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Practical breakdown voltage calculations using dielectric breakdown strength reference values
(2020)
Dielectric breakdown is a catastrophic failure of ceramic substrates and insulators. The use of dielectric breakdown strength (DBS) reference values for the dimensioning of such components is not straightforward, as the DBS depends on sample thickness and electrode area. This fact also hampers a valid comparison of data taken from different literature sources. Based on the empirically confirmed proportionality of DBS to the reciprocal square root of sample thickness and an approach to account for the influence of electrode area on the failure probability, a practical equation is derived to calculate the breakdown voltage for arbitrary sample thickness and electrode area from one set of DBS reference data. To validate the equation, the AC DBS of commercial alumina substrates with thicknesses ranging from 0.3 mm to 1.0 mm was performed using different printed electrodes with varying areas. The breakdown voltages comprise a range from 18 kV for thick samples to 8.5 kV for thin samples, resulting in DBS values from 17 kV/mm for 1.0 mm thick samples to 29 kV/mm for 0.3 mm thin samples, all made from the same material. The influence of electrode area is comparatively smaller. The results calculated with the proposed equation are in reasonable accordance with the measured data. Thus, the equation can be applied for a proper comparison of literature DBS data measured in different setups and for a reasonable estimation of breakdown voltages in DBS tests and applications based on reference data.
The influence of the atomization technique on the suitability of granules for dry pressing is the focus of the presented investigations. Therefore, destabilized alumina, zirconia, and zirconia toughened alumina (ZTA) slurries were spray dried and the obtained granules were used to fabricate green and finally sintered bodies for evaluation.
Granules made in a laboratory spray dryer with a two-fluid nozzle served as a reference. An ultrasonic atomizer was integrated into the same spray dryer and the influence on the granule properties was evaluated. Untapped bulk density, granule size distribution, and flowability are among the evaluated granule-related properties as well as the granule yield which is used as an indicator of the process efficiency.
Yield and flowability as most important granule properties are clearly improved when atomization is realized with ultrasound. The investigated sinter body properties include porosity, sinter body density, and biaxial strength and are as well positively affected by switching the atomization technique to ultrasound. Therefore, the Approach to improve the compressibility of granules by ultrasonic atomization, which leads to an improved microstructure, density, and strength of sintered bodies, has proven to be successful for single-component ceramics (alumina and zirconia) as well as for the multicomponent ceramic ZTA.
Ceramic springs offer versatile possibilities for load bearing or sensor applications in challenging environments. Although it may appear unexpected, a wide range of spring constants can be implemented by material selection and especially by the design of the spring. Based on a rectangular cross-section of the windings, it is possible to design a spring geometry that generates the desired spring constant simply by choosing appropriate diameter, height, widths, and number of windings. In a recent research project the calculation of helical compression springs made of rectangular steel (German standard DIN 2090) was applied for the design of ceramic springs. A manufacturing technology has been worked out to fabricate such springs from hollow cylinders of several highly dense technical ceramics by milling. Ceramic springs with precise rectangular section, without edge damage, and mean surface roughness smaller than 0.2 µm were produced after parameter optimization. Tolerances of less than 10 µm were achieved regarding spring diameter, height, and width of cross section. It is shown that the calculations outlined in the standard are valid for a variety of ceramic materials as well. Demonstrator springs with a wide range of spring constants have been fabricated, including zirconia springs with 0.02 N/mm, alumina springs with 1 N/mm and Si3N4 springs with 5 N/mm. A reproducibility study of six zirconia springs with a constant of 0.3 N/mm showed a relative difference in spring constants of less than +/- 1 %. This combination of a valid calculation approach for spring geometry and a reliable manufacturing technology allows for purposeful development and fabrication of ceramic springs with precise mechanical properties and superior chemical stability.
Calcium cobaltite (Ca3Co4O9) is considered as one of the most promising thermoelectric p-type oxides for energy harvesting applications at temperatures above 500 °C. It is challenging to sinter this material as its stability is limited to 920 °C. To facilitate a practicable and scalable production of Ca3Co4O9 for multilayer generators, a systematic study of the influence of powder calcination, Bi-doping, reaction sintering, and pressure-assisted sintering (PAS) on microstructure and thermoelectric properties is presented. Batches of doped, undoped, calcined, and not calcined powders were prepared, tape-cast, and sintered with and without uniaxial pressure at 900 °C. The resulting phase compositions, microstructures and thermoelectric properties were analysed. It is shown that the beneficial effect of Bi-doping observed on pressureless sintered samples cannot be transferred to PAS. Liquid phase formation induces distortions and abnormal grain growth. Although the Seebeck coefficient is increased to 139 µV/K by Bi-doping, the power factor is low due to poor electrical conductivity. The best results were achieved by PAS of calcined powder. The dense and textured microstructure exhibits a high power factor of 326 µW/mK² at 800 °C but adversely high thermal conductivity in the relevant direction. The figure of merit is higher than 0.08 at 700 °C.
Dielectric strength testing of ceramics can be performed with various setups and parameters. Comparisons of results from different sources are often not meaningful, because the results are strongly dependent on the actual testing procedure. The aim of this study is to quantify the influence of voltage ramp rate, electrode size, electrode conditioning, and sample thickness on the measured AC dielectric strength of a commercial alumina. Mean values, Weibull moduli, and failure probabilities determined in standardized short time tests are evaluated and related to withstand voltage tests. Dielectric strength values in the range from 21.6 to 33.2 kV/mm were obtained for the same material using different testing procedures. Short time tests resulted in small standard deviations (< 2 kV/mm) and high Weibull moduli around 30, while withstand tests at voltage levels with low and virtual zero failure probability in short time tests resulted in large scatter of withstand time and Weibull moduli < 1. The strong decrease in Weibull moduli is attributed to progressive damage from partial discharge and depolarization during AC testing. These findings emphasize the necessity of a thorough documentation of testing procedure and highlight the importance of withstand voltage tests for a comprehensive material characterization.
The ProboStat is a multi-purpose measurement cell suitable for various electrical and physical measurements under different atmospheres and at high temperatures. Disc and bar shaped samples are sandwiched between platinum electrodes at the top of the tubular cell. The gas tight assembly can be inserted into a furnace. Different gases can be flushed through the tube. For this study, a ProboStat was adapted to measure volume resistivity of ceramic insulators at high temperatures according to standards.
The standardized measurement of volume resistivity of ceramic insulators requires the consideration of many specifications including sample diameter, thickness, electrode design, and the proportion of these characteristics. Measurements are ideally performed in a state of dielectric equilibrium. The time-related slope of resistivity of a specific sample follows a power function. Thus, care must be taken when choosing a charge time or defining the duration of a measurement. As fringing of the guarded electrode occurs under high voltage, the effective electrode area for evaluation of the results should be corrected with respect to sample thickness and electrode design. The demands of effective standards on sample geometry and electrode design are stricter for room temperature measurements than for high temperature measurements.
To perform high temperature measurements on ceramic samples that also fulfill the demands on room temperature measurements, a ProboStat was equipped with a dedicated large sample setup for discs with diameters of up to 60 mm. The volume resistivity of different alumina samples was first measured at room temperature in a standard test fixture and then compared to results obtained with the ProboStat. All measurements were performed for at least 100 min using a 26 mm guarded electrode. High temperature measurements at 500 °C were performed using the same samples. Room temperature values obtained with the standard test fixture are in the order of 10^17 Ohm·cm. The quantitative effect of electrode area correction is presented. Practical issues related to the use of the multi-purpose cell are addressed. These include electrode material selection, application of electrodes, and compensation of leakage currents. High temperature results of volume resistivity of the different alumina samples are presented. The validity is discussed with respect to the suitability of the multi-purpose cell for such measurements.
Dielectric breakdown of ceramics is widely believed to originate from microstructural defects. Still, there is no commonly accepted model for the origin and process of dielectric failure that covers all observed phenomena and dependencies. In analogy to mechanical strength, the Weibull distribution is commonly used to evaluate dielectric strength data. This works well for a given group of specimens with constant geometry. But unlike mechanical strength, dielectric strength scales with the inverse square root of sample thickness. This cannot be explained by the classic Weibull concept. The Griffith type energy release rate model of dielectric breakdown proposed by Schneider is based on space charge injection and conducting filaments from the sample surface. This model incorporates the distinct thickness dependence and the pronounced influence of surface defects. Based on this model and the classic Weibull probability of failure, Schneider’s group theoretically derived a probability of breakdown that predicts an increase of failure probability with increasing electrode area. In our study we tested this model with dielectric strength data measured on dense alumina samples using different electrode areas. Weibull modulus and characteristic dielectric strength (scale parameter) were determined for a set of measurements using small electrodes. These values were used to calculate the failure probability under large electrodes according to the model. The calculated data excellently fits the measured values. Thus, our experiments substantiate the assumptions made in the breakdown model and the significance of surface defects for dielectric failure.
The granules commonly yielded by spray drying procedures exhibit a hard shell and an irregular, dimpled shape, which is often described as donut-like morphology. Sintered parts produced from such granules suffer from microstructural defects and reduced mechanical properties resulting from these disadvantageous granule properties.
Using the example of alumina, zirconia and zirconia-toughened alumina (ZTA) batches, this paper shows that the morphology of the granules can be tuned by adjusting slurry stability. High zeta potential is essential to optimally disperse the particles. But to achieve spherical and soft granules the electrostatic repulsion forces between the particles should be reduced before spray granulation. Electrostatic repulsion forces were changed with the addition of nitric acid. Measurements of zeta potential and viscosity, as well as sedimentation investigations with an optical centrifuge were used for precise slurry assessment as a major precondition for optimal and reproducible adjustment of slurries before spray drying. Sedimentation analysis using an optical centrifuge was performed to investigate different influences like that of additive composition, solids content or pH-value on the sedimentation behavior. Adequately flocculated slurries lead to homogeneous, soft granules that can be easily deformed and pressed. The fraction of donut-shaped particles and the rigidity of granules were reduced. Consequently, the sintered parts produced from these granulates show improvements regarding porosity, pore size distribution, sintered density and biaxial strength.
A wide range of solid-state synthesis routes for calcium manganate is reported in the literature, but there is no systematic study about the influence of the solid-state synthesis conditions on thermoelectric properties. Therefore, this study examined the influence of calcination temperature and calcination cycles on the Seebeck coefficient, electrical conductivity, and thermal conductivity. Higher calcination temperatures and repeated calcination cycles minimized the driving force for sintering of the synthesized powder, leading to smaller shrinkage and lower densities of the sintered specimens. As the electrical conductivity increased monotonously with increasing density, a higher energy input during calcination caused deterioration of electrical conductivity. Phase composition and Seebeck coefficient of sintered calcium manganate were not influenced by the calcination procedure. The highest thermoelectric properties with the highest power factors and figures of merit were obtained by means of reaction-sintering of uncalcined powder.
Today, more than 12% of the primary energy is lost in the form of waste heat. Thermoelectric generators (TEGs) can convert waste heat directly into electrical power by utilizing the Seebeck effect. The performance of such a generator is defined by a dimensionless figure of merit ZT of the thermoelectric pairs and the resistance R of the metallic contacts between these pairs. The figure of merit of thermoelectric oxides is considerably smaller compared to semiconductors. Still, thermoelectric oxides like calcium cobaltite (Ca3Co4O9) are attractive for applications at elevated temperatures in air. In contrast to the established π-type architecture of common TEGs, tape casting and multilayer technology may be applied for cost-effective manufacturing of oxide TEGs. Promising demonstrations of multilayer TEGs have been published in the last years. Still, the development of reliable and scalable manufacturing processes and proper material combinations is necessary. The aim of our project is to evaluate the feasibility of low temperature co-fired ceramics (LTCC) technology for a practical manufacturing of oxide multilayer TEGs of Ca3Co4O9 (p-type) and calcium manganate (CaMnO3, n-type). Ca3Co4O9 exhibits an undesired phase decomposition at 926 °C. Because of that, the application of sintering strategies and interconnect concepts well known from LTCC technology is a promising approach. We present results of pressure-assisted sintering of Ca3Co4O9 multilayer at 900 °C and axial pressures of up to 7.5 MPa. Ca3Co4O9 was produced by solid state reaction of CaCO3 and cobalt(II,III)oxide at 900 °C. Green tapes were prepared by a doctor-blade process, manually stacked and laminated by uniaxial thermocompression. Sintering was conducted in a LTCC sintering press between SiC setter plates. The thickness shrinkage was recorded by an in-situ technique. After sintering under 7.5 MPa, the microstructure of the single phase material shows a high density of 95 % and an advantageous alignment of the platelet grains. This results in good electrical conductivity and a comparatively high ZT of 0.018 at room temperature. However, the lowering of CaMnO3 sintering temperature from above 1200 °C to below 920 °C remains a challenge. To select a proper metal paste for interconnections of an oxide TEG, several pastes have been investigated regarding contact resistance of internal and external (soldered) connections in a preliminary study. Commercial pastes containing Ag, Au, Au/Pt, Ag/Pd, and Ag/Pd/Bi were manually applied and post-fired on sintered test bars of Ca3Co4O9 and CaMnO3 at 900 °C for 2 h. All tested pastes formed mechanically stable metallization after firing. For resistance measurement, 4-wire method and a custom-made probe head were used. The contacts on Ca3Co4O9 exhibit significantly (2-sample t-test, α = 5%) higher resistance compared to contacts on CaMnO3. Pure silver paste exhibits the lowest resistance for internal contacts on both materials, lower than 5 mΩ on CaMnO3. Ag/Pd/Bi paste resulted in conspicuously high variance of resistance. EDX analyses clarified an enrichment of Bi in the thermoelectric material near the interface and thereby the formation of an oxide layer with probably high electrical resistance. The thickness of that layer varies with the thickness of metallization. In conclusion, the use of Bi containing pastes is not advisable. Pure Ag paste shows the best results regarding resistance and solderability.
Dielectric strength testing of ceramics is simple and yet challenging. The execution of a breakthrough voltage measurement of a given sample is fast and straightforward. ASTM D149 describes the standardized procedure. But, there are versatile effects of test conditions and sample properties that affect the result of such a measurement. As one example, ASTM D149 allows different sizes of test electrodes and does not unambiguously prescribe the condition of the electrodes. Thus, different electrode configurations are used in the field. We conducted several test series on alumina samples to comprehensively quantify the effect of test conditions and sample properties on dielectric strength results. In our study, testing of alumina substrates using different electrode configurations resulted in differences of mean values of up to 20%. Further test series on alumina focused on the effect of voltage ramp rate. The results are complemented by calculations of failure probability at different voltage levels and corresponding withstand voltage tests. We conclude that a communication and comparison of single dielectric strength values is insufficient and may be misleading. A meaningful comparison of dielectric strength studies from different sources requires a thorough consideration of test conditions.
Calcium cobaltite is one of the most promising oxide p-type thermoelectric materials. The solid-state reaction (or calcination, respectively), which is well known for large-scale powder synthesis of functional materials, can also be used for the synthesis of thermoelectric oxides. There are various calcination routines in literature for Ca3Co4O9 powder synthesis, but no systematic study has been done on the influence of calcination procedure on thermoelectric properties. Therefore, the influence of calcination conditions on the Seebeck coefficient and the electrical conductivity was studied by modifying calcination temperature, dwell time, particle size of raw materials and number of calcination cycles. This study shows that elevated temperatures, longer dwell times, or repeated calcinations during powder synthesis do not improve but deteriorate the thermoelectric properties of calcium cobaltite. Diffusion during calcination leads to idiomorphic grain growth, which lowers the driving force for sintering of the calcined powder. A lower driving force for sintering reduces the densification. The electrical conductivity increases linearly with densification. The calcination procedure barely influences the Seebeck coefficient. The calcination procedure has no influence on the phase formation of the sintered specimens.
The sintering behavior and the thermoelectric performance of Ca3Co4O9 multilayer laminates were studied, and a multilayer thermoelectric generator was fabricated. Compacts and multilayer samples with anisotropic microstructure and residual porosity were obtained after conventional sintering at 920 °C, whereas dense and isotropic multilayer samples were prepared by firing at 1200 °C and reoxidation at 900 °C. A hot-pressed sample has a dense and anisotropic microstructure. Samples sintered at 920 °C exhibit low electrical conductivity due to the low density, whereas the Seebeck coefficient is not sensitive to preparation conditions. However, thermal conductivity of multilayers is very low, and, hence acceptable ZT values are obtained. A ransversal multilayer thermoelectric generator (TMLTEG) was fabricated by stacking layers of Ca3Co4O9 green tapes, AgPd conductor printing, and co-firing at 920 °C. The TMLTEG has a power output of 3 mW at ΔT =200 K in the temperature interval of 25 °C to 300 °C.