Degradation kinetics of Ti-Cu compound layer in transient liquid phase bonded graphite/copper joints

The continuous Ti-Cu compound layer produced in brazing of graphite to copper with Ti foil is found to be seriously detrimental to joint properties due to its brittleness. In this work, a transient liquid phase (TLP) bonding method with a diffusion process below melting point is developed to realize a Ti-Cu compound layer free joint. The degradation of Ti-Cu compound layer depends on two simultaneously occurring processes, namely flow of titanium atoms to copper substrate and that to TiC layer on graphite. The latter is determined by growth kinetics of TiC layer based on carbon diffusion process. A degradation model is proposed and applied to optimize the TLP bonding. The improved graphite/copper joints without Ti-Cu compound layer show 20.8% higher in shear strength compared with that of brazing joints.

, Cu-ABA 11 , TiCuNi 6 ) have been used to join CBMs and copper. For these brazing alloys, the content of Ti is a key factor for joint quality. Generally, Ti concentration is inversely proportional to contact angles of liquid alloy. It's reported that the wetting on CBMs requires the addition of Ti at least 10 at.% so as to offset the influences of pre-oxidation or possible pollution on substrate surface 9 . Nevertheless, excessive Ti may lead to abundant intermetallic compounds (IMCs) in seam. Since residual stress caused by the mismatch of coefficient of thermal expansion (CTE) between CBMs and copper is easily created in the joint, the brittle IMCs dramatically increase the possibility of joint failure in service [12][13][14] . Thus, how to solve the conflict between wetting and IMCs-forming tendency is essential to the property improvement of CBMs/copper joints.
In this work, the graphite is successfully joined to copper by improved transient liquid phase (TLP) bonding with Ti interlayer. It's known that typical TLP bonding involves long isothermal solidification process at joining temperature to make sufficient diffusion of the interlayer element (or a constituent of an alloy interlayer) into substrate materials 15,16 . But in our method, the contact reaction between Ti and Cu is first carried out at 920 °C to promote wetting, then isothermal process (at 860 °C) is set below the melting point so as to prevent sever infiltration of liquid alloy into graphite. In the solid isothermal process, Ti-Cu IMCs produced in the contact reaction can dissolve by two ways: the first is diffusion of Ti to Cu substrate and the second is competing reactions with TiC layer at graphite interface. The degradation of Ti-Cu IMCs is governed both by Ti diffusion behavior and TiC growth kinetics. The degradation model proposed by this work can be used to predict the residual IMCs layer in seam and is helpful to improve the joining technique.
This paper is divided into three parts. In the first one, the microstructure of joint after contact reaction is characterized and the brittle IMCs layer is identified. In the second part, the experimental results as well as calculations on degradation kinetics of Ti-Cu IMCs layer are shown and discussed. In the third part, the microstructure and mechanical properties of graphite/copper joint joined by an optimized TLP bonding are presented.

Results and Discussion
Microstructure of graphite/Cu joint brazed with Ti interlayer. The graphite/Cu brazing involves a series of interfacial reactions in seam. During heating, solid-state diffusion reactions occur first between Ti interlayer and Cu substrate, producing a small quantity of Ti-Cu compounds, such as TiCu, Ti 3 Cu 4 and TiCu 4 . As the temperature rises above the eutectic point (875 °C), the Cu-Ti eutectic liquid forms and fills the gap between graphite and Cu by capillarity. The wetting process on graphite accompanies fast growing of TiC layer at graphite/ liquid interface. Besides, mutual diffusion between Ti and Cu results in enrichment of Cu in Cu-Ti liquid. So in cooling process, the peritectic reaction (Liquid + Cu → TiCu 4 ) happens and a continuous TiCu 4 layer forms in the joint. Figure 1 shows the microstructure of graphite/Cu joint brazed at 920 °C for 10 min. Three regions can be distinguished in the joint. Region I is comprised by a thin TiC layer (point A in Table 1) and nanoparticle layer (as shown in Fig. 1b). It's inferred small amount of carbon atoms diffuse through TiC layer and dissolve into the Cu-Ti liquid. Subsequently, TiC particles precipitate out of the liquid. Region II is the continuous TiCu 4 layer (point B) produced by peritectic reaction. Region III is the transition layer from brazing liquid to Cu substrate. As the solubility of Ti in Cu significantly decreases during cooling, lath like TiCu 4 phases precipitate from the supersaturate Cu ss (point C) to form this two-phase region (TiCu 4 + Cu ss , point D). It is noticed that some  dark TiCu blocks are also found in this layer. As mentioned above, various Ti-Cu compounds are produced by solid-state reactions during heating. But after the melting of Ti interlayer, majority Ti-Cu compounds dissolve in the liquid except for the thermodynamically stable TiCu (∆G = −17530 + 3.37 T J/mol 17 ). Although most TiCu blocks can be extruded to the fillet (as shown in Fig. 1c) by liquid flow, small amount of TiCu are still left in the seam. Figure 2 is the XRD patterns of joint plane prepared by polishing layer by layer. It confirms the existence of TiCu 4 and TiCu.
As indicated in Fig. 1a, it seems that the joints brazed with Ti interlayer are metallurgically sound and defect free. However, after one week's standing without any load, cracks were widely found in all samples as shown in Fig. 3. These cracks initiate in graphite interface, propagate vertically through TiCu 4 layer and stop in Cu ss in region III. Obviously, the residual stress resulted from large mismatch of CTE between the two dissimilar substrates (α Cu = 16.5 × 10 −6 K −1 , α graphite = 3.9 × 10 −6 K −1 ) is the main reason for cracking. In graphite/Cu joints, Cu will be under tension and the graphite under compression during cooling from brazing temperature 18 . The elastic residual stress in Cu substrate, roughly estimated by σ = EΔαΔT (E: Young's module, Δα: CTE mismatch, ΔT: temperature interval) 19 , is 1416 MPa, which exceeds the yield strength of Cu. In region III of the seam, stress can be released by deformation of Cu ss . But in region II, fracture rather than plastic deformation is more likely to happen in the brittle Ti-Cu compounds. This hidden danger may lead to a catastrophic consequence when the joint serves in alternating stress environments. Thus, how to eliminate the Ti-Cu compounds, especially the thick continuous TiCu 4 layer, is a key issue in practical application.
Degradation kinetics of Ti-Cu compound layer in TLP bonding. In order to realize a Ti-Cu compound layer free joint, TLP bonding approach is proposed and the degradation of Ti-Cu compound layer is  studied by using a smaller 4 mm × 4 mm × 20 μm titanium interlayer. Figure 4 shows the microstructure of graphite/Cu joints with solid diffusion times of 0, 1, 3, 4.5 and 6 hours. It is observed that TiCu compounds formed before melting are nearly at the same distance to graphite interface regardless of variation of holding time. The stable positions of TiCu reflect the low fluidity of brazing melt. Besides, Fig. 4k and l show that the Ti-Cu melts are trapped in the seam and no extrusion happens. In this condition, the continuous TiCu 4 layer just after melting is around 34 μm thick. As holding time extended, the thickness of TiCu 4 layer decreases while the thickness of region III (Cu ss + TiCu 4 ) increases. Apparently, the diffusion of Ti to Cu substrate at high temperature consumes TiCu 4 and forms a supersaturated solid solution region in Cu substrate. Another way leading to the reduction of TiCu 4 layer is the growth of TiC on graphite. As TiC is far more thermodynamically stable than TiCu 4 (ΔG TiCu4 = −7600 + 3.12 T J/mol 20 ), the Ti atoms required for growth of TiC nearly all come from dissolving of TiCu 4 (TiCu 4 → Ti + 4Cu). Figure 4 shows that, with extension of holding time, the thickness of TiC layer gradually increases while the boundary of TiCu 4 layer recedes, leaving a narrow Cu ss layer as a decomposition product between TiCu 4 and TiC.
In order to quantitatively predict the dissolving rate of TiCu 4 layer, a diffusion model is developed in terms of error function solutions for Fick's second law. The present joint involves three interfaces at the beginning: graphite/TiC interface, TiC/TiCu 4 interface and TiCu 4 /Cu ss interface. The diffusion of Ti into Cu substrate and growth of TiC layer can both lead to dissolving of TiCu 4 layer. But considering the two processes occur independently at different sides of TiCu 4 layer, the quantity of TiCu 4 consumed on the side of Cu substrate is evaluated by measuring from the graphite/TiC interface to TiCu 4 /Cu ss interface (as shown in Table 2).
The Fick's second law of diffusion, relating the changes in concentration of Ti with time and location is: where D is the diffusion coefficient, c is the concentration, t is diffusion time and x is distance. The copper substrate is considered as semi-infinite medium and the TiCu 4 /Cu ss interface is treated as the not-moving planar boundary. In Ti-Cu system, TiCu 4 has a narrow stoichiometric range. Thus, at the TiCu 4 /Cu ss boundary, the Ti fraction in TiCu 4 is assumed to have the lowest value based on Ti-Cu binary diagram 21 and the solid solubility of Ti in Cu is saturated (6.5 at.%) at 860 °C. Due to the small concentration difference of Ti in Cu, it is assumed that the diffusion coefficient of Ti is independent of the concentration in Cu substrate. With these assumptions, the initial and boundary conditions can be written as: Here c Ti,max Cu ss and c represent Ti atomic concentration (atoms/cm 3 ) in Cu ss at TiCu 4 /Cu ss interface and Cu substrate, respectively. The concentration of Ti could be converted from its atomic fraction (x) by Where ρ and M are density and molar mass of matrix, respectively. N A is Avogadro constant (N A = 6.022 × 10 23 ) and n is the atom number per matrix molecule. In copper solid solution, ρ and M are approximate to that of pure Cu (ρ = 8.93 g/cm 3 ) 22 . So the Ti concentration in saturated Cu ss (6.5 at.% Ti) is calculated as c Ti,max Cu ss = 5.46 × 10 21 atom/cm 3 . The solution for Ti concentration in Cu satisfying Eqs (1-4) can be written as: Cu is the titanium diffusion coefficient in copper. So the flow of Ti atoms (J Ti ) passing though TiCu 4 /Cu interface can be given as   ) in its stoichiometric range. According to Eq. (5), c Ti,min TiCu 4 is 1.50 × 10 22 atoms/cm 3 using the density from ref. 22 . By integration of Eq. (8), the thickness of TiCu 4 layer (w) can be expressed in terms of time (t), 2 . From dynamics, the dissolving of TiCu 4 layer involves two processes including decomposing reaction (TiCu 4 → Ti + 4Cu) and atomic diffusion. But the calculated D Ti Cu in this work is quite similar to the result (6.37 × 10 −14 m 2 /s) obtained from a pure Ti/Cu diffusion couples 23 . This indicates that the kinetics of TiCu 4 decomposing reaction is quite fast, which is possible related to the poor thermodynamic stability of TiCu 4 .
The growth of TiC layer on graphite is considered as another independent process consuming TiCu 4 in seam. Figure 4 shows that decomposing of TiCu 4 on graphite side leads to a narrow Cu ss layer on TiC interface. According to ref. 24 and calculation in this work, the D Ti Cu is much higher than the diffusion coefficient of carbon in TiC = . × − D ( 1 2 74 10 m /s) C TiC 1 6 2 24 , indicating that the Ti flux in Cu ss may satisfy the growth of TiC. Therefore it's assumed the TiC boundary adjacent to Cu ss and all the Cu ss layer have saturated Ti in their phases. The concentration difference within TiC layer can be considered to represent the average compositional gradient in this phase. Figure 6a shows the Ti concentration profile of this reaction system. In this figure, x 1 and x 2 stand for the location of TiC/Cu ss boundary and Cu ss /TiCu 4 boundary, respectively. At the beginning of solid diffusion (t = 0), TiCu 4 layer directly contacts with TiC, the thickness of Cu ss is zero, thus x 1 = x 2 . At time t = t 1 , TiCu 4 layer degrades to location x 2 while TiC layer grows to location x 1 . The decomposing rate of TiCu 4 on graphite side can be derived from the growth rate of TiC. Previous investigations have proved that the diffusion coefficient of carbon is far more higher than that of titanium in TiC 24 . So in this case, it's assumed the growth of TiC layer is dominant by carbon diffusion from graphite interface to TiC/TiCu 4 (or Cu ss ) interface. Additionally, the diffusion of carbon in TiCu 4 and Cu ss is neglected due to the extremely limited solubility of carbon in the two phases. The initial and boundary conditions can be written as: Initial   21 and TiC density (ρ TiC = 4.93 g/cm 3 ) 24 . Figure 6b shows the changing of carbon concentration in TiC within time dt. By using conservation of carbon atoms, the TiC growth can be given as: The expression of TiC layer front location (x 1 ) as a function of time can be obtained by integration of Eq. (16) with an initial position x 1 (t = 0) = 0.53 µm ( Table 2). The diffusion coefficient of carbon in TiC D ( ) C TiC is given as 6.54 × 10 −16 m 2 /s. The result in this work is similar to the reported value 12.74 × 10 −16 m 2 /s at 860 °C 24 . The small deviation of the two values may come from the neglect of carbon diffusion in Cu ss in this work, since small quantity of nano TiC particles indeed precipitate nearby the continuous TiC layer, which is difficult to be taken into the thickness of TiC layer equivalently.
Based on the growth kinetics of TiC, the change of Ti concentration within TiC from time t 1 to t 1 + dt can be approximate to the profile shown in Fig. 6a. The quantity of Ti atoms migrated to TiC is given by:  S is a layer surface area. Applying the rule of Ti atom conservation at x 1 and x 2 , the following is obtained:  Incorporating Eqs (22 and 18) and the initial condition x 2 (t = 0) = 0.53 µm, the movement of TiCu 4 boundary (x 2 ) on the graphite side can be expressed as a function of time: . + .
− . Based on Eqs (18 and 23), the thickness of Cu ss (w Cu (t)) adjacent to TiC layer can be derived from the difference between x 1 (t) and x 2 (t): .  Figure 8a shows the predicted thickness of Cu ss with various holding time at 860 °C compared with the experimental data. A reasonable agreement between the predicted data and experimental data can be seen. For all the samples, the experimental data is 2%~17% higher than the calculated one in Cu ss thickness. The small discrepancy  is probably due to neglect of TiC particles nearby TiC layer. Though the quantity is small, the growth of these particles with large specific surface area may contribute to consuming more TiCu 4 by solid diffusion.
Taking account of diffusion process in Cu substrate (Eq. (10)) and competing reactions with TiC (Eq. (23)), the final equation represents the variation of TiCu 4 layer (Δw) can be expressed as follows: . + . − . + . w t t t 5 29 1 046 0 277 2 78 6 12 in hour (25) Figure 8b shows the predicted variation of TiCu 4 layer as a function of time. Apparently, the quantity of TiCu 4 consumed on diffusing in Cu substrate is prominent due to the high diffusion coefficient of Ti in Cu. The part consumed on TiC growth is around one third of the total at the beginning and it gradually increases with prolonging time. The result here also indicates that the most effective stage to eliminate TiCu 4 is at the beginning of solid diffusion. For example, the average recession rate of TiCu 4 layer within 1 hour (v 1 = 9.43 μm/h) is more than twice of that within 6 hours (v 6 = 4.29 μm/h). Considering excessive diffusion of Ti may change the property of Cu substrate (such as elastic modulus, hardness and thermal conductivity) and thicken TiC layer, rational controlling the time of solid diffusion process is not only beneficial for joining economy but also for joint property.
Optimization of TLP bonding for copper/graphite joints. Above section reveals that solid state diffusion is an effective but time-intensive approach to eliminate residual Ti-Cu compound layer in seam. In order to maintain good performance of joints and remove the time impediment, a combination of liquid alloy extrusion and solid state diffusion is used in the optimized joining process. Figure 9a shows the interfacial microstructure of graphite/Ti/Cu joint by brazing at 920 °C for 5 min with an increased pressure of 8.9 kPa. The large scale liquid flow driven by extrusion during brazing can be evidenced by the fluctuant TiCu 4 layer as well as the positions of TiCu compounds which have been pushed to the graphite interface (see Fig. 9a). The thickness of TiCu 4 layer in this condition is 9.8 ± 3.4 μm thick, less than one third of the one without extrusion (as shown in Fig. 4a). According to the model proposed above, this TiCu 4 layer can be dissipated within 1 hour by solid state diffusion. Figure 9b shows the interfacial microstructure of graphite/Ti/Cu joint by TLP bonding (brazed at 920 °C for 5 min and then solid diffusion at 860 °C for 1 h with pressure of 8.9 kPa). It is found that the residual TiCu 4 is nearly all eliminated. In addition, the quantity of stable TiCu is also decreased significantly after solid state diffusion. This is probably due to the competing reactions between TiCu and TiC: as TiCu compounds are pushed to the graphite interface, the more stable TiC tends to grow by using Ti atoms dissolved from TiCu compounds during solid diffusion. By comparing Fig. 9a,b, it is concluded that the optimized TLP bonding with combination of liquid alloy extrusion and solid state diffusion is a feasible way to eliminate Ti-Cu compounds in a short time. The shear strengths of joints by brazing and the optimized TLP bonding are 24 ± 6 MPa and 29 ± 3 MPa, respectively. The load-displacement curves (Fig. 10) indicate both of the joints are brittle fractured. The extra stage of curve B after the maximum load is caused by the coarse fracture surface which may hinder the relative motion of the two broken parts. It's inferred the microcracks in Ti-Cu compound layer may result in the failure of brazing joints at lower load. As for the joint by TLP bonding, though the residual stress is inevitable, defect is prevented due to the superior microstructure. So the joint has higher load bearing capability.

Conclusion
For brazing of graphite and copper with Ti interlayer, the continuous TiCu 4 layer is believed to be the most dangerous phase due to its cracking tendency under stress. In this work, a TLP bonding method with a diffusion process below melting point is proposed to eliminate Ti-Cu compounds in seam. A model for the degradation of TiCu 4 layer is developed considering the simultaneous diffusion on both sides, one is the Ti diffusion in Cu substrate and the other is the Ti diffusion towards TiC layer. The latter is controlled by the growth kinetics of TiC. Based on this model, the TLP bonding is optimized to realize a Ti-Cu compound layer free joint in a short time. The shear strength of joints prepared by this method increases by 20.8% compared with that of brazing joints.

Methods
Sample preparation. Graphite (Beijing Electrical Carbon Co., Ltd.) and copper (Foshan Huaru Copper Co., Ltd.) are used as substrate materials to be joined in this work. The chemical compositions and mechanical properties are listed in Table 3. Graphite was cut into 7 mm × 7 mm × 2.5 mm pieces for microstructure observation and 15 mm × 10 mm × 3 mm pieces for shear tests. Copper was cut into 5 mm × 5 mm × 2.5 mm pieces. The bonding surfaces of graphite and copper were ground on SiC abrasive papers (2000#) and then polished with 1 μm diamond pastes. All samples were ultrasonically cleaned in acetone for 10 min. Joining process was carried out in a furnace with vacuum better than 1.3 × 10 −3 Pa (oxygen partial pressure of 10 −4 Pa). Three joining methods were carried out in this work. The first one was brazing. A 50 μm thick Ti foil was cut into 6 mm × 6 mm and sandwiched between graphite and copper with normal load of 5.9 kPa. The assembly was kept in graphite jig and heated to 920 °C at 10 °C/min, isothermally held for 10 min, then slowly cooled to room temperature at 10 °C/ min. The second one was TLP bonding for Ti-Cu IMCs degradation kinetics investigation. In order to limit the flow of filler alloy, a smaller Ti foil (4 mm × 4 mm × 20 μm) was sandwiched between graphite and copper with normal load of 5.9 kPa. The assembly was heated to 920 °C at 10 °C/min, isothermally held for 5 min, then cooled to 860 °C, isothermally held for various times (0 h, 1 h, 3 h, 4.5 h and 6 h), and finally cooled to room temperature at 10 °C/min. The third one was an optimized TLP bonding. A Ti foil (6 mm × 6 mm × 20 μm) was used as filler alloy with increased load of 8.9 kPa. The assembly was heated to 920 °C at 10 °C/min, isothermally held for 5 min, then cooled to 860 °C, isothermally held for 1 h, and finally cooled to room temperature at 10 °C/min. Characterization. The microstructure, chemistry and morphology were investigated by scanning electron microscopy (SEM, FEI Quanta 400, Eindhoven, Netherlands) equipped with an energy dispersive X-ray spectroscopy (EDS). The phases in joints were identified by an X-ray diffraction method (XRD, PANalytical Empyrean, Netherlands). The specimens for XRD test were polished layer by layer to expose the filler alloy nearby graphite interface. The thickness measurements of different phases (TiCu 4 , TiC and copper solid solution layers) were made from SEM micrographs of metallographically polished samples. These measurements were done at 10 equally spaced locations on the micrographs. The shear strength of joints at room temperature was examined using a universal testing machine (Instron-1186, Grove City, PA) with a displacement rate of 0.5 mm/min. The scheme of shear testing was reported in ref. 25 . The strength was calculated by dividing the maximum load by the surface of the joint. The tested values for each experimental condition were an average of at least six measurements.

Data Availability Statement
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.