Two-phase diffusion couples

Maugis P, Hopfe WD, Mortal JE, Kirkaldy JS (1996) Degeneracy of diffusion paths in temtiry, two-phase diffusion couples. J Appl Phys 79 7592... 

Thus, the growth of an external oxide scale by the reaction between a pure metal or a metallic alloy and a gaseous or liquid oxidant phase at high temperature is also a combination of diffusion processes and interfacial reactions, and Fig. 2.1 also applies to such corrosion processes that are formally similar to solid-state reactions in poly-phase and multi-constituent systems. Such a similarity will be considered to extend the treatment of the Kirkendall effect for two-phase diffusion couples to the growth of an oxide scale on a pure metal or on an alloy. The roles of interfaces will be analysed more particularly in relation to some specific topics related to oxide scaling processes such as interface displacement, growth stresses and injection of point defects (vacancy or interstitial). 

Specificity of the Kirkendall effect in two-phase diffusion couples... 

Kong et al. [90] applied the electrochemical approach to the study of a two-phase azo coupling facilitated by reverse PTC. Cyclic voltammetry and chronoamperometry were employed to evaluate quantitatively the rate constants for the reaction. The process was interpreted in terms of an EC mechanism, i.e., diffusion-controlled electrochemical charge transfer followed by a homogeneous chemical reaction. The authors highlighted the usefulness of this approach based on the factors that enable the estimation of the contributions of the chemical reaction, mass transfer, partitioning, and the adsorption of reactants at the interface to the overall two-phase reaction. 

Cross-relaxation at the nematic-polymer interface. The liquid crystal protons and the polymer protons constitute a two phase proton system. The cross-relaxation at the boundary leads to an exchange of Zeeman energy between the two phases and couples their spin-lattice relaxation rates [202]. Cross-relaxation affects all molecules in the droplet if the exchange of molecules at the surface is so fast that within the spin-lattice relaxation time each molecule in the droplet takes part in this process. For this to take place, both the time required for a molecule to diffuse from the inside of the droplet to the surface Tog, and the time Tg for which the molecules remain anchored at the surface must be short compared to the spin-lattice relaxation time Ty. In the limit of very rapid cross-relaxation (k > (Tf(Tf )p) both phases relax with the same relaxation rate which is an weighted average... 

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 2.42. The Cu-Zn system phase diagram and microstructure scheme of the diffusion couple obtainable by maintaining Cu and Zn blocks in contact for several days at 400°C. Shading indicates subsequent layers, each one corresponding to a one-phase region. The two-phase regions are represented by the interfaces between the one-phase layers (adapted from Rhines 1956).

A general treatment of a diffusion-controlled growth of a stoichiometric intermetallic in reaction between two two-phase alloys has been introduced by Paul et al. (2006). A reaction couple in which a layer of Co2Si is formed during inter-diffusion from its adjacent saturated phases was used as a model system. In the discussion it has been emphasized that the diffusion couple is undoubtedly one of the most efficient and versatile techniques in solid-state science it is therefore desirable to have alternative theories that enable us to deduce the highest possible amount of information from the data that are relatively easily attainable in this type of experiments. 

One of the first studies of how these secondary phases form was performed by van Roosmalen and Cordfunke. These authors used SEM/EDS and XRD to study postannealed diffusion couples of LSM and YSZ as well as pressed and fired powder mixtures of LSM and YSZ. These experiments showed that reaction products in sufficient quantity to detect by XRD (1—3%) form at temperatures as low as 1170 °C. The two principle reaction products observed were La2Zr207 (LZ) and SrZrOs (SZ), with the relative amount of LZ and SZ depending on the La/Sr ratio in the LSM. Calcia- and baria-doped LaMnOs were found to be similarly reactive with YSZ, and reactivity of LSM with YSZ having 3% or 8% yttria was found to be similar. In the case of the diffusion couples, the layer of reaction products formed at the interface was found (using SEM) to be on the order of 1 /xm after 600 h at 1280 °C and 10—15 fim after 600 h at 1480 °C. By employing Pt diffusion markers... 

Dayanada 1979) and Fig. 4.14 shows the measured composition profiles of the various elements in a diffusion couple from Al-Nb-Ti at 1200°C (Hellwig 1990). In the latter case the diffusion path crosses three two-phase fields, (Nb, Ti) AI3 + TiAl, TiAl + NbzAl, and /3 + Nb2Al. Other good examples of this technique in practice can be found in the work of van Loo and co-workers (1978,1980,1981). 

The diffusion couple discussed above consists of two halves of the same phase. If the two halves are two minerals, such as Mn-Mg exchange between spinel and garnet (Figure 3-5), there would be both partitioning and diffusion. Define the diffusivity in one half (x < 0) to be D, and in the other half (x > 0) to be D. Both and are constant. Let w be the concentration (mass fraction) of a minor element (such as Mn). The initial condition is... 

Relaxation times for water filling the pores of an NaX specimen have been fitted to a model with the following assumptions (a) coupling, as above, of molecular diffusion and rotation (b) the median jump time r is governed by a free volume law (allows the curvature in the plots of jump rate, (3r) x vs. 10S/T in Figure 5), and (c) a broad distribution of correlation times (allows a better fit to the data, accounts for an apparent two-phase behavior in T2 (31, 39), and is reasonable in terms of the previous discussion of Pi(f) and r). 

Figure 4.2 (a, b, c) EPMA scans across diffusion couples of V-C, Nb-C and Ta-C systems corresponding to that shown in the left column of Figure 4.1. The compositions of the 5 phases as well as the boundaries of two-phase fields ji + t, and 5 + 8 could be measured.

Transport is a three-phase process, whereas homogeneous chemical and phase-transfer [2.87, 2.88] catalyses are single phase and two-phase respectively. Carrier design is the major feature of the organic chemistry of membrane transport since the carrier determines the nature of the substrate, the physico-chemical features (rate, selectivity) and the type of process (facilitated diffusion, coupling to gradients and flows of other species, active transport). Since they may in principle be modified at will, synthetic carriers offer the possibility to monitor the transport process via the structure of the ligand and to analyse the effect of various structural units on the thermodynamic and kinetic parameters that determine transport rates and selectivity. 

When a chemical reaction is fast enough to become complete within the diffusion film, the chemical rate and diffusion rates are coupled differently. Fig. 5.4 shows the basis for derivation of the rate expression for a reaction in a two-phase organic reactant/water system when the reaction is first order in solute with rate constant k, the diffusion coefficient of the organic species in water is D and the saturation solubility of the organic reactant in water is Csat. We consider the system at steady state and take a mass balance across a slab... 

In analyzing diffusion couples involving two or more phases, there are two key points ... 

Let us leave to the specialists in phase equilibria to argue whether these are individual phases or compositional polymorphs of the same phase. The results presented appear to be sufficient for the reader to appreciate how complicated phase relations may be and how careful it is necessary to be when interpreting any experimental data on both phase diagrams and compound-layer formation in diffusion couples, especially in those cases where the two-phase fields are narrow compared to the homogeneity ranges of chemical compounds. 

Again, the diffusional theory rests on the assumption of local equilibrium or quasi-equilibrium. However, it is clear that no local equilibrium can exist in any diffusion couple in which the layers of some part of thermodynamically stable compounds are missing. Also, if successive layers of reactants and products are in equilibrium with each other, then all the system is in local equilibrium. Therefore, applying the Gibbs phase rule, it is easy to come to the logical conclusion that under constant temperature and pressure conditions no compound layer can occur at all between two reactants in a binary system since in this case the largest number of co-... 

In this book we are concerned only with mass transport, or diffusion, in solids. Self-diffusion refers to atoms diffusing among others of the same type (e.g., in pure metals). Interdiffusion is the diffusion of two dissimilar substances (a diffusion couple) into one another. Impurity diffusion refers to the transport of dilute solute atoms in a host solvent. In solids, diffusion is several orders of magnitude slower than in liquids or gases. Nonetheless, diffusional processes are important to study because they are basic to our understanding of how solid-liquid, solid-vapor, and solid-solid reactions proceed, as well as [solid-solid] phase transformations in single-phase materials. 

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