inverse magnetostriction
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The inverse magnetostrictive effect, magnetoelastic effect or Villari effect, after its discoverer
Emilio Villari Emilio Villari (25 September 1836 – 20 August 1904) was an Italian experimental physicist and a professor at the University of Bologna and later Naples who contributed to studies on electromagnetism after whom is named the Inverse magnetostrictiv ...
, is the change of the
magnetic susceptibility In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the ap ...
of a material when subjected to a mechanical stress.


Explanation

The
magnetostriction Magnetostriction (cf. electrostriction) 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 change ...
\lambda characterizes the shape change of a ferromagnetic material during magnetization, whereas the inverse magnetostrictive effect characterizes the change of sample magnetization M(for given magnetizing field strength H) when mechanical stresses \sigma are applied to the sample.


Qualitative explanation of magnetoelastic effect

Under a given uni-axial mechanical stress \sigma, the flux density B for a given magnetizing field strength H may increase or decrease. The way in which a material responds to stresses depends on its saturation magnetostriction \lambda_s. For this analysis, compressive stresses \sigma are considered as negative, whereas tensile stresses are positive.
According to
Le Chatelier's principle Le Chatelier's principle (pronounced or ), also called Chatelier's principle (or the Equilibrium Law), is a principle of chemistry used to predict the effect of a change in conditions on chemical equilibria. The principle is named after French c ...
: \left(\frac\right)_=\left(\frac\right)_ This means, that when the product \sigma \lambda_s is positive, the flux density B increases under stress. On the other hand, when the product \sigma \lambda_s is negative, the flux density B decreases under stress. This effect was confirmed experimentally.


Quantitative explanation of magnetoelastic effect

In the case of a single stress \sigma acting upon a single magnetic domain, the magnetic strain energy density E_\sigma can be expressed as: E_\sigma = \frac \lambda_s \sigma \sin^2(\theta) where \lambda_s is the magnetostrictive expansion at saturation, and \theta is the angle between the saturation magnetization and the stress's direction. When \lambda_s and \sigma are both positive (like in iron under tension), the energy is minimum for \theta = 0, i.e. when tension is aligned with the saturation magnetization. Consequently, the magnetization is increased by tension.


Magnetoelastic effect in a single crystal

In fact, magnetostriction is more complex and depends on the direction of the crystal axes. In
iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...
, the 00axes are the directions of easy magnetization, while there is little magnetization along the 11directions (unless the magnetization becomes close to the saturation magnetization, leading to the change of the domain orientation from 11to 00. This
magnetic anisotropy In condensed matter physics, magnetic anisotropy describes how an object's magnetic properties can be different depending on direction. In the simplest case, there is no preferential direction for an object's magnetic moment. It will respond to ...
pushed authors to define two independent longitudinal magnetostrictions \lambda_ and \lambda_. * In cubic materials, the magnetostriction along any axis can be defined by a known linear combination of these two constants. For instance, the elongation along 10is a linear combination of \lambda_ and \lambda_. * Under assumptions of
isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
magnetostriction (i.e.
domain Domain may refer to: Mathematics *Domain of a function, the set of input values for which the (total) function is defined **Domain of definition of a partial function **Natural domain of a partial function **Domain of holomorphy of a function * Do ...
magnetization is the same in any crystallographic directions), then \lambda_ = \lambda_ = \lambda and the linear dependence between the elastic energy and the stress is conserved, E_\sigma = \frac \lambda \sigma (\alpha_1 \gamma_1 +\alpha_2 \gamma_2 + \alpha_3 \gamma_3)^2. Here, \alpha_1 , \alpha_2 and \alpha_3 are the direction cosines of the domain magnetization, and \gamma_1 , \gamma_2 , \gamma_3 those of the bond directions, towards the crystallographic directions.


Method of testing the magnetoelastic properties of magnetic materials

Method suitable for effective testing of magnetoelastic effect in magnetic materials should fulfill the following requirements: * magnetic circuit of the tested sample should be closed. Open magnetic circuit causes
demagnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...
, which reduces magnetoelastic effect and complicates its analysis. * distribution of stresses should be uniform. Value and direction of stresses should be known. * there should be the possibility of making the magnetizing and sensing windings on the sample - necessary to measure
magnetic hysteresis Magnetic hysteresis occurs when an external magnetic field is applied to a ferromagnet such as iron and the atomic dipoles align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become '' ...
loop under mechanical stresses. Following testing methods were developed: * tensile stresses applied to the strip of magnetic material in the shape of a ribbon. Disadvantage: open magnetic circuit of the tested sample. * tensile or compressive stresses applied to the frame-shaped sample. Disadvantage: only bulk materials may be tested. No stresses in the joints of sample columns. * compressive stresses applied to the ring core in the sideways direction. Disadvantage: non-uniform stresses distribution in the core . * tensile or compressive stresses applied axially to the ring sample. Disadvantage: stresses are perpendicular to the magnetizing field.


Applications of magnetoelastic effect

Magnetoelastic effect can be used in development of
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
sensor A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon. In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
s. This effect was used for sensors: * in
civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage ...
. * for monitoring of large
diesel engine The diesel engine, named after Rudolf Diesel, is an internal combustion engine in which ignition of the fuel is caused by the elevated temperature of the air in the cylinder due to mechanical compression; thus, the diesel engine is a so-call ...
s in
locomotive A locomotive or engine is a rail transport vehicle that provides the Power (physics), motive power for a train. If a locomotive is capable of carrying a payload, it is usually rather referred to as a multiple unit, Motor coach (rail), motor ...
s. * for monitoring of
ball valve A ball valve is a flow control device which uses a hollow, perforated and pivoting ball to control fluid flowing through it. It is open when the ball's hole is in line with the flow inlet and closed when it is pivoted 90-degrees by the valve ...
s. * for biomedical monitoring. Inverse magnetoelastic effects have to be also considered as a side effect of accidental or intentional application of mechanical stresses to the magnetic core of inductive component, e.g.
fluxgate A magnetometer is a device that measures magnetic field or magnetic dipole moment. Different types of magnetometers measure the direction, strength, or relative change of a magnetic field at a particular location. A compass is one such device, o ...
s or generator/motor
stator The stator is the stationary part of a rotary system, found in electric generators, electric motors, sirens, mud motors or biological rotors. Energy flows through a stator to or from the rotating component of the system. In an electric mot ...
s when installed with interference fits.


References

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See also

*
Magnetostriction Magnetostriction (cf. electrostriction) 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 change ...
*
Magnetocrystalline anisotropy In physics, a ferromagnetic material is said to have magnetocrystalline anisotropy if it takes more energy to magnetize it in certain directions than in others. These directions are usually related to the principal axes of its crystal lattice. I ...
Magnetism Magnetic ordering