Complex Dielectric Constant Question

[MioTheGreat]

Hello,

I'm trying to follow along in my Solid State Physics book, but I'm getting hung up on an equation for the complex dielectric constant.

$$\widetilde{\epsilon_r}=\epsilon_L+j\widetilde{\sigma}/\omega$$

Multiply through by the definition of the complex conductivity, so that we get something in the form of $$\epsilon_r=\epsilon'_r+j\epsilon''_r$$

where

$$\epsilon'_r$$ is $$\epsilon_L/\epsilon_0 + \sigma_0\tau/\epsilon_0(1+\omega^2\tau^2)$$

What, exactly, is $$\epsilon_L$$? Is it just the old value of the dielectric constant before we introduce this complex stuff (So, a function of $$\omega$$)? The book doesn't really elaborate.

 

[olgranpappy]

yep. it is just convenient to put everything into a "complex" dielectric function. A really good book on dielectrics that I would recommend is called (I think) "Theory of dielectrics" by Frolich. One does not need to introduce a complex dielectric function if one does not want to... as usual it is just convenient... the fact that there are "two" dielectric functions (i.e., two components $\epsilon^'$ and $$\epsilon^{''}$$) is because the response of the system can be out of phase... An external (real) electric field with time dep cos(wt) induces response like Acos(wt)+Bsin(wt) and the coefficient of the sin term is just like the imaginary part of the dielectric function. cheers.

 

[zhanghe]

what does the subscript "L" mean, anyway?

 

[MioTheGreat]

what does the subscript "L" mean, anyway?

From what I understand, it means the effect from only the positively charged cores (Hence, L for Lattice).