III. RESULTS AND DISCUSSIONS

Successful formation of ordered titania NT arrays is achieved upon anodization, Fig. 1. The NTs are open on the top [pore side, Fig. 1(a)] and closed at the bottom [bottom side, Fig. 1(b)], where they are in contact with the titanium substrate prior to being flaked off for study. In their as-anodized state, these highly-ordered and highly-aligned NTs feature an average pore diameter of 100 nm and an average length of 45 μm with a crystallographically amorphous structure confirmed by XRD, Fig. 2. Annealing the NTs produces two simultaneous effects: (i) crystallization and (ii) transformation from a nanotubular to a uniform nanoparticulate morphology.

FIG. 1.

SEM micrographs of the as-anodized titania NTs, (a) top, (b) bottom, and (c) lateral view.

FIG. 2.

X-ray diffraction patterns of titania NTs in the as-anodized state and annealed (ann.) for 2 h at 450 °C in H₂, Ar, and O₂ gases.

The anatase crystal structure develops in all samples after annealing regardless of the annealing gas, Fig. 2. In the anatase structure (tetragonal symmetry, space group I4₁/amd), Fig. 3(a), each titanium atom is surrounded by six oxygen atoms forming a lightly distorted octahedron organized into an edge-sharing arrangement of octahedra.^{Reference Kang and Hybertsen14,Reference Rhodes and Wohlfarth15} This octahedral distortion results in bond lengths that are larger along the c-axis ([001] direction) than those in the basal plane. The XRD data reveal subtle but significant differences in the anatase a-axis parameter upon annealing, producing variations in the anatase unit cell volume that are correlated with the type of annealing gas. Specifically, the anatase a-lattice parameter is expanded in H₂-annealed NTs relative to those produced in Ar or oxygen-rich annealing environments, Fig. 4(a). NTs annealed in an oxygen-rich environment possess lattice parameters that are very close to those of the commercially-available anatase powder (denoted as the anatase reference, shown on the same graph in Fig. 4). The anatase c-lattice parameter remains constant in all samples, within experimental errors. These conditions produce a systematic trend in the anatase unit cell volume of the NTs, Fig. 4(b), where annealing the NTs in the oxygen-deficient (Ar) or reducing (H₂) environments results in a larger unit cell volume as compared to the NTs annealed in an oxygen-rich atmosphere. All annealed samples exhibit larger unit cell volumes compared to that of bulk standard anatase data (PDF#71–1166, M. D. Jade Software, 5^.0^.37 Materials Data Inc.). Furthermore, application of the Scherrer formula to the anatase (101) Bragg reflection of the annealed NTs reveals the presence of larger crystallite sizes in samples annealed in the reducing environment, Fig. 4(c), with a trend that is similar to that of the unit cell volumes, Fig. 4(b).

FIG. 3.

Illustration of the anatase crystal structure of titania: (a) with a stoichiometric ratio of titanium and oxygen atoms and (b) with an oxygen vacancy. The small red spheres and large blue spheres represent oxygen and titanium atoms, respectively.

FIG. 4.

The crystallographic data are displayed for titania NTs subjected to different annealing atmospheres: (a) measured lattice parameters, (b) the anatase unit cell volume, and (c) crystallite size; the dotted curves are a guide for the eye.

Details of the transformation from nanotubular to nanoparticulate morphologies upon annealing in the three different atmospheres (O₂, Ar, and H₂) are shown in Figs. 5(a)–5(f). Note that a few additional larger particles are also observed in electron micrographs, presumably only on the surface of the NTs, Figs. 5(a)–5(f). Regardless of the annealing atmosphere, the NT morphology breaks down into regular faceted crystalline nanoparticles during the annealing process, leaving behind a semi-porous nanotubular structure. A comparison of the unannealed amorphous NTs in Fig. 1 with the annealed crystalline NTs in Fig. 5 confirms that the nanocrystallites appear to nucleate and grow as they replace the amorphous NT walls. Further evidence of this process is derived from transmission electron microscopy performed on samples annealed at lower temperatures (270 °C), which confirms that formation of these nanocrystallites is initiated prior to long-range crystallization of the NTs.^{Reference Hosseinpour, Panaitescu, Lim, Morris, Lewis and Menon16}

FIG. 5.

SEM micrographs of typical perpendicular (left hand side) and parallel (right hand side) views of titania NTs annealed in: (a and b) oxygen-rich, (c and d) oxygen-deficient (Ar), and (e and f) reducing (H₂) environments.

Connections between the NTs’ crystal structure, morphological features and the electronic structure underlying the nanostructured anatase functionality may be appreciated by analysis of the electronic density of states as revealed by the temperature dependence of the magnetic susceptibility. Figure 6 shows that the total magnetic susceptibility, χ_tot(T), for annealed and as-anodized titania NTs is comprised of two major components: a temperature-dependent Curie-Weiss paramagnetism that increases with decreasing temperature for T < 100 K and a temperature-independent Pauli paramagnetism χ_pp as indicated by^{Reference Senftle, Pankey and Grant17}:

(1)$${\rm{\chi }}_{{\rm{tot}}} (T) = C/(T - T_0 ) + {\rm{\chi }}_{{\rm{pp}}}\quad ,$$

FIG. 6.

(a) Temperature dependence of the total magnetic susceptibility, χ_tot, for titania NTs in the as-anodized state and annealed (ann.) in different gas environments for 2 h at 450 °C. Data from the anatase reference powder and single crystal rutile is included for comparison. The dotted curves are fit to the total measured susceptibility data using Eq. (1) encompassing Curie-Weiss and Pauli paramagnetic contributions. The inset shows the low temperature region (T < 50); (b) temperature trend of the inverse Curie-Weiss susceptibility for the annealed and as-anodized NTs [same symbols as part (a)], with a linear fit to the data (dashed lines) that highlight a negative Curie-Weiss temperature for the as-anodized and O₂-annealed NTs.

where C is the Curie-Weiss constant and T ₀ is the Curie-Weiss temperature that provides information on the nature of magnetic exchange interactions in the system. In particular, T ₀ > 0 characterizes ferromagnetic interactions while T ₀ < 0 characterizes antiferromagnetic interactions. The Curie-Weiss paramagnetism is characteristic of electronically-localized magnetism at temperatures above the Curie point; the average effective atomic moment per magnetic entity,$\langle {\rm{\mu }}_{{\rm{eff}}} \rangle$, can be correlated with the Curie-Weiss constant C through the following equation^{Reference Goodenough18,Reference Kittel19}

(2)$$\langle {\rm{\mu }}_{{\rm{eff}}} \rangle = \sqrt {C{{k_{\rm{B}} } \mathord{\left/ {\vphantom {{k_{\rm{B}} } N}} \right. \kern-\nulldelimiterspace} N}} \quad,$$

in which k _B is the Boltzmann constant and N is the number of magnetic entities per mole.

The Pauli paramagnetic contribution to the total magnetic susceptibility, derived from delocalized conduction electrons, allows for an estimate of the electronic density of states at the Fermi level, N(E _f), through the relationship^{Reference Ashcroft and Mermin20–Reference Park, Lee, Jung and Jung22}

(3)$$N(E_{\rm{f}} ) = {{{\rm{\chi }}_{{\rm{pp}}} } \mathord{\left/ {\vphantom {{{\rm{\chi }}_{{\rm{pp}}} } {{\rm{2\mu }}}}} \right. \kern-\nulldelimiterspace} {{\rm{2\mu }}}}_{\rm{B}}^{\rm{2}} \quad,$$

where μ_B is the Bohr magneton. It is important to note that this equivalency provides quantitative information on the nature of the electronic states, which influences photocatalytic functionality associated with the radiation absorption.^{Reference Stewart and Léonard23}

Figure 6(a) and the inset demonstrate that the low-temperature tail of the total susceptibility, dominated by the Curie-Weiss component, is affected by the type of annealing atmosphere. Evolution of the Curie-Weiss component of χ_tot(T) is examined through the Curie-Weiss constants obtained from a fit of the magnetic data to Eq. (1), summarized in Table I. Note that the O₂-annealed NTs exhibit lower values of the Curie-Weiss constant as compared to the H₂-annealed NTs (C = 1.99 × 10⁻³ versus 3.67 × 10⁻³ cm³ K/mole). The commercial anatase powder (anatase reference) shows a significantly lower value for the Curie-Weiss constant, C = 0.60 × 10³ cm³ K/mole, close to that of the Ar-annealed NTs, while single crystal rutile has only a temperature-independent magnetic susceptibility within the temperature range of study.

TABLE I.

Fitting parameters for the measured total magnetic susceptibility, ${\rm{\chi }}_{{\rm{tot}}} (T) = C/(T - T_0 ) + {\rm{\chi }}_{{\rm{pp}}}$, Eq. (2) From data in Fig. 6 for titania NTs annealed in different gas environments, as well as for commercially available anatase powder (anatase reference). C is the Curie-Weiss constant, T ₀ is the Curie-Weiss temperature and χ_pp is the Pauli paramagnetic contribution to χ_tot. The average effective atomic moment per magnetic entity, $\langle {\rm{\mu }}_{{\rm{eff}}} \rangle$, and the relative density of states at the Fermi level, N(E _f), are calculated based on Eqs. (2) and (3), respectively.

Figure 6(b) displays the temperature-dependent behavior of the inverse Curie-Weiss contribution obtained from the annealed and as-anodized titania NTs. The Curie-Weiss temperatures of the as-anodized and O₂-annealed NTs are similar (|T ₀| ∼ 2 K), and negative as is also the case of the anatase reference (|T ₀| ∼ 1 K), indicating the existence of antiferromagnetic interactions, while Ar-annealed and H₂-annealed NTs have T ₀ ∼ 0 K.^{Reference Yang, Dai, Huang and Feng24} The magnitude of the Curie-Weiss constant for the as-anodized and O₂-annealed NTs is similar and is approximately one-half of that characterizing the H₂-annealed NTs, indicative of a higher average effective magnetic moment per titanium atom for the H₂-annealed sample as compared to the other NT samples and is presented in Table I and Fig. 7. The measured values of $\langle {\rm{\mu }}_{{\rm{eff}}} \rangle _{{\rm{Ti}}}$ for the O₂- and H₂-annealed NTs is approximately one order of magnitude smaller than the estimated value reported elsewhere for undoped defect-rich titania thin films at T = 0 K.^{Reference Yoon, Chen, Yang, Goodrich, Zuo, Arena, Ziemer, Vittoria and Harris25} The value of $\langle {\rm{\mu }}_{{\rm{eff}}} \rangle _{{\rm{Ti}}}$ for the anatase reference powder is less than half of that for the H₂-annealed NTs and is close to the value calculated for the Ar-annealed NTs, implying that annealing the NTs in Ar resulted in a low temperature behavior similar to the commercially available anatase powder.

FIG. 7.

Calculated effective atomic moment per titanium atom [Eq. (2)] for the as-anodized and annealed nanotubes (ann. NTs); the dotted curve is a guide for the eye.

The magnitude of the temperature-independent magnetic susceptibility χ_pp for the H₂-annealed titania NTs (∼10⁻⁵ emu/mole Oe) is one order of magnitude smaller than that of metallic Ti (1.5 × 10⁻⁴ emu/mole Oe).^{Reference Lide26} According to Eq. (3), a large χ_pp is associated with a large density of states at the Fermi level, which consequently can result in higher photocurrent values and potentially lead to stronger catalytic activity.^{Reference Neff, Henkel, Hartmannsgruber, Steinbeiss, Michalke, Steenbeck and Schmidt27,Reference Richter, Jaye, Panaitescu, Fischer, Lewis, Willey and Menon28} As summarized in Table I, the observed trend of χ_pp for NTs and anatase reference is ${\rm{\chi }}_{{\rm{pp}}} ({\rm{anatase)}} > {\rm{\chi }}_{{\rm{pp}}} {\rm{(amorphous)}} > {\rm{\chi }}_{{\rm{pp}}} ({\rm{H}}_2 - {\rm{ann}}{\rm{.)}} \approx {\rm{\chi }}_{{\rm{pp}}} ({\rm{O}}_{\rm{2}} - {\rm{ann}}{\rm{.)}} > > {\rm{\chi }}_{{\rm{pp}}} ({\rm{Ar}} - {\rm{ann}}{\rm{.)}}$. This indicates a reduction of the density of states at the Fermi level N(E _f) after annealing the NTs, Table I, regardless of the annealing atmosphere.

The structural and magnetic characters of the titania nanostructures described here confirm that titania NTs annealed in a reducing environment exhibit larger anatase unit cells and crystallite sizes. Additionally, these NTs possess a higher effective magnetic moment per titanium atom as compared to NTs annealed in an oxygen-rich atmosphere. Expansion of the unit cell volume and enhanced localized magnetism in nominally pure anatase NTs are consistent with the presence of oxygen vacancies ($\ddot V_O$, in Kröger-Vink notation^{Reference Kröger and Vink29}) in these nanostructures that trap electrons at low temperature. While stoichiometric titania contains only Ti⁴⁺ ions and is considered to have a temperature-independent magnetic susceptibility,^{Reference Guillemot, Porté, Labrugère and Baquey30,Reference Keys and Mulay31} annealing in oxygen-deficient or reducing environments produces charged structural defects, such as oxygen vacancies.^{Reference Ghicov, Tsuchiya, Macak and Schmuki32} Two Ti ions are reduced from the Ti⁴⁺ state to the Ti³⁺ state for each oxygen vacancy created to achieve localized charge neutrality.^{Reference Xiao, Liu, Garcia and Sepehri33,Reference Xiong, Li, Yang and Yu34} Figure 3(b) illustrates an anatase unit cell possessing an oxygen vacancy; the electronic orbital structure surrounding the vacancy is deformed to foster donation of electrons from adjacent Ti³⁺ ions and thus provide localized charge neutrality.^{Reference Yang, Dai, Huang and Feng24,Reference Yoon, Chen, Yang, Goodrich, Zuo, Arena, Ziemer, Vittoria and Harris25,Reference Xiong, Li, Yang and Yu34,Reference Yoon, Harris, Vittoria and Widom35} Conversion of the quadrivalent Ti⁴⁺ cation to the trivalent Ti³⁺ cation is accompanied by a significant increase in the titanium ionic radius (0.42 Å versus 0.67 Å, or ∼60% increase ^{Reference Lide36}). Moreover, there is electrostatic repulsion between the two mutually-exposed cations in the absence of the bridging oxygen anions in the crystal structure. Both of these effects can contribute to the observed unit cell volume expansion.^{Reference Nah, Paramasivam and Schmuki37–Reference Choi, Jeon, Yang, Park and Song39} Such an expansion in the crystal unit cell upon introducing oxygen vacancies is also reported for other nanostructured transition-metal oxides such as cerium oxide nanoparticles.^{Reference Zhang, Chan, Spanier, Apak, Jin, Robinson and Herman38,Reference Hailstone, DiFrancesco, Leong, Allston and Reed40} Meanwhile, the larger crystallite size attained during annealing in a reducing environment is consistent with enhanced growth conditions that are facilitated in such an environment, with larger, more defective unit cells donating higher atomic mobility pathways for crystallite growth.^{Reference Zhang and Banfield8,Reference Inagaki, Nonaka, Tryba and Morawski41}

Furthermore, the observed changes in the magnetic moment per titanium atom in the titania NTs upon annealing in a reducing environment are consistent with the creation of oxygen vacancies accompanying reduction of Ti⁴⁺ to Ti³⁺.^{Reference Ghicov, Tsuchiya, Macak and Schmuki32,Reference Liu, Ma, Li, Li, Wu and Bao42,Reference Fan, Dongmei, Yan and Xurming43} These vacancies can produce a localized magnetic moment, due to magnetic interactions such as double exchange,^{Reference Yoon, Chen, Yang, Goodrich, Zuo, Arena, Ziemer, Vittoria and Harris25,Reference Yoon, Harris, Vittoria and Widom35} or from Ti³⁺ ions coupled ferromagnetically in donor bound magnetic polarons.^{Reference Coey, Venkatesan and Fitzgerald44,Reference Heiman, Wolff and Warnock45} Observation of such a magnetic behavior arising from oxygen vacancies is reported for other pure transition metal oxide nanostructures such as defective titania single crystals,^{Reference Zhou, Čižmár, Potzger, Krause, Talut, Helm, Fassbender, Zvyagin, Wosnitza and Schmidt46} thin films of titania^{Reference Yoon, Chen, Yang, Goodrich, Zuo, Arena, Ziemer, Vittoria and Harris25} and hafnium oxide.^{Reference Venkatesan, Fitzgerald and Coey47}