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Structure, Curie temperature, and magnetostriction have been systemically investigated for Tb_0.27Dy_0.73 Fe_1.9+xTi_0.05 compounds using X-ray diffraction, vibrating sample magnetometer, and standard strain gauge technique. The samples show pure MgCu₂-type Laves phase when x≥0.2, and a small amount of second phases appear when x>0.2. The lattice parameters and the Curie temperatures change modestly with increasing Fe content. The magnetostriction of Tb_0.27Dy_0.73Fe_1.9+xTi_0.05 compounds shows strong dependence on Fe content.

Giant magnetostrictive (Tb_0.28Dy_0.72)Fe_1.90 thin films were deposited on Si (111) substrates at room temperature by pulsed laser deposition (PLD). The crystalline state and the magnetic properties of the samples were investigated in relation to the different annealing temperatures T_a, which varied between 623K and 923K. X-ray diffraction results indicated the films are in amorphous state after annealing at T_a = 623K-823K for 1h, and were partially crystallized at T_a = 923K for 1h. Meanwhile, the annealing treatment showed a great influence on the magnetic anisotropy. The orientation of the magnetic easy axis of the as-deposited films changed from perpendicular to parallel to the film plane after annealing treatment. The mechanism of the transformation of the magnetic easy axis was explained in terms of the tensile stress which is formed due to the difference in the thermal expansion coefficients of the thin film and substrate.

Fe-Ga thin films were prepared by DC magnetron sputtering on Si (100) substrate and an alloy target consisting of Fe₈₁Ga₁₉ was used. X-ray diffraction techniques were used to quantify the strain in the Fe-Ga thin films by measuring the interplanar spacings of select crystallographic planes. The interplanar spacing, d, for the family of Fe-Ga {211} planes was measured. Using the well-established sin²ψ technique, the residual stress of the Fe-Ga thin films was calculated. It has been found that the stress for Fe-Ga thin films quickly increases with increasing the sputtering power. The residual stress of thin films is almost unchanged in the range of 220-440 nm, and then it decreases with increasing the thickness of thin films.

In order to study the microstructure of Fe–Ga alloy, Fe₈₅Ga₁₅ ribbons prepared with different wheel velocity were studied by high resolution X-ray diffraction (HRXRD) and extend X-ray absorption fine structure (EXAFS). HRXRD patterns showed that only disordered A₂ phase was observed in as-cast Fe₈₅Ga₁₅ alloy. A modified-DO₃ phase was detected in all of the melt spun samples. The HRXRD associated with EXAFS results indicated that Ga atoms were located as second-nearest neighbor along [100] orientation. A little DO₃ phase was found in ribbons annealed at 1000°C under 0.06 MPa Ar atmosphere. The result of magnetostriction measurement revealed that in the ribbon prepared with higher wheel velocity, more modified-DO₃ phase will enhance the magnetostriction. DO₃ phase in the annealed sample will deteriorate the magnetostrictive properties of Fe–Ga ribbons.

An epoxy-resin bonding route was used to produce composite rods of the highly magnetostrictive alloys Tb_1-xNd_x(Fe_0.8Co_0.2)_1.93 (0.20 ≤ x ≤ 0.75). The structure, spin configuration, magnetostriction and particle size are investigated by means of X-ray diffraction (XRD), a standard strain technique and scanning electron microscope (SEM). The epoxy-bonded 0–3 type and pseudo 1–3 type composites are successfully fabricated, respectively. XRD analysis shows that the easy magnetization direction (EMD) for the alloy of x = 0.20 lies along 〈111〉 axis. The magnetic curing field makes the particles align as a particulate chain and also causes the particles rotating along its EMD direction. The pseudo 1–3 type epoxy-bonded composite has a larger magnetostriction than that of the 0–3 type composite, which can be attributed to the larger magnetostriction coefficient λ₁₁₁, EMD lying along 〈111〉 direction, the 〈111〉-textured orientation and the chain structure. A large saturation magnetostriction (λ_0S ~ 570 ppm) is achieved for the 1–3 type epoxy/Tb_0.35Nd_0.65(Fe_0.8Co_0.2)_1.93 composite (about 150–250 μm, 10 kOe), which approaches 70% of its monolithic alloy. Furthermore, it only contains 27 vol.% alloy particles in the insulating epoxy matrix and performs a low magnetic anisotropy, which could make it technologically interesting for the field of Nd-containing magnetostrictive materials.

This paper presents comparison of magnetoelastic properties between the 〈110〉 oriented Tb_xDy_1-xFe_1.95 polycrystalline alloys for x = 0.27, 0.3, 0.45 under coupled loading of magnetic field and compressive stress. The simultaneously measure are investigated for the magnetization and magnetostriction under applied magnetic field from -200 to 200 kA/m and compressive stress from 0 to 50 MPa along the rod axis at room temperature. The results show that, according to the increase of Tb concentration and compressive stress, the hysteresis, coercive force and magnetostriction hysteresis loops of Tb_xDy_1-xFe_1.95 alloys increase rapidly and the distortion of the hysteresis loops occurs at higher compressive stress, especially Tb_0.45Dy_0.55Fe_1.95 alloys, while the maximum relative permeability of Tb_xDy_1-xFe_1.95 alloys monotonously decrease. Meanwhile, the higher the Tb concentration the stronger is magnetostrictive "jump" effect. For these experimental results, the effect of compressive stress and Tb/Dy ratio on magnetoelastic properties of Tb_xDy_1-xFe_1.95 alloys are coupling and remarkable. A tradeoff and optimization are very important for many engineering designs and applications.

The magnetoelectric (ME) effect in a ME composite structure in which a magnetostrictive component is bonded with a piezoelectric component was studied theoretically, based on the hyperbolic nonlinear constitutive relation of magnetostriction and the piezoelectric equations. A quantitative relation was established analytically for the ME effect and the influencing factors, such as the magnetic bias field and the structure dimensions. It was verified that the theoretical model agrees qualitatively with the experimental results published in Ref. 7. It can also be predicted by the model that the ME effect can be improved by optimizing the structure dimensions.

The structural and magnetoelastic properties of polycrystalline samples of Y₃Fe_27.2Cr_1.8 and Ce₃Fe₂₅Cr₄ intermetallic compounds are investigated by means of X-ray diffraction, thermomagnetic, thermal expansion and magnetostriction measurements in the temperature range of 77–500 K under applied magnetic fields up to 1.5 T. The well defined anomalies observed in the linear thermal expansion coefficient curves are associated with the magnetic phase transitions and presence of small amounts of 1:12 phase in the Ce₃Fe₂₅Cr₄ sample; the latter is also confirmed by AC susceptibility measurements. For Y₃Fe_27.2Cr_1.8, saturation behavior is observed in the anisotropic magnetostriction isotherms near the magnetic ordering temperature (T_C), whereas for Ce₃Fe₂₅Cr₄ compound, saturation starts well below T_C. The additional anomalies observed in the volume magnetostriction isotherms of both compounds are explained based on the anisotropy field in the a–b plane and along the c-axis of the unit cell.

This paper presents the magnetoelastic properties for the relative high Tb/Dy composition ratio 〈110〉 oriented Tb_0.45Dy_0.55Fe_1.95 polycrystalline alloys. The simultaneous measurements of the magnetization and magnetostriction are carried out as a function of applied magnetic field range of 0 to 800 kA/m and compressive stress from 0 to 60 MPa. The maximum piezomagnetic coefficient $(d^{\rm max}_{33})$ and magnetostriction hysteresis (W_h) are obtained by differential calculation from the experimental curves. According to the increase of compressive stress, an obvious magnetostriction "jump" effect is observed, and the magnetostriction with the magnetic field of 800 kA/m (λ⁸⁰⁰) and magnetostriction hysteresis monotonously increase, while the maximum piezomagnetic coefficient increases first from 0 to 10 MPa and then decreases from 10 to 60 MPa. Here, results of measuring and calculating on this material are important complement to further understand the rules of the magnetoelastic properties in high Tb/Dy composition ratio Tb_0.45Dy_0.55Fe_1.95 polycrystalline alloys for theoretical approaches and modern technology applications.

A BiFeO₃ thin film was prepared on the (111) Pt/Ti/SiO₂/Si substrate by the solution coating method. In order to detect the effect of an external magnetic field on the BiFeO₃ thin film, a fine scan X-ray diffraction with a scan ratio of 0.002°/s was carried out under the magnetic field parallel to the film surface. The result of the in situ analysis of X-ray diffraction for the thin film in the magnetic field indicates that the magnetic field leads to an increase of the integral intensity ratio of compared with that under no magnetic field. The increase of implies a domain switching under the magnetic field, where the domain switching comes from the decreasing residual tensile stress induced by the magnetostriction of BiFeO₃ in the magnetic field.

In this paper, the magnetostriction and stress of an orthotropic mechanical high-temperature superconducting disk with a concentric small hole are investigated based on the exponential model of the critical state. Approximate solutions of the displacement and stress for the superconducting disk during zero-field cooling (ZFC) and field-cooling (FC) processes are obtained. The results show that tensile stresses will appear in the disk during the decreasing field of ZFC, while the stresses are always compressive during the increasing field of ZFC and FC processes. This indicates that the superconducting disk is easily damaged during the decreasing field of ZFC and FC processes. The critical point where tensile stress is largest is provided. The value of magnetostriction depends on the size of the disk, the applied field and the magnetization process. This research is helpful in the reliability design of high-temperature superconducting disks and cables with high strength for space solar power stations.

Based on the magnetic dipole theory and the elastic mechanical plane strain method, this paper establishes a multi-chain model of ferromagnetic particle inclusions–superconducting matrix and investigates the effects of the distribution form of ferromagnetic particle inclusions and elastic parameters on the effective magnetostriction of superconductors. A dimensionless parameter is introduced to describe the spatial distribution form of ferromagnetic particles in the matrix, and the calculation is carried out using the elastic mechanical plane strain method. The change of the effective magnetostriction following the elastic parameter is given for three kinds of distribution forms: single-chain, planar–laminar, and spatial three-dimensional multi-chain, respectively. The results show that the distribution of ferromagnetic particle inclusions and the change of elastic parameters have a notable influence on the displacement and magnetostrictive distribution of superconductors.

We present a mathematical model for linear magneto-electro-thermo-elastic continua, as sensors and actuators can be thought of, and prove the well-posedness of the dynamic and quasi-static problems. The two proofs are accomplished, respectively, by means of the Hille–Yosida theory and of the Faedo–Galerkin method. A validation of the quasi-static hypothesis is provided by a nondimensionalization of the dynamic problem equations. We also hint at the study of the convergence of the solution to the dynamic problem to that to the quasi-static problem as a small parameter — the ratio of the largest propagation speed for an elastic wave in the body to the speed of light — tends to zero.

The thermodynamic model of viscoelastic deformable magnetic materials at finite strains is formulated in a fully Eulerian way in rates. The Landau theory applied to a ferro-to-paramagnetic phase transition, the gradient theory (due to an exchange energy) for magnetization with general mechanically dependent coefficient, hysteresis in magnetization evolution by the Gilbert equation involving an objective corotational time derivative of magnetization, and the demagnetizing field are considered in the model. The Kelvin–Voigt viscoelastic rheology with a higher-order viscosity (exploiting the concept of multipolar materials) is used, allowing for physically relevant frame-indifferent stored energies and for local invertibility of deformation. The model complies with energy conservation and Clausius–Duhem entropy inequality. An existence and a certain regularity of weak solutions are proved by a Faedo–Galerkin semi-discretization and a suitable regularization.

Vibration energy is scavenged by a beam system based on magnetostrictive material (MsM). The system consists of interconnected substructural beams (aluminum and magnetostrictive layers) with a neutral stress axis shifted away from the axis of symmetry of the magnetostrictive beam. The coil that generates the electromotive force is wound on the composite beam. The study investigates the effects of a tip mass placed at the end of the beam and the beam thickness influence. Multiple solutions are found for high amplitudes, and the optimal configuration of the operating conditions is proposed. In addition, the sensitivity of the system to the initial conditions is compared for the first three resonance areas, leading to determination of two types of solutions with different levels of power output.

In this paper, as a theoretical basis, a foot vibration harvester with a finite support mechanism is proposed based on the Villari effect of magnetostrictive materials and Faraday’s law of electromagnetic induction, where a rod-shaped Terfenol-D is used as a core element for energy conversion, and a multi-stage force amplification mechanism is used as a core mechanical structure. The purpose of the amplification mechanism is to amplify the input force provided to the Terfenol-D rod and increase the output electric power. Moreover, the amplification mechanism is designed based on the bridge amplification structure, microlever amplification structure, and wedge amplification mechanism. A mathematical model of the amplification mechanism was developed using the force analysis and unit stiffness matrix methods, and the size and structure were designed and optimized. The performed simulations yielded an output force amplification ratio of 18.04. Based on the optimization results, a prototype was fabricated, and experiments were conducted. Specifically, experiments on the effect of the bias magnetic field on the harvester’s harvesting capability were performed, and the operating characteristics were tested for one complete cycle. Moreover, the effects of the amplification mechanism and vibration harvester were tested for practical applications. The peak output voltage of the harvester was 397.5mV under 100 N excitation, and the output electrical power on a resistive load could reach 3.33mW. In the application of the human walking process, the voltage could reach a maximum value of 387.3mV. The results of the study initially prove that the designed vibration harvester can stably collect human walking vibration.

We present transport measurements performed on systems of granular ferromagnets (Ni). The samples are prepared by quench condensation, i.e., evaporation of discontinuous films on a substrate held at cryogenic temperatures within the measurement apparatus. This technique enables us to study the magnetotransport properties of unique geometries such as dilute granular films, 1D chains of grains and tunnel junction into a granular system with extremely sensitive control over the grain distance. The granular structures exhibit a unique response of the electric properties to magnetic field which is ascribed to mechanical changes of the grain geometries due to magnetic interactions. We discuss the merits of this phenomenon and suggest that it has potential for future magnetomechanical-based devices.

Filled with certain amount of magnetic particles, an elastomer can be made magneto active for numerous applications. When a magneto-active elastomer (MAE) is subject to a homogeneous magnetic field, both magnetostriction and field-stiffening effect can be observed. Inspired by experimental observations and microstructure simulations in the literature, this paper presents a simplified phenomenological model for MAEs by considering a uniaxial deformation state. The model hypothesizes the field-stiffening effect to be a direct consequence of the inverse magnetostriction, i.e., the strain-dependent magnetization, in the context of finite deformation. By taking the elastic energy to be independent of magnetic field and the magnetization energy to be strain dependent, the model can capture both magnetostriction and field stiffening of an MAE. The functional form of the strain-dependent magnetization energy is determined by the underlying microstructure. MAEs with different microstructures exhibit different magnetostriction and field-stiffening behaviors. To predict the behavior of a specific MAE, one only needs to measure the effective permeability of an MAE as a function of the axial strain. The mathematical simplicity of the model could enable simulation and optimization of MAE-based devices under complex loading conditions.

We investigated how high magnetic field gradients affected the magnetostrictive performance of Tb${}_{0.27}$Dy${}_{0.73}$Fe${}_{1.95}$ during solidification. At high applied magnetic field gradients, the magnetostriction exhibited a gradient distribution throughout the alloy. Increasing the magnetic field gradient also increased the magnetostriction gradient. We attributed the graded magnetostrictive performance to the gradient distribution of (Tb, Dy)Fe₂ phase in the alloy and its orientation.

Magnetostrictive property shows anisotropic characteristics, which are related to phase structure and crystal orientation. In this paper, phase structures and magnetostrictive properties of Fe${}_{71.3}$Ga${}_{28.7}$ at different solidification rates during zone-melting directional solidification were studied. Results show that when the solidification rate exceeds 72 mm/h, the sample has a single A2 structure. A multiphase structure of D0₃ and A2 is formed when the solidification rate is 36 mm/h. The multiphase structure of L1₂ and A2 emerges in the sample prepared with a solidification rate of 18 mm/h. The samples with L1₂ and A2 multiphase structure have excellent low-field magnetostrictive properties, reaching 68 × 10${}^{-6}$ under a magnetic field of 20 kA/m.