Synthesis of nanosize tetratitanium heptoxide and its anomalous phase transition

ABSTRACT Tetratitanium heptoxide, Ti4O7, is known to exhibit a two-step phase transition from the charge-delocalized to charge-localized phase and the charge-disordered to charge-ordered phase around 150 K and 130 K, respectively. Herein, a nanoscopic effect of the Ti4O7 phase transition is studied. A one-step phase transition from the charge-delocalized to charge-localized phase is realized in Ti4O7 nanocrystals where the transition from the charge-disordered to charge-ordered phase is suppressed. Perturbation to the free energy by the surface energy can explain this anomalous phase transition. The present nanoscopic effect, which can control cooperativity in phase transitions, should contribute to develop advanced switching materials. GRAPHICAL ABSTRACT IMPACT STATEMENT Ti4O7 nanocrystal exhibits a one-step phase transition from a charge-delocalized to a charge-localized phase. This anomalous phase transition can be understood by the nanoscopic effect contributed by the surface energy.

Titanium oxides, which are called the Magneli phase and have a composition of Ti n O 2n−1 (n = 3-9), exhibit metal-semiconductor (metal-insulator) transitions. Especially, Ti 3 O 5 and Ti 4 O 7 possess a high electric conductivity and exhibit a metal-semiconductor transition as the temperature changes [32][33][34][35][36][37][38]. In 2010, a nanoscopic effect on the phase transition in Ti 3 O 5 was reported, where a Ti 3 O 5 nanocrystal realized a new phase of λ-Ti 3 O 5 . λ-Ti 3 O 5 exhibits a reversible photo-induced metal-semiconductor phase transition at room temperature [23]. On the other hand, a nanoscopic effect on the phase transition in Ti 4 O 7 has yet to be reported. In a Ti 4 O 7 bulk crystal, a phase transition from the hightemperature (HT) metallic phase to the intermediatetemperature (IT) semiconductor phase occurs at 150 K ( Figure 1). The IT phase transits to the low-temperature (LT) semiconductor phase around 130 K. The Ti ions in the HT phase have a uniform valence state of +3.5, IT phase transits to low-temperature (LT) semiconductor phase around 130 K (phase transition II). Valence state of Ti ions in the HT phase is Ti 3.5+ (gray circles), whereas Ti ions in the IT and LT phases take different valence states of Ti 3+ (white ellipses) and Ti 4+ (colored circles). In the schematic structure of Ti 4 O 7 viewed from the b-axis, oxygen is omitted for clarity and the covalently bonded pair of Ti 3+ is expressed as a white elongated ellipse.
whereas the Ti ions in the IT and LT phases take different valence states of Ti 3+ and Ti 4+ [34][35][36][37]. Due to the phase transition from the IT phase to the LT phase, the arrangement of Ti 3+ and Ti 4+ changes from a disordered to ordered state. Hereafter, the phase transition between the HT and IT phase due to a charge-delocalized and chargelocalized phase is called phase transition I, while that between the IT and LT phase due to charge-disordered and charge-ordered phase is called phase transition II ( Figure 1).
In this work, we synthesize a nanosize Ti 4 O 7 crystal by sintering TiO 2 nanoparticles under a hydrogen flow. The temperature dependences of the magnetic susceptibility, crystal structure, and heat capacity are measured. An anomalous phase transition, where only phase transition I occurs, is observed. This anomalous phase transition originates from a nanoscopic effect contributed by the surface energy. Theoretical calculations using a meanfield thermodynamic model suggest that the nanoscopic effect perturbs the Gibbs free energy, leading to an anomalous phase transition.

Material
The anatase form of TiO 2 nanoparticles with a 7-nm particle size (commercial, Ishihara Sangyo Kaishia, ST-01) was sintered under hydrogen at a flow speed of 0.3 dm −3 min −1 and 1000°C for 5 h to obtain Ti 4 O 7 as a powder.

Measurements
Elemental analysis was performed by X-ray fluorescence (XRF) using a RIGAKU ZSX Primus IV. The morphologies of the sample were measured with a scanning electron microscope (SEM) using a JEOL JSM-7000F and a transmission electron microscope (TEM) using a JEOL JEM 2000EX. X-ray powder diffraction (XRPD) patterns were measured using a Rigaku Ultima IV with Cu Kα (λ = 1.5418 Å). Rietveld analyses for the XRPD patterns were performed using Rigaku PDXL software. The XRPD patterns were calibrated using Si powder [39]. The temperature during the XRPD measurements was controlled by a RIGAKU R-CRT-105 cryostat. Apiezon L was used as a thermal medium to maintain thermal contact between the sample and the Cu holder. X-ray photoelectron spectra (XPS) were measured at room temperature using a JPS 9010 TR (JEOL, Japan) with an ultrahigh vacuum chamber and an Al Kα X-ray source (1486.6 eV). Magnetic measurements were performed using a Quantum Design MPMS superconducting quantum interference device (SQUID) magnetometer. The heat capacity was measured by using the Quantum Design physical properties measurement system (PPMS). The equation based on the two-Debye model was fitted to the observed plots 1 [40].

Material and morphology
The target material was obtained by sintering anatase-TiO 2 nanoparticles under hydrogen flow (Figure 2(a)). A dark blue powder sample was obtained. XRF measurements suggest that the formula is Ti 4.00(2) O 7.00(2) : Calc., Ti 63.1 wt%; Found, Ti 63.1(2) wt%. Figure 2 Temperature dependence of the magnetic susceptibility and crystal structure Figure 3 shows the product of the molar magnetic susceptibility (χ M ) vs. temperature plots of the present sample. As the temperature decreases from room temperature, the χ M value gradually increases, but the χ M value suddenly decreases at 150 K. The decreased value is maintained at a low temperature. As the temperature increases from 60 K, the χ M value returns to the initial value around 150 K. The observed transition at 150 K is consistent with a transition due to the valence change between Ti 3.5+ (HT phase) and Ti 3+ and Ti 4+ (IT phase) [36].
To investigate the crystal structures before and after the transition at 150 K, the XRPD patterns were measured at 200 K and 100 K (Figures S3 and S4).  Table S2). The lattice constant of a at 100 K contracts slightly compared to that at 200 K. By contrast, the lattice constants of b and c at 100 K expand compared to those at 200 K. The volume at 100 K expands slightly compared to that at 200 K. The difference in the lattice constants and volume between 200 K and 100 K are consistent with those of the HT and IT phases reported in a bulk Ti 4 O 7 crystal [34,35].

Temperature dependence of the heat capacity
The molar heat capacity (C p ) of the present sample was measured between 5 K and 275 K (Figure 4). A sharp peak is observed at 150 K. C p can be expressed by the sum of the heat capacity due to the lattice vibration (C lat ) and the phase transition (C trans ) as C p = C lat + C trans . Hence, by estimating C lat , the anomalous heat capacity due to the C trans is extracted (see note 1). Then the values of the thermodynamic parameters of the transition enthalpy ( H trans ) and the transition entropy  [36]. The ratio of H trans of the nanocrystal to that of bulk crystal is 48%, and the ratio of S trans of the nanocrystal to that of bulk crystal is 50%. Below 150 K, a peak is not observed in the  present sample, although a second peak characteristic of the first-order transition has been reported in the bulk crystal around 130 K [36].

Thermodynamic calculations of the phase transition in nanocrystal Ti 4 O 7
The nanocrystal sample exhibits a phase transition at 150 K according to the temperature dependence of χ M and C p . The XRPD patterns indicate that the lattice constant changes due to a phase transition. From these results, the observed phase transition is regarded as phase transition I. In the nanocrystal, phase transition II is not observed. That is, nanocrystal Ti 4 O 7 exhibits a one-step phase transition of phase transition I.
Next, to understand the suppression of phase transition II in nanocrystal Ti 4 O 7 , the Gibbs free energy (G) was calculated using the Slichter and Drickamer meanfield thermodynamic model [42]. In this model, G is expressed as S trans , γ , and R are the transition enthalpy, transition entropy, interaction parameter between two phases, and gas constant, respectively. Phase transition II, which is the transition between the IT and LT phase, is regarded as a semiconductor-to-semiconductor transition from the charge-disordered to charge-ordered phase (Figure 1). In this case, x denotes the fraction of the charge-disordered unit, (Ti 3+ ,Ti 4+ ) 2 O 7 , when G of the charge-ordered phase is taken as the origin of the energies. Using the reported H trans and S trans values of the bulk-crystal Ti 4 O 7 [36], the phase transition II is reproduced, the stable phase turns the charge-ordered phase as temperature decrease ( Figure S5). For the nanocrystal calculation, when the values of H trans and S trans are set to 48% and 50% of those in the bulk crystal, 2 phase transition II does not occur ( Figure 5). In the temperature dependence of the G vs. x curve, the existence of energy barriers prevents the transition to the charge-ordered phase ( Figure 5(b)). Therefore, the charge-disordered phase is maintained at a low temperature.

Conclusion
Herein we report the nanoscopic effect on the phase transition of Ti 4 O 7 . Nanocrystal Ti 4 O 7 shows a onestep phase transition behavior from a charge-delocalized to charge-localized phase (i.e. from HT to IT phase) since the transition from the charge-disordered to the charge-ordered phase is suppressed. This one-step phase transition can be understood by the nanoscopic effect contributed by the surface energy. Controlling the cooperativity in a phase transition is important from the viewpoints of scientific knowledge and the development of sensor-and switching-material applications. The present results may inspire additional advances in the field of nanoelectronic devices.

Notes
1. To investigate the temperature dependence of the C lat , we used two-Debye model, expressed by C(T) h is the reduced Planck constant, ω is phonon frequency, and k B is Boltzmann constant, with the fit parameters of c 1 = 4.1, c 2 = 7.2, θ 1 = 8.9(2) × 10 2 K, and θ 2 = 5.5(2) × 10 2 K [40]. 2. From the heat capacity measurement, the H trans and S trans of phase transition I in nanocrystal were estimated as ca. 48% and 50% of those in the bulk crystal. Such a nanoscopic effect on the thermodynamic parameters was observed in Al 2 O 3 , Fe 2 O 3 , and Ti 3 O 5 [23,24,43,44].

Disclosure statement
No potential conflict of interest was reported by the author(s).