Factors Controlling Stress Generation during the Initial Growth of Porous Anodic Aluminum Oxide

Electrochimica Acta 159 (2015) 16–22

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Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta

Factors Controlling Stress Generation during the Initial Growth of Porous Anodic Aluminum Oxide Ömer Özgür Çapraz a , Pranav Shrotriya b , Peter Skeldon c, George E. Thompson c , Kurt R. Hebert a, * a b c

Department of Chemical and Biological Engineering, Iowa State University, Ames, IA 50011, USA Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA Corrosion and Protection Centre, School of Materials, The University of Manchester, Manchester M13 9PL, UK

A R T I C L E I N F O

A B S T R A C T

Article history: Received 18 December 2014 Received in revised form 28 January 2015 Accepted 29 January 2015 Available online xxx

Anodic oxidation of reactive metals such as Al and Ti produces oxide films with self-organized arrangements of nanoscale pores. Stress-driven mass transport of oxide is considered to play an important role in pore formation and self-ordering. Using in situ stress monitoring during both anodizing and subsequent open-circuit oxide dissolution, distributions of in-plane residual stress were measured in anodic alumina films formed by galvanostatic anodizing in phosphoric acid. Anodizing produced significant stress both in the oxide and at the metal-oxide interface. For oxides grown to 20 nm thickness, the oxide stress was tensile below 3 mA/cm2 and compressive above this current density, while the interface stress exhibited the opposite dependence. Stress generation correlated with interfacial volume change due to reactions and transport processes: oxide or interface stress was compressive when interfacial volume was created, and vice versa. Compressive stress buildup in the oxide is apparently required for self-ordered pore formation by flow-assisted mechanisms. From the present results, a simple criterion was derived specifying the conditions for compressive stress and pore formation in terms of parameters governing film composition, ionic transport and interfacial reaction kinetics. ã 2015 Elsevier Ltd. All rights reserved.

Keywords: anodizing stress oxide nanotube porous anodic oxide self-ordered porous oxide

1. Introduction Porous anodic oxide films are produced by electrochemical oxidation of metals such as aluminum and titanium, in solutions in which the oxide is soluble. For selected voltages and solution compositions, anodizing creates self-organized porous films that contain a high number density of submicron-diameter cylindrical pores, arranged on a hexagonal lattice. The high surface area, controllable geometry, and favorable material properties of these films have stimulated many studies exploring their use as templates and functional materials [1–3]. Much recent work has focused on porous TiO2, e.g. for dye-sensitized solar cells, photocatalysis and sensors. The development of porous layers with favorable geometries and properties has been guided by knowledge of the fundamental processes controlling oxide growth, such as interfacial oxidation and dissolution reactions, and electric field-driven ion migration [1,2]. Optimal design and commercialization of porous oxide-based devices will be

* Corresponding author. E-mail address: [email protected] (K.R. Hebert). http://dx.doi.org/10.1016/j.electacta.2015.01.183 0013-4686/ ã 2015 Elsevier Ltd. All rights reserved.

facilitated by the continuing development of mathematical models for anodizing [4–7]. Such models predict oxide morphology evolution based on kinetic descriptions of ionic transport and interface reactions. Evidence has emerged that mechanical stress should be considered as an important driving force for ionic transport during anodizing [8–14]. For example, stress-driven oxide flow was demonstrated by imaging of metal ion tracers by transmission electron microscopy [12,13]. Models including stress have made encouraging progress in predicting these tracer profiles, as well as conditions for self-ordered films and scaling relations governing the porous layer geometry [5,6,15–17]. However, while experiments show clearly that appreciable stress changes accompany anodizing [8,9,18], there is disagreement as to the mechanism of stress generation. Various explanations for stress generation have been proposed, including the volume change associated with metal oxidation at the metal-oxide interface [10,11,14], electrostatic stress within the film [12,17,19], and ion transfer reactions at the oxide-solution interface [5,20,21]. To elucidate the role of stress-driven transport in pore formation and self-ordering, it is important to characterize both the mechanism and location of stress production during anodizing.

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Recently, we developed methods to determine stress distributions in anodic alumina films through in situ sample curvature measurements [22,23]. Curvature changes are related to the inplane stress integrated through the film thickness. Curvature monitoring during anodic oxidation was continued while the anodic oxide dissolved at open circuit in the acidic anodizing bath; the residual stress distribution in the oxide was then obtained by numerically differentiating the curvature change during dissolution, with respect to the oxide thickness. For current densities relevant to porous oxide formation, the measurements revealed separate stress generation processes within the oxide and at the metal-oxide interface. Here, we investigate the dependences of oxide and interface stress components on current density, in order to determine the mechanisms of stress generation both in the oxide and at the interface. The measured oxide and interface stress are compared to the calculated volume changes at both the metal and solution interfaces of the anodic film. This analysis yielded general relationships governing whether compressive oxide stress is produced during anodizing. Evidence from the literature indicates that compressive oxide stress is necessary for oxide flow, and that flow enables formation of self-ordered porous oxides.

2. Experimental Section As in our prior work, in situ stress measurements were carried out using phase-shifting curvature interferometry [24]. A detailed description of this method, including comparisons with traditional deflectometry measurements, is found in an earlier paper [23]. The aluminum samples for anodizing were rectangular in shape (2.5
3.5 cm) and cut from 1 mm thick hard aluminum sheet of 99.998% purity (Alfa Aesar). The sample surface to be anodized was prepared by etching in sodium hydroxide followed by immersion in nitric acid, with a reflective gold coating applied to the opposite side [23]. The sample was mounted in the anodizing cell so that the etched surface contacted the solution while the reflective surface faced the optical system. Curvature changes of the gold-coated surface were monitored by interferometry, and used to determine the force per unit width change, dF, of the sample using the thin-film Stoney approximation, 2

dF ¼

E s hs dk 6ð1  vs Þ

(1)

where dk is the curvature change; hs,Es and ns are the thickness, elastic modulus and Poisson's ratio of the Al sheet. The force per width F represents the biaxial in-plane stress s xx integrated through the sample thickness, relative to that before anodizing, Z1 F¼

s xx dz;

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3. Results and Discussion 3.1. Stress Evolution During Oxide Growth Force per width and potential transients measured during initial growth of anodic films are displayed in Fig. 1, for applied current densities ranging from 2 to 12.5 mA/cm2. At these anodizing voltages, the oxide thickness increases uniformly, as surface roughening leading to pore formation begins at higher potentials [25]. The rate of voltage increase in Fig. 1 is approximately proportional to the oxide growth rate, because of the nearly constant electric field in the anodic film. Estimates of the anodizing efficiency, defined as the fraction of oxidized Al+3 ions contributing to film growth, were obtained from the slopes of the potential transients and measurements of the electric field at various current densities [19]. The calculated efficiencies increased from 32% to 52% with current density, the range typically found during anodizing in H3PO4 and other acids [26–29]. Fig. 1 shows that the direction of the force change was tensile at current densities below 3 mA/cm2, and compressive at higher current densities. Previous in situ stress measurements during anodizing of Al thin films in both acidic and neutral pH solutions yielded similar trends with current density, including crossover from tensile to compressive stress at around 3 mA/cm2 [19,30]. In this article we refer to the force per width change during anodizing as the “anodizing force.” 3.2. Stress Distributions in Anodized Aluminum At the conclusion of anodizing, the current was set to zero, and stress monitoring continued while the anodic film dissolved on open circuit in the phosphoric acid bath. The force per width measured during oxide dissolution is shown in the main panel of Fig. 2, for the anodizing to 20 V experiments of Fig. 1. In addition, the inset shows the open circuit force transients after anodizing at 5 mA/cm2 to 10 and 20 V. The force per width values in both figures are relative to those before anodizing; thus, the initial force values correspond to the force change during anodizing. The force measurements were carried out until dissolution of the anodic film was complete, at the times marked on the force curves. The overall force change during dissolution was compressive at low current densities where anodizing produced tensile stress, and tensile at higher current densities generating compressive stress. However, at current densities of at least 5 mA/cm2, the force at first decreased sharply to a minimum value at about 1 min, and then increased during the remainder of the dissolution period. This nonmonotonic initial behavior is discussed in detail below. Previously, we presented evidence that the force per width change during dissolution can be interpreted in terms of removal

(2)

0

where the coordinate direction x is parallel to the sample surface, and the z axis extends into the metal. Anodizing was performed at a range of current densities from 2 to 12.5 mA/cm2 in 0.4 M H3PO4 up to 20 V at room temperature, using a two-electrode power supply (Keithley 2400) and a platinum wire counter electrode. After completion of anodizing, the current was set to zero, and the anodic oxide allowed to dissolve at open circuit. Residual stress profiles in anodic oxide films were determined by monitoring stress changes during dissolution. The procedures involved in the open-circuit dissolution experiments are described in a previous communication, along with evidence supporting the validity of this approach to measure residual stress distributions [22].

Fig. 1. Force per width (solid curves) and potential (dashed curves) measured during anodizing to 20 V at the indicated current densities in mA/cm2.

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Fig. 2. Force per width measured during open circuit dissolution after anodizing. Main panel shows force curves after anodizing to 20 V at the indicated current densities in mA/cm2. Inset shows force curves after anodizing to 10 and 20 V at 5 mA/cm2. Forces are relative to those at prior to anodizing. Vertical marks on the force traces represent complete anodic oxide dissolution.

of residual stress in the anodic oxide [22]. Anodic films formed at the same conditions were dissolved at different rates by changing the bath acid concentration after anodizing. Hypothetical residual stress distributions were calculated from the time dependences of the force and thickness during dissolution (as described below), and found to be the same within experimental reproducibility. This implies that temporal stress relaxations do not contribute significantly to the open-circuit force transients; that is, the force change depends on dissolved oxide thickness but not intrinsically on time. Thus, the open-circuit force measurements in fact reveal residual stress distributions in the anodic films. Additionally, several other possible artifacts in the open-circuit and anodizing force transients were considered, and shown to be unimportant: relaxation of electrostriction stress at open circuit, removal of preexisting internal stress in the metal samples, stress generation during dissolution, and thermal expansion mismatch stress due to temperature increases during anodizing. Full details are available in Ref. [22]. Following the interpretation of the open-circuit force change as residual stress removal, the term “oxide force” as used here denotes the negative of the force per width change during dissolution, and represents the residual in-plane stress in the oxide integrated through its thickness. From Fig. 2, the net oxide force was tensile below 3 mA/cm2 and compressive at higher current density. The dissolution measurements in Fig. 2 reveal that nonzero overall force change resulted from anodizing followed by complete oxide removal. As for the oxide force, the dependence of the overall force change on current density indicates that it results from anodizing [22]. The force measured after dissolution is attributable to stress at the metal-oxide interface, which may be localized in either the metal substrate or in the thin (3 nm thick) oxide remaining after open circuit dissolution. Hence, the overall force per width change will be referred to as the “interface force” generated by anodizing. The interface force was compressive at 2 mA/cm2, nearly zero at 3 mA/cm2, and increasingly tensile at higher current density; thus, it follows the opposite trend with current density as that of the oxide force. Stress distributions in the oxide layers were calculated from the time dependence of the open circuit force change [22]. Using the “re-anodizing” method established in the anodizing literature, the oxide thickness after a given dissolution time was determined from the initial voltage measured upon reapplication of current [31,32]. Time intervals were identified corresponding to 1 nm increments of dissolved thickness, and the average

residual in-plane stress in each such increment was determined from the corresponding force and thickness changes. Fig. 3 shows the stress distributions obtained in this manner. At low current densities, stress profiles were approximately uniform within experimental scatter. However, at current densities higher than about 5 mA/cm2, the profiles exhibited elevated tensile stress of 2 to 6 GPa within about 2 nm of the oxide surface, corresponding to the initial compressive deflections in Fig. 2; the stress become uniform at depths greater than 2 nm. The uniform stress in the bulk of the oxide decreased from 0.3 GPa at 2 mA/cm2, to 1.5 to 2.0 GPa at 12.5 mA/cm2. The inset shows the stress profiles at 5 mA/cm2 for 10 to 20 V. The near-surface tensile stress decreases with the final voltage in this range. The prominence of near-surface tensile stress at small thickness and large current density suggests that it is associated with the initial application of anodizing current. The mechanism responsible for the tensile surface layer was investigated with stress measurements after pulses of anodizing current. These experiments employed anodic oxides formed to 83 V. According to the open circuit force transient shown in the inset of Fig. 4, compressive oxide stress in these films is concentrated near the solution interface, such that stress is completely removed after about 3 to 4 min dissolution time. Thus, a nearly stress-free anodic film was produced by anodizing to 83 V followed by 400 s open circuit dissolution. Then a 2.7 s current pulse at 5 mA/cm2 was applied, followed by a 400 s dissolution period, a second 2.7 s current pulse, and a final dissolution step. The two open circuit force transients are shown in the main panel of Fig. 4. Each transient comprises an initial compressive shift followed by tensile recovery, with an overall force change of nearly zero. Interpreting the transients as removal of residual oxide stress indicates that each pulse generated a tensile-compressive stress bilayer, composed of a near-surface tensile stress and an underlying compressive layer, with zero net force contributed by the bilayer. The force transients in Fig. 4 strongly resemble the initial non-monotonic behavior after anodizing to 10 and 20 V at the same current density (inset of Fig. 2). Apparently, the tensile surface layer in Fig. 3 is part of a tensile-compressive bilayer produced by the initial application of anodizing current. As the bilayers contain zero net force, their formation is not detected in the present anodizing force measurements (Fig. 1). It might be possible to capture bilayer formation with fast stress measurements at the time scale of capacitive charging. Creation of near-surface stress bilayers likely involves transfer of volume from the oxide surface to the subsurface region,

Fig. 3. Stress-depth profiles calculated from open circuit force per width measurements. Main panel shows stress profiles after anodizing to 20 V at different current densities. Inset displays stress profiles after anodizing to 10 and 20 V at 5 mA/cm2.

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Fig. 4. Open circuit force evolution after pulses of anodizing current. After first anodizing to 83 V at 5 mA/cm2, the oxide was dissolved for 400 s at open circuit, and then a 2.7 s pulse of anodizing current was applied. An additional cycle was performed consisting of the same dissolution and final anodizing steps. The inset shows the open circuit force transient after anodizing to 83 V.

generating tensile and compressive strains of equal magnitude in both layers. The increase of the stress level of the bilayer with current density suggests that it is generated by electric fieldinduced jumps of anions, either oxygen ions or incorporated phosphate ions. We speculate that the outcome of this process would be creation of negative oxide space charge, because it is likely that solution-phase adsorption processes would rapidly equilibrate the surface charge produced by ion transfer. De Witt and Thornton recently reported an electrostatic analysis of anodizing, pointing out that negative space charge layer may be necessary to generate the electric field in the oxide required to pass the applied current density [7]. Direct evidence of negative nearsurface space charge in anodic films has been found through electrostatic force microscopy [33,34]. Therefore, we suggest that the stress bilayers are associated with creation of negative space charge at the outset of anodizing. 3.3. Relationship of Interface Volume Change and Stress Generation The remainder of this article explores the relationship between stress generation and volume change at the oxidesolution and metal-oxide interfaces. The current density dependences of the oxide, interface and anodizing force components are compiled in Fig. 5a. Since the tensile surface layer was accompanied by equal underlying compressive force, it did not contribute to these force changes. As already noted, each force component changed monotonically with current density: the oxide and anodizing force become more compressive at higher current density, while the interface force changes in the opposite direction. Both the oxide and interface force components are near zero at 3 mA/cm2. Interfacial volume changes can be calculated from measurements of anodizing efficiency, film composition, and ionic conduction rates. The necessary data are not presently available for anodic alumina films formed in the phosphoric acid solutions of this work. However, as mentioned above, the anodizing force measured in various solutions exhibits similar dependences on current density: tensile below 2 to 4 mA/cm2 and compressive at larger current density [30]. Therefore, we calculated interfacial volume changes during anodizing in 0.4 M H2SO4, for which detailed information on film composition is available [28]. Fig. 5(a) confirms that the current density dependence of the anodizing force measured in sulfuric acid closely resembles that in phosphoric acid. The stoichiometry of the anodizing reaction in sulfuric acid can be represented as

Fig. 5. (a). Effect of current density on force components. Force per width measurements in 1.0 M H2SO4 were reported by Van Overmeere [30]. (b) Volume changes associated with interfacial processes during anodizing in 0.4 M H2SO4.

2ð1 þ xÞAl þ 3eH2 O þ 3xeSO2 4 þ3 ! eAl2 O3 þ xeAl2 ðSO4 Þ3 þ 6eHþ þ 2ð1 þ xÞð1  eÞAl  þ 6ð1 þ xÞe

(3)

where e is the anodizing efficiency and x is the ratio of moles of Al2(SO4)3 to moles of Al2O3 in the anodic film. Zhou et al. reported values of e and x determined from Rutherford backscattering spectrometry measurements of oxygen and sulfur content [28]. While Zhou et al. used somewhat longer anodizing times compared to our experiments, efficiency measurements during H2SO4 anodizing indicate only a weak dependence on anodizing time [26]. The total volume change during anodizing, normalized with the volume of metal consumed, includes contributions from oxide and sulfate formation and metal consumption,

DV an e Vox xe VA ¼ þ 1 DV met 2ð1 þ xÞ VAl 2ð1 þ xÞVAl

(4)

Here VA and Vox are the molar volumes of Al2(SO4)3 and Al2O3, respectively 43 and 11 cm3/mol. Calculations from Eq. (4) reveal a significant contribution of the large oxyanion salt to the film volume, ranging from 7 to 19% with increasing current density. The often-reported “volume expansion” due to anodizing is DVan/ DVmet+ 1 [10]. The overall volume change during anodizing is the sum of contributions from processes at the metal and solution interfaces. The volume change at the metal-oxide interface is the volume of Al2O3 formed by the O2 ions migrating to the interface, less the consumed metal volume. On the basis of oxidized metal volume, the volume change is

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DV mo tO Vox ¼ 1 DV met 2 VAl

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(5)

where VAl is the molar volume of Al metal atoms and tO is the oxygen transport number in the anodic film. The oxygen transport number is the fraction of the current density carried by oxygen ion migration, and was determined by interpolating measured values [35,36]. The anodizing volume change includes contributions from both DVmo and the volume change due to reactions at the oxidesolution interface, DVos . Thus, the solution interface volume change is

DV os DV an DV mo ¼  DV met DV met DV met

(6)

The current density dependences of the calculated interface volume changes DVmo and DVos are displayed in Fig. 5 (b). DVmo decreases with current density, because of the relatively slow increase of tO, and hence the oxide formation rate, with current density. The interface volume change is positive below 5 mA/cm2, as the volume of formed oxide exceeds the volume of metal consumed. At higher current densities, DVmo is negative, since oxide volume is produced more slowly than the rate of metal volume consumption. Because the interface remains continuous, volume formation (removal) at the metal interface requires bulk motion of oxide away from (toward) the metal. DVos exhibits the opposite trend to DVmo: oxide is destroyed at the solution interface below about 3 mA/cm2, and new oxide is formed at the interface above this current density (Fig. 4). DVos increases with current density because the film formation efficiency e, which controls the film formation rate, increases more rapidly than the transport number tO, which controls the rate at which oxide “lattice” is destroyed by inward migration of oxygen ions. The interface volume changes and bulk motion velocities are depicted schematically in Fig. 6. Comparison of Fig. 5(a) and (b) reveals parallel trends between the interface volume changes and force components. The oxide force and interface force are always compressive (tensile) at current densities for which the oxide-solution and metal-oxide volume changes are positive (negative). The relationship of interface volume change and stress can be understood in terms of transport of oxygen vacancy-type defects in the oxide, as are

Fig. 6. Illustration of interface volume changes, stress components and oxide bulk motion. Low and high current density regimes are shown in the upper and lower portions of the figure, respectively. Dashed black arrows represent reactions and transport process, with the arrow lengths indicating their relative rates. Compressive and tensile interface stress generation is depicted by black and white squares, respectively, with the red arrows suggesting the bulk oxide motion accompanying internal oxide formation or destruction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

found in thin passive oxide films [37]. Oxygen vacancies are produced by Al oxidation at the metal interface, and migrate toward the solution interface, where they are consumed by incorporation of oxygen and electrolyte anions. Anodic aluminum oxide is amorphous, but large concentrations of vacancy-type defects are suggested by several observations, such as intense photoluminescence attributed to electrons associated with oxygen vacancies (F+ centers) [38], oxygen isotope studies revealing exchange between transported and structural ions [25], and the low density of anodic films compared to crystalline oxide [39,40]. At high current densities producing compressive stress, the oxygen and anion incorporation rate exceeds the vacancy flux. Most of the excess oxide formation results in film growth at the surface. However, some of the oxygen and electrolyte anions diffuse into the film, where internal formation of new oxide generates compressive stress and outward bulk motion of oxide (Fig. 6). In view of the large elastic modulus of anodic alumina (100 GPa) [41,42], only a small rate of internal oxide formation is necessary to account for the measured stress levels in Fig. 3. At low current densities, the volume of oxygen vacancies reaching the surface by migration is greater than that of incorporated oxygen and electrolyte anions. Most of the excess vacancies are annihilated at the surface, causing the interface to recede toward the metal. On the other hand, some vacancies annihilate internally, producing tensile stress and inward bulk motion of the oxide. Analogous processes explain stress generation at the metal interface. The net loss of volume at high current density would lead to vacancy production. Annihilation of these vacancies results in tensile stress, along with bulk motion of the oxide toward the metal. At low current density, the overall production of interface volume results in compressive stress, and outward bulk motion of the overlying oxide layer. Suo et al. used a similar mechanism to explain stress generation at the metal-oxide interface during high-temperature oxidation [43]. Compressive oxide stress has been invoked often in the literature to explain pore formation and self-ordering behavior, either through elastic repulsion between pores [10,44],or by viscous flow of oxide [5,12,14,17]. Oxide flow was first demonstrated by observing stress relaxation of thin Al wires under tension while anodizing [8]. In porous alumina, oxide flow was detected experimentally by the retention in the oxide of tungsten tracers that had been introduced into the Al substrate [12]. Without flow, the W+6 tracer ions migrate through the oxide and dissolve into solution; flow enhances tracer retention because its direction opposes that of migration. For porous anodic films formed in sulfuric or oxalic acid, tracer retention revealed flow at current densities higher than about 2 mA/cm2, at which our results suggest that the oxide stress is compressive [28,29]. At lower current densities, where the oxide stress should be tensile, the loss of tracers indicated the absence of flow. Significantly, hexagonally ordered pore arrays were produced only at higher current densities associated with flow and compressive oxide stress, while at low current densities the porous layers consisted of irregular, branched pores. Irregular porous oxide morphologies are also produced by anodizing in chromic acid and borax solutions, where tracer measurements indicate the absence of flow [45,46]. The oxide stress in these films may not be compressive, because they contain negligible concentrations of incorporated electrolyte anions. Our simulation of oxide flow accurately predicted the tracer profiles, and showed that flow was driven by compressive oxide stress near the solution interface [5]. Therefore, flow driven by compressive oxide stress seems to play a direct role in pore formation and selfordering. The present correlation of stress and interface volume change leads to a simple criterion that determines whether compressive

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stress is generated in the oxide, which helps define conditions where self-ordered films can be formed. Compressive stress is produced when the volume change at the oxide-solution interface is positive, according to Eq. (6). This is the case when a modified anodizing efficiency emod is larger than tO,   e xVA 1þ emod  tO ¼ (7)  tO > 0 1þx Vox The modified efficiency is as much as 17% greater than the usual anodizing efficiency e, because emod includes the effect of incorporated anions on the interface volume change. The significant effect of contamination on the interface volume change, and hence oxide stress, should be typical of most anodizing baths, which are generally solutions of acids of large polyatomic anions. Therefore, anion incorporation seems to play a direct role in controlling oxide stress, and consequently flow and self-ordering. This may help explain the strong influence of anion type on the pore diameter and separation distance [10,47]. It may be possible to apply Eq. (7) to rationalize selfordering behavior during anodizing of other metals. For example, in systems such as anodic ZrO2 or HfO2 where tO is close to unity [48], formation of self-ordered porous films should require bath compositions and current densities where the efficiency e or the contamination level are particularly high. The criterion of positive volume change at the oxide solution interface, as expressed by Eq. (7), may explain the empirical association of self-organized porous alumina films with critical volume expansions of about 1.4 [10]. As mentioned above, volume expansion is directly related to the anodizing volume change in Eq. (4), which in turn correlates with the oxide-solution interface volume change (Fig. 5b). 4. Conclusions Stress in anodic oxide films is thought to control the spontaneous emergence of hexagonally-ordered arrays of cylindrical pores during anodizing. To determine the factors controlling oxide stress, we characterized through-thickness distributions of in-plane stress, in approximately 20 nm thick oxide films formed by anodizing aluminum in phosphoric acid. The stress distributions were obtained by in situ measurement of stress and thickness transients during open-circuit dissolution of the anodic oxide. Separate stress generation processes were identified in the oxide and at the metal-oxide interface. For films formed to the same potential of 20 V, the oxide stress decreased from tensile at low current density to compressive at high current density, with zero stress at about 3 mA/cm2. The interface stress exhibited the opposite trend, increasing from compressive to tensile with higher current density. For comparison to the stress measurements, volume changes associated with reactions and transport processes at both the metal-oxide and oxide-solution interfaces were calculated, using experimental information on film composition, anodizing efficiency and oxygen ion transport number. The calculations revealed that in general, compressive stress was generated at either interface when the volume change was positive, and tensile stress was produced when the volume change was negative. The current density dependences of interfacial stress generation are determined by those of the efficiency, transport number, and the level of contamination by electrolyte anions. These results lead to a simple mathematical criterion for whether compressive stress in the oxide is produced by anodizing. Previous tracer studies and model calculations indicate that compressive stress is required for oxide flow, which in turn is necessary for formation of self-ordered porous films.

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