Preparation of rutile TiO₂ by hydrolysis of TiOCl₂ solution: experiment and theory

Abstract

Titanium slag with a perovskite phase (CaTiO₃) is difficult to use in traditional titanium dioxide production. Herein, we demonstrate that HCl can decompose CaTiO₃ with a high acidolysis ratio of >97 wt% to obtain a TiOCl₂ solution. With subsequent hydrolysis and calcination, rutile TiO₂ was synthesised in one step without crystalline-structure transformation. As hydrolysis of the TiOCl₂ solution to prepare metatitanic acid (H₂TiO₃) is an essential step in the process, a simulated pure TiOCl₂ solution (prepared from TiCl₄ and H₂O) was confirmed to have the same structure in water as HCl-treated CaTiO₃ slag by Raman spectroscopy. The TiOCl₂ solution was also concluded to have the Ti compound cluster of (Ti₂O₂)(H₂O)₄Cl₄, based on DFT calculations from the Raman data and the curve fit for the hydrolysis ratio. By elucidating the relationship between the H₂TiO₃ particle size and the concentration of Ti⁴⁺ and HCl, we identified the nuclear energy as -19.46 kJ mol⁻¹. Moreover, a complete scheme for the production of rutile TiO₂, induced by TiOCl₂ solution hydrolysis, was proposed. Periodic structures show the feasibility of the following transformation occurring through a simple structural rearrangement: (Ti₂O₂)(H₂O)₄Cl₄ (in solution)–Ti(OH)(H₂O)₂Cl₃ (with addition of HCl)–Ti(OH)₂Cl₂ (1-dimentional growth and removal of HCl)–rutile-type Ti(OH)₂Cl₂ (stack)–rutile TiO₂ (with removal of HCl).

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1. Introduction

Titanium dioxide (TiO₂) is widely used as a white pigment, catalyst framework, and photocatalyst.^1–7 It is well known that TiO₂ has three distinct crystallographic phases: rutile, anatase, and brookite.^8,9 Among them, rutile TiO₂ has received the highest attention in commercial preparations; it is the best white pigment for paint, plastic, paper, and cosmetics due to its lack of toxicity, high achromicity, and chemical and heat stability.^7,9,10

At present, the chloride and sulfate processes are the two main industrial methods for titanium dioxide pigment production.^11,12 The chloride process needs rutile (natural or synthetic) or titanium slag containing high-grade Ti and low Mg and Ca contents.^13–15 The sulfate process was the first commercialised technology for making TiO₂ pigments, in which ilmenite or titanium slag react with concentrated sulfuric acid (92–95%) to obtain anatase or rutile products. About 40% of the worldwide TiO₂ pigment production comes from this process because of its low cost and ability to utilise a broad feedstock range. However, there are some disadvantages such as the large amounts of acidic (pH 3–5) wastewater and solid waste generated in the process that lead to serious environmental degradation.^16–18

At present, titanomagnetite concentrates with high titanium contents are smelted in a blast furnace to produce cast iron and titanium slag. The titanium slag contains 22–25% TiO₂ as the perovskite structure (CaTiO₃).^19–22 This titanium mineral and slag cannot be used in the two aforementioned industrial processes; therefore, new methods have been proposed in order to utilize them. Altair Nanomaterials Inc. (US) first produced TiO₂ pigments using a hydrochloric acid process, in which ilmenite was leached with hydrochloric acid, and the resultant insoluble residue was filtered and separated.^23,24 Iron powder was poured into the filtered solution to reduce Fe³⁺ to Fe²⁺, cooled to allow crystallization, and isolated to obtain FeCl₂·4H₂O. Separation of the titanium-containing leaching solution was achieved over two steps to obtain purified titanium chloride. After hydrolysis of the purified titanium chloride solution, metatitanic acid and other titanium dioxide products were obtained by calcining the metatitanic acid.

In Chaoyang, China, a vanadium-bearing titanomagnetite mineral with a high vanadium and titanium content is found that is smelted with additives in an electric furnace to produce cast iron and titanium slag. The titanium slag contains 40–45% TiO₂ (Table 1), mainly existing as perovskite (Fig. 1). Due to the stability of the perovskite structure, refining its titanium components with the chloride or sulfate processes is difficult. Thus, an alternative route for producing TiO₂ white pigments, based on an improved hydrochloric acid process, was proposed that would fully utilise the abundant titanium resources from the slag in Chaoyang. A brief flowchart of the novel process is shown in Fig. 2.

Table 1 Chemical compositions of the titanium slag (wt%)

TiO2	SiO2	CaO	Al2O3	TFe	MgO	V2O5
41.70	14.66	9.53	5.74	5.74	1.36	0.23

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Fig. 1 XRD pattern of low-grade titanium slag.

Fig. 2 Brief flow sheet of the TiO₂ pigment production process.

The novel process for utilising the titanium slag has four key steps: (i) decomposition of the titanium slag with HCl acid at 150 °C, where titanium is converted to a TiOCl₂ solution; (ii) hydrolysis, in which H₂TiO₃ is precipitated by heating the TiOCl₂ solution; (iii) doping with additives such as K, P, Al salts to improve the TiO₂ pigment performance; and (iv) calcination of H₂TiO₃, to obtain the rutile TiO₂ pigment product.^25–29

As in the sulfate process, hydrolysis is an essential step in the new process for controlling the structure of the precipitates, and further deciding the TiO₂ pigment quality. However, information about hydrolysis of both TiOSO₄ and TiOCl₂ has rarely been reported. Many researchers proposed mechanisms of hydrolysis for a low range of titanium concentrations. Ligorio and Work³⁰ found that in the titanyl sulfate solution, the initial Ti cluster exists as Ti(OH₂)₈⁴⁺. Duncan and Richards³¹ used UV spectrum data at 220 nm to study hydrolysis kinetics; the results showed that the initial complex, Ti(OH)₃(OH₂)₂HSO₄, was hydrolysed to hydrated titanium dioxide via the Ti(OH)₃⁺ intermediate. There are also some investigations into TiCl₄ hydrolysis.^32,33 West et al.³⁴ predicted the thermochemical parameters for a number of TiO_xCl_y intermediates using density functional theory (DFT), while Shirley et al.³⁵ considered the possible aluminium-containing species generated from Ti₂O₂Cl₄.

In this work, we mainly focus on the efficient use of titanium slag, as shown in Table 1 and Fig. 1. To prepare rutile TiO₂ with excellent pigment properties and high yield by using this type of titanium slag, we paid more attention on improving the hydrolysis ratio of TiOCl₂ solution and ensuring a suitable particle size of TiO₂. The hydrolysis of a simulated TiOCl₂ solution obtained from a mixture of TiCl₄ and H₂O was investigated. The real and simulated TiOCl₂ solutions were compared by Raman spectroscopy. The nuclear energy was fitted on the basis of titanium and HCl concentrations, and H₂TiO₃ particle size. Moreover, the hydrolysis mechanism was postulated using both experimental and theoretical data.

2. Experimental

2.1 Preparation of titanium chloride solution

In this paper, the simulated TiOCl₂ solution was obtained from the reaction between chemically pure TiCl₄ and water. TiCl₄ was diluted with ice-cold distilled water to prepare a simulated TiOCl₂ solution (5 mol L⁻¹). Evaporation or addition of HCl was used to decrease or increase the molar ratio of H⁺/Ti⁴⁺, respectively, in the simulated solution. The H⁺/Ti⁴⁺ molar ratio was a more important factor in the hydrolysis that was labelled as F_mol, compared with the F value (quality ratio of H₂SO₄/TiO₂) in the sulfate process. Corresponding to the simulated solution, the acid leaching TiOCl₂ solution was prepared from titanium slag (mentioned in Table 1 and Fig. 1) with 35 wt% HCl acid and liquid–solid ratio of 8 : 1, at 150 °C for about 2 h. ​And its chemical compositions were listed in Table 2.

2.2 Preparation of metatitanic acid

TiOCl₂ solutions with different F_mol values were heated at slightly above boiling temperature (105–112 °C). The solution turned grey after <5 min, called the turbidity point. The mixture was stirred at 260 rpm for 4 h, and then cooled to room temperature, filtered, and washed with deionised water to afford metatitanic acid as the product. The hydrolysis equation is as follows:

TiOCl₂(aq) + 2H₂O(l) → H₂TiO₃(s) + 2HCl(aq) (1)

2.3 Preparation of rutile TiO₂

H₂TiO₃ samples generated under different hydrolysis conditions were calcined at 530–900 °C for more than 4 h to complete the crystalline transformation to rutile TiO₂ by removing chemically bound water and HCl.

The equation for H₂TiO₃ decomposition is as follows:

H₂TiO₃(s) → TiO₂(s) + H₂O(g) (2)

2.4 Characterisation

The concentrations of Ti⁴⁺ and H⁺ in the leaching solution and titanium chloride solution were detected by chemical titration. During those titrations, Ti⁴⁺ was first reduced to Ti³⁺ by an aluminium sheet and the reduced Ti³⁺ solution was titrated with 0.1027 mol L⁻¹ ammonium iron(III) sulfate, with ammonium thiocyanate used as the indicator. The concentration of H⁺ was determined by titration with 0.2833 mol L⁻¹ NaOH solution with methyl orange as the indicator.

The titanium chloride solution was mainly analysed by Raman spectra using a Raman spectrometer (LabRAM HR800, HORIBA Jobin Yvon, France) and excitation with the 514.5 nm line of the argon laser at 297 K.

The H₂TiO₃ and rutile TiO₂ products were characterised by a variety of techniques, including X-ray diffraction (XRD), transmission/scanning electron microscopy (TEM/SEM), X-ray fluorescence, and a master 2000 laser particle size analyser (LPSA). SEM (JEOL JSM-6510A, Japan) equipped with energy-dispersive spectroscopy (EDS; INCA X-MAX, Oxford Instruments, UK) was used, at an accelerating voltage of 15 kV, to observe the size and morphology of the samples. The particle size distribution was measured by dynamic light scattering (DLS) using LPSA under ultrasonic agitation. Powder XRD patterns of samples were obtained with an X'Pert PRO MPD diffractometer (PANalytical, Almelo, Netherlands). XRD patterns were recorded at angles of 5–90° using Cu K_α radiation. Crystallography data analysis software (GSAS)³⁶ was used to remove the peaks of K_α2. In order to obtain accurate crystalline information on the unit cell parameters, the GSAS-expgui³⁷ was used to refine the XRD patterns. The average crystal size was determined from the broadening of the corresponding X-ray spectral peaks using the Scherrer formula³⁸ (D = 0.89 λ/(β cos θ); λ = 1.54056 Å, β is the peak width at half height). The chemical composition of the samples was examined by inductively coupled plasma atomic emission spectroscopy (ICP-AES; Optima 5300DV, PerkinElmer, USA). The compositions are shown in Table 2. All crystal structures were visualised with VESTA (Visualization for Electronic and Structural Analysis) Ver. 3.0.1 software.³⁹

Table 2 Chemical compositions of the titanium chloride solution from chloride acid decomposed process of Chaoyang titanomagnetite mineral (g L⁻¹)

TiO2	CaO	Al2O3	FeO	MgO	MnO	V2O5
31.43	6.38	5.25	4.98	1.22	0.83	0.17

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2.5 Theoretical simulations with density functional theory (DFT)

First-principles calculations were performed on the modular structures of (Ti₂O₂)(H₂O)₄Cl₄, Ti(OH₂)₂(OH)₂Cl₂, and [TiO(OH₂)₅]²⁺ by using the Dmol³ software package^40,41 with fine quality and geometry optimisation convergence criteria, the threshold for density convergence during the SCF minimisation of 10⁻⁶, the DNP (double-numerical with d and p polarisation) basis set, and generalised-gradient approximation (GGA) density functional Perdew–Burke–Ernzerhof (PBE).⁴²

After full geometry optimisation, the Raman activity and intensities of vibrational modes were calculated. The Raman spectra were fitted as a function of intensity, at 297 K, incident light wavelength of 514.5 nm and smearing of 5 cm⁻¹.

3. Results and discussion

3.1 Structure of Ti(IV) in HCl solution

The Raman spectra of three samples, including the simulated solutions and hydrochloric acid leaching solution, are shown in Fig. 3, with the three samples clearly having the same structure. The impurity (shown in Table 2) in the TiOCl₂ solution does not affect the existence of the Ti⁴⁺ ion. Therefore, the simulated solution from TiCl₄ diluted in water can represent a hydrochloric acid leaching solution of HCl-treated titanium slag. Moreover, Raman spectroscopy with a high detection concentration has recently been considered a useful method for analysing the structure of TiOSO₄ solutions. Corresponding Raman bands were located at 84, 100–200, 405, 419, 643, and 693 cm⁻¹. Anatase has a body-centred tetragonal structure (space group I4₁/amd, Z = 4) and six Raman active modes (A_1g + 2B_1g + 3E_g); the corresponding Raman bands were located at 144, 197, 399, 513, 519, and 639 cm⁻¹. Brookite has an orthorhombic structure (space group Pbca, Z = 8) and 36 Raman active modes (9A_1g + 9B_1g + 9B_2g + 9B_3g); the corresponding Raman bands were located at about 150, 323, 416, and 636 cm⁻¹. The most intensive Raman band for brookite was at 150 cm⁻¹, which can influence the width of the E_1g Raman mode at 144 cm⁻¹ (ascribed to anatase). Rutile has a tetragonal structure (space group P4₂/mnm, Z = 2) and four Raman active modes (A_1g + B_1g + B_2g + E_g); the corresponding Raman bands were located at about 145, 240, 445, and 610 cm⁻¹. By comparing the Raman spectra, especially in the range 380–700 cm⁻¹ (sharp peaks), we concluded that the Ti clusters in TiOCl₂ solution should have the similar chemical environment or symmetry to the anatase or brookite structures. Therefore, treatment of the TiOCl₂ structure in solution shows that it should have Ti–O–Ti bond. This means that Ti clusters in TiOCl₂ solution should contain two or more than two Ti atoms.

Fig. 3 Comparison of the Raman spectra between the simulated and real solution of samples: (a) 2.5 mol L⁻¹ TiO₂ (b) 0.5 mol L⁻¹ TiO₂ (c) hydrochloric acid leaching solution.

As is known, although the state of the hydrated TiO²⁺ ion in solution is difficult to determine, Raman spectroscopy and DFT computing are good ways to study the state of hydrated ions in solution. In this work, many structures of the hydrated TiO²⁺ ion were anticipated, and their Raman spectra were calculated by Dmol³ code. By comparing the Raman spectra from the experimental data of the TiOCl₂ solution with those calculated from the expected structures, the forms of the hydrated TiO²⁺ ions present can be obtained. At present, the major problem is obtaining the expected structures.

In the current method, a series of structures for the hydrated TiO²⁺ ions described as TiOCl_x(H₂O)_y(OH)_z need to be optimised, and the stable structures should be the most probable forms present. As this method requires huge computational resources, this method had not been chosen. We found that the Raman spectra of anatase and brookite are similar to that of the TiOCl₂ solution. The periodic structures of TiOCl₂·nH₂O were designed based on the crystal structures of anatase and brookite, respectively. However, the calculated Raman spectra are different from the experimental data. Therefore, another method to model the structures of TiOCl₂·nH₂O was tried. We proposed that the crystalline structures of TiOCl₂·nH₂O could be used to analyse the existing forms of hydrated TiO²⁺ ion in the solution. However, there were no reports about the crystalline structures of TiOCl₂·nH₂O. By comparing the chemical formulae of TiOCl₂·nH₂O and Fe(H₂O)Cl₂·(m − 1)H₂O, a series of crystalline structures for TiOCl₂·nH₂O could be built from Fe(H₂O)Cl₂·(m − 1)H₂O by only removing some H⁺ ions. Therefore, the structures of TiOCl₂·3H₂O and TiOCl₂·H₂O can be designed based on the crystal structure of FeCl₂·4H₂O (space group P2₁/c) and that of FeCl₂·2H₂O (space group C2/m), respectively. The periodic structure of (Ti₂O₂)(H₂O)₄Cl₄ (treated as a crystal) was then built with the space group Immm, with its initial unit cell parameters being derived from the crystal structure of FeCl₂·2H₂O (space group C2/m). The elements had to be changed from Fe to Ti in the crystallographic information files (CIF), the super cell was made 1 × 1 × 3, one Ti was deleted, the bridging atoms were changed from Cl to O, and then the periodic structure of (Ti₂O₂)(H₂O)₄Cl₄ was finally built. Based on its crystal structure, each (Ti₂O₂)(H₂O)₄Cl₄ cluster was treated as a single molecule. We recognised that the (Ti₂O₂)(H₂O)₄Cl₄ cluster, where two Ti atoms were bridged with two O atoms, and coordinated to four H₂O and four Cl⁻ ligands, had D_2h symmetry. This structure is corresponding to our speculation from experimental data.

To examine the structure of Ti(IV) ions in water, we recorded the Raman spectra for real and calculated titanium chloride solutions (Fig. 4). The Raman spectrum of (Ti₂O₂)(H₂O)₄Cl₄ cluster was calculated by Dmol³ code, and important corresponding structures are depicted in Fig. 5. Based on the calculated vibrational modes of the (Ti₂O₂)(H₂O)₄Cl₄ cluster with D_2h symmetry, most of the peaks are consistent with the experimental data, but there is no obvious peak 0 appearing at 251 cm⁻¹ as in the calculated spectrum. According to the calculated result, the Ti–Cl symmetric stretching vibration (shown in Fig. 5) should be the dominant contribution to a band at this position. Therefore, the importance of the Ti–Cl bond must be lower in real life. Some of the Cl⁻ may be replaced by OH⁻ and the corresponding structure of (Ti₂O₂)(H₂O)₄Cl_4−x(OH)_x seems to be a more reasonable one. The peak 1 located at 385 (cal. 375) cm⁻¹ which cannot be readily found in the calculated Raman spectrum is mainly caused by a Ti–O₂ vibration. The peak 2 at 405 (cal. 402) cm⁻¹, and peak 3 at 418 (cal. 450) cm⁻¹ correspond with the vibrational modes of Ti–O1 shown in Fig. 5. Due to the deviation of experimental and calculated value of peak 3, we speculated that the free H⁺ ions in TiOCl₂ solution were adsorbed by O1 in (Ti₂O₂)(H₂O)₄Cl₄ and formed strong bonds as O1–H⁺. As we know the bond length of Ti–OH (∼2.0 Å) is much longer than that of Ti–O (∼1.9 Å), protonation of O increases the Ti–Ti distance, the Raman bad to move to lower wave number. The spectral line intensity at 643 (cal. 617) and 693 (cal. 689) cm⁻¹ are caused by the vibration of the O2–H bond of structured water in (Ti₂O₂)(H₂O)₄Cl₄ cluster.

Fig. 4 Comparison of the Raman spectra between experimental and calculated data: (a) calculated Raman data from (Ti₂O₂)(H₂O)₄Cl₄; (b) experimental Raman data of TiO₂ = 2.5 mol L⁻¹.

Fig. 5 Vibrational modes of the important Raman peaks of (Ti₂O₂)(H₂O)₄Cl₄.

3.2 Hydrolysis of TiOCl₂ solution

3.2.1 Hydrolysis ratio. Fig. 6 shows the hydrolysis ratio curve of TiOCl₂ with different H⁺ concentrations. It exhibits a regular pattern, but not as predicted, since we expected the hydrolysis ratio of TiOCl₂ to decrease monotonically as the concentration of H⁺ increased. However, the hydrolysis ratio pattern had peaks showing the highest values at H⁺ concentrations of 4.17 and 4.77 mol L⁻¹, for TiO₂ concentration of 0.46 ± 0.02 mol L⁻¹ and 0.93 ± 0.03 mol L⁻¹; the hydrolysis ratios were highest at 71.5% and 91.6%, respectively. Therefore, we considered the (Ti₂O₂)(H₂O)₄Cl₄ cluster to be very stable and difficult to aggregate in HCl solution. The addition of H⁺ was propitious for breaking the stable Ti–O bond and forming an active intermediate labelled as Ti(OH)(H₂O)₂Cl₃ (shown as chemical reaction (3)). Using the hydrolysis process of chemical reaction (4), the single Ti atom cluster of Ti(OH)(H₂O)₂Cl₃ could be aggregated by removing HCl. Further aggregation and rearrangement may have taken place between the active clusters of Ti(OH)₂Cl₂. We concluded that an intermediate rutile-like structure of Ti(OH)₂Cl₂ may have existed.

n/2(Ti₂O₂)(H₂O)₄Cl₄ + nHCl → nTi(OH)(H₂O)₂Cl₃ (3)

nTi(OH)(H₂O)₂Cl₃ → [Ti(OH)₂Cl₂]_n + nHCl (4)

[Ti(OH)₂Cl₂]_n → [TiO₂]_n + 2nHCl (5)

Fig. 6 The relationship between hydrolysis ratio and the concentration of H⁺ (before hydrolysis). (a) The concentration of TiO₂ is 0.93 ± 0.03 mol L⁻¹; (b) the concentration of TiO₂ is 0.46 ± 0.02 mol L⁻¹.

3.2.2 Particle size of hydrated TiO₂. The TiO₂ samples were obtained by drying the precipitated hydrated TiO₂ at 80 °C to remove the adsorbed water and make the XRD peaks sharper and more intense. In this work, all the TiO₂ samples exhibited the rutile TiO₂ phase.

The calculated lattice parameters for rutile phase hydrated TiO₂ are a = b = 4.612–4.624 Å and c = 2.956–2.962 Å. Table 3 shows the detailed parameters of hydrated TiO₂ in the rutile phase. The crystallite size (crystalline grain) of nuclei measurements was calculated from XRD patterns using the Scherrer equation (see Section 2.4). The average particles D(0.5) of the agglomerated precipitate from solution were found to be 1–24 μm by a LPSA.

Table 3 The parameters of unit cell and crystalline grain under different initial concentration of TiO₂^a

Rwp (%)	Rp (%)	a (Å)	b (Å)	c (Å)	A (nm)	B (nm)	C (nm)	S (nm^2)	n	D(0.5) (μm)	CH^+ (mol L^−1)	CTiO2 (mol L^−1)
a The parameter n representatives the number of TiO2 in a crystal particle (similar to Z value), n = Z(ABC)/(abc) A, B and C are the crystalline grain parameters calculated by Scherrer equation. S is the surface of crystalline grain, S = 2(AB + AC + BC).
The initial concentration of TiO2 is 0.93 ± 0.03 mol L^−1
5.14	3.51	4.615	4.615	2.957	3.121	3.121	7.642	114.884	2364	23.71	6.13	0.701
6.11	4.05	4.612	4.612	2.956	3.701	3.701	8.519	163.592	3712	22.18	5.82	0.313
6.03	4.05	4.621	4.621	2.958	3.915	3.915	8.489	153.510	4120	21.12	5.22	0.137
6.36	4.23	4.617	4.617	2.962	4.049	4.049	9.018	178.844	4683	6.827	4.02	0.091
6.04	4.25	4.614	4.614	2.958	5.118	5.118	10.215	261.509	8498	1.257	3.24	0.115
The initial concentration of TiO2 is 0.46 ± 0.02 mol L^−1
7.13	4.39	4.624	4.624	2.960	4.268	4.268	10.254	211.488	5903	14.58	5.65	0.305
6.80	4.33	4.616	4.616	2.960	3.780	3.780	9.579	173.411	4340	10.16	4.78	0.190
6.42	4.29	4.621	4.621	2.961	3.921	3.921	9.242	175.700	4494	11.62	3.79	0.141
5.84	3.99	4.621	4.621	2.959	5.147	5.147	9.767	254.066	8190	4.600	2.80	0.151
5.41	3.79	4.622	4.622	2.957	5.136	5.136	8.933	236.277	7460	5.129	1.69	0.176

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On the basis of chemical reactions (3)–(5), and the Gibbs free energy formula (6), the formula (7) can be obtained as follows:

ΔG = −RT ln k + Sγ_sl (6)

ΔG = −RT(2 ln[H⁺] − ln[Ti⁴⁺]) + Sγ_sl (7)

where, ΔG = Gibbs free energy, R = ideal gas constant, T = temperature, S = surface of crystalline nuclei, γ_sl = surface tension between the solution and the nuclei.

Based on formula (7), we calculated ΔG and γ_sl, shown in Fig. 7, as equal to the intercept of a and the slope of –b, respectively. Therefore, ΔG was −19.46 ± 1.70 kJ mol⁻¹ and γ_sl was 0.0237 ± 0.0085 kJ mol⁻¹ nm⁻² (=3.93 ± 1.41 × 10⁻⁵ Nm⁻¹). Some points in Fig. 7 were excluded, due to some concentrations of H⁺ and TiO₂ giving rise to unusual values. From the data in Table 4, the removed point at 114.884 nm² can be calculates as corresponding to concentrations of H⁺ and TiO₂ of 6.13 and 0.701 mol L⁻¹, respectively. The other removed point at 236.277 nm² has H⁺ and TiO₂ concentrations of 1.69 and 0.176 mol L⁻¹, respectively. At the two removed points, the F_mol values are 8.74 and 9.20 which are much lower than the other values of 18.5–44.18. It is clear that the F_mol values obtained after the hydrolysis process were nearly ranged in the left side separated by a dotted line in Fig. 6. As it was mentioned in Fig. 5, some Ti⁴⁺ ions in the solution should not be treated as the hydrate structure with only one Ti atom, but as containing two Ti atoms. Therefore, the formula (7) needed to be adjusted, and some hydrated Ti⁴⁺ ions with the Ti(OH)₂Cl₂ structure transform to that of (Ti₂O₂)(H₂O)₄Cl₄. However, the mole ratio of Ti(OH)₂Cl₂ to (Ti₂O₂)(H₂O)₄Cl₄ is difficult to obtain. Therefore, we excluded the two aberrant points.

Fig. 7 The linear fitting between the superficial area of particle grain and Gibbs free energy of chemical reaction.

Table 4 The chemical composition of the sample (wt%)

TiO2	Al2O3	CaO	P2O5	SiO2	Cl
99.44	0.276	0.091	0.044	0.041	0.058

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The average particle size, D(0.5), of TiO₂ gradually decreased with increasing n value, and a D(0.5) of 1.257 μm indicated a narrower particle size distribution than that obtained under other conditions. The appropriate particle size and narrow particle size distribution were also beneficial for improving the pigment properties of TiO₂. However, the hydrolysis ratio of the TiOCl₂ solution under these conditions was only about 23.7%. For the highest hydrolysis ratio with different concentrations of Ti⁴⁺, the n value was about 4000, with an average particle size D(0.5) of about 10–20 μm, which was much higher than the optimum particle size. Therefore, balancing the relationship between D(0.5) and the hydrolysis ratio was the key issue for preparing useful rutile TiO₂ pigments.

3.3 Preparation of rutile TiO₂

The acid leaching TiOCl₂ solution (real solution) with C_Ti⁴⁺ = 0.92 mol L⁻¹ and C_H⁺ = 6.01 mol L⁻¹ were hydrolyzed at boiling temperature for 4 hours. After calcination of rutile-type TiO₂·nH₂O, samples that were not doped and coated contained more than 99 wt% of TiO₂. As shown in Table 4, the composition of samples prepared in this work met the commercial requirements of pigments. However, this kind of sample did not have properties suitable for use as pigment. It is well known that the samples with good crystallinity exhibit excellent refrangibility (rutile > 1700, anatase > 1250) and that the optimum particle size for TiO₂ pigments is between 0.2 and 0.3 μm (half the visible wavelength). In the sulfate processes, high temperatures (>900 °C) make anatase transform to rutile. In this work, we did not need to consider this conversion because most of the hydrolysed TiO₂·nH₂O exhibited the rutile phase, but both the crystallinity and size distribution of the samples was highly affected by calcination temperature. The effects of temperature were investigated by comparing the size of particle grains under different initial concentrations of Ti⁴⁺ and H⁺. The results in Table 5 show that larger particle grains were obtained on increasing the temperature at C_Ti⁴⁺ = 0.908 mol L⁻¹ and C_H⁺ = 3.47 mol L⁻¹. It was also found that the calcined product exhibited a typical mesoporous structure, as detected by SEM (Fig. 8(b)). The mesoporous structure should be direct evidence of the migration pathway generated by HCl.

Table 5 The parameters of unit cell and crystalline grain under different temperature^a

Temperature (°C)	Rwp (%)	Rp (%)	a (Å)	b (Å)	c (Å)	A (nm)	B (nm)	C (nm)	Diameter (μm)
a Diameters were measured by SEM.
530	6.55	4.46	4.5928	4.5928	2.9571	12.396	12.396	16.009	0.3–1
630	6.46	4.42	4.5962	4.5962	2.9593	18.308	18.308	22.318	4–6
830	7.77	5.27	4.5972	4.5972	2.9606	54.627	54.627	67.365	6–10
900	8.21	6.26	4.6001	4.6001	2.9625	132.247	132.247	190.657	6–9

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Fig. 8 SEM image of rutile TiO₂ calcinates at 830 °C.

3.4 Formation mechanism of hydrated titanium dioxide

According to Wang⁴³ and Zheng⁴⁴ reports, when the concentration of HCl is low, rutile is the prominent crystalline phase. They found that [TiO(OH₂)₅]²⁺ monomer⁴⁵ should be the dominant structure in TiOCl₂ solution when C_HCl < 2 mol L⁻¹. In this way, octahedral TiO₆ corner/edge-sharing structure can be formed, which leads to the rutile phase. If C_HCl > 3 mol L⁻¹, Ti(OH)₂Cl₂(H₂O)₂ (ref. 46) is the dominant structure, which then aggregates to form the anatase phase. Their study showed that rutile can be formed with low concentration of HCl but it can be converted to anatase by increasing the concentration of HCl. However, according to Cheng's report,⁴⁷ [Ti(OH)_mCl_n]²⁻ (n + m = 6) is the reasonable structure in TiOCl₂ solution, and n and m are determined by the acidity and concentration of Cl⁻ anions. As the acidity in TiOCl₂ solution increases, the number of OH⁻ ligands in [Ti(OH)_nCl_m] decreases, leading to the aggregation of Ti clusters where octahedral TiO₆ corner/edge-sharing structures are more probable than octahedral TiO₆ edge-sharing structures. Therefore, higher acidity and concentrations of TiOCl₂ could be beneficial for the formation of the rutile TiO₂ phase. Unfortunately, different researchers who have investigated the influence of acidity have obtained different results. To better explain the experimental results, we proposed a novel mechanism for hydrolysis of TiOCl₂ solutions as follows.

The Raman spectra displayed in Fig. 4 show that the Ti⁴⁺ ion in TiOCl₂ solution occurs in the stable (Ti₂O₂)(H₂O)₄Cl₄ structures. Based on the Ti₂O₂Cl₄ cluster (point group: D_2h) reported by Shirley et al.,³⁵ we proposed a similar structure for (Ti₂O₂)(H₂O)₄Cl₄ in solution, as discussed in Section 3.1. In order to simplify the postulated reaction pathway from (Ti₂O₂)(H₂O)₄Cl₄ to TiO₂, a series of periodic structures are described in Fig. 9 (e.g. the cluster of (Ti₂O₂)(H₂O)₄Cl₄ shown in Fig. 5 can be expressed as Fig. 9(a)). When HCl is removed from between the adjacent (Ti₂O₂)(H₂O)₄Cl₄ moieties, the anatase structure forms due to TiO₆ edge-sharing. Because the clusters of [(Ti₂O₂)(H₂O)₄Cl_4−m]^m+ and [(Ti₂O₂)(H_2−nO)₄Cl₄]⁴ⁿ⁻ are generated rapidly due to ionisation reactions, the reaction kinetics play significant roles. A high concentration of the (Ti₂O₂)(H₂O)₄Cl₄ cluster is beneficial for the formation of the anatase TiO₂ phase. Moreover, the size of generating nuclei should be smaller. Under hydrolysis by adding H⁺, some Ti–O bonds in (Ti₂O₂)(H₂O)₄Cl₄ (Fig. 9(a)) break, leading to the formation of the active cluster. In this work, we supposed that Ti(OH)(H₂O)₂Cl₃ (Fig. 9(b)) was the intermediate phase in the formation process of the 1-dimensional periodic structure, Ti(OH)₂Cl₂ (Fig. 9(c)). The 1-dimensional periodic structure of Ti(OH)₂Cl₂ can stack to rutile-type Ti(OH)₂Cl₂ (Fig. 9(d)). Further aggregation and removal of HCl may have taken place between adjacent Ti(OH)₂Cl₂ complexes. It is well known that both anatase and rutile TiO₂ phases can grow from octahedral TiO₆ complexes, and that the phase transition proceeds by octahedral rearrangement. The arrangement of octahedral TiO₆ through edge-sharing initiates the anatase phase, while corner/edge-sharing leads to the rutile phase. In this system, rutile-type Ti(OH)₂Cl₂ easily lost Cl and H from the –OH groups of adjacent Ti(OH)₂Cl₂ to form rutile-type H₂TiO₃. Therefore, the intermediate structure of Ti(OH)₂Cl₂ determines the final crystal structures of TiO₂. Under high acidity, (Ti₂O₂)(H₂O)₄Cl₄ should easily form Ti(OH)₂Cl₂, and Ti(OH)₂Cl₂ should also easily convert to rutile-type Ti(OH)₂Cl₂. Thus, higher acidity of TiOCl₂ should be beneficial for the formation of a rutile TiO₂ phase. Moreover, the size of generating nuclei should be bigger. After calcination of rutile-type H₂TiO₃, we found mesoporous structures by SEM (Fig. 8(b)); therefore, intermediate rutile-type structure of Ti(OH)₂Cl₂ may also exist. Moreover, we expected the unit cell parameters to decrease with higher calcination temperatures due to the removal of HCl from rutile-type Ti(OH)₂Cl₂ (in this work, the predicted unit cell parameters for rutile-type Ti(OH)₂Cl₂ of a = b = 9.273 Å and c = 3.210 Å were larger than that of rutile TiO₂, with a = b = 4.59 Å and c = 2.96 Å). This contradiction in experimental findings, shown in Table 5, most likely occurred because the calcination temperatures of 530–900 °C were too high, causing nearly all Cl to be eliminated. Table 5 shows that the size of the crystal grain clearly becomes larger with increasing temperature.

Fig. 9 The schematic diagram of the hydrolysis process. (a) Cluster of (Ti₂O₂)(H₂O)₄Cl₄; (b) the intermediate cluster of Ti(OH)(H₂O)₂Cl₃; (c) 1-dimensional periodic structure of Ti(OH)₂Cl₂; (d) rutile-type Ti(OH)₂Cl₂; (e) rutile TiO₂.

4. Conclusions

The Raman spectra of Ti(IV) structures in HCl solution have been studied in close comparison with DFT calculations. Ti(IV) was stable, existing with two Ti atoms in a cluster and forming a (Ti₂O₂)(H₂O)₄Cl₄ structure with D_2h symmetry. By determining the relationship between the surface area of H₂TiO₃ and the concentrations of Ti⁴⁺ and HCl, we identified that the nuclear energy was −19.46 kJ mol⁻¹. Moreover, a complete scheme for the formation and transformation of rutile, TiO₂, induced by the hydrolysis of a TiOCl₂ solution, was proposed. Using DFT simulations, it was shown that the periodic structure can lead to this transformation occurring through a simple structural rearrangement, as follows: (Ti₂O₂)(H₂O)₄Cl₄ (in solution)–Ti(OH)(H₂O)₂Cl₃ (with addition of HCl)–Ti(OH)₂Cl₂ (1-dimentional growth and removal of HCl)–rutile-type Ti(OH)₂Cl₂ (stack)–rutile TiO₂ (with removal of HCl).

Acknowledgements

The authors would like to thank National Supercomputing Center in Shenzhen for providing the computational resources and materials studio (version 6.1, MS Dmol³ Parallel). We gratefully acknowledge support from the Major State Basic Research Development Program of China (Grant No. 2013CB632604), National Science Foundation for Distinguished Young Scholars of China (Grant No. 51125018), and National Natural Science Foundation of China (Grant No. 51402303, 21403243, 51504230, 21506233).

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Footnote

† These authors contributed to this work equally.

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