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_

water

quartz

_@

real permittivity, K' 1 MHz 78.30 [1] 4.7 - 12.8 [1]

relative magnetic permeability, ýLr 0.999910 [3]

0.999985 [2]

conductivity, a [S/m] a=f(c) * 10-1- _10 3

[4]

pyrite (semiconductor) 1.0015 [2] 101 [1] iron (99.91% Fe) 5000 [2] 107 [1] * The conductivity of electrolytes is a function of the ionic concentration - see below. Permittivity The dielectric permittivity characterizes the polarizability of a material subjected to an electric field. The relative permittivity is a complex quantity: 137

Mat. Res. Soc. Symp. Proc. Vol. 500 © 1998 Materials Research Society

K*K =

(1)

jK"(f

The real relative part K' reflects the polarizability of the material and it is the number of dipole moments per unit volume. The effective imaginary permittivity K"eff reflects conduction and polarization losses: 1

K teff = K "polarization -I"

(2)

where a is the dc conductivity, Fo is the permittivity of free space (c. = 8.85. 10-12 F/m), and 0) is the angular frequency [rad/s].

The mechanisms that cause polarization depend on the frequency of the applied electric field and the composition of the material. Single-phase, homogeneous materials only experience high frequency polarization mechanisms including electronic, ionic, and molecular polarization [5]. Electronic and ionic polarization manifest as resonance at ultraviolet and infrared frequencies, respectively. Multi-phase, heterogeneous mixtures experience polarization mechanisms at both high and low frequencies. Low frequency polarization mechanism include: Maxwell-Wagner interphasial-spatial polarization, bound water polarization, and double layer polarization [5, 6, 7, 8, 9]. Interfacial-spatial polarization occurs due to charge accumulation at the interface between two materials with different electrical properties; electrochemical effects may develop at the interface between the host medium and a metal inclusion. Bound water polarization is the relaxation of water molecules adsorbed onto the surface of a soil particle. Double layer polarization occurs when the double layer surrounding negatively charged clay particles is displaced due to the application of a low frequency electric field; charges within the double layer have non-uniform ionic mobility ("membrane polarization"). These polarizations manifest as relaxations. Multiple relaxations may occur within one material if more than one polarization mechanism is present. Conductivity - Resistivity In the context of this publication, conductivity is treated as a real parameter. The microlevel interpretation of conductivity involves the availability and mobility of ions. The conductivity ao of a mono-ionic electrolyte is: Go = c z vi°" E F=c z uF

(3)

[S/m]

where vion is the velocity of the ion [m/s], E is the strength of the electric field [V/m], c is 3 concentration [molmm ], u = Iv I/ IE I is ionic mobility [m2/V.s], F is Faraday's constant [96484.6 C/mol], and z is the valence of the ion [10]. Conduction in geomaterials is largely electrolytic, taking place within connected pore spaces [4].