Diffusion coupled with interface reaction

Diffusion processes coupled with interface reactions... 

A general transport phenomenon in the intercalation electrode with a fractal surface under the constraint of diffusion mixed with interfadal charge transfer has been modelled by using the kinetic Monte Carlo method based upon random walk approach (Lee Pyim, 2005). Go and Pyun (Go Pyun, 2007) reviewed anomalous diffusion towards and from fractal interface. They have explained both the diffusion-controlled and non-diffusion-controlled transfer processes. For the diffusion coupled with facile charge-transfer reaction the... 

Several studies addressing the formation of solder alloys in Ni/Pb-Sn diffusion couples have been performed at temperatures above the liquidus [7,8,10,71-74]. Early during the reaction, scallops are found at the Ni interface, with grooves between the scallops that extend to the Ni interface. For instance, in diffusion couples with eutectic Pb-Sn and electroplated Ni/Pd metallization, Ni3Su4 scallops were observed [7,8] to form on the Ni surface and to coarsen over time. Kinetic data for the radial growth of the scallops and for the increase in the average thickness of the Ni3Su4 layer were computed. It was determined that the data fit well as an empirical relation between scallop radius, r, and time, r = with B a proportionality factor... 

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... 

If the diffusion process is coupled with other influences (chemical reactions, adsorption at an interface, convection in solution, etc.), additional concentration dependences will be added to the right side of Equation 2.11, often making it analytically insoluble. In such cases it is profitable to retreat to the finite difference representation and model the experiment on a digital computer. Modeling of this type, when done properly, is not unlike carrying out the experiment itself (provided that the discretization error is equal to or smaller than the accessible experimental error). The method is known as digital simulation, and the result obtained is the finite difference solution. This approach is described in more detail in Chapter 20. 

In these types of laboratory reactor, the flow of the liquid is very carefully controlled so that, although the mass transfer step is coupled with the chemical reaction, the mass transfer characteristics can be disentangled from the reaction kinetics. For some reaction systems, absorption of the gas concerned may be studied as a purely physical mass transfer process in circumstances such that no reaction occurs. Thus, the rate of absorption of C02 in water, or in non-reactive electrolyte solutions, can be measured in the same laboratory contactor as that used when the absorption is accompanied by the reaction between C02 and OH ions from an NaOH solution. The experiments with purely physical absorption enable the diffusivity of the gas in the liquid phase DL to be calculated from the average rate of absorption per unit area of gas-liquid interface NA and the contact time te. As shown in Volume 1, Chapter 10, for the case where the incoming liquid contains none of the dissolved gas, the relationship is ... 

It is most convenient to compare the growth rates of the layer of the same chemical compound in various reaction couples with the rate of its growth at the interface of elementary substances. Therefore, let us first briefly analyse the case in which the ArBs compound layer is formed at the A-B interface (Fig. 4.1). To avoid considerable changes in the designations of the reaction-diffusion constants describing the layer-growth kinetics, the numeration of the interfaces of the ArBs layer, shown in Fig. 3.1, will be retained. 

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. 

The layered structure cannot be refined indefinitely by deformation due to the increasing hardness with decreasing crystallite size (for details see Sect. 3.3.2). The main alloying, therefore, occurs by an interdiffusion reaction at the created clean interfaces, if a thermodynamic driving force (negative free enthalpy of mixing) exists for this diffusion couple. The required temperature rise is provided by the heat released during the ball collisions (Sect. 3.3.2). 

The fundamental processes involved in the mediating process are identified as charge introduction at the modifying/electrode interface, charge introduction at the layer/electrolyte interface, and reaction of the target analyte with the modifying layer. Coupled to these reactions, one may observe substrate diffusion into the film as dictated by the partition coefficient, K. If the substrate is capable of penetrating the film, then the diffusion rate of the substrate, Dy, within the layer will in all but a few cases be considerably less than the solution value Z). ... 

The two-film theory certainly lacks physical reality in postulating the existence of stagnant films at the interface, but nevertheless contains the essential features of dissolution and diffusion prior to the transfer in the turbulent bulk of the fluid. It also describes quantitatively quite well the phenomena of mass transfer coupled with a chemical reaction, as discussed in the subsequent chapters. Thereby, the following cases, as depicted in Figure 4.4.2, will be inspected ... 

In 2002, Uhneanu et al. used a thin organic layer that is supported by a porous hydrophobic membrane such as porous Teflon or poly vinylidenedifluoride (PVDF), or sandwiched between two aqueous dialysis membranes [295]. With this setup, they showed that the transfer of highly hydrophilic ions at one interface can be studied by limiting the mass transfer of the other ion-transfer reaction at the other interface. They have also shown that cyclic voltammetry for coupled ion-transfer reactions at the two interfaces in series is analogous to cyclic voltammetry for electron-transfer reactions studied by Stewart et al. [207], as the diffusion equations of the reactants and products are analogous, and as the overall Nernst equation for the coupled ion transfer equal to the two individual Nemst equations for ion distribution is also analogous to the Nemst equation for the heterogeneous ET. 

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