Diffusion Constants in Metals

To measure the concentration gradient in a metal, one may conveniently employ the method of Bramley (i, 2,3,4,5) and his co-workers. They heated iron in a suitable gas atmosphere of which the following are examples. 

After the metal in the form of bars had been heated to a definite temperature for a suitable period it was removed, and successive thin layers taken off in the lathe and analysed. In this way the concentration gradient was determined and the solution of Pick s law in the form 

The concentration-distance curves into the metal are, however, not always of a shape to which a simple solution of the Pick law is applicable. Pigs. 73 and 74 give different types of concentration-distance curve, for which the solution given above is manifestly not correct. In the former case a saturated carbon layer has established itself at the surface, and in the latter the surface has been to some extent decarburised by hydrogen present in the carburising atmosphere. An attempt has been made to treat diffusion problems of the type illustrated by Pig. 73(6), but a complete treatment of Pig. 74 is not available. However, Bramley and his co-workers neglected the initial parts of these unusual forms of concentration distance curve, and applied the simple solution of Pick s law only to the tail of the curves. The error involved in evaluating D is therefore smaller. 

In addition to this analytical method of determining the concentration gradient it should in some cases be possible to 

When one does not require the concentration gradient, but simply the total quantity absorbed or desorbed, one may use 

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This review of the possible ways of measuring diffusion constants in metals indicates the lines of approach which have been developed. Future work should aim at the establishment of the relative importance of phase-boundary reactions and volume diffusion the estimation of the influence of concentration upon the diffusion constant the understanding of the role of impurities and mechanical treatment and measurements of the influence of temperature and other variables upon the diffusion constants. In this way the investigations will ultimately contribute to the problems of mobility and reaction in solids. Unfortunately there is so far a great scarcity of data. 

The determination of diffusion constants in metals may be made by a number of rather special experimental techniques,... 

Table 67. Diffusion constants in metals according to the equation D =... 

An applied electrical potential gradient can induce diffusion (electromigration) in metals due to a cross effect between the diffusing species and the flux of conduction electrons that will be present. When an electric field is applied to a dilute solution of interstitial atoms in a metal, there are two fluxes in the system a flux of conduction electrons, Jq, and a flux of the interstitials, J. For a system maintained at constant temperature with Fq = -V = E, Eq. 2.21 gives... 

The problem of hydrogen storage in metals is related with the problem of determination of hydrogen binding energy and diffusion constants in the metals. 

It has been indicated how the diffusion constant in a salt may be calculated from the ionic mobility of the current carrier (p. 268), or from the use of a radioactive isotope as an indicator (p. 244). Von Hevesy(3i) considers that it will be possible to use the latter method to follow the self-diffusion of numerous metals (Table 59). The method can be extended in a few instances by using as indicators small quantities of certain salts in solid solution in a closely related salt (77,78). For example, (78) small amounts of CuCl or NaCl were dissolved in AgCl. These mixtures are all cationic conductors in the temperature and concentration range investigated. The diffusion constants Z>Na+ were measured, and also the conduc-... 

Oxide movements are determined by the positioning of inert markers on the surface of the oxideAt various intervals of time their position can be observed relative to, say, the centreline of the metal as seen in metal-lographic cross-section. In the case of cation diffusion the metal-interface-marker distance remains constant and the marker moves towards the centreline when the anion diffuses, the marker moves away from both the metal-oxide interface and the centreline of the metal. In the more usual observation the position of the marker is determined relative to the oxide/ gas interface. It can be appreciated from Fig. 1.81 that when anions diffuse the marker remains on the surface, but when cations move the marker translates at a rate equivalent to the total amount of new oxide formed. Bruckman recently has re-emphasised the care that is necessary in the interpretation of marker movements in the oxidation of lower to higher oxides. 

Summary of experimental data Film boiling correlations have been quite successfully developed with ordinary liquids. Since the thermal properties of metal vapors are not markedly different from those of ordinary liquids, it can be expected that the accepted correlations are applicable to liquid metals with a possible change of proportionality constants. In addition, film boiling data for liquid metals generally show considerably higher heat transfer coefficients than is predicted by the available theoretical correlations for hc. Radiant heat contribution obviously contributes to some of the difference (Fig. 2.40). There is a third mode of heat transfer that does not exist with ordinary liquids, namely, heat transport by the combined process of chemical dimerization and mass diffusion (Eq. 2-162). 

Much less attention has been paid to the dynamic properties of water at the solution/metal interface (or other interfaces). Typical dynamic properties that are of interest include the diffusion constant of water molecules and several types of time correlation functions. In general, the time correlation function for a dynamic variable of interest A(t) is defined as... 

Argenlalion chromalography, 261 Aromatic acids in human urine, 285 Aromatic hydrocarbons, 69 Arylhydroxylamines, 298 Ascorbic acid, 296 Aspirin, 282 Asymmetric diens, 290 Asymmetrical peaks, 58, 82, 160 AIT, stability constants of metal complexes. 278 Atrazine, 292 Atropine, 297 Axial diffusion mobile phase. 8 stationary phase, 8,9 Aza-arenes, 293 Azoxybenzenes, 298... 

Platinum-based catalysts are widely used in low-temperature fuel cells, so that up to 40% of the elementary fuel cell cost may come from platinum, making fuel cells expensive. The most electroreactive fuel is, of course, hydrogen, as in an acidic medium. Nickel-based compounds were used as catalysts in order to replace platinum for the electrochemical oxidation of hydrogen [66, 67]. Raney Ni catalysts appeared among the most active non-noble metals for the anode reaction in gas diffusion electrodes. However, the catalytic activity and stability of Raney Ni alone as a base metal for this reaction are limited. Indeed, Kiros and Schwartz [67] carried out durability tests with Ni and Pt-Pd gas diffusion electrodes in 6 M KOH medium and showed increased stability for the Pt-Pd-based catalysts compared with Raney Ni at a constant load of 100 mA cm and at temperatures close to 60 °C. Moreover, higher activity and stability could be achieved by doping Ni-Al alloys with a few percent of transition metals, such as Ti, Cr, Fe and Mo [68-70]. 

The dilutions arc too groat to alter sensibly the diffusion constant of the medium, Friend suggeata that the extraneous material or addition agent is selectively adsorbed and thus protects the iron from attack. An alternative explanation is the formation of an insoluble compound on the metal surface such as obtains in many cases of passivity. 

The dielectric function of a metal can be decomposed into a free-electron term and an interband, or bound-electron term, as was done for silver in Fig. 9.12. This separation of terms is important in the mean free path limitation because only the free-electron term is modified. For metals such as gold and copper there is a large interband contribution near the Frohlich mode frequency, but for metals such as silver and aluminum the free-electron term dominates. A good discussion of the mean free path limitation has been given by Kreibig (1974), who applied his results to interpreting absorption by small silver particles. The basic idea is simple the damping constant in the Drude theory, which is the inverse of the collision time for conduction electrons, is increased because of additional collisions with the boundary of the particle. Under the assumption that the electrons are diffusely reflected at the boundary, y can be written... 

Macroscopic experiments allow determination of the capacitances, potentials, and binding constants by fitting titration data to a particular model of the surface complexation reaction [105,106,110-121] however, this approach does not allow direct microscopic determination of the inter-layer spacing or the dielectric constant in the inter-layer region. While discrimination between inner-sphere and outer-sphere sorption complexes may be presumed from macroscopic experiments [122,123], direct determination of the structure and nature of surface complexes and the structure of the diffuse layer is not possible by these methods alone [40,124]. Nor is it clear that ideas from the chemistry of isolated species in solution (e.g., outer-vs. inner-sphere complexes) are directly transferable to the surface layer or if additional short- to mid-range structural ordering is important. Instead, in situ (in the presence of bulk water) molecular-scale probes such as X-ray absorption fine structure spectroscopy (XAFS) and X-ray standing wave (XSW) methods are needed to provide this information (see Section 3.4). To date, however, there have been very few molecular-scale experimental studies of the EDL at the metal oxide-aqueous solution interface (see, e.g., [125,126]). 

Let us refer to Figure 5-7 and start with a homogeneous sample of a transition-metal oxide, the state of which is defined by T,P, and the oxygen partial pressure p0. At time t = 0, one (or more) of these intensive state variables is changed instantaneously. We assume that the subsequent equilibration process is controlled by the transport of point defects (cation vacancies and compensating electron holes) and not by chemical reactions at the surface. Thus, the new equilibrium state corresponding to the changed variables is immediately established at the surface, where it remains constant in time. We therefore have to solve a fixed boundary diffusion problem. 

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