Robert W. Schwartz

A Maxwell Garnett Model for Dielectric Mixtures Containing Conducting Particles at Optical Frequencies

Mathematical modeling of composites made of a dielectric base and randomly oriented metal inclusions is considered. Different sources of frequency-dependent metal conductivity at optical frequen- cies are taken into account. These include the skin-effect, dimensional (length-size) resonance of metal particles, and the Drude model. Also, the mean free path of electrons in metals can be smaller than the char- acteristic sizes of nanoparticles, and this leads to the decrease in con- ductivity of the metal inclusions. These effects are incorporated in the Maxwell Garnett mixing formulation, and give degrees of freedom for forming desirable optical frequency characteristics of composite media containing conducting particles.

Prediction of Effective Permittivity of Diphasic Dielectrics Using an Equivalent Capacitance Model

An analytical model based on an equivalent capacitance circuit for expressing a static effective permittivity of a composite dielectric with complex-shaped inclusions is presented. The dielectric constant of 0–3 composites is investigated using this model. The geometry of the capacitor containing a composite dielectric is discretized into partial parallel-plate capacitor elements, and the effective permittivity of the composite is obtained from the equivalent capacitance of the structure. First, an individual cell diphasic dielectric (a high-permittivity spherical inclusion enclosed in a lower permittivity parallelepiped) is considered. The capacitance of this cell is modeled as a function of an inclusion radius/volume fraction. The proposed approach is extended over a periodic three-dimensional structure comprised of multiple individual cells. The results of modeling are compared with results obtained using different effective medium theories, including Maxwell Garnett, logarithmic, Bruggeman, series, an...

MODELING OF DIELECTRIC MIXTURES CONTAINING CONDUCTING INCLUSIONS WITH STATISTICALLY DISTRIBUTED ASPECT RATIO

An analytical model of composites made of a dielectric base and randomly oriented metal inclusions in the form of nanorods is presented. This model is based on the generalized Maxwell Garnett (MG) mixing rule. In this model, the nanorod particles are modeled as prolate spheroids with a statistically normal distribution of their aspect ratios. It is shown that parameters of the distribution laws affect the frequency characteristics of the composites both at microwave and optical frequencies. The results of computations are represented.

Growth and optical properties of SrBi2Nb2O9 ferroelectric thin films using pulsed laser deposition

High quality SrBi2Nb2O9 ferroelectric thin films were fabricated on platinized silicon using pulsed laser deposition assisted with dc glow discharge plasma. Microstructure and ferroelectric properties of the films were characterized. Optical properties of the thin films were studied by spectroscopic ellipsometry and photoluminescence from the ultraviolet to the infrared region. Optical constants, n∼0.56 in the infrared region and n∼2.24 in the visible spectral region, were determined through multilayer analyses on their respective pseudodielectric functions. The band-gap energy is estimated to be 3.60 eV. A photoluminescence peak at 0.78 μm, whose intensity decreases with decreasing temperature, was observed when excited with subband-gap energy (2.41 eV). This emission process may involve intermediate defect states at the crystallite boundaries. A possible mechanism for the observed photoluminescence, a Nb4+–O− exciton in the NbO6 octahedron, is discussed.

DOUBLE STATISTICAL DISTRIBUTION OF CONDUCTIVITY AND ASPECT RATIO OF INCLUSIONS IN DIELECTRIC MIXTURES AT MICROWAVE FREQUENCIES

An analytical model of a composite dielectric presented in this paper is the extension of Maxwell Garnett formulation. It takes into account the simultaneous statistical (Gaussian) distribution of conductivity and aspect ratio of inclusions. The inclusions are randomly oriented elongated conducting spheroids at concentrations below the percolation threshold. The formulation presented herein is limited to microwave frequencies. However, taking subtle frequency- dependent effects that play important part at optical frequencies into account is straightforward. Some results of computations of microwave complex effective permittivity of composites with different input parameters have been obtained using analytical and numerical integration in Maple 10 software. It is shown how the parameters of the distribution laws — mean values and standard deviations of aspect ratio and conductivity — affect the resultant complex effective permittivity. The results of computations demonstrate that the most important factors affecting frequency characteristics of microwave effective permittivity are the mean values of the aspect ratio and conductivity. As for the standard deviations of aspect ratio and conductivity, their effects are the most noticeable in the transition between the static and optical limits of the Debye characteristic for the effective permittivity. There is almost no effect in the static and optic regions of the Debye curves.

Maxwell Garnett Rule for Dielectric Mixtures with Statistically Distributed Orientations of Inclusions

An analytical model of an efiective permittivity of a composite taking into account statistically distributed orientations of inclusions in the form of prolate spheroids will be presented. In particular, this paper considers the normal Gaussian distribution for either zenith angle, or azimuth angle, or for both angles describing the orientation of inclusions. The model is an extension of the Maxwell Garnett (MG) mixing rule for multiphase mixtures. The resulting complex permittivity is a tensor in the general case. The formulation presented shows that the parameters of the distribution law for orientation of inclusions afiect the frequency characteristics of the composites, and that it is possible to engineer the desirable frequency characteristics, if the distribution law is controlled.

Prediction of Effective Permittivity of Diphasic Dielectrics as a Function of Frequency

An analytical model based on an equivalent impedance circuit for effective permittivity of a composite dielectric as a function of frequency with complex-shaped inclusions is presented. The geometry of the capacitor containing this composite dielectric is discretized into partial impedance elements, the total equivalent impedance is calculated, and the effective permittivity of the composite dielectric is obtained from this equivalent impedance. An example application using this method is given for an individual cell of a diphasic dielectric consisting of a high-permittivity spherical inclusion enclosed in a low-permittivity parallelepiped. The capacitance and resistance for individual discretized elements in the composite cell are modeled as a function of an inclusion radius. The proposed approach is then extended to a periodic three-dimensional structure comprised of multiple individual cells. The equivalent impedance model is valid for both static and alternating applied electric fields, over the entire range of volume fraction of inclusions. The equivalent impedance model has a few advantages over existing effective medium theories, including no limitations on the shape of inclusions or their separation distance.

Thermal properties of La0.5Sr0.5Co1−xNixO3−δ ceramics using photopyroelectric technique

La0.5Sr0.5Co1−xNixO3−δu200a(0⩽x⩽0.6) ceramics were prepared using a conventional solid-state ceramic route. The thermal properties—thermal conductivity and heat capacity—of these ceramics were measured by the photopyroelectric technique. The thermal conductivity was found to increase with increasing Ni content. These materials were also found to exhibit a metallic-type variation of thermal conductivity with temperature, and no metal-insulator (M-I) transition was found to occur in any of the samples prepared by this route. However, a M-I transition was found to occur in La0.5Sr0.5CoO3−δ samples prepared by hot pressing. The difference is attributed to variations in oxygen content in the samples.

Modeling of Field Distribution and Energy Storage in Diphasic Dielectrics

Modeling of electrostatic field distribution and energy storage in diphasic dielectrics containing high-permittivity BaTiO3 in a glass host has been carried out using analytical modeling based on the Maxwell Garnett (MG) mixing rule, and numerical simulations accomplished using boundary element method (BEM) method software. The field distribution was studied as a function of the dielectric contrasts and volume fractions of the phases. For the geometry with a high-permittivity sphere enclosed in a low-permittivity glass cube it was found that a dielectric contrast of 75 and volume fraction of 46.8% led to higher energy storage densities than other geometries. For composites with lower volume fractions of high-permittivity inclusions, field enhancement factors of 2.6 were observed, whereas for higher volume fraction composites, field enhancements of 10 were noted. Higher field enhancement factors are expected to lead to dielectric breakdown at lower applied fields, limiting energy density. The upper limit of applicability of the MG formulation in terms of the inclusion volume fraction was also established and is a function of dielectric contrast. The host material permittivity causes a substantial variation in the applicability limit of the MG mixing rule, while the permittivity of inclusion phase does not affect the limit.

HP007 modeling permittivity and conductivity contrast on electric energy storage properties of dielectric composites

The electric field distribution, field and power density enhancement factors, power loss and stored electric energy in dielectric composites were calculated using the boundary-element method (BEM). The composites consist of a low permittivity host containing either spherical conducting inclusions having dielectric coating shells, or dielectrically or conductively graded spherical dielectric particles. It is shown that the local electric field and power density enhancement effects diminish as the thickness of shells, the number of grading layers or the degree of nonlinearity of grading increases. The reduced enhancement effects significantly increase the normalized stored electric energy due to the fact that with a reduced enhancement factor a higher voltage can be applied. Frequency effects for composites with conductivity-graded particles were also considered. The results of these studies have implications for the design of high energy density dielectric composites.