Nucleation and growth of TiAl3 intermetallic phase in diffusion bonded Ti/Al Metal Intermetallic Laminate

A novel nucleation and growth phenomenon for TiAl3 intermetallic phase in Ti/Al diffusion couple is proposed based on diffusion kinetics. The interdiffusion and intrinsic diffusion co-efficients are calculated to make evident of dominant diffusion of Al towards Ti in Ti/Al diffusion couple obtained by solid state diffusion bonding. It was surprising to observe that the diffusion rate of Al was around 20 times higher than Ti with the formation of Kirkendall pores near the Al/TiAl3 interface. With such dominant diffusion of Al towards Ti, the nucleation and growth of TiAl3 intermetallic phase in Ti/Al couple happens mainly at the Ti/TiAl3 interface rather than Al/TiAl3 interface which is evident by the presence of very fine nearly nano-sized TiAl3 nuclei/grains near the Ti/TiAl3 interface. Even though the intermetallic phase is expected to nucleate at Al/TiAl3 interface, the relatively larger TiAl3 grains near that interface depicts grain growth with minimal nucleation. The theoretical calculations on diffusion parameters are in accordance with experimental observations of TiAl3 intermetallic growth phenomenon in Ti/Al system.

Ti/TiAl 3 /Al metal intermetallic laminates (MILs) are considered to be one of the promising materials for defense and aerospace applications due to its combined properties such as lower density, high specific strength and relatively good oxidation and corrosion resistance [1][2][3][4] . In these MILs, TiAl 3 is the only intermetallic phase that formed between Ti and Al at relatively lower temperatures (below Al melting point) as other intermetallic phases such as Ti 3 Al, TiAl and TiAl 2 are expected to form either at higher temperatures or after the consumption of Al 5 . The nucleation and growth of TiAl 3 intermetallic phase (below Al melting temperature) in the Ti/Al system mostly depends on the interdiffusion and relative rates of diffusion of Ti and Al atoms as well on thermodynamic factors. Almost, the studies conducted on Ti/Al system depicts, Al to be the dominant diffusing species at temperatures below Al melting point while Ti was considered to diffuse faster at higher temperatures especially above Al melting temperature [6][7][8][9] . This led to the conclusion that TiAl 3 nucleates due to the high diffusion of Al towards Ti and the nucleation of TiAl 3 phase should be concentrated mostly at Ti/TiAl 3 interface. In contrast, Xu et al. 10 observed the diffusion of both Al and Ti through TiAl 3 layer in the Ti/Al system regardless of the bonding temperature (below or above Al melting point) employed, emphasizing the growth of TiAl 3 on both Ti/TiAl 3 and Al/TiAl 3 interfaces. It is also assumed that the solid solution formation of Al(Ti) preceding the TiAl 3 nucleation on Al/ TiAl 3 interface helps in the faster nucleation of TiAl 3 nuclei at Al/TiAl 3 side due to less solubility of Ti in Al 10,11 . On the other hand, Mirjalili et al. 9 observed dominant diffusion of Al towards Ti layer and formation of fine equiaxed TiAl 3 grains near Ti/TiAl 3 interface, claiming dominant nucleation of TiAl 3 nuclei at the Ti/TiAl 3 interface. While at the Al/TiAl 3 interface, coarse grains were observed indicating the growth of initial TiAl 3 grains than nucleation. It is now obvious that there exist contradictory viewpoints or observations regarding the nucleation and growth of TiAl 3 phase and there are no supporting interdiffusion parameter calculations to validate dominant diffusion of Al atoms in Ti/Al system. As the nucleation and growth of TiAl 3 is also dependent on the diffusion kinetics, the diffusion parameter calculation helps in understanding the nucleation and growth phenomenon in the system. Hence, the present work is mainly focused on calculating interdiffusion co-efficient of Ti and Al and thereby to clarify the contradictions in nucleation and growth phenomenon of TiAl 3 intermetallic phase in multi-laminated Ti/Al diffusion couple.

Methods
Ti/TiAl 3 /Al MILs were prepared using commercially pure Ti and Al sheets of 0.5 mm thickness through solid state diffusion bonding technique. The bonding was carried out at temperatures 550 and 575 °C for bonding times of 2, 4 and 6 h in vacuum (−760 mm of Hg). The sheets were rinsed with 10% HF solution and ultrasonically cleaned prior to bonding to remove surface oxides and impurities. The cleaned sheets were stacked alternatively in the bonding setup and a uniaxial pressure of 4 MPa was applied throughout the bonding time to prepare MILs with a total thickness of 5 mm. To analyse the growth of the intermetallic phases on Ti/TiAl 3 and Al/TiAl 3 interfaces, the 6 h bonded MILs already containing a specific intermetallic phase along the Ti/Al interface, were again annealed for 12, 24, 36 and 48 h duration at their respective bonding temperatures without external pressure. A brief schematic of the sample preparation process can be found elsewhere (See Supplementary Fig. S1). The microstructural characterization and phase analysis were performed on the cross section of the MILs using Hitachi S3000H scanning electron microscope (SEM) attached with Thermo USA energy dispersive spectroscopy (EDS). X-Ray diffraction (XRD) study was performed on the annealed sample to analyse the phases formed in the intermetallic region. Totally three samples in each condition are used to analyse the results.
The diffusion parameters such as interdiffusion co-efficient and tracer diffusion co-efficient were calculated using Wagner's method 12 in the MILs annealed for different duration. The nucleation and growth phenomenon of TiAl 3 phase at Ti/TiAl 3 and Al/TiAl 3 interfaces are analysed based on the grain size distribution of TiAl 3 , obtained through orientation imaging microscopy (OIM) micrographs taken using electron backscattered diffraction (EBSD) technique.

Results
Microstructure Evolution. Figure 1a shows the back scattered electron (BSE) mode SEM image of the MIL bonded at 575 °C for 6 h duration. The bright and dark regions in the image represent the Ti and Al sheets used for multi-laminated Ti/Al diffusion couple. The grey coloured layer in between the Ti and Al sheets denotes the product phase that was formed due to the inter-diffusion of Ti and Al atoms. Through EDS analysis, the composition of the product phase was found to be nearly 25 at% Ti and 75 at.% Al, which reveals that the phase formed was TiAl 3 intermetallic compound and its growth is mainly facilitated due to low free energy of formation 6,[13][14][15] . Figure 1b shows a typical EDS spectrum obtained from the product phase of the MIL bonded at 575 °C for 6 h. The TiAl 3 phase was found to grow with further annealing at both the annealing temperatures, with increase in annealing time, by which complete consumption of the Al layer was achieved after 48 h annealing at 575 °C. Figure 1c,d shows the SEM images exhibiting the TiAl 3 layer growth in the MILs annealed for 36 h duration at temperatures 550 and 575 °C respectively. It can be seen from the Fig. 1c that the Ti/TiAl 3 interface is smoother than Al/TiAl 3 interface and fine pores are found near the Al/TiAl 3 interface. These pores are considered to be Kirkendall pores which are formed mainly due to the difference in the diffusivities of the bonding materials. In Ti/Al diffusion couple, the diffusion rates of Ti and Al atoms are different due to the difference in the melting temperature of the diffusing species. The pore formation is also directly associated with vacancy motion as unequal flow of Ti and Al atoms towards either side results in equivalent flow of vacancy to the net flow of atoms 16 .  Figure 1e shows the highly-magnified SE image of the Kirkendall pore as encircled in Fig. 1d. The XRD patterns of the sample annealed at 575 °C for 48 h duration is shown in Fig. 1f. Only peaks corresponding to Ti and TiAl 3 were identified during the analysis, as Al was fully consumed during the annealing process. It is evident from the XRD results that the intermetallic phase formed is TiAl 3 . The presence of any phase gradient in the intermetallic layer was analysed using EDS line scan and area mapping. The line scan across the intermetallic layer revealed that there is no concentration gradient of Ti and Al in the intermetallic region (See Supplementary Fig. S2(a)). The elemental area map over the TiAl 3 layer exhibited the density and elemental distribution of Al is higher than Ti which evidently confirms the TiAl 3 phase formation (See Supplementary Fig. S2). To, support the claim of dominant diffusion of Al towards Ti side, it is important to calculate the diffusion parameters for Ti and Al in the TiAl 3 intermetallic region.
is the integrated interdiffusion co-efficient of the phase of interest integrated over unknown homogeneity range of the phase, is the unknown homogeneity range of phase of interest and ∼ D is the interdiffusion co-efficient. Since TiAl 3 is the only intermetallic phase formed as a result of inter-diffusion of Al and Ti atoms which has narrow homogeneity range 13 and there is no influence of other phases on the growth of TiAl 3 , the contribution of other phases in equation (1) can be neglected and rewritten as Ti Ti TiAl 3 is the integrated interdiffusion co-efficient of Ti and Al in TiAl 3 phase, β is the TiAl 3 phase, ∆ x TiAl 3 is the layer thickness of the TiAl 3 in the Ti/Al diffusion couple, N Ti TiAl 3 is atomic fraction of Ti in the TiAl 3 phase, + N Ti and − N Ti is the atomic fraction of Ti on the Ti and Al sides respectively in the diffusion couple. The values of the parameters involved in equation (2) can be obtained from the composition profile across Ti/TiAl 3 /Al layer using EDS analysis. From Al-Ti phase diagram 13 , it can be seen that TiAl 3 exists as a line compound with 25 at.% of Ti. Hence, N Ti TiAl 3 is equal to 0.25. − N Ti is the atomic fraction of Ti on the Al side which is equal to zero and + N Ti is the atomic fraction of Ti on Ti side which is equal to one. The schematic of the diffusion couple before and after bonding and the composition profile are shown in Fig. 2a. Using equation (2), the integrated diffusion co-efficient for intermixing of Al and Ti in MIL bonded at 550 °C and 575 °C for 36 h duration was found to be 5.882 × 10 −15 m 2 /s and 34.42 × 10 −15 m 2 /s respectively. The values indicate that the integrated diffusion co-efficient is higher for the MILs annealed at 575 °C.
For better understanding of relative diffusion between Al and Ti atoms, it is necessary to calculate the intrinsic diffusivities of the individual Al and Ti components. It is difficult to calculate the absolute intrinsic diffusivities of individual Ti and Al, as the intrinsic diffusivities can only be measured at a composition indicated by inert markers/tracer. So, the basic criteria to calculate the tracer diffusivities is to find the position of the tracer in the   TiAl  Ti  Ti   TiAl  Al   TiAl   3  3  3 where N Al TiAl 3 and N Ti TiAl 3 are the atomic fraction of Al and Ti present in the TiAl 3 phase respectively, ∆fg TiAl 3 is the free energy for the formation of TiAl 3 , R is the universal gas constant and T is the bonding temperature. The free energy for the formation of TiAl 3 was obtained from the work of Peng et al. 6 and is used for the calculation. Table 1 shows the calculated absolute values of tracer diffusivity and integrated diffusion co-efficient for the Ti/Al diffusion couple annealed at 550 °C and 575 °C for 36 h duration respectively. It is now evident from the tracer diffusion co-efficient calculation, that Al is diffusing dominantly which is almost 20 times faster than Ti near the marker plane in Ti/Al diffusion couple.

Diffusion, Nucleation and Growth.
In Ti/Al diffusion couple, the initial TiAl 3 intermetallic phase nucleates as a result of reaction between Ti and Al atoms along the Ti/Al interface. In the present work, the grey coloured coarse globular like TiAl 3 phase (as shown in Fig. 1a) shows the initial stage of nucleation and the couple is further employed for different annealing runs to study the nucleation and growth phenomenon of TiAl 3 along Ti/TiAl 3 to Al/TiAl 3 interfaces. Figure 3a,b shows the IPF Z map and band contrast image of such MIL annealed at 550 °C for 36 h obtained through EBSD. It can be observed from Fig. 3b that the distribution of TiAl 3 grains is varying along the intermetallic layer thickness starting from Ti/TiAl 3 to Al/TiAl 3 interface.
The TiAl 3 grains near the Ti/TiAl 3 interface appears to be nearly nano-sized, which spans over a definite length starting from that interface, following, as indicated by the arrows at the centre portion in Fig. 3b, larger grains are concentrated over that region representing grain growth. While at the Al/TiAl 3 interface, as shown by the arrows near that interface in Fig. 3b, the grain size again gets reduced than at the centre portion but relatively larger than the grains at Ti/TiAl 3 interface. This depicts that the TiAl 3 grains nucleated at Ti/TiAl 3 interface appears to be smaller and uniform than at the other end. These fine grains of TiAl 3 phase on both the interfaces can be considered as the TiAl 3 nuclei which are nucleated as a result of diffusion of both Ti and Al across the intermetallic layer and through reactions at the respective interfaces.
Similar pattern of TiAl 3 grain structure was also observed in the MIL annealed at 575 °C for 36 h which is shown in Fig. 4a,b. Here also, as it can be seen from Fig. 4b, the TiAl 3 nuclei at Ti/TiAl 3 interface appears to be nearly nano-sized than the grains near Al/TiAl 3 interface depicting dominant nucleation and growth. Also, the centre region is almost concentrated of larger grains than at the interfaces. The straight line of Kirkendall pores are visible in the grey scale image which are denoted by the arrows in Fig. 4b. These Kirkendall pores are always

Discussion
On discussing the TiAl 3 growth phenomenon in Ti/Al couple, diffusion kinetics plays an important role in determining the interface where the faster growth of TiAl 3 takes place, as the individual Ti and Al atoms diffuse across the intermetallic layer to react with the respective interfaces. It is expected that Ti(Al) and Al(Ti) solid solution formation precedes the TiAl 3 nucleation at both Ti/TiAl 3 and Al/TiAl 3 interfaces. From Ti-Al binary phase  solid solution regime appears to be narrow signifying higher solubility of Al in Ti rather than Ti in Al. With the above phenomenon, Xu et al. 10 claimed earlier saturation of Al(Ti) solid solution than Ti(Al), due to less solubility resulting in faster nucleation of TiAl 3 nuclei along Al/TiAl 3 interface and supposed that the extended solubility of Al in Ti is for Ti 3 Al nucleation rather than TiAl 3 . It was also expected that the distribution of TiAl 3 nuclei near Al/ TiAl 3 interface must be fine and uniform, while on the other side it would be relatively coarse 10 .
In the present study, the distribution of these TiAl 3 nuclei/grains are exactly opposite, that fine, uniform and densely populated TiAl 3 nuclei are visible only at the Ti/TiAl 3 interface whereas relatively larger nuclei are observed at the Al/TiAl 3 interface as shown in Figs 3 and 4. Also, the formation of Ti(Al) and Al(Ti) solid solution phases are not visible along the interfaces. Figure 5a,b shows the schematic of the Ti/Al diffusion process and TiAl 3 grains distribution in which black dots represents the TiAl 3 nuclei. Considering the diffusion kinetics in the present system, as Al diffuses faster (at the employed temperatures) than Ti, more number of Al atoms are expected to present near the Kirkendall marker plane than Ti. These Al atoms, with respect to the basic diffusion law tends to move from high to low concentration region i.e. it always move from Al to Ti side through the intermetallic layer, ensuring high flow of Al atoms towards Ti/TiAl 3 interface for reaction. In other words, the chemical reactivity/potential for Al atoms to interact with Ti/TiAl 3 is higher than at the Al/TiAl 3 interface. As the activation energy for grain boundary diffusion is generally lower than lattice diffusion, the TiAl 3 grain boundaries acts as faster diffusion channels for the moving Al atoms.
In contrast, even if grain boundary diffusion dominates, relatively low diffusivity of Ti towards Al is expected (annealing temperature is almost 1/3 rd of melting temperature of Ti), resulting in less availability of Ti atoms at Al/TiAl 3 interface for TiAl 3 nucleation. This strongly suggests, although Al(Ti) solid solution saturates earlier than Ti(Al), the limited availability of Ti atoms for interaction with Al at the Al/TiAl 3 interface restricts faster nucleation, ensuing relatively coarse and not so densely populated TiAl 3 nuclei. On the other hand, at the Ti side, as solubility of Al in Ti is higher, TiAl 3 nuclei should form at the Ti grain boundaries which facilitates faster diffusion of Al and earlier saturation of Ti(Al) solid solution when the solubility gets locally exceeded, than at the lattice. The activation energy for such grain boundary diffusion controlled (~33 kJ mol −1 ) TiAl 3 intermetallic layer growth is always lower than lattice diffusion controlled growth (~295 kJ mol −1 ) 9 . This concludes that abundant availability of Al atoms at the Ti/TiAl 3 interface facilitates faster TiAl 3 nucleation than at Al/TiAl 3 side resulting in tri-modal grain structure of TiAl 3 phase. Figure 5b shows the schematic of TiAl 3 grain structure after annealing.
A better understanding of nucleation and growth phenomenon of TiAl 3 intermetallic phase can be achieved by considering a Ti/Al/Ti tri-layer system rather than Ti/Al diffusion couple. Figure 6 shows the schematic of TiAl 3 growth phenomenon in a Ti/Al/Ti tri-layer system. Figure 6a shows the stacking of Ti/Al/Ti sheets of equal thickness before bonding. While diffusion bonding, the individual Ti and Al atoms inter-diffuse over time to form initial TiAl 3 intermetallic phase along the Ti/Al interface which is shown in Fig. 6b. After annealing, a tri-modal TiAl 3 grain structure was observed between Ti and Al sheets, consisting of nearly nano-sized TiAl 3 grains/nuclei near Ti/TiAl 3 interface, coarse grain structure at the centre part and relatively small TiAl 3 grains/nuclei at the Al/ TiAl 3 interface. Figure 6c shows the schematic of Ti/Al/Ti tri-layer system with tri-modal TiAl 3 grain structure, which are represented as region A, B and C respectively. As Al diffuses faster than Ti, we can expect huge mass transport from Al to Ti side i.e. more number of Al atoms will be moved towards Ti side. Whereas relatively lower diffusivity of Ti does not ensure equivalent mass transport towards the Al side ensuring net mass transport of atoms towards Ti. This is illustrated in Fig. 6d by the presence of red (Al atoms) and blue (Ti atoms) dots of different densities at the Ti/TiAl 3 and Al/TiAl 3 interfaces. As relatively faster growth of TiAl 3 nuclei occurs at Ti/TiAl 3 interface than at Al/TiAl 3 side, the growth of new TiAl 3 nuclei at Ti/TiAl 3 side will shift the already present TiAl 3 grains i.e. Region A towards Al side, simultaneously shifting the regions B and C towards Al side. The arrows near the denoted regions A, B and C in Fig. 6d represents the shifting direction. When the annealing is continued for further growth of new TiAl 3 nuclei at Ti/TiAl 3 side, the regions A, B and C always tend to move towards Al side, such that if complete consumption of Al is achieved in the growth process, intermixing of the regions B and C is expected at the center portion of the intermetallic layer. Figure 6e shows the schematic of TiAl 3 grain structure after complete consumption of Al sheet. Thus, the final TiAl 3 grain structure consists of newly grown fine TiAl 3 nuclei at Ti/TiAl 3 interface (Region D), Region A with minimal growth shifted towards Al side, adjacent to region D and intermixed regions B and C at the centre portion. The above-mentioned grain structure was observed in the MIL annealed at 575 °C for 48 h in which Al sheet was completely consumed in the TiAl 3 growth process. Figure 7a,b shows the IPF Z map and band contrast image of MIL annealed at 575 °C for 48 h obtained through EBSD where the different grain structures are denoted as A, B, C and D. We can observe that the TiAl 3 grains near both the Ti/TiAl 3 interfaces are very fine-sized (Region D), with moderately grown TiAl 3 grains (Region A), adjacent to Region D and the presence of both coarse and fine grains at the centre part (intermixed regions B and C). This clearly denotes that diffusion kinetics plays an important role in nucleation of TiAl 3 phase in Ti/Al system which is mainly concentrated along the Ti/TiAl 3 interface during annealing due to the dominant diffusion of Al towards Ti side. Whereas, TiAl 3 grains near the Al/TiAl 3 interface are found to grow during annealing with minimal nucleation due to less diffusion of Ti towards Al side. And if, solid solution formation precedes the TiAl 3 nucleation, the formation of Ti(Al) solid solution near Ti/TiAl 3 interface is in favour of growth of TiAl 3 than Ti 3 Al due to low free energy of formation of TiAl 3 6 . Thus, in contrast to the viewpoints of Xu et al. 10 , the low solubility of Ti in Al did not favour faster nucleation of TiAl 3 near Al/TiAl 3 interface and it is faster only at the Ti/TiAl 3 interface.  In conclusion, a novel growth phenomenon for TiAl 3 intermetallic phase in Ti/Al diffusion couple was proposed based on diffusion kinetics. The dominant diffusion of Al towards Ti in Ti/Al binary diffusion couple was strongly revealed through the interdiffusion and intrinsic diffusion co-efficient calculations based on Wagner's approach. The nucleation site of TiAl 3 intermetallic phase was found to be concentrated mostly along Ti/TiAl 3 interface rather than Al/TiAl 3 due to dominant diffusion of Al towards Ti side which was supported by the diffusion parameter calculations. Thus, the present work provides better phenomenon and clears the ambiguity involved in the nucleation and growth sites of TiAl 3 intermetallic phase in Ti/Al diffusion system.