Design of a bilayer ceramic capacitor with low temperature coefficient of capacitance.

We show how a simple bilayer system that combines a layer of undoped BaTiO3 (BT) with a second layer of Ba0.975Na0.025Ti0.975Nb0.025O3 (2.5NNBT) can be used to improve the temperature coefficient of capacitance (TCC) of BaTiO3-based materials for capacitor applications. The bilayer system emulates the volume ratio between a conventional core and shell phase microstructure allowing a simple resource efficient approach to optimise the system for low TCC. Optimisation was achieved with a volume ratio of 0.67 2.5NNBT with 0.33 BT and results in a TCC of ±6% over the temperature range ∼25 to 125 °C whilst maintaining a permittivity of εr ∼ 3000 and low dielectric loss

The analysis of impedance spectra for core–shell microstructures : why a multiformalism approach is essential

The impedance response of a core–shell microstructure with 80% core volume fraction has been simulated using finite‐element modeling and compared to two equivalent circuits for a wide range of shell permittivity and conductivity values. Different equivalent circuits, corresponding to different variants of the well‐known brick layer model, are applicable for different combinations of material properties in the microstructure. When the shell has a similar conductivity or permittivity to the core, adding a parallel pathway increases the accuracy of the fit by ≈±10%. When both the conductivity and permittivity values of the core and shell regions are different the series circuit is a better fit. This is confirmed by multiformalism impedance analysis, which reveals features in the data that are not apparent using a single formalism. Finally, the conductivity and permittivity values for both the shell and core are extracted from the simulated spectra using all formalisms and compared to the original input values. The accuracy of the extracted values often depends on the impedance formalism used. It is concluded that impedance spectroscopy data must be analyzed using multiple formalisms when considering core–shell microstructures

Finite element modeling of resistive surface layers by micro‐contact impedance spectroscopy

Micro‐contact impedance spectroscopy (MCIS) is potentially a powerful tool for the exploration of resistive surface layers on top of a conductive bulk or substrate material. MCIS employs micro‐contacts in contrast to conventional IS where macroscopic electrodes are used. To extract the conductivity of each region accurately using MCIS requires the data to be corrected for geometry. Using finite element modeling on a system where the resistivity of the surface layer is at least a factor of ten greater than the bulk/substrate, we show how current flows through the two layers using two typical micro‐contact configurations. This allows us to establish if and what is the most accurate and reliable method for extracting conductivity values for both regions. For a top circular micro‐contact and a full bottom counter electrode, the surface layer conductivity (σs) can be accurately extracted using a spreading resistance equation if the thickness is ~10 times the micro‐contact radius; however, bulk conductivity (σb) values can not be accurately determined. If the contact radius is 10 times the thickness of the resistive surface, a geometrical factor using the micro‐contact area provides accurate σs values. In this case, a spreading resistance equation also provides a good approximation for σb. For two top circular micro‐contacts on thin resistive surface layers, the MCIS response from the surface layer is independent of the contact separation; however, the bulk response is dependent on the contact separation and at small separations contact interference occurs. As a consequence, there is not a single ideal experimental setup that works; to obtain accurate σs and σb values the micro‐contact radius, surface layer thickness and the contact separation must all be considered together. Here we provide scenarios where accurate σs and σb values can be obtained that highlight the importance of experimental design and where appropriate equations can be employed for thin and thick resistive surface layers

A total rip-off—crack propagation in paper

The explanation of material properties starts at a young age identifying materials using words such as strong or brittle, but it is not until higher education that we teach how and why materials break along with what brittle really means. It is an important concept to understand, as a material that could be thought strong can be made to appear weak with the addition of a very small crack. As force is applied, these cracks, introduced through dents, scratches or even from the manufacturing process, can rapidly grow, leading to catastrophic failure. To help educators explain this concept in class without the need for specialised equipment or teaching complex theory, we present a set of accessible experiments on the fracture strength of paper strips. We show how the complexity of the experiment can be modified for various age groups, ranging from an engaging session for younger students pulling paper strips to a more involved extended practical using analytical solutions and fitting to determine the fracture strength of paper. These experiments have been delivered successfully to students of various ages and have led to stimulating discussions on the subject of materials science and engineering

Using metadynamics to obtain the free energy landscape for cation diffusion in functional ceramics : dopant distribution control in rare earth-doped BaTiO3

Barium titanate is the dielectric material of choice in most multilayer ceramic capacitors (MLCCs) and thus in the production of ≈3 trillion devices every year, with an estimated global market of ≈$8330 million per year. Rare earth dopants are regularly used to reduce leakage currents and improve the MLCC lifetime. Simulations are used to investigate the ability of yttrium, dysprosium, and gadolinium to reduce leakage currents by trapping mobile oxygen defects. All the rare earths investigated trap oxygen vacancies, however, dopant pairs are more effective traps than isolated dopants. The number of trapping sites increases with the ion size of the dopant, suggesting that gadolinium should be more effective than dysprosium, which contradicts experimental data. Additional simulations on diffusion of rare earths through the lattice during sintering show that dysprosium diffuses significantly faster than the other rare earths considered. As a consequence, its greater ability to reduce oxygen migration is a combination of thermodynamics (a strong ability to trap oxygen vacancies) and kinetics (sufficient distribution of the rare earth in the lattice to intercept the migrating defects)

Finite element study of the effect of particle interaction on the energy storage density of composite dielectrics

Finite element methods can be used to study the effect of microstructure on the electrical properties of dielectric materials. These tools are utilized here to study particle interaction in composite dielectrics. The orientation and alignment of particles with each other and the applied potential difference are shown to have varying effects on the electrical breakdown strength of the composite and consequently the energy storage density. Due to an increased electrical field magnitude in the polymer matrix between particles. This increased electric field may initiate electrical breakdown in the polymer at a lower applied potential difference than would be expected for the pure polymer adversely affecting the energy storage density of dielectric composites

Material and magnetic properties of Sm2(Co, Fe, Cu, Zr)17permanentmagnets processed by Spark Plasma Sintering

Improvements to the properties of Rare Earth Permanent Magnets (REPMs) are needed to advance the capabilities of electric motors and generators, and refinement of the microstructure by the use of different approaches to processing may be a key means to achieving this. We report here a systematic study into the use of Spark Plasma Sintering to process Sm2(Co, Fe, Cu, Zr)17permanent magnets. This unfamiliar method for Sm2(Co, Fe, Cu, Zr)17offers the potential for efficiency savings in reduced processing temperatures and times versus the industry standard vacuum sinter powder metallurgical route, and also offers a refined microstructure of the materials produced. The optimised processing conditions for achieving near-to-theoretical density are reported, and the microstructure and magnetic properties of the materials produced are compared with conventional vacuum sintering. The results provide a basis for further optimisation of these materials

Morphology characterisation of inclusions to predict the breakdown strength in electro-ceramic materials: Microstructure modelling

Microstructural features such as pores, secondary phases and inclusions can significantly alter the electrical response of ceramics. Here we present a morphological finite element approach to better understand the effect of such microstructural defects on the behaviour of electroceramics. We generate irregular three-dimensional geometric models with realistic features and controllable parameters providing a method of characterising their morphology using sphericity, signifying irregularity, and projected area. The inclusion models are solved for their electrical response for changes in the material properties, making the feature either insulating or conductive in relation to the surrounding material. The electric field distribution analysis indicates the irregularity has a significant effect on the electric response, increasing the field concentration up to 12 times more than the applied field. Plotting the electric field distribution using a Weibull cumulative Probability Distribution Function we have also estimated the breakdown strength of the material. This shows that a material's breakdown strength can be reduced to 55% for an 87.5% dense sample if the inclusion is insulative and has a low sphericity or high projected area. This can be further reduced to only 40% if the feature is more conductive than the ceramic

Electric field enhancement in ceramic capacitors due to interface amplitude roughness

The electrical behaviour of the interface between the ceramic and electrode layers in multi layer ceramic capacitors has been studied using finite element modelling. Interface models were produced with varying amplitudes of roughness based upon analysis of micrographs both captured in-house and from the literature. The impedance responses, direct current electric field and current density distributions of the different interfaces were compared. Increasing the root-mean-squared amplitude roughness from 0 to 0.16 μm increased the maximum field strength by over a factor of four. The electric field distribution showed that fluctuations in the increase of field strength were due to local interface morphology. Sharp intrusions of the electrode into the ceramic layer resulted in particularly large field enhancements and should be avoided to reduce the likelihood of device breakdown

Predicting the energy storage density in poly(methyl methacrylate)/methyl ammonium lead iodide composites

In high-energy density pulsed power capacitors, high permittivity particles are dispersed within a high breakdown strength polymer matrix. In theory, such composites should be able to achieve higher volumetric energy densities than is possible with either of the individual constituents. CH3NH3PbI3 (MALI) has a perovskite structure and may be fabricated at room temperature using a mechanosynthesis route in ethanol. In this study, MALI is used to form a dielectric composite with poly(methyl methacrylate) (PMMA) used as the matrix. Theoretical models are used to predict composite permittivity values that are compared to experimental values. Finite element modeling is used to simulate their effective permittivity and, beyond what the theoretical models can achieve, predicts their energy storage capabilities by analyzing electric field intensification. The simulations show increasing energy storage capability with penetration of MALI, but this is limited experimentally by their mixing capability