Quantum Model of Hysteresis in a Single-Domain Magnetically Soft Ferromagnet

A quantum model of a magnetically soft ferromagnet constructed based on a single domain of an α-Fe crystal magnetized to saturation and placed in an alternating magnetic field is suggested. Based on the method of an effective Hamiltonian, the model takes into account the Zeeman energy, the spin-orbital interaction, and the interaction with the crystal field. In order to take into account the magnetic anisotropy, an expansion of a trial single-electron wave function into a series in terms of a small parameter of the spin-orbital interaction is suggested. The nonlinear equations of motion for the magnetization and orbital moment of the domain have been determined within the Heisenberg representation. The parameters of the nonlinear equations have been determined by comparing with the experimental data on the magnetic anisotropy of iron. The equations were solved numerically using the Runge–Kutta method with taking into account the magnetic friction introduced phenomenologically. The dependence of the magnetization of a single domain on the strength of the applied magnetic field has been characterized by hysteresis. The main parameters of the hysteresis loop are in quantitative agreement with the experimentally measured magnetic properties of nanoparticles of iron and iron oxide. A method of simulating the magnetization dynamics of a multidomain ferromagnet in the approximation of a strong crystal field has been suggested.     

Hysteresis minor loop analysis of plastically deformed low-carbon steel

This work investigates applicability of magnetic hysteresis method for non-destructive testing of plastically deformed low-carbon steel. Recently introduced Magnetic Adaptive Testing procedure was used for evaluation of hysteresis minor loop data-sets to find the most sensitive parameter/s for indication of the material degradation stage. Inductive measurements were carried out on two identically degraded series of samples: magnetically closed window-shaped specimens, equipped with the magnetizing and the induction coils, and magnetically open strips, measured by an attached magnetizing yoke. The aim was to compare the results between these sample series in order to determine applicability and limitations of the single-yoke measurement technique. As a result, new magnetic parameters with the best sensitivity–stability ratio in a wide deformation range were introduced and proposed for utilization. Good qualitative coincidence between the measurement results on the closed and the open sample series was obtained in all range of magnetization. Several quantitative distinctions were explained and analyzed in order to improve the single-yoke technique.     

On the Rayleigh law of magnetization: A new mathematical model of hysteresis loops

A mathematical model of magnetic hysteresis loops for weak ac magnetic fields, which is applicable for both symmetrical hysteresis loops that are described by the Rayleigh law of magnetization and asymmetrical loops that are not, has been formulated. The asymmetrical hysteresis loops take place when the ferromagnet is affected, along with an ac magnetizing field, by a dc field. The frequency spectrum of a ferromagnet magnetization has been analyzed as a time function. A technique for experimental determination of parameters that enter into this model is proposed, which uses amplitudes and phases of the first three magnetization harmonic components (the first, the second, and the third ones).     

Stress dependence of ferromagnetic hysteresis loops for two grades of steel

Residual stress is an essential input into calculations of the remaining life of operational plant. However, many life predictions are inherently conservative because measurements of the absolute stress are unavailable. The magnetic properties of material are sensitive to stress, and in this paper, the magnetic properties (at maximum magnetisation, at remnance, and at the coercive field) of two grades of steel (Durehete 1055 and AS1548-7-46OR) under uni-axial stress are presented. The magnetic parameters are more sensitive to compressive stress than to tensile stress. A mathematical model using the Jiles–Atherton theory for ferromagnetic hysteresis is used to explain the trends in the experimental data. The ability of magnetic techniques to measure stress is demonstrated.     

Alternative magnetic parameters for characterization of plastic tension

The applicability of magnetic techniques (hysteresis and Barkhausen noise) in the detection of plastic deformation was comprehensively studied. Structural low-carbon steel subjected to uniaxial plastic tension was accurately measured for a wide range of residual strains and at different magnetization angles with respect to the stress direction. In addition to classical magnetic parameters, new quantities with better sensitivity-stability ratios were introduced on the basis of two-phase remagnetization caused by compressive residual stress. The magnetic methods had highest sensitivity in the deformation direction (hard magnetization axis). The parameters changed as cos² with rotation to the perpendicular easy magnetization axis, where the magnetic sensitivity was lowest. In this direction, only the root mean square value of Barkhausen noise considerably changed with the strain. The extremes of the Barkhausen parameters with respect to the magnetization angle did not exactly correspond to the hysteresis extremes (real easy and hard magnetization axes) in that there was a shift of about ±10°.     

Velocity effect analysis of dynamic magnetization in high speed magnetic flux leakage inspection

The investigation described in this paper focuses on the velocity effect of dynamic magnetization and magnetic hysteresis due to rapid relative motion between magnetizer and measured specimens in high-speed magnetic flux leakage (MFL) inspection. Magnetization intensity and permeability of ferromagnetic materials along with the duration of dynamic magnetization process were analyzed. Alteration of the intensity and distribution of magnetic field leakage caused by permeability of specimen were investigated via theoretical analysis and finite-element method (FEM) combined with the actual high-speed MFL test. Following this, a specially designed experimental platform, in which motion velocity is within the range of 5 m/s–55 m/s, was employed to verify the velocity effect and probability of a high-speed MFL test. Preliminary results indicate that the MFL technique can achieve effective defect inspection at high speeds with the maximum inspection speed of about 200 km/h being verified under laboratory conditions.     

M7C3的形态分布对铁基复合层耐磨性能的影响

研究了在电磁搅拌的作用下,硬质相M7C3(主要是(Fe, Cr)7C3和Cr7C3)的数量和形态分布对堆焊层金属耐磨性的影响规律.对堆焊试件进行耐磨、硬度试验,并采用SEM,XRD对堆焊进行显微组织和成分分析.发现随着磁场参数的改变,硬质相M7C3由杂乱无章的分布逐渐转变为较规则的六方块状分布,堆焊层金属的耐磨性也随之增强;当磁场电流为3A,磁场频率为10Hz时,堆焊层金属的性能达到最佳状态,此时堆焊层中硬质相(M7C3)均成较规则的六方块状分布.结果表明,在适当的磁场参数作用下,硬质相(M7C3)成较规则的六方块状分布可以显著的提高堆焊层金属的耐磨性.     

纳秒激光微刻蚀取向硅钢的形貌特征及磁性能

为有效降低取向硅钢铁损、改善其磁性能，采用红外纳秒激光对取向硅钢进行微刻蚀试验。利用3D共聚焦显微镜、扫描电镜与能谱仪研究典型工艺参数下的硅钢表面烧蚀形貌特征及表面质量，利用铁损仪测试不同刻蚀参数下取向硅钢的铁损、相对磁导率等磁性能参数及动态磁滞回线，对比分析刻痕前后磁性能的变化行为、规律及磁滞特性。结果表明：激光刻痕后，硅钢的铁损、相对磁导率、矫顽力及剩磁等性能得到明显改善，铁损的改善表现在高磁感强度下、相对磁导率的改善表现在低磁场强度下，回线特性得到优化。扫描速度为800 mm/s、脉冲能量为0.25 mJ时，刻痕边界呈近似规则的“波浪线”，且刻痕表面质量较高，铁损降低高达11.6%、剩磁降低12.8%等；刻痕后相对相对磁导率明显提高，提高约为5.7%~15.16%，最大可达2.598×10⁴。激光频率与扫描速度的耦合关系是影响刻痕边界形状与磁畴细化效果的重要因素。     

Magnetic transitions and magnetocaloric effect in MnAs0.9P0.1

The compound MnAs0.9P0.1 exhibits a multistep magnetic order-order transition from a helimagnetic γ-phase with Hα-type magnetic order to a ferromagnetic β-phase at 80 K and then to a helimagnetic α-phase at 203 K. The γ-β transition exhibits the characteristics of a first-order transition with a thermal hysteresis as large as 6 K, while the β-α transition is of second order with a thermal hysteresis smaller than 2 K and without magnetic hysteresis. With these two successive helimagnetism-related transitions, magnetic-entropy changes of -2.1 J/(kg·K) at 203 K for a field change from 0 to 5 T and 0.1 J/(kg·K) at 83 K for a field change from 0 to 1 T are obtained. Investigation of the magnetocaloric effect associated with a transition from Hα-type magnetic order to FM order may open a new route to explore candidates for magnetic refrigeration.     

Implementation procedure for the generalized moving Preisach model based on a first order reversal curve diagram

Ftrst order reversal curves (FORC) of nanoeomposite Nd2Fe14B/Fe3B magnetic materials were measured to attain a FORC diagram, which characterizes reversible magnetization, irreversible magnetization, and magnetic interactions in a hysteresis system. Then, generalized mov-ing Preisach model (GMPM) was implemented based on the FORC diagram. Reversible and irreversible magnetizations shown in FORCs and a FORC diagram were used as an input of GMPM. Coupling interaction between reversible and irreversible magnetizations was added when calculating reversible magnetization. Meanwhile, irreversible magnetic moments' interaction was approximately represented by mean field interaction. The result shows that the simulated main curves mostly coincide with the experimental curves.     

电磁材料的电磁参数及测量

本文主要介绍了电磁材料的磁滞回线及电阻率与磁阻几种电磁参数以及它们的测量方法。用磁通计测量磁滞回线从而得到其他参数如饱和磁化强度、矫顽力以及磁导率等。凯尔文直流双臂电桥具有灵敏度高、读数准确和使用方便的优点，是测量材料电阻率和磁阻的有效工具。     

Assessments of coefficients of linear thermal expansions for magnetic elements Fe,Co and Ni

The coefficients of linear thermal expansions(CLEs) of magnetic elements Fe, Co and Ni were assessed from experimental information using theoretical models combined with MATLAB calculations. Model parameters can be determined accurately, and the assessed data are in good agreement with the experimental results. To facilitate the assessments, theories of thermal expansion were applied to separate CLEs into its nonmagnetic and magnetic components. The calculations of nonmagnetic contribution to CLEs were based on the modified Gru¨ neisen–Debye model, in which the Debye temperature was regarded as an undetermined constant. In order to put the prediction of CLEs at the magnetic transition region on a sound physical basis, two kinds of theoretical models were innovatively used to calculate the magnetic contribution to CLEs, i.e., the Bragg–Williams model and the Fermi–Dirac distribution function. Model parameters were evaluated from experimental data using least square method. Detailed comparisons were made with the published experimental data and the calculated total CLEs. A satisfactory agreement is reached.     

Magnetic losses and their components in rapidly quenched magnetically soft Fe-based alloys

Studying the dependence of the specific magnetic losses on the frequency and induction of magnetically soft electricotechnical materials has shown the inefficiency of the conventional method of separation of the specific magnetic losses into components. For example, according to the conventional technique, one can find that there are ranges of frequencies where the total magnetic losses are smaller than the hysteresis component; besides, at comparatively high inductions it is possible to reduce the dynamic component of magnetic losses to virtually zero. The investigation carried out allowed us to suggest a new method of separation of magnetic losses into components taking into account a frequency dependence of the hysteresis losses. The results of the analysis of the magnetic-loss components in the context of the suggested method for ribbons of rapidly quenched soft magnetic alloys allowed us to eliminate the contradictions revealed. Besides, they have shown that the formation of a low-frequency resonance peak of absorption in the region of displacement of 180° domain walls is mainly caused by the frequency-dependent component of the hysteresis losses, whereas in the interval of inductions where the processes of displacement of 90° domain walls are active, this formation is caused by both the dynamic and frequency-dependent hysteresis components of magnetic losses.     

Correlation between the stress-strain state parameters and magnetic characteristics of carbon steels

A method for reconstruction of the stress-strain diagrams of steel objects from their magnetic characteristics determined directly during tension has been suggested. The coercive force, residual induction in the major hysteresis loops, and the maximum magnetic permeability are recommended as parameters for nondestructive testing of stresses and strains.     

Magnetic properties and microstructure of nanocrystalline soft magnetic Fe73.5−x Co x Cu1Nb3Si13.5B9 alloys

The influence of the annealing temperature, cooling rate, and magnetic field frequency in thermomagnetic treatment on the magnetic parameters of nanocrystalline Fe_73.5?x Co _x Cu₁Nb₃Si_13.5B₉ (x=0, 10, 20, and 30) alloys has been investigated. It has been revealed that a thermomagnetic treatment in a dc magnetic field of the nanocrystalline alloys containing cobalt leads to a shift of their hysteresis loop. With increasing Co content in the alloy, the shift of the hysteresis loop increases. This fact is, apparently, connected with the precipitation of α-Co and β-Co clusters and (Fe,Co)₃Si and (Fe,Co)₂B nanophases in which the magnetization direction is determined by the direction of the magnetic field during treatment.     

Magnetic property and magnetocaloric effect in TmCoAl compound

A large reversible magnetocaloric effect accompanied by a second order magnetic phase transition from paramagnetic (PM) to ferromagnetic (FM) has been observed in TmCoAl intermetallic compound. For the magnetic field change of 5 T, the maximum value of magnetic entropy change (−ΔS_M^max) and the value of refrigerant capacity (RC) are evaluated to be 18.2 J/kg K and 211 J/kg, respectively. In particular, a large −ΔS_M^max (10.2 J/kg K) is achieved at 7.5 K under a low magnetic field change from 0 to 2 T with no thermal hysteresis and magnetic hysteresis loss. The large reversible magnetocaloric effect (both the large −ΔS_M and the high RC) indicates that TmCoAl is one of a promising material for magnetic refrigeration in low temperature.     

Ni52Mn21+xGa27-x(x=0-5)磁性形状记忆合金的相变

研究了非化学计量成分的多晶Ni52Mn21+xGa27-x(x=0-5)系列合金的热弹性马氏体相变和磁相变.合金的马氏体相变温度Ms随Mn含量的增加而升高,当x＞4时,Ms已经升高到室温以上,而马氏体相变滞后△T随z的增大而减小;合金的磁相变温度TC随z增加而升高,但变化范围不大,在z＞2后,Tc保持在348 K左右.实验获得了一种具有实用前景的合金成分--Ni52Mn25Ga23合金,其马氏体相变温度在室温以上,相变滞后仅为5 K.     

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 一阶回转曲线（first order reversal curve 简称FORC）图谱法被视为研究滞后效应领域中的“指纹鉴定”，受到了地质学界和物理学界的科学家极大的关注。在磁滞后系统中，FORC图谱可以相当敏感地表征磁性颗粒间的交换作用和矫顽力的分布情况，并且能够对磁化过程中的动态问题如不同的磁场变化速率等情况做出精确的分析。FORC图谱法也可应用到其它有滞后效应的领域如铁电滞后、热滞后、弹性滞后等。文章将从磁性领域入手，通过比较Preisach模型引入FORC图谱法，利用Takacs模型验证FORC图谱的计算过程，并列举出FORC图谱在纳米双相磁性材料的应用。     

A study of microstructural analysis for nondestructive evaluation of thermal annealing using magnetic properties

Two kinds of thermally aged Fe-Cu alloys with different Cu proportions 0.05% and 0.45% were prepared and their magnetic properties were investigated to apply magnetic nondestructive testing techniques for the assessment of irradiation embrittlement of materials. Initially, the alloy is 10% cold rolled and then isothermally aged at 500 °C and 400 °C with different aging time up to 1000 h in order to create Cu-precipitates in the Fe metal matrix. The hysteresis loop (HL), Barkhausen noise (BN) and Magnetic Adaptive Testing (MAT) parameter were measured for magnetic properties studies and mechanical properties were investigated by Vickers hardness. The HL, BN were decreased and the MAT parameter was increased by thermal aging. The changes of these parameters were explained by copper rich precipitations (CRPs) formation, interaction with domain walls and dislocation movement pinned by CRPs. It was confirmed by TEM and EDX analysis.     

基于响应面法的钛合金Halbach阵列增强磁流变抛光工艺参数优化

目的 提高钛合金磁流变抛光的表面质量和抛光效率。方法 用Halbach磁场阵列强化磁场,通过载液盘与磁铁反向旋转来增强磁流变抛光效率,使抛光头拥有更强的恢复性与自锐性。通过仿真模拟和实际测量对比研究Halbach阵列与N-S阵列的磁场分布和磁场梯度。依照试验结果描述抛光剪切力、表面粗糙度与表面微观形貌随时间的变化规律。采用响应面法优化载液盘转速、磁铁转速和加工间距等3个工艺参数,建立剪切力和表面粗糙度的拟合方程数学预测模型,并对其中的不显著项进行优化。结果 在响应面交互作用分析中,工艺参数对剪切力的影响的大小顺序为加工间距、磁铁转速、载液盘转速;对表面粗糙度影响的大小顺序为载液盘转速、磁铁转速、加工间距。根据不同的需求,确定选定范围内的工艺参数组合,需要快速去除材料时,使剪切力趋于最大值的工艺参数组合为载液盘转速227 r/min,磁铁转速64 r/min,加工间距0.1 mm,通过20 min抛光后得到了表面粗糙度Sa为34.911 nm的光滑表面。抛光过程中,钛合金抛光所受剪切力τ为0.812 N。需要最优表面质量时,使表面粗糙度值趋于最小值的工艺参数组合为载液盘转速300 r/min,磁铁转速150 r/min,加工间距0.1 mm,通过20 min抛光后得到了表面粗糙度Sa为26.723 nm的光滑表面。抛光过程中,钛合金抛光所受剪切力τ为0.796 N。结论 Halbach阵列拥有较高的磁场强度和富有空间变化的磁感线,能够使磁流变液中的磁链呈现出更多的姿态变化。根据响应面法优化后的剪切力和表面粗糙度预测模型,预测结果与验证试验结果相差很小,预测模型的准确度与可信度较高。