TMS Outstanding Student
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Although diffusion bonding achieves more homogeneous chemical and physical properties throughout the structure, it necessitates extreme care with surface preparation prior to bonding as well as the application of large loads during bonding. Brazing, on the other hand, inherently results in a bonded region which is substantially different from the bulk. It would therefore be beneficial to combine these processes in an attempt to more closely approach the "ideal joint". It was exactly this desire that led Owczarski, Duvall and Paulonis2 to develop a process for the joining of nickel based superalloys which they subsequently coined "Transient Liquid Phase" (TLP) bonding.
To date a significant amount of work has been done in an attempt to quantify the mass transport phenomena which occur during TLP bonding. All attempts to predict this behaviour to date have focused on two component systems, e.g. pure elemental base material joined by a one solute interlayer or braze material. The obvious reason for the choice of such model systems is based on the complexities that arise as extra components are introduced. In practice, however, such simple material combinations are rarely encountered and it is not to be expected that these models will accurately predict complex materials.
To understand the fundamental basis for TLP bonding it is constructive to consider the model for the two component system. With this as a basis, the problems associated with the more difficult situation of a ternary material system can be tackled.
Initially a liquid layer comprised of fast diffusing solute is situated between the components to be joined. The formation of such a liquid layer can occur in a number of ways as described in3 and.4 Most commonly a binary alloy foil, electroplate, sputter coating, etc., containing a low melting point solute and the chemical constituent of the base material are placed in intimate contact. The low melting point solute is selected such that upon alloying with the base material it forms a low melting point alloy.
Any of the processes used to form a liquid result in a similar situation; a liquid layer of nearly constant composition (high in solute) in contact with a pure (or nearly pure) base metal. Because of the order of magnitude difference in diffusivities on either side of the liquid/solid interface dissolution of the base metal into the liquid layer occurs much faster than diffusion of the solute out of the liquid. As such, the liquid layer will initially grow in width due to the unbalanced flux across the solid/liquid interface. This process is considered in figure 1 for the situation were a base material (A) and an alloy interlayer (A-B) are used. This schematic shows the progressive widening with relation to the phase diagram for the A-B system. Widening of the liquid layer will occur until the concentration within the liquid becomes saturated throughout with the constituent of the base metal.
The seminal work of Tuah-Poku et. al.5 revealed that the time for the liquid to attain the liquidus composition occurs in a matter of seconds, thus making the solid state diffusion of solute negligible for all but the fastest diffusing solutes.
Upon reaching the liquidus the liquid has reached a state of equilibrium and as such there is no driving force for flux within the liquid. The process then converts to being controlled by diffusion in the solid state. The subsequent solid state diffusion then results in a shrinking of the liquid layer. The interfacial equilibrium between liquid and solid is thus predicted by the tie line as shown in figure 2. The diffusion field ahead of the solid/liquid interface for this situation is illustrated in figure 3.
If the base material is solute free then the solution to Fick's Second Law within the base metal for the above problem is,
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(1) |
where 
is the change of variable, = 
, which converts Fick's Second Law to the Boltzmann equation.4 The constant 
in (1) is the position of the solid/liquid interface in - space, i.e.
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(2) |
Thus, can be used as a measure of the interface velocity, and as such will be further referred to as the isothermal solidification rate constant. Similar rate constants have been defined and experimentally verified by other researchers.5,7 One significant deviation from the above described model is the increase in kinetics which can be associated with increased interfacial areas and short circuit diffusion paths attributable to grain boundaries.4,5,8
Solidification proceeds until all of the liquid interlayer has consumed. This results in a solid joint with a solute peak at its centerline. Although the joint centerline has a high level of solute, it is within the solid solution range of the base metal and thus has properties attributable to the bulk material. The solute peak may be eliminated through a conventional solution anneal.
| f = n - p | (3) |
where
is the number of phases involved. In the binary case considered above the number of degrees of freedom available to the system is zero and so the diffusion path is completely specified by the starting conditions. However, as the number of components in the system is increased the freedom allowed to the system also increases. Thus, for such systems some rules must exist beyond those previously described for the binary system. These then should allow for the prediction of the diffusion behaviour during isothermal solidification.
It is in this case easiest to consider a ternary system to introduce the complexities of isothermal solidification in a multicomponent system. Due to the fact that the dissolution is controlled by diffusion in the liquid there is little difference between dissolution in binary and multicomponent systems (at least for those multicomponent systems considered here). Thus, if it is assumed that no solid state diffusion occurs during dissolution, the diffusion path may be drawn on the Gibbs isotherm as a straight line connecting the compositions of the base metal and the interlayer as shown in figure 4. As for the binary case, dissolution ends when the composition of the liquid reaches that of the liquidus.
If cross diffusional effects are ignored for the two solutes (labeled 2 and 3 in figure 4), then the diffusion profile of each may be considered separately. The profile given in equation (1) is thus appropriate for each of the solutes in the ternary couple.
Consider first isothermal solidification predicted by the tie line at the liquidus position first attained by the liquid. A mass balance can be performed on both solute profiles to solve for the rate constant of the solidification front. Doing so gives the rate constant as,
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(4) |
where in this case Ki is the ratio of liquidus to solidus equilibrium concentrations (i.e. partition coefficient) for the ith component, and Di
is the diffusion coefficient in the solid for the ith solute (i = 2,3). If one makes the approximation of linear phase boundaries and defines the tie lines by,
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(5) |
where the terms in equation 5 are defined in Figure 5, then all of the terms in equation (4) are constant for a given temperature and solute. Thus, unless the two solutes have a specific combination of Di and Ki which equate 1 and 2, the predicted rate constants for the two solutes will be different across the entire composition range of the two phase field. Because the interface obviously cannot satisfy the predicted rates simultaneously, some other means must be found to accommodate isothermal solidification.
The extra degree of freedom afforded the ternary system provides a means of forcing a single interface velocity for both solutes. Equilibrium across the liquid/solid interface and an interface velocity equally predicted by both solutes may be obtained if the liquid and solid composition tracks along the phase boundaries.14 In this situation the liquid composition becomes dependent on the rate of diffusion of the solutes within the solid. Consider the situation described above which occurs when the mean liquid composition first reaches the liquidus composition. Equation (4) then predicts two rate constants for solidification on that specific tie line. One rate will generally be larger than the other due to a higher flux and/or higher solid state solubility. It is this solute with the higher predicted interface velocity which then will drive the movement of the interfacial concentrations along the phase boundaries. The solute which predicts a lower interface velocity must then partition into the liquid to conserve mass balance across the interface. The initial isothermal solidification in this situation can thus be considered as a series of infinitesimal steps of equilibrium solidification and the observed velocity of the interface will be a composite of the velocity at each of these tie lines. In other words, this is a process of isothermal solidification by a shifting tie line.
Depending on the level of detail considered two possible situations may arise during ternary isothermal solidification. These will be dealt with separately below.
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(6) |
A ratio of the velocities predicted for each of the solutes can then be produced to give,
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(7) |
Equation (7) gives a simple means to decide in which way the interfacial concentrations will be driven. If the solute fluxes in the solid corresponding to any tie line is known (e.g. tie line where flux of the two solutes are the same) then all that is left to be determined is the slope of that tie line for the prediction of the direction of movement of the interfacial concentrations. If the ratio v1:v2 is greater than one then the liquid becomes enriched in solute 2, if it is less than one then the liquid becomes enriched in solute 1.
For the phase diagram defined by linear phase boundaries and tie lines described by (5), the rate constant was shown to be independent of concentration and so the ratio of the velocities predicted by the two solutes would be constant across the entire isotherm. In such a situation complete isothermal solidification occurs as interfacial concentrations are changing, i.e. no one tie line can ever be found which satisfies equal rate constants predicted by both solutes.
This argument also suggests that there are generally two regimes of control within the Gibbs isotherm. Starting concentrations on either side of the tie line predicting equal rate constants would be pushed towards the position of equal predicted interfacial velocities. This is shown schematically in Figure 6.
Such a situation does not lend itself easily to analytical techniques. As such, computations were performed based on a simple numerical technique in an attempt to verify the above discussion.
C (Figure 7). This corresponds to a change in the interfacial concentration on the solid side for the same solute as given by (5). This relation along with the rest of the Gibbs isotherm has been defined in a similar manner to that described by Maugis et. al.13
A simple mass balance made before and after the iteration of the concentration then provides the time for shrinkage of the liquid layer by some amount between the endpoints of each iteration step. The mass balance allowing for this is given by
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(8) |
The subscript i = 1,2 represents the two solutes while the subscript j = 0 .. N represents the position of the solidification front on the Gibbs isotherm prior to iteration. The value of "N" is then determined by the selected size of concentration step.
| D1 = 16.2 µm2/min | (9a) |
| D2 = 0.014 µm2/min | (9b) |
The phase diagram for this model system was taken to be one with only two phases (liquid + solid solution). The phase diagram was again defined as in.13 The relevant features used to define the linear phase boundary relations for the computation are shown in Figure 8.
First, data corresponding to the effect of interlayer thickness on the solidification will be presented. Figure 9a shows the effect of reducing the interlayer thickness prior to solidification (i.e. post dissolution) from 100 µm to 5 µm. More interesting is Figure 9b which shows how the interlayer thickness varies with interfacial composition as solidification progresses. One can see that regardless of starting thickness, the liquid composition upon completion of solidification is the same. This is consistent with the proposed mechanism in that the solidification is assumed to be controlled by the solid state diffusion. As such, the concentration end points should be independent of liquid thickness.
Next, the dependence of solidification on the starting concentration of solutes within the liquid was modeled. Figure 10 depicts the results of three different initial (i.e. prior to dissolution) concentrations for interlayers plotted using the same axis as used in Figure 9. Figure 10a shows that the model predicts that the interlayer with the lowest starting composition of low diffusivity (i.e. low flux and low interfacial velocity) will solidify first. This can be understood by reference to Figure 10b which shows the interlayer thickness versus the interfacial concentration as in Figure 9b. However, in this case the composition at which solidification occurs varies with the starting composition. The interlayers with the smaller amount of slow diffuser solidify the quickest simply because there is less tin to diffuse out of the liquid. Thus, initially, the interface motion will be controlled by the fast diffuser. At higher starting concentrations of this fast diffuser the interfacial flux of this solute will be large and thus the rate of solidification will be larger.
Figure 9b and Figure 10b both also have the points of inflection for the curves labeled. In this situation the point of inflection corresponds to the concentration at which the flux of both solutes across the interface are the same. As such, to the right of this inflection point the solidification kinetics become dominated by the slower diffuser (initially the solute with the low flux). This explains why the solidification rate increases as one moves away from this point to the right. The inflection point is the same for all curves for the same system regardless of initial concentration or liquid width.
Finally, the diffusion coefficient of the second solute (2) was varied while that of the first (1) was held constant so as to observe its effect on the solidification behaviour of the couple. The results are plotted in Figure 11. As one can observe, the time for solidification increases drastically when a slow diffusing solute is introduced. When the difference in diffusivities is very large, a plateau is reached in the time vs. thickness plot. This can be explained with reference to Figure 11b. As the diffusivity of one of the solutes becomes very small the liquid composition is forced nearly to the slow diffuser - solvent binary. Since the rate of interface motion slows as one approaches the point of inflection and the point of inflection is situated nearly on the slow diffuser - solvent binary, the rate of interface motion becomes negligible. In the limiting case of an infinitely slow diffusing solute, the liquid composition would be required to reach that of the binary and, as such, solidification would only occur after an infinite amount of time. The only way to limit the effects of the slow diffuser is to ensure that its concentration is very low in the liquid. This will ensure that solidification occurs prior to the point of inflection (as the 5% curve shows in Figure 10b).
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(10a) |
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(10b) |
For the sake of simplifying the necessary computations linear phase boundaries were assumed for the Al-Zn-Sn Gibbs isotherm at 500°C. To check the validity of this assumption the true Al-Zn-Sn isotherm for 500°C was constructed using the common tangent approach and thermodynamic data compiled by Fries et. al.10 and Dinsdale.11 The model isotherm and computed isotherm are shown in Figure 12. The assumption of linear phase boundaries in this system is obviously poor. A more refined computation method should take into account such deviation from ideality, as it can have a significant effect on the kinetics of solidification.
In an attempt to predict the kinetics of the isothermal solidification in the Al-Zn-Sn system, the computations described above were performed. The results of these computations are shown in Figure 13. Because of the large differences in diffusivities and solubility's of tin and zinc in aluminum, the liquid composition must shift nearly to the Al-Sn binary. Complete solidification was not achieved in the model due to the fact that too large a iterative concentration step size was used. The computation thus ended before the final tie line was achieved. This shows just how significantly the kinetics are hindered when the liquid composition is forced close to the slow diffuser-solvent binary.
The surface of the aluminum was prepared by an immersion plating technique which reportedly removes the oxide layer and deposits a thin film of zinc.12 Samples with a starting interlayer composition of 50% Sn and approximately of 50 µm in thickness were observed. The above model predicts that the interfacial concentration of the liquid will need to become highly enriched in tin. To test this in a semi-quantitative manner, two samples were prepared. One was left in a fluidized bed at 500°C for 15 minutes the other left in the fluidized bed for 3 days. These samples were then broken open so as to reveal the bonding faces. Energy Dispersive X-Ray Spectroscopy was then used to determine the intensity of K peaks for the solutes at the interface. Ratios of the intensity of the solute (zinc and tin) peaks were then obtained using the software available with the Electroscan ESEM 2020 microscope. This provides a semi-quantitative measure of changing solute concentrations within the liquid. After 15 minutes the average Sn:Zn ratio in the interface was measured as 0.39. However, after 3 days the average Sn:Zn ratio at the interface was measured to be 7.85. This suggests a substantial enrichment of tin within the liquid in accordance with the above model.
Attempts were also made to observe the kinetics of the solidification process by optically observing polished sample cross-sections and measuring interface thickness. After 3 days at 500°C solidification still had not been achieved. However, full solidification of a binary Al-Zn couple was also never observed within a 3 day period. Interlayer brittleness suggests that the surface preparation technique was unable to remove all oxide thus slowing the kinetics of the process (Figure 14).
This model predicts that isothermal solidification in multicomponent TLP bonding will occur, at least initially, by a process of tie line shifting. The driving force for such behaviour is the difference in interfacial rate constants as predicted by a single tie line for the two (or more) solutes. The sense in which the interfacial concentrations will move during this isothermal solidification can be simply predicted if the slope of the individual tie lines in the liquid + solid solution region and the fluxes associated with these tie lines are known.
More experimental work must be done in an attempt to verify the above model. As well, more sophisticated numerical models must be attempted to take into account the complex behaviour of the Gibbs isotherm. Future experiments may also consider the situations where the interlayer is a pure material and the base metal is an alloy or when both the base metal and interlayer are multicomponent alloys.
| FIGURES |
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Figure 1: Schematic showing the widening of liquid layer due to interdiffusion. A=base material, B=solute.
Figure 2: This schematic follows from figure 1. The process of isothermal solidification is predicted by the tie line as shown. Figure 3: Boundary conditions for isothermal solidification. Figure 4: Ideal diffusion path in liquid after dissolution. Figure 5: Schematic depicting concentrations needed for the definition of a Gibbs isotherm by the method outlined in (13). Figure 6: Schematic depicting two regimes of control which depend on starting position on phase boundary. This possibility of two regimes only occurs if there is a tie line which matches the rate constants for the two solutes.
Figure 7: Numerical simulation of isothermal solidification made by iterating the concentration of one solute by Figure 8: Gibbs isotherm for model system showing the solubilities used to define it. Figure 9: Solidification dependence on initial liquid thickness (after dissolution). Initial tin concentration = 20%. Figure 9a shows the temporal evolution of solidification. Figure 9b shows solidification referred to interfacial concentration. Figure 10: The effect of initial interlayer composition on solidification (interlayer thickness = 50 µm). Figure 10a shows the temporal evolution of solidification. Figure 10b shows the concentration dependence of solidification. Figure 11: Effect of slow solute diffusivity on solidification behaviour (initial concentration = 20% slow diffuser, initial liquid width = 50 µm). Figure 11a shows the temporal evolution of solidification. Figure 11b shows the variation of solidification with concentration. Figure 12: Computed Al-Zn-Sn isotherm (light gray) and constant partition coefficient assumption used in calculation superimposed for 500°C. Figure 13: Model as applied to Al-Sn-Zn system. Figure 13a shows liquid thickness as a function of time and initial interlayer thickness. Figure 13b shows liquid thickness as a function of liquidus concentration and initial interlayer composition. Figure 14: Micrographs of Al-Sn-Zn couple held at 500°C for 15 minutes in Figure 14a, and 18.5 hours in Figure 14b. |
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