Phenomenological Coefficients and Kinetic Theory

Atoms taking part in diffusive transport perform more or less random thermal motions superposed on a drift resulting from field forces (V//,-, Vrj VT, etc.). Since these forces are small on the atomic length scale, kinetic parameters established under equilibrium conditions (i.e., vanishing forces) can be used to describe the atomic drift and transport, The movements of atomic particles under equilibrium conditions are Brownian motions. We can measure them by mean square displacements of tagged atoms (often radioactive isotopes) which are chemically identical but different in mass. If this difference is relatively small, the kinetic behavior is 

In a zeroth order treatment, ), is often equated with D,. Closer inspection shows that this is often incorrect. If, for example, transport occurs by a vacancy (V) mechanism, / can jump only if V and / have an encounter. The jump pattern between V and / during the encounter, however, is by no means random. Therefore, let us set D, = f, D where f, is the so-called correlation factor. 

In order to investigate the relation between the phenomenological transport coefficients Ljj and Z) we formulate for the isotope (tracer) diffusion of A in A 

Since transport occurs solely by the exchange of A and A it follows that /a + Ja = 0. The isotope tracer solution is also ideal with /VA + /VA = 1, so Eqn. (5.52) yields 

Equation (5.56) relates the correlation factor fA with the cross coefficient LAA . From the Nernst-Einstein relation we know that LAA = bA-cA = DAcA/R T. For a tracer experiment with a negligible fraction of A, the jump conservation requires that Da = Dv-Nv, so that instead of Eqn. (5.56) we have 

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