Estimation of permittivity of a compact crystal by dielectric measurements on its powder: A stochastic mixture model for the powder-dielectric

Abstract

A stochastic mixture model is proposed for the dielectric formed by the powder of an isotropic polycrystalline material included in an embedding medium of air or a non-polar substance. The relevant expression of the complex dielectric constant of the mixture is obtained in terms of the dielectric parameters of the mixture constituents and the volume fraction of the crystalline material. Hence the possibility of deducing the dynamic state dielectric characteristics of the solid (compact) crystal from the measured data on the powder is indicated. Theoretical results obtained for 1-cyanoadamantane using the present model over a wide spectral range (1 kHz to 1 GHz) are compared with corresponding experimental data available elsewhere. Results due to the present method agree more closely with the measured values for both low and high volume fractions, when compared with the results based on other existing models due to Bottcher and Looyenga.

Geometrical Description in Binary Composites and Spectral Density Representation

“…[3,54,55,56,57,58,59,60,61,62,63,64,65,66,67] for examples). $\begin{array}{c}trueright{\left[{\epsilon }_{\mathrm{sans-serife}}^{\mathrm{LLL}}(\omega ;{\epsilon }_{\mathrm{sans-serifm}},{\epsilon }_{\mathrm{sans-serifi}},q)\right]}^{1/3}=(1-q){\epsilon }_{\mathrm{sans-serifm}}^{1/3}+q{\epsilon }_{\mathrm{sans-serifi}}^{1/3}\end{array}$ This expression is used extensively in the literature for powdered materials and optical properties of material mixtures [3,56].…”

“…Landau and Lifshitz [ 52 ] and Looyenga [ 53 ] independently, using different approaches, developed an expression for dielectric mixtures, that implies the additivity of cube roots of the permittivities of mixture constituents when taken in proportion to their volume fractions (see Refs. [ 3 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 ] for examples). This expression is used extensively in the literature for powdered materials and optical properties of material mixtures [ 3 , 56 ].…”

“…The LLL expression was extensively used to describe the dielectric properties of dispersive systems composed of powders or exhibiting porous structure [ 3 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 ]. It was even shown [ 55 ] that the LLL formula was more reliable when mixtures contained strongly dissipative particles and was compared to others like Maxwell Garnett (MG) [ 68 , 69 ], Bruggeman [ 70 ], etc.…”

Properties of Ferroelectric Nanodots Embedded in a Polarizable Medium: Atomistic Simulations

“…Interestingly, the possibility for the dipoles to form a vortex structure has been omitted in the previous studies (see, e.g., Refs. 6,7,8 that used an effective medium approximation) aimed in determining the properties of ferroelectric or paraelectric nanoparticles that are embedded in a polarizable medium. As a result, original features may have been overlooked in these composite systems.…”

Temperature Effects on Threshold Counterion Concentration to Induce Aggregation of fd Virus

“…In Fig.1(b), C c is measured under different ethanol concentrations at T = 20 • C. Adding ethanol to a solution effectively changes its dielectric constant. ε for a mixture of ethanol and water is determined by ε(T ) = (1 − c e )ε w (T ) + c e ε e (T ) [23], where ε w (T ) and ε e (T ) are dielectric constants of water and ethanol at temperature T respectively, and c e is the volume fraction of ethanol in the solution. At 20 • C, ε w = 80.37 and ε e = 25.00.…”