Corrosion layer growth on Magnesium galvanic ...

Corrosion layer growth on Magnesium galvanic coupled to Aluminium simulated by FEM Daniel Höche, Helmholtz-Zentrum Geesthacht Centre for Materials and Costal Research, Max-Planck Str. 1, 21502 Geesthacht, Germany Abstract Galvanic corrosion of magnesium alloy based components coupled to more noble materials is a known problem. This work presents a simulation based study for predicting corrosion of bare magnesium galvanic coupled to aluminium including corrosion layer formation due to Mg(OH)2 precipitation. It introduces into the involved mechanisms and discusses transport phenomena in the porous layer, the surface coverage by reaction product deposit and the time dependent anodic resp. cathodic electrochemical electrode response. The analysis via computer offers the possibility to study the corrosion performance and can be utilized for virtual studies of various process parameters. At the end future requests and challenges on modelling corrosion will be listed. 1

Introduction

Light weight structural materials like Mg and Al are less noble materials compared to other metallic engineering materials like high strength steels and even between bare Mg and Al an critical electrochemical potential difference arise. This work will figure out the possibilities of predicting galvanic corrosion of magnesium by FEM simulations based on fundamental modelling including the corrosion induced layer growth due reaction product deposit. Simulation of galvanic corrosion between magnesium and aluminium has been performed by Lacroix [1] (macro), Desphande [2-4] (micro and macroscopic) or in own previous work [5]. Jia [6] or Trinh [7] have studied the corrosion of magnesium alloys in contact to mild steel under static conditions. The publications of Murer [8-10] or Shi [11] in this context also gave an extended insight into the topic, especially in the very important choose of boundary conditions. Further information and work on the steel-zinc system was published in other related articles like [12]. New studies of Sun [13] based on the approach of Yan [14] on modelling the deposit formation under seawater conditions, clearly introduces a possible way of useful model built-up for the mentioned purpose. The following studies and results based on the progress being achieved by them. Basic galvanic current density computations were modified by layer growth aspects leading to time dependent variations in the electrochemical response of the electrodes. This study shows the simulation of galvanic corrosion between pure Mg and Al by solving electrochemical fundamental equations. Both materials were characterized by potentiodynamic polarization to setup the model parameters. Layer growth will be compared to impedance spectroscopy (EIS) investigations. The model assumes a neutral 0.1% NaCl solution film saturated with O2. For subsequent studies the exposure conditions have been varied. Starting from the initial model setup and related to the scientific challenge, the mathematical model requires fundamental assumptions. As always in modelling action they define the quality and accuracy of simulation results. Most important for the presented studies are: a. Al is non-corroding (anodic branch is neglected) b. dilute solution theory is applicable

c. precipitates (corrosion products) do not re-dissolve d. layer formation occurs at the interface and is contributed to magnesium hydroxide formation e. hydrogen gas bubbles are not interacting and influencing the reaction chains f. the model discusses “macro” galvanic corrosion, which means: impurity levels are below tolerance limits and the Mg does not contain secondary metallic phases/precipitates (from simulation point of view) g. it assumes homogeneous surfaces conditions at the beginning h. localised corrosion effects do not occur (e.g. Cl- induced pitting) Especially point e. is a strong limitation. It means that the influence of surface coverage by gas bubbles and the change of electrolyte properties based on gas dissolution have been neglected. This assumption is just valid for moderate corrosion conditions. 2

Theory

Just a brief summary into the approach can be provided. The model based on the Nernst equation including diffusion and migration at the beginning. At the electrode – electrolyte interface Faraday reactions take place. Table 1 summarises the used specimens and values. The electrochemical response was modelled by the standard Butler-Volmer (B-V) equation at magnesium and by a modified diffusion limited version (1) on aluminium based on recent work [15] which has been extended by water reduction. Mg(OH)2 precipitation/formation has been considered as shown in the following paragraphs. Table 1: Simulation parameter electrolyte film: thickness 0.8 mm, mobility - Einstein relation

species D [m²/s]*10-9 C0 [mol/m³]

Mg2+ 0.71 0

OH5.27 10-4

H+ 9.31 10-4

Na+ 1.33 17

Cl5.27 17

O2 1.98 0.233

The required electrochemical parameters were taken from the experimental studies and fittings in figure 1 according B-V (Mg2+ and partial cat. H2O) on Mg and by equation (1)  η  -β   c

 ηH 

 -β  i0 exp  H − + ⋅ ⋅ θ εθ iAl = (1 − θ + εθ ) ⋅ i + (1 ) 10 0H  η    β  i 1 −  0  1 − i0 exp c    id    

(1)

on aluminium, where z (zMg=2) is the electron number, η is the overpotential, i0 the exchange current, αa,c the anodic and cathodic coefficient on Mg resp. βc the (oxygen related) cathodic Tafel coefficient (empirical value), id describes the current limitation due to diffusion (O2 reduction) processes and i0H, ηH =(UH-U0), βH the alkaline water reduction based current, potential and Tafel coefficient. As expected the process is limited by the diffusion within the deposit and the interface. The application of Tafel slopes at high cathodic overpotentials is allowed and based on the Heyrovsky reactions of hydrogen desorption on metals [16]. The Tafel slope in the Heyrovsky range follows the relation 2RT/F ≤ βH ≤ 3RT/F [17]. It was shown by measurements at Al that this behaviour relates to and the slope varies between -110 and -175 mV/dec [18]. Variations are related to the Al-OH bond affinity.

Figure 1: Potentiodynamic polarization curves and its evaluation by fitting.

Layer growth simulation takes into account the precipitation of hydroxide. Therefore, a surface coverage θ was defined. By assuming Mg(OH)2 formation occurs direct at the surface and the deposits are porous, θ can be computed by 1  RMg 2+ M Mg (OH)2 dθ =−  dt l (1 − ε )  ρ Mg (OH)2

 2  with RMg 2+ =−(1 − θ ) k Mg (OH)2 (c Mg 2+ cOH − − K Mg (OH)2 ) 

(2)

The transport properties within the porous layer are changed. Due to precipitation at inner surface structures the porosity of the deposit εdep will be computed according (10) [17]: R 2+ M Mg (OH)  2 = −ε dep  dep Mg  2  = dt ρ Mg (OH)   Rdep Mg 2+ kdep Mg (OH)2 (c Mg 2+ cOH − − K Mg (OH)2 ) 2

dε dep

(3)

whereby Rdep Mg2+ describes the reaction rate and the induced Mg(OH)2 precipitation within the electrolyte solution at the interspaces (pores or hydroxide needle skins) inside of the deposited layer.

Figure 2: Physical meaning of modelling parameters (l - deposit thickness, ε – porosity, τ – tortuosity) exemplary shown on a Mg(OH)2 “flake” cross section after magnesium alloy AZ31 immersion into 3.5% NaCl solution after three days exposure.

The required solubility product constant has been computed according [19] by K Mg (OH)2 = 1.24 ⋅10−11 + 4.8 ⋅10−11 log10 Cl− 

(4)

Deposit thickness l is computed according to l = ∫ u total n dt ( [14, 20]) with ρ being the

density (2.45 g/cm³) and M the molar mass (58 g/mol). The interface movement (system X = (X,Y,Z) will be computed by the ALE – method (Arbitrary Lagrange Euler) by solving equation (3)

∂X (5) ⋅n ∂t The deformation is ΔX=(x-X,y-Y,z-Z) and the free surface movement includes the Mg dissolution and the growth by hydroxide and will be calculated by equation (4) = u corrosion

utotal ⋅ n =−

RMg (OH)2 M Mg (OH)2 M ⋅ iMg (θ ) + udep with udep = (1 − ε ) ρ Mg (OH)2 zF ρ

(6)

Layer growth on the cathode (Al) due to Mg(OH)2 precipitation was also included. The velocity can be computed by ulayer [14, 20] as well. 3

Experimental

Simulation parameters were taken from experiments on bare magnesium 99.94% and aluminium 99.8%. Potentiodynamic polarization shown in figure 2 was performed in 0.1% NaCl solution at a starting pH of 6.3. The corrosion cell (333 ml) with a three electrode set-up consisted of an Ag/AgCl reference, a Pt counter electrode and the specimen as working electrode. The electrolyte temperature was 22 ± 0.4°C and the electrolyte was stirred during the experiments. Impedance spectroscopy measured on magnesium applying the same setup, was performed without stirring (to avoid convection) at a potentiostatic anodic load of +30 mV in order to match the electrochemical galvanic conditions of the galvanic couple computed by subsequent simulations. 4

Results

The deposit can be characterised by its barrier properties which are related to the porosity, the tortuosity and at least its electrical resistance. Standard layer growth models for passivation [21-23] are based on oxide formation which typically show logarithmic or parabolic growth behaviour. Considering the model assumptions (no re-dissolution, thick film, etc.) and by considering the approach of Deslouis et al. [24], a logarithmic behaviour has been assumed (similar to Fehlner-Mott [25] and to the point defect model [26]). For a qualitative study and to facilitate the model validation impedance spectroscopy was carried out at highly pure-Mg under an anodic potentiostatic load offset of +30 mV “simulating” the galvanic couple conditions. Figure 3 shows the Nyquist plots for three days in the test solution. A typical “two semi-circle” behaviour was observed and fitted by ZView [27] according to the simple equivalent circuit model being shown. The evaluation revealed a film resistance according to the plot.

Figure 3: a) Nyquist plot of HP-Mg in unstirred 0.1% NaCl solution at +30 mV potentiostatic anodic polarisation for 60 h

Simulations were carried out for corrosion durations of 24 hours initially starting with neutral conditions. Figure 4 shows the arising surface topology for different initial porosities. The straight line corresponds to the layered system and the dashed line to the base material. Since the porosity directly relates to the barrier properties the inhibition effect looks rather strong. The shape is mainly related to the alternating influence of degradation velocity vector downwards and the opposite growth of the deposit.

Figure 4: Surface topology after 24 h corrosion for different initial porosity values. Straight lines illustrate the deposit shape and the dashed lines the metallic surface and surface coverage θ vs. t evaluated at the edge.

The fast growth within the first couple of hours also relates to the surface coverage θ by the deposit as shown in the top-right by plotting θ at the contact point between Mg and Al over time. This “θ-effect” is also observed by the experiments like in figure 3. Reaching 1 complies with a fully covered surface. Nevertheless, corrosion still takes place due to the porosity and the ionic conductivity with the deposit. The temporal evolution of the porous deposit has been shown in figure 5 as well in combination

with an illustration of the developing Mg2+ ion concentration, which is balanced by the Faraday reaction at the interface and the formation of hydroxide. Latter is controlled by the solubility product constant and can be varied during the simulations.

Figure 5: Surface topology after 24 h corrosion for different initial porosity values. Straight lines illustrate the deposit shape and the dashed lines the metallic surface.

By comparing to a real-life structure like shown in figure 6 the approximation level is still not adequate. The main challenge still keeps the addition of additional acting chemical reactions and the correct formulation of barrier properties of deposits. The agglomeration is affecting as well and hard to describe. With respect to the long term behaviour in figure 3 it can be entitled the “ε-effect”.

Figure 6: Surface morphology after 72 hours exposure in unstirred 0.1% NaCl solution evolving at a galvanic couple on the aluminium and on the magnesium side at a distance of 1 mm to the contact edge and a modelled film resistance (evaluated at the contact edge) matching the experiments of figure 3.

This barrier parameter is the main driving-force for the corrosion properties itself and can be mathematically described by the factor (1-θ+θε). In the present showcase the best matching value at the contact point corresponds to ε0 = 0.3. The directly linked time dependent electrode response is described in good approximation. Anyway the comparison is just of qualitative manner since the evaluation is carried out just at a point whereas measurements deliver an average resistance of a surface element. 5

Conclusion and Outlook

The simulations provide useful information on aspects of galvanic corrosion between magnesium and aluminium and its time dependent evolution including surface reactions and hydroxide precipitation. In summary, the most important results are: 1. Mg dissolution performance is contributed to the mathematical factor (1-θ+θε) being the parameter to describe the insulation performance of the self-induced corrosion product layer. It can be stated: When the factor becomes zero then corrosion would stop. 2. Corrosion product deposition at the cathode slightly reduces the cathodic current. 3. Alkaline water reduction is the dominant cathodic reaction and thus, the use of Tafel approximation according to the Heyrovsky description at the cathode even at high overpotentials is more or less allowed. 4. Time dependent electrochemical electrode boundary conditions have been setup. They allow describing the electrode response during the corrosion process regarding deposit formation. 5. Layer growth kinetics mainly depends on the solubility product constant of corrosion product compounds which can vary according to local conditions. Critical issues, especially in context of a modelling approach, and not included till now are convective flow, hydrogen bubbles and (de-) alloying aspects. Additionally, the model requires extensions to technical alloys (e.g. Almac coated/AA6082/AZ31). Cl- forced reactions and hydrolysis [28]. Aluminium surface activity has to be taken into account especially at high pH values. Despite all limitations the control of magnesium corrosion towards a knowledge base process and geometry design becomes not beyond reach. 6

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