ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
ISSN-L : 0915-1559
Regular Article
Solid-state Reaction Studies in Al2O3–TiO2 System by Diffusion Couple Method
Jianchao ZhengXiaojun HuZhongshan RenXiangxin XueKuochih Chou
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2017 Volume 57 Issue 10 Pages 1762-1766


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 ED 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

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 ( α ) +Ti O 2 ( rutile ) =A l 2 Ti O 5 ( β ) (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).   

L ¯ = i=1 10 L i 10 (2)
Table 2. The values of the thickness of Al2TiO5 at different diffusion time.

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× 10 -7 t 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( c * ) =- 1 2t ( c x ) x= x * 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( c * ) =- 1 2t ( dx dc ) c= c * ( 0 c 1e xdc+ c 2e c * xdc-( c 2e - c 1e ) X ) (5)

Where c* is the mole fraction of the interest at random position (X), c1e and c2e 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):   

D( N 2 * ) = ( N 2 + - N 2 - ) V m ( N 2 * ) 2t ( N 2 /x ) x= x * ×( ( 1- Y * ) - x * Y V m dx+ Y * x * + 1-Y V m dx ) (6)
Y= ( N 2 - N 2 - ) ( N 2 + - N 2 - ) = N 2 0.33 ; Y * = ( N 2 * - N 2 - ) ( N 2 + - N 2 - ) = 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. Vm is the mole volume of component, and Vm (N2*) is the mole volume at concentration N2*. Because the change of the molar volume Vm was so small that the equation can be revised as   

D( N 2 * ) = 1 2t ( N 2 /x ) x= x * ×( ( 1- N 2 * 0.33 ) - x * N 2 dx+ N 2 * 0.33 x * + ( 0.33- N 2 ) dx ) (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. NTi=0.013 presented the mole fraction of Ti ions in Al2O3 side. NTi=0.125 is the intermediate phase of Al2TiO5 and NTi=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 ED 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)
Fig. 5.

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

Table 4. The values of ln D0 and ED at different mole fraction of Ti4+.
NTiln(D0) (cm2/s)ED (kJ/mol)

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 Al 3+ =3 Ti 4+ +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.


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

© 2017 by The Iron and Steel Institute of Japan