Magnetostriction

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Magnetostriction

The change of length of a ferromagnetic substance when it is magnetized. More generally, magnetostriction is the phenomenon that the state of strain of a ferromagnetic sample depends on the direction and extent of magnetization. The phenomenon has an important application in devices known as magnetostriction transducers. See Ferromagnetism

The magnetostrictive effect is exploited in transducers used for the reception and transmission of high-frequency sound vibrations. Nickel is often used for this application. See Ultrasonics

Magnetostriction

 

a change in the shape and size of a body upon magnetization. The phenomenon was discovered in 1842 by J. Joule. In ferromagnets and ferrimagnets (such as iron, nickel, cobalt, gadolinium, and terbium, as well as a number of alloys and ferrites), magnetostriction reaches a significant magnitude (relative extension Δl/l ~ 10-6-102). Magnetostriction is very small in antiferromagnets, paramagnets, and diamagnets.

The phenomenon that is the inverse of magnetostriction—a change in the magnetization of a ferromagnetic specimen upon deformation—is called the magnetoelastic effect, or sometimes the Villari effect.

In the modern theory of magnetism, magnetostriction is considered to be a result of the manifestation of the fundamental types of interactions in ferromagnetic bodies (electrical exchange interaction and magnetic interaction). Accordingly, two types of essentially different magnetostriction deformations of a crystal lattice are possible: those resulting from a change in magnetic forces (dipole-dipole and spin-orbital deformations) and those resulting from a change in exchange forces.

Upon magnetization of ferromagnets and ferrimagnets, magnetic forces act in the range of fields from 0 to a field with intensity Hs, in which a specimen reaches its technical magnetic saturation Is. Magnetization in this range of fields is caused by processes of displacement of domain boundaries and rotation of domain magnetic moments. Both processes change the energy state of the crystal lattice, which is manifested in the change of the equilibrium distances between its points. As a result, the atoms are shifted and magnetostrictive deformation of the lattice takes place. Magnetostriction of this type is anisotropic (it depends on the direction and maguitude of the magnetization J) and is manifested primarily in a change in the shape of the crystal with virtually no change in its volume (linear magnetostriction). Semiempirical formulas are used to calculate linear magnetostriction. For example, the magnetostriction of ferromagnetic crystals of cubic symmetry that are magnetized to saturation is calculated from the formula

where si, Sj and βi, βj are the direction cosines of the vector Js and the direction of measurement with respect to the cube edges, respectively, and a1 and a2 are the constants of magnetostrictive anisotropy, which are numerically equal to a1 = (3/2) (Δl/l)[100] and a2= (3/2)(Δl/l)[111], where (Δl/l)[100] and (Δl/l)[111] are the maximum linear magnetostriction in the direction of the edge and diagonal of the crystal cell, respectively. The quantity λs = (Δl/l)s is called the saturation magnetostriction or the magnetostriction constant.

Magnetostriction caused by exchange forces is observed in ferromagnets in the region of magnetization above technical saturation, where the magnetic moments of the domains are fully oriented in the direction of the field and only an increase in the absolute magnitude of Js (the paraprocess, or true magnetization) takes place. Magnetostriction caused by exchange forces in cubic crystals is isotropic—that is, it is manifested in a change in the volume of the body. In hexagonal crystals (such as gadolinium), such magnetostriction is anisotropic. In most ferromagnetic substances at room temperature, magnetostriction resulting from the paraprocess is small; it is also small close to the Curie point, where the paraprocess almost entirely determines the ferromagnetic properties of a substance. However, in some alloys that have a low coefficient of thermal expansion (Invar magnetic alloys) magnetostriction is great (in magnetic fields of the order of 8 ×l04 amperes per meter [A/m], or 103 oersteds, the ratio ΔV/V is of the order of 10-5). Significant magnetostriction of the paraprocess is also found in ferrites upon annihilation or creation of noncollinear magnetic structures by a magnetic field.

Magnetostriction is among the even magnetic effects, since it is independent of the sign of the magnetic field. Magnetostriction in polycrystalline ferromagnets has been studied to the greatest extent. The relative elongation of the specimen in the direction of the field (longitudinal magnetostriction) or perpendicular to the direction of the field (transverse magnetostriction) is usually measured. For metals and most alloys the longitudinal and transverse magnetostriction in the region of technically magnetized

Figure 1. Longitudinal magnetostriction (curve I) and transverse magnetostriction (curve II) of a 36% Ni-64% Fe alloy. In weak fields the two types of magnetostriction have opposite signs, but in strong fields

fields have opposite signs, and the magnitude of transverse magnetostriction is smaller than that of longitudinal magnetostriction; in the region of the paraprocess the magnitudes are identical (Figure 1). For most ferrites both longitudinal and transverse magnetostriction are negative; the reason for this is still unclear.

The magnitude, sign, and curve shape of the dependence of magnetostriction on field intensity and magnetization depend on the structural peculiarities of the specimen (crystallographic texture, impurity elements, and heat treatment and cold working). In iron (Figure 2) longitudinal magnetostriction is positive (elongation of the body) in a weak magnetic field and negative (shortening of the body) in a stronger field. For nickel, longitudinal magnetostriction is negative for all field values. The complex nature of magnetostriction in polycrystalline specimens of ferromagnets is determined by the peculiarities of magnetostrictive anisotropy in the crystals of the corresponding metal. Most FeNi, Fe-Co, and Fe-Pt alloys have positive longitudinal magnetostriction: Δl/l ≈ (1-10) ×10-5. The greatest longitudinal magnetostriction is found among Fe-Pt, Fe-Pd, Fe-Co, Mn-Sb, Mn-Cu-Bi, and Fe-Rh alloys. Among the ferrites, CoFe2O41, Tb3Fe5O12, and Dy3Fe5O12 have the highest magnetostriction: Δl/l ≈ (2-25) ×10 -4. Certain rare earths and their alloys and compounds, such as terbium and dysprosium and TbFe2 and DyFe2, have the highest magnetostriction: Δl/l ≈ 103-102 (depending on the strength of the applied field). Magnetostriction of approximately the same order has been observed for a number of uranium compounds (such as U3AS4 and U3P4).

Figure 2. Dependence of longitudinal magnetostriction of a number of polycrystalline metals, alloys, and compounds on magnetic field intensity

Magnetostriction displays a hysteresis effect in the region of technical magnetization (Figure 3). It is also strongly affected by temperature, elastic stresses, and even the character of the demagnetization to which the specimen was subjected before measurement.

Figure 3. Magnetostrictive hysteresis of iron caused by its magnetic hysteresis

Comprehensive study of magnetostriction contributes, above all, to the elucidation of the physical nature of the forces that determine the ferrimagnetic, antiferromagnetic, and ferromagnetic behavior of matter. The study of magnetostriction, especially in the region of technical magnetization, also plays an important role in the search for new magnetic materials; for example, the high magnetic permeability of Permalloy-type alloys has been observed to be associated with their low magnetostriction (in addition to a low constant of magnetic anisotropy).

Anomalies of the thermal expansion of ferromagnetic, ferrimagnetic, and antiferromagnetic bodies are associated with magnetostriction effects. The anomalies are due to the fact that the magnetostrictive deformations caused by exchange forces (and by magnetic forces in general) in the lattice are manifested not only when the bodies are placed in a magnetic field but also when they are heated in the absence of a field (thermostriction). The change in the volume of bodies as a result of thermostriction is especially significant in magnetic phase transitions (at the Curie and Neel temperatures and at the temperature of transition of collinear magnetic structure into noncollinear structure). The superposition of these volumetric changes on ordinary thermal expansion, which is due to the thermal oscillations of atoms in the lattice, sometimes leads to an anomalously low value of the coefficient of thermal expansion in some materials. For example, experiments have proved that the low thermal expansion of Invar-type alloys is due to the influence of the negative magnetostrictive deformations that arise during heating and that compensate almost entirely for the “normal” thermal expansion of these alloys.

Various anomalies of elasticity in ferromagnets, ferrimagnets, and antiferromagnets are related to magnetostriction. The sharp anomalies in the elastic modulus and modulus of internal friction that are observed in these substances in the area of the Curie and Neel points and other magnetic phase transitions result from the magnetostriction that arises upon heating. In addition, redistribution of the magnetic moments of domains takes place when ferromagnetic and ferrimagnetic bodies are affected by elastic stresses even in the absence of an external magnetic field (in the general case the absolute value of the spontaneous magnetization of a domain also changes). The processes are accompanied by additional magnetostrictive deformation of the body, mechanostriction, which leads to deviations from Hooke’s law. The phenomenon of the change in the elastic modulus E of ferromagnetic metals (the A£ effect) upon exposure to a magnetic field is directly related to mechanostriction.

Apparatus that operates on the principle of a mechano-optical lever and that makes possible observation of relative changes of up to 10-6 in the length of a specimen is most commonly used to measure magnetostriction. Electronic and interference methods provide still greater sensitivity. The method of wire-type resistance strain gauges, in which a strain gauge connected to one of the arms of a measuring bridge is glued to the specimen, is also used extensively. The change in the length and resistance of the strain gauge upon a magnetostrictive change in the dimensions of the specimen can be recorded with high precision by an electrical measuring device.

Magnetostriction is widely used in technology. It is the basis for the operation of magnetostriction transformers (sensors) and relays, ultrasonic radiators and receivers, filters and frequency stabilizers in electronic devices, and magnetostriction delay lines.

REFERENCES

Vonsovskii, S. V. Magnetizm. Moscow, 1971.
Belov, K. P. Uprugie, teplovye i elektricheskie iavleniia v ferromagnetikakh, 2nd ed. Moscow-Leningrad, 1957.
Bozorth, R. Ferromagnetizm. Moscow, 1956. (Translated from English.)
Redkozeme’nye ferromagnetiki i antiferromagnetiki. Moscow, 1965. Ul’trazvukovye preobrazovateli. Edited by I. P. Goliamina. Moscow, 1972. (Translated from English.)

K. P. BELOV

magnetostriction

[mag‚nēd·ō′strik·shən]
(electromagnetism)
The dependence of the state of strain (dimensions) of a ferromagnetic sample on the direction and extent of its magnetization.
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