The thermal conductivity of the Earth's core can be estimated from its electrical resistivity via the Wiedemann–Franz law. However, previously reported resistivity values are rather scattered, mainly ...due to the lack of knowledge with regard to resistivity saturation (violations of the Bloch–Grüneisen law and the Matthiessen's rule). Here we conducted high-pressure experiments and first-principles calculations in order to clarify the relationship between the resistivity saturation and the impurity resistivity of substitutional silicon in hexagonal-close-packed (hcp) iron. We measured the electrical resistivity of Fe–Si alloys (iron with 1, 2, 4, 6.5, and 9 wt.% silicon) using four-terminal method in a diamond-anvil cell up to 90 GPa at 300 K. We also computed the electronic band structure of substitutionally disordered hcp Fe–Si and Fe–Ni alloy systems by means of Korringa–Kohn–Rostoker method with coherent potential approximation (KKR-CPA). The electrical resistivity was then calculated from the Kubo–Greenwood formula. These experimental and theoretical results show excellent agreement with each other, and the first principles results show the saturation behavior at high silicon concentration. We further calculated the resistivity of Fe–Ni–Si ternary alloys and found the violation of the Matthiessen's rule as a consequence of the resistivity saturation. Such resistivity saturation has important implications for core dynamics. The saturation effect places the upper limit of the resistivity, resulting in that the total resistivity value has almost no temperature dependence. As a consequence, the core thermal conductivity has a lower bound and exhibits a linear temperature dependence. We predict the electrical resistivity at the top of the Earth's core to be 1.12×10−6Ωm, which corresponds to the thermal conductivity of 87.1 W/m/K. Such high thermal conductivity suggests high isentropic heat flow, leading to young inner core age (<0.85 Gyr old) and high initial core temperature. It also strongly suppresses thermal convection in the core, which results in no convective motion in inner core and possibly thermally stratified layer in the outer core.
•Resistivity of Fe–Si alloys has been measured up to 90 GPa in a DAC.•Resistivity of hcp Fe–Si and Fe–Ni alloys has been calculated by means of KKR-CPA.•Experimental and theoretical results show excellent agreement and indicate resistivity saturation.•The saturation effect leads to the high thermal conductivity of the Earth's core.•The high conductivity strongly suppresses thermal convection in both liquid and solid cores.
First-principles calculation based on density functional theory is a powerful tool for understanding and designing magnetic materials. It enables us to quantitatively describe magnetic properties and ...structural stability, although further methodological developments for the treatment of strongly correlated 4f electrons and finite-temperature magnetism are needed. Here, we review recent developments of computational schemes for rare-earth magnet compounds, and summarize our theoretical studies on Nd
2
Fe
14
B and RFe
12
-type compounds. Effects of chemical substitution and interstitial dopants are clarified. We also discuss how data-driven approaches are used for studying multinary systems. Chemical composition can be optimized with fewer trials by the Bayesian optimization. We also present a data-assimilation method for predicting finite-temperature magnetization in wide composition space by integrating computational and experimental data.
To study the temperature dependence of magnetic properties of permanent magnets, methods of treating the thermal fluctuation causing the thermal activation phenomena must be established. To study ...finite-temperature properties quantitatively, we need atomistic energy information to calculate the canonical distribution. In the present review, we report our recent studies on the thermal properties of the Nd
2
Fe
14
B magnet and the methods of studying them. We first propose an atomistic Hamiltonian and show various thermodynamic properties, for example, the temperature dependences of the magnetization showing a spin reorientation transition, the magnetic anisotropy energy, the domain wall profiles, the anisotropy of the exchange stiffness constant, and the spectrum of ferromagnetic resonance. The effects of the dipole-dipole interaction (DDI) in large grains are also presented. In addition to these equilibrium properties, the temperature dependence of the coercivity of a single grain was studied using the stochastic Landau-Lifshitz-Gilbert equation and also by the analysis of the free energy landscape, which was obtained by Monte Carlo simulation. The upper limit of coercivity at room temperature was found to be about 3 T at room temperature. The coercivity of a polycrystalline magnet, that is, an ensemble of interactinve grains, is expected to be reduced further by the effects of the grain boundary phase, which is also studied. Surface nucleation is a key ingredient in the domain wall depinning process. Finally, we study the effect of DDI among grains and also discuss the distribution of properties of grains from the viewpoint of first-order reversal curve.
Surface magnetism of Fe (001) was investigated by the
in situ
iron-57 probe layer method with a synchrotron Mössbauer source. The observed layer-by-layer internal hyperfine field shows a marked ...reduction at the surface and an oscillatory behavior with increasing depth in the individual layers below the surface. The calculated layer-by-layer hyperfine interactions (hyperfine field, isomer shift, and quadrupole shift) were consistent with the experimental results. The results give direct evidence for the magnetic Friedel oscillations, penetrating several layers from the Fe (001) surface.
The magnetic and magnetocaloric properties of Ni–Co–Mn–(Ga, In, Sn) Heusler intermetallics are discussed on the basis of ab initio and Monte Carlo calculations. The main emphasis is on the different ...reference spin states and magnetic exchange coupling constants of high-temperature austenite and low-temperature martensite which are very important for the calculation of magnetocaloric effect. The origin of metamagnetic behavior is considered in the framework of orbital resolved magnetic exchange parameters of austenite and martensite. The decomposition of exchange constants on orbital contributions has shown that a strong ferromagnetic interaction of magnetic moments in austenite is caused by the more itinerant d-electrons with t2g states while a strong antiferromagnetic interaction in martensite is associated with the more localized eg states. In addition, the appearance of a paramagnetic gap between magnetically weak martensite and ferromagnetically ordered austenite can be realized because of strong competition of magnetic exchange interactions. As a result, large magnetization drop and giant inverse magnetocaloric effect can be achieved across the magnetostructural phase transition.
•The magnetic and magnetocaloric properties of Ni–Co–Mn–(Ga, In, Sn) alloys are discussed.•The metamagnetic behavior results in a jump of magnetization.•The reason of metamagnetism is the antiferromagnetic interaction between Mn atoms.•The size of magnetocaloric effect is determined by the magnetic exchange parameters.
Rare-earth elements like neodymium, terbium and dysprosium are crucial to the performance of permanent magnets used in various green-energy technologies like hybrid or electric cars. To address the ...supply risk of those elements, we applied machine-learning techniques to design magnetic materials with reduced neodymium content and without terbium and dysprosium. However, the performance of the magnet intended to be used in electric motors should be preserved. We developed machine-learning methods that assist materials design by integrating physical models to bridge the gap between length scales, from atomistic to the micrometer-sized granular microstructure of neodymium-iron-boron permanent magnets. Through data assimilation, we combined data from experiments and simulations to build machine-learning models which we used to optimize the chemical composition and the microstructure of the magnet. We applied techniques that help to understand and interpret the results of machine learning predictions. The variables importance shows how the main design variables influence the magnetic properties. High-throughput measurements on compositionally graded sputtered films are a systematic way to generate data for machine data analysis. Using the machine learning models we show how high-performance, Nd-lean magnets can be realized.
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