Mechanistic Aspects of the Self-Organization Process for Oxide Nanotube Formation on Valve Metals

Current-time curves for the first 1 hour during the anodization at in solution are shown in Fig. 2 for the anodization of Ti, , and Zr. For all metals, the current decreases with the time due to the increase of the diffusion length for the ionic species in the electrolytes.²¹ The magnitude of the current is the largest for Zr, followed by , and followed by Ti.

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Figure 3a1, b1, and c1 shows surface SEM images of initial layers obtained after short time anodizations (2 to ) for Ti, Zr, and , respectively, which consist of small and random pores. With the pore growth, these pores become self-organized, and finally an oxide nanotube structure is produced as Fig. 1d. As shown in Fig. 3a2–c2 for long time anodization (1 to ), the diameter for the ordered nanotube is larger than that for the pores in the initial layer (Fig. 3a1–c1). In Fig. 4 we present a more detailed analysis of the initial stages for the titanium case. Figure 4a shows a cross section of a sample anodized for a short time at . Clearly a two-layer structure is apparent with a perforated top layer (former compact layer) and underneath the first formation stage of the organized porous layer.

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To investigate the significance of the top layer for the self-organization process a second set of samples was preanodized in fluoride-free electrolyte at to form a compact ≈50 to 60 nm thick oxide layer; then, these samples were exposed, in the fluoride containing electrolyte, to the same anodization sequence as samples in Fig. 4a. Figure 4b and 4c shows the cross section morphology of these samples after 3 and anodization. Figure 4d and 4e shows for both treatments (not preanodized and preanodized) cross sections after of anodization in fluoride containing electrolyte, and Fig. 4f the corresponding polarization behaviors. From a comparison of the two cases a very clear picture is obtained. Obviously the presence of a compact preanodization layer does only slow down the self-organization process in time but does not affect the morphological stages of the final geometry of the ordered structures (as after in both cases an thick self-organized layer is present (Fig. 4d and 4e), growing at approximately the same current density (Fig. 4f) into the substrate material). Please note that in Fig. 4e still some patches of the initial layer can be found; these typically fully disappear (are dissolved) after of anodization. The formation of these layers and the ordering mechanism of the pores can be explained as follows.

The early stage of the self-organized nanotube formation is shown in Fig. 5, which corresponds to Fig. 1a, 1b and 1c. After the formation of the passivation barrier layer (Fig. 5a), several breakdown sites are randomly produced on the surface (Fig. 5b). In Fig. 5, the deeper pores (A, C) and the shallower pore (B) are expressed as "strong pore" and "weak pore" hereafter, respectively. When the voltage is applied to the initial layer in Fig. 5b, the oxidation starts at the oxide/electrolyte interface and oxidation distance is linearly determined by the voltage. Considering the layer morphology, the oxidation frontier is the tip of the pore bottom; it is the closest to the metal substrate where local acidification is highest and electrochemical oxidation is therefore going to occur preferentially. In order to compare the oxidation rates between the pores, the oxidation area from the bottom tip is schematically shown with a circle of broken lines in Fig. 5c, whose diameter is identical for the three pores. The active area overlapping between two neighboring pores is divided into halves so that these divided areas always belong to the closer tip. Comparing the area available for oxidation (equidistant from a breakdown point) between the strong pore (A) and weak pore (B), the strong pore clearly has a larger aria available for oxidation because the strong pore is deeper in the substrate material than the weak pore. Thus, the amount of substrate material available for electrochemical oxidation at the strong pore is larger than for the weak pores, and as a result, a large amount of ions are produced according to Eq. 1. As seen from Eq. 2, the existence of ions accelerates the chemical dissolution of oxide. Therefore, the strong pore becomes deeper and deeper. The weak pore generates a smaller amount of ions, and its growth becomes slower and slower. Finally, the weak pore stops to grow when the whole neighbor metals are already oxidized by the near strong pores (Fig. 5d).

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This pore selection process is summarized by the autocatalysis sequence shown in Fig. 6. The higher oxidation range (and rate) of a deeper pore induces a formation of more ions. The large amount of ions accelerates the dissolution of oxide, resulting in an accelerated advancement of the deeper pore. The combination of these steps results in the self-organization of the pores. The autocatalysis system was already reported for the difference of reactions between the tube bottom and top.⁵ The discussion in this section shows that the autocatalysis appears not only in the depth direction but also at the same depth level.

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The direction of the pore growth is also affected by the neighboring pore. For example, in pore (A) in Fig. 5, the oxidation area on the left side is larger than on the right side, because some area on the right side is overlapped against pore (B). As a result, the oxidation and production are larger on the left side in pore (A), leading to the bending of the pore (A) into the left side in Fig. 5d. This bending growth produces a wormlike structure. When the competition for oxidizable area is equilibrated, the formation of the wormlike structure finishes and all the remaining pores grow straight until the end of anodization, thus producing a tubular morphology.

The final diameter of the nanotube is closely related with the anodic growth factor of valve metals, i.e., the growth rate of layer thickness of a compact oxide against the voltage. In the case of compact oxide layer formation on valve metals, it is known that for electrochemical oxidation the limiting oxide thickness increases linearly with the applied voltage, e.g., for Ti anodization the growth rate is approximately. . After a certain voltage the oxide layer thickness reaches the limiting value, the layer growth, i.e., electrochemical oxidation virtually stops.

Figure 7 shows the schematic drawing of the cross section of the tube bottom in nanotube formation, which is drawn without the initial layer in order to simplify the discussion. As in Fig. 5, the frontier spot for anodization is the tip of the tube bottom. The maximum oxidation length follows the growth rate of compact oxide formation. As indicated in Fig. 7a, this value appears as the radius of a hemisphere for the oxidizable area. Here, it should be noted that the diameter of the hemisphere is 2 times as large as the oxidation length, i.e., for Ti oxidation, as indicated in Fig. 7a (we call it "2-times relationship," hereafter). The relationship between the growth rates of compact oxide and the diameter of self-organized nanotubes is plotted in Fig. 8. The broken line shows the 2-times relationship. For Ti ⁸ and ,²¹ the rates for the tube diameter are two times larger than the values for compact oxides (a little deviation for from the broken line may come from the difference between the inner and outer diameters, and the standard deviation shown as an error bar is due to the nanotube formation on two size scales in alloy anodization¹⁸). Apart from nanotubes, the formation of porous alumina hole-array should basically have the same oxidation behavior with Fig. 7a, in which the diameter of the oxidation area is 2 times larger than the value for the compact layer. In the porous alumina case, the pore distance has the same meaning as the nanotube diameter, and it follows the 2-times relationship as shown in Fig. 8 in any electrolytes such as , , etc.^28–31 The relationship for porous alumina strongly supports that the final diameter of nanotubes basically becomes 2 times as large as the oxidation length. However, for Zr,¹¹ the growth rate for tube diameter negatively deviates from the 2-times relationship. This may be attributed to the fast chemical dissolution rate of oxide; it has been demonstrated in previous work that the fast chemical dissolution of Zr oxide leads to a larger current and fast nanotube growth.²¹ As explained in the first section, the nanotube formation proceeds by a combination between an electrochemical oxidation (Reaction 1) and chemical dissolution of oxide by fluoride ions (Reaction 2). When the dissolution is rather slow compared to the oxidation, the oxidation reaction has enough time to reach the maximum oxidation length (Fig. 7b), and therefore the diameter follows the 2-times relationship. Hence, it may be argued that in the case of a fast oxide dissolution, the position of tube bottom proceeds to the depth direction before the oxidation reaches the maximum value of diameter as shown in Fig. 7d. Therefore, the diameter becomes smaller than the expected value from the s relationship.

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A remarkable feature about nanotubes growth is that the oxide structure originating from the wormlike porous structure changes into a nanotube morphology by formation of gaps between the tubes. (If gaps are not produced, the structure is not tubular but a hexagonal hole-array.³²) One of the main factors for the generation of gaps is the mechanical stress in the oxide tubes. As for a formation of compact oxide layer by anodization of valve metals, the mechanical stress was well investigated.^33–39 The main reasons causing stress is an electrostriction and the volume expansion from the metal to the oxides. The stress is classified into compressive stress and a tensile stress depending on the transport number of the anion and cation in the oxides.³⁷ The growth of anodic oxide layer takes place at the metal/oxide and the oxide/electrolyte interfaces. When the transport through the oxide is mainly anionic, the volume of oxide formed at the metal/oxide interface, and the oxide shows a compressive stress. In contrast, when the transport is mainly cationic, vacancies are produced in the metal at the metal/oxide interface, producing free volume. Thus, the metal/oxide interface shrinks and tensile stress is generated. Also in the case of oxide nanotubes, these stresses should be generated, because the oxidation mechanism is basically the same as for compact oxide formation. In order to discuss the stress at the metal/oxide interface, the volume expansion is schematically drawn in Fig. 9, based on the marker experiments by Garcia-Vergara et al. for porous alumina formation.⁴⁰ As clarified in our previous report,²¹ the volume expansion from alloy to zirconium titanate occurs only one-dimensionally to -axis into 1.68 times, which is the vertical direction to the plate. In Fig. 9, five marker lines from (A) to (E) are drawn in the alloy before anodization with a constant interval. The broken and the solid lines show the positions of the atoms before and after oxidation, respectively. When the metal is oxidized, volume expansion from the metal to the oxide is generated, and the atoms move to the positive direction of the -axis. For the line (B) (initial stage of oxidation), the oxidation starts at the bottoms of the tubes, and the solid line slightly bends to -axis. With a progress of oxidation [lines (C) and (D)], the bending becomes larger due to the increase of oxidized length in -direction, and the bent location shifts to the center between the two tubes. As the curvature of the solid lines shows, the largest stress is generated at the metal/oxide interface. The stress reaches the maximum at the center between the tubes as shown with line (E). Furthermore, the oxidation proceeds to the side closer to the surface, that is, the atoms locating at the right side compared to the gap are oxidized from the right side and vice versa, as indicated with the arrows in Fig. 9. Therefore, the center between the two tubes can be oxidized by either of the neighboring tubes, i.e., this location has two different oxidation directions, and considerable stress is generated at the center. This stress leads to a generation of gaps between the pores, resulting in a transformation of the morphology into tubular.

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Nanotube multilayer stacks were in previous work produced by a combination of two anodization steps and stopping an anodization between them.^{16, 22} Figure 10 shows the SEM images of the zirconium titanate oxide nanotube multilayer produced by the anodization at for in solution. As shown in Fig. 10a, two nanotube layers are produced, in which the upper and lower layers are produced in the first and second anodization steps, respectively. In contrast to multilayers grown on pure Ti,¹⁶ formation of new nanotubes in the lower layer starts in the gaps between the existing tubes in the upper layer (Fig. 10b).²²

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This result shows that new tube formation starts in the gaps, indicating that the gaps in the case of alloys are more electrochemically active than the tube bottom. In order to consider the meaning of "electrochemically active," the reactions in the nanotube formation should be discussed. We already clarified for a single nanotube layer formation that the nanotube formation occurs due to a combination of an electrochemical oxidation of metals (or alloys) and chemical dissolution of oxide by fluoride ions expressed as Eq. 1, 2, respectively. As discussed previously, the oxidation reaction and the oxide thickness stop in fluoride-ion-free electrolytes, when the oxide thickness reaches the maximum value determined by the growth rate. In contrast, in the case of nanotube formation in ion containing electrolytes, the oxide thickness at the tube bottom is smaller than the limiting value, because the ions produced at the tube bottom in Reaction 1 result in a thinning of a bottom oxide due to the chemical dissolution of oxide bottom according to Eq. 2. The above anodization process in nanotube formation shows that the more electrochemical active point should have a smaller oxide thickness. Therefore, in the formation of nanotube multilayer, for sufficiently fast dissolving oxides as for the case it is predicted that the thickness of the bottom oxide at the gaps is smaller than the oxide at the tube bottom (and the limiting value), and new tube formation starts in the gaps (Fig. 11a).

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In order to further elucidate the gaps and bottom formation, a sealing step was conducted after formation of the nanotube layer. In this step, the nanotubes produced at for in electrolyte are oxidized again at in a electrolyte (F-free). As shown in Fig. 11b, the oxide thickness at the gaps is expected to increase up to the limit value as in the compact oxide formation. Figure 12a shows the current-time curve during the sealing step. The anodic current was first observed and then decreases exponentially, which is a typical behavior for a formation of a compact oxide layer.^{33, 41} As shown in Fig. 12b, before the sealing, the bottom part of the nanotube layer has a curved morphology reflecting the tube bottom. Figure 12c shows an area (scratched with a knife) of the bottom part of the layer after the sealing step. A new layer is produced on the nanotube bottom, and covers the whole part of the bottom. The increase of the oxide thickness occurs not only below the gaps but also below the tube bottoms, since the oxide thickness of the tube bottom is smaller than the limiting value; the thickness of the tube bottom is ,²¹ and the limiting value is according to the potential value of and the growth rate of compact oxide for the alloy at.⁴² Consequently, the thickness of the oxide reaches both at the gaps and at tube bottoms. The sealed sample is expected to be no more active for further electrochemical oxidation, because the oxide thickness reached the limiting value.

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In order to compare the oxidation behavior, in other words, to determine how active the sealed and nonsealed samples are, a second anodization step in fluoride containing electrolyte was conducted for both samples. Figure 13a and 13b shows the current-time transient during the first and the second anodization steps, respectively. In the first step, the current gradually decrease with time due to the increase in the diffusion length of the ions.²¹ In the second step for the nonsealed sample, the current first exponentially decreases to in the same manner as observed for a compact oxide formation, and then increases to a steady level at , i.e., the current returns to a similar level as in Fig. 13a. The difference in the anodic current between in Figs. 13a and 13b is explained by the growth of the nanotube in the initial stage in Fig. 13b, which causes the increase in the diffusion length of the ions, i.e., affects the rate-determining step of the tube growth process.²¹ In the case of the sealed sample, the anodic current is very small in the initial stage, and gradually increases with time, finally reaching almost the same value as in the case of nonsealed nanotubes. SEM images of nanotubes for the nonsealed and for the sealed sample are shown in Figs. 13c and 13d. Also for the sealed sample, a new nanotube layer is produced underneath the first one and initiated at gap locations, even though the gaps are sealed with oxide layer. This result can be explained as follows. For the nonsealed sample, the oxide thickness at the gaps is smaller than the limit value. The current decrease in the very initial stage in Fig. 13b is ascribed to the slow dissolution rate of the oxide owing to the low concentration. Then, the anodic current increases because the oxide thickness becomes smaller than the limiting value due to the increasing dissolution rate of oxide accelerated by the produced ions. Alternatively, the current increase may be also ascribed to the increase of the electrode area with a progress of anodization due to the shape of the curve of the bottom (see Fig. 11a). In the case of the sealed sample, although the gaps are sealed with oxide layer by the sealing step, the oxide wall very slowly dissolves to the electrolyte by a chemical reaction into the containing electrolyte (the dissolution rate was reported as ²¹). Thus, the oxide thickness becomes slowly smaller than the limit value of . The applied voltage works to supply the thickness of the oxide up to and the autocatalytic cycle of Fig. 6 is restarted again. To explain, why the second layer starts at the gaps, even in the sealed case, one may consider a higher chemical dissolution of the oxide at the gaps, because of a higher internal energy due to large stress at these locations as discussed above. Therefore, whether, or not the second layer formation starts at gaps or through the bottoms is predicted to largely depend on the oxide layer thickness in the gaps in relation to the stress enhancement of the chemical oxide dissolution rate.

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