Diffusion-coupled methods

The purpose of most experimental studies of diffusion is to obtain accurate diffusion coefficients as a function of temperature, pressure, and composition of the phase. For this purpose, the best approach is to design the experiments so that the diffusion problem has a simple anal3hical solution. After the experiments, the experimental results are compared with (or fit by) the anal3hical solution to obtain the diffusivity. The method of choice depends on the problems. The often used methods include diffusion-couple method, thin-source method, desorption or sorption method, and crystal dissolution method. 

In the diffusion-couple method, two cylinders of the same radius and roughly the same length are prepared. Each cylinder (called a half) is uniform in com-... 

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) ... 

A diamond-anvil-cell (DAG) is a small high pressure cell most suitable for the spectroscopic measurement of molecular or atomic diffusion. The DAG is used for various kinds of spectroscopic investigations on liquids and solids at pressures up to several tens of GPa [19-22]. The optically transparent nature of diamond over a wide wavelength span allows in situ optical measurements in combination with conventional equipment such as visible light or infrared spectrometers. The protonic diffusion in ice is measured by a traditional diffusion-couple method, in the present case, with an H2O/D2O ice bilayer. The mutual diffusion of hydrogen (H) and deuteron (D) in the ice bUayer is monitored by measuring the infrared vibrational spectra. The experimental details are described in the following sections. 

Ahm, 1974Zap] Diffusion couple method Corrosion tests, micro-hardness tests Homogenization degree of sintered of Cr-Cu-Fe alloys with 2 to 18 tnass% Cr and 2 to 4 mass% Cu at 1050 to 1410°C, diffusion coefficient and activation energy of diffusion of Cr in a and -y phases. Microhardness and eorrosion resistance... 

Wan] Diffusion couple method Diffusion coefficients of copper and chromium in liquid Cr-Cu-Fe alloys at 1550°C... 

Cha] Diffusion couple method, light microscopy, microprobe analysis (Camebax-Micro) 700, 750 and 1000°C... 

Interdiffusion coefficients in wiistite solid solutions containing BaO were measured by using a diffusion couple method at between 1073 and 1473K, in a controlled atmosphere for which the CO/CO2 ratio was equal to unity. It was found that the... 

Typically, diffusion coefficients are determined using the diffusion couple method giving (volume diffusion in parabolic growth) and diffusivities... 

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 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... 

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. 

In the above diffusion-couple problem (as in other diffusion problems), the concentration C depends on two independent variables, x and t. Briefly, the Boltzmann transformationuses one variable v[ = x/ / (some authors use p =xj ft) some others use p x/s/Dt if D is constant they are all equivalent) to replace two variables x and t. This works only under special conditions. Below, the method is described first and the conditions for its use are discussed afterward. 

In the above application of the Boltzmann method to a diffusion couple, it is necessary to find the position of the interface accurately. A modified method that makes this step unnecessary is proposed by Sauer and Freise (1962) ... 

Tracer diffusivities are often determined using the thin-source method. Self-diffusivities are often obtained from the diffusion couple and the sorption methods. Chemical diffusivities (including interdiffusivity, effective binary diffusivity, and multicomponent diffusivity matrix) may be obtained from the diffusion-couple, sorption, desorption, or crystal dissolution method. 

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. 

The present study showed that substantial information can be gained from the investigation of diffusion couples which otherwise would be difficult to obtain with bulk-sample methods. This information includes reliable homogeneity and stability ranges of phases as well as data for the nonmetal diffusivities. 

Figure 1. (a) Schematic diagram of the method to make the compositionally graded diffusion couple. 

Figure l-(a) shows the schematic diagram of the method to make the compositional ly graded diffusion couple. The couple of Cu/Cu-10 massXSn has the diffusion zone of 2 mm in length after heating. 

When silicon is deposited from the vapor phase at ambient temperature, it solidifies as amorphous silicon. Vapor deposited bilayers and multilayers of silicon with metals thus consist of polycrystallinc metal and amorphous silicon. The earliest observations of amorphous silicide formation by SSAR were made on such diffusion couples [2.51, 54], Similar results were also obtained earlier by Hauser when Au was diffused into amorphous Tc [2.56], Figure 2.15 shows an example of an amorphous silicide formed by reaction of amorphous silicon with polycrystallinc Ni-metal at a temperature of 350"C for reaction times of 2 and 10 s [2.55,57], The reaction experiments were carried out by a flash-healing method (see [2.55] for details). In this example, the amorphous phase grows concurrently with a crystalline silicide. The amorphous phase is in contact with amorphous Si and the crystalline silicide in contact with the Ni layer. As in the case of typical mctal/metal systems, the amorphous interlayer is planar and uniform. It is also interesting that the interface between amorphous silicon and the amorphous silicide appears to be atomically sharp despite the fact that both phases are amorphous. This suggests that amorphous silicon (a covalently bonded non metallic amorphous phase with fourfold coordinated silicon atoms) is distinctly different from an amorphous silicide (a metallically bonded system with higher atomic coordination number). These two phases are apparently connected by a discontinuous phase transformation. 

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. 

Depending on method of evaluation, Kopp et al, (95) found that diffusion into a piece of pure ice from one containing a high HF concentration, in intimate contact with the former (diffusion couple), is limited by a filter effect/ This means that, regardless of actual concentration, only a limiting concentration of 1.4 X lO M can be admitted to the pure ice. If this filter effect is not taken into account, the computed diffusion coefficients will be too low by orders of magnitude. 

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