Activity coefficients degenerate

According to equation (12.17), the fluxes of electrons and holes are driven by concentration and potential gradients. This distinction is a result of the separation of the chemical and electrical contributions given in equation (12.15). If desired, degenerate semiconductor conditions can be modeled by calculating the value of the activity coefficients f for electrons and holes as described by Hwang and Brews and Bor ham and Orazem. The flux expression for species i is constrained by the equation of continuity, i.e.. 

Experimental results have been used to obtain averaged activity coefficients.60 Another approach toward characterization of degenerate semiconductors has been to include the nonidealities associated with degeneracy within a modified Nernst-Einstein relationship.61"64 The modified Nernst-Einstein relationship is given by65... 

Other names used for the medium effect are solvent activity coefficient (Chapter 6), degenerate activity coefficient and distribution coefficient. 

If > D > (for AgaS at 500 K, is of the order of 10 ), then = ju° + Tln N. h kT where the logarithm of the activity coefficient y > can be immediately taken from Fig. 4-6. In this case, the electron gas is said to be partially degenerate. The activity coefficient describes the degeneracy. Deviations from ideality (y / = 1) do not arise, as in the case of ionic defects, because of electrical or elastic interactions, but rather they are a result of a maximum permissible occupancy of the existing energy terms. 

F. W. G. Rose, On the mass action laws in degenerate semiconductors, Proc. Phys. Soc. London 71, 699-701 (1958) A. J. Rosenberg, Activity coefficients of electrons and holes at high concentrations, J. Chem. Phys. 33, 665-667 (1960). 

The symmetry argument actually goes beyond the above deterniination of the symmetries of Jahn-Teller active modes, the coefficients of the matrix element expansions in different coordinates are also symmetry determined. Consider, for simplicity, an electronic state of symmetiy in an even-electron molecule with a single threefold axis of symmetry, and choose a representation in which two complex electronic components, e ) = 1/v ( ca) i cb)), and two degenerate complex nuclear coordinate combinations Q = re " each have character T under the C3 operation, where x — The bras e have character x. Since the Hamiltonian operator is totally symmetric, the diagonal matrix elements e H e ) are totally symmetric, while the characters of the off-diagonal elements ezf H e ) are x. Since x = 1, it follows that an expansion of the complex Hamiltonian matrix to quadratic terms in Q. takes the form... 

Predicting activation barriers and rate coefficients of isomerization reactions For the degenerate rearrangements of arenium ions realized by the 1,2-shift of the CHj group, according to ... 

---