Chapter 20. Magnetic Properties – Material Science and Metallurgy

20

Magnetic Properties

20.1 INTRODUCTION

From the beginning of civilization magnet has been in the service of mankind as magnetite ore or lodestone. But for the past 100 years, numerous applications of magnetization and magnetic materials have come up. In the more recent years, development of new magnetic materials has played important role in computer revolution.

Large powerful magnets are crucial for advanced technologies as magnetic levitation trains float above tracks using strong magnets. Powerful magnetic fields are used in nuclear magnetic resonance as a very useful diagnostic instrument used by doctors.

The magnetic forces are produced by the motion of charged particles such as electrons, which indicate close relationship between magnetism and electricity underlying the electromagnetic theory. The magnetic fields are used to control the path of charged particles.

This chapter discusses various types of magnetisms, magnetization and demagnetization processes including different types of soft and hard magnetic materials.

20.2 MAGNETISM

For the past thousands of years, magnet has been in use in day-to-day activities. A magnet is characterized by attractive and repulsive forces, yet the phenomenon of magnetism is complex and difficult to understand. However, there are enormous contributions of magnetism in the service of society, which are as follows:

  1. Computer, electric power generation, transformers and electric motors
  2. Radio, telephone and television
  3. Sound and video reproduction systems
  4. Recorders and tape players using magnetic tapes
  5. Compass to determine North direction
  6. Magnetic latches
  7. Use of magnets in healing several diseases
  8. Computer memories fabricated using bubble domains
  9. Magnetic levitation trains float above the tracks using strong magnets
  10. Powerful magnetic fields are used in nuclear resonance imaging
  11. Superconducting magnets—most powerful particle accelerator

20.2.1 Magnetic Behaviour

Iron, steel and naturally occurring lodestone exhibit magnetic properties. The magnetic force or forces arise from the movement of electrical charge. Maxwell’s equation and Bio-Savart law describe the origin and behaviour of the fields that govern these forces. So, magnetism is observed whenever electrically charged particles are in motion. This can arise either from the movement of electrons in an electrical circuit resulting in electromagnetism or from the quantum mechanical spin or orbital motion of electrons resulting in permanent magnets. Electron spin is the dominant effect within the atoms and orbital motion of electrons around the nucleus is a secondary effect. The magnetic field can be best visualized within a magnetic coil (carrying electric current) as shown in Figure 20.1. The figure shows the imaginary lines of force drawn to show the direction of force in the vicinity of field source (a loop carrying current).

Figure 20.1 Magnetic Field Around a Loop Carrying Current

Figure 20.2 Magnetic Lines of Force Around a Bar Magnet

The magnetic field generated by a coil (current loop) is termed as magnetic field, H. Magnetic dipoles are found to exist in magnetic materials, which in some respect are analogous to electric dipoles. Magnetic dipoles consist of small bar magnets composed of north and south poles and magnetic dipole moment is represented by an arrow (south to north pole). Figure 20.2 shows the magnetic field distribution by lines of force for a bar magnet and a magnetic moment by an arrow.

20.3 MAGNETIC FIELD VECTORS

Figure 20.3 shows the magnetic field, H generated by a cylindrical coil. This magnetic field is dependent on the current, I, number of turns, n, and coil length, L. The units of H are Ampere-turn/m. The magnetic field, H is also termed as ‘magnetic field strength’.

Figure 20.3 Magnetic Field by a Coil

H = n.I/L, i.e. (number of turns × current)/length, L

Due to external field H, an internal field is generated, which is represented by B, the magnetic flux density (or magnetic induction). Units of B are tesla (T) (Websters/m2, or Wb/m2). Both H and B are vectors.

The magnetic field strength is related by, B = μH, where μ is called permeability, which is a specific property of the specific medium through which the field H passes and in this medium the flux density B is measured. Permeability, μ has a unit of Wb/A-m or H/m (Henry /meter).

In the presence of vacuum, magnetic flux density, B0 = μ0 × H, where μ0 is the permeability of the vacuum.

 

μ0 = 4 ×10−7 H/m

The magnetic flux within a solid material, B = μH, where μ is the permeability of a solid. Moreover, μ = μr x μ0, i.e. relative permeability × permeability in vacuum. Figure 20.4 shows flux within a solid material (bar).

The relative permeability of a material is a measure of the degree to which a material can be magnetized or the ease with which a magnetic flux field B can be induced in the presence of an external field H.

For magnetization of a solid, another field quantity, M is defined as B = μ0H + μ0M. In the presence of field H, the magnetic moments within a material tend to become aligned with the field and to reinforce it by virtue of their magnetic field; the term μ0M is a measure of this contribution. The magnitude of magnetization, M is proportional to the applied field, H.

 

M = XmH,

where Xm is called magnetic susceptibility, which is unit-less.

Figure 20.4 Magnetic Flux in a Solid Bar

                     Xm

=

(μr − 1) = relative permeability − 1

 

=

(μr − 1)H

20.3.1 Magnetic Moments

Each electron in an atom has magnetic moments due to (1) orbital motion of electron around the nucleus and (2) spinning motion of the electron about its axis. Orbital motion around the nucleus, a moving charge on electron can be considered as a small current loop, generating a very small magnetic field, having a magnetic moment about the axis of rotation. Similarly, each electron can be considered as spinning around an axis, so other magnetic moment generates from an electron spin. Therefore, each electron in an atom is thought of as a small magnet having (1) permanent orbital magnetic moment and (2) spin magnetic moment.

Bohr has given magnetron, μB, the most fundamental magnetic moment of magnitude 9.27 × 10−24 A-m2. For each electron, spin magnetic moment is μB, while the orbital magnetic moment is m1μB, where m1 is the magnetic quantum number of the electron.

Some of the orbital magnetic moments of some electron pairs cancel each other. Similarly, some spin moments are cancelled because spin-up moment will cancel spin-down moment. The net magnetic moment for an atom is the sum of the total magnetic moments minus the moments that are cancelled out.

For an atom having completely filled shells or subshells, when all electrons are taken into account, there is total cancellation of both orbital and spin moments. Therefore, the materials composed of atoms having completely filled electron shells are not capable of being permanently magnetized. For example, atoms of some inert gases like He, Ne and Ar in which shells are completely filled.

Different types of magnetisms are diamagnetism, paramagnetism and ferromagnetism. Subclasses of ferromagnetism are anti-ferrimagnetism and ferrimagnetism. All materials exhibit at least one of these types of magnetisms. The magnetic behaviour depends on the response of electrons and magnetic dipoles to the applied magnetic field.

20.4 MAGNETIZATION CURVES

The magnetic properties of a material are well understood by a magnetization or BH curve, i.e. a curve between flux and magnetic field as shown in Figure 20.5(a)(c).

These curves are all straight lines and drawn for magnetic flux density, B versus magnetic field strength, H. Negative values are not shown, but the graphs are symmetrical about vertical axis.

Figure 20.5(a) shows the curve between B and H, in the absence of any material, i.e., in a vacuum.

Figure 20.5 Magnetization Curves (a) Vacuum (b) Diamagnetic Material (c) Paramagnetic Material

The gradient of this curve is 4π × 10−7 H/m, which corresponds to the fundamental physical constant, μ0. Of greater interest is to see how placing a specimen of some material affects the gradient, μ0. Manufacturers of a particular grade of ferrite metal generally provide this curve because the shape reveals how the core material in any component made from it will respond to changes in the applied field.

Every material exhibits magnetic properties when placed in a magnetic field, hence the materials can be classified according to their interaction with this magnetic field.

Diamagnetism is a classification used to describe materials that line up at right angles to a non-uniform magnetic field and are slightly repelled by the field. Diamagnetism occurs as a result of interference of magnetic field with the motion of electrons orbiting the atoms or molecules of an element or a compound. When a material is placed in the magnetic field, the magnetic force acts upon the moving electrons in the material, causing the electrons to speed up or slow down. The movement of electrons interferes with the motion of the magnetic field, so the atoms internally oppose the field, causing the material to be slightly repelled by the magnetic field.

Diamagnetism is a characteristic of elements or compounds that possess complete sets of valence electrons, which means that all their electrons are paired. Electrons orbit an atom while spinning about their own axis. If a spinning electron is orbiting singly, then its movement generates a magnetic field. But two paired electrons have opposite spins, so that magnetic field generated by each is cancelled out. So, when all the electrons of an atom are paired, the element will not have any magnetic field. When this element is placed in a magnetic field, it is repelled. The atomic dipole configuration of a diamagnetic material with or without magnetic field is shown in Figure 20.6. In the presence of a field, dipoles are induced and are aligned opposite to the field.

In the case of diamagnetism, relative permeability μr is slightly less than 1 and the magnetic susceptibility is negative, that is, the magnitude of magnetic flux B within a diamagnetic material is less than that in vacuum. The volume susceptibility Xm for a diamagnetic solid material is of the order of −10−5. When placed between the poles of a strong electromagnet, the diamagnetic material is attracted towards a region where the field is weak. Table 20.1 presents relative permeability values of some diamagnetic materials.

Figure 20.6 Diamagnetic Material

Table 20.1 Relative Permeability of Some Diamagnetic Materials

20.4.1 Paramagnetism

Paramagnetism generally occurs in elements or compounds possessing unpaired electrons. Many compounds consisting of iron, palladium, platinum and rare earth elements have single electron that generates a small magnetic field. In this case, atom acts as a small permanent magnet. If a substance containing such atoms is placed in a magnetic field, the field of the atom aligns with the applied magnetic field and causes the atom to be slightly attracted to that magnetic field. This attraction to an applied magnetic field is called paramagnetism. Figure 20.7 shows atomic dipole configuration with or without external magnetic field for a paramagnetic material.

Figure 20.7 Paramagnetism

The dipoles align with the external field; they enhance it by giving rise to a relative permeability, μr, greater than 1 and to a relatively small but positive magnetic susceptibility. Table 20.2 gives relative permeability values of some paramagnetic materials.

Both diamagnetic and paramagnetic materials are considered to be non-magnetic as they exhibit magnetism only in the presence of an external field. Flux density B within them is almost the same as it would be in a vacuum, because relative permeability is either slightly less than 1 or slightly more than 1. Tables 20.3 and 20.4 demonstrate susceptibility of some diamagnetic and paramagnetic materials.

 

Table 20.2 Relative Permeability of Some Paramagnetic Materials

Table 20.3 Susceptibility of Some Diamagnetic Materials

Table 20.4 Susceptibility of Some Paramagnetic Materials

20.5 FERROMAGNETISM

In ferromagnetic materials, there are permanent magnetic dipoles, even when no external field acts on the material; as a result, there is long and permanent magnetization. Figure 20.8 shows that when all dipoles are aligned and H = 0, applied field is zero.

Figure 20.8 All Dipoles Aligned—Ferromagnetic Material

This property of ferromagnetism is displayed by α iron (BCC structure), nickel, cobalt and some rare earth metals such as gadolinium (Gd). The magnetic susceptibility of this material is as high as 106, therefore, in this case, H << M and the magnetic flux M = μ0M.

  1. Permanent magnetic moments in ferromagnetic materials result from atomic magnetic moment due to electron spin, which are not cancelled as a result of electronic configuration.
  2. Interactions between adjacent atoms, called coupling interaction, cause the adjacent atoms to align with one another or causing the spin moments to align with one another.
  3. The contribution of orbital magnetic moment is smaller in comparison to spin moments.
  4. Origin of coupling forces is not well understood, but it may be due to the electron structure of the metal.

This mutual spin alignment (coupling) exists in a large volume of region of a crystal, called domains. At a temperature below Curie temperature, Tc, a ferromagnetic material is composed of small volume regions, in which there is mutual alignment of all magnetic dipole moments in the same direction. Figure 20.9 shows the domains in a ferromagnetic material. Arrow represents the atomic magnetic dipole moments.

Figure 20.9 Domains of Aligned Dipoles—Magnetic Moments

Within each domain, all the dipoles are aligned. When the external field is applied, all the magnetic dipoles in a solid piece are mutually aligned with the external field H, causing saturation magnetization, Ms, the maximum possible magnetization. Similarly, there is a corresponding value of saturation flux density, Bs.

Saturation magnetization,

 

Ms = net magnetic moments for each atom × number of atoms per unit volume.

For iron, cobalt and nickel, the net magnetic moment per atom is 2.22, 1.72 and 0.6 times the Bohr’s magnetron, respectively.

Example 20.1   Calculate (1) saturation magnetization and (2) saturation flux density for cobalt, which has a density of 8.9 g/cc, net magnetic moment per atom is 1.72 × Bohr’s magnetron and atomic weight is 58.93 amu.

Solution:

 

   Bohr’s magnetron per atom

 

=

1.72

   Saturation magnetization,

Ms

=

1.72 μB × N

 

N

=

(ρ × Na)/Aw = (density × Avogadro’s number)/atomic weight

 

 

=

(8.9 × 106 × 6.023 × 1023)/58.93

 

 

=

9.096 × 1028 atoms/m3

 

Ms

=

1.72 × 9.27 × 10−24 × 9.096 × 1028 = 14.5 × 105 A/m

   Saturation flux density,

Bs

=

μ0Ms = 4π × 10−7 × 14.5 × 105 = 1.82 T

where T Stands for tesla.

20.5.1 Anti-ferromagnetism

In ferromagnetism, the magnetic moment coupling in adjacent atoms or ions, i.e. dipole moments are parallel and in the same direction, but in anti-ferromagnetism alignment of spin moments in adjacent atoms or ions are completely in opposite directions (anti-parallel). For example, in MnO (manganese oxide) there are Mn2+ and O2− ions.

  1. No net magnetic moment is associated with oxygen ions as there is total cancellation of spin and orbital moments.
  2. Mn2+ ions are arrayed in crystal structure so that the moments in adjacent ions are anti-parallel, i.e. opposing moments cancel each other.
  3. Solid (MnO) does not possess any magnetic moment.

Figure 20.10 shows anti-parallel alignment of spin magnetic moments of Mn2+ ions.

Figure 20.10 Anti-parallel Alignment of Mn2+ Ions

20.6 FERRIMAGNETISM

Almost every item of electronic equipment produced today contains some ferrimagnetic materials like loudspeakers, motor, interference suppressor, antenna rods, proximity sensors, recharge heads, transformers and inductors that are frequently based on ferrites.

Ferrimagnetic materials are oxides of iron compounded with one or more transition metals such as Mn, Ni and Zn, for example, MnFe2O4. Permanent magnets include barium.

Raw material is ground into a powder, which is then fired in a kiln or sintered to produce grey, hard, brittle ceramic materials, having cubic crystalline structure.

On an atomic scale, the magnetic properties depend upon interaction between the electrons associated with metal ions. Neighbouring atomic magnetic moments become locked in anti-parallel with neighbours (which contrast with ferromagnetism), but the magnetic moments in one direction are weaker than the magnetic moments in the opposite direction, resulting in overall magnetic moments. Garnets and ferrites show this behaviour.

Ferrites are compounds of two metallic oxides out of which one is invariably iron oxide. The other metal oxide may be of bivalent elements such as Ni, Mn, Zn, Cu or Fe. Symbolically, ferrites may be designated as (MetO.Fe2O3) in which Met stands for metal and expresses the element. Magnetite, Fe3O4, is composed of FeO.Fe2O3. It has a cubic structure. Few examples of more common ferrites are MnFe2O4, Nickel ferrite, NiFe2O4, Zn-Mn ferrite and Zn-Ni ferrite.

Ferrites are ceramic materials having the following properties:

  1. Very high electrical resistivity
  2. Lower power loss at high frequencies
  3. Due to their spontaneous magnetism, suitable for both temporary and permanent magnet applications

They suffer from poor machinability and brittleness. The magnetization hysteresis loop of ferrite may vary from very narrow to very wide. Ferrites with narrow hysteresis loop form soft magnets, which is used in audio, TV transformer, gyration and inductance cores.

The Mn-Mg ferrites with almost square hysteresis loop are used in memory cores of computers. Barium ferrite (BaO.6Fe2O3) is used to make permanent magnets.

20.6.1 Spinal and Garnet Ferrites

Ferrites have three types of crystals as shown in Table 20.5

 

Table 20.5 Three Types of Crystals of Ferrites

The spinal ferrite unit cell contains 8 × MFe2O3, where M is a bivalent metal ion. The iron and metal ions occupy octahedral and tetrahedral sites of the spinal lattice, respectively. Spinal can be normal or inverse. Zn ferrite (ZnFe2O4) is a normal spinal, while Magnetite (Fe3O4) is an inverse spinal. Curie temperatures of spinal ferrites are in the range of 700–860 K. The conductivity varies from 102 to 10−11 (Ωcm)-1.

Ferrites exhibit hysteresis during magnetization. The hysteresis loops of Cu-Mn ferrite and Mg-Mn ferrite are square, which is used in memory cores of the computers.

Ferrites are also classified as soft and hard ferrites. For example, lithium ferrite is a soft ferrite. It forms square hysteresis loop and has a low dielectric loss. It is mainly used in low-mobility semiconductors and in applications of microwave frequency.

Barium, strontium and lead ferrites exhibiting semiconducting behaviour are hard ferrites. A general-purpose Ni-Zn ferrite has a high relative permeability of the order of 104 and a high resistivity of the order of 107 Ω-m.

20.7 MAGNETOSTRICTION

The dimensions of a bar of a material change when it is magnetized. Depending upon the field, the length of the bar extends or contracts and its area of cross section decreases or increases, respectively. But, when the bar is subjected to a rapidly alternating magnetic field, there is rapid extension and contraction in the length of the bar. This phenomenon is known as magnetostriction. As a result of rapid extension/contraction, longitudinal vibrations are set up in the bar. The phenomenon of magnetostriction is used in audio-frequency oscillators at sonic and ultrasonic frequencies.

20.8 EFFECT OF TEMPERATURE ON MAGNETIC BEHAVIOUR

The magnetic behaviour of a material is very much dependent on the temperature rise as increase in temperature directly affects the saturation magnetization.

As the temperature of a solid is increased, thermal vibrations of the atoms also increase in magnitude and the increased thermal motion of the atoms tends to randomize the direction of magnetic moments. The atomic thermal vibrations counteract the coupling forces between the adjacent atomic dipole moments causing dipole misalignment in ferromagnetic, anti-ferromagnetic and ferromagnetic materials. The dipole misalignment results in decrease in saturation magnetization in ferromagnetic and ferrimagnetic materials.

The saturation magnetization, Ms is maximum at 0 K, because thermal vibrations at 0 K are minimum. So, with increasing temperature, the saturation magnetization gradually decreases and finally it becomes zero at Curie temperature, Tc. At Curie temperature, the mutual spin coupling forces are fully destroyed. For temperatures above Curie temperature, ferromagnetic and ferrimagnetic materials become paramagnetic. For iron, cobalt, nickel and Fe3O4, the Curie temperatures are 768°C, 1120°C, 335°C and 585°C, respectively.

The magnetization behaviour of Fe3O4 is shown in Figure 20.11. Magnetization, Ms becomes zero at Curie temperature and it is maximum at 0 K.

Figure 20.11 Saturation Magnetization of Fe3O4

By temperature variation, anti-ferromagnetism is also affected. The behaviour of anti-ferromagnetism vanishes at Neel temperature. At temperatures above Neel temperature, anti-ferromagnetic material becomes paramagnetic.

20.9 DOMAINS

At temperatures below Curie point, Tc, in ferromagnetic and ferrimagnetic materials, there exist domains, i.e. small volume regions in each of which there is mutual alignment of all magnetic dipoles in the same direction as shown in Figure 20.12.

Figure 20.12 Aligned Magnetic Dipoles in Each Domain

On microscopic scale, there are several domains in each grain. But on macroscopic scale, considering a solid piece, there are multitudes of domains. There is magnetization in each domain. For a solid piece, the overall magnetization is the vector sum of magnetizations in all the domains.

Flux density, B and field density, H are not proportional to each other in ferromagnetic and ferrimagnetic materials. A curve between B and H is shown in Figure 20.13. As the external field H is increased, the flux density B begins to increase slowly (the flux B lags behind the applied field H) and more rapidly and finally the curve becomes asymptotic at saturation as shown. Maximum flux is Bs.

Figure 20.13 Magnetic Flux Density Versus Magnetic Field

As the field H is applied, domains change shape and size by the movement of domain boundaries. As the field H increases, the domains, which are favourably oriented grow at the expense of other domains that are not favourably oriented. As the process of magnetization continues, at saturation point in all the domains dipole moments are aligned with the external field, H as shown in Figure 20.13. The magnetic dipoles in all domains are aligned with external field, H.

20.10 HYSTERESIS

A hysteresis effect is produced in which the flux field, B lags behind applied magnetic field, H. At zero H, there exists a residual flux that is called remanence or remanent. Flux density, Br (the material receives magnetization in the absence of external field H) is shown in Figure 20.14.

Figure 20.14 Magnetic Flux Density B Versus Magnetic Field H

The hysteresis behaviour can be explained by the motion of domain walls. From saturation, when the field is reversed, the process by which the domain structure changes is also reversed. First of all, there is rotation of a single domain in the reversed field, then domains having magnetic moments aligned with the new field form and grow at the expense of the former domains. When the applied field reaches zero, there is still some net volume fraction of domains oriented in the former direction, flux field −Br, exists. To reduce the flux field B to zero within the domain, the field Hc has to be applied as shown in the Figure 20.14, which is called the coercivity or sometimes the coercive force. During the application of reverse field -H, saturation is reached at a point S′. A second reversal of the field (+H direction) to the point of saturation S completes the symmetrical hysteresis loop and provides negative remanence (−Br) and a positive coercivity +Hc. The B–H curve shown represents hysteresis loop taken to saturation.

Energy loss due to hysteresis, Uh = AfV, where A is the area of loop in J/m2, f is the frequency in Hz and V is the volume in m3.

Example 20.2   Determine the power loss due to hysteresis in a transformer core, having a volume of 0.008 m3 at a frequency of 50 Hz if the area of the loop is 600 J/m2.

Solution:

 

            Area of the loop, A

=

600 J/m2

                     Frequency, f

=

50 Hz

                        Volume, V

=

0.008 m3

                Power loss, Uh

=

600 × 50 × 0.008 = 240 W

20.11 SOFT MAGNETIC MATERIALS

The area within the hysteresis loop represents the energy loss per unit volume during magnetization and demagnetization cycles. Energy loss is converted into heat and the temperature of the specimen is raised. On the basis of energy loss in the loop, both ferromagnetism and ferrimagnetism can be classified into soft and hard magnetic materials. Soft magnetic materials are used in devices subjected to alternating magnetic fields such as in transformer cores, where the energy loss must be low (Figure 20.15).

Figure 20.15 Magnetization Curve for Soft and Hard Magnetic Materials

Following are the properties of a soft magnetic material:

  1. Area within the loop is small as shown in Figure 20.15.
  2. High initial permeability.
  3. Low coercivity.
  4. Saturation magnetization is reached at low applied field H.
  5. Easily magnetized and demagnetized.

The structural defects as voids and impurity particles tend to restrict the motion of domain walls and so increase the coercivity, Hc. Therefore, a soft magnetic material must be free from structural defects.

An electrical current may be induced in the material by a magnetic material and field varies in magnitude and time, resulting in eddy currents. The losses due to eddy currents must be minimized by increasing electrical resistivity of the material. To increase resistivity, solid solution alloys of Fe-Si and Fe-Ni are used.

In some magnetic amplifier and pulse transformer applications, a square hysteresis loop is desired, which can be obtained by proper heat treatment of the magnetic material. Soft magnetic materials are used in the following:

  1. Generators
  2. Motors
  3. Dynamos
  4. Switching circuits
  5. Magnetic amplifiers
  6. Pulse transformers

Table 20.6 gives composition, initial relative permeability, hysteresis loss area and resistivity of some soft magnetic materials

 

Table 20.6 Soft Magnetic Materials

20.12 HARD MAGNETIC MATERIALS

Permanent magnets are made from hard magnetic materials. They possess high resistance to magnetization. They also possess high values of remanence Br, coercivity Hc and saturation flux density Bs. However, they have low initial relative permeability and suffer from high hysteresis energy losses as shown in Figure 20.16.

Energy product (BH)max corresponds to the largest area that can be constructed in the II quadrant of the loop. Larger the value of (BH)max, harder will be the magnetic material.

There are two types of hard magnetic materials: conventional and high-energy hard magnetic materials. For conventional material (BH)max < 80 kJ/m3 and for high-energy hard material (BH)max > 80 kJ/m3.

Figure 20.16 (BH)max in II Quadrant, Magnetization Curve

Hard magnetic steel employs tungsten and chromium as alloying elements. Hard precipitates of tungsten and chromium carbides obstruct the movement of domains. Table 20.7 gives the composition, remanent flux, energy product, Curie temperature Tc and resistivity of some hard magnetic materials.

 

Table 20.7 Hard Magnetic Materials

20.12.1 High-energy Hard Magnetic Materials

These are permanent magnetic materials with an energy product > 80 kJ/m3. Two such alloys are commercially available.

  1. Samarium-cobalt magnet (SmCo5)

    Sm is a rare earth element and is expensive, exhibits the properties of high-energy hard magnetic material.

    (BH)max = 120–240 kJ/m3, Br = 0.92, Hc = 720,000 ampere-turn/m, Tc = 725 and ρ = 5 × 10−7 Ωm.

     

  2. Neodymium iron boron magnet (Nd2Fe14B)

    This is used in wide variety of applications. The coercivity and energy product of this alloy are more than those of SmCo5 alloy.

A few applications of hard magnetic materials as follows:

  1. Motors
  2. No heat is generated during operation
  3. Cordless drills and screw drivers
  4. Automobiles, starters, window winders, wipers, washers and fan motors
  5. Audio-video recorders
  6. Clocks
  7. Lightweight earphones, hearing aids
  8. Computer peripherals
20.13 MAGNETIC STORAGE

There are wide applications of magnetic recording:

  1. Storage of electronic information is in the form of audio tapes, VRSs, computer hard disks and floppy disks. A typical desktop computer now has a capacity of 40 Gbytes/disk. For magnetic data storage, the key parameter is electron spin, which is the fundamental origin of magnetic moments.
  2. Recording and television industry rely on magnetic tapes for storage and reproduction of audio and video sequences. Transference to and retrieval from the tape or disk is accompanied by an inductive read-write head, which consists of basically a wire coil wound around a magnetic material core into which a gap is cut. Data are written by electrical signal within the coil, which generates a magnetic field across the gap. The field in turn magnetizes a very small area of the tape within the proximity of the head. When the applied field is removed, magnetization remains and signal has been stored.
  3. There are two principal types of magnetic media: (a) particulates of iron oxide or chromium oxide and (b) polymeric thin film (for magnetic tape). The storage density of thin film is greater than that of particulate media.

Storage is permanent and magnetization reversal will result in a narrow range of applied field.

20.14 COMMONLY USED MAGNETIC MATERIALS

Commonly used magnetic materials are as follows:

  1. Permalloy: Magnetic properties depend upon the percentage of nickel in the alloy. Increased percentage of nickel improves the magnetic properties. Low nickel permalloy with 40–50 per cent nickel is cheap, but high nickel alloy with 72–80 per cent of nickel is costly. Relative permeability of Permalloy is as high as 8 × 105.
  2. Alsifier: It contains 9.5 Si, 5.6 Al and 84.9 Fe. It is hard, brittle and cheaper than Permalloy. It has a relative permeability of 1.0 × 104−3.5 × 104. It is used in magneto dielectric capacitors.
  3. Cammalloys: Contains 66.5 Ni, 30 Cu and 3.5 Fe. It is a soft magnetic material. Its Curie point is 100°C.
  4. Magnetostrictive materials: Pure nickel and some alloys of iron with chromium, cobalt and aluminium are magnetostrictive. They are used in audio frequency oscillators at sonic and subsonic frequencies.
  5. Magneto dielectric materials: These are made from powders of carbonyl iron, alsifer and permalloy. They reduce eddy current losses. These materials are used as cores in magnetic circuits in such instruments, which operate at very high frequencies.
  6. Powder magnets: Pure iron is powdered by applying high pressures. These are kept in benzene to prevent from spontaneous combustion.
  7. Mumetals: These are used to obtain huge flux densities in weak magnetic field in transformers. It contains some percentage of copper and eddy current losses are reduced. It has high permeability.
  8. Perminvar: Sometimes it is necessary to have a magnetic material for which the permeability is independent of the field strength. Such materials find applications in chokes and transformers. Perminvar is an alloy of nickel, iron and cobalt. But the material is very expensive.
  9. Supermalloy: It consists of iron and nickel alloyed with copper and molybdenum. It is characterized by very high purity and high permeability of the order of 105.
  10. Ferrites (Fe2O3.NiO.ZnO): They are ceramic compounds of ferric oxide with NiO and ZnO. These oxides are finely powdered with organic binders. Binders burn out when fired at 1100–1400°C. The permeability of ferrites varies with field frequency. The resistivity is of the order of 102−107 Ωm.

Like semiconducting materials, their applications are in very high-frequency devices.

20.15 SUPERCONDUCTIVITY

As most of the high purity metals are cooled down gradually to temperature nearing 0 K, the electrical resistivity also decreases gradually approaching to a very small quantity. There are a few materials for which resistivity plunges down virtually to zero at temperatures very near to 0 K. Such materials are known as superconducting materials. The temperature at which they attain superconductivity is called critical temperature, Tcs. The critical temperature varies from 0.02 to 7.2 K for pure metals, from 10.2 to 23 K for compounds and alloys and from 92 to 153 K for ceramic compounds developed for super conduction.

The state of superconductivity results from attractive interaction between pairs of conducting electrons. The motion of these paired electrons becomes co-ordinated such that the scattering by thermal vibrations and impurity is highly inefficient. The resistivity that is proportional to the incidence of scattering becomes zero. There are two types of superconducting materials: Type I and II.

  1. Type I: They are completely diamagnetic in superconducting state. Elements like Al, Pb, Sn and Hg belong to this group. All of an applied magnetic field will be excluded from the body of the material, i.e. Meissner effect, as shown in Figure 20.17(a). As field H is increased, the material remains diamagnetic until Hc magnetic field is reached. After this, conduction becomes normal and complete magnetic flux penetrates the body as shown in Figure 20.17(b)

    Figure 20.17 (a) Exclusion of Body by Magnetic Flux (b) Magnetic Flux Penetration in Body

  2. Type II: Superconductors are totally diamagnetic at low applied fields and field exclusion is total-transition from superconducting state to normal state occurs between lower critical field, Hc1 and upper critical field, Hc2. At Hc1, flux lines begin to penetrate into the body and at Hc2 penetration is complete. Between the two critical fields, the material exists in a mixed state—both normal and superconducting states are present.

Three most commonly used superconductors are niobium-zirconium alloy, niobium-titanium alloy and niobium-tin alloy. Properties of these intermetallic compounds are given in Table 20.8.

 

Table 20.8 Properties of Intermetallic Compounds

Alloy Critical Temperature (K) Critical Flux Density (Bc)

Nb—Ti

10.2
12 T (tesla)

Nb—Zr

10.8
11 T (tesla)

Nb3Sn

18.3
12 T (tesla)

Several ceramic materials, which are normally electrically insulative have been found to be superconducting with higher critical temperatures. For example,

 

 

YBa2Cu3O7Tc is 92 K

 

HgBa2Ca2Cu2O8Tc is 153 K

But these ceramic superconductors are brittle in nature, and cannot be fabricated in the form of wires.

20.15.1 Applications of Superconductors

Superconductors are mainly used in following fields:

  1. Magnetic resonance imaging in medical field.
  2. Electrical power transmission through superconductors, power loss is extremely low, and transmission at low voltage is possible.
  3. Magnets of high-energy particle accelerators.
  4. High-speed switching and signal transmission in computers.
  5. High-speed magnetically levitated trains.
KEY POINTS TO REMEMBER
  • Magnetic forces arise from the movement of electrical charge.
  • Electron spin has a dominant effect and electron orbital motion has a secondary effect on the magnetic behaviour.
  • Magnetic dipoles are found to exist in magnetic materials.
  • Magnetic flux is generated within the coil/cylinder subjected to external field.
  • Magnetic flux B = μH, = permeability × field
  • Permeability in vacuum, μ0 = 4π × 10−7 H/m
  • Magnetization,

     

              M

    =

    XmH

     

    =

    magnetic susceptibility × field

     

    =

    (μr − 1)H, where μr is the relative permeability

     

  • Flux, B = μ0(H + M)
  • Bohr’s magnetron, μB = 9.27 × 10−24 A-m2
  • Diamagnetism: All the electrons are paired but with opposite spin. Diamagnetic material when placed in a magnetic field is repelled, and the relative permeability is less than 1.
  • Paramagnetism: Electrons are unpaired. When magnetic field is applied, dipoles align with the external field, giving rise to a relative permeability greater than 1.
  • Ferromagnetism: Permanent magnetic moments result from atomic magnetic moments; electron spins are not cancelled, and dipoles are aligned even when H = 0.
  • Domain: Within each domain all the dipoles are aligned.
  • Saturation magnetization, Ms = net magnetic moment for each atom × number of atoms per unit volume.
  • Anti-ferromagnetism: Alignment of spin moments of adjacent atoms or ions is completely in opposite directions. MnO is anti-ferromagnetic.
  • Ferrimagnetism: Atomic magnetic moments are locked in anti-parallel in neighbouring atoms. Magnetic moments are weaker in one direction than in the opposite direction, resulting in overall net magnetic moment. Ferrites are ferrimagnetic materials.
  • Magnetostriction: Under applied alternating magnetic field, there are rapid extension/contraction in a bar, which starts oscillating.
  • At Curie temperature, magnetization becomes zero as mutual spin coupling forces are fully destroyed.
  • At saturation, dipole moments in all domains are aligned with the applied field.
  • For soft magnetic materials, a narrow hysteresis loop and for hard magnetic materials, wide hysteresis loop is generated.
  • Area within the hysteresis loop represents the energy loss per unit volume during magnetization-demagnetization cycle.
  • Soft magnetic material (BH)max < 80 kJ/m3
  • Hard magnetic material (BH)max > 80 kJ/m3
  • Magnetic recording of sequences is done on magnetic tapes, computer hard disks and floppy disk.
  • Superconductivity: Electrical resistivity of some high-purity metals approaches zero close to 0 K; power can be transmitted at low power loss and low voltage.
  • Temperature at which superconductivity is attained is called critical temperature.
  • For a pure metal, critical temperature is very close to 0 K.
MULTIPLE CHOICE QUESTIONS
  1. Permeability of a vacuum is
    1. 4π × 10−6 H/m
    2. 4π × 10−7 H/m
    3. 4π × 10−8 H/m
    4. None of these
  2. What is the value of Bohr’s magnetron?
    1. 9.27 × 10−24 A-m2
    2. 7.29 × 10−24 A-m2
    3. 9.33 × 10−24 A-m2
    4. None of these
  3. Susceptibility of a ferromagnetic material can be as high as
    1. 100
    2. 10,000
    3. 106
    4. None of these
  4. Bohr’s magnetron for iron is
    1. 0.60
    2. 1.72
    3. 2.22
    4. None of these
  5. For MnO, an anti-ferromagnetic material, which of following statements is correct?
    1. O2− ions are arrayed in a crystal structure and moments of adjacent ions are anti-parallel
    2. Mn2+ ions, moments of adjacent ions are anti-parallel and opposing moments cancel each other
    1. Both (A) and (B)
    2. Only (A)
    3. Only (B)
    4. None of the above
  6. Special application of barium ferrite (BaO.6Fe2O3)
    1. Transformers
    2. Memory cores of computers
    3. Permanent magnets
    4. None of these
  7. Which one of the following is a correct statement?
    1. Cunife is the high-energy hard magnetic material
    2. Si-Fe compound is a soft magnetic material
    3. The losses due to eddy currents can be minimized by reducing the electrical resistivity of the material
    4. None of these
  8. Permanent magnets are made of
    1. High-energy hard magnetic material
    2. 45 Permalloy
    3. Commercial iron
    4. None of these
  9. For transformer cores, which material is most suitable?
    1. Soft magnetic material
    2. High-energy hard magnetic material
    3. Both (a) and (b)
    4. Neither (a) nor (b)
  10. For a hysteresis loop, area of loop is 120 J/m3 and transformer core volume is 0.012 m3 at a frequency of 50 Hz, what is hysteresis loss?
    1. 144 W
    2. 72 W
    3. 14.4 W
    4. None of these
  11. For cordless drilling, which magnetic material is used?
    1. Soft magnetic material
    2. Hard magnetic material
    3. High-energy hard magnetic material
    4. None of these

Answers

1. (b)

2. (a)

3. (c)

4. (c)

5. (c)

6. (c)

7. (b)

8. (a)

9. (a)

10. (b)

11. (c)

 

 

 

 

REVIEW QUESTIONS
  1. Explain the magnetic field, flux field and magnetic moment.
  2. Define the following:

    Relative permeability, magnetization and susceptibility

  3. What are spinning and orbital moments of an electron?
  4. Differentiate between diamagnetism and paramagnetism with the help of sketches.
  5. Explain ferromagnetism and ferrimagnetism with the help of sketches.
  6. What are ferrites? What are the characteristics of ferrites? Name a few ferrites.
  7. What are magnetostriction, Curie point and domains?
  8. Explain BH curve and show domains at saturation point.
  9. Differentiate between soft and hard magnetic materials with the help of hysteresis loop.
  10. Explain the following in the case of hysteresis loop

    Remanent, saturation flux and coercive force

  11. Enumerate the properties of soft magnetic materials. Name a few soft magnetic materials with composition and initial relative permeability.
  12. Name a few hard magnetic materials.
  13. What do you mean by magnetic storage?
  14. Write a short note on superconductivity.
PRACTICE PROBLEMS
  1. Calculate the saturation magnetization and saturation flux density for nickel with a density of 8.9 g/cm3. Bohr’ magnetron per atom is 0.60 and atomic weight is 58.69.

     

    Ans. (5.08 × 105 A/m, 0.639 T)

  2. Determine the power loss due to hysteresis in a transformer core having a volume of 0.012 m3 at a frequency of 50 Hz. The area of the loop is 550 J/m3.

     

    Ans. (330 W)