8(a)) roughly corresponds to the negative voltage region in the SKP mapping (Fig. 8(b)). This suggests that SKP does to some degree reflect the corrosion damage of the Mg surface. However, the area and position of the blue color zone in the SKP map are slightly different from the corrosion pattern shown in Fig. 8(a). Moreover, the SKP mapping shows some small voltage variation in the non-corrosion surface areas (Fig. 8(b)). This voltage distribution does not match the surface morphology (Fig. 8(a)) or

G.-L. Song, Z. Xu / Corrosion Science 63 (2012) 100–112

follow the anodic–cathodic activity pattern (Fig. 6). A possible explanation is that due to the intense anodic dissolution in the corrosion zone, some corrosion products may also be non-uniformly deposited in the non-corrosion areas, which not only conceals the original Mg surface morphology, but more importantly also affects the SKP voltage results in these areas. In other words, the presence of the surface film reduces the sensitivity of SKP measurement in detecting the difference in Volta potential of the substrate Mg. Fig. 8(b) also shows that the contrast in SKP mapping between corroded and uncorroded zones is about 500 mV after immersion in the NaCl solution, much larger than that between the anodic and cathodic areas (about 20 mV) in the Mg(OH)2 solution (Fig. 7(b)). The corrosion product film in a corroded zone is very different from the surface film on an uncorroded area in either thickness or composition. This relatively big difference results in a relatively large SKP difference. The surfaces after immersion were further analyzed by element mapping and XPS. The surface after immersion in the saturated Mg(OH)2 did not show significant or meaningful non-uniformity in Mg and O contents (and thus its element mapping is not shown this paper). Therefore, the slightly different colors or visible features developed on the Mg surface under an optical microscope (Fig. 7(a)) cannot be a result of the variation in surface film composition. The distinction could be caused by film thickness difference. In 0.01 M NaCl, the corroded zone is different from the uncorroded areas in chemical composition. Fig. 9 shows that the corrosion products in the corroded zone are mainly composed of Mg and O. The Mg concentration is lower and O content is higher. In other words, corrosion damage on the element mapping can be characterized by a high O zone. Literature [10,14,30] has suggested that the corrosion products of Mg in NaCl solution are mainly Mg(OH)2. O signal cannot come from the Mg substrate, but from the Mg(OH)2 corrosion product layer. The strong O signal presented in Fig. 9 implies that the corrosion product layer built up in the corrosion zone must be very thick. In the uncorroded areas, the surface film is very thin and thus the EPMA signals mainly come from the substrate Mg; no O signal was detected. It is interesting that Cl ion distribution in the corroded area is not uniform. Only a few isolated chloride spots sit in the corroded areas, particularly along the edges and tips of the corroded areas. This is

105

probably because chlorides participate in corrosion initiation along the edges of a corroding zone. In corroded areas, due to the high solubility of chloride salts, most chlorides in the corrosion products might have been dissolved and thus only the less soluble Mg(OH)2 remains there. An important result of the element mapping is that the corrosion product film built in the corrosion zone is much thicker than that in the uncorroded areas. It implies that the film is thicker on an active area than on a stable or corrosion resistant area. If this implication is extended to the Mg sample in the Mg(OH)2 saturated solution, one would expect that the films on the different areas of the Mg surface will have different film thickness. The earlier polarization curve (Fig. 3), AC EIS (Fig. 4) and SVP (Fig. 5) results have suggested that area D is more stable than area E. The surface film on D should be thinner than that on E. The films formed on these grains in Mg(OH)2 are too thin to be detected by EPMA element mapping, but they can be distinguished by XPS profiles. Mg and O depth profiles obtained from spots u and / are shown in Fig. 10. On area D, the Mg/O atomic ratio increases until at the depth of about 250 nm where the Mg concentration is close to 100 at.% and the O content becomes sufficiently low, meaning that the Mg(OH)2 film is about that thick in area D. On area E, the atomic ratio of Mg to O keeps increasing all the way up to 450 nm and still has an increasing trend; implying that the film is thicker than 450 nm. Therefore, the XPS results in Fig. 10(a) confirm that a faster dissolution of Mg can lead to a thicker film building up in a less stable surface area for Mg in either a Mg(OH)2 or NaCl solution. 3.5. Corrosion mechanism Based on the results shown above, the corrosion of the Mg coupon can be summarized in a simple model as schematically illustrated in Fig. 11. On Mg surface, the original surface film can to some extent retard electrochemical reactions, including anodic Mg dissolution (reaction rate ka) and cathodic water/oxygen reduction (reaction rate kc). It has been reported [13] that mono-valence Mg+ ions and ‘‘anodic hydrogen evolution (AHE)’’ may be involved in the anodic process in a surface film free area; but in film covered area, the anodic process is simply Mg ? Mg2+ through the film. The cathodic process involved the following reactions:

Fig. 9. EPMA element mapping for the Mg coupon after 180 min immersion in the 0.01 M NaCl solution.

G.-L. Song, Z. Xu / Corrosion Science 63 (2012) 100–112

Area D

100 80

Concentration (at. %)

Concentration (at. %)

106

Mg

60 40

O

20 0

Area D

100

60 40

O

20 0

0

100

200

300

400

500

0

50

Depth (nm) 100

100

Area E

80

Mg

60 40

O

20 0 0

100

200

300

100

150

200

250

Depth (nm)

Concentration (at. %)

Concentration (at. %)

Mg

80

400

500

Area E

80

Mg

60 40 20

O

0 0

50

100

150

200

250

Depth (nm)

Depth (nm)

(a)

(b)

Fig. 10. XPS spectra obtained from regions D and E of the Mg coupon after 2 h immersion in (a) the Mg(OH)2 saturated solution and (b) the 1 M NaOH solution.

2H2 O þ 2e ! H2 þ 2OH

ð1Þ



ð2Þ

O2 þ 2H2 O þ 4e ! 4OH

Reaction (1) is the main process. Oxygen reduction (2) can also occur, but it is not a principal cathodic process. Both the water and oxygen reduction reactions can lead to generation of OH. The overall cathodic process can be summarized as a OH generation

reaction. The dissolved Mg2+ can react with OH and form Mg(OH)2 precipitation (reaction rate kf). At the same time, the precipitated film can also be chemically dissolved at a rate of kd. Under an ideal condition, all these reactions are uniformly distributed over Mg which is assumed to be uniform in electrochemistry (see Fig. 11(a)). At a steady state, over a unit surface area (surface area is assumed to be 1 cm2) there is:

Fig. 11. Schematic illustration of electrochemical processes occurring on Mg in case of (a) ideal uniform corrosion, (b) uniform corrosion slightly deviated from steady state and (c) localized corrosion significantly deviated from steady state.

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G.-L. Song, Z. Xu / Corrosion Science 63 (2012) 100–112 a

f

k ¼k ¼k

d

ð3Þ f

d

The film thickness L is determined by k and k . It should be noted that ka is an electrochemical reaction rate through the surface film, and thus a function of applied potential V and film thickness L; kd is the film dissolution rate determined by the film composition and microstructure, and therefore is independent from potential V and film thickness L. The variation rate (or growth rate) L of the film thickness can be written as:

@L f d L_ ¼ ¼ K L ðk  k Þ @t

ð4Þ

where KL is a constant for converting the chemical reaction rate to the film growth rate. When kf > kd, the film grows and becomes thicker. If kf < kd, the film becomes thinner. In reality, due to fluctuation in reactions involved in the corrosion, the electrochemical processes cannot always stay in a steady state. After deviation from its original steady state, there are two possibilities: (1) the fluctuation is not significant and the system will return to its original steady state eventually; (2) the change to the system caused by disturbance is so significant that the system cannot come back to its original steady state. Fig. 11(b) and (c) schematically illustrate these two possibilities. In case (1), the disturbance can only result in film non-uniformity in different areas. For example, the film becomes thinner in area a and thicker in area b (see Fig. 11(b)). Due to different degrees of retarding effect of the thin and thick films, the dissolution of Mg a a in area a will be faster than that in area b (ka > kb ), which will result f f in ka > kb according to Eq. (3), while the film dissolution has the d d same rate over a and b (ka ¼ kb ) assuming the film composition f d has not been significantly changed. This means that ka > ka and f d kb < kb . Therefore, the film will grow on a, but dissolve on b. Consequently, the film becomes uniform again over a and b. This kind of uniform corrosion can occur on the Mg surface in the Mg(OH)2 saturated solution, because the Mg(OH)2 solution is not very corrosive to Mg. The variation in electrochemical activity cannot be significantly large enough to remove or break down the surface film. The surface film can still have a relatively uniform coverage. The above discussion is based on an assumption that the Mg surface is uniform and reaction variation is a result of a fluctuation of solution concentration, temperature, or flow etc. If the substrate Mg is slightly different in activity from area to area, there will be a slight difference in Mg(OH)2 film thickness L or microstructure according to the model. One can reasonably assume that the film resistance (Rf) is determined by film thickness L and film resistivity q. Over a unit surface area, there is:

Rf ¼ q L

ð5Þ

where q is a constant. The anodic dissolution rate ka and cathodic OH generation rate kc can be simply expressed as: a

k ¼ Qa



 V  V 0a ; qL

V 0c  V c k ¼ Q cð Þ qL

ð6Þ

where V is the electrode potential; V0a and V0c are equilibrium potentials for the anodic and cathodic reactions; Qa and Qc are constants for converting anodic and cathodic currents to chemical reaction rates, respectively. In this study, area E is more active than area D on the Mg surface in the Mg(OH)2 (Figs. 3–5), i.e., ka is larger a a in area E than in area D (kD < kE ). Since the film thickness on area E is larger than area D (LD < LE) (see Fig. 10(a)), according to Eq. (6) the film resistivity should be larger on area D than on area E (qD > qE), which means that the deposited Mg(OH)2 film formed on an active area is looser or less compact than on a passive area. In other words, a more stable substrate normally has a more protective surface film. This is a reasonable expectation. If the substrate is active, its surface film is looser even though it is thicker. An actively corroded area

normally has a very thick but non-protective corrosion product film (see Fig. 9). In case (2), the deviation is too large, far away from the original steady state, and the surface film is locally removed in some areas. Thus, the substrate Mg is exposed in some local areas (see Fig. 11(c)). For example, when the Mg coupon was exposed in the 0.01 M NaCl solution which is much more aggressive than the Mg(OH)2 saturated solution, a corroding pit was formed on a relatively active area (e.g., area B, C or E in this study), where the surface film has been removed (e.g., area a in Fig. 11(c)) and the Mg dissoa lution rate ka is significantly fast. Even a small fluctuation in Cl concentration, temperature, solution flow, or hydrogen evolution etc. may lead to a large variation in anodic and cathodic reactions there. It should be noted that reactions (Fig. 11(c)) on the film free area in the NaCl solution are much more complicated than those on the film covered area in the Mg(OH)2 solution (see Fig. 11(b)). Mg can turn into Mg+ (ka) which is either immediately further eleca trochemically oxidized to Mg2+ (ka ) on the surface or chemically a reacts with water (kha ) producing H2 (‘‘anodic hydrogen evolution’’) and Mg2+ in the solution [13]: a

a

a

k ¼ ka þ kha

ð7Þ

Due to the intense anodic hydrogen evolution in the broken film area, the deposition of Mg(OH)2 there becomes difficult and can be neglected. The hydrogen evolution brings the dissolved Mg2+ to the adjacent surface area b, reacting with OH to form Mg(OH)2 depof a a sition (kb ). The rapid anodic dissolution processes (ka, ka and kha ) in f the film free area a result in a rapid deposition (kb ) of Mg(OH)2 in the film covered area b. The quickly precipitated Mg(OH)2 is looser than the original film. After this new loose film precipitates in cord roded area, its dissolution (kb ) is quicker than that of the original a one. At the same time Mg dissolution (kb ) and OH generation c (kb ) reactions similar to those in the saturated Mg(OH)2 solution can also occur in the Mg(OH)2 deposited area, and their rates are higher due to the loose nature of the deposited film. An important outcome of the above corrosion model is that the localized dissolution in the film free area will continue and the surface film will not be repaired due to the vigorous ‘‘anodic hydrogen evolution’’, i.e., the corrosion system will never return to its original state. On a unit surface area, if the film free or substrate Mg exposed area is h, and the surface film covered area is 1  h, the precipitation of Mg(OH)2 (Kf) would depend on the supply of a a a Mg2+ (ka , kha and kb ) and h: f

f

a

a

a

a

k ¼ ð1  hÞkb ¼ hðka þ kha Þ þ ð1  hÞkb ¼ hka þ ð1  hÞkb

ð8Þ

d

The dissolution (K ) of deposited Mg(OH)2 can be expressed as: d

d

K ¼ ð1  hÞkb

ð9Þ

Further corrosion is likely to occur at the edge of the corroded area where new Mg(OH)2 cannot be deposited due to the vigorous ‘‘anodic hydrogen evolution’’ and the original surface film has a tendency to be dissolved. Therefore, the corrosion develops forward to the original film covered area and the corrosion product film is built up behind the corroded area. This is a mechanism similar to that of the filiform corrosion in which the corroding ‘‘head’’ is an active anode and the corroded ‘‘tail’’ is a passive cathode. Since reactions in the film free area are much faster than in the film covered area, the film thickness and resistivity are not critical parameters determining the overall anodic dissolution rate. Instead, the film coverage or film free area (h) becomes a major factor. The variation rate (h) of the film free area can be expressed as

@h h_ ¼ ¼ K h ðKf  KdÞ ¼ K h ½hka þ ð1  hÞkab  ð1  hÞkdb @t

ð10Þ

where Kh is a parameter for converting the chemical reaction rate to the surface film coverage variation rate.

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G.-L. Song, Z. Xu / Corrosion Science 63 (2012) 100–112

The above analysis and discussion is about the localized corrosion in an active area of the Mg in corrosive NaCl solution. On a less active area, such as area D, the change in Mg dissolution and hydrogen evolution will be less significant, although this area is subjected to the same Cl concentration, temperature, and solution flowing fluctuations as an active area. Compared with an active area, the biggest difference of a passive area is that the surface film can stay on the surface and no film free area is exposed. Even the film may become significantly thinner in some areas; it can grow and be repaired. Therefore, the electrochemical behavior of a stable surface area in the 0.01 M NaCl solution is similar to that in the Mg(OH)2 solution. 3.6. EIS analysis The corrosion mechanism illustrated above can be verified with AC EIS results (Fig. 4). The EIS behavior of the Mg coupon in the Mg(OH)2 and NaCl solutions is analyzed as follows through an EIS theory proposed for an electrode system without considering diffusion processes [31]. When the deviation from steady state is small (see Fig. 11(a) and (b)), the equivalent circuit should be the one shown in Fig. 12(a). Detailed mathematical derivation can be found in the appendix section. In Nyquist plot, it has a high frequency capacitive loop ascribed to Cdl and Rt and a low frequency loop associated with Ra and Ca, where Cdl and Rt are the double layer capacitance and resistance at the film/substrate interface, Ra, and Ca are pseudo resistance and capacitance related to the film formation and dissolution process, Rs is the solution resistance. Fig. 4 shows that the Mg coupon in the less aggressive solution Mg(OH)2 and the less active area of the Mg surface in the corrosive NaCl solution have two capacitive loops as predicted by the EIS analysis and the equivalent circuit (Fig. 12(a)). When the deviation from the original steady state is large enough to remove the surface film in a local area, the equivalent circuit is shown in Fig. 12(b), where R0 and H are pseudo resistance and inductance associated with the film breakdown and dissolution. This circuit can produce an EIS spectrum with a high frequency capacitive loop and a low frequency inductive loop on Nyquist plot. The theoretically predicted EIS behavior has been verified by the experimental spectrum for the active area E in the corrosive NaCl solution (see Fig. 4(b)). Based on the proposed equivalent circuits (Fig. 12), EIS parameters can be extracted through curve-fitting of the measured spectra (Fig. 4). It should be noted that the equivalent circuits are theoretical modes resulting from mathematic deduction without considering the practical dispersion effect. However, dispersion effect cannot be ignored in experimental spectra. Therefore, capacitive CPE components were used instead of pure capacitances in the equivalent circuits to fit the experimental impedance spectra. The curve-fitted results are listed in Table 1. A more compact film is more resistant and has a larger Rt. The value of a double layer capacitance is dependent on film thickness; a thinner film corresponds to a larger double layer capacitance value. Area D has slightly larger Rt and smaller Cdl than area E in the Mg(OH)2 satu-

(a)

rated solution, suggesting that the film on D is slightly thinner but more compact or resistant than that on E. This not only experimentally supports the theoretical discussion in this paper, it is also consistent with literature reported results [12,32] that the grain oriented near (0 0 0 1) has higher charge transfer resistance and is relatively more corrosion resistant. In NaCl, the estimated Cdl significantly increases and Rt becomes evidently smaller, implying the surface film becomes less resistant. Particularly, the Rt on area E is only half of that on area D, which can be a result of disappearance of the surface film or direct exposure of the substrate Mg to the solution in some local sites due to the increased solution corrosivity. It should be noted that the Rt and Cdl for area D obtained in the NaCl solution are average values over the film free area and the area with newly deposited Mg(OH)2 film coverage. They cannot have values typical of a bare metal surface. The Ca has a value much larger than a normal double layer capacitance, indicating that this parameter cannot have a physical meaning like a double layer capacitance. In fact, Ra, R0, Ca and H are pseudo resistance, capacitance and inductance whose mathematical expressions are complicated and will not be discussed in this paper. For a polycrystalline pure Mg, its EIS spectrum is a result of various grains, including basal and non-basal crystal planes. A combination of the two equivalent circuits as shown in Fig. 12 would yield an EIS spectrum with two capacitive loops and one inductive loop according to the above discussion. These kinds of EIS results have been obtained experimentally [33–35], suggesting the rationality of the above EIS analysis of differently oriented Mg grains. 3.7. Grain orientation The different areas shown in Fig. 2 correspond to different grains of the Mg coupon. Different grains in a sample normally have different orientations. If the metallographic photo (Fig. 2(a)) and the area division (Fig. 2(b)) truly reflect the grain distribution over the Mg coupon surface, these areas should have different crystallographic orientations, which can be confirmed by EBSD. Fig. 13(a) shows an inverse pole figure (IPF) map of the Mg coupon surface. The colors in the IPF map correspond to the crystallographic axes of the grains in the stereographic triangle (Fig. 13(a)). The specimen consisting of grains with different orientations are schematically illustrated in Fig. 13(b). Area B in a blue to green color is oriented near the  0Þ direction. Grain C, represented by a yellow color, is oriented ð1 1 2  0Þ prisat an angle between the (0 0 0 1) basal plane and the ð1 1 2 matic plan. Grains D and G in the colors between red and purple has an orientation very close to (0 0 0 1). The green colored grain E  0Þ oriented. Overall, grains D and G is another grain nearly ð1 1 2 are most close to the basal plane; grains B and E are close to prismatic planes; while the orientation of grain C is between D and E. A comparison of this grain orientation map (Fig. 13) with the electrochemical activity distribution and corrosion damage pattern (Figs. 3–8) can lead to a conclusion that the basal plane or (0 0 0 1) orientated grain is more stable and corrosion resistant than the other planes or non-basal orientated grains in the NaCl and Mg(OH)2 solutions. This is in good accordance with our pre-

(b)

Fig. 12. Equivalent circuits for Mg (a) slightly deviated from its original steady state with surface film covered on its surface and (b) significantly deviated from its original state with broken surface film.

109

G.-L. Song, Z. Xu / Corrosion Science 63 (2012) 100–112 Table 1 EIS parameters extracted from Fig. 4 according to the equivalent circuit shown in Fig. 12.

Area D in Mg(OH)2 Area E in Mg(OH)2 Area D in 0.01 M NaCl

Area E in 0.01 M NaCl

Rs (X cm2)

Cdl (lF/cm2)

Rt (X cm2)

Ca (lF/cm2)

Ra (X cm2)

13.7 13.4 0.5

73 69 98

328.7 201.4 60.4

4100 6600 9000

163.7 93.8 24.1

Rs (X cm2)

Cdl (lF/cm2)

Rt (X cm2)

H (S/cm)

R0 (X cm2)

0.8

100

30.7

4.8

130.2

vious theoretical conjecture based on the simple observation of the corrosion depth of Mg in an acid and the average electrochemical corrosion results of AZ31 polycrystalline grains in a NaCl solution [23,24]. The direct electrochemical measurements over individual grains with different orientations (Figs. 3 and 4) and the in situ corrosion monitoring over these grains (Figs. 5 and 6), as well as the examination of corrosion products and morphologies (Figs. 7–9) provide unambiguous evidence to draw a firm conclusion that corrosion does prefer to propagate on a loosely packed crystallographic plane which is more active than a close packed plane. Since the results in this study were obtained from individual pure Mg grains, and they were not averaged information from a surface consisting of hundreds of alloy (e.g., AZ31) grains [24], the influence of segregation of alloying elements, presence of secondary phases or precipitation of impurity containing particles [5,36] on corrosion can be excluded. The only metallurgical factor that can influence the corrosion performance of the Mg coupon is its grain orientation. For a Mg coupon without a surface film in an acid as demonstrated previously [23], it is not surprising that different Mg crystal surfaces have different dissolution rate due to their different coordinating atom numbers or atomic densities. However, in this study, Mg grains are covered by surface films in the selected neutral and alkaline solutions. These grains still exhibit different electrochemical corrosion performance. Although the different corrosion performance over different gains has to be associated with different grain orientations, the correlation between corrosion behavior and crystallographic orientation is actually indirect in this case because of the surface film. Two possible facts should be considered:

Fig. 13. (a) EBSD grain distribution, and (b) schematic illustration of grain orientations of the Mg coupon.

(1) the surface films on different grains are almost the same in composition and microstructure, but they are not compact or resistant enough to effectively conceal the difference of the substrate grain orientation in corrosion; (2) the surface film varies from grain to grain in compactness and resistance due to different film formation processes on the grains with different electrochemical activities; the differences in surface film on different grains are responsible for the different corrosion performance of the gains. 3.8. Influence of surface film and solution Fig. 10(a) clearly shows that the film formed on basal-oriented grain D is much thinner than on grain E with a prismatic orientation. The difference in surface film thickness for different grains suggests that under the same condition different grains may develop their surface films differently. The growth of a surface film can be affected by solution composition. Hence, the film differences on different grains should vary from solution to solution. Fig. 10(b) shows elemental depth profiles on grains D and E of the Mg coupon after 2 h of immersion in a 1 M NaOH solution. The film on gain E is only slightly thicker than that on grain D, suggesting the basal plane develops a slightly thinner, but perhaps slightly more compact film than the prismatic plane. It should be noted that the films formed on the grains in the NaOH solution (Fig. 10(b)) are considerably thinner than those in the Mg(OH)2 solution (Fig. 10(a)). The most important finding is that the difference in film thickness between grains D and E is remarkably diminished in the NaOH solution compared with that in the Mg(OH)2 solution. If the surface morphology of the Mg coupon after 2 h immersion in the NaOH solution (shown in Fig. 14(a)) is compared with that in the Mg(OH)2 solution, one will find that the former’s grain boundaries and grain texture features are still visible, while those of the latter are barely seen. Fig. 14(b) shows that after two hours of immersion in the NaOH solution, the SKP potential difference between different grains becomes less significant than that in the Mg(OH)2 solution (shown in Fig. 7(b)). The SVP mapping (Fig 14(c)) does not show a significant current density difference over different grains when the sample is immersed in the NaOH solution, indicating that the films formed in the NaOH solution on different grains are resistant enough to prevent the dissolution of the substrate grains. The high resistance of the films effectively conceals the electrochemical activity difference between the substrate grains. Thus, some original grain texture features can be preserved and no new differences are developed or built up between grains in color, corrosion products or corrosion damages. The above results and discussion suggest that while the corrosivity of a solution decreases or the passivity of the metal increases, the surface films on different grains tend to become thinner, more compact, more resistant and more uniform (less different), and their ability to conceal the grain orientation influence improves. In a corrosive solution, both substrate grain orientation and surface film affect Mg corrosion behavior. The substrate grain orientations are primarily responsible for the different corrosion performance. The different surface films on the grains can further enlarge the difference. In a strong passivating or less aggressive solution, although the difference between films on different grains becomes

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G.-L. Song, Z. Xu / Corrosion Science 63 (2012) 100–112

Fig. 14. (a) Corrosion morphologies and (b) SKP of the Mg coupon after 2 h immersion in 1 M NaOH solution; (c) SVP of Mg coupon in 1 M NaOH solution at 0 min.

small, their high corrosion resistance can significantly reduce the activity of the substrate grains, and therefore reduce or eliminate the grain orientation effect on corrosion performance. If a solution contains a stronger passivator, such as chromate, to form a very thin and compact film, but also includes aggressive species, like chloride ions, to enlarge any localized difference in the film and substrate grains, then a different corrosion behavior will be expected. Cl will selectively attack the film formed along dislocations, twins and grain boundaries, because they have atomic arrangements or crystal orientations very different from the bulk grain. Meanwhile, chromates stabilize the surface film to prevent overall or uniform corrosion development. In such a solution, the competition between corrosive and passivating species in defects and bulk grains will lead to different corrosion morphology, filiform damage [27–29]. Although the localized corrosion of the Mg coupon in the 0.01 M NaCl solution follows a corrosion mechanism discussed earlier is similar to the reported filiform of Mg in the chromate and chloride containing solution, the former’s corrosion damage after initiation can spread out due to the penetration of Cl through the less protective surface film on the surface. 4. Conclusions 1. This work verifies the effect of grain orientation on corrosion of Mg; the basal plane is much more corrosion resistant than the prismatic and other crystal planes in a neutral chloride containing solution or an alkaline Mg(OH)2 saturated solution. 2. The non-basal crystal planes are subjected to localized corrosion attack in the NaCl solution, while their corrosion in a saturated Mg(OH)2 solution is relatively uniform. The basal plane is stable enough in both solutions to resist the corrosion attack.

3. The corrosion product film formed in a corroded area is much thicker than in an uncorroded area after immersion in the NaCl solution. In the Mg(OH)2 solution the surface film on the basal plane is significantly thinner than those on the prismatic and other planes. The difference in film resistance on different grains is another factor responsible for the different corrosion behavior of Mg grains with different orientations. The film formed on a non-basal oriented grain is less resistant, while that on the basal plane surface is more protective. 4. With increasing passivity or decreasing corrosivity of the solution, the films on Mg grains become more resistant and the difference in films diminishes, which can more effectively conceal the effect of the gain orientation on corrosion performance of Mg.

Acknowledgements The authors would like to thank Dr. Raja K. Mishra, Mr. Robert C Kubic Jr, Mr. Nicholas P. Irish, Mr. Richard A. Waldo and Mr. James Simpson for their assistance in some experiments.

Appendix A. EIS equivalent circuits Case. 1 When the deviation from steady state is small (see Fig. 11(a) and (b)), the total Faraday current density or steady polarization current density IF can be written as: a

IF ¼ 2Fk  Fk

c

ð11Þ

111

G.-L. Song, Z. Xu / Corrosion Science 63 (2012) 100–112

where F is Faradic constant. Both ka and kc are potential V and film thickness L dependent. During AC impedance measurement, sinusoidal potential dV is applied to the Mg: ix t

dV ¼ Dh

c

a

a

ð13Þ

The dV perturbation can also cause a variation in film growth or dissolution rate L. According to Eq. (4), there is: a

a

@k @k dV þ K L dL @V @L

ð14Þ

    @L @ejxtþU ¼ d L0 ¼ dL0 ejxtþU ðjxÞ ¼ jxdL dL_ ¼ d @t @t

ð16Þ

a

dV @ka

ð17Þ

@L

a   a c a c K L @k dV @k @k @k @k @V dV þ F 2 dIF ¼ F 2   a @V @V @L @L jx  K L @k @L

ð18Þ

Let:

Rt ¼

ZF ¼

1 Ra ¼ Rt þ YF jxRa C a þ 1

ð26Þ

This ZF impedance expression describes a resistance Rt in series connecting with a circuit that has a resistance Ra and a capacitance Ca connected together in parallel. Please note that so far, only Faraday reaction processes are considered in deducing Eq. (26). In fact, due to the AC signal perturbation, the non-Faradic charging and discharging current INF originating from the double layer capacitance Cdl at the interface between the Mg surface and the solution cannot be neglected:

ð27Þ

An equivalent circuit that can comprehensively represent the AC EIS responses should have a double layer capacitance Cdl in parallel connection with the above ZF circuit. In addition, the solution resistance (Rs) between the Mg coupon and reference electrode should also be included. Hence, a complete equivalent circuit should be the one shown in Fig. 12(a).

When the deviation from the original steady state is large enough to remove the surface film in a local area (Fig. 11(c)), then the Faraday current density IF can be expressed as following: c

IF ¼ hvFka þ 2ð1  hÞFK ab  2ð1  hÞFkb

ð28Þ

where v is apparent valence of dissolved Mg ion at the film free area. When dV (Eq. (12)) is applied,

# a c a @kb @k c @kb dV dIF ¼ hvF þ 2ð1  hÞF  2ð1  hÞFkb @V @V @V   a c þ vFka  2Fkb þ 2Fkb dh

ð29Þ

According to Eq. (10), we have:

@IF @V

ð19Þ 1 a

c

Fð2 @k  @k Þ @V @V

s¼

Eq. (23) becomes:

"

Substitution of Eq. (17) into Eq. (13) yields:

YF ¼

ð25Þ

Case. 2

From Eq. (14) and (16), the following equation can be obtained:

jx  K L

>0

ð15Þ

The left side of Eq. (14) can be rewritten:

K L @k @V

HR2t

ð24Þ

INF ¼ jxC dl

As the potential perturbation is so small that the Mg electrode can be approximately regarded as a linear system, the response of any state parameters in such a linear system to a sinusoidal perturbation is also a sinusoidal function with the same frequency but a different phase angle. If the phase angle between the perturbation signal dV and the response dL is U, then

dL ¼ L0 ejxtþU

1

Ca ¼ 

c

@f @k @k @k dIF ¼ 2F dV  F dV þ 2F dL  F dL @V @V @L @L   a c a c @k @k @k @k dV þ F 2 dL   ¼F 2 @V @V @L @L

dL ¼

NsR2t 1 þ N sRt

Ra ¼ 

ð12Þ

where D is amplitude of this sinusoidal potential which is very small (<5 mV) in experiment, x is its frequency, and j is imaginary unit. In response to such a potential perturbation, the variation of IF according to Eq. (11) will be:

dL_ ¼ K L

As Ns < 0, Eq. (23) needs to be further developed. Let:

1 a

K L @k @L

 a c a @k @k @k N ¼ FK L 2  @L @L @V

ð20Þ

# a h i @kb @ka a d dV þ K h ka  kb þ kb dh þ ð1  hÞ @V @V

ð21Þ

ð22Þ

ð31Þ

Thereby,

dh ¼

h i @ka a K h h @k þ ð1  hÞ @Vb @V a

d

jx  K h ðka  kb þ kb Þ

ð32Þ

dV

Substitute Eq. (32) into Eq. (29) and let:

s0 ¼ 

Rt ¼

H¼ ð23Þ

ð30Þ

dh_ can also be written into:

dh_ ¼ jxdh

according to Eq. (6), we have s > 0 and Rt > 0. If the composition, microstructure and resistivity of the surface film are independent of its thickness, an anodic process is normally more significantly inhibited by a thicker or more resistant film than a cathodic reaction. For example, a Mg alloy after anodizing normally has a positively shifted open-circuit potential and much more inhibited anodic current densities than cathodic current densities [37]. Therea c fore, 2 @k < @k , i.e., N < 0. Eq. (18) can be rearranged: @L @L

1 Ns YF ¼ þ Rt jxs þ 1

" dh_ ¼ K h h

1 a

ð33Þ

d

K h ðka  kb þ kb Þ 1

hvF h

@ka @V

a K h h @k @V

þ 2ð1  hÞF

þ ð1 

@kab @V

1 ih

@ka hÞ @Vb

c c @kb @V

ð34Þ

 2ð1  hÞFkb

i

vka  2kab þ 2kcb F

ð35Þ

112

R0 ¼

G.-L. Song, Z. Xu / Corrosion Science 63 (2012) 100–112

H

ð36Þ

s0

then we have:

YF ¼

dIF 1 1 ¼ þ @V Rt jxH þ R0

ð37Þ

It should be kept in mind that ka is an anodic dissolution process at a film free area, which is much faster and more significantly dependent on potential V than the reactions or processes on a film covered surface. That means: a

c

ka  kb ;

ka  kb ; a

@ka @k b > 0;  @V @V

d

ka  kb

ð38Þ c

@kb @ka  >0 @V @V

ð39Þ

Therefore, s0 , Rt and H have positive values. In this case, Eq. (37) is an admittance expression for a circuit consisting of a resistance R0 and an inductance H in a series connection and then connecting to another resistance Rt in parallel. After the double layer capacitance Cdl at the interface between the Mg coupon surface and the solution is considered, a comprehensive admittance expression for this electrode will be:

Y ¼ jxC dl þ

1 1 þ Rt jxH þ R0

ð40Þ

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