Ternary diffusion couple

Figure 6.1 General evolution of a ternary diffusion couple with initial conditions...

The solution for a diffusion couple in which two semi-infinite ternary alloys are bonded initially at a planar interface is worked out in Exercise 6.1 by the same basic method. Because each component has step-function initial conditions, the solution is a sum of error-function solutions (see Section 4.2.2). Such diffusion couples are used widely in experimental studies of ternary diffusion. In Fig. 6.2 the diffusion profiles of Ni and Co are shown for a ternary diffusion couple fabricated by bonding together two Fe-Ni-Co alloys of differing compositions. The Ni, which was initially uniform throughout the couple, develops transient concentration gradients. This example of uphill diffusion results from interactions with the other components in the alloy. Coupling of the concentration profiles during diffusion in this ternary case illustrates the complexities that are present in multicomponent diffusion but absent from the binary case. 

Figure 6.2 Concentration profiles for Ni and Co in ternary diffusion couple fabricated...

Consider a ternary diffusion couple in which each component has an initial step-function profile and boundary conditions similar to those given by Eq. 4.44. Integrating and changing variables, as in the development leading up to Eqs. 4.48 and 4.49 for the binary case,... 

A schematic illustration of the method, and of the correlation between binary phase diagram and the one-phase layers formed in a diffusion couple, is shown in Fig. 2.42 adapted from Rhines (1956). The one-phase layers are separated by parallel straight interfaces, with fixed composition gaps, in a sequence dictated by the phase diagram. The absence, in a binary diffusion couple, of two-phase layers follows directly from the phase rule. In a ternary system, on the other hand (preparing for instance a diffusion couple between a block of a binary alloy and a piece of a third... 

Figure 3-21 Calculated diffusion profiles for a diffusion couple in a ternary system. The diffusivity matrix is given in Equation 3-102a. The fraction of Si02 is calculated as 1 - MgO - AI2O3. Si02 shows clear uphill diffusion. A component with initially uniform concentration (such as Si02 in this example) almost always shows uphill diffusion in a multi-component system.

Figure 3-22 A diagram for the representation of compositions in a ternary system, with two hypothetical diffusion couples a-b and c-d. The compositional gradient of the two diffusion couples are orthogonal to each other. For a given point inside the triangle, to find the fraction of a component (such as A), first draw a straight line parallel to BC, and then find where the straight line intersects the CA segment (with fraction indicated on the CA segment).

Trial A.F. and Spera F.J. (1988) Natural convection boundary layer flows in isothermal ternary systems role of diffusive coupling. Int. J. Heat Transfer 31, 941-955. 

The coupled ternary diffusion equations in one dimension are obtained from the accumulation fluxes in Eq. 6.11 ... 

If the interdiffusivities are each constant and uniform, the coupled ternary diffusion equations, Eq. 6.20, are a linear system,... 

Find the diffusion profile solutions for ternary diffusion in a diffusion couple fabricated by bonding two semi-infinite alloy blocks face to face along a planar interface. Assume constant diffusivities. 

From an economic viewpoint, the classical determination of alloy phase diagrams is a laborious process, involving alloy preparation and heat treatment, compositional, structural, and microstructural analysis (and, even then, not yielding reliable phase boundary information at low temperatures due to kinetic limitations). While this investment is justified for alloys of major technical importance, the need for better economics has driven an effort to use alternative methods of phase discovery such as multiple source, gradient vapor deposition or sputter deposition followed by automated analysis alternatively, multicomponent diffusion couples are used to map binary or ternary alloy systems structurally and by properties (see Section 6). These techniques have been known for decades, but they have been reintroduced more recently as high-efficiency methodologies to create compositional libraries by a combinatorial approach, inspired perhaps by the recent, general introduction of combinatorial methods in chemistry. 

Smi] Smith, B.J., Goldstein, J.I., Marder, A.R., Application of the Diffusion Couple to Study Phase Equilibria in the Fe-Cr-S Ternary System at 600°C , Metall. Mater. Trans. A, 26A (1), 41-55 (1995) (Experimental, Phase Relations, 24)... 

At reaction-diffusion processes in ternary systems, the phase spectram of the diffusion zone, even for small annealing times, depends on the initial composition of the diffusion couple and on the set of diffusion parameters [28- 33]. Furthermore, the choice of the diffusion path may appear to be ambiguous [34, 35). In such a case, the stage of nucleation becomes a decisive one. 

At that boundary, the composition of the alloy BC shifts along the BC side. Indeed, if the intermetaUide requires different quantities of B and C, the initial alloy BC will become depleted of these components to a certain extent This, in particular, leads to homogeneity violation of the initial alloy of the BC couple, which in turn, causes fluxes in this part of the diffusion couple, and this influences the kinetics of the boundary movement When there are several intermediate phases on the phase diagram, the mentioned effect may cause competition between them. The failure of the two indicated modes may lead to the formation of the two-phase zone in the ternary system during the diffusion process the boundary concentration may appear to lie on different conodes and the diffusion path will not be able to bypass them. 

Maugis P, Hopfe WD, Mortal JE, Kirkaldy JS (1997) Multiple interface velocity solutions for ternary biphase infinite diffusion couples. Acta Mater 45 1941... 

As mentioned above, Sn is the major component of Pb-free solders. In addition, in Pb-Sn solders, Sn is the most active component in the formation of IMCs. Therefore, the formation of IMCs in Pb-Sn solder/metallization diffusion couples is considered hrst, as a basis for examination of Pb-free solder alloys. This treatment is followed by a discussion of the formation of Auo,5Nio,5Sn4 compound in Pb-Sn solder joints, because the mechanisms for its formation are similar to the formation of ternary IMCs in some Pb-free solder joints. 

In a significant contribution, [1995Pal] determined two complete isofiiermal sections at 800 and 1000°C. They prepared 59 ternary alloys in a cracible-free levitation furnace and cast into a copper mold. They used elements of following purity 99.99% Al, 99.97% Fe and 99.77% Ti. The alloys were heat treated at 1000 and 800°C for 100 and 500 h, respectively, followed by quenching in brine solution. In addition, they also performed six diffusion couple experiments at 1000°C. 

Solution Answering this question requires the assumption that there are no ternary diffusion effects in this system. These effeets may arise because the diffusion of sodium ion couples with the diffusion of ehloride ion, whieh in turn affects the diffusion of La. However, these effects vanish for any solute present in high dilution, as LaCls is in this case (see Section 7.4). 

Figure 4-1. Chemical diffusion of a (ternary) couple with linear geometry. Initial compositions are c° and c°. Schematic diffusion (reaction) path.

Generally, a set of coupled diffusion equations arises for multiple-component diffusion when N > 3. The least complicated case is for ternary (N = 3) systems that have two independent concentrations (or fluxes) and a 2 x 2 matrix of interdiffusivities. A matrix and vector notation simplifies the general case. Below, the equations are developed for the ternary case along with a parallel development using compact notation for the more extended general case. Many characteristic features of general multicomponent diffusion can be illustrated through specific solutions of the ternary case. 

Coefficients Lqq and Lt] are associated with the thermal conductivity k and the mutual dififusivity D, respectively, while the cross coefficients Liq and Lqi define the coupling. Thermal conductivity (k) is related to Lqq by k = LqJT, while the thermal diffusion coefficient is related to Liq by Liq = pDTi. Tables 7.9 and 7.10 show the values of the phenomenological cofficients Lq for the ternary mixture of toluene (l)-chlorobenzene (2)-bromobenzene (3) at 298.15 and 308.15 K. 

For a ternary mixture, equations above can describe thermodynamically and mathematically coupled mass and energy conservation equations without chemical reaction, and electrical, magnetic and viscous effects. To solve these equations, we need the data on heats of transport, thermal diffusion coefficient, diffusion coefficients and thermal conductivity, and the accuracy of solutions depend on the accuracy of the data. 

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