Solid-state Reaction Studies in Al₂O₃–TiO₂ System by Diffusion Couple Method

Abstract

In order to study the formation mechanism of Al₂TiO₅, the solid-state inter-reaction between Al₂O₃ and TiO₂ under Ar atmosphere was investigated in the temperatures range from 1723 to 1873 K by the diffusion couple method. The phase of the inter-compound and the change of the concentration of Ti across the diffusion layers were confirmed by the electron probe microanalysis (EPMA). Based on the concentration profile of Ti element, the thickness of diffusion layers was obtained and the interdiffusion coefficients which were affected by temperature and concentration of Ti were calculated by the Wagner method. The experimental results indicate that the thickness of diffusion layers increases with the diffusion time. The magnitudes of interdiffusion coefficients were in the range of 10⁻¹⁰~10⁻¹² cm²/s and the range of diffusion activity energy E_D was from 266.77 kJ/mol to 309.96 kJ/mol.

1. Introduction

The polycrystalline Al₂TiO₅ ceramics are one of the excellent material for thermal shock resistance. Due to the low thermal expansion,¹⁾ low Young’s modulus and high melting point of 2133 K, they had been used as an insulation material in engine components such as piston bottom, port-liners, and turbochargers etc.²⁾ There has been some investigations on the synthesis and properties of Al₂TiO₅. Hans Wohlfromm³⁾ studied the formation of Al₂TiO₅ by sintering the Al₂O₃/TiO₂ multilayers in the temperature range from 1473 to 1773 K, and it was found that TiO₂ played an important role in the initial growth of Al₂TiO₅. In the work by M. Nagano,⁴⁾ coprecipitation method was applied to prepare the Al₂TiO₅ in air in the temperature range of 1573 to 1773 K. A fine grained-structure was obtained at 1573 K, but resulted in large-grained and cracked microstructures at 1673 and 1773 K. Addition of ZrO₂, BaO or ZrSiO₄ was effective in suppressing the thermal decomposition of Al₂TiO₅.

Moreover, Non-metallic inclusions of (Al, Ti) oxide were found in the steel containing Ti and the formation of (Al, Ti) oxide, such as Al₂TiO₅, TiO₂, Ti₂O₃, can be utilized as nuclei for MnS and the intragranular ferrite, which improve the toughness and strength of steel.⁵⁾ Generally, in the process of steel making, Ti is added as an alloying element after the deoxidation process by Al. The angular Al₂O₃ inclusions formed during Al deoxidation, which will be evolved to spherical inclusion after the addition of Ti.⁶⁾ In addition, the excess addition of Ti may cause the nozzle clogging, specially for Ti bearing Al-killed steel. Therefore, it is necessary to study the reaction mechanism between Al–Ti oxides to understand above problems better. In-Ho JUNG et al. presented the optimized phase diagram of Al₂O₃–Ti₂O₃–TiO₂ system for Ti-Bearing and Al-killed steels.⁷⁾ Cong Wang et al. reported that the effect of Ti addition on the transient behavior of inclusion.^8,9,10) Morphological change of inclusion was found when Ti/Al ratio reached 0.5. Min-Ki Sun et al. studied that various Al and Ti deoxidation techniques had influences on the morphology and chemistry compositions of inclusions.¹¹⁾

Most researches were related to the formation of Al₂TiO₅ or Al/Ti oxides, however, the solid-state reaction kinetics of Al₂O₃–TiO₂ system was studied rarely. In the present study, the diffusion between Al₂O₃ and TiO₂ was processed by a diffusion couple method in the temperature range from 1723 to 1873 K under Ar atmosphere. The influences of time and temperature on the formation of intermediate products were investigated. The kinetic parameters, inter-diffusivity and apparent activation energy, were calculated.

2. Experimental

The analytical reagent grade TiO₂ (>99%) was used for diffusion experiments, which was pre-dried at 393 K for 4 h in a drying oven under forced convection. The powers of TiO₂ were pressed to pellet of 10 mm diameter and about 5 mm thickness in a stainless steel die under 500 MPa. The prepared pellets of TiO₂ were put into the muffle furnace and sintered at 1773 K for 12 h in air atmosphere. The purchased Al₂O₃ sheets (the relative density 99.4%) were cut into the same as TiO₂ pellets. The samples of Al₂O₃ and TiO₂ were ground and mechanically polished. Then the polished surface was clean in alcohol by ultrasonic.

To obtain a good contact between TiO₂ and Al₂O₃ pellets, the diffusion couple was fixed in a clamp made by Al₂O₃ with a constant load.^12,13,14) The diffusion experiments were carried out in a SiC-heated furnace, and temperature was controlled by an B-type thermocouple. After reaching the target temperature, the diffusion couple was gradually pushed into the constant temperature zone. The diffusion couple was preheated for 20 min from the room temperature zone to the constant temperature zone. The gas flow of high purity argon was 400 ml/min. The diffusion experiments were performed with the conditions presented in Table 1. After the desired heat treatment, the diffusion couples were quenched in air atmosphere to the room temperature rapidly.

Table 1. The conditions for diffusion experiment.

No.	Temperature (K)	Time (ks)	Atmosphere
1	1723	7.2	Ar
2	1773	7.2	Ar
3	1823	7.2	Ar
4	1873	3.6	Ar
5	1873	5.4	Ar
6	1873	7.2	Ar
7	1873	14.4	Ar

The completed samples were mounted into the epoxy and triethanolamine mixture (the mass ratio of 9 to 1). The treated samples were cut perpendicular to the contact plane with a diamond saw. One side of the pellet was polished with the SiC sand paper and diamond polishing paste (size of W1.5), the flatness of polished diffusion interface was observed by an optical microscope, then cleaned by ultrasonic in ethyl alcohol. The quantitative analysis of the composition profile was by electron probe microanalysis (EPMA, JEOL JXA-8230). Pure metal aluminum and titanium used as the standard material. An electron volt of 20 kV and specimen current of 10⁻⁸ A were used for the analysis. The peak concentrations of Al, Ti and O ions were measured with 1 μm interval near the interface of the diffusion couple. The thickness of the diffusion layers were determined by the diffusion profiles.

3. Results and Discussion

3.1. Al₂O₃–TiO₂ System

Figure 1 shows the phase diagram of Al₂O₃–TiO₂.^{15,16,17,18,19)} When the temperature is in the range from 1556 to 2073 K, the inter-compound in the diffusion is the only phase of Al₂TiO₅, below 1556 K, Al₂TiO₅ decomposes into Al₂O₃ and TiO₂. The reaction can be expressed as Eq. (1):²⁰⁾   

$$A{l}_2{O}_3\left(\alpha \right)+Ti{O}_2\left(rutile\right)=A{l}_{2}Ti{O}_5\left(\beta \right)$$(1)

Fig. 1.

The phase diagram of Al₂O₃–TiO₂.

So the compound Al₂TiO₅ is metastable at room temperature and the tendency that the compound decomposes to Al₂O₃ and TiO₂ between 1023 K and 1573 K was reported by H. A. J. Thomas and R. Stevens.²¹⁾

In the present study, the reaction temperature range was determined from 1723 to 1873 K, which was corresponded to the conditions of the generation of intermediate product.

3.2. Growth of Intercompound, Al₂TiO₅

The multilayer structure after thermal treatment at different temperatures for 7.2 ks is shown in Fig. 2. The dark side of the view was Al₂O₃ and the light side was TiO₂. From the diffusion profiles of elements, the molar ratios of Al:Ti:O in the product layer was about 2:1:5. So it should be Al₂TiO₅, which was grown by the solid-solid reaction due to the interdiffusion between Al₂O₃ and TiO₂. It is difficult to reach the stable state for the system of Al₂O₃–TiO₂ in 14.4 ks at temperature range from 1723 to 1873 K. So there could be the concentration gradients in Al₂O₃, TiO₂ and Al₂TiO₅ phases. Besides, Al₂TiO₅ was so brittle that the diffusion interface resulted in cracking as shown in Fig. 2(d). The crack appeared after the dropping of Al₂TiO₅.

Fig. 2.

Cross-sectional view of the diffusion interface after annealing for 7.2 ks at (a) 1723 K, (b) 1773 K, (c) 1823 K, (d) 1873 K.

The average thickness of the Al₂TiO₅ layer (Δx) determined by the concentration of Ti and Al in Al₂TiO₅ phase is shown in Fig. 2. For getting the values of the Al₂TiO₅ layer thickness, ten measured values were averaged to obtain the average thickness (L), which is listed in Table 2. The average thickness L can be calculated by Eq. (2).   

$$\overline{L}=\frac{{\sum }_{i=1}^{10}{L}_i}{10}$$(2)

Table 2. The values of the thickness of Al₂TiO₅ at different diffusion time.

No.	Temperature/K	Time/ks	Thickness/μm
1	1873	3.6	10.18
2	1873	5.4	11.80
3	1873	7.2	12.51
4	1873	14.4	19.40

As shown in Fig. 3, the thickness against the square root of diffusion time represents a liner relation, described by Eq. (3):   

$$L=1.59\times {10}^{-7}{t}^{\frac{1}{2}}$$(3)

Fig. 3.

Effect of diffusion time on the thicknesses of different layers.

This linear relationship indicates that the rate controlling step in this reaction of Al₂TiO₅ formation could be the interdiffusion of Ti and Al ions.²²⁾

3.3. The Calculation of the Interdiffusion Coefficent

Generally, traditional Boltzmann-Matano method can be used to calculate the interdiffusion coefficient by Eq. (4):   

$$D\left(c^{*}\right)=-\frac{1}{2t{\left(\frac{\partial c}{\partial x}\right)}_{x=x^{*}}}{\int }_{c_1}^{c^{*}}xdc$$(4)

Where D(c*) is the diffusion coefficient at random position x* and c* is the mole fraction, t is the diffusion time, c₁ is mole fraction at the Matano interface.

However, when the inter-composition generates, the traditional Boltzmann-Matano method is invalid because the diffusion profiles is discontinuous. For the complex binary system, Jost²³⁾ and Appel²⁴⁾ modified the Boltzmann-Matano equation, which can be expressed as Eq. (5):   

$$D\left(c^{*}\right)=-\frac{1}{2t}{\left(\frac{dx}{dc}\right)}_{c=c^{*}}\left({\int }_0^{c_{1e}}xdc+{\int }_{c_{2e}}^{c^{*}}xdc-\left(c_{2e}-c_{1e}\right)X\right)$$(5)

Where c* is the mole fraction of the interest at random position (X), c_1e and c_2e are the respective equilibrium concentrations of the diffusing species in the two phases in contact. The X is measured from the Matano interface (x=0), which is determined difficultly.

In order to reduce the error of Matano interface determining, the Wagner method was used to determine the variation of interdiffusivity. The Wagner equation²⁵⁾ is shown as Eq. (6):   

$$\begin{array}{l}D\left(N_2^{*}\right)=\frac{\left(N_2^{+}-N_2^{-}\right)V_m\left(N_2^{*}\right)}{2t{\left(\partial N_2/\partial x\right)}_{x=x^{*}}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\times \left(\left(1-Y^{*}\right){\int }_{-\infty }^{x^{*}}\frac{Y}{V_m}dx+Y^{*}{\int }_{x^{*}}^{+\infty }\frac{1-Y}{V_m}dx\right)\end{array}$$(6)

  

$$Y=\frac{\left(N_2-N_2^{-}\right)}{\left(N_2^{+}-N_2^{-}\right)}=\frac{N_2}{0.33};\hspace{1em}{Y}^{*}=\frac{\left(N_2^{*}-N_2^{-}\right)}{\left(N_2^{+}-N_2^{-}\right)}=\frac{N_2^{*}}{0.33}$$(7)

Where x^* is the distance at which N₂=N₂^*, N₂^* is the mole fraction of Ti⁴⁺ at random position which is the concentration of interest for interdiffusivity calculation, N₂⁺ is the initial mole fraction of Ti⁴⁺ in TiO₂ and N₂⁺=0.33, N₂⁻ is the initial mole fraction of Ti⁴⁺ in Al₂O₃ and N₂⁻=0. V_m is the mole volume of component, and V_m (N₂^*) is the mole volume at concentration N₂^*. Because the change of the molar volume V_m was so small that the equation can be revised as   

$$\begin{array}{l}D\left(N_2^{*}\right)=\frac{1}{2t{\left(\partial N_2/\partial x\right)}_{x=x^{*}}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\times \left(\left(1-\frac{N_2^{*}}{0.33}\right){\int }_{-\infty }^{x^{*}}{N}_{2}dx+\frac{N_2^{*}}{0.33}{\int }_{x^{*}}^{+\infty }\left(0.33-N_2\right)dx\right)\end{array}$$(8)

As shown in Fig. 4, the left side is Al₂O₃ and another side is TiO₂, the curve represents the concentration of Ti span the boundaries of Al₂O₃/Al₂TiO₅ and Al₂TiO₅/TiO₂. The first integral is expressed as the area A and the second integral is the area B. Compared with the method of modified Boltzmann-Matano, Matano interface is not necessary to confirm, which will make the calculation more convenient.

Fig. 4.

The graphic interpretation of Wagner equation.

The results of interdiffusion coefficients calculated by Eq. (8) are shown in Table 3. At different position of boundary layer, the interdiffusion coefficients are different. N_Ti=0.013 presented the mole fraction of Ti ions in Al₂O₃ side. N_Ti=0.125 is the intermediate phase of Al₂TiO₅ and N_Ti=0.25 presented the TiO₂ side. According to Arrhenius equation, the plots of ln D vs T⁻¹ for different mole fraction of Ti⁴⁺ ions are shown in Fig. 5. The values of E_D and D₀ are listed in Table 4.

Table 3. The values of interdiffusion coefficients at different diffusion temperatures.

Temperature (K)	Time (ks)	D×1012 (NTi=0.013 ±0.001) (cm2/s)	D×1012 (NTi=0.125 ±0.01) (cm2/s)	D×1012 (NTi=0.25 ±0.01) (cm2/s)
1723	7.2	0.63	1.64	0.69
1773	7.2	1.05	2.86	1.24
1823	7.2	1.65	5.28	2.56
1873	7.2	2.86	7.61	3.73

Fig. 5.

The relationship of lgD and T⁻¹ for different concentration of Ti⁴⁺.

Table 4. The values of ln D₀ and E_D at different mole fraction of Ti⁴⁺.

NTi	ln(D0) (cm2/s)	ED (kJ/mol)
0.013±0.001	−9.63±1.99	266.77±10.29
0.125±0.01	−7.55±0.69	280.31±16.14
0.25±0.01	−6.35±1.49	309.96±22.22

As shown in Fig. 5, the magnitudes of interdiffusion coefficients were in the range of 10⁻¹⁰~10⁻¹² cm²/s. The values in the phase of Al₂TiO₅ were larger than Al₂O₃ side and TiO₂ side. It is possible that vacancy defect concentration in the intermediate phase is more than that of two sides. In the Al₂TiO₅ phase, the interdiffusion phenomenon of Ti ions and Al ions is more frequent and the effect of temperature on the interdiffusion coefficient was obvious.

Many literatures reported the solid-solid reaction in diffusion systems belong to the type of A₂O₃–BO₂ system. The apparent activation energy value in Fe₂O₃–TiO₂ system obtained by Z. S. Ren²⁶⁾ by a diffusion method was (92.14±26.34) kJ/mol during 1323–1473 K. The value in Al₂O₃–SiO₂ system reported by Davis and Pask²⁷⁾ was about 310 kJ/mol (about 4 wt% Al₂O₃) at 1907 K. Besides, P. Zhang²⁸⁾ determined the apparent activation energy value in Al₂O₃–MgO system as 374.1 kJ/mol in the range of 1573–1873 K. In the present work, the values were 266.77±10.29 kJ/mol in Al₂O₃ side, 280.31±16.14 kJ/mol in the phase of Al₂TiO₅, and 309.96±22.22 kJ/mol in TiO₂ side which lay within the range of values reported in the literatures.

3.4. The Solid-state Reaction Mechanism in the System of Al₂O₃–TiO₂

Above mentioned, the diffusion of Al³⁺ and Ti⁴⁺ was related to the presence of vacancies. The vacancies are created by the dissolution of Al³⁺ in TiO₂ and Ti⁴⁺ in Al₂O₃ at high temperature.^26,28,29,30) Among three ions, the diffusion rate of oxygen ions is slower than Ti ions and Al ions due to the larger radius of oxygen ions. Generally, the diffusion of oxygen ions can be neglected. As shown in Fig. 6, in order to maintain the charge balance, on cation vacancy is created for every three Ti⁴⁺ ions entering the Al₂O₃ structure.   

$$4{\text{Al}}^{3+}=3{\text{Ti}}^{4+}+\text{h}$$(9)

Fig. 6.

Schematic diagram of formation process of Al₂TiO₅ in Al₂O₃–TiO₂ diffusion couple.

Where h represents a vacancy. The balanced concentration of vacancies increases with temperature and more vacancies makes it easier for ions to move.

4. Conclusions

The diffusion couple method was used to investigate the solid-solid reaction in the system of Al₂O₃–TiO₂ in the temperature range of 1723–1873 K.

(1) The Wagner method was applied to calculate the diffusion coefficients and the order of magnitudes in Al₂O₃–TiO₂ system was in the range of 10⁻¹⁰~10⁻¹² cm²/s.

(2) The vacancy mechanism was applied to interpret the solid-solid reaction of Al₂O₃–TiO₂ system. The diffusion coefficients increase with the temperature and the rate controlling step in this reaction of Al₂TiO₅ formation could be the interdiffusion of Ti and Al ions.

(3) The apparent diffusion activation energy is calculated by the Arrhenius equation. The values were 266.77±10.29 kJ/mol in Al₂O₃ side, 280.31±16.14 kJ/mol in the phase of Al₂TiO₅, and 309.96±22.22 kJ/mol in TiO₂ side.

Acknowledgement

This work appreciates the financial support of the National Natural Science Foundation of China (No. 51090384).

References

• 1)   G.  Bayer: J. Less Common Met., 24 (1971), No. 2, 129.
• 2)   I. J.  Kim: J. Ceram. Process. Res., 11 (2010), No. 4, 411.
• 3)   H.  Wohlfromm,  P.  Pena,  J. S.  Moya and  J.  Requena: J. Am. Ceram. Soc., 75 (1992), No. 12, 3473.
• 4)   M.  Nagano,  S.  Nagashima,  H.  Maeda and  A.  Kato: Ceram. Int., 25 (1999), No. 8, 681.
• 5)   Y.  Song,  G. Q.  Li and  F.  Yang: Int. J. Miner. Metall. Mater., 33 (2011), No. 10, 1214.
• 6)   M.  Van Ende,  M.  Guo,  R.  Dekker,  M.  Burty,  J.  Van Dyck,  P. T.  Jones,  B.  Blanpain and  P.  Wollants: ISIJ Int., 49 (2009), No. 8, 1133.
• 7)   I. H.  Jung,  G.  Eriksson,  P.  Wu and  A.  Pelton: ISIJ Int., 49 (2009), No. 9, 1290.
• 8)   C.  Wang,  N. T.  Nuhfer and  S.  Sridhar: Metall. Mater. Trans. B, 41 (2010), No. 5, 1084.
• 9)   C.  Wang,  N.  Verma,  Y.  Kwon,  W.  Tiekink,  N.  Kikuchi and  S.  Sridhar: ISIJ Int., 51 (2011), No. 3, 375.
• 10)   C.  Wang,  N. T.  Nuhfer and  S.  Sridhar: Metall. Mater. Trans. B, 40 (2009), No. 6, 1022.
• 11)   M. K.  Sun,  I. H.  Jung and  H. G.  Lee: Met. Mater. Int., 14 (2008), No. 6, 791.
• 12)   Z. S.  Ren,  X. J.  Hu,  J. C.  Zheng,  K. C.  Chou and  X. X.  Xue: Int. J. Miner. Metall. Mater., 37 (2015), No. 7, 867.
• 13)   Z. S.  Ren,  X. J.  Hu,  X. X.  Xue and  K. C.  Chou: Int. J. Miner. Metall. Mater., 36 (2014), No. 5, 597.
• 14)   Z. S.  Ren,  X. J.  Hu,  X. X.  Xue and  K. C.  Chou: J. Alloy. Compd., 580 (2013), No. 12, 182.
• 15)   C. W.  Bale,  P.  Chartrand,  S. A.  Degterov,  G.  Eriksson,  K.  Hack,  R.  Ben Matfoud,  J.  Melancon,  A. D.  Petersen and  S.  Petersen: Calphad, 26 (2002), No. 2, 189.
• 16)   R. G.  Berman: J. Petrol., 29 (1988), No. 2, 445.
• 17)   S. M.  Lang,  C. L.  Fillmore and  L. H.  Maxwell: J. Res. Nat. Bur. Stand., 48 (1952), No. 4, 298.
• 18)   A. M.  Lejus,  D.  Goldberg and  A.  Revcolevschi: C. R., Acad. Sci., Ser. C, 263 (1966), No. 20, 1223.
• 19)   S. A.  Azimov,  D. D.  Gulamova,  N. N.  Mel’nik,  M. Kh.  Sarkisov,  S. S.  Sulejmanov and  L. M.  Tsapenko: Inorg. Mater., 20 (1984), No. 3, 469.
• 20)   B.  Freudenberg and  A.  Mocellin: J. Am. Ceram. Soc., 70 (1987), No. 1, 33.
• 21)   H. A. J.  Thomas and  R.  Stevens: Br. Ceram. Trans., 88 (1989), No. 5, 184.
• 22)   V.  Buscaglia,  M. T.  Buscaglia,  L.  Giordano,  A.  Martinelli,  M.  Viviani and  C.  Bottino: Solid State Ion., 146 (2002), No. 3, 257.
• 23)   W.  Jost: Z. Physik, 127 (1950), No. 3, 163.
• 24)   M.  Appel: Scr. Metall., 2 (1968), No. 4, 217.
• 25)   C.  Wagner: Acta Metall., 17 (1969), No. 2, 99.
• 26)   Z. S.  Ren,  X. J.  Hu,  S. Y.  Li,  X. X.  Xue and  K. C.  Chou: Int. J. Miner. Metall. Mater., 20 (2013), No. 3, 273.
• 27)   R. F.  Davis and  J. A.  Pask: J. Am. Ceram. Soc., 55 (1972), No. 10, 525.
• 28)   P.  Zhang,  T.  Debroy and  S.  Seetharaman: Metall. Mater. Trans. A, 27 (1996), No. 8, 2105.
• 29)   W. S.  Whitney and  V. S.  Stubican: J. Phys. Chem. Solids, 32 (1971), No. 2, 305.
• 30)   C.  Greskovich and  V. S.  Stubican: J. Phys. Chem. Solids, 30 (1969), No. 4, 909.