A. Structure and morphology

Figure 1 shows XRD profiles of as-anodized samples (a) and those heated up to 1058 K (b) and 1128 K (c) in an argon atmosphere. (The latter two are those used for the TG-DTA measurements (Sec. III. B), where the heat treatment was given.) The broad maxima around 30° and 54° in the profiles of as-anodized samples (a) and those annealed up to 1058 K (b) (in the lower frame) indicate that they are essentially amorphous. After annealing up to 1128 K (c) (in the upper frame), the amorphous oxide transformed into a crystalline phase. All the peaks, including small ones, are identified as those corresponding to the low temperature phase, orthorhombic β-Ta₂O₅^{Reference Roth, Waring and Parker20}; the largest five peaks of them correspond to 100 (2θ = 22.9°), 0$\underline{1} \underline{1}$1 (28.4°), 1$\underline{1} \underline{1}$1 (36.8°), 200 (46.7°), and 2$\underline{1} \underline{1}$1 (55.5°). The crystallization behavior is in good agreement with the result by Gonçalves et al.^{Reference Gonçalves, Migowski, Wender, Eberhardt, Weibel, Sonaglio, Zapata, Dupont, Feil and Teixeira15} At temperatures below 1058 K, the amorphous structure was virtually maintained, although weak diffraction peaks corresponding to 100, 0$\underline{1} \underline{1}$1, and 1$\underline{1} \underline{1}$1 of β-Ta₂O₅ appeared, as indicated by arrows. It should be noted that the shape and intensity of the broad diffraction maxima around 30° in a profile (b) clearly differ from those in (a), suggesting that some changes occurred in the amorphous structure during the annealing. Detailed discussion is given in Sec. III. D on the basis of radial distribution function analyses.

FIG. 1.

XRD profiles of (a) as-anodized and (b, c) annealed Ta–O NTs: (b) up to 1058 K and (c) up to 1128 K.

Figure 2 shows bright-field electron-microscopy images and selected-area electron diffraction patterns of as-anodized samples (a, a’), and those annealed up to 1058 K (b, b’) and 1128 K (c, c’). The as-prepared samples are amorphous and have uniform NT structures with inner and outer diameters of ∼80 and ∼170 nm, respectively. Samples annealed up to 1128 K (c, c’) fully crystallized into Ta₂O₅ with nanosized grains, retaining the NT morphology.

FIG. 2.

Bright-field electron-microscopy images of as-anodized Ta–O NTs (a), and those annealed up to 1058 K (b) and 1128 K (c). (a’–c’) The corresponding selected-area electron diffraction patterns.

Figure 3 shows a low-energy portion of characteristic x-ray spectra observed by TEM-EDS. The intensities are normalized to that of Ta M_α at around 1.75 keV. The characteristic x-rays of C and Cu come from contamination and from the grid, respectively. The S K_α peak was observed in (a) and (b), but not in (c). The intensity of S K_α peak is almost unchanged from (a) to (b), i.e., by annealing up to 1058 K. It is also the case for the O K_α peak. After annealing up to 1128 K (c), S K_α peak disappeared and the intensity of O K_α peak decreased, indicating that impurity sulfur and excess oxygen were released on crystallization. The presence and release of impurity sulfur and excess oxygen were also reported by Gonçalves et al.^{Reference Gonçalves, Migowski, Wender, Eberhardt, Weibel, Sonaglio, Zapata, Dupont, Feil and Teixeira15} Figure 4 shows intensity line-profiles of the characteristic x-rays of Ta, O, and S obtained across a single nanotube in (a) an as-anodized sample and (b) a sample annealed up to 1058 K. The position, x = 0, corresponds to the center of the nanotube, as shown in the corresponding BFI (a’) to the profile (a). The arrow in (a’) indicates a trace by beam-scanning. The thickness near the edges of the NTs is too small to detect sufficient x-ray intensity by line-scanning. The intensities of O K_α and S K_α lines normalized to that of Ta M_α except the edges are almost constant. The relative intensities of O K_α and S K_α to that of Ta M_α from an edge area were observed to be comparable to those from an entire nanotube. Therefore, oxygen and sulfur are not concentrated near the surfaces of a nanotube but distributed homogeneously.

FIG. 3.

Energy-dispersive x-ray spectra at lower energy region for the anodic Ta–O corresponding to Fig. 2. (a) As-anodized Ta–O NTs and those annealed (b) up to 1058 K and (c) 1128 K. These spectra are normalized to the peak height of Ta M_α.

FIG. 4.

Line-profiles of characteristic x-ray intensity obtained across a single nanotube of (a) as-anodized Ta–O and (b) that annealed up to 1058 K. Intensity of O K_α and S K_α normalized to that of Ta M_α is shown in the upper frame. (a’) The BFI of the as-anodized nanotube corresponding to the profile (a) taken after beam-scanning. The arrow indicates a trace by beam-scanning.

B. Thermal analysis

Figure 5(a) shows a TG-DTA profile, obtained at a heating rate of 10 K/min in a stream of argon, of the amorphous Ta–O NTs. An endothermic peak appears at around 1100 K, where the weight of the sample, 21.7 mg, decreased by 2.2 mg. The simultaneously obtained thermal desorption spectra, shown in Fig. 5(b), indicate desorption of molecules of specific mass of 16, 32, 48, and 64 in the same temperature range as the endothermic peak. At 3 K/min, the endothermic peak started at 1058 K and completed at 1128 K. The anodized samples were subjected to heating in the TG-DTA instrument up to 1058 and 1128 K, respectively, and then furnace-cooled to ambient temperature. The results of XRD and TEM analyses, shown in Figs. 1–4 and 6, were obtained from those samples. The molecular species detected at temperatures around 400 K must be C (12), H₂O (18), and CO₂ (44), which are all likely to come from the sample surface and/or the environment. As observed by EDS (Fig. 3), amorphous NTs contain impurity sulfur and excess oxygen. The molecules detected at the temperature of the endothermic reaction, of specific mass 16, 32, 48, and 64, are most probably related with excess oxygen and sulfur contained in the amorphous NTs, and are identified as O, O₂, SO, and SO₂, respectively. Transformation of a metastable amorphous solid to its crystalline counterpart is usually an exothermic reaction. The observed endothermic peak must be due to the removal of the oxygen and sulfur from the amorphous oxide; the loss of the chemical bonding energies associated with these extra constituents was probably larger in magnitude than the lowering of the enthalpy on the crystallization. This point is further discussed in Sec. III. E.

FIG. 5.

(a) TG-DTA profile of anodic amorphous Ta–O NTs, measured at a heating rate of 10 K/min in a stream of high purity argon. (b) Simultaneously measured desorption curves. The number on each profile indicates the mass number of the detected species.

FIG. 6.

Atomic pair distribution function g(r) of (a) a-Ta₂O_6.6S_0.7 and (b) a-Ta₂O₅ prepared by sputtering.^{Reference Nakamura, Ishimaru, Sato, Tanaka, Nakajima and Konno21} Dotted black and red solid lines represent as-anodized (as-sputtered) and annealed samples, respectively. The experimental details for sputtered samples are in Refs. Reference Nakamura, Tanaka, Ishimaru, Sato, Konno and Nakajima17,Reference Nakamura, Ishimaru, Sato, Tanaka, Nakajima and Konno21. g(r) of annealed a-Ta₂O₅ is an original data for this publication.

The enthalpy of the endothermic reaction was estimated from the enclosed area of the peak, obtained by DSC measurement at 5, 10, 20, and 30 K/min, to be 13.4 ± 0.9 kJ/mol of Ta₂O₅.

C. Composition of anodized amorphous Ta–O

From the results of the thermal and XRD analyses, the endothermic reaction that occurs at around 1073 K must be described as

(1)$${\rm{Ta}}_{\rm{2}} {\rm{O}}_{{\rm{5}} + x} {\rm{S}}_y \,({\rm{amorphous}}) \to\; \beta {\hbox -} {\rm{Ta}}_{\rm{2}} {\rm{O}}_{\rm{5}} + x{\rm{O}} + y{\rm{S}} - 13.4\;{\rm{kJ/mol}}$$

The amount of extra oxygen, x, and impurity sulfur, y, can be evaluated from the weight reduction before and after the endothermic reaction in the TG measurement and the intensities of characteristic x-rays of sulfur and oxygen measured by EDS. As the specific mass of oxygen, sulfur, and Ta₂O₅, are 16, 32, and 441.8 g/mol, respectively, x and y satisfy the following relation

(2)$${{(16x + 32y)} \mathord{\left/ {\vphantom {{(16x + 32y)} {441.8}}} \right. \kern-\nulldelimiterspace} {441.8}} = {{m_{\rm{d}} } \mathord{\left/ {\vphantom {{m_{\rm{d}} } {m_{\rm{c}} }}} \right. \kern-\nulldelimiterspace} {m_{\rm{c}} }}$$

where m _d and m _c are the total mass of desorbed oxygen and sulfur, and the mass of Ta₂O₅, respectively. The molar ratio of sulfur to total oxygen in the amorphous oxide is roughly estimated from the intensities of the characteristic x-rays in the EDS spectra to be 0.11, i.e.,

(3)$${y \mathord{\left/ {\vphantom {y {(5 + x)}}} \right. \kern-\nulldelimiterspace} {(5 + x)}} = 0.11$$

From the TG measurement, m _d and m _c were obtained to be 2.2 and 19.5 mg, respectively. By using Eqs. (2) and (3), x and y are calculated to be 1.6 and 0.7, respectively; the composition of the amorphous Ta–O NTs is Ta₂O_6.6S_0.7.

D. Pair distribution analysis

As mentioned earlier, the evolution of the broad maxima of the amorphous Ta₂O_6.6S_0.7 (a-Ta₂O_6.6S_0.7) in the XRD profiles [Figs. 1(a) and 1(b)] suggests structural changes during annealing. To characterize them quantitatively, the short-range atomic structures were evaluated in terms of RDFs by analyzing the selected-area electron diffraction patterns taken from a single NT in the electron beam of ∼300 nm in diameter. To avoid contamination, electron diffraction intensities were measured at a cryogenic temperature using a cooling holder. From the recorded intensity profiles, reduced interference functions, F(Q), were calculated. Here, Q is the scattering vector defined as Q = 4π sinθ/λ, where θ and λ are the scattering angle and the electron wavelength, respectively. The details of distribution function analysis using electron diffraction are described elsewhere.^{Reference Hirotsu, Ishimaru, Ohkubo, Hanada and Sugiyama18,Reference Ishimaru19}

The atomic pair distribution function, g(r) of a-Ta₂O_6.6S_0.7, extracted by the Fourier transform of F(Q), is shown in Fig. 6(a). For comparison, g(r) of an amorphous Ta₂O₅ (a-Ta₂O₅) prepared by sputtering^{Reference Nakamura, Ishimaru, Sato, Tanaka, Nakajima and Konno21} is shown in Fig. 6(b). Peaks appear at around 0.19, 0.27–0.28, 0.34, and 0.37 nm. It is known that the truncation of scattering vector (Q _max) in the reciprocal lattice space sometimes leads to spurious termination ripples, the so-called “ghost” peak, in RDFs.^{Reference Waseda22–Reference Ishimaru, Zhang and Weber24} We confirmed that the locations of the peaks and shoulders remain unchanged regardless of Q _max, suggesting that the peaks and shoulders discussed here are not ghost but real ones. These peaks are in good agreement with the bond lengths of Ta–O, O–O, Ta–Ta(1), and Ta–Ta(2), respectively (the number within the parentheses indicates the shorter and longer distance), in a-Ta₂O₅.^{Reference Nakamura, Ishimaru, Sato, Tanaka, Nakajima and Konno21,Reference Bassiri, Borisenko, Cockayne, Hough, MacLaren and Rowan25} Therefore, the atomic distribution in a-Ta₂O_6.6S_0.7 prepared via anodization is essentially similar to that in a-Ta₂O₅. The bars at the bottom of Fig. 6(b) indicate the bond-length ranges of Ta–O, O–O, Ta–Ta(1), and Ta–Ta(2) in crystalline β-Ta₂O₅ (a = 0.389 nm, b = 4.029 nm, c = 0.620 nm^{Reference Roth, Waring and Parker20}). The bond-lengths in its large unit cell are widely distributed and are located at longer distances than in the amorphous structure.

Although the peak intensity for Ta–O, Ta–Ta(1), and Ta–Ta(2) bonds increases slightly by annealing, g(r) of annealed a-Ta₂O₅ is almost consistent with that of as-deposited a-Ta₂O₅. This tendency is true for amorphous transition-metal oxides such as Al₂O₃,^{Reference Nakamura, Ishimaru, Sato, Tanaka, Nakajima and Konno26} WO₃, and Nb₂O₅ (R. Nakamura et al., to be submitted). It is evident, on the other hand, that g(r) of the annealed a-Ta₂O_6.6S_0.7 differs clearly from that of the as-anodized one. A notable feature is that the broad peak in g(r) corresponding to Ta–O and Ta–Ta(2) in the as-anodized state becomes sharper by annealing. A considerable amount of sulfur, whose concentration is 7.5 at.%, is contained in the NTs. Thus, sulfur-related configurations such as Ta–S or O–S probably exist. In fact, the distance between Ta and S is known to be around 0.24 nm in the stable phase of tantalum sulfide, TaS₂, and in related compounds.^{Reference Jellinek27–Reference Suzuki, Yamashita, Matsui and Doyama29} In addition, a large amount of excess oxygen may be located at positions deviating from the Ta–O configuration around 0.19 nm; excess oxygen may contribute to the broadening of the Ta–O peak. It is probable, therefore, that the shoulder at 0.24 nm of the as-anodized sample is due to Ta–S and Ta–O bonds, and their bond length becomes closer to that of the distribution around 0.19 nm as a result of atomic rearrangements at elevated temperatures. As can be seen in the partial pair distribution function of Ta–O bonds in a-Ta₂O₅,^{Reference Bassiri, Borisenko, Cockayne, Hough, MacLaren and Rowan25} the correlation corresponding to the second nearest Ta–O bonds appears weakly around 0.38 nm, which is close to the peak position of Ta–Ta(2). In the case of a-Ta₂O_6.6S_0.7 with higher concentration of oxygen than a-Ta₂O₅, the correlation of the second nearest Ta–O bonds is expected to be stronger and appear near the Ta–Ta(2) peak. The rearrangement of oxygen and sulfur by annealing makes the peak intensity for not only Ta–O but also Ta–Ta(2) increase. This can be interpreted as a unique structural change, which occurs owing to excess oxygen and sulfur. Radial distribution analysis revealed that excess oxygen and sulfur are introduced with a variety of bond lengths around Ta cations by the anodization process and then are rearranged by annealing toward a regular amorphous structure.

E. Origin of the thermal stability

Amorphous Ta₂O₅ thin films prepared by sputtering start to crystallize at 973 K and fully crystallize at 1023 K in 1 h in air.^{Reference Nakamura, Tanaka, Ishimaru, Sato, Konno and Nakajima17} With the same heat treatment, the amorphous structure of the a-Ta₂O_6.6S_0.7 was confirmed to be maintained by XRD measurements; in terms of the crystallization temperature, a-Ta₂O_6.6S_0.7 NTs are more stable than a-Ta₂O₅ films. The stabilization is most probably due to the presence of excess oxygen and impurity sulfur introduced in the anodization process.

The transformation of the anodically fabricated oxide to the stoichiometric crystalline phase by annealing is schematically illustrated in Fig. 7, including some hypothetical states, with the changes in enthalpy. The oxide contains excess oxygen and impurity sulfur in the as-prepared state (I). By annealing at around 1073 K, it releases extra oxygen and sulfur and crystallizes into stoichiometric β-Ta₂O₅ (IV), whose enthalpy is higher than the initial state by 13.4 kJ/mol. For convenience, we consider two hypothetical states, II and III, between them. First, the extra oxygen and sulfur are removed from state I (II), and next, the volume of the material is reduced, by eliminating the vacancies, to be the same as the ordinary stoichiometric amorphous oxide (III). The enthalpy is raised in state II by the loss of chemical bonds associated with the extra constituents. It is compensated to some extent in III (by elimination of vacancies) and IV (by crystallization), but not fully to the original level, leaving 13.4 kJ/mol, which was observed in the DSC. The oxygen and sulfur atoms released from the oxide must form stable molecules such as O₂, SO, and SO₂, as observed by mass spectroscopy, and leave the sample cell (state V). Since the sum of the heats of formation of those molecules is estimated to be at least 400 kJ/mol, the enthalpy of the final state (V) is far lower than the initial state (I) so that reaction (1) proceeds inevitably and irreversibly. (If all the excess O of 1.6 mol form O₂ molecules of 0.8 mol, the heat of formation amounts to −494 kJ/mol × 0.8 mol = −400 kJ/mol of Ta₂O₅.)

FIG. 7.

Schematic diagrams for enthalpy at various stages of transformation, including hypothetical states: (I) a-Ta₂O_6.6S_0.7, (II, III) amorphous Ta₂O₅, and (IV, V) β-Ta₂O₅. State II contains an extra volume due to the removal of extra oxygen and sulfur from a-Ta₂O_6.6S_0.7. State V includes released molecules consisting of excess oxygen and sulfur.

The enthalpy difference between a-Ta₂O_6.6S_0.7 and a-Ta₂O₅, H _III is due to chemical bonds by the extra oxygen and impurity sulfur. The difference between H _III and H _IV, i.e., crystallization enthalpy, ΔH _x, of a-Ta₂O₅, is unknown. Here, we assume it to be of similar magnitude to the crystallization enthalpy of other amorphous oxides, TiO₂, Nb₂O₅, and Al₂O₃, which is in the range of 17–40 kJ/mol.^{Reference Xie, Zhang, Xi, Wang and Liu30–Reference Tane, Nakano, Nakamura, Ogi, Ishimaru, Kimizuka and Nakajima32} With this assumption, the decrease in enthalpy of a-Ta₂O₅ per an extra atom is estimated to be 0.16–0.23 eV, which is a few percent of the bond energy, or the cohesive energy of a-Ta₂O₅, 5.34 eV.^{Reference Gad-Allah, Abd El-Rahman and Abou-Romia33} (Decrease in enthalpy (per mole of Ta₂O₅) per mole extra atoms (1.6 mol of O and 0.7 mol of S) is (ΔH _x + 13.4 kJ/mol)/2.3 mol = 13.2−23.2 kJ/mol = 0.16 − 0.23 eV.)

Both the enthalpy and entropy of a-Ta₂O₅ (state III), which corresponds to a-Ta₂O₅ prepared by sputtering, are higher than those of crystalline β-Ta₂O₅ (state IV), and so is the free energy. For a-Ta₂O₅, therefore, the driving force of crystallization, that is the difference in free energy, must be negative. In contrast, it turned out that the enthalpy of a-Ta₂O_6.6S_0.7 (I) is 13.4 kJ/mol lower than that of β-Ta₂O₅ (IV), as discussed above, while the entropy of a-Ta₂O_6.6S_0.7 must be higher than that of β-Ta₂O₅. As a result, the free energy of a-Ta₂O_6.6S_0.7 is apparently lower than that of β-Ta₂O₅ (IV). However, the free energy of a-Ta₂O_6.6S_0.7 is far higher than that of β-Ta₂O₅ with desorbed molecules (V). Therefore, a-Ta₂O_6.6S_0.7 is not thermodynamically stabilized. The desorption of impurity sulfur and excess oxygen, which occurs simultaneously with the crystallization, rather indicates that the transformation is kinetically limited. For reaction (1) to proceed, impurity sulfur and excess oxygen are to be released from the amorphous solid, which is possible only at temperatures where atomic mobilities are high enough. At such high temperatures, the extra atoms diffuse out, leaving the composition of the solid closer to stoichiometry, and then crystallization eventually occurs.