Multiscale modelling of the corrosion of metals under atmospheric corrosion

Electrochimica Acta 56 (2011) 1856–1865

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Multiscale modelling of the corrosion of metals under atmospheric corrosion I.S. Cole a,∗ , T.H. Muster a,b , N.S. Azmat a,b , M.S. Venkatraman a,b , A. Cook b a b

CSIRO Materials Science and Engineering, PO Box 56, Highett, Victoria 3190, Australia University of Manchester, Manchester, UK

a r t i c l e

i n f o

Article history: Received 15 July 2010 Received in revised form 10 October 2010 Accepted 11 October 2010 Available online 15 October 2010 Keywords: Multiscale Aerosol Oxide Zinc Corrosion

a b s t r a c t This paper describes a multiscale (from global to micron) model for the prediction of atmospheric corrosion. The model has a modular structure, in which the higher scales set the boundary conditions for the lower scales, and the lower scales alter some of the constants in the upper scales. The model has primarily been designed for Australian conditions and so focuses on corrosion by marine aerosols. The upper level modules look at aerosol production by oceans and surf beaches, salt transport and deposition, and cleaning events such as rain and wind, to provide an estimate of salt retention on surfaces. Separate modules that define surface temperature, surface relative humidity, and wetting and drying of deposited hygroscopic salts, enable the prediction of the (three-hourly) ‘state’ of a surface, where ‘state’ is defined as dry, wet from rain or wet from the wetting of hygroscopic salts. The state model is combined with a damage model to estimate the progression of damage with time. Currently, damage models are either probabilistic (define the occurrence, growth or death of pits as probability functions) or empirical (define a single relationship between mass loss in a given state on the basis of measured data) in nature, but new experimental and modelling research is being undertaken to develop first-principle models of corrosion under established oxide films. Crown Copyright © 2010 Published by Elsevier Ltd. All rights reserved.

1. Introduction Throughout the 1990s and early 2000s, a number of workers looked at developing models of corrosion based on an understanding of the physical processes occurring during the corrosion process (rather than from statistical studies). The early models of Spence and Haynie [1] and Lyon et al. [2] looked at the processes of oxide dissolution and formation, and the electrochemical processes within a droplet on a metal surface, respectively. Graedel [3] made a major advance in the field with the ‘Gildes’ (Gas, interface, liquid, deposition layer, electrodic regime and solid) model, which systematically looked at the chemical interactions across a range of interfaces. However, Graedel applied the model to relatively simple gaseous and interface regimes, and therefore a greater understanding of the external environment was required. Cole et al. [4] developed their holistic model to deal with the complex environments that occur in atmospheric corrosion. The model development was promoted by two main aims: 1. To accurately predict the life of corrodible components in order to guide material selection, maintenance and ensure the safety of structures.

∗ Corresponding author at: CSIRO Materials Science and Engineering, PO Box 56, Highett, Private Bag 33, Clayton Sth MDC, Victoria 3168, Australia. Tel.: +61 3 9252 6000; fax: +61 3 9252 6244. E-mail address: [email protected] (I.S. Cole).

2. To guide the development of more corrosion resistant alloys or protective systems. Thus the model aims to produce two distinct outputs: A. An estimate of corrosion and lifetime of components on fixed (buildings, bridges, etc.) or mobile infrastructure (airplanes) as a function of the geographical position of the infrastructure, the location of the component (and the exposure conditions) on the infrastructure and of local climate (derived from 3 hourly meteorological records). B. Strategies to enhance the design of alloys or passivation systems to prolong the life of components. These strategies will derived from an understanding of the relationship between metal microstructure, oxide development and properties and electrochemical and chemical processes across the metal/oxide/electrolyte interface. In order to accomplish these aims the model defines the processes controlling atmospheric corrosion on a range of scales (see Fig. 1): • ‘Macro’ – the gross meteorological conditions (polar, subtropical, etc.). • ‘Meso’ – regions within 100 km2 of a material surface. • ‘Local’ – the immediate vicinity of a material surface. • ‘Micro’ – the absolute proximity of a material surface.

0013-4686/$ – see front matter. Crown Copyright © 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2010.10.025

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etc.) on the ground. Thus, marine aerosol transport is likely to be favoured in dry climates with low rainfall and low ground coverage, while it will be restricted in humid and high rainfall climates and forest terrain. Aerosols produced by surf tend to be coarse (dry diameter 10–50 ␮m) and those produced by whitecaps are generally smaller (dry diameter 0.5–10 ␮m), and so surf-produced aerosols rapidly deposit (due to gravity), while ocean-produced aerosols may be transported considerable distances. Experimental studies [5,6] support the terrain, climate and distance effects outlined above. The multi-scale model was developed primarily to predict and understand corrosion in Australia where corrosion is primarily associated with marine effects so does not consider industrial pollutants. Clearly these effects must be considered when dealing with locations with significant heavy industry and thus the multi-scale model would need to be upgraded for such locations. 3. Salt deposition and transport

Fig. 1. Definition of the scale domains for the holistic model [4].

• ‘Surface’ – the physical responses of a surface, such as deposition and retention of pollutants, or condensation and evaporation. • ‘Micron’ – interactions within the metal/oxide/electrolyte interfaces. • ‘Electrochemical’ – establishment of anodic and cathodic reactions, potential fields and charge transfer. To this date modules defining the processes from the macroscale to the surface have been completed. This allows the state of a metal surface to be defined (on a 3 h interval) in terms of 4 state conditions: wet from rain, wet from the deliquescence of hygroscopic salts, drying or dry. Given a knowledge of the surface state, the corrosion rate over that time interval is estimated from empirical relationships derived from chamber tests. This allows the prediction of corrosion rate as a function of geographic position and component type and forms the basis of information technology tools for materials selection. This work is outlined in Sections 1–5 of the paper. This approach being based on empirical model cannot guide strategies for the design of new alloys or protective systems. To facilitate such design models that define micron level and electrochemical processes are being developed as outlined in Sections 6–8. 2. Salt production and transport Marine aerosols are produced both by the whitecaps of waves in the open ocean, and by breaking surf [4] and thus initially have the same composition as seawater (this initial composition may be altered by interaction with gases in the atmosphere as detailed in Section 6.1). In the open ocean, whitecap production varies systematically with latitude and season, being at a maximum at low latitudes in July and at high latitudes in December, and low all year round in tropical seas. Thus, tropical seas produce a relatively low volume of marine aerosols, resulting in decreased marine corrosion in near-equatorial regions relative to marine corrosion in low or high latitudes. Experimental studies support this observation [5,6]. Surf aerosol production depends only on local wind speed and fetch [7]. Aerosol residence times and thus transport distances [4] are controlled by convection, gravity and aerosol scavenging by cloud drops, raindrops and physical objects (trees, buildings,

Marine aerosol deposition is primarily controlled by wind turbulence, and its deposition onto an object is a function of turbulence intensity, wind speed, object shape and, to a lesser extent, aerosol size [8]. For marine aerosols of 0.1–10 ␮m, deposition efficiency (as a function of size) is relatively constant. Deposition efficiency increases rapidly for aerosol sizes above 20 ␮m, and for 100 ␮m aerosols it is roughly four times that of 20 ␮m aerosols. The size and shape of an object is also important, for example the deposition on an exposed plate (at 45◦ ) is likely to be more than 1.5 times that on an equivalently exposed salt candle. For complex forms such as buildings, deposition efficiency will vary across a structure, and will be highest at the edges of the structure where turbulence is highest. 3.1. Modes of deposition When an aerosol first breaks free from the whitecap of a wave, it has a seawater composition before it gradually equilibrates (and thus decreases in size). Thus, marine aerosols may take four forms [9] depending on time of flight and ambient relative humidity (RH), viz.: non-equilibrium near-ocean aerosol (size range 6–300 ␮m), wet aerosol (3–150 ␮m), partially wet aerosol (1–60 ␮m) and dry aerosol (<1–20 ␮m). When these aerosols are deposited onto a metal surface, a number of characteristic surface ‘forms’ result from the surface–aerosol reaction [9], which will differ in the extent of retained salts, the degree of surface alteration and in the formation of corrosion nodules. For example, when a wet aerosol impacts on an aluminium surface (limited initial reactivity), a cluster of deposited salt crystals with compositions of either NaCl, MgCl2 or CaSO4 will form, indicating that the original seawater solution has segregated. In contrast, the same aerosol impacting on a galvanized steel surface will produce a strong oxide growth on the surface (predominantly simonkolleite and gordaite), that will retain an NaCl crystal layer. 3.2. Geographic Information System (GIS) for airborne salinity A GIS system has been developed [10] to define the shoreline concentration of both surf- and ocean-produced aerosol, and then to estimate the transport of this aerosol to a given point inland. An Australia-wide map of airborne salinity has been derived and is presented in Fig. 2. 4. Wetting and surface temperature As stated above the multi-scale model predicts whether the surface is wet from rain, wet from the deliquescence of hygroscopic salts, drying or dry. Wetting from rain is assumed to occur when-

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Fig. 3. Map of zinc corrosion rates in Australia (g/m2 year). Fig. 2. Australia-wide map of airborne salinity for [10].

ever rain happens at the given locality while deliquescence occurs when the RH at the metal surface exceeds the deliquescent RH for a contaminating salt (e.g. 75% for NaCl at a temperature of 20 ◦ C). After rain wetting or deliquescence the surface will take some time to dry depending on local conditions. The deliquence and drying rates depend on both the surface RH and the surface temperature. To estimate the surface temperature of an exposed surface, a mathematical model that considers undercooling to the night sky, and daytime solar heating and convection effects has been derived [11], and validated experimentally [12]. Another model [13] predicts the RH at a metal surface, and thus when hygroscopic salts (NaCl, MgCl2 ) on the surface will wet. The evaporation of such moisture films has also been modelled [11] and validated experimentally [14], so a complete picture of moisture cycles has been developed. It is apparent that evaporation rates on a metal surface are slowed by the cooling effect of the evaporative cycle, so that evaporation times may be from minutes to several hours. The role of wind and rain in removing deposited salts from a surface has also been modelled and validated experimentally [15,16], and it is apparent that while rain (if sufficiently intense) is an effective mechanism for removing deposited salts, wind is not. Thus the model predicts the retention of salts, the surface RH and temperature and from these factors the state of the surface. A data stream of states is thus developed for a year with a new state every 3 h. Similarly a data stream of the salinity level over a year is also developed.

A map of the estimated rates of corrosion of exposed zinc in Australia is presented in Fig. 3. Fig. 4 shows the model predictions compared with yearly measured corrosion rates of openly exposed zinc plates at 40 sites around Australia. Given the large number of variables in both the model and measured atmospheric corrosion, the correlation (R2 = 0.82) is thought to be encouraging. The model has been extended from predicting corrosion rate of exposed metal (as in Fig. 3) to predicting corrosion rate of component on or within a face of a building. To do so it estimates the microclimate conditions on different parts of a dwelling and how these conditions effected the states or retained salinity levels. For example components under eaves in a dwelling are sheltered from rain and still be exposed to winds that can deposit salts so that cleaning of salts by rain does not occur allowing significant build up of retained salts and promoting formation of moisture films by the wetting of such salts. 6. Refinements to state model The state model outlined above can thus met one of our prime aims, the prediction of the life of components in order to guide materials selection and maintenance, however because the

5. Corrosion models For each state outlined above (and depending on retained salt level), a corrosion rate is determined from dose function tests in accelerated test chambers. For example the corrosion rate of a surface wetted by hygroscopic salts is estimated as. Mass loss(over 3 h) =  + ˇ∗ S where mass loss is in g/m2 , S is the salinity level (mg/m2 )on the surface, , ˇ and are constants having values of 8.3 × 10−4 , 11.3 × 10−4 and 0.5. Thus from the data stream of states and restrained salts a data stream of corrosion rates is estimated and then annual corrosion can be determined by summing the three-hourly corrosion rates.

Fig. 4. Comparison of measured and predicted corrosion rates for openly exposed zinc panels.

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Table 1 Chemistry of droplets and number of tests. Base solution

Concentration

HNO3 pH = 1

0.1 M HCl pH = 1

H2 SO4 pH = 1

CF3 SO3 H pH = 1

No addition

Natural seawater NaCl NaCl NaCl MgCl2 MgCl2 MgCl2

20%/3.42 M 3.5%/0.6 M 2.4%/0.42 M 1.7 M 0.3 M 0.05 M

5 5 5 5 5 5 5

5 5 5 5 5 5 5

5 5 5 5 5 5 5

5 5 5 5 5 5 5

5 5 5 5 5 5 5

corrosion damage module is derived from empirical data it does not take into account microstructural features or the development of oxide layers and so cannot met the second aim: guiding the development of more corrosion resistant alloys or protective systems. Further the model assumes that the chemistry of marine aerosols is unaffected by transport from the source to the corroding object. Since the development of the original model an appreciation of how marine aerosol react with gases in the atmosphere (changing their composition significantly from the point of source to the point of deposition) has arisen [16]. As stated in Section 1, strategies for design of corrosion resistant systems should be based on a fundamental understanding of the relationship between metal microstructure, oxide development and properties and electrochemical and chemical processes across the metal/oxide/electrolyte interface. To this end studies are being undertaken to define: • The physical/chemical and electrochemical mechanisms that occur under a droplet including development of anodes and cathodes, local or general metal attack and oxide development. • Models of the physical/chemical and electrochemical mechanisms including the particular electrochemistry and solution chemistry that occurs under a droplet and how development of porous oxides may regulate diffusional and electrochemical processes controlling droplet/metal interactions. Secondly to redress the limitation discussion above on aerosol chemistry studies are being undertaken on: • The effect of acidified marine aerosols on atmospheric corrosion. Once these studies are complete the empirical damage model in the current multi-scale model will be replaced by series of processbased models that define the chemistry and electrochemistry that occur under a droplet as a function of metal microstructure and oxide development and so can be used to estimate the effect of changes in alloy or passivation design on component life.

represents the total salt concentration in seawater, and 2.4% represents the NaCl concentration in seawater, while 0.05 M is the amount of MgCl2 in seawater, and the other MgCl2 concentrations match the Cl concentrations in the NaCl solutions. This matrix of tests was performed on 0.1 and 0.5 ␮L droplets, using the following experimental method. High-purity (99.9%) zinc mini-plates (20 mm × 20 mm) were polished using 9, 6, 3 and 1 micron diamond particles, then cleaned in ethanol and distilled water prior to the application of droplets and exposure for 5 h in a high humidity (90%) atmosphere. At the end of exposure, the droplets were allowed to evaporate in laboratory conditions, before the plates were etched in a 20% chromium trioxide solution. The volume loss of the zinc plates was determined using optical profilometry. While full results will be published in a later paper, Figs. 5 and 6 present some interesting comparisons. Fig. 5 shows the variation in zinc volume loss after exposure to 0.5 ␮L drops of either natural seawater or seawater acidified to a pH of 1 using the four different acids. Each result is the average of the five replicates. Interestingly, compared to natural seawater, acidification with HCl and H2 SO4 significantly and moderately increased volume loss, respectively, while acidification with HNO3 and CF3 SO3 H (triflic or triflouromethanesulfonic acid) led to lower volume losses. Fig. 6 shows the volume losses after exposure to 0.5 ␮L drops of NaCl and MgCl2 solutions (not acidified) with varying Cl concentration. Interestingly, volume loss decreased with increased salinity in the NaCl solutions, while it reached a maximum at a Cl concentration of 0.6 M in the MgCl2 solution. The volume losses at the higher salinity concentrations of both solutions are comparable. We are currently investigating the factors that cause these variations, such as the development of oxides and passivating layers, and the effect of anion concentration on oxygen solubility, and thus the rate of cathodic reduction.

160000

6.1. Effect of changes in the chemistry of marine aerosols on atmospheric corrosion

120000

Volume loss / μm3

As a marine aerosol is transported from its source to a corroding surface, it will react with the atmosphere and its chemistry may change [16]. Of particular importance is the absorption of acids (e.g. H2 SO4 , HCl, HNO3 ) or acid precursors (e.g. SO2 ) into moist aerosols, which may shift the pH value of an aerosol from 5 to 1, depending on conditions and aerosol size [16]. It is important to understand these processes not only to ensure that correct estimates of corrosion rates and thus component life are made but also to ensure that corrosion resistant materials are designed against the correct environments. In order to assess the impact of acidified marine aerosol on the corrosion of zinc, a matrix of tests was undertaken in which the chemistry of droplets was changed (see Table 1). The solution concentration of 20% represents the near-saturation level of NaCl, 3.5%

140000

100000 80000 60000 40000 20000 0 natural

HCl

H2SO4

HNO3

CF3SO3H

Acids/pH Fig. 5. Volume loss of zinc after exposure to 0.5 ␮L drops of acidified natural seawater.

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NaCl MgCl2

350000

Volume loss / μm3

300000 250000 200000 150000 100000 50000 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-

[Cl ] / mol dm-3 Fig. 6. Effect of chloride ion concentration (NaCl and MgCl2 ) on volume loss of zinc. Note where error bars are not visible they are smaller than the data point.

The data indicates that acidification can lead to significant enhancement in the corrosion of zinc under droplets. Thus the current multi-scale models estimate of components life may not be accurate in industrial coastal environments. Further in developing corrosion resistant materials for these environments models and tests regimes need to incorporate such combined acid/saline effects. 6.2. Physical/chemical and electrochemical mechanisms controlling droplet/metal interactions In order to model the electrochemical and chemical properties (at the level of detail required to assist design) two critical issues must be addressed: • What are the kinetics of the anode and cathode processes and therefore what controls the positions of anodes or cathodes. • What is the form of attack on the metal (local or general attack) and what factors control the mode and rate of this attack. 6.2.1. Coupled micro-electrode array experiments Recent work [17] in our laboratories has concentrated on the use of coupled micro-electrode arrays to monitor the kinetics of anodic and cathodic processes under small droplets. As seen in the experimental setup shown schematically in Fig. 7, a fine droplet is placed onto a closely packed array of small cross-section wires of the metal being studied, whereby the array of wire ‘microelectrodes’ replicates a planar surface. Initial studies using this

Fig. 7. Experimental setup for monitoring the electrochemical kinetics of droplets using micro-electrode arrays.

Fig. 8. Position of anodes and cathodes under a 5 ml droplet. Each square represents one electrode. The squares with the cross in them indicate that these electrodes have net anodic current whereas those of just grey scale are cathodic, with the shade of darkness represents the magnitude of the cathodic current. The droplet will occupy approximately 48 squares and is centered on the innermost cross.

approach have enabled the mechanisms and kinetics of zinc corrosion to be studied under saline droplets of <10 ␮L and down to 0.5 ␮L. Fig. 8 shows whether an electrode behaved as a net cathode or a net anode over the course of the test in the case of a 5 ml droplet. It is evident that electrodes with a net anodic current occur at the centre of the droplet and those with a net cathodic current at the edge. The method has also shown that it may be possible to gather enough systematic data to enable the prediction of corrosion, if the state of the electrolyte on the surface is known. The multi-electrode approach does, however, have its own limitations: at present it is unable to characterize the corrosion processes under the very small aerosols that commonly contaminate structures, and it is not known how the build up of surface oxides will influence the fundamental corrosion processes under droplets. Further work on validating the output of the micro-electrode technique against damage measured on real surfaces will reveal the true power of this approach. The results indicate that for large drops the position of anodes and cathodes is highly influenced by droplet geometry with cathodes occurring preferentially at the drop edge. This implies that cathodic reaction will be influenced by the rate of diffusion from the air through the drop to the metal surface 6.2.2. Pitting of zinc As highlight above to develop useful model of corrosion of zinc under droplets it is vital to know what form metal attack takes. Although it is generally considered that zinc suffers from general corrosion a scanning electron microscopic study [25] of focused ion beam sections into oxide layers that develop under saline droplets on zinc for short durations (15 min to 6 h) indicated that localized attack of the zinc metal may occur under an oxide film. Further analysis of zinc specimens in field for a year also indicated that under some conditions local attack was observed [27]. To define the conditions under which pits will propagate in zinc some experimentation using one dimensional artificial pit electrodes were undertaken. The artificial pit electrode was fabricated by mounting a 50 ␮m zinc wire (purity 99.95%) on end in a rod of Araldite resin and polishing one end flat. These were mounted in the short arm of a j-shaped insulating tube with the electrical connection threaded through the other arm. As such the electrode

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3.0 1.0

i Eapp

2.5

-2

j / A cm

1.5

0.0

1.0 -0.5

Eapp vs. SCE / V

0.5

2.0

0.5

A

-1.0

0.0 0

700

1400

2100

Time / s

j / A cm

i Eapp

0.0

0.50 -0.5 0.25

Eapp vs. SCE/ V

-2

0.75

-1.0 0.00

B 1200

1500

1800

2100

Time / s Fig. 9. (A) Dissolution kinetics of a 50 ␮m diameter Zn artificial pit determined via a step potential technique in a bulk solution 0.01 mol dm−3 NaCl; (B) Enlarged view of the region in which the current becomes potential dependent. The blue line in both plots is a non-linear fit of the current-density data in the diffusion controlled region, i.e. the path the current would take under purely diffusion controlled conditions.

faced upwards in all tests; the test solution was in all cases naturally aerated 0.01 mol dm−3 NaCl. All tests were performed with an Ivium CompaqStat under the control of IviumSoft versioin1.204. A platinum mesh served as counter electrode and an SCE was used as the reference electrode; all potentials quoted in the remainder of the text in this section refer to this scale. The local chemistry within artificial pits during propagation at various potentials prior to repassivation was determined via a method similar to that used by Cook and Newman [28] to determine stability conditions in pits in pure aluminium; effectively a step-potential version of the technique employed by Ernst and Newman [29] to establish the critical conditions for pit growth in type 304 stainless steel. In short, the potential was initially stepped to 1 V vs. SCE (well above the pitting potential) so that stable pitting occurred; coalescence of these pits leads to general dissolution of the wire and formation of a one-dimensional pit cavity. After 1000 s the electrode was subjected to a series of stepwise reductions in applied potential until repassivation occurred at ca. −1 V vs. SCE. Prior work via standard potential-dynamic scans had indicated that Ecorr in 0.01 M NaCl was 1.1 V vs. SCE and thus the reversible potential of zinc (Erev ) should be lower than Ecorr and thus the pit repassivation potential is greater than Erev . The duration to which the electrode was subjected to each of the various applied potentials and the response of the current density are shown in Fig. 9. The initial peak in current density of ca. 15 mA cm−2 observed on stepping the potential to 1 V is omitted from the figure for the sake of clarity. The blue line represents the path the current density would follow if the potential was not stepped below the value at which diffusion controlled conditions

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may be maintained. In brief, at potentials between 1 and 0 V vs. SCE dissolution is potential independent (diffusion controlled) and occurs across a surface salt-layer (ZnCl2 or ZnOHCl). Upon stepping from zero volts through to −0.3 V vs. SCE dissolution becomes potential dependent (Ohmic/activation controlled) and occurs in the salt-free state. This potential dependence persists until the pit repassivates at ca. −1 V vs. SCE. The degree of saturation in salt required for pit growth may be estimated by dividing the current density observed at 2080 s just prior to pit repassivation (i.e. the instant at which the potential is stepped from −0.95 to −1 V vs. SCE,) by that which would be observed at the same time under purely diffusion controlled conditions (i.e. the same time on the blue line). This calculation suggests pits in Zn can propagate with a salt solution as low as 5% of saturation in metal–salt solution adjacent to their corroding surface. In addition an estimate of the value of the critical quantity in pit growth, as established by Galvele [26], i.e. the product of the pit current density and pit depth, ix, may also be obtained from these data using the charge density associated with pit growth from 0 to 2080 s in conjunction with Faraday’s second law. Assuming a current efficiency of 1 an ix value of 6 × 10−4 A cm−1 is obtained. While these results are very preliminary and will be verified with further experimentation they do indicate that a relatively low degree of saturation is required to maintain pitting in zinc (possibly as low as 5%) when compared with pits in other metals such as 300 series stainless steels, where pit stability may only be achieved above ca. 70% of saturation in metal–salt solution [30]. Thus this result together with the previous observation on pitting in zinc oxides [25,27] indicate that local attack of zinc may occur below oxide layers and as it could dramatically affect both the rate of corrosion and so should be accounted for in the development of damage models. 6.3. Models of the physical/chemical and electrochemical mechanisms controlling droplet/metal interactions As indicated previously in order to assist material design it is desirable to develop a process based modelling framework that can incorporate both microstructural and oxide effects into corrosion under a droplet. For simplicity this modelling effort has been broken into 2 components: • Development of a model of corrosion under a droplet. This model will concentrate on how droplet geometry may affect the position and rate of anodic and cathodic reactions. • Development of a model of corrosion of a metal covered with a porous oxide. This model will concentrate on how the nature of the porous oxide regulates both diffusional effects and the location and rate of cathodic reactions. Although the models will be developed separately the intention is to link the models and so have a model capable of defining the role of porous oxides in controlling corrosion under droplets. Such a model has the potential to guide intervention strategies to enhance passivation of metal surfaces. 6.3.1. Droplet model The pioneering work of Evans [18] revealed that a droplet can establish zones of differing oxygen concentration, and thus zones that favour either cathodic or anodic activity. However, despite some interesting refinements to Evans’ original work by Lyon et al. [2], there have been no rigorous studies defining the establishment of anodes and cathodes and associated potential fields under droplets of varying size. This is of particular importance in atmospheric corrosion, which is promoted by aerosol (size range 1–150 ␮m) or raindrop (0.5–3 mm) deposition, as the balance of

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oxygen diffusion and electrochemical activity (and thus the Evans mechanisms) may be expected to vary across these droplet size ranges. A model has been developed that assumes that when a hemispherical aerosol droplet deposits onto a bare metal surface devoid of oxide and/or other films, oxygen diffuses through the droplet from the atmosphere to the metal surface, and is reduced. The metal undergoes anodic dissolution. The species that are involved in the system are Mz+ , OH− , O2 , Na+ and Cl− . The model also assumes isothermal conditions with no convection or gas generation, dilute solution theory, and that anodic and cathodic reactions can be described by the Butler–Volmer equation, while no heterogeneous (including precipitation) or homogeneous chemical reactions occur in the film. For a full description of the governing equations, see Venkatraman et al. [19]. The model predicts that initially there is no separation of anodic and cathodic regions. Once the oxygen gradients are established, the regions where there is less depletion of oxygen due to sufficient replacement by diffusion would become cathodic, and vice versa. The local rate and extent of the reactions would depend on local concentrations and overpotential, and anode–cathode separation would evolve as a result. The results of a simulation of zinc corrosion under a droplet is shown in Fig. 10, in which the arrows represent the current density vectors and the contours represent the concentration of Zn2+ ions (non-dimensionalized against initial concentration of 10−6 M). According to the simulation, the highest concentration of zinc ions is near the metal surface, with an accumulation towards the cathodic region. This is attributed to the lack of any scavenging mechanism, such as the precipitation of corrosion products (i.e. oxides, hydroxides, chloro-hydroxides, sulfates and carbonates). Fig. 10 also shows how the current within the droplet enters

Fig. 10. (CZn2+ /C 0 2+ ) of zinc ions and arrow plot of current density vectors showing Zn separation of metal surface into anodic and cathodic regions over time.

from the anodic region and terminates in the cathodic region, thus indicating separation. Fig. 11 shows the oxide concentration in the droplet as a function of kR/D, where k is the cathodic reaction rate constant, R is the radius of the droplet, and D is the diffusion coefficient of dissolved oxygen. If the oxygen diffusion rate is greater than or equal to consumption, the insignificant variation in oxygen concentration would not favour the establishment of cathodic zones. As drop size decreases,

Fig. 11. Oxygen concentration in the droplet as a function of kR/D, where k is the cathodic reaction rate constant, R is the radius of the droplet, and D is the diffusion coefficient of dissolved oxygen.

Porosity (ε)

1 0.8 0.6 0.4 0.2 0.1 0.05 0.01

Droplet diameter (D) 1␮

100 ␮

1000 ␮ (1 mm)

3 mm

2.15 × 10−5 3.00 × 10−5 4.60 × 10−5 8.49 × 10−5 2.40 × 10−4 6.79 × 10−4 1.92 × 10−3 2.14 × 10−2

2.15 × 10−3 3.00 × 10−3 4.60 × 10−3 8.49 × 10−3 2.40 × 10−2 6.79 × 10−2 1.92 × 10−1 2.14

2.15 × 10−2 3.00 × 10−2 4.60 × 10−2 8.49 × 10−2 2.40 × 10−1 6.79 × 10−1 1.92 21.4

6.45 × 10−2 9 × 10−2 1.38 × 10−1 2.55 × 10−1 7.2 × 10−1 2.04 5.76 64.2

the oxygen diffusion rate will increase, while the consumption rate will remain approximately the same. In contrast, as the consumption rate increases above the diffusion rate, sharp gradients in concentration will be established, and cathodic zones will form at the edge of a drop. Table 2 presents values of kR/D as a function of drop diameter and oxide porosity (ε), under the following assumptions: • The annual corrosion rate is with a time of wetness of 33%, and thus an effective corrosion rate of 21 g/m2 /year when the surface is wet. • The diffusivity of oxygen is 1.97 × 10−9 m2 /s at 20 ◦ C. 7 g/m2 /year

Therefore, significant cathodes will occur if porosity is <0.2 for large raindrops or 0.1 for small drops, and 0.01 for 100 ␮m aerosol droplets. The value of ε will vary according to the oxide structure, but according to Aurian–Blajeni and Tomkiewicz [20], a typical value for zinc oxide is 0.276. Thus, this model predicts that significant oxygen differentials will only occur when oxide is covered by large drops. The droplet model can define the potentials, cathodic and anodic sites, ion and oxygen concentrations that are established in the solution and on the metal surface as a function of drop size. This current version can be extended to included microstructural effects. This will permit a determination of whether geometric or microstructural effects (intermetallics, grain boundaries) control electrochemical cell development. 6.3.2. Porous model The droplet model described above treats oxides as homogeneous films and does not take into consideration their structure. In fact the oxides that develop on metals and particularly on zinc may have in homogeneous and porous structures [25]. Such structures may regulate diffusion between the metal surface and the liquid phase (limiting the rate of cathodic and anodic reactions) and if the oxide is a semi-conductor (such as zinc oxide) pores in, and the surface of, such an oxide may act as sites for the cathodic reaction. A model that addresses the effects of a porous oxide layer on the corrosion of a metallic surface has been developed [21], based on the macro-homogeneous theory of porous electrodes and the dilute solution theory with a Nernst–Planck formalism. The porous electrode theory has been successfully applied to battery electrodes [22,23] and membranes to predict the concentration of ionic species and current distributions, but never in the context of corrosion. The theory assumes a superposition of two macroscopic continua – a solid matrix and a fluid electrolyte – and develops equations based on the interfacial reactions between the matrix and the fluid, and the conservation of species and electric charge. In our model, we consider that both the metal surface and the porous oxide are potential sites for cathodic oxygen-reduction reaction. Such a situation arises with zinc, since zinc oxide is a semiconductor and the work functions of both zinc and zinc oxide are similar [24].

Non-dimensional concentrtion of zinc ions in the oxide

Table 2 Values of kR/D as a function of porosity and drop diameter.

Non-dimensional concentrtion of oxygen in the oxide

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Specific Internal Surface Area = 5000 m -1 1.0

(a) τ=0 τ=0.003 τ=0.007 τ=0.02 τ=0.03

0.5

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Non-dimensional oxide length

Specific Internal Surface Area = 5000 m -1 10000

(b) τ=0 τ=0.003 τ=0.007 τ=0.02 τ=0.03

1000

100

10

1 0.0

0.2

0.4

0.6

0.8

1.0

Non-dimensional oxide length

Fig. 12. Variation in non-dimensional concentration of oxygen and zinc in the porous oxide as a function of non-dimensional oxide length for various nondimensional times.

Thus, oxygen-reduction reaction, which needs a supply of electrons, can be supported on zinc oxide. The model computes the preferred location for the cathodic reaction, at the zinc metal surface or on the zinc oxide pore boundaries, and predicts the corrosion potential and corrosion current density as a function of time. Fig. 12 shows the associated variation of non-dimensional oxygen and zinc ion concentration (base level zinc ion and oxygen concentrations being taken as 1 ␮M and 240 ␮M respectively) where normalized time is given by:  = tD/L2 where t is time (seconds), and L is the oxide thickness. Measurements by Cole et al. [25] indicate that under a saline drop, a porous oxide thickness of around 1 ␮m will develop after 15–30 min, thus  = 500 t and the change in ion concentration indicated in Fig. 11 will be very rapid for a zinc system. These calculations are based on a specific internal surface area of 5000 m−1 as estimated by Volkman [31]. Apart from the electrocatalytic activity (i.e. the exchange current density of ORR on the oxide surface), the specific internal surface area a of the porous corrosion product also influences the rate of oxygen consumption and further oxide formation. Lowering this specific internal surface areas will reduce the rate of change in

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ion concentrations, though they will still change at a fast rate for a highly active system like zinc. The model indicates that cathodic activity may take place across the porous oxide which will in turn drive an initial high rate of metal dissolution at the metal surface and consume oxygen across the porous oxide. Thus, the oxygen diffusion finally is pushed to a state where the oxygen concentration along the porous oxide tends to zero and the supply of oxygen at the mouth of the oxide largely determines the corrosion rate. At the same time zinc ion concentration will build up at the pore bottom restricting anodic activity. In its present form, the model does not include precipitation, however it identifies where cathodic reactions occur (on the metal surface or on the oxide). It would be expected that local variations in pH would be significantly influenced by the cathodic position, so that if oxygen reduction occurred on pore walls, higher pH values would be established at that point, which would promote precipitation. Therefore, the model can link microstructure (by accounting for the variable electrochemical activity on the surface) with oxide formation, and thus electrochemical activity and oxide growth, and so has the potential to simulate how corrosion rates can change with time. When linked to the droplet model the combination of models will have the ability to determine not only the corrosion rate under droplets but how microstructure and oxide development may alter the corrosion rate. 7. Discussion of finer scale experiments and models The experimental program has highlighted a number of interesting phenomena. From the acidified marine aerosol tests, it is apparent that acidified aerosols may lead to changes in corrosion rate, but this is highly dependent on the acidifying species, and that an increase in chloride concentration from moderate to high leads to a decrease in corrosion rate. It has often been reported (including by the current authors [27]) that in atmospheric corrosion, the corrosion rate increases as a function of salt dosage (in chamber tests) or salt deposition (in field experiments). These results are not necessarily inconsistent, as the salt dosage/deposition will determine how many salt crystals or droplets are on a metal surface, with each individual salt crystal or droplet then expected to exhibit the salinity dependence observed in this paper during any chamber test or field exposure diurnal cycle. Assume that droplets of seawater are deposited onto a surface. The number of droplets on the surface can be determined by the total dosage (typically in g/m2 ) of salt applied, but each individual drop will have the same chloride concentration (i.e. that of seawater -approx. 0.6 M) regardless of the dosage. In the evaporation phase, the seawater concentrations of droplets will increase (towards 3.4 M). Similarly, if salt is deposited dry and then the humidity is raised, the concentration of each droplet will be determined by the rate of deliquescence and will be independent of the total dosage of salt applied,which will determine the number of salt crystals. The multi-electrode studies are reported more fully in Muster et al. [17]. They demonstrated that separate anodes and cathodes are established, with a tendency for the cathodes to occur at the drop edge, which is consistent with the droplet model for large drops presented here. The artificial pit experiments indicated that pits in zinc may propagate until quite a low salt concentration, whereas the porous electrode model indicated that very large variations in ion concentration may be established within the pores of an oxide. While these effects need to be investigated further, it does appear that the critical salt concentration to maintain pitting could develop at the bottom of a pore in zinc and which is consistent with the observation of localized attack on zinc below an oxide layer [25].

8. Integration of model refinements into holistic framework To develop a fully integrated model that ranges from the micron to the macro-scale two issues must be resolved. These are how to integrate the finer electrochemical/micron-scale modules together and secondly how to integrate these finer models into the overall holistic model. The combined fine scale model will be able to predict corrosion rates (and oxide formation) under a single droplet but the Holistic model requires information on corrosion rate over a whole metal surface which will undergo cycles of multiple droplet formation and evaporation in response to climatic cycle. The following schema is proposed to integrate data on corrosion rate under a single drop into the full holistic model (while maintaining a record of conditions at each part of an exposed surface): 1. The component surface will be divided into a fine grid, and a series of attributes (oxide type, thickness, porosity, deposited salts, summed corrosion) will be defined for each grid unit. 2. The holistic model will then be run with deposition phenomena (aerosol and rain) randomized onto the grid, so that each grid unit is either covered or partially covered by an aerosol or raindrop, or free of such forms. 3. The results of the combined electrochemical model will be parameterized to define changes in oxide properties and thickness, and corrosion rate, as a function of droplet chemistry, pre-existing oxide and over a period over 3 h. The parameterized rules can then be applied to each grid unit and a new set of characteristics determined. 4. At each time is then rerun for the next 3 h interval followed by the application of the parameterized results from the combined electrochemical model. This procedure is repeated for an extended period (up to 10 years) or until the corrosion rate and oxide form stabilize. Returning to the development of a combined fine scale model, the following stages are proposed: 1. The present droplet and porous electrode model will be integrated. The systems features a system of PDE’s (current solved using COMSOL) with variable boundary conditions (derived from the droplet model). In addition the current system will be extended to include hydrolysis of metal ions, acid base equilibrium. 2. This stage of the model will incorporate oxide growth and precipitation and will use a finite element mesh or boundary element mesh framework. The percolation of the electrolyte through the porous oxide and passivation will be addressed. The model will allow a moving oxide boundary. Thus at the completion of the integration the fine scale models will be able to stimulate oxide growth and changes in oxide properties over time and how these changes are driven by and in turn affect both anodic and cathodic activity and pore and solution chemistry. The fine scale model will thus be able to model corrosion rates under a single droplet. This approach assumes that corrosion progresses in a uniform way into a metal surface. However, the focused ion beam (FIB) electron microscope studies of Cole et al. [25] indicates that localized attack may occur under an oxide film, while the micro-electrode studies reported in this paper indicate that pits may propagate in zinc at relatively low salt concentrations. Thus, it may be necessary to develop a module that defines local attack under an oxide film (possibly based on a modified Galvele [26] approach), and integrate this into the combined electrochemical model.

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The revised holistic model should also be able to account for the effect of acidified marine aerosols. The combined electrochemical model should be able to account for the effect of variations in droplet chemistry on oxide growth and electrochemical activity. It will, however, need to incorporate oxide dissolution due to the initial reactions between an oxide and acidified drops. For the holistic model, consideration will also need to be given to the decision on how to incorporate the damage forms that result from acidic dissolution into the ‘attributes’ that define the state of the oxide. For example, acidic dissolution could be considered a general phenomenon that changes oxide porosity. 9. Conclusions A multiscale model for the prediction of the life of components subject to atmospheric corrosion has been presented. This model has two main aims, firstly to predict corrosion rate of metal components to enable appropriate material selection and assist maintenance programs and secondly to determine how microstructure and oxide development influence corrosion rates in order to develop strategies for the development of corrosion resistant materials. The model contains two parts. One predicts the chemical and physical conditions that are likely to occur on a metal surface, and in particular, if the surface is dry, drying, wet from rain or wet from the wetting of hygroscopic salts, as well as the level of retained salts on the surface. The model has been combined with empirical dose functions for each surface state and applied to predict the corrosion rates of zinc plates around Australia, with reasonably accurate results when compared to measured corrosion. By providing accurate estimates of corrosion rate this part of the model can and is being used to guide materials selection fulfilling the models first aim. However as it estimates the corrosion rate in each state using an empirical relationship it cannot assist in the design of corrosion resistant oxides or passivation systems. Thus to replace the empirical dose functions, research is being carried out to develop the process-based models that define the electrochemical and chemical processes that occur on a metal surface under a saline drop as a function of metal microstructure and oxide development. To date, two models have been developed—the droplet model and the porous oxide model. A means of integrating these models into the overall multiscale model is proposed. Initial results from these models indicate that: • For a large drop, oxygen depletion leads to preferential cathodic activity at the droplet edge, while for a small drop, oxygen concentration remains relatively uniform, and therefore cathodic activity is not controlled by droplet geometry.

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• The formation of a porous oxide may dramatically influence the electrochemical activity on a metal surface as the oxide can in some cases support cathodic activity while concentration gradients of both metal ions and oxygen will develop that can in turn limit both cathodic and anodic activity. References [1] J.W. Spence, F.H. Haynie (Eds.), Corrosion Testing and Evaluation: Silver Anniversary Volume, ASTM STP 1000, ASTM, Philadelphia, 1990, p. 208. [2] S.B. Lyon, C.W. Wong, P. Ajiboye, in: W.W. Kirk, H.H. Lawson (Eds.), Atmospheric Corrosion, ASTM STP 1239, ASTM, Philadelphia, 1995. [3] T.E. Graedel, Corros. Sci. 38 (12) (1996) 2153. [4] I.S. Cole, D.A. Paterson, W.D. Ganther, Corros. Eng. Sci. Technol. 38 (2) (2003) 129. [5] I.S. Cole, W.D. Ganther, D.A. Paterson, G.A. King, S.A. Furman, D. Lau, Corros. Eng. Sci. Technol. 38 (4) (2003) 259. [6] I.S. Cole, D.A. Paterson, W.D. Ganther, B. Hinton, G. McAdam, M. McGechie, R. Jeffery, L. Chotimongkol, C. Bhamornsut, N.V. Hue, S. Purwadaria, Corros. Eng. Sci. Technol. 38 (4) (2003) 267. [7] W.A. McKay, J.A. Garland, D. Livesley, C.M. Halliwell, M.I. Walker, Atmos. Environ. 28 (1994) 299. [8] I.S. Cole, D.A. Paterson, Corros. Eng. Sci. Technol. 39 (2) (2004) 125. [9] I.S. Cole, D. Lau, D.A. Paterson, Corros. Eng. Sci. Technol. 39 (3) (2004) 209. [10] I.S. Cole, W.Y. Chan, G.S. Trinidad, D.A. Paterson, Corros. Eng. Sci. Technol. 39 (1) (2004) 89. [11] I.S. Cole, D.A. Paterson, Corros. Eng. Sci. Technol. 41 (1) (2006) 67. [12] I.S. Cole, W.D. Ganther, Corros. Eng. Sci. Technol. 40 (4) (2005) 328. [13] I.S. Cole, W.D. Ganther, J.D. Sinclair, D. Lau, D.A. Paterson, J. Electrochem. Soc. 151 (12) (2004) B627. [14] I.S. Cole, W.D. Ganther, Corros. Eng. Sci. Technol. 41 (2) (2006) 161. [15] T.H. Muster, I.S. Cole, J. Electrochem. Soc. 152 (3) (2005) B125. [16] I.S. Cole, Int. Mater. Rev. 54 (3) (2009) 117. [17] T.H. Muster, A. Bradbury, A. Trinchi, I.S. Cole, T. Markley, D. Lau, S. Dligatch, A. Bendavid, P. Martin. Accepted for publication in Electrochimica Acta. [18] U.R. Evans, The Corrosion and Oxidation of Metals: Scientific Principles and Practical Applications, Edward Arnold Publishers Ltd, London, 1960, Reprinted 1981. [19] M.S. Venkatraman, I.S. Cole, D.R. Gunasegaram, B. Emmanuel, Mater. Sci. Forum 1650 (2010) 654–656. [20] B. Aurian–Blajeni, M. Tomkiewicz, J. Electrochem. Soc. 132 (4) (1985) 869. [21] M.S. Venkatraman, I.S. Cole, B. Emmanuel, ECS Transactions - Vancouver, Canada 28 (24) (2010) 145–156, Corrosion (General) - 217th ECS Meeting-. [22] J. Newman, W. Tiedemann, AlChE J. 21 (1975) 25. [23] J.S. Newman, Electrochemical Systems, 2nd ed., Prentice Hall, Englewood Cliffs, 1991. [24] D.R. Lide, CRC Handbook of Chemistry and Physics, Chemical Rubber Company, 2006. [25] I.S. Cole, T.H. Muster, D. Lau, N. Wright, N. Shahzad, J. Electrochem. Soc. 157 (6) (2010) C213. [26] J.R. Galvele, J. Electrochem. Soc. 123 (1976) 464. [27] I.S. Cole, W.D. Ganther, S.A. Furman, T.H. Muster, A.K. Neufeld, Corros. Sci. 52 (2010) 848. [28] A.B. Cook, R.C. Newman, in: S. Virtanen, P. Schmuki, G.S. Frankel (Eds.), Critical Factors in Localized Corrosion IV, The Electrochemical Society, Pennington, NJ, USA, 2002, p. 187. [29] P. Ernst, R.C. Newman, Corros. Sci. 44 (2002) 943. [30] G.T. Gaudet, W.T. Mo, J. Tilly, J.W. Tester, T.A. Hatton, H.S. Isaacs, R.C. Newman, AIChE J. 32 (1986) 949. [31] Yg’Al Volkman, vol. 24, Electrochem. Acta, p. 1145 (1979).