Stress in aluminum induced by hydrogen absorption during cathodic polarization

Accepted Manuscript Title: Stress in Aluminum Induced by Hydrogen Absorption during Cathodic Polarization Author: Jae Wook Shin Gery R. Stafford Kurt R. Hebert PII: DOI: Reference:

S0010-938X(15)00210-3 http://dx.doi.org/doi:10.1016/j.corsci.2015.05.015 CS 6302

To appear in: Received date: Revised date: Accepted date:

22-2-2015 19-5-2015 20-5-2015

Please cite this article as: Jae Wook Shin, Gery R. Stafford, Kurt R. Hebert, Stress in Aluminum Induced by Hydrogen Absorption during Cathodic Polarization, Corrosion Science (2015), http://dx.doi.org/10.1016/j.corsci.2015.05.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

In situ stress measurements detect hydrogen absorption in aluminum electrodes.

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Hydrogen absorption induces potential-dependent compressive stress.

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The potential dependence of stress is consistent with equilibrium solubility data.

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Hydrogen concentrations inferred from stress agree with analytical measurements.

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Stress in Aluminum Induced by Hydrogen Absorption during Cathodic Polarization Jae Wook Shina , Gery R. Stafforda , Kurt R. Hebertb a

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Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899 b Department of Chemical and Biological Engineering, Iowa State University, Ames, Iowa 50011, USA

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Abstract

Hydrogen concentrations in metals during aqueous corrosion are influenced

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by absorption kinetics. In situ measurement of hydrogen-induced stress was used to characterize hydrogen absorption into aluminum thin films during

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cathodic polarization in sulfuric acid, in the presence of competing gas evo-

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lution. Absorption-induced compressive stress increased with decreasing potential, reaching levels indicating average H concentrations of 0.3 at.%. De-

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pendences of stress on potential and scan rate suggested that rates of hydrogen desorption but not absorption were kinetically limited. Keywords:

Email address: [email protected] (Kurt R. Hebert) Preprint submitted to Corrosion Science

May 18, 2015

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1. Introduction

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Hydrogen absorption during corrosion processes results in embrittlement

of engineering alloys [1, 2]. The susceptibility of a material to embrittlement

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is determined by the hydrogen concentration near the metal surface, which is governed by the rates of absorption and diffusion [3, 4]. Studies of absorption

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kinetics are facilitated by in situ detection of hydrogen near metal surfaces under electrochemical polarization. Samples in the form of thin metal films

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are useful for adsorption kinetics studies, because the generally rapid diffusion of interstitial hydrogen provides a uniform concentration through the

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film thickness [5, 6]. If hydrogen absorption is the dominant electrochemical reaction, the hydrogen concentration can be accurately determined from the electrochemical charge accompanying absorption [5]. However, such meth-

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ods do not apply to absorption accompanying metallic corrosion, because of

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the high rates of competing metal dissolution and gas evolution reactions. Recently, measurements of hydrogen chemical potential on the back side of

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metal layers have been developed as methods to to sense hydrogen during corrosion [7, 8].

In situ stress measurements can provide highly sensitive methods for de-

tection of hydrogen in thin metal films [5, 9-11]. Absorption of hydrogen atoms at interstitial sites in the metal produces elastic volume expansion of the lattice [12]. If the metal is attached to a rigid substrate, it can expand only in the direction perpendicular to the metal-solution interface. Therefore, biaxial stress is generated parallel to the interface. The substrate in turn bends to equilibrate this stress, and the resulting substrate curvature changes can be monitored to determine the absorption-induced stress. The 2

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sensitivity of stress measurements for hydrogen is high, because of the large

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magnitude of the elastic moduli of substrates typically used in these experiments. Curvature measurements also have time resolution as small as

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several milliseconds, and hence can be used to track fast absorption kinetics

[13]. The measured stress change can be directly related to the quantity of

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absorbed hydrogen, even in the presence of gas evolution and corrosion reactions. While stress measurements have been used to study electrochemical

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hydrogen absorption into Pd, apparently no studies of reactive metals have been reported [11, 14-16].

The present work describes exploratory in situ stress measurements ac-

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companying hydrogen absorption in aluminum thin films. Stress is monitored during cyclic voltammetry in sulfuric acid, in the potential region of rapid

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cathodic hydrogen evolution. A hydrogen absorption model is developed

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that predicts the experimental stress response, on the basis of hydrogen absorption in combination with electrochemical charge-transfer kinetics. The

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results demonstrate that the concentration of absorbed hydrogen in the metal film approaches that determined by the potential-dependent absorption equilibrium. Such extensive absorption at low pH values is apparently possible because of the slow hydrogen recombination kinetics on the oxide-covered aluminum surface.

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2. Experimental Methods

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Cathodic charging experiments were carried out using thin film aluminum

samples deposited on borosilicate glass cantilevers. Curvature of the can-

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tilevers caused by electrochemically induced stress in the metal film was monitored continuously during the experiments. Curvature was measured

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by reflecting a HeNe laser off the glass-metal interface on the back side of the sample, onto a duo-lateral position-sensitive detector (PSD). The borosili-

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cate glass cantilever dimensions were 60 mm x 3 mm x 0.108 mm. Layers of Ti (4 nm thick), Au (250 nm), Cu (10 nm) and Al (250 nm) were se-

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quentially vapor-deposited on the cantilevers by electron-beam evaporation. The function of the Au layer was to provide a reflective interface, the Ti was an adhesion layer between the Au and glass, and the Cu prevented alloying

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between Au and Al. Hydrogen absorption into the Au layer is not expected,

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based on measurements of hydrogen absorption into Pd films on Au/Ti/glass cantilevers fabricated in the same way as those used here [11]. The deposited

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Al film had a strong (111) crystallographic orientation. The (200) reflection was not apparent in θ − 2θ X-ray scans and rocking curves of the (111) reflec-

tion generally yielded a full width half-maximum on the order of 2.9◦ . The average grain size, obtained from plan view field emission microscopy, was 170 ± 30 nm.

Since the Al film was much thinner than the cantilever, the relation-

ship between cantilever curvature and stress is given by the thin-film Stoney equation, Fw =

Z

hAl

σxx dz = 0

Yc h2c κ 6(1 − νc )

(1)

where Yc , νc , and hc are the Young’s modulus, Poisson’s ratio and thick4

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ness of the glass cantilever, hAl is the aluminum layer thickness, and κ is

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the curvature change. The x and z directions are respectively parallel and perpendicular to the metal surface. The measured curvature is related to the

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force per width Fw , which represents the biaxial in-plane stress σxx in the Al film integrated through its thickness. A single stationary laser measures

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only the change in curvature, rather than absolute curvature, by measuring the deflection of the cantilever. A small angle approximation was used to

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estimate the curvature of the glass cantilever directly from the reflected laser position on the PSD.

The electrochemical cell was a single compartment Pyrex cell holding

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approximately 15 ml of electrolyte solution. The counter electrode was a platinum foil placed parallel to and in the same solution as the working

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electrode. The reference electrode was a saturated mercury - mercurous

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sulfate electrode (SSE) that was separated from the working compartment by a Vycor-tipped bridge filled with saturated K2 SO4 solution. Potentials

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reported here are converted to the Ag/AgCl reference electrode scale, for consistency with prior work. The electrolyte solution was 0.1 M H2 SO4

(Aldrich, 99.999%) and was prepared using 18 MΩ-cm ultrapure water. The solution was de-aerated with ultra-pure argon prior to being added to the electrochemical cell with the cantilever in place. The Al cantilever electrode sat at its open circuit potential for about 30 s while cell and PSD adjustments were made. Cathodic charging experiments were then initiated from the open circuit potential using a potentiostat/galvanostat (Princeton Applied Research Model 273). A more detailed description of the optical bench and stress measurement is published elsewhere [13, 17].

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3. Results and Discussion

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3.1. Stress measurements

Cyclic polarization experiments revealed large compressive stress increases

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in the Al films at cathodic potentials. Figure 1 shows the force per width

and current density measured during cycles of cathodic polarization, at po-

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tential scan rates from 20 to 200 mV/s. The hydrogen evolution current density reached large values of 0.15 to 0.2 A/cm2 . Compressive force in the

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Al film accumulated during the cathodic (negative) potential scan, and was then removed during the anodic (positive) scan. In the cathodic sweep, the

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increase of cathodic current at potentials less than -1.0 V vs. Ag/AgCl preceded the stress increase, which initiated below about -1.2 V vs. Ag/AgCl. The large fluctuations in the force signal are caused by gas bubble evolution

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from the electrode that causes rapid changes in the cantilever position. The

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potential dependence of the stress signal is easily extracted from the noise. Successive polarization cycles with the same scan rate and potential limits

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demonstrated a good level of reproducibility between the scans. Compressive elastic stress during hydrogen evolution can be caused by

absorption of cathodically-produced hydrogen atoms [12]. The largest inplane stress in the Al film is estimated as the maximum force per width of 3 N/m divided by the film thickness of 250 nm, or about 10 MPa. This stress is much smaller than the typical yield stress of Al samples of about 100 MPa. Also, it was generally found that the stress recovered to zero after the cathodic polarization cycle (for the 200 mV/s experiment in Figure 1, the anodic scan was stopped before the stress had recovered completely). Both the low stress level and the reversibility of the stress increase indicate 6

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that elastic rather than plastic deformation accomodates the cathodically-

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induced volume expansion. As mentioned in the Introduction, in-plane stress is produced because the substrate constrains the expansion of the film in

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this direction. Because of concurrent gas evolution and Al corrosion it is not possible to obtain H loading from electrochemical charge, in order to confirm

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the relationship of stress and hydrogen concentration [5]. Instead, below we develop a model for hydrogen absorption induced stress and compare its

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predictions with the stress measurements.

A significant dependence of the cathodically-induced stress on scan rate would suggest that hydrogen absorption is influenced by diffusion or kinetic

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limitations [6]. Figure 2 (a) compares the force per width measured during the cathodic scans at the various sweep rates. A similar plot for the anodic

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scans is given in Figure 2 (b). The cathodic-direction force increase was not

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influenced significantly by scan rate. Apparently, hydrogen absorption and diffusion within the metal film were fast enough to achieve a steady-state

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stress at a given potential during the scan. However, there was appreciable hysteresis between the cathodic and anodic scans. The hysteresis was insignificant at 20 mV/s, but increased at higher scan rates; thus, the anodic scans removed cathodically-induced stress more effectively at the smaller scan rates. This suggests that a slow kinetic or transport process limits the rate of stress removal during the anodic sweep. 3.2. Potential dependence of stress The remainder of the paper focuses on interpreting the potential dependence of stress in the cathodic sweep. To clarify the dependence of stress on the potential at the Al surface, contributions to the measured potential 7

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from ohmic and concentration overpotential must be considered. Linearity

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of the current-potential curves below about -1.5 V vs. Ag/AgCl (Figure 1) suggests that the ohmic potential drop in the cell solution was indeed signif-

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icant at these potentials. Linear fitting of the current-potential dependence in this range revealed a consistent apparent cell resistance 5.9 ± 0.2 Ω-cm2

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(Table 1). A similar resistance for this cell of 5.5 Ω-cm2 was determined by electrochemical impedance spectroscopy, in experiments using Pt cantilever

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electrodes and 0.1 M HClO4 solution [13]. Figure 3 shows the dependence of current density on the potential after correcting for the ohmic potential drop. The cathodic hydrogen evolution rate in each experiment was well-

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approximated by the Tafel relationship, i = −iC0 exp(−bC U), where U is the potential corrected for ohmic resistance. Consistent values of the potential

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coefficient bC and pre-exponential current density iC0 were found at the three

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smaller scan rates, while the 200 mV/s scan suggested an appreciably larger pre-exponential current density (Table 1). The different kinetic resistance

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may be caused by variations of oxide layer on the Al electrode. The good fit of the polarization curves with Tafel kinetics suggests that

concentration polarization was not significant. The surface H+ ion concen-

tration can be estimated from the steady-state diffusion layer thickness at gas-evolving electrodes [18], Cs = Cb +

i(1 − t+ )δ F DH +

(2)

where Cb is the H+ concentration in the bulk solution, i the current density, and t+ and DH + are the cation transport number and electrolyte diffusivity of 0.1 M H2 SO4 . On hydrogen-evolving electrodes the diffusion layer thickness is given by δ = δ0 i−0.505 , where δ0 = 0.0190 cm and the current density is in 8

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mA/cm2 [18]. Using DH + = 9.3 x 10−5 cm2 /s and t+ = 0.88 [19], the surface

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pH increase calculated from Equation 2 was found be no greater than 0.06 at the highest current densities in Figure 1. Thus, enhanced mass transfer rates

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due to gas evolution strongly attenuated the pH increase in the diffusion

layer, and accordingly concentration polarization during the cathodic scan

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was not significant.

Plots of force per width vs. the ohmic-corrected potential U are displayed

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in Figure 4. The corrected potential was calculated at a given current density from the Tafel kinetic parameters (Table 1). In each experiment, an exponential relationship between force and potential was obtained. The experiments

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with the three smaller sweep rates yielded quantitatively consistent forcepotential relations with similar intercepts and slopes of -68 mV/decade. The

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-76 mV/decade.

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200 mV/s scan produced a somewhat more positive intercept with a slope of

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3.3. Hydrogen absorption model

In this section, we develop a model for hydrogen absorption, which is

then used to quantitatively interpret the observed stress increase during the cathodic sweeps. Concurrent gas evolution and stress generation can be described by the Volmer mechanism of the hydrogen evolution reaction [3]. Protons in solution are reduced to adsorbed hydrogen atoms at the metaloxide interface,

H+ (aq) + e− → H(m/o)

(3)

The adsorbed H atoms then recombine to form hydrogen gas, 2H(m/o) → H2 (g)

(4)

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but can also absorb into the metal according to (5)

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H(m/o) ↔ H(Al)

and thereby produce the compressive stress increase. The absorption step has

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been found to be close to equilibrium in experiments with other oxide-covered

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metals [12, 20]. In order to explain the observed stress increase, the chemical potential of adsorbed H atoms must be elevated relative to that of hydrogen gas molecules. Therefore, recombination of H2 gas must be kinetically slow

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process, as is the case on many oxide-covered metal surfaces [3]. With the assumption that Equation 5 is approximately at equilibrium, the potential

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of the aluminum electrode (with respect to a normal hydrogen reference electrode) can be written in terms of the hydrogen chemical potential in the metal,

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  1 0 RT µH (Al) − µH2 − 2.303 pH + ηad 2 F

(6)

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1 U =− F

where µAl is the chemical potential of H(Al) in Equation 5, and µ0H2 is that

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of H2 gas at standard conditions. The overpotential ηad is the driving force for formation of adsorbed H(m/o) atoms by Equation 3. As argued above in Section 3.2, stress in the metal is assumed to result

from elastic deformation, caused by the volume expansion upon absorption of hydrogen atoms. The compliance of the thin film with the substrate requires that the overall in-plane strain is zero, and so the strain produced by H diffusion into the metal is balanced by elastic strain, 1 − ν ∂σxx ΩH ∂JH = Y ∂t 3 ∂z

(7)

where Y and ν are Young’s modulus and Poisson’s ratio of Al, ΩH is the volume expansion per mole of H atoms, and JH is the hydrogen diffusion 10

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flux. The force per width Fw is obtained by integrating Equation 7, first

ΩH Y h ¯ CH 3ΩAl (1 − ν)

(8)

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Fw = −

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spatially through the Al film thickness, and then over time,

where C¯H is the average H atomic fraction in the Al film and ΩAl is the

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molar volume of Al atoms. Equation 8 assumes that the hydrogen diffusion flux at the Al/Cu interface is zero. The mechanical parameters in Equation

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8 are Y = 70 GPa and ν = 0.33, and ΩH /ΩAl = 0.15 [21]. The maximum force per width of -3.5 N/m in Figure 2 corresponds to an average hydrogen concentration of 3 x 10−3 atom fraction. Significantly, this value is consistent

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with H concentrations on the order of 10−3 atom fraction that were measured after extended periods of cathodic charging, using vacuum extraction and

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γ− activation analysis [21,22]. This agreement supports the ability of in situ

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stress measurements to monitor hydrogen absorption during corrosion. The force per width at a given potential is determined by Equation 8, with

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C¯H related to the hydrogen chemical potential in Equation 6 with the help

of solubility equilibria. Solubility equilibrium data are typically reported in terms of Sievert’s Law, the empirical relationship between hydrogen solubility

in Al and hydrogen partial pressure. Sievert’s law is expressed as CH = √ C0 pH2 exp (−∆Hs /RT ), where ∆Hs is the enthalpy of solution and C0 is

a constant related to the entropy of solution [23]. The hydrogen chemical potential in terms of these quantities is 1 µH (Al) − µ0H2 = −RT ln C0 + ∆Hs + RT ln C¯H 2

(9)

Combining Equations 6, 8 and 9, the relationship between ohmic-corrected 11

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potential and force per width is RT RT pH + ηad − ln(−Fw ) F F

where the constant UH′ is given by

  ∆Hs RT 3ΩAl (1 − ν) RT ln(C0 ) − − ln = F F F ΩH Y h

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UH′

(10)

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U = UH′ − 2.303

(11)

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Equation 10 predicts a linear dependence of ohmic-corrected potential on ln(−Fw ), consistent with that derived from the experiments (Figure 4).

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The equilibrium absorption model was compared quantitatively with the force measurements, based on values of the solubility parameters ∆Hs and

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C0 from the literature. Several experimental studies have found consistent values of these quantities, as indicated in Table 2 [24-27]. First-principles

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calculations have also yielded comparable formation energies of 0.6 - 0.7 eV for absorption into interstitial lattice sites [28-30]. The force-potential

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curves predicted from Equation 10 using these values, and with ηad set to

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zero, are shown as the dashed black lines in Figure 4. The calculated lines are displaced from the measurements by 0.1 to 0.2 V in the anodic direction, and their slope is about 15% higher. However, despite this discrepancy, the potential dependence of the stress measurements parallels that expected for equilibrium hydrogen absorption. A possible source of disagreement between the model and experiment in

Figure 4 is the contribution of H adsorption kinetics to the potential, via the overpotential ηad in Equation 10. ηad should be a function of current density according to a Tafel rate law, ηad = − ln(−i/i0 )/bad . Therefore, adsorption

kinetics could account for the more negative slope d ln(−Fw )/dU relative to −F/RT . On the other hand, including hydrogen absorption kinetics in 12

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the model would introduce a scan rate dependence in Equation 10, which is

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inconsistent with the results in Figure 4. Accordingly, the extent of hydrogen absorption during the cathodic scan seems to be determined primarily by

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equilibrium and electrochemical kinetic considerations.

In addition to lattice interstitials, hydrogen segregated at grain bound-

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aries could contribute to the measured compressive stress. Both experimental and theoretical evidence for significant grain boundary segregation in pure

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aluminum has been reported; Edwards and Eichenauer estimated the grain boundary binding energy of H interstitials to be 0.15 eV [26,31]. However, appreciable grain boundary segregation would increase the extent of absorp-

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tion and hence compressive stress at a given potential, and thus shift the theoretical ln(−Fw ) curves in Figure 4 toward anodic potentials. Hence,

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deep hydrogen traps such as grain boundaries cannot by themselves explain

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the finding of lower than expected absorption potentials. On the other hand, grain boundary segregation could be significant if the electrochemical adsorp-

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tion overpotential is larger in magnitude than 0.1 to 0.2 eV, corresponding to the potential difference between the theoretical and experimental curves in Figure 4. We conclude that the discrepancy between model and experiment is due primarily to electrochemical adsorption kinetics, but that contributions from trapping of hydrogen at grain boundaries are also possible. The scan-rate dependent hysteresis during the anodic potential sweep

(Figures 1 and 2) indicates the presence of a kinetic barrier specifically for hydrogen desorption, as no scan-rate dependence is evident during the cathodic sweep. Two possible barriers are suggested: the surface oxide layer and kinetically irreversible traps. At pH 1, the equilibrium potential of Al ox-

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idation is -1.7 V vs. Ag/AgCl, more negative than the potential range of the

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CV experiments [32]. Hence, the surface oxide is expected to grow in thickness during the anodic potential sweeps on Al [33-34]. The anodically formed

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oxide could inhibit outward transport of absorbed H atoms into solution. At

a given potential during the anodic sweep, greater retention of hydrogen and

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hence larger compressive stress would be expected when the time elapsed during the anodic sweep is small (200 mV/s), as opposed to large (20 mV/s).

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This trend would explain the inverse dependence of hysteresis on scan rate in Figure 2. Hysteresis might also be explained by deep hydrogen traps that have higher activation energy barriers for desorption compared to absorption

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[35]. As discussed above, such traps are not directly apparent from the stress measured during cathodic sweep; however, their presence cannot be ruled

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out owing to the unknown magnitude of the H+ adsorption overpotential.

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In prior work, we found that open-circuit corrosion of Al thin films in alkaline solutions produced large tensile force increases of 10 to 40 N/m,

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as opposed to the compressive deflections observed in this work [36]. Both investigations used nearly the same samples and procedures. In the present experiments, the hydrogen chemical potential µH (relative to the ideal gas

reference) calculated from the corrosion potential and pH value ranged from 0.64 to 0.84 eV. The chemical potential calculated similarly in the alkaline experiments was about 0.94 eV; hence, a somewhat larger compressive stress should have been measured on the basis of equilibrium hydrogen absorption. Therefore, some process other than hydrogen absorption likely accounts for the high tensile forces measured in alkaline solutions. It was suggested that the tensile stress might arise from the lattice contraction associated with

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vacancies introduced by dissolution [36]. Another possibility is contraction

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due to diffusion of metal atoms out of grain boundaries, as is observed to produce tensile forces of tens of N/m during electrochemical etching of Sn

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films [37]. However, it is noteworthy that anodic oxidation, in which no significant hydrogen is absorbed, produces much lower stress in Al compared

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to alkaline dissolution, even at comparable rates of metal oxidation [38]. Therefore, rapid metal oxidation alone may not explain the large tensile stress

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produced during open-circuit dissolution. Mechanisms might be envisioned that involve synergism between hydrogen absorption and metal corrosion

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reactions.

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4. Conclusions

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In this article, we report exploratory measurements of stress generation

in Al thin films in 0.1 M H2 SO4 solution, during cycles of cathodic polariza-

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tion in the potential region of vigorous hydrogen gas evolution. Compressive

stress in the film increased during potential sweeps in the cathodic direc-

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tion, and was recovered during subsequent anodic sweeps. The dependence of stress on potential was compared to that expected from literature hy-

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drogen solubility data, assuming that elastic stress accommodates volume expansion accompanying hydrogen absorption. This comparison revealed no

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rate limitations associated with slow absorption kinetics during the cathodic sweep. However, stress during the anodic sweep depended on scan rate as well as potential, suggesting the presence of a kinetic barrier limiting the rate

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of hydrogen desorption. The maximum compressive stress during cathodic

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polarization was equivalent to an average hydrogen concentration of 0.003 atomic fraction in the metal film, consistent with earlier analytical measure-

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ments on cathodically charged aluminum. The present results demonstrate that in situ stress measurements in thin metal films are a viable method to characterize hydrogen absorption kinetics, in situations where competing gas evolution prevents direct electrochemical determination of absorption rates.

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M

boundaries in superpure aluminum, Scripta Metall., 14 (1980) 971-973. [27] M. Ichimura, H. Katsuta, Y. Sasajima, M. Imabayashi, Hydrogen and

te

(1988) 1259-1267.

d

deuterium solubility in aluminum with voids, J. Phys. Chem. Solids, 49

[28] C. Wolverton, V. Ozolins, M. Asta, Hydrogen in aluminum: First-

Ac ce p

principles calculations of structure and thermodynamics, Phys. Rev. B, 69 (2004) 144109.

[29] L. Ismer, M.S. Park, A. Janotti, C.G. Van de Walle, Interactions between hydrogen impurities and vacancies in Mg and Al: A comparative analysis based on density functional theory, Phys. Rev. B, 80 (2009) 184110.

[30] M. Ji, C.Z. Wang, K.M. Ho, S. Adhikari, K.R. Hebert, Statistical model of defects in Al-H system, Phys. Rev. B, 81 (2010) 024105.

20

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[31] X. J. Shen, D. Tanguy, D. Conn´etable, Atomistic modelling of hydrogen

ip t

segregation to the Σ2 2 1[1 1 0] symmetric tilt grain boundary in Al, Philos. Mag., 94 (2014) 2247-2261.

cr

[32] M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions,

us

NACE International, Houston, 1974.

[33] M.M. Lohrengel, Thin anodic oxide layers on aluminum and other valve

an

metals - high-field regime, Mat. Sci. Eng. R, 11 (1993) 243-294. [34] C.J. Boxley, J.J. Watkins, H.S. White, Al2 O3 film dissolution in aqueous

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chloride solutions, Electrochem. Solid State Lett., 6 (2003) B38-B41. [35] G. A. Young, J. R. Scully, The Diffusion and Trapping of Hydrogen in

d

High Purity Aluminum, Acta Mater., 46 (1998) 6337-6349.

te

[36] K.R. Hebert, J.H. Ai, G.R. Stafford, K.M. Ho, C.Z. Wang, Vacancy defects in aluminum formed during aqueous dissolution, Electrochim. Acta,

Ac ce p

56 (2011) 1806-1809.

[37] J.W. Shin, E. Chason, Compressive stress generation in Sn thin films and the role of grain boundary diffusion, Phys. Rev. Lett., 103 (2009) 056102.

¨ O. ¨ C [38] O. ¸ apraz, P. Shrotriya, P. Skeldon, G.E. Thompson, K. Hebert, Factors Controlling Stress Generation during the Initial Growth of Porous

Anodic Aluminum Oxide, Electrochim. Acta, 159 (2015) 16-22.

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Page 22 of 28

List of Figures

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Figure 1. Force per width and current density (smooth curves) measured

during cyclic potential scans. In each polarization cycle, the force during the

cr

anodic sweep was more compressive compared to that during the cathodic

us

sweep.

Figure 2. Force per width measured during cathodic and anodic potential

an

scans. Labels are potential sweep rates in mV/s.

Figure 3. Exponential Tafel-type relationship between cathodic current den-

M

sity and potential, after correcting the potential for cell ohmic resistance. Labels are potential sweep rates in mV/s.

d

Figure 4. Exponential relationship between force per width measured during

te

the cathodic scan and potential corrected for ohmic resistance. Labels are potential sweep rates in mV/s. Dashed lines represent force calculated using

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hydrogen solubility data from the literature references indicated by bracketed labels (Table 2)

22

Page 23 of 28

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Table 1: Parameters derived from fitting of cathodic-direction scans. Rs is cell resistance,

cr

and i0C and bC are exchange current density and potential coefficient in Tafel kinetic expression.

Rs (Ω-cm2 ) i0C (A/cm2 )

bC (V−1 )

us

Scan Rate (mV/s) 20

6.23

2.4 x 10−9

16.0

50

5.86

5.1 x 10−9

100

5.58

1.9 x 10−8

14.7

200

5.77

4.5 x 10−7

12.6

Ac ce p

te

d

M

an

15.7

Table 2: Representative values of the hydrogen solubility in aluminum

Source

∆Hs (eV)

C0 (at. fraction)

Eichenauer et al. [24]

0.603

0.0022

Eichenauer [25]

0.655

0.0031

Edwards and Eichenauer [26]

0.673

0.0034

Ichimura et al. [27]

0.663

0.0018

23

Page 24 of 28

te

d

M

an

us

cr

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Figure1

1-

50 mV/s

20 mV/s

-4

-100 -150

0

0

-50 -2

-100 100 mV/s

2-

m N / htdiW rep ecroF

-2

-50

mc Am / ytisneD tnerruC

0

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0

200 mV/s

-150

-4

-2.0

-1.6

-1.2

-0.8

-2.0

-1.6

-1.2

-0.8 Page 25 of 28

Potential vs. (Ag/AgCl) / V

te

d

M

an

us

cr

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Figure2

1-

m N / htdiW rep ecroF

-2

-4

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0

200 100 50 20

Cathodic Scan

0

-2 50

100

20

200 Anodic Scan

-4 -2.0

-1.6

-1.2

Potential vs. (Ag/AgCl)/ V

-0.8

Page 26 of 28

2-

d

M

an

us

cr

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Figure3

10

te

200

Ac ce p

mc Am / ytisneD tnerruC evitageN

100

20 50

100

1

0.1 -1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5 Page 27 of 28

Potential vs (Ag/AgCl) / V

te

d

M

an

us

cr

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Figure4

m N / htdiW rep ecroF evitageN

2

1 8 6 4

2

0.1 8

[23]

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1-

4

[24]

20

[25]

50

[26]

100

200

6

-1.2

-1.1

-1.0

-0.9

Potential (vs. Ag/AgCl) / V

-0.8

-0.7

Page 28 of 28