Design and Selection of Magnetic Materials

Question taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)
Select an appropriate magnetic material for the following applications: a high electrical-efficiency motor, a magnetic device to keep cupboard doors closed, a magnet used in an ammeter or voltmeter, and magnetic resonance imaging.
High electrical-efficiency motor: To minimize hysteresis losses, we might use an oriented silicon iron, taking advantage of its anisotropic behavior and its small hysteresis loop. Since the iron-silicon alloy is electrically conductive, we would produce a laminated structure with thin sheets of the silicon iron sandwiched between a nonconducting dielectric material. Sheets thinner than about 0.5 mm might be recommended.
Magnet for cupboard doors: The magnetic latches used to fasten cupboard doors must be permanent magnets; however, low cost is a more important design feature than high power. An inexpensive ferritic steel or a low-cost ferrite would be recommended.
Magnets for an ammeter or voltmeter: For these applications, alnico alloys are particularly effective. We find that these alloys are among the least sensitive to changes in temperature, ensuring accurate current or voltage readings over a range of temperatures.
Magnetic resonance imaging: One of the applications for MRI is in medical diagnostics. In this case, we want a very powerful magnet. A Nd2Fe12B magnetic material, which has an exceptionally high BH product, might be recommended for this application. We can also make use of very strong electromagnets fabricated from
superconductors.
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Soft Magnetic Materials and Permanent Magnets

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Soft Magnetic Materials:
Ferromagnetic materials are often used to enhance the magnetic flux density (B) produced when an electric current is passed through the material. The magnetic field is then expected to do work. Applications include cores for electromagnets, electric motors, transformers, generators, and other electrical equipment. Because these devices utilize an alternating field, the core material is continually cycled through the hysteresis loop.Note that in these materials the value of relative magnetic permeability depends strongly on the strength of the applied field.
These materials often have the following characteristics:
1. High-saturation magnetization.
2. High permeability.
3. Small coercive field.
4. Small remanance.
5. Small hysteresis loop.
6. Rapid response to high-frequency magnetic fields.

7. High electrical resistivity.
High saturation magnetization permits a material to do work, while high permeability
permits saturation magnetization to be obtained with small imposed magnetic
fields. A small coercive field also indicates that domains can be reoriented with small magnetic fields. A small remanance is desired so that almost no magnetization remains when the external field is removed. These characteristics also lead to a small hysteresis loop, therefore minimizing energy losses during operation.
Eddy current losses are particularly severe when the material operates at high frequencies. If the electrical resistivity is high, eddy current losses can be held to a minimum. Soft magnets produced from ferrimagnetic ceramic materials have a high resistivity and therefore are less likely to heat than metallic ferromagnetic materials.

Permanent Magnets:
Finally, magnetic materials are used to make strong permanent magnets.Strong permanent magnets, often called hard magnets, require the following:

What is Curie Temperature ?

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When the temperature of a ferromagnetic or ferrimagnetic material is increased, the added
thermal energy increases the mobility of the domains, making it easier for them to become
aligned, but also preventing them from remaining aligned when the field is removed.
Consequently, saturation magnetization, remanance, and the coercive field are all reduced
at high temperatures.
If the temperature exceeds the Curie temperature (Tc), ferromagnetic or ferrimagnetic behavior is no longer observed. Instead, the material behaves as a paramagnetic material. The Curie temperature which depends on the material, can be changed by alloying elements. French scientists Marie and Pierre Curie (the only husband and wife to win a Nobel prize; Marie Curie actually won two
Nobel prizes) performed research on magnets, and the Curie temperature refers to their
name. The dipoles still can be aligned in a magnetic field above the Curie temperature,
but they become randomly aligned when the field is removed.
Figure and Table taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)

Magnetic Domains

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Domains are regions in the material in which all of the dipoles are aligned in a certain direction. In a
material that has never been exposed to a magnetic field, the individual domains have a random
orientation. Because of this, the net magnetization in the virgin ferromagnetic or ferrimagnetic
material as a whole is zero.

Boundaries, called Bloch walls, separate the individual magnetic domains. The Bloch walls are narrow zones in which the direction of the magnetic moment gradually and continuously
changes from that of one domain to that of the next. The domains are typically very small, about 0.005 cm or less, while the Bloch walls are about 100 nm thick.

Figure taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)

Effect of Applying Magnetic Field:

Types of Magnetic Materials

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Diamagnetic Behavior: A magnetic field acting on any atom induces a magnetic dipole for the entire atom by influencing the magnetic moment caused by the orbiting electrons. These dipoles oppose the magnetic field, causing the magnetization to be less than zero. This behavior, called diamagnetism, gives a relative permeability of about 0.99995 (or a negative susceptibility approximately -10^-6, note the negative sign). Materials such as copper, silver, silicon, gold, and alumina are diamagnetic at room temperature.

Superconductors are perfect diamagnets (χ_m=-1) ; they lose their superconductivity at higher temperatures or in the presence of a magnetic field. In a diamagnetic material, the magnetization (M) direction is opposite to the direction of applied field (H).

Paramagnetism: When materials have unpaired electrons, a net magnetic moment due to electron spin is associated with each atom. When a magnetic field is applied, the dipoles align with the field, causing a positive magnetization. Because the dipoles do not interact, extremely large magnetic fields are required to align all of the dipoles. In addition, the effect is lost as soon as the magnetic field is removed. This effect, called paramagnetism, is found in metals such as aluminum, titanium, and alloys of copper. The magnetic susceptibility (χ_m) of paramagnetic materials is positive and lies between 10^-4 and 10^-5.

Ferromagnetism: Ferromagnetic behavior is caused by the unfilled energy levels in the 3d level of iron, nickel, and cobalt. Similar behavior is found in a few other materials, including gadolinium (Gd). In ferromagnetic materials, the permanent unpaired dipoles easily line up with the imposed magnetic field due to the exchange interaction, or mutual reinforcement of the dipoles. Large magnetizations are obtained even for small magnetic fields, giving large susceptibilities approaching 10⁶. Similar to ferroelectrics, the susceptibility of ferromagnetic materials depends upon the intensity of the applied magnetic field. This is similar to the mechanical behavior of elastomers with the modulus of elasticity depending upon the level of strain. Above the Curie temperature, ferromagnetic materials behave as paramagnetic materials and their susceptibility is given by the following equation, known as the Curie-Weiss law:

In this equation, C is a constant that depends upon the material, T_c is the Curie temperature, and T is the temperature above Tc. Essentially, the same equation also describes the change in dielectric permittivity above the Curie temperature of ferroelectrics. Similar to ferroelectrics, ferromagnetic materials show the formation of hystereis loop domains and magnetic domains.

Antiferromagnetism: In materials such as manganese, chromium, MnO, and NiO, the magnetic moments produced in neighboring dipoles line up in:

Figure taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)

opposition to one another in the magnetic field, even though the strength of each dipole is very high. This effect is illustrated for MnO in above Figure. These materials are antiferromagnetic and have zero magnetization. The magnetic susceptibility is positive and small. In addition, CoO and MnCl₂ are examples of antiferromagnetic materials.

Ferrimagnetism: In ceramic materials, different ions have different magnetic

moments. In a magnetic field, the dipoles of cation A may line up with the field,

while dipoles of cation B oppose the field. Because the strength or number of dipoles is

not equal, a net magnetization results. The ferrimagnetic materials can provide good

amplification of the imposed field. We will look at a group of ceramics called ferrites that

display this behavior in a later section. These materials show a large, magnetic-field

dependent magnetic susceptibility similar to ferromagnetic materials. They also show

Curie-Weiss behavior (similar to ferromagnetic materials) at temperatures above the Curie

temperature. Most ferrimagnetic materials are ceramics and are good insulators of electricity.

Thus, in these materials, electrical losses (known as eddy current losses) are much

smaller compared to those in metallic ferromagnetic materials. Therefore, ferrites are used

in many high-frequency applications.

Superparamagnetism: When the grain size of ferromagnetic and ferrimagnetic

materials falls below a certain critical size, these materials behave as if they

are paramagnetic. The magnetic dipole energy of each particle becomes comparable to

the thermal energy. This small magnetic moment changes its direction randomly (as a

result of the thermal energy). Thus, the material behaves as if it has no net magnetic

moment. This is known as superparamagnetism. Thus, if we produce iron oxide

(Fe3O4) particles in a 3 to 5 nm size, they behave as superparamagnetic materials. Such

iron-oxide superparamagnetic particles are used to form dispersions in aqueous or

organic carrier phases or to form “liquid magnets” or ferrofluids. The particles in the

fluid move in response to a gradient in the magnetic field. Since the particles form a stable

sol, the entire dispersion moves and, hence, the material behaves as a liquid magnet.

Such materials are used as seals in computer hard drives and in loudspeakers as

heat transfer (cooling) media. The permanent magnet used in the loudspeaker holds the

liquid magnets in place. Superparamagnetic particles of iron oxide (Fe3O4) also can be

coated with different chemicals and used to separate DNA molecules, proteins, and

cells from other molecules.

Magnetic Materials

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Strictly speaking, there is no such thing as a “nonmagnetic” material. Every material consists of atoms; atoms consist of electrons spinning around them, similar to a current carrying loop that generates a magnetic field. Thus, every material responds to a magnetic field. The manner in which this response of electrons and atoms in a material is scaled determines whether a material will be strongly or weakly magnetic. Examples of ferromagnetic materials are materials such as Fe, Ni, Co, and some of their alloys. Examples of ferrimagnetic materials include many ceramic materials such as nickel zinc ferrite and manganese zinc ferrite. The term “nonmagnetic,” usually means that the materia is neither ferromagnetic nor ferrimagnetic. These “nonmagnetic” materials are further classified as diamagnetic (e.g., superconductors) or paramagnetic. In some cases, we also encounter materials that are antiferromagnetic or superparamagnetic.

Ferromagnetic and ferrimagnetic materials are usually further classified as either soft or hard magnetic materials. High-purity iron or plain carbon steels are examples of a magnetically soft material as they can become magnetized, but when the magnetizing source is removed, these materials lose their magnet-like behavior. Permanent magnets or hard magnetic materials retain their magnetization. These are permanent “magnets.” Many ceramic ferrites are used to make inexpensive refrigerator magnets. A hard magnetic material does not lose its magnetic behavior easily.

The magnetic behavior of materials can be traced to the structure of atoms. The orbital motion of the electron around the nucleus and the spin of the electron about its own axis  cause separate magnetic moments. These two motions (i.e., spin and orbital) contribute to the magnetic behavior of materials. When the electron spins, there is a magnetic

moment associated with that motion. The magnetic moment of an electron due to its spin is known as the Bohr magneton (µ_B). This is a fundamental constant and is defined as:

Figure taken from :The Science and Engineering of Materials by Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright (Very good Book)

Figure shows origin of magnetic dipoles: (a) The spin of the electron produces a magnetic field with a direction dependent on the quantum number ms. (b) Electrons orbiting around the nucleus create a magnetic field around the atom.

The magnetization M represents the increase in the inductance due to the core material, so we can rewrite the equation for inductance as

The first part of this equation is simply the effect of the applied magnetic field. The second part is the effect of the magnetic material that is present. In materials, stress causes strain, electric field (E ) induces dielectric polarization (P), and a magnetic field (H) causes magnetization (µ₀M) that contributes to the total flux density B.

The magnetic susceptibility (χ_m) , which is the ratio between magnetization and the applied field, gives the amplification produced by the material:

Both µ_r and χ_m refer to the degree to which the material enhances the magnetic field and are therefore related by

As noted before, µ_r and χ_m, therefore, the  χ_mvalues for ferromagnetic and ferromagnetic

materials depend on the applied field (H). For ferromagnetic and ferrimagnetic materials, the term µ₀M>>µ₀H . Thus, for these materials,

We sometimes interchangeably refer to either inductance or magnetization. Normally, we are interested in producing a high inductance B or magnetization M. This is accomplished by selecting materials that have a high relative permeability or magnetic susceptibility.