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Magnetostriction
Magnetostriction
Magnetostriction
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Magnetostriction is a property of magnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation of materials' magnetization due to the applied magnetic field changes the magnetostrictive strain until reaching its saturation value, λ. The effect was first identified in 1842 by James Joule when observing a sample of iron.[1]

Magnetostriction applies to magnetic fields, while electrostriction applies to electric fields.

Magnetostriction causes energy loss due to frictional heating in susceptible ferromagnetic cores, and is also responsible for the low-pitched humming sound that can be heard coming from transformers, where alternating currents produce a changing magnetic field.[2]

Explanation

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Internally, ferromagnetic materials have a structure that is divided into domains, each of which is a region of uniform magnetization. When a magnetic field is applied, the boundaries between the domains shift and the domains rotate; both of these effects cause a change in the material's dimensions. The reason that a change in the magnetic domains of a material results in a change in the material's dimensions is a consequence of magnetocrystalline anisotropy; it takes more energy to magnetize a crystalline material in one direction than in another. If a magnetic field is applied to the material at an angle to an easy axis of magnetization, the material will tend to rearrange its structure so that an easy axis is aligned with the field to minimize the free energy of the system. Since different crystal directions are associated with different lengths, this effect induces a strain in the material.[3]

The reciprocal effect, the change of the magnetic susceptibility (response to an applied field) of a material when subjected to a mechanical stress, is called the Villari effect. Two other effects are related to magnetostriction: the Matteucci effect is the creation of a helical anisotropy of the susceptibility of a magnetostrictive material when subjected to a torque and the Wiedemann effect is the twisting of these materials when a helical magnetic field is applied to them.

The Villari reversal is the change in sign of the magnetostriction of iron from positive to negative when exposed to magnetic fields of approximately 40 kA/m.

On magnetization, a magnetic material undergoes changes in volume which are small: of the order 10−6.

Magnetostrictive hysteresis loop

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Magnetostrictive hysteresis loop of Mn-Zn ferrite for power applications measured by semiconductor strain gauges

Like flux density, the magnetostriction also exhibits hysteresis versus the strength of the magnetizing field. The shape of this hysteresis loop (called "dragonfly loop") can be reproduced using the Jiles-Atherton model.[4]

Magnetostrictive materials

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Cut-away of a transducer comprising: magnetostrictive material (inside), magnetising coil, and magnetic enclosure completing the magnetic circuit (outside)

Magnetostrictive materials can convert magnetic energy into kinetic energy, or the reverse, and are used to build actuators and sensors. The property can be quantified by the magnetostrictive coefficient, λ, which may be positive or negative and is defined as the fractional change in length as the magnetization of the material increases from zero to the saturation value. The effect is responsible for the familiar "electric hum" (Listenⓘ) which can be heard near transformers and high power electrical devices.

Cobalt exhibits the largest room-temperature magnetostriction of a pure element at 60 microstrains. Among alloys, the highest known magnetostriction is exhibited by Terfenol-D, (Ter for terbium, Fe for iron, NOL for Naval Ordnance Laboratory, and D for dysprosium). Terfenol-D, TbxDy1−xFe2, exhibits about 2,000 microstrains in a field of 160 kA/m (2 kOe) at room temperature and is the most commonly used engineering magnetostrictive material.[5] Galfenol, FexGa1−x, and Alfer, FexAl1−x, are newer alloys that exhibit 200-400 microstrains at lower applied fields (~200 Oe) and have enhanced mechanical properties from the brittle Terfenol-D. Both of these alloys have <100> easy axes for magnetostriction and demonstrate sufficient ductility for sensor and actuator applications.[6]

Schematic of a whisker flow sensor developed using thin-sheet magnetostrictive alloys.

Another very common magnetostrictive composite is the amorphous alloy Fe81Si3.5B13.5C2 with its trade name Metglas 2605SC. Favourable properties of this material are its high saturation-magnetostriction constant, λ, of about 20 microstrains and more, coupled with a low magnetic-anisotropy field strength, HA, of less than 1 kA/m (to reach magnetic saturation). Metglas 2605SC also exhibits a very strong ΔE-effect with reductions in the effective Young's modulus up to about 80% in bulk. This helps build energy-efficient magnetic MEMS.[citation needed]

Cobalt ferrite, CoFe2O4 (CoO·Fe2O3), is also mainly used for its magnetostrictive applications like sensors and actuators, thanks to its high saturation magnetostriction (~200 parts per million).[7] In the absence of rare-earth elements, it is a good substitute for Terfenol-D.[8] Moreover, its magnetostrictive properties can be tuned by inducing a magnetic uniaxial anisotropy.[9] This can be done by magnetic annealing,[10] magnetic field assisted compaction,[11] or reaction under uniaxial pressure.[12] This last solution has the advantage of being ultrafast (20 min), thanks to the use of spark plasma sintering.

In early sonar transducers during World War II, nickel was used as a magnetostrictive material. To alleviate the shortage of nickel, the Japanese navy used an iron-aluminium alloy from the Alperm family.

Mechanical behaviors of magnetostrictive alloys

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Effect of microstructure on elastic strain alloys

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Single-crystal alloys exhibit superior microstrain, but are vulnerable to yielding due to the anisotropic mechanical properties of most metals. It has been observed that for polycrystalline alloys with a high area coverage of preferential grains for microstrain, the mechanical properties (ductility) of magnetostrictive alloys can be significantly improved. Targeted metallurgical processing steps promote abnormal grain growth of {011} grains in galfenol and alfenol thin sheets, which contain two easy axes for magnetic domain alignment during magnetostriction. This can be accomplished by adding particles such as boride species [13] and niobium carbide (NbC) [14] during initial chill casting of the ingot.

For a polycrystalline alloy, an established formula for the magnetostriction, λ, from known directional microstrain measurements is:[15]

λs = 1/5(2λ100+3λ111)

Magnetostrictive alloy deformed to fracture

During subsequent hot rolling and recrystallization steps, particle strengthening occurs in which the particles introduce a "pinning" force at grain boundaries that hinders normal (stochastic) grain growth in an annealing step assisted by a H2S atmosphere. Thus, single-crystal-like texture (~90% {011} grain coverage) is attainable, reducing the interference with magnetic domain alignment and increasing microstrain attainable for polycrystalline alloys as measured by semiconducting strain gauges.[16] These surface textures can be visualized using electron backscatter diffraction (EBSD) or related diffraction techniques.

Compressive stress to induce domain alignment

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For actuator applications, maximum rotation of magnetic moments leads to the highest possible magnetostriction output. This can be achieved by processing techniques such as stress annealing and field annealing. However, mechanical pre-stresses can also be applied to thin sheets to induce alignment perpendicular to actuation as long as the stress is below the buckling limit. For example, it has been demonstrated that applied compressive pre-stress of up to ~50 MPa can result in an increase of magnetostriction by ~90%. This is hypothesized to be due to a "jump" in initial alignment of domains perpendicular to applied stress and improved final alignment parallel to applied stress.[17]

Constitutive behavior of magnetostrictive materials

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These materials generally show non-linear behavior with a change in applied magnetic field or stress. For small magnetic fields, linear piezomagnetic constitutive[18] behavior is enough. Non-linear magnetic behavior is captured using a classical macroscopic model such as the Preisach model[19] and Jiles-Atherton model.[20] For capturing magneto-mechanical behavior, Armstrong[21] proposed an "energy average" approach. More recently, Wahi et al.[22] have proposed a computationally efficient constitutive model wherein constitutive behavior is captured using a "locally linearizing" scheme.

Applications

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See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Magnetostriction

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Magnetostriction is a fundamental property of ferromagnetic materials that causes them to undergo a change in shape or dimensions when exposed to a , effectively converting into mechanical strain. This reversible deformation, typically on the order of parts per million in common materials like iron and , arises from the alignment of internal magnetic domains with the applied field. Discovered in 1842 by during experiments on iron samples, the effect—often termed the Joule effect—marks the interplay between and in solids. The underlying mechanism of magnetostriction involves spin-orbit coupling, where the process induces anisotropic strain through the rotation of magnetic domains and lattice distortions at the atomic level. In ferromagnetic crystals, the saturation magnetostrictive strain λs\lambda_s is defined as the relative change in length Δl/l\Delta l / l upon reaching magnetic saturation, with positive values indicating elongation along the field direction and negative values contraction. The inverse effect, known as the Villari effect, occurs when mechanical stress alters the material's magnetic permeability, highlighting the bidirectional magnetoelastic coupling. Notable advancements include the development of "giant" magnetostrictive materials in the 1970s, such as (Tb0.3Dy0.7Fe2), which exhibit strains up to 2000 ppm at due to rare-earth elements enhancing magnetoelastic interactions. More recent developments include giant magnetostriction in ultrathin Fe-Mn-Ga alloys without rare-earth elements, as reported in 2025. Magnetostriction finds diverse applications across and , leveraging its high and rapid response times. In industrial settings, it powers ultrasonic transducers, systems, and dampers, while in transformers, the iron core—made of silicon steel sheets—slightly expands and contracts 120 times per second under 60 Hz alternating magnetic fields, causing vibrations that produce a buzzing or humming sound at twice the line frequency; this noise is louder under higher load, voltage, or humid conditions and is generally normal and safe unless abnormally loud, which may indicate issues like core looseness or overload. Emerging biomedical uses include sensors for implant monitoring and microactuators for , where Fe-Ga alloys stimulate cell growth in repair with strains around 350 ppm. These applications underscore magnetostriction's role in precision control, though challenges like material brittleness and energy efficiency continue to drive into novel alloys.

Fundamentals

Definition and Principles

Magnetostriction is the observed in ferromagnetic and ferrimagnetic materials wherein their dimensions change in response to an applied . This effect stems from the intrinsic coupling between the material's magnetic and elastic properties, resulting in deformation that accompanies changes in . The magnetostrictive strain is quantified as λ=ΔLL,\lambda = \frac{\Delta L}{L}, where ΔL\Delta L is the change in length along a specified direction and LL is the original length. The basic principles of magnetostriction arise from magnetoelastic coupling, a interaction at the atomic level where spin-orbit effects link electron spins to the crystal lattice, altering the material's shape as varies. In these materials, magnetic domains—regions of aligned atomic moments—exist in a demagnetized state; an external HH induces alignment of these domains through growth, rotation, or reorientation, which in turn generates mechanical strain via the magnetoelastic interaction. The MM thus serves as the intermediary, with the strain proportional to changes in MM. Magnetostriction encompasses distinct forms, including volume magnetostriction, which produces an isotropic change in the material's overall volume, and linear (or Joule) magnetostriction, an anisotropic effect causing elongation or contraction primarily along the direction of the applied field. The saturation magnetostriction λs\lambda_s represents the maximum achievable strain when the material reaches full magnetic saturation. Typical strains range from 10−610^{-6} to 10−310^{-3}, with corresponding stress equivalents up to several MPa, influenced by the material's . For example, displays a negative λs≈−30×10−6\lambda_s \approx -30 \times 10^{-6}, while iron exhibits a negative value on the order of -7 ×10−6\times 10^{-6}.

Historical Development

The discovery of magnetostriction traces back to 1842, when English physicist observed that a sample of iron underwent a small elongation when subjected to a along its length, while contracting perpendicularly. This phenomenon, initially termed the Joule effect, represented the first empirical identification of dimensional changes in ferromagnetic materials due to magnetization. Shortly thereafter, in 1865, Italian physicist Emilio Villari noted the inverse process, where mechanical stress altered the of iron, laying the groundwork for understanding bidirectional magnetoelastic coupling. The term "magnetostriction" was coined in 1881 by Scottish physicist James Ewing to describe this class of effects more broadly. Early 20th-century research expanded on these observations, with Japanese physicists Hantaro Nagaoka and Kotaro Honda conducting detailed measurements in the late 1890s and early 1900s on , revealing its negative magnetostriction—characterized by contraction along the magnetization direction, in contrast to iron's positive response. Their work highlighted material-specific behaviors and influenced subsequent studies on alloys. By the 1930s, German physicist Richard Becker advanced theoretical frameworks, linking magnetostriction to through models that incorporated spin-orbit interactions and effects. Post-World War II developments in the 1940s saw magnetostriction applied practically in sonar transducers, where nickel-based devices operated at frequencies like 24 kHz for underwater detection, driven by wartime needs for antisubmarine warfare. This era spurred material refinements to address limitations such as low strain amplitudes. In the 1970s, the U.S. Naval Ordnance Laboratory pioneered rare-earth alloys, culminating in the invention of Terfenol-D (TbDyFe2), which exhibited giant magnetostriction strains up to 2000 ppm—orders of magnitude larger than nickel—enabling high-performance actuators and sensors. From 2020 to 2025, research has focused on and composites to enhance performance while mitigating brittleness and cost issues of bulk rare-earth materials. Advances include ferromagnetic composites achieving reversible giant magnetostriction through aligned fibers or nanoprecipitates, yielding strains over 1000 ppm with improved flexibility. Similarly, TbDyFe/ composites with spherical single crystals have demonstrated enhanced magnetostriction via optimized particle orientation, alongside explorations in Fe-Ga-based for damping-integrated applications. In 2025, studies demonstrated room-temperature giant magnetostriction in ultrathin FexMn1–xGa4 films, enabling advancements in micro-nano electromechanical systems. These innovations emphasize scalable synthesis and hybrid structures for broader device integration.

Physical Mechanisms

Direct Magnetostriction

Direct magnetostriction, commonly referred to as the Joule effect, describes the change in shape or dimensions of a when subjected to an external . This phenomenon arises primarily from the reorientation of magnetic domains under the influence of the applied field, which aligns the vector M\mathbf{M} with the field direction. As domains rotate or grow, the experiences anisotropic lattice distortions driven by energy, where the preferred easy magnetization directions in the crystal lattice dictate the nature of . The resulting tensor ε\boldsymbol{\varepsilon} is directly coupled to the , expressed as ε=f(M)\boldsymbol{\varepsilon} = f(\mathbf{M}), reflecting the magnetoelastic interaction that minimizes the total energy of the system. In polycrystalline materials, the linear magnetostriction λ\lambda along the field direction follows the quadratic dependence λ=32λs(MMs)2\lambda = \frac{3}{2} \lambda_s \left( \frac{M}{M_s} \right)^2, where λs\lambda_s is the saturation magnetostriction constant and MsM_s is the saturation magnetization; this relation captures the progressive alignment from random initial states to full saturation. The Joule effect is typically volume-conserving, with the relative volume change ΔV/V≈0\Delta V / V \approx 0, as the distortions are shear-like rather than isotropic expansions. The sign and magnitude of the depend on the crystal's easy axes—such as ⟨100⟩\langle 100 \rangle or ⟨111⟩\langle 111 \rangle in cubic ferromagnets—where alignment along these axes induces either elongation or contraction; for instance, iron displays positive magnetostriction (expansion) in certain directions due to its one-ion , whereas exhibits negative magnetostriction (contraction). Microstructural elements play a significant role in modulating the direct magnetostriction response by affecting domain dynamics. Grain boundaries impede or facilitate motion, leading to inhomogeneous strain distributions that can enhance or suppress overall deformation compared to ideal single crystals. Defects, such as dislocations or inclusions, further alter the elastic strain variations by pinning s, thereby influencing the efficiency of reorientation and the resulting magnetoelastic coupling. These effects are particularly pronounced in polycrystalline or nanostructured materials, where surface proximity can amplify local strains.

Inverse Magnetostriction

Inverse magnetostriction, also known as the Villari effect, refers to the change in a ferromagnetic material's , permeability μ, or M induced by applied mechanical stress σ. Discovered by Italian Emilio Villari in 1865, this phenomenon arises from the bidirectional magnetoelastic coupling inherent in magnetostrictive materials. Under stress, magnetic domains reorient to minimize the total , leading to variations in magnetic induction B, often quantified by the relation ΔB/Δσ. This domain wall motion and rotation effectively alter the material's magnetic response without requiring an external . The underlying mathematical model incorporates the magnetoelastic interaction into the material's free energy density. A key term in this energy expression is the magnetoelastic contribution, typically written as -b σ ε, where b denotes the magnetoelastic , σ is the applied stress, and ε is the resulting strain. This term couples mechanical deformation to magnetic orientation, influencing domain configurations. The inverse effect is characterized by the piezomagnetic coefficient d, defined as d ≈ ∂M/∂σ, which by thermodynamic reciprocity equals the direct magnetostrictive coefficient ∂λ/∂H (where λ is the magnetostrictive strain and H is the strength). In more detailed models, stress induces an effective magnetic field H_σ = (1/μ_0) [∂(3/2 σ ε)/∂M], driving toward an anhysteretic state through unpinning. Theoretically, inverse magnetostriction explains the high sensitivity of magnetic sensors to mechanical loads, as stress modulates permeability and induces magnetic shifts that alter domain alignment. In soft magnetic materials, such as amorphous alloys or ferrites, applied stresses can produce relative permeability changes Δμ/μ exceeding 50%, highlighting the effect's scale for sensing applications. These shifts arise from stress-dependent domain reorientation, providing a basis for detecting subtle mechanical perturbations via magnetic measurements.

Characterization and Measurement

Magnetostrictive Hysteresis

Magnetostrictive hysteresis refers to the nonlinear, path-dependent relationship between the magnetostrictive strain and the applied in ferromagnetic materials, manifesting as a closed loop when strain λ is plotted against the magnetic field strength H. This loop illustrates the lag in strain response during increasing and decreasing field cycles, analogous to the magnetic B-H hysteresis loop but featuring mechanical deformation as the primary output. Prominent features include the H_c, the reverse field magnitude needed to nullify the strain after reaching saturation, and the saturation strain λ_s, the peak strain value attained at high fields. Minor loops within the major loop represent partial reversals, often asymmetric, and may exhibit unique distortions such as twisted sections in certain materials like due to multiple equilibria. The primary causes of magnetostrictive hysteresis stem from irreversible processes in dynamics, including the pinning of s by microstructural defects, inclusions, and internal stresses, which impede smooth wall motion under changing fields. Irreversible rotations of magnetic moments within domains further contribute to the lag, as moments do not revert precisely along the same path upon field reversal. These mechanisms lead to energy dissipation, predominantly as heat through eddy currents induced by motion and viscous damping in the material lattice; the area enclosed by the loop directly quantifies this cyclic energy loss. Key quantitative characteristics of the loop include the remanent λ_r, the residual deformation persisting after the is removed, reflecting incomplete domain relaxation. The initial magnetostrictive susceptibility χ, defined as the dλ/dH near zero field, measures the material's low-field responsiveness and slope of the loop's initial branch. Temperature exerts a profound influence on these properties, with hysteresis amplitude and increasing as temperature decreases below the point, where ferromagnetic ordering persists; above this point, the effect vanishes as the material transitions to . Variations in hysteresis loops occur across material types and operating conditions. Soft magnetostrictive materials, such as certain alloys with low , exhibit narrow loops with small H_c and minimal area, enabling efficient, low-loss operation in cyclic applications. In contrast, hard magnets display wide loops with large , signifying substantial pinning and higher energy dissipation suited for stable, permanent-like responses. For dynamic scenarios, loop shape and area show frequency dependence, with widening and increased losses at higher frequencies due to enhanced effects and rate-limited domain dynamics, critical for high-speed actuators.

Experimental Techniques

Experimental techniques for quantifying magnetostriction primarily involve precise measurements under controlled , often combined with mechanical stress to capture coupled effects. Strain gauges, attached directly to the sample surface, provide reliable detection of dimensional changes (ΔL/L) with resolutions typically around 10^{-6} m/m, suitable for bulk materials where direct contact is feasible. For higher precision, non-contact methods such as interferometry or capacitive sensors achieve resolutions down to 10^{-9} m/m by monitoring variations or shifts induced by sample deformation. Magnetic fields are applied using electromagnets or solenoids, generating uniform fields (H) up to 100 kA/m along the sample axis to induce saturation or directional effects. Simultaneous uniaxial stress is imposed via loading frames or clamps, allowing investigation of magnetoelastic coupling without altering field uniformity. Standard techniques include static tests following protocols like those standardized for electrical steels using single-sheet testers with optical sensors for detection at resolutions of 0.01 μm/m. Dynamic measurements employ vibrating sample magnetometers (VSM) to simultaneously record (M) and strain (λ), enabling coupled M-λ characterization. For the inverse effect, permeability bridges measure changes in magnetic permeability under applied stress, quantifying stress-induced magnetization variations. Key challenges in these measurements include maintaining up to Curie temperatures (often exceeding 700°C for ferrimagnets), where phase transitions can introduce artifacts requiring cryogenic or furnace-integrated setups. High-frequency AC fields (up to kHz ranges) for applications demand specialized coils and fast-response sensors to capture dynamic responses without interference. Recent advances in the feature optical methods like profilometry and deflection for thin films, offering non-contact, sub-ppm sensitivity in nanoscale structures. These techniques briefly reference hysteresis loops to validate full-cycle strain-magnetic field dependencies but focus on practical implementation.

Materials and Properties

Types of Magnetostrictive Materials

Magnetostrictive materials are broadly classified into several categories based on their composition and , each exhibiting distinct strain responses under magnetic fields. Traditional ferromagnetic metals, such as , iron, and , represent the earliest explored class, with relatively modest saturation magnetostriction coefficients (λs\lambda_s) that make them suitable for basic applications despite limitations in strain magnitude. Nickel displays a negative λs≈−41\lambda_s \approx -41 ppm, leading to contraction upon , while iron exhibits a small negative λs≈−9\lambda_s \approx -9 ppm in polycrystalline form, resulting in minimal dimensional change. Cobalt, in contrast, shows a larger negative λs≈−52\lambda_s \approx -52 ppm but is limited by its , which restricts practical use in high-stress environments. Alloys like (Ni-Fe compositions, e.g., 80% Ni-20% Fe) achieve near-zero magnetostriction (typically <5 ppm), enabling low-strain applications such as magnetic shielding and sensor cores where dimensional stability is critical. Rare-earth alloys, particularly those based on Laves-phase intermetallics, offer "giant" magnetostriction due to strong magnetoelastic coupling from 4f electron contributions. Terfenol-D, with the composition Tb0.3_{0.3}Dy0.7_{0.7}Fe2_2, achieves λs\lambda_s up to 2000 ppm at room temperature, enabling significant strains for actuators, though its brittleness and high cost pose challenges. Galfenol (Fe1−x_{1-x}Gax_x alloys, typically x≈0.17−0.19x \approx 0.17-0.19) provides moderate λs≈300−350\lambda_s \approx 300-350 ppm with excellent ductility (tensile strength ~500 MPa), making it advantageous for dynamic, high-cycle applications like vibration control. Other types include amorphous ribbons, such as Metglas (Fe-based alloys like Fe40_{40}Ni38_{38}Mo4_4B18_{18}), which exhibit high magnetic permeability (>10,000) and tunable magnetostriction around 50 ppm, ideal for flexible sensors and transformers. Composites and thin films incorporate magnetostrictive particles (e.g., in matrices) to enhance flexibility and reduce brittleness, achieving strains up to 1000 ppm while maintaining processability for microdevices. Ferrimagnetic ferrites, such as CoFe2_2O4_4 or NiFe2_2O4_4, display weaker effects with λs\lambda_s typically 100-300 ppm in polycrystalline forms, suitable for low-strain, high-frequency applications due to their electrical insulation and moderate . Material selection hinges on key properties: the magnitude of λs\lambda_s for desired strain levels, Curie temperature TcT_c exceeding room temperature (e.g., >300°C for ) to ensure operational stability, and mechanical strength to withstand cyclic loading without fracture. Emerging , including Fe nanowires fabricated via template methods post-2015, show promise for enhanced magnetostriction through shape anisotropy, potentially exceeding 100 ppm in nanoscale configurations for biomedical and .

Mechanical and Constitutive Behaviors

Magnetostrictive materials demonstrate a variation in under applied magnetic fields, known as the ΔE effect, which stems from magnetoelastic coupling and can alter the by up to 30% in alloys like FeCoSiB. This effect is particularly pronounced in giant magnetostrictive materials such as , where the modulus decreases with increasing field strength due to domain reorientation, impacting performance and requiring careful modeling for dynamic applications. Under cyclic loading, these materials undergo , with crack propagation accelerated by combined magnetic and mechanical stresses; for instance, in cracked giant magnetostrictive alloys, the influences fatigue life, often reduced under high fields but extended by constant bias fields that can increase cycles to failure by orders of magnitude. Microstructure plays a critical role in mechanical behavior, as grain size refinement lowers coercivity and enhances domain wall motion, thereby improving magnetostrictive responsiveness in materials like Nd₂Fe₁₄B-based alloys; finer grains near the single-domain limit reduce pinning and hysteresis losses, though excessive refinement can introduce defects that degrade fatigue resistance. Constitutive models for magnetostrictive materials often incorporate via extensions of the Jiles-Atherton framework, which couples anhysteretic magnetization with pinning mechanisms to predict both magnetic and strain responses under preload; this approach accurately captures butterfly loops in and Galfenol, with parameters tuned for stress-dependent behavior. A simpler quadratic model approximates saturation magnetostriction as λ=λs(MMs)2\lambda = \lambda_s \left( \frac{M}{M_s} \right)^2, augmented by higher-order terms to account for anhysteretic and minor loops, providing good fits for low-to-moderate fields in polycrystalline samples. Stress influences these models through the piezomagnetic coefficient d33d_{33}, which quantifies how compressive or tensile loads alter strain output, peaking at optimal biases in TbDyFe alloys. Advanced constitutive relations address nonlinear magnetoelastic via equations like σ=c(ε−λ(M))\sigma = c (\varepsilon - \lambda(M)), where σ\sigma is stress, cc the elastic stiffness, ε\varepsilon total strain, and λ(M)\lambda(M) field-dependent magnetostriction, enabling prediction of coupled dynamics in transducers. To achieve linear operation, bias fields are optimized around the point of maximum d33d_{33}, typically 100-200 kA/m for stacks, minimizing nonlinearity and enhancing bandwidth in actuators. Compressive prestress aligns magnetic domains transverse to the rod axis, boosting peak strain by up to 90% at 50 MPa in polycrystalline variants, though excessive stress induces saturation. High-strain alloys like suffer from brittleness, with tensile strengths limited to 25-50 MPa, restricting applications to compressive modes and necessitating composites for durability. Temperature rises induce demagnetization, shifting anisotropy and significantly reducing the modulus between 20-80°C in soft magnetostrictives, while temperatures around 380°C in rare-earth alloys limit operational range. Recent models from the 2020s for multiferroic composites incorporate strain-mediated coupling in heterostructures, such as Fe₃O₄/BaTiO₃, predicting reversible magnetic modulation via nonlinear magnetoelastic terms for low-energy logic gates.

Applications

Actuators and Transducers

Magnetostrictive actuators leverage the direct magnetostriction effect in materials like to generate linear or rotary motion for precision positioning applications. stacks can achieve strains exceeding 1000 parts per million (ppm), enabling displacements on the order of millimeters in compact devices, while delivering blocked forces greater than 10 kN in larger configurations suitable for structural control. These actuators are particularly valued in for their high force density and rapid response times, often outperforming piezoelectric alternatives in low-frequency, high-load scenarios. For instance, -based linear actuators provide sub-micrometer resolution over strokes up to several centimeters, making them ideal for and systems. In , magnetostrictive actuators serve as sonar projectors, converting electrical signals into mechanical vibrations for sound wave generation. Originating from World War II-era designs using nickel-based magnetostrictive transducers on surface ships and , these devices evolved into modern high-power projectors for submarine communication and detection, operating at frequencies below 10 kHz with power outputs exceeding kilowatts. The robustness of magnetostrictive materials under high pressure and corrosion in marine environments has sustained their use, with contemporary systems incorporating for enhanced efficiency and bandwidth. Magnetostrictive transducers exploit the inverse effect for energy conversion, primarily in ultrasonic applications such as and non-destructive testing (NDT). These devices generate high-amplitude s at frequencies ranging from 20 kHz for to several hundred kHz for guided wave flaw detection in metals, where the transducer's rod expands and contracts to drive a horn or . In adaptive structures, magnetostrictive transducers enable active control by counteracting structural resonances in real time, as seen in components where they dampen aeroelastic flutter. Key design considerations for magnetostrictive actuators and transducers include incorporating bias magnets to linearize the response and mitigate hysteresis-induced nonlinearity. Permanent magnets provide a static field that shifts the to the steepest portion of the magnetostriction curve, enabling bidirectional motion without "double-frequency" artifacts. For high-power operation, cooling systems are essential to dissipate heat from losses, which can raise temperatures above 100°C and degrade performance; water-cooled enclosures maintain in continuous-duty cycles. Overall , defined as η=PmechPelec\eta = \frac{P_{\text{mech}}}{P_{\text{elec}}} where PmechP_{\text{mech}} is mechanical output power and PelecP_{\text{elec}} is electrical input power, reaches up to 50% in resonant configurations, balancing energy conversion with thermal management. Historically, magnetostrictive delay lines emerged in the late 1940s as acoustic memory storage for early computers, using nickel wires to propagate torsional pulses for data retention in systems like the EDSAC prototype. In modern applications, post-2010 advancements have integrated magnetostrictive thin films into MEMS actuators, enabling micro-scale motion for biomedical devices and optical switches with displacements up to 10 μm under low magnetic fields. These evolutions highlight the transition from bulk sonar and computing components to compact, high-precision micro-actuators.

Sensors and Energy Harvesting

Magnetostrictive sensors leverage the inverse magnetostrictive effect, also known as the Villari effect, where mechanical stress induces changes in magnetic induction (ΔB), enabling passive detection of forces and torques without requiring external power supplies. This effect allows for non-contact measurement through variations in magnetic permeability or , providing high sensitivity in harsh environments. Torque and force sensors based on the Villari effect are widely used in automotive and applications, where applied stress alters the magnetization of the material, detectable via encircling coils. For instance, magnetostrictive torque sensors employ this principle to measure rotational forces with resolutions better than 0.1% of full scale, offering robustness against . These sensors achieve high linearity over a wide , with sensitivities suitable for industrial applications. Magnetic field sensors utilizing magnetostriction exploit strain-induced changes in permeability for non-contact detection, where external fields modulate the material's magnetic response under controlled stress. This configuration enhances sensitivity to DC and AC fields, with mechanical quality factors and optimizing performance for applications like structural monitoring. In biomedical contexts, such sensors enable precise navigation of catheters by tracking magnetic perturbations in real-time, facilitating minimally invasive procedures with sub-millimeter accuracy. Energy harvesting devices convert vibrational energy to through the inverse magnetostrictive effect in structures, where mechanical oscillations induce variations that generate voltage in surrounding coils. Typical configurations use or Galfenol rods bonded to beams, achieving power densities on the order of 1 mW/cm³ at frequencies around 40-50 Hz. Developments in the focused on Terfenol-based generators to power sensors in , delivering sufficient output (up to 200 µW) for autonomous operation in remote environments. These applications benefit from magnetostrictive sensors' and harvesters' high sensitivity and self-powered nature, eliminating the need for batteries and enabling long-term deployment in inaccessible locations. However, challenges include losses, which introduce nonlinearity and reduce by up to 30% in dynamic cycles. Recent advances through 2025 have addressed these issues via optimized magnetoelectric composites and flexible designs, including flexible magnetic films for enhanced strain response and switching control strategies for multimodal vibrations, improving IoT integration with bandwidth and power outputs exceeding 4 mW/cm³ for low-frequency vibrations.

Transformers and Noise Generation

In electrical transformers, the magnetostriction effect manifests as audible humming or buzzing sounds produced by the vibration of the silicon steel core under alternating magnetic fields. The core, composed of thin laminated sheets, undergoes slight expansion and contraction twice per cycle of the alternating current, resulting in a fundamental vibration frequency of 120 Hz for a standard 60 Hz power system. This dimensional change occurs as the ferromagnetic material responds to the varying magnetic flux, causing mechanical vibrations that generate the characteristic noise. The intensity of the humming increases with higher electrical loads, elevated voltage levels, or conditions such as humidity that may exacerbate core degradation, leading to greater flux density and intensified magnetostriction. Over time, aging effects like the breakdown of adhesives binding the core laminations can cause layer separation, further amplifying the noise. This phenomenon is a normal aspect of transformer operation and is generally safe, provided the sound remains consistent and within expected levels. However, abnormally loud humming or changes in noise patterns, such as irregular tones or additional sounds like cracking or sizzling, may indicate underlying issues including core looseness, overload, insulation breakdown, or mechanical faults, necessitating professional inspection.

References

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