Conductivity of Ionic Crystals Frequency Dependence

Since j-c-v, the electrical current density autocorrelation function and the velocity autocorrelation function are proportional to each other. The latter function, however, can be expressed with the help of the time derivative of the decaying pro- 

Using linear response theory and noting (according to the results at the end of Section 5.1.3) that the (complex) electrical conductivity a is the Fourier transform of the current density autocorrelation function, we obtain from Eqn. (5.75) (see the equivalent Eqn. (5.21)) 

If one uses the abbreviation V0-ll = ( Ab(0)-F ba(0)) accordance with the harmonic (parabolic) potential approximation, then inserting Eqns. (5.79) — (5.81) into Eqn. (5.78) gives 

Equation (5.82) yields W(i) after integration. The electrical conductivity o(co) in Eqn. (5.76) can now be calculated if g(i), the relaxation function of the (Debye-Htickel) defect cloud, is known. In a first order approach let us assume that g(t) relaxes with a single relaxation time r, that is, g(t) = e, /T (r is roughly given by T= 0 (°° )/ct(°° )). Integration of Eqn. (5.82) then results in 

Let us summarize by modeling the velocity autocorrelation function using Debye-Huckel type interactions between charged point defects in ionic crystals, one can evaluate the frequency-dependent conductivity and give an interpretation of the universal dielectric response. 

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