Effect of TiO₂ Content on the Structure of CaO–SiO₂–TiO₂ System by Molecular Dynamics Simulation

Abstract

The change of structure in the ternary system CaO–SiO₂–TiO₂ with TiO₂ varying from 0 to 25% mole fraction at a fixed basicity of 0.8 was investigated by means of molecular dynamics simulation. The present simulation demonstrates that most Si is coordinated with 4 O within a tetrahedron while the majority of Ti with 6 O in an octahedron. With the addition of TiO₂, the coordination number for Si (CN_Si–O) changes from 4.12 to 4.03, while the CN_Ti–O varies from 5.83 to 5.52. The fraction of bridging oxygen (Si–O–Si) decreases resulting in the depolymerization of silicate structure and the Si–O–Ca is gradually replaced by Si–O–Ti with increasing TiO₂ fraction. Two [TiO₆] octahedrons are connected by two ways with the angles of Ti–O–Ti equaling to 100° and 140°, and the fraction of them are almost the same for sample with 10 mol-% TiO₂ addition. The variation of network connectivity Qⁿ of Si also agrees with the above conclusion. Thus, TiO₂ is regarded as basic oxide which acts as modifier in this ternary system in terms of its structure within this system.

1. Introduction

There is a lot of vanadium-titanium magnetites (VTM) in Panxi region, China, in which the proven VTM reserves is approximately 10 billion tons. The VTM is a very complex ore containing Ti, V, Co, Ni, Sc et al. besides Fe,¹⁾ and the phase of Ti exists in ilmenite (FeTiO₃), titanomagnetite (Fe₃O₄·Fe₂TiO₄), ulvite (Fe₂TiO₄) and pseudobrookite (Fe₂TiO₅). After decades of basic research and industrial production practice, a complete set of blast furnace-converter smelting process has been successful developed to produce steel and vanadium/titanium products. Although it has high production efficiency and large scale, the blast furnace-converter smelting process has many severe defects, especially in blast furnace process to reduce the VTM ore. In the blast furnace process, most of the iron and part of vanadium can be reduced into the hot metal, however, almost all of the titanium enters into the slag in phase formation of perovskite and titanaugite, Ti-rich diopside, forming the high titanium slag with the content of TiO₂ varying from 22 to 25%,^1,2) which results in the foaming behavior, the increase of melting temperature and viscosity of slag,³⁾ as well as the difficult separation of slag-iron.^4,5) In particular, viscosity which is sensitive to the structure change of the slag plays a prominent role in the blast furnace. It’s well known that the physicochemical properties of high temperature slag are determined by the degree of polymerization of the structure.^6,7)

The structures of calcium-silicate-based slags have been investigated by steelmakers using Fourier transformation infrared spectra, Raman spectra, XPS, XRD, NMR spectroscopy, etc.^6,8,9) The Properties of slag such as the viscosity have also been measured by metallurgist due to its important impact on the metallurgical process.^{6,8,10,11,12,13)} It’s known that the silicate network is depolymerized with the addition of basic oxide which offers O^2– such as CaO, MgO, Na₂O, etc. The alkali metal ions react with the bridged oxygen of the silicate to form non-bridged oxygen resulting in lower viscosity. In particular, Al³⁺ is surrounded by 4 O^2– , acting as an amphoteric cation.⁹⁾

Additionally, TiO₂ has been reported as an amphoteric oxide, too. It’s reported that TiO₂ can increase the viscosity of the CaO–SiO₂–Al₂O₃–TiO₂ slag under reducing atmosphere indicating that it behaves as a network-former which increase the polymerization of the network of the slags by Ohno and Ross.⁵⁾ However, the viscosity experiments conducted by Saito et al. indicated that TiO₂ decreases the viscosity in quaternary CaO–SiO₂–Al₂O₃–TiO₂ slag system.¹²⁾ Shankar et al. found that TiO₂ up to 2 mass% lower the viscosity in CaO–SiO₂–MgO–Al₂O₃.³⁾ Handfield et al. described industrial high TiO₂ slags are very fluid melts once completely molten.⁴⁾ Park et al.,¹⁴⁾ Sohn et al.¹⁵⁾ and Liao et al.¹⁰⁾ revealed that TiO₂ acts as a basic oxide resulting in the depolymerization of the slags under neutral conditions in CaO–SiO₂–MgO–TiO₂–Al₂O₃ quinary slag systems with varying basicity and TiO₂ content although the content of MgO and Al₂O₃ are different in their systems. Park et al. has also used FTIR and Raman spectroscopy to study the influence of TiO₂ on the silicate structure in CaO–SiO₂-17 mass% Al₂O₃-10 mass% MgO contributing to the same conclusion.¹⁴⁾ Nevertheless, the detailed structure of the slags with high TiO₂ content has not been studied systematically. The content of CaO–SiO₂–TiO₂ system is approximately 75% within the blast furnace slags containing high TiO₂. So it is important that a deep understanding for the structure of this system produced from the smelting process of blast furnace with Ti-bearing ores.

The molecular dynamics (MD) simulation is an excellent tool for studying the microstructure with classical dynamics, which was generally used in numerous fields these years. Owing to the difficulty in high temperature experiments the molecular dynamics simulation is also applied into research of the metallurgical melt. The CaO–Al₂O₃ melts were studied by Belashchenko et al. with the method of MD simulation with Born–Mayer pair potentials taking into account the effective dipole–dipole interaction and the thermodynamic, structural, and topological properties of the system were calculated.¹⁶⁾ Zheng et al. revealed the effect of Al₂O₃/SiO₂ ratios on the structure of calcium aluminosilicate slags by MD simulation.¹⁷⁾ Shimoda also investigated the chemical structure and dynamic properties of an amorphous slag CaO–SiO₂–MgO–Al₂O₃ using MD simulation.¹⁸⁾ However, the microstructure of CaO–SiO₂–TiO₂, which has prominent effect on the physicochemical properties, has not been studied by MD simulation. Thus, this study attempts to analyse the change of the microstructure of the CaO–SiO₂–TiO₂ system resulting from the variation of TiO₂ content by means of MD simulation at a given basicity.

2. Simulation Methods

The key point for the classical molecular dynamics simulation is the choice of a suitable potential function. In the present study, the simulation was performed using the Born-Mayer-Huggins (BMH) interatomic potentials which has been generally used in the research of structure of glasses or slags during past years and has been proved successfully compared to the experiment results using XRD, NMR, Raman spectroscopy, etc.^{16,17,19,20,21)} The BMH interatomic potentials are composed of coulombic interaction, repulsion interaction and vander Waals force, with the algebraic expression as follows,   

$${\text{U}}_{\text{ij}}=\frac{{\text{Z}}_{\text{i}}{\text{Z}}_{\text{j}}{\text{e}}^2}{4\pi {\mathit{\text{ε}}}_0{\text{r}}_{\text{ij}}}+{\text{f}}_0({\text{b}}_{\text{i}}+{\text{b}}_{\text{j}})\text{exp}\left[\frac{{\text{a}}_{\text{i}}+{\text{a}}_{\text{j}}-{\text{r}}_{\text{ij}}}{{\text{b}}_{\text{i}}+{\text{b}}_{\text{j}}}\right]-\frac{{\text{C}}_{\text{i}}{\text{C}}_{\text{j}}}{{\text{r}}_{\text{ij}}^6}-\frac{{\text{C}}_{\text{i}}{\text{C}}_{\text{j}}}{{\text{r}}_{\text{ij}}^8}$$(1)

Where, f₀ is the unit constant ( = 6.9511*10^–11 N), a_i and a_j the parameters which reflect the repulsive radius, and the b_i, b_j are the softness parameters. The last two terms which represent the dipole-dipole and dipole-quadruple interactions could be omitted due to the minuteness values compared with the first and the second terms. Therefore, the potential function is simplified as,   

$${\text{U}}_{\text{ij}}=\frac{{\text{Z}}_{\text{i}}{\text{Z}}_{\text{j}}{\text{e}}^2}{4\pi {\mathit{\text{ε}}}_0{\text{r}}_{\text{ij}}}+{\text{B}}_{\text{ij}}exp(-{\text{R}}_{\text{ij}}\cdot {\text{r}}_{\text{ij}})$$(2)

where, U_ij is the interatomic potential, Z_i, Z_j the charge of the atoms corresponding to the valence of every element, e the electron charge, and r_ij denotes the interatomic distance between a pair of atoms. The potential function consists of two parts. The first term on the right hand of the Eq. (2) represents the Coulombic interaction which was calculated by the Ewald method and the cutoff of the potential is always equal to the half of the box in which the ions were inserted. It was set to 10 Å in this work to simplify the computation. B_ij and R_ij are the parameters to describe the short-range repulsion interaction between two atoms corresponding to the second term in Eq. (2). The adopted values are listed in Table 1.

Table 1. Potential parameters used in this study.

Atom i	Atom j	Bij (eV)	Rij (1/Å)
Ca	Ca	330000.0	0.16
Ca	Si	26718.7	0.16
Ca	Ti	107000.0	0.16
Ca	O	720000.0	0.165
Si	Si	2162.5	0.16
Si	Ti	8687.5	0.16
Si	O	62500.0	0.165
Ti	Ti	35187.5	0.16
Ti	O	240000.0	0.165
O	O	150000.0	0.17

The simulation of the ternary system CaO–SiO₂–TiO₂ was performed with varying mole fraction (mol-%) of TiO₂ from 0 to 25% at a constant basicity of 0.8. The samples were divided into 6 groups with varying fraction of TiO₂. Correspondingly, the numbers of the atoms, based on the mole fraction, were listed as Table 2. The total number of each group is about 4199, with the density equaling to 2.95 g/cm³. All atoms were put into a cubic box, whose lengths are listed in Table 2, too.

Table 2. The composition of slags, number of atoms.

No.	R	Composition (mol-%)			Atomic number					Length of box (Å)
		CaO	SiO2	TiO2	Ca	Si	Ti	O	Total
1	0.8	44.4	55.6	0	730	913	0	2556	4199	37.78
2	0.8	42.2	52.8	5	688	860	81	2570	4199	37.90
3	0.8	40	50	10	646	807	162	2584	4199	38.02
4	0.8	37.8	47.2	15	605	756	240	2597	4198	38.13
5	0.8	35.6	44.4	20	565	706	317	2611	4199	38.25
6	0.8	33.3	41.7	25	524	655	395	2624	4198	38.36

The three-dimensional periodic boundary conditions were applied on the model box, in which all of the atoms were inserted randomly and the Gear integration of motion equations was used. The atoms were equilibrated at 5000 K for 8000 time steps with a time step Δt = 1 fs (10^–15 s). Subsequently, it was cooled down to 1723 K within 2000 steps and equilibrated at 1723 K for 10000 time steps in order to acquire the information of the structure by statistics. The simulation was performed with more steps but little variation was observed.

3. Results and Discussion

3.1. Pair Distribution Function and Coordination Number

The pair distribution function (PDF), g_ij(r) is generally used to describe the feature of short-range order of the slag melt, which gives the probability to find an ion within Δr at a distance r from a specified ion. This function can be calculated by the following equation,   

$${\text{g}}_{\text{ij}}(\text{r})=\frac{1}{\rho }\frac{\text{n}(\text{r})}{\text{V}}=\frac{\text{V}}{{\text{N}}_{\text{i}}{\text{N}}_{\text{j}}}{{{\displaystyle \sum }}^{}}_{\text{j}}\frac{\text{n}(\text{r})}{4\pi {\text{r}}^2\mathrm{\Delta }\text{r}}$$(3)

Where, N_i and N_j are the total number of ions i and j, respectively. V is the volume of the system, and the n(r) denotes the average number of the ions j surrounding the ion i in a spherical shell within r ± Δr/2. Structure information such as the bond length and the mean coordination number (CN) can be obtained from the pair distribution function g_ij(r). The CN is calculated by integrating the g_ij(r) curve to the first valley of it, and the formula is presented as,   

$${\text{N}}_{\text{ij}}(\text{r})=\frac{4\pi {\text{N}}_{\text{j}}}{\text{V}}{{{\displaystyle \int }}^{}}_0^{\text{r}}{ \text{r}}^2{\text{g}}_{\text{ij}}(\text{r})\text{dr}$$(4)

The PDF and the average CN curves of No. 5 group, reflecting the local structure information of the systems, were obtained as Fig. 1, from which it can be acquired the bond length of atomic pair as well as the CN. The bond length of Si–O, Ti–O, Ca–O and O–O, corresponding to the first peaks of the PDFs, which were paid more attention to by investigators, are 1.6, 1.9, 2.3 and 2.6 Å, respectively. The bond length of Si–O, Ca–O and O–O are in accordance with previous results although in different slag systems,^17,18,22) but the value of Ti–O was rarely reported in slag system to the authors’ knowledge. All of the values are listed in Table 3. Correspondingly, the average CNs of Si–O, Ti–O and Ca–O are approximately 4, 6 and 6, respectively. The bond length of Si–O is the minimum, secondly the Ti–O, indicating that the combining capacity between Si–O is stronger than others. A sharp and narrow peak of Si–O also agrees with the result above. Furthermore, the coordination number of Si–O, which is nearly equal to 4, suggests the [SiO₄] tetrahedron exists and has a higher stability. This is consistent with the other reports in silicate.^17,18) The [SiO₄] tetrahedron units are connected by O atoms which are called bridging oxygen resulting in a more complex structure as well as the increase of the viscosity. The atomic pair Ti–O has also plays a prominent role in the structure of the slag system. It can be observed that the CN_Ti–O is approximately equals to 6 (less than 6), implying that the majority of Ti is in 6-fold coordination with O, which is agreement with other work.²³⁾

Fig. 1.

The (a) PDFs and (b) CNs of the No. 5 group in this ternary system.

Table 3. The length of the atomic pairs in the No. 5 group.

Atomic pair	Ca–Ca	Ca–Si	Ca–Ti	Ca–O	Si–Si	Si–O	Si–Ti	Ti–O	Ti–Ti	O–O
Length of bond(Å)	3.45	3.40	3.30	2.30	3.15	1.60	3.35	1.90	3.10	2.60

The Ca–O has no stable structure, corresponding to the absence of a platform in the CN_Ca–O curve. However, its coordination number can be obtained at a distance of 3.0 Å with the value approximately corresponding to 6. It’s obvious that the CN_Ti–O and the CN_Ca–O have almost the same value 6. Ca²⁺ is considered to be as network-breaker, which depolymerizes the 3D network formed by Si and O. It can be concluded that the Ti⁴⁺ is in an octahedron which can break up the complex structure of silicate by breaking the Si–O–Si. It’s known that the Ca²⁺ cation can break up the Si–O bond by forming non-bridging oxygen (NBO) and small fraction of free oxygen. The combining capacity of Ca–O and Ti–O are all weaker than that of Si–O, thus we regarded them as the network-modifiers owing to the same role which depolymerizes the 3D network of silicate. Numberous studies have also demonstrated that the TiO₂ acts as a basic oxide in blast furnace slags under neutral atmosphere through their experiments.^{10,11,14,15,24)} However, the Ti–O has a stable octahedron unit which is different from the Ca–O, resulting in the amphoterism of TiO₂ like Al₂O₃.

The structure information of No. 5 group is described above, the variation of the structure in the ternary system with the addition of TiO₂ was also studied which is expressed by Figs. 2 and 3. The PDFs of Si–O (a) and Ti–O (b) with varying TiO₂ are presented in Fig. 2, from which we can obtain the corresponding bond length with different TiO₂ additions. Figure 3 shows effect of TiO₂ content on the average CNs of Si–O (a) and Ti–O (b) which reflect the change of local structure. The CN_Si–O varies from 4.12 to 4.03 with the addition of TiO₂ but the variation of the CN_Ti–O is observed with the values varying from 5.83 to 5.52 in Table 4 which is larger than that of CN_Si–O as the concentration of TiO₂ increases. Therefore, it can be seen that the stability of [SiO₄] tetrahedron is stronger than [TiO₆] from the larger alteration of the CNs with varying mole fraction (mol-%) of TiO₂ from 0 to 25%. The results above also indicate that the higher coordinated Si and the lower coordinated Ti exist, which can be observed from Fig. 4. The figure shows the change of concentration of the Si^IV, Si^V, Ti^VI, etc., which is deduced from the amount of TiO₂. It can be seen that the Si^IV preponderates over others with the fraction of more than 80% and increases with the increasing TiO₂ content. It’s noted that the content of Si^IV increases from 80% to 93% monotonically, implying that the TiO₂ contributes to the stability of [SiO₄] unit. It’s inferred that the acidity of SiO₂ is affected by the basic oxide CaO and TiO₂. Additionally, the CN of Ti is also studied and the results showed in Fig. 4 suggest that the lower of the TiO₂ content, the higher stability of the [TiO₆] octahedron. The tendency above means that the lower TiO₂ content contributes to higher CN_Ti–O which promotes the depolymerization of the network. The majority of Ti cations are coordinated with 6 O, but the 4-coordinated and 7-coordinated Ti barely appear. Thus, the two equilibriums within this system are showed as Eq. (5), and shift towards right with the increasing TiO₂ content.   

$$\{\begin{array}{c}{ \text{Si}}^{\text{IV}}+\text{O}\leftrightarrow {\text{Si}}^{\text{V}},\\ {\text{Ti}}^{\text{VI}}\leftrightarrow {\text{Ti}}^{\text{V}}+\text{O}\end{array}$$(5)

Fig. 2.

The PDFs of the atomic pair (a) Si–O, (b) Ti–O with varying mole fraction of TiO₂.

Fig. 3.

The CNs of the atomic pair (a) Si–O, (b) Ti–O with varying mole fraction of TiO₂.

Table 4. The coordination number of Si and Ti with varying fraction of TiO₂.

CN	TiO2 (mol-%)
	0	5	10	15	20	25
Si–O	4.12	4.09	4.07	4.05	4.04	4.03
Ti–O	…	5.83	5.76	5.69	5.60	5.52

Fig. 4.

The effect of content of TiO₂ on the coordination number of Si and Ti.

3.2. The Different Types of Oxygen Atoms

The species of oxygen atoms classified by the cations they connect to have been mentioned in the previous chapter. The bridging oxygen (BO) which connects two tetrahedrons increases the degree of polymerization while the non-bridging oxygen (NBO) which connects a tetrahedron and a modifier has the contrary impact within the silicate. In addition, a small fraction of free oxygen (fO) which links two modifiers and contribute to the depolymerization exists. The types of O atoms play a prominent role on the structure within the ternary system, thus it’s essential to investigate the content of them for a deep understanding of the structure. As shown in Fig. 5, a clear trend, as expected, is observed, that the concentration of Si–O–Si corresponding to BO decreases from 49% to 22% monotonically. Sohn’s et al.¹⁵⁾ work demonstrated that the fraction of BO (bonded to two tetrahedrons) and the NBO (bonded to a single tetrahedron) decreased with TiO₂ additions, but the fO (no bonding with tetrahedron) increased with TiO₂ additions in the CaO–SiO₂-17% Al₂O₃-10% MgO slags. In this work, the BO (Si–O–Si) and NBO (Si–O–Ca) have the same tendency, while the free O in this work is not in agreement with it. The reason may be the definition of free oxygen within this system is not only the Ca–O–Ca but also the Ti–O–Ca, Ti–O–Ti, etc. The tendency implies that the Ti⁴⁺ breaks up the 3-D network formed by [SiO₄]. The concentration of Si–O–Ca and Si–O–Ti show the opposite trend with the increasing TiO₂ content, indicating that the Ca²⁺ is replaced by Ti⁴⁺ with the addition of TiO₂ into the calcium silicate. In the calcium silicate the 3-D network is broken up by Ca²⁺ while in this ternary system the function is gradually replaced by Ti⁴⁺. The two interactions may be described by Eqs. (6) and (7). In can be concluded that the rank of stability is [SiO₄] > [TiO₆] > [CaO_x] from above, resulting in the lower viscosity with the incorporation of TiO₂ given a fixed basicity. A clear trend, as expected, the concentration of Ti–O–Ti increases due to the increase of TiO₂, which is consistent with the study conducted by Park using Raman spectroscopy.¹⁴⁾   

$$\text{Si}-\text{O}-\text{Si}+\text{Ti}-\text{O}-\text{Ti}\leftrightarrow 2\text{Si}-\text{O}-\text{Ti}$$(6)

  

$$\text{Si}-\text{O}-\text{Ca}+\text{Ti}-\text{O}-\text{Ti}\leftrightarrow \text{Si}-\text{O}-\text{Ti}+\text{Ti}-\text{O}-\text{Ca}$$(7)

Fig. 5.

Fraction of different types of O vs the amount of TiO₂.

3.3. The Angles within the Different Bonds

The bond lengths and coordinations of different atomic pairs are presented above contributing to knowing about the microstructure of the polymers. The angles between the bonds should also be investigated for the steric configuration. The distribution of Si–O–Si, O–Si–O, Ti–O–Ti and O–Ti–O are presented in Figs. 6 and 7. The distribution of the angles of O–Si–O in the [SiO₄] tetrahedron shows a good symmetric structure with the average values varying between 105° and 110° which is consistent with the results of 109.3°and 108.8° by ZHENG et al.¹⁷⁾ and close to 109.5° in ideal tetrahedron. The average angle of Si–O–Si is approximately 145° indicating that two [SiO₄] tetrahedrons are connected by an O atom which is close to the values (144°) obtained by Mozzi and Warren.²⁵⁾ It’s obviously that the major angles of O–Ti–O are 90° and a small fraction of that vary from 167° to 173°, from which it can be concluded that the Ti⁴⁺ prefers to form an octahedron with 6 O atoms. However, compared with the ideal octahedron, the small fraction of the angel of O–Ti–O is not equals to 180° with a deviation of 7°–13°. It can be seen from Fig. 7 the two [TiO₆] octahedrons are connected by two ways with the angles of Ti–O–Ti equaling to 100° and 140°, which is shown in Fig. 8. The distribution of the angles of Ti–O–Ti has a obvious variation with the TiO₂ additions. When the TiO₂ fraction is small the angle of 140° is the main connectivity angle, the percentage of angle of 140° decreases with TiO₂ increasing and it reaches the minimum of 17% for 10% TiO₂ addition, then it increases to 24% for 25% TiO₂ addition. The angle of Ti–O–Ti in slags with TiO₂ was barely reported to the authors’ knowledge, with insufficient theoretical foundation to explain the reason now. It needs further study in the following work.

Fig. 6.

The distribution of angles of (a) O–Si–O and (b) Si–O–Si with different TiO₂ content.

Fig. 7.

The distribution of angles of (a) O–Ti–O and (b) Ti–O–Ti with different TiO₂ content.

Fig. 8.

Configuration of the two ways (a), (b) in which [TiO₆] octahedrons are connected.

3.4. The Network Connectivity Qⁿ of Si

The degree of polymerization can not only be described by the species of oxygen atoms but also be represented by the Qⁿ, which denotes the connectivity of the network, where n means the number of bridging oxygens within a tetrahedron such as [SiO₄] in this ternary system. Figure 9(a) shows the concentration of the five Qⁿ with varying mole fraction (mol-%) of TiO₂. The most noticeable feature is the increase of Q⁰ and Q¹ fraction accompanied by the decrease of Q³ and Q⁴, demonstrating the depolymerization of the structure. It can be seen the sum of Q³ and Q¹ decrease and the sum of Q² and Q⁰ increase with TiO₂ varying from 5 to 15 (mol-%) from Fig. 9(b) while the sum of Q³ and Q¹ has a little rising tendency from 0 to 5% (mol-%). The study performed by Park¹⁴⁾ with Raman spectra shows that the sum of Q³ and Q¹ decrease and the sum of Q² and Q⁰ increase with TiO₂ addition in CaO–SiO₂–17Al₂O₃–10MgO (wt-%) slags with the mass fraction of TiO₂ varying from 0 to 10%. The difference between Park et al.’s work and ours might results from two reasons. 1) The Al₂O₃ and MgO may have influence on the degree of polymerization. 2) Some Q⁴ was recognised as Q³ when calculating the fraction of Q³ with Raman spectra. In the present work, the Q² fraction increases firstly and subsequently decreases from the mole fraction of 15%. Although in different systems, the Q² fraction exhibits the same tendency.

Fig. 9.

The variation of Qⁿ fraction versus TiO₂ content.

4. Conclusion

The structure of the ternary system CaO–SiO₂–TiO₂ was simulative investigated by molecular dynamics technology with variation of TiO₂ contents under a fixed basicity. The obtained results are clarified as follow.

(1)　The microstructure in this system was obtained through the simulation. In the No. 5 group, the bond length of Si–O, Ti–O, Ca–O are 1.6, 1.9 and 2.3Å, respectively, reflecting the attracting capability with O is Si > Ti > Ca. The majority of Ti⁴⁺ is coordinated by 6 O atoms but the 4-coordinated Ti⁴⁺ barely present within this system.

(2)　CN is a key parameter to present the structure of the short-range ordering. The CN_Si–O almost equals to 4 and has a little variation from 4.12 to 4.03 with varying mole fraction of TiO₂, while the CN_Ti–O decreases from 5.83 to 5.52 as the mole fraction of TiO₂ varies from 0 to 25%.

(3)　Two [TiO₆] octahedrons are connected by two ways with the angles of Ti–O–Ti equaling to 100° and 140°. When the TiO₂ fraction is small the angle of 140° is the main connectivity angle, the percentage of angle of 140° decreases with TiO₂ increasing and it reaches the minimum of 17% for 10% TiO₂ addition.

(4)　The TiO₂ acts as a basic oxide within this ternary system deduced by the decreasing fraction of bridging oxygen with increasing content of TiO₂ and the variation of network connectivity Qⁿ (Si) also contributes to this conclusion.

Acknowledgements

This work is supported by the Major Program of National Natural Science Foundation of China (Grant No. 51090383) and the Fundamental Research Funds for the Central Universities (Grant No. CDJZR12130054).

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