Spatial equilibria in inhomogeneous systems

The formalism of chemical reactions can be taken even further and applied to transport within one and the same phase. Let us consider two different sites x and x in medium MX, which is considered to be isotropic. Equilibrium conditions of the form  

These intricacies are not, of course, important when the particles are neutral, but also not if processes between charged particles are considered within a region where 

Analogously it is necessary, in the general case, to take account of elastic fields, gravity fields 

Here InKxk measures the pure chemical effect (total effect if the species were uncharged), that is —(jUk(x ) —/ik(x))/R-T, while ln xx measures the electrical effect , — (c (x ) — 0(x))zF/RT. However, the two parameters are not independent of each other a detailed analysis must refer k to chemical constants and variables of state (cf. Section 5.8). In particular Eq. (4.74) shows that concentration differences now also appear within the same structure Afi° = 0), and that this is at the cost of an electrical field. Such contact problems are not exotic in nature, but rather the normal case when mobile, charged particles are involved  

On contact between two different semiconductors both interfaces become charged. Well-known consequences are, for example, the thermo-electric effect for semiconductors, p-n transitions, and many other major issues in electronics .  

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