Diffusion chemical potential form

Another problem in the construction of tlrese devices, is that materials which do not play a direct part in the operation of the microchip must be introduced to ensure electrical contact between the elecuonic components, and to reduce the possibility of chemical interactions between the device components. The introduction of such materials usually requires an annealing phase in the construction of die device at a temperature as high as 600 K. As a result it is also most probable, especially in the case of the aluminium-silicon interface, that thin films of oxide exist between the various deposited films. Such a layer will act as a banier to inter-diffusion between the layers, and the transport of atoms from one layer to the next will be less than would be indicated by the chemical potential driving force. At pinholes in the AI2O3 layer, aluminium metal can reduce SiOa at isolated spots, and form the pits into the silicon which were observed in early devices. The introduction of a tlrin layer of platinum silicide between the silicon and aluminium layers reduces the pit formation. However, aluminium has a strong affinity for platinum, and so a layer of clrromium is placed between the silicide and aluminium to reduce the invasive interaction of aluminium. 

These facts would suggest that die electrolysis of molten alkali metal salts could lead to the inuoduction of mobile elecU ons which can diffuse rapidly through a melt, and any chemical reduction process resulting from a high chemical potential of the alkali metal could occur in the body of the melt, rather than being conhned to the cathode volume. This probably explains the failure of attempts to produce tire refractoty elements, such as titanium, by elecU olysis of a molten sodium chloride-titanium chloride melt, in which a metal dust is formed in the bulk of the elecU olyte. 

Several authors " have suggested that in some systems voids, far from acting as diffusion barriers, may actually assist transport by permitting a dissociation-recombination mechanism. The presence of elements which could give rise to carrier molecules, e.g. carbon or hydrogen , and thus to the behaviour illustrated in Fig. 1.87, would particularly favour this mechanism. The oxidant side of the pore functions as a sink for vacancies diffusing from the oxide/gas interface by a reaction which yields gas of sufficiently high chemical potential to oxidise the metal side of the pore. The vacancies created by this reaction then travel to the metal/oxide interface where they are accommodated by plastic flow, or they may form additional voids by the mechanisms already discussed. The reaction sequence at the various interfaces (Fig. 1.87b) for the oxidation of iron (prior to the formation of Fe Oj) would be... 

Diffusion is the movement of mass due to a spatial gradient in chemical potential and as a result of the random thermal motion of molecules. While the thermodynamic basis for diffusion is best apprehended in terms of chemical potential, the theories describing the rate of diffusion are based instead on a simpler and more experimentally accessible variable, concentration. The most fundamental of these theories of diffusion are Fick s laws. Fick s first law of diffusion states that in the presence of a concentration gradient, the observed rate of mass transfer is proportional to the spatial gradient in concentration. In one dimension (x), the mathematical form of Fick s first law is... 

If all values of y are decreased, then differences between the activities also decrease - it is these differences in activity that cause the diffusion in the first place. Accordingly, after addition of a swamping electrolyte, fewer ions diffuse and so the chemical potentials equalize, with a smaller junction potential being formed. 

Diffusion That form of mass transport in which motion occurs in response to a gradient in concentration or composition, itself caused by a gradient of the chemical potential fi. Diffusion is ultimately an entropy-driven process. 

Chemical reaction steps Even if the overall electrochemical reaction involves a molecular species (O2). it must first be converted to some electroactive intermediate form via one or more processes. Although these processes are ultimately driven by depletion or surplus of intermediates relative to equilibrium, the rate at which these processes occur is independent of the current except in the limit of steady state. We therefore label these processes as chemical processes in the sense that they are driven by chemical potential driving forces. In the case of Pt, these steps include dissociative adsorption of O2 onto the gas-exposed Pt surface and surface diffusion of the resulting adsorbates to the Pt/YSZ interface (where formal reduction occurs via electrochemical-kinetic processes occurring at a rate proportional to the current). 

It is interesting to frame these very tentative considerations in terms of rod diffusion, since this is the process by which the polymer-rich phase must be formed. However, care must be taken to isolate the effects of mutual diffusion of the collection of rods as a (phenomenological) response to a concentration (chemical potential) gradient and simple self diffusion of a single rod, which is the case treated by Doi and Edwards.(24)... 

Fluxes of chemical components may arise from several different types of driving forces. For example, a charged species tends to flow in response to an applied electrostatic field a solute atom induces a local volume dilation and tends to flow toward regions of lower hydrostatic compression. Chemical components tend to flow toward regions with lower chemical potential. The last case—flux in response to a chemical potential gradient—leads to Fick s first law, which is an empirical relation between the flux of a chemical species, J, and its concentration gradient, Vcj in the form J, = —DVcj, where the quantity D is termed the mass diffusivity. 

As discussed above, a thermodynamically unstable surface will reduce its total surface energy by forming facets. From the point of view of kinetics, gradients in the chemical potential on a nonequilibrium surface will drive the movement of surface materials toward equilibrium. The transport mechanisms are the same as those that can operate during sintering (47) (a) surface diffusion, (b) bulk diffusion, (c) evaporation-condensation, and (d) plastic or viscous flow. 

In contrast to the case for metals, positronium can be formed in the bulk of many insulators and molecular crystals, and any positronium which subsequently diffuses to the surface can be emitted into the vacuum with a kinetic energy < — Ps, where (f)Ps is the positronium work function. Its value can be expressed in terms of the binding energy of the positronium when in the solid, EB, and the positronium chemical potential, /xPs, as (Schultz and Lynn, 1988)... 

Multicomponent diffusion in the films is described by the Maxwell-Stefan equations, which can be derived from the kinetic theory of gases (89). The Maxwell-Stefan equations connect diffusion fluxes of the components with the gradients of their chemical potential. With some modification these equations take a generalized form in which they can be used for the description of real gases and liquids (57) ... 

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