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The sintering behavior of ellipsoidally-shaped particles, particularly spheroids, were studied using a numerical kinetic Monte Carlo model for solid state sintering. Compact packings of spheroids with five different aspect ratios from 0.5 to 2.0, thus comprising both oblate, spherical and prolate particles were generated by simulating the pouring of such particles into a cubic container. For each spheroid particle aspect ratio five different packings were generated to provide statistics on the sintering properties. The sintering behavior is quantified by the densification rate, relative density, anisotropic strain, grain size and grain coordination number, as determined from the Monte Carlo model. The spherical particles were found to sinter to a relative density of 0.87 before grain growth occurs, while the oblate and prolate particles reach a relative density of 0.91 before grain growth sets in, with the prolate particles sintering slightly better compared to oblate particles. The more extreme the particle aspect ratio, the more anisotropic the strain is. Finally, the oblate and prolate spheroids have a slightly higher mean grain coordination number and a slightly higher initial relative density compared to the spherical particles.

In deep learning, neural networks consisting of trainable parameters are designed to model unknown functions based on available data. When the underlying physics of the system at hand are known, e.g., Maxwell’s equation in electromagnetism, then these can be embedded into the deep learning architecture to obtain better function approximations.

Four different magnet bearing configurations, with varying number of combined radially and axially magnetized rings, are studied both experimentally and using the modeling framework MagTense. First, the optimal vertical position of the radially magnetized ring is determined using the numerical model. Then, the model is validated using experimental data. Finally, we show that a bearing where the rotor and the stator each consist of a single ring of axially magnetized magnets and a single ring of radially magnetized magnets has the smallest radial force per axial lift force at an axial air gap of 1 mm. For this bearing, the ratio of the radial force per axial lift here is 0.383 times that of the same bearing without the radially magnetized ring.

We present the processing of functionally graded multi-material freeze-cast structures, i.e. structures with varying material properties but continuous and homogeneous microchannels. We demonstrate this for stepwise, continuous, highly viscous and gelation freezing to achieve freeze-cast structures of graded La0.66Ca0.24Sr0.09Mn1.05O3 (LCSM9) and La0.67Ca0.27Sr0.06Mn1.05O3 (LCSM6) ceramics. The two phases are successfully distinguished from one another by the addition of 10 wt% Ce0.9Gd0.1O2 (CGO) to the LCSM6 phase. The relative Ce-content facilitates tracking of the LCSM6 phase using energy-dispersive X-ray (EDS) elemental analysis. Coupled with scanning electron microscopy, we show well-defined interfaces with continuous microchannels between the two LCSM phases in both green and sintered samples. By implementing constant freezing rates of −1.5 K/min a consistent freezing front velocity of ∼13 μm/s is maintained, and we found that a structural continuity can be maintained across the LCSM9–LCSM6/CGO interface, however, with varying pore morphology depending on the various freezing procedures.

An elliptically shaped electromagnetic vibration energy harvester is presented for two- and one-dimensional motions with the easy tuning of the resonance frequency. The harvester consists of a free-to-move ring-shaped permanent magnet with radial magnetization, a set of cube magnets distributed elliptically in a fixed holder, and two coil windings located above and below the harvester. When the device is exposed to vibrations, the free-to-move ring magnet moves until the magnetic restoring force from the fixed cube magnets pushes it back while inducing an electromagnetic force on the fixed coils. The performance of the device is characterized using an XY-shaker, whose frequency is swept from 1 Hz to 10 Hz with motion amplitudes of 2 mm and 4 mm on both axes simultaneously. Unlike 1-D harvesters, the resulting output power shows two resonant frequencies at 4.5 Hz and 7 Hz, at which the harvester can generate around 1.5 mW. The device also displays a nonlinear hardening resonator behaviour. Finally, 1D vibration experimental results show that the output power of the prototype depends on its angular position with respect to the motion direction of the vibration source, reaching a maximum at an angular position of 45 degree.

The four main points raised by Turki et al. in their letter “Facts to consider when analyzing the references of Nobel Prize scientific background” are discussed. It is argued that while the suggestions of Turki et al. are interesting, most require subjective choices to be made regarding the data analysis. Both in the analysis of author rank, of articles with multiple references, and of citation networks suggested by Turki et al. subjective choices on behalf of the analyzer is required, clouding the raw data obtained from the Nobel Foundation Scientific Background material. Finally, we show that the references specified in the “Further reading” section is already included in the discussed analysis.

We use the Nobel Foundations Scientific Background material to determine which journals have published Nobel Prize-awarded papers in physics since 1995. Analysing all references in the Nobel Prize Scientific Background material reveals that the journal Physical Review Letters published 28.5% of the Nobel Prize-awarded papers. It is followed by the Astrophysical journal, which accounts for 11.2%, Science, accounting 5.6% and Nature, accounting 4.7%. This is contrary to the journals respective Impact Factors, where Physical Review Letters and the Astrophysical Journal have much lower impact factors than Nature and Science. If works cited for background by the Nobel Foundation in the Scientific Background material are included in the analysis, the most referenced journal is still Physical Review Letters, now followed by Physical Review. The conclusion is that the most ground-breaking scientific work in physics is not necessarily published in the journals with the highest Impact Factor.

Freeze‐casting is a technique used to produce structures with anisotropic porosity in the form of well‐defined microchannels throughout a sample. Here, this technique is used on the magnetocaloric ceramic La0.66Ca0.26Sr0.07 Mn1.05O3. We show that a dynamic freezing profile, where the temperature is decreased continuously at −10 K/min, results in homogeneous, lamellar channels with widths of ∼15 µm, while static freezing, where the temperature is kept constant at 177 K, results in channels of increasing size away from the initial ice crystal nucleation site. The effect of gelation before freeze‐casting is also investigated. Gelation inhibits ice crystal growth, which significantly changes the morphology by making channel cross sections less elongated, while additionally introducing more dendrites and ceramic bridges in the structure. The latter significantly dominates the flow path through the gelated structures, affecting the calculated tortuosity, which increases to τ ≈ 4 when compared to non‐gelated samples where calculated tortuosities are in the range of ∼1.3 to ∼3. Finally, we present a systematic and automatic approach for evaluating channel and wall sizes and calculating tortuosities. This is based on analysis of images obtained by scanning electron microscopy using a continuous particle size distribution method and the TauFactor application in MATLAB®.

The stray- and demagnetization tensor field for a homogeneously magnetized tetrahedron is found analytically. The tetrahedron is a special case of four triangular faces with constant magnetization-charge surface density, for which we also determine the tensor field. The tensor field is implemented in the open source micromagnetic and magnetostatic simulation framework MagTense and compared with the obtained magnetic field from an FEM solution, showing excellent agreement. This result is important for modeling magnetostatics in general and for micromagnetism in particular as the demagnetizing field of an arbitrary body discretized using conventional meshing techniques is significantly simplified with this approach., Comment: 5 pages, 4 figures

In this chapter, thermoelectrics is introduced, with special focus on oxide materials. The history of thermoelectrics is briefly described, after which the thermoelectric effect and different thermoelectric materials are discussed in detail. The relevant material parameters for various oxide thermoelectric materials are also given. After this, thermoelectric devices, such as leg, unicouples, and modules are discussed, along with their efficiencies. A numerical model for calculating the efficiency of a thermoelectric system, if material properties are known, is also presented. Advanced ways to improve the performance of thermoelectric devices, such as segmentation of legs or cascaded designs are also discussed in detail. Finally, the joining of thermoelectric materials and the associated detrimental effect of contact resistance on thermoelectric performance is discussed.

We present the open source micromagnetic framework, MagTense, which utilizes a novel discretization approach of rectangular cuboid or tetrahedron geometry "tiles" to analytically calculate the demagnetization field. Each tile is assumed to be uniformly magnetized, and from this assumption only, the demagnetization field can be analytically calculated. Using this novel approach we calculate the solution to the mmag standard micromagnetic problems 2, 3 and 4 and find that the MagTense framework accurately predicts the solution to each of these. Finally, we show that simulation time can be significantly improved by performing the dense demagnetization tensor matrix multiplications using NVIDIA CUDA., 10 pages, 7 figures

We reply to Dr. Xu's comment on our paper ‘Performance of Halbach magnet arrays with finite coercivity’ (JMMM 407 (2016), 369–376). Contrary to Dr. Xu's objections we show that the procedure employed by us correctly accounts for the shape effects of the magnet elements. We show that the partial differential equation for the magnetic vector potential, derived from the Maxwell equations, incorporates all shape effects. On the other hand, the local constitutive relations express a point-wise link between, e.g., magnetic field and magnetic flux density, and are as such independent of geometry. We confirm that the results of our computations are perfectly consistent with the constitutive relation which is assumed as starting point.

The optimal segmentation of three-dimensional permanent-magnet systems into uniformly magnetized blocks to generate a desired field is a question that has been studied extensively in recent years. We present a procedure that generates the theoretically optimal shape and magnetization direction of all the magnet segments in the system, given only the total number of blocks as a constraint. Materials of arbitrary magnetic permeability can be included in this optimization framework. As an optimization objective we consider any functional that is linear with respect to the magnetic field distribution. We furthermore assume that all magnetic materials obey a linear constitutive relation. We show that with these assumptions calculating an optimal three-dimensional segmentation is equivalent to determining a centroidal Voronoi tessellation. We use the most-well-known and most-straightforward algorithm for the generation of centroidal Voronoi tessellations, known as "Lloyd's method," which can also be thought of as a fixed-point iteration. We show that the procedure is guaranteed to lead to a configuration that is at least locally optimal with respect to the assumed linear objective functional. However, we present results providing a strong indication that for most design problems applying our technique a few times starting from different random configurations is very likely to lead to the globally optimal solution.

We present an optimization approach that can be employed to calculate the globally optimal segmentation of a 2-D magnetic system into uniformly magnetized pieces. For each segment, the algorithm calculates the optimal shape and the optimal direction of the remanent flux density vector, with respect to a linear objective functional. We illustrate the approach with results for magnet design problems from different areas, such as a permanent magnet electric motor, a beam-focusing quadrupole magnet for particle accelerators, and a rotary device for magnetic refrigeration.

In Part I of this study, the performance of an experimental integrated thermoelectric generator (TEG)-heat exchanger was presented. In the current study, Part II, the obtained experimental results are compared with those predicted by a finite element (FE) model. In the simulation of the integrated TEG-heat exchanger, the thermal contact resistance between the TEG and the heat exchanger is modeled assuming either an ideal thermal contact or using a combined Cooper–Mikic–Yovanovich (CMY) and parallel plate gap formulation, which takes into account the contact pressure, roughness and hardness of the interface surfaces as well as the air gap thermal resistance at the interface. The combined CMY and parallel plate gap model is then further developed to simulate the thermal contact resistance for the case of an interface material. The numerical results show good agreement with the experimental data with an average deviation of 17% for the case without interface material and 12% in the case of including additional material at the interfaces. The model is then employed to evaluate the power production of the integrated system using different interface materials, including graphite, aluminum (Al), tin (Sn) and lead (Pb) in a form of thin foils. The numerical results show that lead foil at the interface has the best performance, with an improvement in power production of 34% compared to graphite foil. Finally, the model predicts that for a certain flow rate, increasing the parallel TEG channels for the integrated systems with 4, 8, and 12 TEGs enhances the net power per TEG with average values of 2.5%, 3% and 5%, respectively.

A numerical method to study the effect of finite coercivity on the Halbach cylinder geometry is presented. Despite the fact that the analytical solution available for this geometry does not set any limit to the maximum air gap flux density achievable, in real life the non-linear response of the magnetic material and the fact that the coercivity is not infinite will limit the attainable field. The presented method is able to predict when and where demagnetization will occur, and these predictions are compared with the analytical solution for the case of infinite coercivity. However, the approach presented here also allows quantification of the decrease in flux density and homogeneity for a partially demagnetized magnet. Moreover, the problem of how to realize a Halbach cylinder geometry using a mix of materials with different coercivities without altering the overall performance is addressed. Being based on a numerical approach, the presented method can be employed to analyze the demagnetization effects due to coercivity for any geometry, even when the analytical solution is not available.

Experiments with a recently constructed rotary multi-bed active magnetic regnenerator (AMR) prototype have revealed strong impacts on the temperature span from variations in the resistances of the flow channels carrying heat transfer fluid in and out of the regenerator beds. In this paper we show through numerical modeling how unbalanced flow in the beds decreases the cooling power and COP for a dual bed device. Furthermore, it is shown how resistance variations in multi-bed devices give rise to unbalanced flow in the individual beds and how this decreases cooling powers and COPs of the machines by approximately 30% and 50%, respectively.

We investigate whether field homogeneity of a magnetic assembly can be optimized by varying the remanence of its constituting magnetic segments. We specifically study this hypothesis for a Halbach cylinder using a numerical model, MagTense. We consider a Halbach cylinder consisting of six layers of three concentric rings, each ring made from 16 segments. We show that ideally, the homogeneity can reach close to 1 ppm for a finite magnet. We then proceed to consider a real world set of magnet segments, i.e. non-ideal magnets with a variation in their remanence. This reduces the field homogeneity to about 1000 ppm when considering a Gaussian perturbation of the remanence with a standard deviation of 1 %. However, we also show that the reduction in homogeneity may be countered by organizing the magnet pieces found through optimization, which is possible if each magnet segment is well characterized experimentally. We note that the presented method is applicable to any case where homogeneity of the field is important. The results we present are considered for the specific case of nuclear magnetic resonance for concretenes.

Micromagnetic simulations are employed for predicting the behavior of magnetic materials from their microscopic properties. In this paper we focus on hysteresis loops, which are computed by assuming quasistatic conditions: i.e. the magnetization distribution remains at equilibrium while the applied magnetic field is slowly varied.The dynamic behavior of micromagnetic systems is governed by the Landau-Lifshitz equation. In order to apply the dynamic equation to a quasistatic problem, it is necessary to artificially decouple the relaxation dynamics from the time-scale of the variation of the applied field. This decoupling is normally done in an iterative fashion: the field is considered fixed until the equilibrium point is reached, and subsequently updated. However, this approach is indirect and also has the potential issue that a system might switch to a different equilibrium configuration before the previous equilibrium becomes unstable, which is a behavior not possible in the quasistatic regime.Instead, here we derive the differential equation, which directly describes the evolution of the equilibrium states of the Landau-Lifshitz equation as a function of the external field, or any other externally varied parameter. This approach is a more rigorous description of quasistatic processes and inherently enforces the system to follow a given equilibrium configuration until this disappears or becomes unstable. We demonstrate this approach with simple examples and show it to be as or more stable than the previously used approaches.

The heat transfer and flow resistance of a novel freeze-cast porous regenerator of the magnetocaloric ceramic La0.66Ca0.27Sr0.06Mn1.05O3 was experimentally characterized. Such a porous architecture may be useful as a regenerator geometry in magnetic refrigeration applications due to the sub-millimeter hydraulic diameters that can be achieved. Here the heat transfer effectiveness and friction losses are characterized using experiments and processed with a 1D numerical model. Empirical correlations of the friction factor and Nusselt number are reviewed and chosen for modelling the specific geometry. The experimental results show that the freeze-cast regenerator has increased heat transfer effectiveness and pressure drop compared to reference packed bed regenerators made from epoxy bonded spherical and irregular particles, as well as packed, unbonded spheres. Fixing the pressure drop and regenerator size, the freeze-cast regenerator achieves 10-15% higher heat transfer performance compared to packed bed regenerators.

This is a correction to the letter “Response to the comments of Turki et al. on “The journals that publish Nobel Prize research”” [1], which failed to provide the full reference to the Turki et al. letter “Facts to consider when analyzing the references of Nobel Prize scientific background” [2]. The reason for this was that the DOI was not available at the time of submission of the said letter.

We show that low ramp rate differential scanning calorimetry of the magnetocaloric material La ( Fe 11.47 Si 1.28 Mn 0.25 ) H 1.65 at different applied magnetic fields reveals the presence of distributed phase transitions. Experimentally, we find that with or without an applied magnetic field, samples show a distinct peak pattern in their heat capacity around the transition temperature ( T t ≈ 30 ° C), i.e., multiple heat capacity peaks occur as a function of sample temperature. Additionally, these reproducible patterns occur asymmetrically when heating and cooling. At finite applied fields higher than 0.15 T, we observe clearly distinguishable peaks of identical shape, albeit with different intensities. According to the latter, we re-identify the peaks under seven applied magnetic fields up to 1 T. We find that the peaks shift differently relative to each other as a function of field. In particular, for cooling experiments, the peak temperatures vary linearly in the field, although with different slopes. Through Bean–Rodbell (BR) modeling, we show that the experimentally observed behavior can be simulated by small decoupled variations in the BR parameters η and T 0, indicating a distributed composition of the magnetocaloric material.

A rotary active magnetic regenerator (AMR) prototype with efficiency and compact design as focus points has been designed and built. The main objective is to demonstrate improved efficiency for rotary devices by reducing heat leaks from the environment and parasitic mechanical work losses while optimizing the utilization of the magnetized volume. Heat transfer calculations combined with 1D AMR modeling have revealed the necessity for an insulating air gap between magnet and regenerator when designing for high efficiency. 2D finite difference AMR modeling capturing the interplay between heat transfer fluid flow and an inhomogenous time-varying magnetic field in the individual regenerator beds has been used in the design process. For one operating point a COP of 3.1 at a temperature span of 10.2 K and a cooling power of 103 W were measured. Major issues limiting the performance have been identified and improvements are outlined for future work.

We report a high-performance thermoelectric (TE) oxide-based module using the segmentation of half-Heusler Ti_(0.3)Zr_(0.35)Hf_(0.35)CoSb_(0.8)Sn_(0.2) and misfit-layered cobaltite Ca_3Co_4O_(9+δ) as the p-leg and 2 % Al-doped ZnO as the n-leg. The maximum output power of a 4-couple segmented module at ΔT=700 K attains a value of approximately 6.5 kW m^(−2), which is three times higher than that of the best reported non-segmented oxide module. The TE properties of individual legs, as well as the interfacial contact resistances, were characterized as a function of temperature. Numerical modeling was used to predict the efficiency and to evaluate the influence of the electrical and thermal losses on the performance of TE modules. Initial long-term stability tests of the module at the hot and the cold side temperatures of 1073 K and 444 K, respectively, showed a promising result with 4 % degradation for 48 h operating in air.

Finite-element simulation of a thermoelectric (TE) module was conducted to optimize its geometrical dimensions in terms of mechanical reliability and performance. The TE module consisted of bismuth telluride n- and p-type legs. The geometrical dimensions of the module, i.e., leg length and leg cross-sectional area, were varied, and the corresponding maximum thermal stress, output power, and efficiency of the module obtained. An optimal design for the module was then suggested based on minimizing the thermal stresses and maximizing the performance, i.e., power and efficiency. The optimal dimensions at maximum von Mises stress of 75 MPa were leg length of 2 mm to 2.5 mm and leg width of 1.5 mm to 2 mm, resulting in efficiency of 7.2%. Finally, the influence of solders, i.e., solder material between the leg, the interconnector, and the top ceramic layer, on the induced thermal stresses and module performance was investigated. The results revealed that the transition from elastic to plastic deformation in the solder decreased the induced thermal stresses significantly. Moreover, beyond the elastic limit, the stress magnitude was highly dependent on the magnitude and mechanism of plastic deformation in the module. The present study provides a basis for a unique and new optimization scheme for TE modules in terms of endurance and performance.

Constrained sintering of tubular bi-layered structures is being used in the development of various technologies. Densification mismatch between the layers making the tubular bi-layer can generate stresses, which may create processing defects. An analytical model is presented to describe the densification and stress developments during sintering of tubular bi-layered samples. The correspondence between linear elastic and linear viscous theories is used as a basis for derivation of the model. The developed model is first verified by finite element simulation for sintering of tubular bi-layer system. Furthermore, the model is validated using densification results from sintering of bi-layered tubular ceramic oxygen membrane based on porous MgO and Ce0.9Gd0.1O1.95−d layers. Model input parameters, such as the shrinkage kinetics and viscous parameters are obtained experimentally using optical dilatometry and thermo-mechanical analysis. Results from the analytical model are found to agree well with finite element simulations as well as measurements from sintering experiment.

The maximum efficiency for photovoltaic (PV) and thermoelectric generator (TEG) systems without concentration is investigated. Both a combined system where the TEG is mounted directly on the back of the PV and a tandem system where the incoming sunlight is split, and the short wavelength radiation is sent to the PV and the long wavelength to the TEG, are considered. An analytical model based on the Shockley-Queisser efficiency limit for PVs and the TEG figure of merit parameter $zT$ is presented. It is shown that for non-concentrated sunlight, even if the TEG operates at the Carnot efficiency and the PV performance is assumed independent of temperature, the maximum increase in efficiency is 4.5 percentage points (pp.) for the combined case and 1.8 pp. for the tandem case compared to a stand alone PV. For a more realistic case with a temperature dependent PV and a realistic TEG, the gain in performance is much lower. For the combined PV and TEG system it is shown that a minimum $zT$ value is needed in order for the system to be more efficient than a stand alone PV system., Comment: 6 pages, 5 figures

The need for understanding the mechanisms and optimization of shape distortions during sintering of bilayers is necessary while producing structures with functionally graded architectures. A finite element model based on the continuum theory of sintering was developed to understand the camber developments during sintering of bilayers composed of La0.85Sr0.15MnO3 and Ce0.9Gd0.1O1.95 tapes. Free shrinkage kinetics of both tapes were used to estimate the parameters necessary for the finite element models. Systematic investigations of the factors affecting the kinetics of distortions such as gravity and friction as well as the initial geometric parameters of the bilayers were made using optical dilatometry experiments and the model. The developed models were able to capture the observed behaviors of the bilayers’ distortions during sintering. Finally, we present the importance of understanding and hence making use of the effect of gravity and friction to minimize the shape distortions during sintering of bilayers.

Models for deformational behaviors of porous bodies during sintering often rely on limited number of internal variables as they are formulated based on simplified or ideal microstructures. Considering realistic microstructures can improve the predictive capabilities of the already established theories like the continuum theory of sintering. A new multi-scale numerical approach for modeling of shape distortions during sintering of macroscopically inhomogeneous structures combined with a microstructure model is developed. The microstructures of the porous body are described by unit cells based on kinetic Monte Carlo (kMC) model of sintering. During the sintering process the shrinkage rate is calculated from the kMC model. With the help of computational homogenization, the effective viscosity of the powder compact is also estimated from a boundary value problem defined on the microstructures of unit cells simulated by the kMC model. Examples of simulation of sintering of bi-layers based on different material systems are presented to illustrate the multi-scale model. The approach can be considered as an extension to the continuum theory of sintering combined with the meso-scale kinetic Monte Carlo model.

A novel rotary magnetic refrigeration device has been designed and constructed following the concepts recently outlined in Bahl et al. (2011). The magnet and flow system design allow for almost continuous usage of both the magnetic field and the magnetocaloric material in 24 cassettes, each containing an active magnetic regenerator (AMR) bed. The prototype design facilitates easy exchange of the 24 cassettes, allowing the testing of different material amounts and compositions. Operating with 2.8 kg of commercial grade Gd spheres a maximum no-span cooling power of 1010 W and a maximum zero load temperature span of 25.4 K have been achieved. For the purpose of actual operation, simultaneous high span and high performance is required. At a heat load of 200 W a high temperature span of 18.9 K has been obtained, dropping to a span of 13.8 K at the higher heat load value of 400 W.

Shape distortions during constrained sintering experiment of bi-layer porous and dense cerium gadolinium oxide (CGO) structures have been modeled. Technologies like solid oxide fuel cells require co-firing thin layers with different green densities, which often exhibit differential shrinkage because of different sintering rates of the materials resulting in undesired distortions of the component. An analytical model based on the continuum theory of sintering has been developed to describe the kinetics of densification and distortion in the sintering processes. A new approach is used to extract the material parameters controlling shape distortion through optimizing the model to experimental data of free shrinkage strains. The significant influence of weight of the sample (gravity) on the kinetics of distortion is taken in to consideration. The modeling predictions indicate good agreement with the results of sintering of a bi-layered CGO system in terms of evolutions of bow, porosities and also layer thickness.

Experimental analyses of shrinkage and distortion kinetics during sintering of bilayered porous and dense gadolinium-doped ceria Ce0.9Gd0.1O1.95−δ structures are carried out, and compared with the theoretical models developed in Part I of this work. A novel approach is developed for the determination of the shear viscosities ratio of the layer fully dense materials. This original technique enables the derivation of all the input parameters for the bilayer sintering modeling from one set of optical dilatometry measurements, including the conversion between real and specific times of sintering, the layers’ relative sintering intensity, and the shear viscosities ratio of the layer fully dense materials. These optical dilatometry measurements are conducted simultaneously for each individual layer and for a symmetric trilayered porous structure based on the two layers utilized in the bilayered system. The obtained modeling predictions indicate satisfactory agreement with the results of sintering of a bilayered cerium–gadolinium oxide system in terms of distortion and shrinkage kinetics.

Permanent-magnet systems are widely used for generation of magnetic fields with specific properties. The reciprocity theorem, an energy-equivalence principle in magnetostatics, can be employed to calculate the optimal remanent flux density of the permanent-magnet system, given any objective functional that is linear in the magnetic field. This approach, however, yields a continuously varying remanent flux density, while in practical applications, magnetic assemblies are realized by combining uniformly magnetized segments. The problem of determining the optimal shape of each of these segments remains unsolved. We show that the problem of optimal segmentation of a two-dimensional permanent-magnet assembly with respect to a linear objective functional can be reduced to the problem of piecewise linear approximation of a plane curve by perimeter maximization. Once the problem has been cast into this form, the globally optimal solution can be easily computed employing dynamic programming.

Microstructural evolution and sintering behavior of powder compacts composed of spherical particles with different particle size distributions (PSDs) were simulated using a kinetic Monte Carlo model of solid state sintering. Compacts of monosized particles, normal PSDs with fixed mean particle radii and a range of standard deviations, and log-normal PSDs with fixed mode and a range of skewness values were studied. Densification rate and final relative density were found to be inversely proportional to initial PSD width. Grain growth was faster during the early stages of sintering for broad PSDs, but the final grain sizes were smaller. These behaviors are explained by the smallest grains in the broader PSDs being consumed very quickly by larger neighboring grains. The elimination of the small grains reduces both the total number of necks and the neck area between particles, which in turn reduces the regions where vacancies can be annihilated, leading to slower densification rates. The loss of neck area causes grain growth by surface diffusion to become the dominant microstructural evolution mechanism, leading to poor densification. Finally, pore size was shown to increase with the width of PSDs, which also contributes to the lower densification rates.

There is a tendency for multiple functional ceramic layers used in various applications to have increasing surface areas and decreasing thicknesses. Sintering samples with such geometry is challenging, as differential shrinkage of the layers causes undesired distortions. In this work, a model, which describes the combined effect of sintering and gravity of thin multilayers, is derived and later compared with experimental results. It allows for consideration of both uniaxial and biaxial stress states. The model is based on the Skorohod-Olevsky viscous sintering framework, the classical laminate theory and the elastic-viscoelastic correspondence principle. The modeling approach is then applied to illustrate the effect of gravity during sintering of thin layers of cerium gadolinium oxide (CGO), and it is found to be significant.

Magnetocaloric materials with a Curie temperature near room temperature have attracted significant interest for some time due to their possible application for high-efficiency refrigeration devices. This review focuses on a number of key issues of relevance for the characterization, performance and implementation of such materials in actual devices. The phenomenology and fundamental thermodynamics of magnetocaloric materials is discussed, as well as the hysteresis behavior often found in first-order materials. A number of theoretical and experimental approaches and their implications are reviewed. The question of how to evaluate the suitability of a given material for use in a magnetocaloric device is covered in some detail, including a critical assessment of a number of common performance metrics. Of particular interest is which non-magnetocaloric properties need to be considered in this connection. An overview of several important materials classes is given before considering the performance of materials in actual devices. Finally, an outlook on further developments is presented.

Active magnetic regenerator (AMR) refrigerators represent an alternative to vapor compression technology and have great potential in realizing cooling devices with high efficiency, which are highly desirable for a broad range of applications. The technology relies on the magnetocaloric effect in a solid refrigerant rather than the temperature change that occurs when a gas is compressed/expanded. This paper presents the general considerations for the design and construction of a high frequency rotary AMR device. Experimental results are presented at various cooling powers for a range of operating conditions near room temperature. The device exhibited a no-load temperature span of over 25 K and can absorb a 100 W cooling load at a 20.5 K temperature span.

The magnetocaloric properties of inhomogeneous ferromagnets that contain distributions of Curie temperatures are considered as a function of the width of such a distribution. Assuming a normal distribution of the Curie temperature, the average adiabatic temperature change, Δ T ad , the isothermal magnetic entropy change, Δ s , and the heat capacity, c p , in zero magnetic field and an applied magnetic field of μ 0 H = 1 T , have been calculated using the mean field model of ferromagnetism. Interestingly, both the peak position and amplitude of each of these parameters vary differently with the width of the distribution, explaining the observed mismatch of peak temperatures reported in experiments. Also, the field dependence of Δ T ad and Δ s is found to depend on the width of the distribution.

Design considerations for a prototype magnetic refrigeration device with a continuously rotating AMR are presented. Building the active magnetic regenerator (AMR) from stacks of elongated plates of the perovskite oxide material La0.67Ca0.33−xSrxMn1.05O3, gives both a low pressure drop and allows grading of the Curie temperature along the plates. This may be accomplished by a novel technique where a compositionally-graded material is tape cast in one piece. The magnet assembly is based on a novel design strategy, to create alternating high- and low magnetic field regions within a magnet assembly. Focus is on maximising the magnetic field in the high field regions but also, importantly, minimising the flux in the low field regions. The design is iteratively optimised through 3D finite element magnetostatic modelling.

A general scheme for increasing the difference in magnetic flux density between a high and a low magnetic field region by removing unnecessary magnet material is presented. This is important in, e.g., magnetic refrigeration where magnet arrays has to deliver high field regions in close proximity to low field regions. Also, a general way to replace magnet material with a high permeability soft magnetic material where appropriate is discussed. As an example these schemes are applied to a two dimensional concentric Halbach cylinder design resulting in a reduction of the amount of magnet material used by 42% while increasing the difference in flux density between a high and a low field region by 45%., Comment: 7 pages, 8 figures

A La0.67Ca0.26Sr0.07Mn1.05O3 (LCSM) perovskite was prepared for the first time as a ceramic monolithic regenerator used in a regenerative magnetic refrigeration device. The parameters influencing the extrusion process and the performance of the regenerator, such as the nature of the monolith paste and the influence of the sintering on the adiabatic temperature change, were investigated. Comparisons between the extruded monolithic structure before and after the sintering showed that an increase of the adiabatic temperature change was seen after the sintering. Furthermore, calculations show that the performance of the monolithic structure is potentially superior to a parallel plate regenerator, indicating the potential cost and structural benefit of using such structure, i.e. a mechanically stable ceramic thin wall structure, which can be produced in one processing step.

The influence of the time variation of the magnetic field, termed the magnetic field profile, on the performance of a magnetocaloric refrigeration device using the active magnetic regeneration (AMR) cycle is studied for a number of process parameters for both a parallel plate and packed bed regenerator using a numerical model. The cooling curve of the AMR is shown to be almost linear far from the Curie temperature of the magnetocaloric material. It is shown that a magnetic field profile that is 10% of the cycle time out of sync with the flow profile leads to a drop in both the maximum temperature span and the maximum cooling capacity of 20-40\% for both parallel plate and packed bed regenerators. The maximum cooling capacity is shown to depend very weakly on the ramp rate of the magnetic field. Reducing the temporal width of the high field portion of the magnetic field profile by 10% leads to a drop in maximum temperature span and maximum cooling capacity of 5-20%. An increase of the magnetic field from 1 T to 1.5 T increases the maximum cooling capacity by 30-50% but the maximum temperature span by only 20-30%. Finally, it was seen that the influence of changing the magnetic field was more or less the same for the different regenerator geometries and operating parameters studied here. This means that the design of the magnet can be done independently of the regenerator geometry., 13 pages, 13 figures

A magnet designed for use in a magnetic refrigeration device is presented. The magnet is designed by applying two general schemes for improving a magnet design to a concentric Halbach cylinder magnet design and dimensioning and segmenting this design in an optimum way followed by the construction of the actual magnet. The final design generates a peak value of 1.24 T, an average flux density of 0.9 T in a volume of 2 L using only 7.3 L of magnet, and has an average low flux density of 0.08 T also in a 2 L volume. The working point of all the permanent magnet blocks in the design is very close to the maximum energy density. The final design is characterized in terms of a performance parameter, and it is shown that it is one of the best performing magnet designs published for magnetic refrigeration., Comment: 6 pages, 6 figures

This paper investigates the possible use of space probes to explore the Milky Way, as a means both of finding life elsewhere in the Galaxy and as finding an answer to the Fermi paradox. I simulate exploration of the Galaxy by first examining how long time it takes a given number of space probes to explore 40,000 stars in a box from -300 to 300 pc above the Galactic thin disk, as a function of Galactic radius. I then model the Galaxy to consist of $\sim{}260,000$ of these 40,000 stellar systems all located in a defined Galactic Habitable Zone and show how long time it takes to explore this zone. The result is that with 8 probes, each with 8 subprobes $\sim{}4%$ of the Galaxy can be explored in $2.92\cdot{}10^{8}$ years. Increasing the number of probes to 200, still with 8 subprobes each, reduces the exploration time to $1.52\cdot{}10^{7}$ years., Comment: 6 pages, 4 figures, accepted by International Journal of Astrobiology (Published online by Cambridge University Press 20 Apr 2007)

International audience; The aim of this work is to assess the influence of a magnetic sample on the applied magnetic field inside the air gap of a magnetic circuit. Different magnetic sources including an electromagnet, a permanent magnet in a soft ferromagnetic toroidal yoke, as well as 2D and 3D Halbach cylinders are considered, using a numerical model. Gadolinium is chosen as magnetic material for the sample, due to its strong magnetocaloric properties and its wide use in magnetic refrigeration prototypes. We find that using uniform theoretical demagnetizing factors for cylinders or spheres results in a deviation of less than 2% in the calculation of internal magnetic fields at temperatures above the Curie point of gadolinium. Below the Curie point, a stronger magnetization of the cylinders and spheres leads to a larger deviation which can reach 8% when using uniform demagnetizing factors for internal magnetic field calculations.

The magnetocaloric properties of three samples of LaFe$_{13-x-y}$Co$_x$Si$_y$ have been measured and compared to measurements of commercial grade Gd. The samples have (x=0.86, y=1.08), (x=0.94, y=1.01) and (x=0.97, y=1.07) yielding Curie temperatures in the range 276-288 K. The magnetization, specific heat capacity and adiabatic temperature change have been measured over a broad temperature interval. Importantly, all measurements were corrected for demagnetization, allowing the data to be directly compared. In an internal field of 1 T the maximum specific entropy changes were 6.2, 5.1 and 5.0 J/kg K, the specific heat capacities were 910, 840 and 835 J/kg K and the adiabatic temperature changes were 2.3, 2.1 and 2.1 K for the three LaFeCoSi samples respectively. For Gd in an internal field of 1 T the maximum specific entropy change was 3.1 J/kg K, the specific heat capacity was 340 J/kg K and the adiabatic temperature change was 3.3 K. The adiabatic temperature change was also calculated from the measured values of the specific heat capacity and specific magnetization and compared to the directly measured values. In general an excellent agreement was seen., Comment: 9 pages, 8 figures

An expression is determined for the mass of the magnet and magnetocaloric material needed for a magnetic refrigerator and these are determined using numerical modeling for both parallel plate and packed sphere bed regenerators as function of temperature span and cooling power. As magnetocaloric material Gd or a model material with a constant adiabatic temperature change, representing a infinitely linearly graded refrigeration device, is used. For the magnet a maximum figure of merit magnet or a Halbach cylinder is used. For a cost of \$40 and \$20 per kg for the magnet and magnetocaloric material, respectively, the cheapest 100 W parallel plate refrigerator with a temperature span of 20 K using Gd and a Halbach magnet has 0.8 kg of magnet, 0.3 kg of Gd and a cost of \$35. Using the constant material reduces this cost to \$25. A packed sphere bed refrigerator with the constant material costs \$7. It is also shown that increasing the operation frequency reduces the cost. Finally, the lowest cost is also found as a function of the cost of the magnet and magnetocaloric material., Comment: 12 pages, 10 figures