Diffusion couple technique

As concluding remarks about these techniques, their increasing interest and the advantages of their combination with other techniques, we may mention, as an example, that within the European research project COST 535, concerning the Thermodynamics of Alloyed Aluminides , a meeting (Diisseldorf, December 2004) was dedicated to The Diffusion Couple Technique , presenting the principles of the method and the results obtained in the examination of several alloy systems. Zhao (2004) has developed an efficient variant of the diffusion couple technique (the diffusion multiple approach ). 

In experimental studies of diffusion, the diffusion-couple technique is often used. A diffusion couple consists of two halves of material each is initially uniform, but the two have different compositions. They are joined together and heated up. Diffusive flux across the interface tries to homogenize the couple. If the duration is not long, the concentrations at both ends would still be the same as the initial concentrations. Under such conditions, the diffusion medium may be treated as infinite and the diffusion problem can be solved using Boltzmann transformation. If the diffusion duration is long (this will be quantified later), the concentrations at the ends would be affected, and the diffusion medium must be treated as finite. Diffusion in such a finite medium cannot be solved by the Boltzmann method, but can be solved using methods such as separation of variables (Section 3.2.7) if the conditions at the two boundaries are known. Below, the concentrations at the two ends are assumed to be unaffected by diffusion. 

Van Loo and co-workers33,34 and Wakelkamp31 have measured chemical diffusion coefficients for TiC, ZrC, and VC using a diffusion couple technique. They find that concentration and temperature dependencies for these carbides can be represented by an equation of the form... 

Hao] Diffusion couples technique, optical microscopy, EPMA Isothermal section at 1000°C, (Cu)/"y, (Cu)/a and a/y phase boundaries... 

The nonlinearity of the system of partial differential equations (51) and (52) poses a serious obstacle to finding an analytical solution. A reported analytical solution for the nonlinear problem of diffusion coupled with complexation kinetics was erroneous [12]. Thus, techniques such as the finite element method [53-55] or appropriate change of variables (applicable in some cases of planar diffusion) [56] should be used to find the numerical solution. One particular case of the nonlinear problem where an analytical solution can be given is the steady-state for fully labile complexes (see Section 3.3). However, there is a reasonable assumption for many relevant cases (e.g. for trace elements such as... 

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. 

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). 

In the profiling technique, the dependence of D on C may be obtained using either the Boltzmann method, or fitting the concentration profile with numerically calculated profile by assuming a specific relation between D and C, similar to the diffusion-couple method. For the Boltzmann method, the equation can be found by following steps in Section 3.2.B.2 and is as follows (Equation 3-58e) ... 

Ca0-Si02 melt 1600 0.1 Capillary technique 0 Enriched diffusion couple... 

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. 

We need to understand what controls the rate of a phase transformation. We can monitor both chemical and structural changes to address the sometimes subtle question— which change (chemistry or structure) occurs first The answer depends on why the phase change itself occurs. The experimental techniques we use are those given in Chapter 10, so we just give some specific illustrations here. The classical approach used to study the kinetics of solid-state reactions between two ceramic oxides is to react a bulk diffusion couple in much the same way as, for example, when studying the Kirkendall effect in metals. 

One of the modern hi -accuracy experimental methods is tomography atom probe (TAP). It enables the investigation of reactions in thin metallic diffusion couples by means of spatially resolved chemical analysis with a local accuracy up to interatomic distance [11, 12]. This technique was also applied to reactive diffusion in the thin film system Al-Co within the temperature range of 200-400 °C [6]. In accordance with the previous results obtained by the authors [13, 14] by DSC, the first phase to nucleate and grow in the temperature interval from 200 to 400 °C is AI9C02. The authors of [6] have established that in the diffusion zone between A1 and Co formation and growth of a solid solution layer occurs first, and nucleation of AI9C02 particles is never observed before the diffusion zone reaches about 3-4 nm thickness. Thus, the appearance of the product phase is controlled by the width... 

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