Showing papers on "Relative permittivity published in 2012"

Tables of the complex permittivity of dielectric reference liquids at frequencies up to 5 GHz.

Abstract: This report summarises the results of a recent programme of dielectric reference liquid measurements at National Physical Laboratory (NPL). It is intended that full details of the methods of measurement will be published in the scientific literature in the near future. Comprehensive tables of dielectric relaxation parameters for high purity methanol, ethanol, propan-1-ol, propan-2-ol, butan-1-ol, dimethyl sulphoxide and ethanediol are presented over a range of temperatures (in most cases at 5o intervals in the range 10 - 50 oC). These were derived from measurements at NPL between the years 1997 and 2000 at frequencies extending up to 5 GHz. The relaxation parameters are generally those of the single or double Debye models, which are found to offer a good fit to the measured data in nearly all cases. In addition, static permittivity data are presented for pure water, acetone, silicone oil and cyclohexane. All of the data presented is traceable to UK National Standards. Advisory notes on the use of the tables are provided.

High-temperature dielectrics in CaZrO3-modified Bi1/2Na1/2TiO3-based lead-free ceramics

Abstract: Materials in two composition regimes, Bi1/2Na1/2TiO3–BaTiO3–CaZrO3 (BNT–BT–CZ) and Bi1/2Na1/2TiO3–BaTiO3–K0.5Na0.5NbO3–CaZrO3 (BNT–BT–KNN–CZ), were synthesized via the mixed oxide route and their structural, dielectric and electrical properties were investigated. CZ was identified to render the two local maxima in permittivity more diffused. This resulted in temperature-insensitive relative permittivity spectra with average values from ∼470 up to ∼2300 and operational windows of at least ∼400 °C with less than 15% of variation in the temperature range from −100 up to above 500 °C. Moreover, loss factors are below ∼10% and RC constants range from ∼0.03 s up to ∼4 s at 300 °C. The materials of current investigation are highly attractive for developing capacitors of wide temperature usage.

Co-sputtering yttrium into hafnium oxide thin films to produce ferroelectric properties

Abstract: Thin film capacitors were fabricated by sputtering TiN-Y doped HfO2-TiN stacks on silicon substrates. Yttrium was incorporated into the HfO2 layers by simultaneously sputtering from Y2O3 and HfO2 sources. Electric polarization and relative permittivity measurements yield distinct ferroelectric properties as a result of low yttrium dopant concentrations in the range of 0.9-1.9 mol. %. Grazing incidence x-ray diffraction measurements show the formation of an orthorhombic phase in this range. Compared to atomic layer deposition films, the highest remanent polarization and the highest relative permittivity were obtained at significantly lower doping concentrations in these sputtered films.

Higher Order Mode Excitation for High-Gain Broadside Radiation From Cylindrical Dielectric Resonator Antennas

Abstract: A resonant mode (HEM12δ), other than those ( HEM11δ and TM01δ) conventionally excited and used in a cylindrical dielectric resonator antenna (CDRA) has been examined with a view for using it as another radiating mode with broadside radiation patterns. Excitation of the mode, being the most challenging aspect, has been discussed and resolved by employing an innovative technique. The proposed concept has been successfully verified and experimentally demonstrated for the first time. More than 8-dBi peak gain with excellent broadside radiation has been obtained from a prototype shaped from a commercially available low-loss dielectric material with relative permittivity 10.

Simulations of high permittivity materials for 7 T neuroimaging and evaluation of a new barium titanate-based dielectric

Abstract: High permittivity "dielectric pads" have been shown to increase image quality at high magnetic fields in regions of low radiofrequency transmit efficiency. This article presents a series of electromagnetic simulations to determine the effects of pad size and geometry, relative permittivity value, as well as thickness on the transmit radiofrequency fields for neuroimaging at 7 T. For a 5-mm thick pad, there is virtually no effect on the transmit field for relative permittivity values lower than ∼90. Significant improvements are found for values between 90 and ∼180. If the relative permittivity is increased above ∼180 then areas of very low transmit efficiency are produced. For a 1-cm thick pad, the corresponding numbers are ∼60 and ∼120, respectively. Based upon the findings, a new material (barium titanate, relative permittivity ∼150) is used to produce thin (∼5 mm) dielectric pads which can easily be placed within a standard receive head array. Experimental measurements of transmit sensitivities, as well as acquisition of T(2) - and T 2*-weighted images show the promise of this approach. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.

Nanocomposites of ferroelectric polymers with surface-hydroxylated BaTiO3 nanoparticles for energy storage applications

Abstract: A facile surface hydroxylation treatment using hydrogen peroxide to modify the surface of BaTiO3 nanofillers dispersed in a ferroelectric copolymer host has been investigated. We demonstrate that the surface functionalization of the BaTiO3 nanofillers (<100 nm) with hydroxyl groups results in as much as two orders of magnitude reduction in the leakage current of nanocomposite thin-film capacitors. This reduction is observed concurrently with the enhancement of the effective permittivity and breakdown strength of the thin-film nanocomposites. Surface modified BaTiO3 particles display better dispersion within the polymer matrix, resulting in enhanced relative permittivity and reduced dielectric loss. The dielectric behavior of the nanocomposite films containing up to 30 vol.% BaTiO3 agreed well with the Bruggeman model. These results demonstrate the potential of facile surface hydroxylation of nanoparticles towards the fabrication of higher energy-density nanocomposites.

BaTiO3–Bi(Zn1/2Ti1/2)O3–BiScO3 Ceramics for High-Temperature Capacitor Applications

Abstract: Ceramics based on solid solutions of xBaTiO3–(100−x)(0.5Bi(Zn1/2Ti1/2)O3–0.5BiScO3), where x = 50, 55, and 60 were prepared by solid-state reaction which resulted in a single perovskite phase with pseudocubic symmetry. Dielectric property measurements revealed a high relative permittivity (>1000), which could be modified with the addition of Bi(Zn1/2Ti1/2)O3 (BZT) and BiScO3 (BS) to engineer a temperature-stable dielectric response with a temperature coefficient of permittivity (TCe) as low as −182 ppm/°C. By incorporating 2 mol% Ba vacancies into the stoichiometry, the resistivity increased significantly, especially at high temperatures (>200°C). Vogel–Fulcher analysis of the permittivity data showed that the materials exhibited freezing of polar nanoregions over the range of 100–150 K. An analysis of optical absorption near the band edge for the Ba-deficient compositions suggested that the enhanced resistivity values were linked to a decrease in the concentration of defect states. An activation energy of ~1.4 eV was obtained from DC resistivity measurements suggesting that an intrinsic conduction mechanism played a major role in the high temperature conductivity. Finally, multilayer capacitors based on these compositions were fabricated, which exhibited dielectric properties comparable to the bulk material. Based on these results, this family of materials has great promise for high-temperature capacitor applications.

A High-Temperature-Capacitor Dielectric Based on K0.5Na0.5NbO3-Modified Bi1/2Na1/2TiO3–Bi1/2K1/2TiO3

Abstract: A high-temperature dielectric, (1–x)(0.6Bi1/2Na1/2TiO3–0.4Bi1/2K1/2TiO3)–xK0.5Na0.5NbO3, off the morphotropic phase boundary of the parent matrix 0.8Bi1/2Na1/2TiO3–0.2Bi1/2K1/2TiO3, has been developed for application as a high-temperature capacitor. In addition to temperature-dependent permittivity and dielectric loss, DC conductivity and field-dependent permittivity are reported. These properties are correlated with temperature-dependent structure data measured at different length scales using Raman spectroscopy and neutron diffraction. It is suggested that all materials investigated are ergodic relaxors with two types of polar nanoregions providing different relaxation mechanisms. The most attractive properties for application as high-temperature dielectrics are obtained in a material with x = 0.15 at less than 10% variation of relative permittivity of about 2100 between 54°C and 400°C.

High Energy Density, High Temperature Capacitors Utilizing Mn-Doped 0.8CaTiO3–0.2CaHfO3 Ceramics

Abstract: Single layer air co-fired capacitors with Pt internal electrodes were prototyped for the compositions 0.8CaTiO3–0.2CaHfO3 (CHT) and 0.5 mol% Mn-doped 0.8CaTiO3–0.2CaHfO3 (CHT + Mn) to yield a material with a room-temperature relative permittivity of er ~170, thermal coefficient of capacitance (TCC) of ±15.8% to ±16.4% from −50°C to 150°C, and a band gap of ~4.0 eV. Impedance spectroscopy revealed that doping with Mn reduces both the ionic and electronic conductivity. Undoped CHT single layer capacitors exhibited ambient energy densities as large as 9.0 J/cm3, but showed a drastic decrease in energy density above 100°C. When doped with 0.5 mol% Mn, the temperature dependence of the breakdown strength was minimized, and energy densities similar to ambient values (9.5 J/cm3) were observed up to 200°C. At 300°C, energy densities as large as 6.5 J/cm3 were measured. The design rationale for these dielectrics centered on materials with large band gaps, linear or weakly nonlinear permittivities, and high breakdown strengths. These observations suggest that with further reductions in grain size and dielectric layer thickness, the CaTiO3–CaHfO3 system is a strong candidate for integration into future power electronics applications.

Rectification of evanescent heat transfer between dielectric-coated and uncoated silicon carbide plates

Abstract: Here, we show analytically that the thermal rectification via evanescent waves is obtained in the parallel semi-infinite bodies of the dielectric-coated silicon carbide and uncoated silicon carbide. The permittivity and the thickness of the dielectric coating are derived for maximizing the thermal rectification. In the nonequilibrium situation holding temperatures of 500 K for one body and 300 K for the other, either a coating with a high permittivity of 14 and a thickness of 1 nm or a coating with a low permittivity of 2 and a thickness exceeding 10 nm, results in rectifying coefficients of 0.4 to 0.44.

Fabrication and characterization of aluminum nitride polymer matrix composites with high thermal conductivity and low dielectric constant for electronic packaging

Abstract: Polymethyl methacrylate (PMMA) composites filled with Aluminum Nitride (AlN) were prepared by powder processing technique. The microstructures of the composites were investigated by scanning electron microscopy techniques. The effect of AlN filler content (0.1–0.7 volume fraction (vf)) on the thermal conductivity, relative permittivity, and dielectric loss were investigated. As the vf of AlN filler increased, the thermal conductivity of the specimens increased. The thermal conductivity and relative permittivity of AlN/PMMA composites with 0.7 vf AlN filler were improved to 1.87 W/(m K) and 4.4 (at 1 MHz), respectively. The experimental thermal conductivity and relative permittivity were compared with that from simulation model.

ZnLi2/3Ti4/3O4: A new low loss spinel microwave dielectric ceramic

Abstract: A new low loss spinel microwave dielectric ceramic with composition of ZnLi2/3Ti4/3O4 was synthesized by the conventional solid-state ceramic route. The ceramic can be well densified after sintering above 1075 °C for 2 h in air. X-ray diffraction data show that ZnLi2/3Ti4/3O4 ceramic has a cubic structure [Fd-3m (227)] similar to MgFe2O4 with lattice parameters of a = 8.40172 A, V = 593.07 A3, Z = 8 and ρ = 4.43 g/cm3. The best microwave dielectric properties can be obtained in ceramic with relative permittivity of 20.6, Q × f value of 106,700 GHz and τf value of −48 ppm/°C. The addition of BaCu(B2O5) (BCB) can effectively lower the sintering temperature from 1075 °C to 900 °C and does not induce much degradation of the microwave dielectric properties. Compatibility with Ag electrode indicates that the BCB added ZnLi2/3Ti4/3O4 ceramics are good candidates for LTCC applications.

Anomalous behaviour of the dielectric spectroscopy response of nanocomposites

Abstract: A study on the dielectric spectroscopy of epoxy-based nanocomposites filled with different types of particles, such as Al2O3, AlN, MgO, SiO2 and BN, is presented. The surface of the nanoparticles was modified with a silane coupling agent, in order to make them compatible with the organic host and create a system with homogeneously dispersed filler material. Morphological characterizations of individual particles and fabricated composites were performed by means of transmission and scanning electron microscopy. The present research addresses an analysis of the complex permittivity. The relative permittivity of nanocomposites shows an unusual behaviour. Introduction of a low percentage of high permittivity filler results in a decrease of the permittivity of the bulk polymer material. We propose a qualitative explanation for the reduction of the relative permittivity, compared to the reference samples. The interface layer of surface modified particles plays a more important role than the nature of the particles themselves. The immobilization caused by the surface treatment of the nanoparticles seems to be the main factor determining the relative permittivity of the composites with fillgrade below 5 wt.%. The imaginary part of the complex permittivity, which represents the dielectric losses in the system, does not change significantly with addition of nanofiller up to 5 wt.%.

Dielectric Relaxation in BaTiO3–Bi(Zn1/2Ti1/2)O3 Ceramics

Abstract: A dramatic improvement in the dielectric and electrical properties has been observed in ceramics of 0.8BaTiO3–0.2Bi(Zn1/2Ti1/2)O3 through the introduction of Ba vacancies. It possesses a high relative permittivity (er > 1150) along with a low dielectric loss (tan δ 255°C), a complex plane analysis of Z″ versus Z′ and the frequency dependence of Z″ suggests an electrically inhomogeneous microstructure for the stoichiometric composition. The stoichiometric composition exhibited activation energies of ~1 eV which suggests an extrinsic conduction mechanism. However, the introduction of Ba vacancies resulted in electrically homogeneous microstructure. An overlap of the Z″ and M″ peaks in the frequency domain and much larger activation energies were observed, on the order of half of the band gap, suggesting an intrinsic conduction mechanism. A more detailed analysis of the data reveals insights into the physical mechanisms underpinning the dielectric and ac conductivity.

An electrically tunable-focusing liquid crystal lens with a low voltage and simple electrodes

Abstract: An electrically tunable focusing LC lens with a low voltage and simple planar electrodes is demonstrated. The inhomogeneous electric field of the LC lens without any hole-patterned-electrode is generated by using an embedded polymeric layer with a gradient distribution of dielectric constants (or relative permittivity). LC directors in the LC layer experience spatially inhomogeneous voltages even though a single voltage is applied to the planar electrodes. Such a LC lens has a low voltage (~2.6 Vrms) and simple design of electrodes. The gradient distribution of dielectric constants of polymeric layer is discussed and the performance of the LC lens is investigated. The applications of such a LC lens are cell phones, webcam, and pico projectors.

Low dielectric permittivity and high thermal conductivity silicone rubber composites with micro-nano-sized particles

Abstract: Compared with the inorganic particles/silicone rubber (IOP/SR) composites filled with single-sized particle solely, the IOP/SR composites cofilled with micro-sized Si3N4 and nano-sized Al2O3 particles show a low relative dielectric permittivity (5.25) and high thermal conductivity (1.62 W m−1K−1), which are a bit higher than the permittivity (4.1) and remarkably larger than the thermal conductivity (0.16 W m−1K−1) of pure SR. Agari model gives a better prediction for these results. The images indicate that the nano-sized Al2O3 particles are closely filled into the gaps between the micro-sized Si3N4 particles and play a role as a bridge-link action to form a continuous thermally conductive network. This also confirms that the loading of the micro-sized Si3N4 particles in the SR composites prepared by the cofilled model contributes a positive thermal conduction and induces the low dielectric permittivity of the IOP/SR composites.

Enhanced high thermal conductivity and low permittivity of polyimide based composites by core-shell Ag@SiO2 nanoparticle fillers

Abstract: A kind of polymer based composites was prepared by embedding the fillers of core-shell Ag@SiO2 nanoparticles into the polyimide (PI) matrix. The obtained Ag@SiO2/PI (50% vf of fillers) composites show remarkably improved high thermal conductivity and low relative permittivity. The maximum value of the thermal conductivity of composites is 7.88 W/(mK) and the relative permittivity and dielectric loss are about 11.7 and 0.015 at 1 MHz, respectively. Compared with self-passivated nanometer Al* particles composites, core-shell Ag@SiO2 nano-composite is beneficial to increase the thermal conductivity and reduce the permittivity of the composites. The relative mechanism was studied and discussed.

Towards Experimental Perfectly-Matched Layers With Ultra-Thin Metamaterial Surfaces

Abstract: In this paper, we modify uniaxial perfectly matched layer to an entirely passive medium and demonstrate its experimental realization using a deep sub-wavelength metamaterial surface. The relative permittivity and permeability of the surface are matched, mostly imaginary-valued, and far greater than unity. These conditions allow the impedance of the metamaterial surface to be completely matched to air, and produce an extremely large internal dissipation, resulting in a 99.97% power absorption at normal incidence and within a layer thickness of about 1/40 of the free space wavelength.

Analytical estimation of the thrust generated by a surface dielectric barrier discharge

Abstract: The thrust induced by a set of microdischarges forming a surface dielectric barrier discharge (SDBD) at sinusoidal alternating voltage is estimated analytically by a phenomenological model based on available experimental data and achieved understanding of SDBD physics. Qualitative coincidence between theoretical predictions and experimental observations for thrust dependence on voltage at different dielectric thicknesses and its relative permittivity is demonstrated by the developed phenomenological model. The volumetric force is primarily induced by the negative voltage half-cycle. The origin of the force is the accumulation of volumetric negative charge carried by negative long-lived and ions. This accumulation is proportional to the third power of discharge length giving a strong force dependence on applied voltage. The directions of further SDBD investigation and actuator performance improvement are discussed.

A Study on the Effective Permittivity of Carbon/PI Honeycomb Composites for Radar Absorbing Design

Abstract: Radar absorbing honeycomb composites with different coating thicknesses are prepared by impregnation of aramid paper frame with solutions containing conductive carbon blacks (non-magnetic) and PI (polyimide). Expressions for the effective permittivity of the composites are studied and validated both in theory and experiment. It is found that a theoretical equivalent panel with given permittivity can be obtained to represent the honeycomb structure in the quasistatic approximation, which provides a feasible way to optimize the design of radar absorbing honeycomb structure by connecting the effective electromagnetic parameters with the unit cell dimensions. The effective permittivity is measured by a network analyzer system in the frequency range of 8-12 GHz and compared with the theoretical result.

Dielectric characterization of materials using a modified microstrip ring resonator technique

Abstract: The goal of this study is to present a simple model based on the ring-resonator technique to measure nondestructively the permittivity and loss tangent of dielectric materials. The proposed measurement model utilizes a modified ring-resonator technique in one-layer and two-layer microstrip configurations. This method eliminates the requirement to metalize the samples and enables characterization of permittivity and dielectric loss from 2 to 40 GHz. The effects of conductor and radiation losses that may introduce significant errors in the calculation of the loss tangent, especially at very high frequencies, are minimized. The measurement precision is evaluated by comparing the results with those obtained by using two well-known standard techniques. Uncertainties associated with the proposed model are addressed.

Compact, low power radio frequency cavity for femtosecond electron microscopy.

Abstract: Reported here is the design, construction, and characterization of a small, power efficient, tunable dielectric filled cavity for the creation of femtosecond electron bunches in an existing electron microscope without the mandatory use of femtosecond lasers. A 3 GHz pillbox cavity operating in the TM110 mode was specially designed for chopping the beam of a 30 keV scanning electron microscope. The dielectric material used is ZrTiO4, chosen for the high relative permittivity (ɛr = 37 at 10 GHz) and low loss tangent (tan δ = 2 × 10−4). This allows the cavity radius to be reduced by a factor of six, while the power consumption is reduced by an order of magnitude compared to a vacuum pillbox cavity. These features make this cavity ideal as a module for existing electron microscopes, and an alternative to femtosecond laser systems integrated with electron microscopes.

High‐Frequency Negative Permittivity from Fe/Al2O3 Composites with High Metal Contents

Abstract: For conventional metal/ceramic composites, we report an interesting negative permittivity behavior, which was usually observed in artificial metamaterials. The Fe/Al2O3 composites with different Fe volume contents ranging from 10% to 40% were prepared through hot-pressing sintering. The impedance and dielectric properties of the composites in high frequency range present a distinct dependence on the composition, and the negative permittivity is obtained when Fe content exceeds 20 vol%. The experimental results of negative permittivity from the composites above percolation threshold are in good agreement with fitting results from Drude model. The tunability of negative permittivity makes Fe/Al2O3 composites promising candidates for the double negative materials.

Advanced dielectric properties of BaTiO 3 /polyvinylidene-fluoride nanocomposites with sandwich multi-layer structure

Abstract: To endow excellent dielectric properties for embedded capacitors application, high-permittivity BaTiO3/polyvinylidene fluoride (BT/PVDF) nanocomposites with sandwich multi-layer structure were fabricated via a spin-coated and hot-molding technique. Dependences of dielectric properties of the BT/PVDF multi-layer nanocomposites on frequency and temperature were studied. Results show that concentration and dispersion of BT particles in multi-layer structure nanocomposites had an obvious influence on the final dielectric permittivity. Influence of the compatibility between adjacent layers on dielectric permittivity was also discussed. We use the effective-medium theory and capacitance series model to predict the theoretical values of the dielectric permittivity of the nanocomposites.

Thermal and Electrical Properties of Nanocomposites, Including Material Properties

Abstract: The research described in this thesis is part of a state-funded IOP-EMVT project in cooperation with industrial companies, aiming at the design, assessment and implementation of new, environmental friendly (e.g. oil and SF6 - free) solid dielectric materials. A large disadvantage of solid polymer dielectrics is their relatively low thermal conductivity. Therefore, the focus in this thesis is on if and how nanotechnology can improve the thermal conductivity without deteriorating existing electrical properties. Epoxy resin, which is very common polymer material in the electrical and power industry, has been used as a host to create new insulating materials: nanocomposites. In order to improve the thermal conductivity of epoxy resin, thermally conducting but electrically insulating nanofillers, such as aluminum and magnesium oxides (Al2O3 and MgO), silicon dioxide (SiO2), boron and aluminum nitrides (BN and AlN) were used to dope the polymer matrix. Good compatibility and adhesion was achieved by surface modification of the nanoparticles, using a silane coupling agent. Proper dispersion of nanoparticles is a vital factor for the final properties of nanocomposites. Good and stable dispersion of nanoparticles in polymer matrices have been achieved by mechanical mixing and ultrasonic vibration. The quality of the dispersion of nanoparticles was satisfactory for most of the nanocomposite samples. The fabricated composites were classified into three types, according to the average particle size and the extent of agglomerates observed inside the polymer matrix. Dielectric spectroscopy revealed that the relative permittivity of many nanocomposites is lower than that of the pure epoxy. This surprises, since the relative permittivity of the bulk materials of the fillers used is higher than that of the epoxy. The anomalous dielectric behaviour of nanocomposites was explained by the existence of an interface layer between polymer matrix and inorganic filler, and its influence on the macroscopic properties of the composite. The dielectric spectroscopy investigations demonstrated a reduction of the real and imaginary parts of the complex permittivity for all samples after subjecting the samples to postcuring. The postcuring process leads to evaporation of absorbed water and finalizes the process of epoxy curing. It was postulated that the interface polymer volume, which is affected by the alignment of polymer chains around surface treated nanoparticles, conducts the heat much better than an amorphous polymer that is not altered by nanoparticles. We proposed a three-phase Lewis-Nielsen model to fit the thermal conductivity behaviour of nanocomposites, which have a third phase of aligned polymer layers. The model fits the experimental data very well and takes the thermal resistance of the interface into account. Besides the interfacial layer and its nature, the size of the particles, their aspect ratio, crystal structure and alignment inside the polymer as well as surface modification are important aspects in determining the thermal conductivity of composites. Several ways are proposed to optimize the nanocomposite processing to enable scaling up to large industrial volumes. Finally, possible harmful effects of nanoparticles on health and required precautions for the workplace are discussed in the course of this thesis.

Measurement of insulating and dielectric properties of acrylic elastomer membranes at high electric fields

Abstract: This work reports on the investigation of VHB 4910 acrylic elastomer insulating and dielectric properties. This material is widely exploited for the realization of actuators with large deformations, dielectric elastomer actuators (DEA), and belongs to the group of so-called electroactive polymers (EAP). Extensive investigations concerning its mechanical properties are available in literature while its electric behavior at working conditions has not received the same level of attention. In this work, the relative permittivity and the volume resistivity have been measured on VHB 4910 membranes under different fixed stretch conditions (λ1, λ2 = 3, 3.6, 4, 5) using circular gold electrodes sputtered onto both sides of the specimens. The measured values of relative permittivity are in fairly good agreement with the results previously published by other groups. The volume resistivity, at field values close to the operational ones, has shown a field-dependent behavior revealing dissipative properties that should...

Effect of 90° domain walls on the low-field permittivity of PbZr(0.2)Ti(0.8)O3 thin films.

Abstract: We report on the contribution of 90° ferroelastic domain walls in strain-engineered PbZr(0.2)Ti(0.8)O(3) thin films to the room-temperature permittivity. Using a combination of phenomenological Ginzburg-Landau-Devonshire polydomain thin-film models and epitaxial thin-film growth and characterization, the extrinsic or domain wall contribution to the low-field, reversible dielectric response is evaluated as a function of increasing domain wall density. Using epitaxial thin-film strain we have engineered a set of samples that possess a known quantity of 90° domain walls that act as a model system with which to probe the contribution from these ferroelastic domain walls. We observe a strong enhancement of the permittivity with increasing domain wall density that matches the predictions of the phenomenological models. Additionally, we report experimentally measured bounds to domain wall stiffness in such PbZr(0.2)Ti(0.8)O(3) thin films as a function of domain wall density and frequency.