Types of Magnetic Materials (1)

Chapter 1

Types of Magnetic Materials

1.1 Nature of magnetic materials

Assume we take a simple model of an atom to obtain some differences in behavior of various types of magnetic materials in the magnetic field.

The simple atomic model contains central positive nucleus surrounded by electrons in various circular orbits.

Rotation of electron in circular orbit generates a small current loop oppositely to the direction of electron travel.

1.2 Types of dipole moment inside the atom

1- Orbital motion of electron

In the absence of magnetic field, the rotation of electron around the nucleus produce a dipole moment m=IS

2- Spin motion of electron

Rotation of electrons around itself or around it's axis produce a dipole moment=±9×10-24A.m2, and sign positive or negative means that the dipole moment may be in direction of external magnetic field or may be opposite direction of external magnetic field.

3- Spin motion of nucleus

Rotation of nucleus around itself or around it's axis produce a dipole moment which it's value is small.

So we can neglect this dipole comparing to the first and second dipole.

1.3 Classification of magnetic types

We can classify any material according to the summation of all these dipole moment and give the material the magnetic characteristics.

1.4 Types of magnetic materials:

1- Diamagnetic

2- Paramagnetic

3- Ferromagnetic

4- Anti-ferro magnetic

5- Ferrimagnetic

6- Super Paramagnetic

1- Diamagnetic

In the absence of applied magnetic field, each atom has net zero magnetic dipole moment.

In the presence of applied magnetic field, the angular velocities of electronic orbits must be changed.

These induced magnetic dipole moments align themselves opposite to the applied fields.

The relative permeability of these materials must less than one µr< 1.

When placed in magnetic field, the lines of force tend to avoid the substance as shown in fig.1.1.

Fig.1.1 Lines of Force around Diamagnetic Material

When placed in nonuniform magnetic field, it moves from stronger to weaker field.

When diamagnetic rod is freely suspended in a uniform magnetic field, it aligns itself in a direction perpendicular to the field.

Ex:

Hydrogen, Helium, inert gases, metallic bismuth, sodium chloride, copper, gold, Silicon.

2- Paramagnetic

In the absence of applied magnetic field, each atom has net none zero magnetic dipole moment.

These Magnetic dipoles moments are randomly oriented so that the net magnetization is zero.

In the presence of an applied magnetic field, the magnetic dipoles align themselves with the applied field.

The relative permeability of these materials more than one µr>1.

When placed in magnetic field, the lines of force prefer to pass through the substance rather than air as shown in fig.1.2

Fig.1.2: lines of force around Paramagnetic Material

When placed in nonuniform magnetic field, it moves from weaker to stronger field.

When Paramagnetic rod is freely suspended in a uniform magnetic field, it aligns itself in a direction parallel to the field.

Ex:

Potassium, oxygen, tungsten, rare earth elements, Platinum

3- Ferromagnetic

In the absence of applied magnetic field, each atom has very strong magnetic dipole moment due to uncompensated electron spins.

Domain form is the region of many atoms with aligned dipole moments.

In the absence of applied magnetic field, the domains are randomly oriented so that the net magnetization is zero.

In the presence of an applied magnetic field, the domains align themselves with the applied field.

The permeability of these materials is more than one µr>>>1.

When placed in magnetic field, the lines of force tend to crowd into specimen as shown in fig.1.3.

Fig.1.3: lines of force around Ferromagnetic Material

When placed in nonuniform magnetic field, it moves from weaker to stronger field.

When a Ferromagnetic rod is freely suspended in a uniform magnetic field, it aligns itself in a direction parallel to the field "very quickly".

Ex:

Iron, Nickel, cobalt, gadolinium

4- Anti ferromagnetic

The forces between the atoms cause alignment of dipole moments in antiparallel fashion so that the net magnetic dipole moment equal zero.

Ex:

Nickel oxide "NIO", Ferrous sulfide "Fes", cobalt chloride "cocl2"

5- Ferrimagnetic

The forces between the atoms cause alignment of dipole moments in antiparallel fashion but there is net dipole moment although the response is less than ferromagnetic.

It has a higher resistance so it reduces the effect of eddy current.

Ex:

FeO4, NiFe2O4

6- Super paramagnetic

This material is used in magnetic tape which is used in "Audio tape" recorders, "Video tape" recorders.

1.5 Eddy current

Look at the Fig.1.4 where a rectangular core of magnetic material is shown along with the exciting coil wrapped around it.

Without any loss of generality, one may consider this to be a part of a magnetic circuit.

If the coil is excited from a sinusoidal source, exciting current flowing will be sinusoidal too.

Now put your attention to any of the cross section of the core and imagine any arbitrary rectangular closed path abcd.

An emf will be induced in the path abcd following Faraday’s law.

Here of course we don’t require a switch S to close the path because the path is closed by itself by the conducting magnetic material (say iron). Therefore a circulating current ieddy will result.

The direction of ieddy is shown at the instant when B (t) is increasing with time. It is important to note here that to calculate induced voltage in the path, the value of flux to be taken is the flux enclosed by the path i.e.,
∅max=Bmax×area of the loop abcd

The magnitude of the eddy current will be limited by the path resistance, Rpath neglecting reactance effect.

Eddy current will cause power loss in Rpath and heating of the core.

To calculate the total eddy current loss in the material we have to add all the power losses of different eddy paths covering the whole cross section.

Fig.1.4: Eddy current paths

1.6 Use of thin plates or laminations for core

We must see that the power loss due to eddy current is minimized so that heating of the core is reduced and efficiency of the machine or the apparatus is increased.

It is obvious if the cross sectional area of the eddy path is reduced then eddy voltage induced too will be reduced (Eeddy α area), hence eddy loss will be less.

This can be achieved by using several thin electrically insulated plates (called laminations) stacked together to form the core instead a solid block of iron.

The idea is depicted in the Fig.1.5 where the plates have been shown for clarity, rather separated from each other. While assembling the core the laminations are kept closely pact.

Conclusion is that solid block of iron should not be used to construct the core when exciting current will be ac. However, if exciting current is dc, the core need not be laminated.

Fig.1.5: Laminated core to reduce eddy loss.

1.7 Hysteresis Loss

1.7.1 Unidirectional time varying exciting current

Consider a magnetic circuit with constant DC excitation current I0.
Flux established will have fixed value with a fixed direction.

Suppose this final current I0 has been attained from zero current slowly by energizing the coil from a potential divider arrangement as depicted in Fig.1.6 Let us also assume that initially the core was not magnetized.

The exciting current therefore becomes a function of time till it reached the desired current I and we stopped further increasing it.

The flux too naturally will be function of time and cause induced voltage e12 in the coil with a polarity to oppose the increase of inflow of current as shown.

The coil becomes a source of emf with terminal-1, +ve and terminal-2, -ve.

Recall that a source in which current enters through its +ve terminal absorbs power or energy while it delivers power or energy when current comes out of the +ve terminal. Therefore during the interval when i (t) is increasing the coil absorbs energy. Is it possible to know how much energy does the coil absorb when current is increased from 0 to I0? This is possible if we have the B-H curve of the material with us.

Fig.1.6: Coil around Ferromagnetic Material

What happens if now current is gradually reduced back to 0 from I0?

The operating point on B-H curve does not trace back the same path when current was increasing from 0 to I0.

In fact, B-H curve (PRT) remains above during decreasing current with respect the B-H curve (OGP) during increasing current as shown in fig.1.7 this lack of retracing the same path of the curve is called hysteresis.

Fig.1.7: B-H curve

1.8 Hysteresis loop with alternating exciting current

Let us see how the operating point is traced out if the exciting current is i = Imaxsin ωt.

The nature of the current variation in a complete cycle can be enumerated as follows:

In the interval 0 ≤ ωt ≤ π2                          i is +ve and didt is +ve.

In the interval π2  ≤ ωt ≤ π                         i is +ve and didt  is –ve.

In the interval π ≤ ωt ≤  3π2                       i is –ve and didt   is –ve.

In the interval 3π2  ≤ ωt ≤ 2π                     i is –ve and didt   is +ve.

Let the core had no residual field when the coil is excited by i = Imaxsin ωt.

In the interval 0 < ωt < π2 , B will rise along the path OGP. Operating point at P corresponds to +Imaxor +Hmax.  

For the interval  π2 < ωt < π operating moves along the path PRT. At point T, current is zero. However, due to sinusoidal current, i start increasing in the –ve direction as shown in the Fig.1.8 and operating point moves along TSEQ.

It may be noted that a –ve H of value OS is necessary to bring the residual field to zero at S. OS is called the coercivity of the material.

At the end of the interval π < ωt < 3π2 current reaches –Imaxor field –Hmax.

In the next internal, 3π2 < ωt < 2π, current changes from –Imaxto zero and operating point moves from M to N along the path MN.

After this a new cycle of current variation begins and the operating point now never enters into the path OGP.

The movement of the operating point can be described by two paths namely:

(i) QFMNKP for increasing current from –Imaxto +Imax and (ii) from +Imax to –Imax along PRTSEQ.

Fig.1.8: B-H loop with sinusoidal current

1.9 Hysteresis loss & loop area

In other words the operating point trace the perimeter of the closed area QFMNKPRTSEQ. This area is called the B-H loop of the material.

We will now show that the area enclosed by the loop is the hysteresis loss per unit volume per cycle variation of the current.

In the interval 0 ≤ ωt ≤ π2 , i is +ve and didt   is +ve., moving the operating point from M to P along the path MNKP. Energy absorbed during this interval is given by the shaded area MNKPLTM shown in Fig.1.9 (i).

In the interval π2  ≤ ωt ≤ π, i is +ve and didt  is –ve, moving the operating point from P to T along the path PRT.

Energy returned during this interval is given by the shaded area PLTRP shown in Fig.1.9 (ii).  

Thus during the +ve half cycle of current variation net amount of energy absorbed is given by the shaded area MNKPRTM which is nothing but half the area of the loop.

In the interval π ≤ ωt ≤  3π2 , i is –ve and didt  is –ve, moving the operating point from T to Q along the path TSEQ.

Energy absorbed during this interval is given by the shaded area QJMTSEQ shown in Fig.1.9 (iii).  

In the interval 3π2  ≤ ωt ≤ 2π, i is –ve and didt is +ve, moving the operating point from Q to M along the path QEM. Energy returned during this interval is given by the shaded area QJMFQ shown in Fig.1.9 (iv).

Thus during the –ve half cycle of current variation net amount of energy absorbed is given by the shaded area QFMTSEQ which is nothing but the other half the loop area.

Fig.1.9: B-H loop with sinusoidal current.

Therefore total area enclosed by the B-H loop is the measure of the hysteresis loss per unit volume per unit cycle.

To reduce hysteresis loss one has to use a core material for which area enclosed will be as small as possible.