Metal Wagner theory

The main difficulty with the first mode of oxidation mentioned above is explaining how the cation vacancies that arrive at the metal/oxide interface are accommodated. This problem has already been addressed in Section 7.2. Distinct patterns of dislocations in the metal near the metal/oxide interface and dislocation climb have been invoked to support the continuous motion of the adherent metal/oxide interface in this case [B. Pieraggi, R. A. Rapp (1988)]. If experimental rate constants are moderately larger than those predicted by the Wagner theory, one may assume that internal surfaces such as dislocations (and possibly grain boundaries) in the oxide layer contribute to the cation transport. This can formally be taken into account by defining an effective diffusion coefficient Del( = (1 -/)-DL+/-DNL, where DL is the lattice diffusion coefficient, DNL is the diffusion coefficient of the internal surfaces, and / is the site fraction of cations located on these internal surfaces. 

A.J. Ardell. Experimental Confirmation of the Lifshitz-Wagner Theory of Particle Coarsening, pages 111-116. Institute of Metals, London, 1969. 

In order to explain the corrosion process of metals, Wagner and Traud [54] developed the mixed potential theory, which assumes that the current-potential relationship is given by... 

The Wagner theory [10] for a coupled diffusion and migration (also known as ambipolar diffusion) mass transfer during oxidation of metals and alloys is briefly described. This theory treats the parabolic kinetic behavior of high temperature oxides given by eq. (10.19) with n = 1/2. 

By measuring the cell potential for this ideal case, where the oxide would behave as a tme electrolyte and where no polarization losses at the electrodes would occur, the Gibbs energy of formation for the oxide can be determined. However, for most metal oxides (exceptions would be calcia- or yttria-stabilized zircoiua above 800°C or pure b-BijOj above 650°C) the transport number of the ions is smaller than 1, thus making a direct measurement of the equilibrium cell potential in Figure 15.3 impossible. Alternatively, it could be formulated that the cell is partially short circuited by the electronic current. For oxides growing on a metal substrate under stationary conditions as described by the Wagner theory in Section n, this is the normal situation. 

According to the Wagner metal oxidation theory, the metal oxidation process is controlled by the crystal lattice diffusion in the oxide phase and by diffusion along the GB. It also conforms to the parabola rule at high temperatures ... 

An important aspect of any theory of the oxidation of a pure metal is that it enables us to see how the protective power of the oxide layer can be altered by the introduction of alloying constituents into the metal. According to Wagner s theory, the parabolic rate constant for the system Ni/NiO for example depends upon the concentration of cation vacancies in the oxide in equilibrium with oxygen gas. If this concentration can be reduced, the oxidation rate is reduced. Now this can be done if cations of lower valency than Ni can be got into the oxide (Fig. 1.77). Suppose, for example, that a little Li is added to the Ni. Each Li ion which replaces Ni is a negative... 

Whether the rate of oxidation of an alloy of copper with a baser metal is less or more than that of copper will depend on the concentration of the alloying element and the relative diffusion velocities of metal atoms or ions in the oxide layers. There is extensive literature on the oxidation behaviour of copper alloys According to Wagner s theory the rate of oxida-... 

An electrochemical model for the process of electroless metal deposition was suggested by Paunovic (10) and Saito (8) on the basis of the Wagner-Traud (1) mixed-potential theory of corrosion processes. According to the mixed-potential theory of electroless deposition, the overall reaction given by Eq. (8.2) can be decomposed into one reduction reaction, the cathodic partial reaction. 

In solid state physics, it is well known that many inorganic solids, e.g., the oxides and sulfides, can dissolve metals and nonmetals in excess, and that by this process electron and ion defects in the lattice will be formed. Wagner and co-workers (1) have developed the basic theory of... 

In 1937, dost presented in his book on diffusion and chemical reactions in solids [W. lost (1937)] the first overview and quantitative discussion of solid state reaction kinetics based on the Frenkel-Wagner-Sehottky point defect thermodynamics and linear transport theory. Although metallic systems were included in the discussion, the main body of this monograph was concerned with ionic crystals. There was good reason for this preferential elaboration on kinetic concepts with ionic crystals. Firstly, one can exert, forces on the structure elements of ionic crystals by the application of an electrical field. Secondly, a current of 1 mA over a duration of 1 s (= 1 mC, easy to measure, at that time) corresponds to only 1(K8 moles of transported matter in the form of ions. Seen in retrospect, it is amazing how fast the understanding of diffusion and of chemical reactions in the solid state took place after the fundamental and appropriate concepts were established at about 1930, especially in metallurgy, ceramics, and related areas. 

An appreciable number of special monographs on metal oxidation are available. These presentations normally start with Wagner s theory of scale formation [C. Wagner (1933), (1951)], which represented the first consistent and quantitative treatment of a solid state reaction model. As Figure 7-1 shows, metal oxidation has quite... 

Wagner s theory of metal oxidation is phenomenological. Many questions concerning atomic aspects of the oxidation process cannot be answered within the frame of this phenomenological theory. Since atomic aspects are important when we analyze the boundary conditions, this will be exemplified by two pertinent problems. Firstly, let us ask about the coherence of the metal/oxide interface during the oxida-... 

C. Wagner and W. Traud, Z. Elektrochem. 44 391 (1938). The original formulation of the mixed potential concept and the basic theory of corrosion of a pure metal. 

Metals are obtained by the treatment of oxides and sulfide ores found in the earth. However, there is an initial difficulty—the desirable ores are often mixed up with those of little commercial value, and the problem is to obtain the desired ore free from those of lesser worth. For many years now, largely due to the initiative of Australian workers, it has been possible to find organic substances which, when added to a suspension of mixed ores, pick out the desired one, and (when air is bubbled into the system) float it to the surface, from which it can be raked off, i.e., separated and made available for chemical or electrochemical extraction of the metal. It turns out that the basis of this mineral flotation technology involves the Wagner and Traud mixed-potential concept and is thus indirectly related to corrosion theory. 

Walter Haus Schottky (1886-1976) received his doctorate in physics under Max Planck from the Humboldt University in Berlin in 1912. Although his thesis was on the special theory of relativity, Schottky spent his life s work in the area of semiconductor physics. He alternated between industrial and academic positions in Germany for several years. He was with Siemens AG until 1919 and the University of Wurzburg from 1920 to 1923. From 1923 to 1927, Schottky was professor of theoretical physics at the University of Rostock. He rejoined Siemens in 1927, where he finished out his career. Schottky s inventions include the ribbon microphone, the superheterodyne radio receiver, and the tetrode vacuum tube. In 1929, he published Thermodynamik, a book on the thermodynamics of solids. Schottky and Wagner studied the statistical thermodynamics of point defect formation. The cation/anion vacancy pair in ionic solids is named the Schottky defect. In 1938, he produced a barrier layer theory to explain the rectifying behavior of metal-semiconductor contacts. Metal-semiconductor diodes are now called Schottky barrier diodes. 

Secondly, from Wagner s theory, the metallic coatings forming the electrodes are viewed as mere electronic probes for the local electronic distribution in the auxiliary phase. They should be chemically inert. For operation in the lean regime, it is highly desirable that their... 

The preceding theory was used by Wagner to describe oxide film growth on metals [49,50]. The driving force for diffusion is not a concentration gradient. 

Solid materials, in general, are more or less subject to corrosion in the environments where they stand, and materials corrosion is one of the most troublesome problems we have been frequently confronted with in the current industrialized world. In the past decades, corrosion science has steadily contributed to the understanding of materials corrosion and its prevention. Modem corrosion science of materials is rooted in the local cell model of metallic corrosion proposed by Evans [1] and in the mixed electrode potential concept of metallic corrosion proved by Wagner and Traud [2]. These two magnificent achievements have combined into what we call the electrochemical theory of metallic corrosion. It describes metallic corrosion as a coupled reaction of anodic metal dissolution and cathodic oxidant reduction. The electrochemical theory of corrosion can be applied not only to metals but also to other solid materials. 

The implication of Wagner s theory was that the parabolic scaling rate constants, memy of which were known for certain gas-metal combinations, should be quantitatively related to two basic types of information. 

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