Frequency dependent conductivity, microwave dielectric relaxation and proton dynamics

How are ions able to move in a solid The standard answer to this question states that two different kinds of ionic motions can be discerned, namely oscillatory motion and jump difiusion (see Chapter 30). In fact, the motion is not only limited to osdUations and to statistical hopping from site to site. Polyatomic ions (NH4.+, HjO ) may undergo more or less complex rotations and other non-periodic local, non-hopping translational and non-statistical hopping motions are also possible. Such phenomena can be studied experimentally by neutron scattering and dynamic conductivity spectra (see Chapters 21 30). 

The interaction between an electromagnetic wave and condensed matter can be expressed by the equation 

In the domain of optical frequencies, we could define the complex refractive index n ((w) from the complex permittivity by the relation 

Chemists often reason in terms of dielectric permittivity (e) or infrared spectra (a) while electrical engineers and physicists consider tangent loss (tg = e /s ) and alternative current conductivity ( r), respectively. It turns out that in most materials, free charges (where the complex impedance formalism is well-suited) and bound charges (where the description of the permittivity s = e (co) — ie (co) is more suitable) can be distinguished. Such a distinction is not straightforward in superionic conductors, however, in which some conducting species are in a quasi-liquid state and in particular, for proton conductors. In the latter, the proton (attached 

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Frequency dependent conductivity, microwave dielectric relaxation and proton dynamics... 

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