Espen Sagvolden

Alnico magnets have gained renewed interest in the search for rare-earth free permanent magnets due to their high thermal stability and magnetisation. However, the limited coercivity of these shape-anisotropy-based alloys constrains their performance. Their coercivity can be improved by tailoring their structure at the micro- and nano-levels and by identifying the elemental composition and crystal structure that would increase anisotropy. Alnico alloys are composed of millimetre-to-micrometer-sized grains of different sizes and orientations. Inside each grain, magnetic nanorods embedded in a non-magnetic matrix form as a result of thermo-magnetic treatment of the cast alloy. Starting from a reference Alnico sample, we realised a finite elements micromagnetic study of exchange-decoupled rods by varying their dimensions and interrod spacing across those observed experimentally. We computed the hysteresis properties by progressing from micromagnetic simulations of a small number of rods within the magnetostatic field of their neighbours to large systems treated statistically based on the distribution of orientations of the grains. We compared the coercivity of an isolated rod with that of the exchange-decoupled system to highlight the effect of magnetostatic interactions. We computed analytically the stray field acting on a single rod as a consequence of its surrounding rods in order to confirm the scaling of the coercivity with the packing fraction p . We explored how intrinsic material properties influence magnetic behaviour by examining materials with different magnetocrystalline anisotropy constants and saturation polarisation values. Results from several hundred simulations were used to train a multi-layer perceptron regressor and predict the magnetic properties as function of the dimensions of the rods, interrod spacing and orientation of the grains. With this approach, we highlight the underlying trends by which nanoscale structuring, intrinsic material properties and grain alignment can be tailored to improve the magnetic properties of Alnico alloys.

Within this study, a methodology for the numerical simulation of droplet freezing, including a micrometer texturized pattern, was developed. The finite volume method was then applied to simulate the behavior of water droplets. The procedure was divided into two processes: stabilization and freezing. In the stabilization step, the droplet was dropped onto the material surface and took an equilibrium shape. In the second step, additional energy equation and temperature boundary conditions were applied to perform freezing simulation. Based on the laser-texturized samples of polyurethane-coated metal substrates studied with freezing delay experiments, numerical models were generated, and droplet freezing simulations were performed. Three cases were studied—non-texturized and texturized with respectively linear and triangular patterns. The obtained simulation results of freezing time were compared with experimental measurements to evaluate the proposed methodology. The study revealed that despite the inability to predict accurate freezing delay time, the proposed methodology can be used to compare the freezing delay capabilities for different texturized patterns. Additionally, the proposed model renders it possible to analyze additional aspects of wetting and freezing of the droplet on rough surfaces, which may be helpful in understanding these processes.

As the world’s focus is turned even stronger toward miscellaneous energy efficiency and saving aspects, the development of new high-performance thermal insulation materials for building applications will play an important role in this regard. The aim of the presented study is to develop an understanding for the governing thermal transport mechanisms and utilize the Knudsen effect in nanoporous insulation materials through theoretical concepts and experimental laboratory explorations, thus being able to synthesize nano insulation materials (NIM) with very low thermal conductivity values as a major goal. NIMs based on hollow silica nanospheres (HSNS) have been synthesized by a sacrificial template method, where the idea is that the heat transport by gas conductance and gas/solid state interactions decreases with decreasing pore diameters in the nano range as predicted by the Knudsen effect. HSNS with reduced thermal conductivity compared to their solid counterparts have been prepared where the hollow sphere cavities and voids between the spheres are filled with air at atmospheric pressure, i.e. eliminating the need for various measures like e.g. protective metallized foils to maintain a vacuum or expensive low-conducting gases in the cavities and voids. Hence, HSNS represent a promising stepping-stone toward the future high-performance thermal insulation materials.

Ab initio calculations of the solid-state diffusivity of solute atoms in bulk aluminium have previously been based on transition state theory (TST), employing transition state searches and systematic assessments of single jumps together with appropriate models of jump frequencies and correlation factors like the five-frequency model. This work compared TST benchmark predictions of diffusivities with first-principles molecular dynamics (FPMD). The TST calculations were performed at unprecedented high precision, including the temperature dependent entropy of vacancy formation which has not been included in previous studies of diffusion in Al; this led to improved agreement with experimental data. It was furthermore demonstrated that FPMD can yield sufficient statistics to predict the frequency of single jumps, and FPMD was used to successfully predict the macroscopic diffusivity of Si in Al. The latter is not possible in systems with higher activation energies, but it was demonstrated that FPMD in such cases can identify which jumps are prevalent for a given defect configuration. Thus, information from FPMD can be used to simplify the calculation of correlation terms, prefactors and effective transition barriers with TST significantly. This can be particularly important for the study of more complicated defect configurations, where the number of distinct jumps rapidly increases to be intractable by systematic methods.

Exchange-correlation density functionals at the meta-generalised gradient approximation level typically use the Kohn–Sham orbitals as an ingredient to create the isoorbital indicator , where is the von Weizsäcker kinetic energy density and is the kinetic energy density of the Kohn–Sham orbitals. When a magnetic field is included in the treatment, the Kohn–Sham orbitals vary with the vector-potential gauge, as does and implicitly the exchange-correlation energy. However, it is a known result in current density functional theory that the exact exchange-correlation energy is gauge independent. Three different gauge-independent replacements for have been proposed by other authors. Only one of these is, however, known to stay between 0 and 1. We modify one of the others, the Maximoff–Scuseria isoorbital indicator, so that it also stays between 0 and 1. We investigate the ability of the isoorbital indicators evaluated in a system with density and paramagnetic current density to reproduce the value of in a system having no paramagnetic current, but the same density . We provide the first example known to us where the Tao–Perdew isoorbital indicator goes outside of the interval from 0 to 1.

The selection of basic variables in current-density-functional theory and formal properties of the resulting formulations are critically examined. Focus is placed on the extent to which the Hohenberg-Kohn theorem, constrained-search approach, and Lieb's formulation (in terms of convex and concave conjugation) of standard density-functional theory can be generalized to provide foundations for current-density-functional theory. For the well-known case with the gauge-dependent paramagnetic current density as a basic variable, we find that the resulting total energy functional is not concave. It is shown that a simple redefinition of the scalar potential restores concavity and enables the application of convex analysis and convex (or concave) conjugation. As a result, the solution sets arising in potential-optimization problems can be given a simple characterization. We also review attempts to establish theories with the physical current density as a basic variable. Despite the appealing physical motivation behind this choice of basic variables, we find that the mathematical foundations of the theories proposed to date are unsatisfactory. Moreover, the analogy to standard density-functional theory is substantially weaker as neither the constrained-search approach nor the convex analysis framework carry over to a theory making use of the physical current density.

We present an analysis of the dispersion interaction energy and forces in density-functional theory from the point of view of the adiabatic connection between the Kohn–Sham non-interacting and fully interacting systems. Accurate coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] densities are computed for the helium dimer and used to construct the exchange-correlation potential of Kohn–Sham theory, showing agreement with earlier results presented for the Hartree–Fock–Kohn–Sham method [M. Allen and D. J. Tozer, J. Chem. Phys. 117, 11113 (2002)10.1063/1.1522715]. The accuracy of the methodology utilized to determine these solutions is checked by calculation of the Hellmann–Feynman forces based on the Kohn–Sham densities, which are compared with analytic CCSD(T) forces. To ensure that this comparison is valid in a finite atomic-orbital basis set, we employ floating Gaussian basis functions throughout and all results are counterpoise corrected. The subtle charge-rearrangement effects associated with the dispersion interaction are highlighted as the origin of a large part of the dispersion force. To recover the exchange-correlation components of the interaction energy, adiabatic connections are constructed for the supermolecular system and for its constituent atoms; subtraction of the resulting adiabatic-connection curves followed by integration over the interaction strength recovers the exchange-correlation contribution relevant to the density-functional description of the dispersion interaction. The results emphasize the long-ranged, dynamically correlated nature of the dispersion interaction between closed-shell species. An alternative adiabatic-connection path is also explored, where the electronic interactions are introduced in a manner that emphasizes the range of the electronic interactions, highlighting their purely long-ranged nature, consistent with the success of range-separated hybrid approaches in this context.