Wagner diffusion mechanism

The diffusion of charged particles plays a very important role in solid electrolytes. Sometimes, it can be referred to as the Wagner diffusion mechanism [14], In accordance with the electrostatic laws, the following condition of electronentrality can be fulfilled in any element of the volume of solid state ... 

The mechanism of the reaction (a) whether the reaction is phaseboundary- or transport-controlled, (b) whether the transport mechanism is unidirectional solid-state diffusion [Wagner ( ) diffusion, Hauffe ( ) diffusion], vapor, etc., and (c) whether the geometry of the reaction is nucleus growth or diffusion through a continuous product layer. 

Wagner (1961) examined theoretically the growdr kinetics of a Gaussian particle size distribution, considering two growth mechanisms. When the process is volume diffusion controlled... 

An example of a material (Li3Sb) with a very large Wagner factor is shown in Fig. 8.3. The effective chemical diffusion coefficient is compared with the diffusivity as a function of non-stoichiometry. These data were determined by electrochemical techniques (see Section 8.5). An increase of the diffusion coefficient is observed at about the ideal stoichiometry which corresponds to a change in the mechanism from a predominantly vacancy to interstitial mechanism. The Wagner factor W is as large as 70 000 at the ideal stoichiometry. This gives an effective diffusion coefficient which is more typical of liquids than solids. It is a common... 

Iso-UP has ester bonds only in the main chain where hydrolysis occurs, so a part of reaction products from the main chain dissolves into the solution. While the crosslink formed by styrene remains unaffected because of its stable C-C bonding. As a result, the corroded surface layer resists the diffusion of NaOH solution. This mechanism is just like an oxidation of the metal at high temperature with formation of thick, cohered oxide scale, and can be expressed by similar relation of Wagner s parabolic law as shown in Equation 2. The concept of corrosion in metals can be applied in this case too. 

Several points are to be noted. Firstly, pores and changes of sample dimension have been observed at and near interdiffusion zones [R. Busch, V. Ruth (1991)]. Pore formation is witness to a certain point defect supersaturation and indicates that sinks and sources for point defects are not sufficiently effective to maintain local defect equilibrium. Secondly, it is not necessary to assume a vacancy mechanism for atomic motion in order to invoke a Kirkendall effect. Finally, external observers would still see a marker movement (markers connected by lattice planes) in spite of bA = bB (no Kirkendall effect) if Vm depends on composition. The consequences of a variable molar volume for the determination of diffusion coefficients in binary systems have been thoroughly discussed (F. Sauer, V. Freise (1962) C. Wagner (1969) H. Schmalzried (1981)]. 

Wagner (1902) published an analysis of the oxidation of the surface of a metal, based on diffusion reactions, which has remained a classic. This mechanism is called by various names including "Tarnishing". The surface of a metal consists of metal atoms bound to the inner structure by a series of hybrid-bonds. If oxygen gas is present (air), the metal, particularly iron, will form an oxide coating, vis ... 

However, 0 ion diffusion is not very common. Due to their larger ionic radius, 0 ions are expected to have a considerably lower mobility than most cations. When cations are the only transporting species, the mechanism is known as the Wagner mechanism (Wagner, 1936). Formation of the spinel phase can be easily explained by diffusion of Mg " and counter-diffusion of AP". To maintain electro-neutrality, the mechanism involves the counter-diffusion of three Mg " ions for every two Al ions (Carter, 1961). 

A more complete test of the Wagner mechanism and treatment has been carried out by Fueki and Wagner and by Mrowec and Przybylski who derived values for the diffusion coefficient of nickel in NiO and cobalt in CoO from measurements of the parabolic oxidation rate constant. Since the parabolic rate constant can be expressed in the form of Equation (3.48),... 

The mechanism for VLS was proposed by Wagner in 1964. Under deposition conditions, the catalyzer has to form a liquid solution with the desired material. It should also have a low vapor pressure and be chemically inert. In the process, the vapor diffuses into the liquid catalyzer and, as the concentration becomes too high, the growth species precipitate to form the nanowire. The liquid phase is a preferential condensation site, and this causes a higher growth rate of the VLS with respect to the VS. Furthermore, by controlling the dimension and dispersion of the catalyzer, control can be achieved over the diameter of the nanowire. 

In the volume diffusion model, developed by Wagner [5], it was proposed that bulk diffusion of the less noble (LN) component to the dealloying front was the mechanism by which the selective dissolution reaction proceeded into the alloy. It was shown later by Cook and Hilliard [6] that bulk diffusion at room temperature was too slow to account for the rates of dealloying that were observed. 

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