Ternary systems diffusion

This concept has also been demonstrated at ambient temperature in the case of the Li-Sn-Cd system [47,48]. The composition-de-pendences of the potentials in the two binary systems at ambient temperatures are shown in Fig. 15, and the calculated phase stability diagram for this ternary system is shown in Fig. 16. It was shown that the phase Li4 4Sn, which has fast chemical diffusion for lithium, is stable at the potentials of two of the Li-Cd reconstitution reaction plateaus, and therefore can be used as a matrix phase. 

Nevertheless, many investigators have used the molecular diffusivities measured by Cole and Gordon (C12a) for CuS04 in the ternary system CuS04- H2S04-H20. The validity of these diffusivities for the purpose of limiting-current correlations has been questioned repeatedly (see Section IV,C,1). 

Carbon dioxide supply, for the molten carbonate fuel cell, 72 220 Carbon dioxide ternary systems, phase behavior of, 24 4—5 Carbon diselenide, 22 75t Carbon disulfide, 4 822-842 23 567, 568, 621. See also CS2 in cellulose xanthation, 77 254 chemical reactions, 4 824—828 diffusion coefficient in air at 0° C, 7 70t economic aspects, 4 834-835 electrostatic properties of, 7 621t handling, shipment, and storage, 4 833-834... 

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... 

Values of a diffusion coefficient matrix, in principle, can be determined from multicomponent diffusion experiments. For ternary systems, the diffusivity matrix is 2 by 2, and there are four values to be determined for a matrix at each composition. For quaternary systems, there are nine unknowns to be determined. For natural silicate melts with many components, there are many unknowns to be determined from experimental data by fitting experimental diffusion profiles. When there are so many unknowns, the fitting of experimental concentration... 

Solving the diffusion profiles given the diffusivity matrix (ternary systems)... 

To solve a diffusion equation, one needs to diagonalize the D matrix. This is best done with a computer program. For a ternary system, one can find the two eigenvalues by solving the quadratic Equation 3-lOOe. The two vectors of matrix T can then be found by solving... 

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).

Start from the diffusion equations in a ternary system ... 

Diffusive dissolution in ternary systems analysis with applications to... 

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. 

Figure 3-22 Design of diffusion experiments in a ternary system 262...

Polymer transport in ternary systems including an analysis of the cross diffusion coefficients and component distribution within the systems. 

In comparison with the qualitative description of diffusion in a binary system as embodied by Eqs. (11), (12) or (14), the thermodynamic factors are now represented by the quantities a, b, c, and d and the dynamic factors by the phenomenological coefficients which are complex functions of the binary frictional coefficients. Experimental measurements of Dy in a ternary system, made on the basis of the knowledge of the concentration gradients of each component and by use of Eqs. (21) and (22), have been reviewed 35). Another method, which has been used recently36), requires the evaluation of py from thermodynamic measurements such as osmotic pressure and evaluation of all fy from diffusion measurements and substitution of these terms into Eqs. (23)—(26). 

The rapid transport of the linear, flexible polymer was found to be markedly dependent on the concentration of the second polymer. While no systematic studies were performed on these ternary systems, it was argued that the rapid rates of transport could be understood in terms of the dominance of strong thermodynamic interactions between polymer components overcoming the effect of frictional interactions this would give rise to increasing apparent diffusion coefficients with concentration 28-45i. This is analogous to the resulting interplay of these parameters associated with binary diffusion of polymers. 

In the ternary system, therefore, the diffusional flux of water is determined by two of the ternary diffusional coefficients. For a binary system, it was shown earlier that the mutual diffusion of solvent and solute is identical and essentially independent of the magnitude of the osmotic pressure gradient across the boundary 30). 

There is, however, another statement of the necessary and sufficient condition of thermodynamic stability of the multicomponent system in relation to mutual diffusion and phase separation that is less stringent than equation (3.20) because it may be fulfilled not for every component of the multicomponent system. For example, in the case of the ternary system biopolymeri + biopolymer2 + solvent, it appears enough to fulfil only two of the inequalities (Prigogine and Defay, 1954)... 

In discussing AO-BO interdiffusion, we saw that the two independent fluxes of this ternary system can lead to different chemical diffusion coefficients D. They depend upon the constraints which define the physical situation (e.g., VjuG = 0 or Vy/v = 0). The analysis of this relatively simple and fundamental situation is already rather complex. The complexity increases further if diffusion occurs between heterovalent components of compound crystals. This diffusion process is important in practice (e.g., heterovalent doping) and its treatment in the literature is not always adequate. We therefore add a brief outline of the relevant ideas for a proper evaluation of D. 

Let us systematize the possible boundary conditions for cation diffusion in a spinel. Since in the ternary system (at a given P and T) the chemical potentials of two components are independent, we may distinguish between three different transport situations. If A denotes a change across the product layer and O and AO are chosen as the independent components, the possibilities are... 

In Section 4.3.3, it was explained how to construct the reaction (diffusion) path for ternary and higher solid solution systems. In practice, one plots, for example, in a ternary system, the composition variables (measured along the pertinent space coordinate of the reacting solid) into a Gibbs phase triangle, noting that the spatial information is thereby lost. For certain boundary conditions, such a reaction path is independent of reaction time and therefore characterizes the diffusion process. For a one dimensional ternary system with stable interfaces, these boundary conditions are c,-( = oo,f) = c°( oo) q( <0,0) = c (-oo) c,(f>0,0) = c (+oo). 

Normally, it is not possible to obtain analytical solutions for this transport problem and so we cannot a priori calculate the reaction path. Kirkaldy [J. S. Kirkaldy, D. J. Young (1985)] did pioneering work on metal systems, based on investigations by C. Wagner and the later work of Mullins and Sekerka. They used the diffusion path concept to formulate a number of stability rules. These rules can explain the facts and are predictive within certain limits if applied properly. One of Kirkaldy s results is this. The moving interface in a ternary system is morphologically stable if... 

There are extensive reviews of the many measurements of the Ay, particularly in ternary systems [1]. Numerous systems exhibit uphill diffusion, due to strong particle-particle interactions, and efforts have been made to interpret the diffusivity behavior in terms of thermodynamic activity data and particle-particle interaction models. In many cases the diffusion behavior has been explained, and more details and discussion are found in Kirkaldy and Young s text [1]. 

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