Growth Characterization of Intermetallic Compound at the Ti/Al Solid State Interface

Ti-Al diffusion couples, prepared by resistance spot welding, were annealed up to 112 h at 823, 848, and 873 K in ambient atmosphere. The interfacial microstructure was observed and analyzed using SEM and TEM. The growth characterization of intermetallic compound formed at the Ti/Al solid state interface was investigated. Only TiAl3 phase was detected in the interfacial zone, and its growth was governed by reaction-controlled mechanism in the previous period and by diffusion-controlled mechanism in the latter period. The activation energies were 198,019 and 122,770 J/mol for reaction-controlled and diffusion-controlled mechanism, respectively.


Introduction
Titanium and aluminum are attractive engineering metals in industrial applications because of their excellent properties, therefore, achieving the joining between two kinds of materials not only can combine their excellent characteristics, reduce the weight of the structure, but also save costs and further expand their application prospects. In view of this, some welding methods such as friction stir welding [1,2], roll-bonding [3], explosive welding [4], ultrasonic welding [5], resistance spot welding [6], laser welding [7] and arc welding-brazing [8,9] were applied to join titanium and aluminum. Previous studies reveal that the brittle intermetallic compounds (IMCs) layer formed at the welding interface seriously impair the mechanical properties of the joint [10,11]. On the other hand, Ti-TiAl 3 metal-intermetallic laminate (MIL) composites are considered as a great potential material for aerospace, automotive, and other structural applications because of its combination of high strength, toughness, and stiffness at a lower density than monolithic titanium or other laminate systems [12]. To fabricate the MIL composites, aluminum and titanium sheets are pressed together by use of explosive welding [12][13][14] and hot press bonding [15][16][17][18]. During producing of MIL, it is indispensable to form a continuous IMCs layer at Al/Ti interface, so much so that a post-bonding annealing treatment is often employed [12][13][14][15][16][17]. Therefore, it is necessary to understand the growth characteristics of IMCs layer in both cases of Al/Ti welding and MIL production so as to control its growth.
In recent years, the growth kinetics of Ti-Al IMCs, especially in solid state, has attracted wide attention [12][13][14][15][16][17][18][19][20][21][22][23]. In general, the thickness of interfacial IMCs layer depends on growth time (t), kinetic exponent (n) and growth rate constant (k) for certain temperature [19,21,23]. According to the value of kinetic exponent, the IMCs growth mechanism can be divided into reaction-controlled and diffusion-controlled [13]. In works of Mirjalili et al., Ti/Al diffusion couples were annealed in time range from 0 to 96 h at 823, 848, 873, 898, 913 and 923 K, and it was demonstrated that  The welded specimens were annealed up to 112 h at three different temperatures: 823, 848, and 873 K in ambient atmosphere. After annealing, the samples were cooled in air and prepared for metallographic examination by sectioning transverse to the reaction interface. The specimens were mounted in epoxy resin, then ground with abrasive paper up to 2000 grits and polished to obtain mirror-finished surfaces for microstructure observation and chemical composition analysis. The interfacial microstructure of the samples were investigated by using a transmission electron microscope (TEM, JEM-2100, JEOL, Tokyo, Japan; acceleration voltage: 200 kV) and a scanning electron microscope (SEM, JSM-6300, JEOL, Tokyo, Japan) equipped with energy dispersive X-ray spectroscopy (EDX, EDAX, Phoenix, USA). The thickness of the reaction layers at Ti/Al interfaces was measured from scanning electron microscope micrographs of the cross-sections. An X-ray diffractometer (XRD, Bruker, Karlsruhe, Germany) was used to identify the phases of the samples. Figure 1a shows the typical SEM image of Ti-Al initial interface after welding. The interface was fairly flat and no defects such as voids and cracks were found in the interface region, which indicate that Ti and Al were boned well. It is pretty obvious that IMCs can not be observed at the Ti-Al initial interface. Figure 1b shows EDX results detected from M to N. As can be seen from the curves, there is a distinct element diffusion region near the Ti-Al interface.  Figure 1a shows the typical SEM image of Ti-Al initial interface after welding. The interface was fairly flat and no defects such as voids and cracks were found in the interface region, which indicate that Ti and Al were boned well. It is pretty obvious that IMCs can not be observed at the Ti-Al initial interface. Figure 1b shows EDX results detected from M to N. As can be seen from the curves, there is a distinct element diffusion region near the Ti-Al interface.  and 96 h, respectively. It can be seen that a deep gray reaction layer formed between Ti and Al, and the thickness of the reaction layer increased remarkably with the increase of the annealing time. As shown, the interfaces between the reaction layer and the base materials were slightly wavy, and the shapes of the waves become larger with the increase of annealing time, which means that the growth of the reaction layer is not absolutely homogeneous. Figure 2d shows the results of EDX along line PQ (see Figure 2b). It can be seen from the composition distribution curves that there is a platform at the interfacial zone. This means that the composition of reaction layer is stable and it is an intermetallic compound (IMC) layer.  It can be seen that a deep gray reaction layer formed between Ti and Al, and the thickness of the reaction layer increased remarkably with the increase of the annealing time. As shown, the interfaces between the reaction layer and the base materials were slightly wavy, and the shapes of the waves become larger with the increase of annealing time, which means that the growth of the reaction layer is not absolutely homogeneous. Figure 2d shows the results of EDX along line PQ (see Figure 2b). It can be seen from the composition distribution curves that there is a platform at the interfacial zone. This means that the composition of reaction layer is stable and it is an intermetallic compound (IMC) layer.  Figure 1a shows the typical SEM image of Ti-Al initial interface after welding. The interface was fairly flat and no defects such as voids and cracks were found in the interface region, which indicate that Ti and Al were boned well. It is pretty obvious that IMCs can not be observed at the Ti-Al initial interface. Figure 1b shows EDX results detected from M to N. As can be seen from the curves, there is a distinct element diffusion region near the Ti-Al interface.  and 96 h, respectively. It can be seen that a deep gray reaction layer formed between Ti and Al, and the thickness of the reaction layer increased remarkably with the increase of the annealing time. As shown, the interfaces between the reaction layer and the base materials were slightly wavy, and the shapes of the waves become larger with the increase of annealing time, which means that the growth of the reaction layer is not absolutely homogeneous. Figure 2d shows the results of EDX along line PQ (see Figure 2b). It can be seen from the composition distribution curves that there is a platform at the interfacial zone. This means that the composition of reaction layer is stable and it is an intermetallic compound (IMC) layer. The quantitative analysis results by EDX at the positions of A, B and C shown in Figure 2b are listed in Table 2. As shown, a rough composition of the reaction layer (position of B) is of 75.12 at.% Al and 24.84 at.% Ti which corresponds to TiAl 3 . Therefore, the reaction layer formed at the interfacial zone was identified as TiAl 3 layer. In addition, Ti and Al were also detected in Al (position of A) and Ti (position of C) side near the interface, respectively. This reveals that Ti and Al atoms diffused through the TiAl 3 layer to Al and Ti side, respectively.  Figure 3a shows the typical bright field image of interfacial zone taken from the Ti/Al sample annealed for 1 h at 873 K. In this image, an approximately 1 µm thick layer structure was observed. Figure 3b shows the selected area electron diffraction patterns of interfacial IMC layer. According to the analyses of selected area electron diffraction patterns, it was identified that the interfacial IMC was TiAl 3 . The quantitative analysis results by EDX at the positions of A, B and C shown in Figure 2b are listed in Table 2. As shown, a rough composition of the reaction layer (position of B) is of 75.12 at.% Al and 24.84 at.% Ti which corresponds to TiAl3. Therefore, the reaction layer formed at the interfacial zone was identified as TiAl3 layer. In addition, Ti and Al were also detected in Al (position of A) and Ti (position of C) side near the interface, respectively. This reveals that Ti and Al atoms diffused through the TiAl3 layer to Al and Ti side, respectively.  Figure 3a shows the typical bright field image of interfacial zone taken from the Ti/Al sample annealed for 1 h at 873 K. In this image, an approximately 1 µm thick layer structure was observed. Figure 3b shows the selected area electron diffraction patterns of interfacial IMC layer. According to the analyses of selected area electron diffraction patterns, it was identified that the interfacial IMC was TiAl3.  Figure 4a shows the TiAl3 side fracture surface morphology of the Ti/Al sample annealed for 4 h at 873 K, from which residual aluminum was removed by use of mechanical methods to expose TiAl3. Some particles with a diameter of approximately 1 µm were observed. Figure 4b shows X-ray diffraction pattern of the fracture surface. Only TiAl3 phase was detected except for Ti and Al. This also verifies that only TiAl3 formed at the interface during annealing.  Figure 4a shows the TiAl 3 side fracture surface morphology of the Ti/Al sample annealed for 4 h at 873 K, from which residual aluminum was removed by use of mechanical methods to expose TiAl 3 . Some particles with a diameter of approximately 1 µm were observed. Figure 4b shows X-ray diffraction pattern of the fracture surface. Only TiAl 3 phase was detected except for Ti and Al. This also verifies that only TiAl 3 formed at the interface during annealing.  Table 2. As shown, a rough composition of the reaction layer (position of B) is of 75.12 at.% Al and 24.84 at.% Ti which corresponds to TiAl3. Therefore, the reaction layer formed at the interfacial zone was identified as TiAl3 layer. In addition, Ti and Al were also detected in Al (position of A) and Ti (position of C) side near the interface, respectively. This reveals that Ti and Al atoms diffused through the TiAl3 layer to Al and Ti side, respectively.  Figure 3a shows the typical bright field image of interfacial zone taken from the Ti/Al sample annealed for 1 h at 873 K. In this image, an approximately 1 µm thick layer structure was observed. Figure 3b shows the selected area electron diffraction patterns of interfacial IMC layer. According to the analyses of selected area electron diffraction patterns, it was identified that the interfacial IMC was TiAl3.  Figure 4a shows the TiAl3 side fracture surface morphology of the Ti/Al sample annealed for 4 h at 873 K, from which residual aluminum was removed by use of mechanical methods to expose TiAl3. Some particles with a diameter of approximately 1 µm were observed. Figure 4b shows X-ray diffraction pattern of the fracture surface. Only TiAl3 phase was detected except for Ti and Al. This also verifies that only TiAl3 formed at the interface during annealing.

Intermetallic Layer Thickening and the Kinetics of TiAl 3 Formation
The average thickness of TiAl 3 layer at different experiment conditions were measured. The layer thickness variation as a function of annealing time in normal scale is shown in Figure 5a. Two stages depending on the relationship between the thickness of TiAl 3 layer and annealing time at three temperatures can be seen in Figure 5a, where the linear and parabolic stage represent that the layer thickness increases with time in the form of straight line and parabola, respectively. Obviously, as the temperature increases, the linear stage became shorter and shorter. In addition, there is a transition region between the linear and parabolic stage under the condition of parameters used in this study.

Intermetallic Layer Thickening and the Kinetics of TiAl3 Formation
The average thickness of TiAl3 layer at different experiment conditions were measured. The layer thickness variation as a function of annealing time in normal scale is shown in Figure 5a. Two stages depending on the relationship between the thickness of TiAl3 layer and annealing time at three temperatures can be seen in Figure 5a, where the linear and parabolic stage represent that the layer thickness increases with time in the form of straight line and parabola, respectively. Obviously, as the temperature increases, the linear stage became shorter and shorter. In addition, there is a transition region between the linear and parabolic stage under the condition of parameters used in this study. As well known, the thickness of interfacial IMC layer is a power function of time. Therefore, the TiAl3 layer thickness at each temperature can be described by the following equations: As well known, the thickness of interfacial IMC layer is a power function of time. Therefore, the TiAl 3 layer thickness at each temperature can be described by the following equations: in which x, k, t, and n are the thickness of the TiAl 3 layer (m), growth rate constant (m/s n ), annealing time (s), and kinetic exponent, respectively. The layer thickness variation as a function of annealing time in logarithmic scale is shown in Figure 5b. Taking into account the experimental errors, the present data were fitted a line. The slope and intercept of each line represent its n and lnk value. These values are collected in Table 3. As mentioned above, the IMC layer growth mechanism is divided into reaction-controlled (n value is 1) and diffusion-controlled (n value is 0.5) mechanism. As shown in Figure 5b, TiAl 3 layer growth was governed by reaction-controlled mechanism in the previous period and by diffusion-controlled mechanism in the latter period for each annealing temperature in this study; and the reaction-controlled stage broadened by decreasing the temperature. This is consistent with the results reported by Farzad et al. [12]. The growth rate constant k can be expressed as an Arrhenius function as follows: where k 0 is a temperature-independent constant, T is the absolute temperature (K), R is the gas constant, and Q is the activation energy for TiAl 3 growth (J/mol). According to Equation (4), lnk is plotted versus reciprocal temperature in Figure 6. The slope of line represents the value of −Q/R. Accordingly, the activation energies of Q r (reaction-controlled mechanism) and Q d (diffusion-controlled mechanism) for TiAl 3 growth can be calculated. They were 198,019 and 122,770 J/mol, respectively. Moreover, the corresponding values of k0r and k0d were calculated to be 240.11 and 2.13 m/s, respectively. It should be mentioned that the subscripts r and d at Q and k0 represent the reactioncontrolled and diffusion-controlled mechanism, respectively. Finally, growth kinetics model based on two growth mechanisms were described by two equations: xr = 240.11 exp(−198019/RT)t (Reaction-controlled) (5) Figure 6. lnk versus the reciprocal temperature for two different growth mechanisms.
Moreover, the corresponding values of k 0r and k 0d were calculated to be 240.11 and 2.13 m/s, respectively. It should be mentioned that the subscripts r and d at Q and k 0 represent the reaction-controlled and diffusion-controlled mechanism, respectively. Finally, growth kinetics model based on two growth mechanisms were described by two equations: x r = 240.11 exp(−198019/RT)t (Reaction-controlled) (5) x d = 2.13 exp(−122770/RT)t 0.5 (Diffusion-controlled) (6) where x r and x d are the thickness of TiAl 3 layer governed by reaction-controlled and diffusion-controlled, respectively.

Formation of TiAl 3
In this study, only TiAl 3 phase formed at the Ti-Al interface during annealing in the temperature range of 823-873 K, even though the Ti-Al binary phase diagram suggests other IMCs, such as Ti 2 Al 5 , TiAl 2 , TiAl and Ti 3 Al, should also be formed between Ti and Al [24]. This can be explained from both thermodynamics and diffusion kinetics. From thermodynamics side, TiAl 3 has lowest Gibbs standard free energy of formation among Ti 3 Al, TiAl and it [25]. In comparison with TiAl 3 , the formation of TiAl 2 or Ti 2 Al 5 with lower Gibbs standard free energy starts with TiAl and goes through a series of chemical reactions, thus TiAl 2 and Ti 2 Al 5 can be ignored here. In terms of diffusion dynamics, TiAl 3 has the most negative effective heat of formation (∆H m ), and is expected to be the first phase to form in the diffusion zone among Ti-Al binary system compounds [21]. And so, only TiAl 3 was detected at the interface of annealed Ti/Al sample in the study. This is in agreement with the results obtained in other studies [13,19,20,23].
It should be noted that there is no obvious incubation period of TiAl 3 formation in Figure 5a. This is not in accordance with previous reports [12,20,23]. The incubation means a period of time for Ti and Al atoms diffusing with each other at the interface before the formation of TiAl 3 . However, the mutual solubility of Al and Ti is very small, so it is easy to reach saturation state. And a distinct element diffusion region at the Ti-Al interface has been formed during spot welding process (Figure 1), which greatly shortens the incubation period. Therefore, in this experiment, it is reasonable to believe that the incubation period of TiAl 3 formation cannot affect the calculation of the growth kinetics and can be neglected.

Govern Mechanism Criterion of TiAl 3 Layer Growth
As mentioned above, derived Equations (5) and (6) are formulas for calculating the thickness of TiAl 3 layer (x) in the case of both reaction-controlled and diffusion-controlled mechanism, respectively. However, this is not enough to predict TiAl 3 layer thickness for certain annealing temperature and time, because it is unclear whether reaction-controlled and diffusion-controlled mechanism to be employed. Therefore, it is necessary to determine which govern mechanism to be used before predicting TiAl 3 layer thickness. Unfortunately, there are few reports on this aspect so far. Based on this, a criterion for the govern mechanism of TiAl 3 layer growth was put forward in this study. Theoretically, at the theoretical critical point shown in Figure 5b, the growth of TiAl 3 layer can be seen as governed by either reaction-controlled mechanism or diffusion-controlled mechanism, which indicate that the value of x r and x d are equal. Then, a relationship between the critical time and temperature can be derived from Equations (5) and (6). The relationship was diagrammed as a theoretical critical boundary in Figure 7.
In fact, there is a transition region between reaction-controlled and diffusion-controlled mechanism as shown in Figure 5a, rather than a definite line. This was also reported as a mixed mechanism of both reaction-controlled and diffusion-controlled mechanism (n = 0.5~1.0) in other studies [12,21,23]. This can be qualitatively explained by use of theories reported by Dybkov as shown in Figure 8 [26]. The growth of TiAl 3 is a result of reaction between diffusion atoms through IMC layer and base metals at both interfaces of Ti/TiAl 3 and Al/TiAl 3 . In the previous period, the growth of TiAl 3 layer are governed by reaction-controlled mechanism at both interfaces of Ti/TiAl 3 and Al/TiAl 3 , which is attributed to that the diffusion of Al and Ti atoms across the TiAl 3 layer is sufficient because the TiAl 3 layer is thinner. With the thickening of TiAl 3 layer, the growth of TiAl 3 layer at an interface is governed by diffusion-controlled mechanism when its thickness reaches X 0.5 , whereas its growth is still controlled by reaction-controlled mechanism at the other interface. This is because the reaction between Al and Ti at the both interfaces are not synchronized and the diffusion rates of Al and Ti atoms across the TiAl 3 layer are also different. In the transition region, the growth of total TiAl 3 layer is governed by the mixing mechanism of both reaction-controlled and diffusion-controlled mechanism (n = 0.5~1.0). When the thickness of TiAl 3 layer reaches X 1.0 , its growth is governed by diffusion-controlled mechanism at both interfaces, which is due to that the diffusion of Al and Ti atoms are not sufficient because the TiAl 3 layer is thicker. theoretical critical boundary in Figure 7.
In fact, there is a transition region between reaction-controlled and diffusion-controlled mechanism as shown in Figure 5a, rather than a definite line. This was also reported as a mixed mechanism of both reaction-controlled and diffusion-controlled mechanism (n = 0.5~1.0) in other studies [12,21,23]. This can be qualitatively explained by use of theories reported by Dybkov as shown in Figure 8 [26]. The growth of TiAl3 is a result of reaction between diffusion atoms through IMC layer and base metals at both interfaces of Ti/TiAl3 and Al/TiAl3. In the previous period , the growth of TiAl3 layer are governed by reaction-controlled mechanism at both interfaces of Ti/TiAl3 and Al/TiAl3, which is attributed to that the diffusion of Al and Ti atoms across the TiAl3 layer is sufficient because the TiAl3 layer is thinner. With the thickening of TiAl3 layer, the growth of TiAl3 layer at an interface is governed by diffusion-controlled mechanism when its thickness reaches X0.5, whereas its growth is still controlled by reaction-controlled mechanism at the other interface. This is because the reaction between Al and Ti at the both interfaces are not synchronized and the diffusion rates of Al and Ti atoms across the TiAl3 layer are also different. In the transition region, the growth of total TiAl3 layer is governed by the mixing mechanism of both reaction-controlled and diffusion-controlled mechanism (n = 0.5~1.0). When the thickness of TiAl3 layer reaches X1.0, its growth is governed by diffusion-controlled mechanism at both interfaces, which is due to that the diffusion of Al and Ti atoms are not sufficient because the TiAl3 layer is thicker.  Therefore, there is a transition region between reaction-controlled and diffusion-controlled mechanism as shown in Figure 7. When the annealing time and temperature employed are in the transition region, the growth of TiAl3 layer is governed by the mixing mechanism. Its growth is governed by reaction-controlled and diffusion-controlled mechanism when the annealing time and temperature employed are under and above the transition region, respectively.
In the study, the growth kinetics model based on mixing mechanism, the boundaries between reaction-controlled and mixing mechanism, and between diffusion-controlled and mixing Therefore, there is a transition region between reaction-controlled and diffusion-controlled mechanism as shown in Figure 7. When the annealing time and temperature employed are in the transition region, the growth of TiAl 3 layer is governed by the mixing mechanism. Its growth is governed by reaction-controlled and diffusion-controlled mechanism when the annealing time and temperature employed are under and above the transition region, respectively.
In the study, the growth kinetics model based on mixing mechanism, the boundaries between reaction-controlled and mixing mechanism, and between diffusion-controlled and mixing mechanism are not yet uncertain. This needs further study and will be reported separately.

Growth Process of TiAl 3
In summary, the growth process of TiAl 3 layer at Ti/Al solid state interface is illustrated in Figure 9. During spot welding, Ti and Al atoms diffused with each other and formed a solid solution region of Ti(Al) and Al(Ti) respectively on both sides of the welding interface of Ti/Al as illustrated in Figure 9a. And then, the IMC of TiAl 3 nucleated and grew during annealing process as illustrated Figure 9b-f.
In the initial stage of annealing, diffusion of Ti and Al atoms with each other caused that the solid solution of Ti(Al) and Al(Ti) reached saturation on both sides of the welding interface and TiAl 3 nucleated at the part of the interface where would be higher energy as illustrated in Figure 9b. As the heating continues, TiAl 3 also nucleated at another part of the interface because it is harder that Ti and Al atoms diffuse through formed TiAl 3 in comparison with where TiAl 3 was not formed. Whereupon, a thin continuous layer of TiAl 3 formed at the welding interface as illustrated in Figure 9c.
After the formation of TiAl 3 continuous layer, Ti and Al atoms diffused through the layer and reacted with each other, and then generated TiAl 3 at the Ti/TiAl 3 and the TiAl 3 /Al interfaces as illustrated in Figure 9d. Because the TiAl 3 layer was thinner, the growth of TiAl 3 layer was governed by reaction-controlled mechanism at both interfaces of Ti/TiAl 3 and TiAl 3 /Al. With the growth of the TiAl 3 layer, its growth was governed by mixing mechanism as illustrated Figure 9e. At the interface of Ti/TiAl 3 , the control mechanism of TiAl 3 layer growth first changed from reaction-controlled to diffusion-controlled. This is because the diffusion of Al atoms is not sufficient for the reaction at the Ti/TiAl 3 interface where need more Al atoms to react with Ti from the stoichiometry of the product phase in comparison with the interface of TiAl 3 /Al. When TiAl 3 layer reached a certain thickness (X 1.0 ), its growth was governed by diffusion-controlled mechanism after the control mechanism of TiAl 3 layer growth also changed to diffusion-controlled at the interface of Ti/TiAl 3 as illustrated in Figure 9f. During growth of TiAl3 layer, one Ti atom needs three diffused Al atoms to react at the Ti/TiAl3 interface, whereas three Al atoms need one diffused Ti atom to react at the TiAl3/Al interface. From this respect, the growth rate in atom percent at the TiAl3/Al interface is nine times higher than the Ti/TiAl3 interface. Therefore, TiAl3 layer mainly grew toward the Al side, although diffusion Al atoms in TiAl3 layer is slight faster than that of Ti atom [27]. This is also consistent with the experimental results. During growth of TiAl 3 layer, one Ti atom needs three diffused Al atoms to react at the Ti/TiAl 3 interface, whereas three Al atoms need one diffused Ti atom to react at the TiAl 3 /Al interface. From this respect, the growth rate in atom percent at the TiAl 3 /Al interface is nine times higher than the Ti/TiAl 3 interface. Therefore, TiAl 3 layer mainly grew toward the Al side, although diffusion Al atoms in TiAl 3 layer is slight faster than that of Ti atom [27]. This is also consistent with the experimental results.

Conclusions
The growth mechanism of interfacial IMC layer formed in the Ti/Al diffusion couples has been investigated. The main conclusions are summarized as follows: (1) Only TiAl 3 phase was detected in the interfacial zone of Ti/Al sample annealed for up to 112 h at 823, 848, and 873 K. (2) The growth of TiAl 3 layer was governed by reaction-controlled mechanism in the previous period and by diffusion-controlled mechanism in the latter period for annealing temperature of 823, 848, and 873 K. (3) The activation energies for reaction-controlled and diffusion-controlled mechanism were calculated to be 198,019 and 122,770 J/mol, respectively. (4) A criterion for the govern mechanism of TiAl 3 layer growth was put forward.