In physics, we have:
σ = ω εo ε- tan δ
also, in dielectrics, the permittivity is complex number
ε = ε- - jε=
if I have the conductivity how can I calculate the dielectric constant
In fact, the conductivity is related to the dielectric permittivity as
σ=ω ε0 ε*(1-1/tgδ), i.e. the conductivity is included into the imaginary part of complex dielectric permittivity: ε*=ε0[ε'-i(ε"-σ/ω)].
Therefore, you can make the transition from conductivity to dielectric constant (ε') only at very low frequencies, when Debye dielectric loss ε" may be neglected, i.e. ε*=ε0(ε'-iσ/ω)
In this case, if you know tgδ at very low frequencies, roughly ε'=σ/(ωtgδ). Problem is that doing such a thing makes no sense because it will be low-frequency dielectric permittivity, which is about the static (at zero frequency) dielectric permittivity that you have to measure anyway to define the tgδ. Not to mention, ε(0) would give you a little at higher frequencies when you have to know ε(ω).
Thanks Michael, but my measurements within high frequency conditions
(50 MHz)
This article or references may be helpful.
https://www.researchgate.net/publication/255961160_Piezoelectric_impedance_electric_modulus_and_ac_conductivity_studies_on_Bi05Na05095Ba005TiO3_ceramic
Article Piezoelectric, impedance, electric modulus and AC conductivi...
Aseel,
probably the answer is much simpler - you're talking about the specific admittance (reverse specific impedance), Ys, which you can measure. For the dielectric, one may consider Ys* = iωCs* = iωε0(ε'-iε"), i.e. ε' corresponds to the imaginary part of Ys*, Im(Ys*) = ωε0ε' =ωε0|Ys|/(1+tgδ), where Cs* is the specific complex capacitance and |Ys*| is the magnitude of Ys*. Looks like you are confusing yourself with the conductance, σ, which you can measure only at zero frequency (DC).
Thanks Michael,
so as I understand from your answer, there is no relationship between electrical conductivity and dielectric constant?
Microscopically yes, Aseel, you understood this right.
Macroscopically the conductivity leads to the so-called interfacial (Maxwell-Wagner) polarization or so-called absorption polarization (space charge at electrodes) which affect the measurement, mostly the imaginary part of it.