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.

KEYWORDS:

• Titanium oxide
• Ti₄O₇
• phase transition
• nanoscopic effect

Introduction

Phase transition phenomena are attracting widespread attention from the viewpoints of fundamental sciences and practical applications. For example, spin-crossover, charge-transfer, metal–semiconductor, and crystal–amorphous transitions have been aggressively studied [1–17]. Controlling the cooperative behavior of a phase transition is an important topic. To date, several approaches have been reported, including metal doping and crystal size control [18–31]. For example, the cooperative effect on phase transition of spin-crossover complexes, charge-transfer cyano complexes, and metal–semiconductor transition materials can be altered by controlling the crystal size [18–26].

Titanium oxides, which are called the Magneli phase and have a composition of Ti_nO_2n−1 (n = 3–9), exhibit metal–semiconductor (metal–insulator) transitions. Especially, Ti₃O₅ and Ti₄O₇ possess a high electric conductivity and exhibit a metal–semiconductor transition as the temperature changes [32–38]. In 2010, a nanoscopic effect on the phase transition in Ti₃O₅ was reported, where a Ti₃O₅ nanocrystal realized a new phase of λ-Ti₃O₅. λ-Ti₃O₅ 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 Ti₄O₇ has yet to be reported. In a Ti₄O₇ bulk crystal, a phase transition from the high-temperature (HT) metallic phase to the intermediate-temperature (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, whereas the Ti ions in the IT and LT phases take different valence states of Ti³⁺ and Ti⁴⁺ [34–37]. Due to the phase transition from the IT phase to the LT phase, the arrangement of Ti³⁺ and Ti⁴⁺ changes from a disordered to ordered state. Hereafter, the phase transition between the HT and IT phase due to a charge-delocalized and charge-localized 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).

Figure 1. Schematic of the two-step phase transition in a Ti₄O₇ conventional bulk crystal. High-temperature (HT) metallic phase transits to intermediate-temperature (IT) semiconductor phase at 150 K (phase transition I). 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 Ti³⁺ (white ellipses) and Ti⁴⁺ (colored circles). In the schematic structure of Ti₄O₇ viewed from the b-axis, oxygen is omitted for clarity and the covalently bonded pair of Ti³⁺ is expressed as a white elongated ellipse.

In this work, we synthesize a nanosize Ti₄O₇ crystal by sintering TiO₂ 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 mean-field thermodynamic model suggest that the nanoscopic effect perturbs the Gibbs free energy, leading to an anomalous phase transition.

Methods

Material

The anatase form of TiO₂ 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 Ti₄O₇ 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 plots¹ [40].

Results and discussion

Material and morphology

The target material was obtained by sintering anatase-TiO₂ 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(b) shows the SEM (right) and TEM (left) images of the synthesized sample along with the size distributions. The sample has a flake-like morphology with an apparent particle size of 450 ± 140 nm and is composed of aggregates of square-shaped nanocrystals, where the majority is 54 ± 19 nm. The XRPD pattern and Rietveld analysis at room temperature indicate that the synthesized sample is pure Ti₄O₇ with a triclinic crystal structure (space group; $P\overline{1}$) with the lattice constants of a = 5.5966 (1) Å, b = 7.1238 (2) Å, c = 12.4622 (7) Å, α = 95.051 (1)°, β = 95.172 (1)°, and γ = 108.753(1)° (Figure 2(c), left and middle). The crystallite size estimated by Rietveld analysis is 58.1 ± 0.4 nm. This value agrees well with the estimated size by the TEM images. The XPS spectra at room temperature are shown in Figure 2(c) (right), and Figures S1 and S2. The observed peaks at 459.0 eV and 530.4 eV are assigned to the binding energies of Ti 2p and O 1s, respectively. These are similar to those of the HT phase in Ti₄O₇ bulk crystal, indicating that the valence state of Ti in the synthesized sample is 3.5+ [41].

Figure 2. Synthesis, morphology, crystal structure, and valence state of nanocrystal Ti₄O₇. (a) Schematic of the synthetic procedure. (b) TEM image and size distribution (left) and SEM image and size distribution (right) of nanocrystal Ti₄O₇. (c) Crystal structure (left) and Rietveld analysis (middle). Red dots, black line, and gray dots are the observed pattern, calculated pattern, and their difference, respectively. Green bars represent the calculated positions of the Bragg reflections of Ti₄O₇. XPS spectrum (right) for the Ti 2p peak.

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 Ti³⁺ and Ti⁴⁺ (IT phase) [36].

Figure 3. χ_M vs. temperature plot of the sample with a temperature sweeping rate of ±1.0 K min^-1 under an external field of 5000 Oe.

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). From the Rietveld analyses, the crystal structure at 200 K is triclinic (space group; $P\overline{1}$) with lattice constants of a = 5.5866(3) Å, b = 7.1155(4) Å, c = 12.4443(7) Å, α = 95.073(2)°, β = 95.195(2)°, γ = 108.760 (2)°, and V = 462.83(5) ų (Table S1), whereas the crystal structure at 100 K is triclinic ($P\overline{1}$) with lattice constants of a = 5.5863(4) Å, b = 7.1197(5) Å, c = 12.4720(8) Å, α = 95.031(2)°, β = 95.337(2)°, γ = 108.907(2)°, and V = 463.58(5) ų (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 Ti₄O₇ 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 (ΔH_trans) and the transition entropy (ΔS_trans) are estimated based on the relationship of ΔH_trans = $\int C_{\text{trans}}\text{d}T$ and ΔS_trans = $\int C_{\text{trans}}\text{dln}T$, i.e. ΔH_trans = 941.4 J mol^-1 and ΔS_trans = 6.4 J K^-1 mol^-1. These values are approximately half of the reported ΔH_trans and ΔS_trans values of the first-order transition at 150 K in the bulk crystal, respectively [36]. The ratio of ΔH_trans of the nanocrystal to that of bulk crystal is 48%, and the ratio of ΔS_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].

Figure 4. Molar heat capacity (C_p) of the sample as a function of temperature. A Debye model (red line) was fitted to the experimental data (circle).

Thermodynamic calculations of the phase transition in nanocrystal Ti₄O₇

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 Ti₄O₇ exhibits a one-step phase transition of phase transition I.

Next, to understand the suppression of phase transition II in nanocrystal Ti₄O₇, the Gibbs free energy (G) was calculated using the Slichter and Drickamer mean-field thermodynamic model [42]. In this model, G is expressed as G = x ΔH_trans + γ x(1 − x) + T{R[x ln x + (1 − x)ln(1 − x)] − x ΔS_trans}, where ΔH_trans, ΔS_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, (Ti³⁺,Ti⁴⁺)₂O₇, when G of the charge-ordered phase is taken as the origin of the energies. Using the reported ΔH_trans and ΔS_trans values of the bulk-crystal Ti₄O₇ [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 ΔH_trans and ΔS_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.

Figure 5. One-step phase transition in a nanocrystal Ti₄O₇. (a) Schematic of the one-step phase transition. Charge-delocalized HT phase transits to the charge-localized IT phase at 150 K (phase transition I). Charge-disordered IT phase does not transit to the charge-ordered phase (i.e. charge-disordered IT phase is maintained at low temperature). In the schematic structure of Ti₄O₇ viewed from b-axis, oxygen is omitted for clarity. Gray and red (or blue) circles indicate Ti^3.5+ and Ti⁴⁺, respectively, and the covalently bonded pair of Ti³⁺ is expressed as a white–elongated ellipse. (b) Calculated Gibbs free energy (G) vs. fraction (x) curves between the charge-disordered and charge-ordered phase at 130 K and 120 K. Phase transition II from the charge-disordered to charge-ordered phase does not occur using values of ΔH_trans = 191 J mol^-1, ΔS_trans = 1.5 J K^-1 mol^-1, and γ = 2.3 kJ mol^-1. Red circles indicate the thermal populations.

Conclusion

Herein we report the nanoscopic effect on the phase transition of Ti₄O₇. Nanocrystal Ti₄O₇ shows a one-step 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.

Acknowledgments

We acknowledge the Cryogenic Research Center, The University of Tokyo, and Nanotechnology Platform, which are supported by MEXT.

Disclosure statement

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

ORCID

Hiroko Tokoro http://orcid.org/0000-0002-3431-0643

Takahiro Kondo http://orcid.org/0000-0001-8457-9387

Shin-ichi Ohkoshi http://orcid.org/0000-0001-9359-5928

Additional information

Funding

The present research was supported in part by JSPS Grant-in-Aid for scientific research on innovative areas [grant number 16H06521 (Coordination Asymmetry)], JSPS Grant-in-Aid for specially promoted Research [grant number 15H05697], and Quantum Leap Flagship Program (Q-LEAP) by MEXT.

Notes

1 To investigate the temperature dependence of the C_lat, we used two-Debye model, expressed by $C\left(T\right)=\sum _{i=1}^{2}9R{c}_i{\left(T/{\theta }_i\right)}^3{\int }_0^{{\theta }_i/T}{x}^4{e}^x/{\left(e^x-1\right)}^{2}dx$, where R is gas constant, c_i is coefficient, θ_i is Debye temperature, x is $\hslash \omega /k_{\text{B}}T$, ħ is the reduced Planck constant, ω is phonon frequency, and k_B is Boltzmann constant, with the fit parameters of c₁ = 4.1, c₂ = 7.2, θ₁ = 8.9(2) × 10² K, and θ₂ = 5.5(2) ×10² K [40].

2 From the heat capacity measurement, the ΔH_trans and ΔS_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 Al₂O₃, Fe₂O₃, and Ti₃O₅ [23,24,43,44].