ph2161-engineering physics-ii - vidyarthiplus

Introduction

Can all magnetic materials exhibit ferromagnetism? Can one have elemental and compound ferromagnetic materials? How is a ferromagnetic material characterised?

How does a hysteresis loop help one to find the suitability of a magnetic material for a specific application?

What are the different energies involved in domain theory?

What does a BH product of a ferromagnetic material convey?

Learning ObjectivesOn completion of this topic you will be able to understand:

1. What is a ferromagnetic material? 2. What is ferromagnetic domain theroy?3. What is hysteresis?4. The meaning of BH product.

Ferromagnetism:The ability of a substance to become permanently magnetized by exposure to an external

magnetic field.OR

Ferromagnetism is a phenomenon exhibited by materials like iron (nickel or cobalt or any other suitable alloy) that become magnetized in a magnetic field and retain their magnetism when the field is removed.

OR

Ferromagnetism is a property exhibited by certain metals, alloys, and compounds of the transition (iron group), rare-earth, and actinide elements in which, below a certain temperature called the Curie temperature, the atomic magnetic moments tend to line up in a common direction.

Ferromagnetism is characterized by the strong attraction of one magnetized body for another.

Atomic magnetic moments arise when the electrons of an atom possess a net magnetic moment as a result of their angular momentum. The combined effect of the atomic magnetic moments can give rise to a relatively large magnetization, or magnetic moment per unit volume, for a given applied field. Above the Curie temperature, a ferromagnetic substance behaves as if it were paramagnetic: Its susceptibility approaches the Curie-Weiss law. The Curie temperature marks a transition between order and disorder of the alignment of the atomic magnetic moments. Some materials having atoms with unequal moments exhibit a special form of ferromagnetism below the Curie temperature called ferrimagnetism.

The characteristic property of a ferromagnet is that, below the Curie temperature, it can possess a spontaneous magnetization in the absence of an applied magnetic field. Upon application of a weak magnetic field, the magnetization increases rapidly to a high value called the saturation magnetization, which is in general a function of temperature. For typical ferromagnetic materials, their saturation magnetizations, and Curie temperatures.

Small regions of spontaneous magnetization, formed at temperatures below the Curie point, are known as domains. As shown in the illustration, domains originate in order to lower the magnetic energy.

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In illus. b it is shown that two domains will reduce the extent of the external magnetic field, since the magnetic lines of force are shortened. On further subdivision, as in, this field is still further reduced.

Figure 1. Lowering of magnetic field energy by domains. (a) Lines of force for a single domain. (b) Shortening of lines of force by division into two domains. (c) Reduction of field energy by further subdivision.

Another way to describe the energy reduction is to note that the interior demagnetizing fields, coming from surface poles, are much smaller in the long, thin domains of Fig. 1(c) than in the “fat” domain of Fig. 1(a).

The question arises as to how long this subdivision process continues. With each subdivision there is a decrease in field energy, but there is also an increase in Heisenberg exchange energy, since more and more magnetic moments are aligning antiparallel. Finally a state is reached in which further subdivision would cause a greater increase in exchange energy than decrease in field energy, and the ferromagnet will assume this state of minimum total energy.

Materials easily magnetized and demagnetized are called soft; these are used in alternating-current machinery. The problem of making cheap soft materials is complicated by the fact that readily fabricated metals usually have many crystalline boundaries and crystal grains oriented in many directions. The ideal cheap soft material would be an iron alloy fabricated by some inexpensive technique which results in all crystal grains being oriented in the same or nearly the same direction. Various complicated rolling and annealing methods have been discovered in the continued search for better grain-oriented or “cube-textured” steels.

Materials which neither magnetize nor demagnetize easily are called hard; these are used in permanent magnets. A number of permanent-magnet materials have enjoyed technological importance. The magnet steels contain carbon, chromium, tungsten, or cobalt additives, serving to impede domain wall motion and thus to generate coercivity. Alnicos (Alnico is an acronym referring to alloys which are composed primarily of aluminium (symbol Al), nickel (symbol Ni) and cobalt (symbol Co), hence al-ni-co, with the addition of iron, copper, and sometimes titanium, typically 8–12% Al, 15–26% Ni, 5–24% Co, up to 6% Cu, up to 1% Ti, and the balance is Fe) are alloys containing finely dispersed, oriented, elongated particles precipitated by thermal treatment in a field. Hard ferrite magnets are based on the oxides BaFe12O19 and SrFe12O19. Hard ferrite magnets are relatively

inexpensive and are used in a great variety of commercial applications. Rare earth–transition metal materials whose rare-earth component provides huge magneto-crystalline anisotropy can be translated into large coercivity in a practical magnet, while the magnetization arises chiefly from the transition-metal component. Examples include samarium-cobalt magnets based on the SmCo5 or Sm2Co17 intermetallic compounds.

Domain theory of ferromagnetism:The domain structure of a ferromagnetic material is determined by many types of energies, with

the most stable structure being attained when the overall potential energy of the material is a minimum. The total magnetic energy of a ferromagnetic material is the sum of the contributions of the following energies:

1. exchange energy,





2. magnetostatic energy, 3. magnetocrystalline anisotropy energy, 4. domain wall energy, and 5. magnetostrictive energy.

Exchange energy:

The potential energy within a domain of a ferromagnetic solid is minimized when all its atomic dipoles are alligned in one direction. This alignment is associated with a positive exchange energy. However, even though the potential energy within a domain is minimized, its external potential energy is increased by the formation of an external magnetic field (Fig. 2a).

Figure 2Magnetostatic energy:

Magnetostatic energy is the potential magnetic energy of a ferromagnetic material produced by its external field (Fig. 2a). This potential energy can be minimized in a ferromagnetic material by domain formation, as illustrated in Fig. 2. For a unit volume of a ferromagnetic material, a single-domain structure has the highest potential energy, as indicated by Fig. 2a. By dividing the single domain of Fig. 2a into two domains (Fig. 2b), the intensity and extent of the external magnetic field is reduced. By further subdividing the single domain into four domains, the external magnetic field is reduced still more (Fig. 2c). Since the intensity of the external magnetic field of a ferromagnetic material is directly related to its magnetostatic energy of a unit volume of material.

Magnetocrystalline anisotropy energy:The magnetization of a single

crystalline ferromagnetic material depends on the orientation of the same with respect to the applied magnetic field. Figure 3 shows magnetic induction B versus applied field H curves for magnetizations in the <100> and <111> directions for single crystals of BCC iron. As indicated in Fig. 3, saturation magnetization occurs easiest (or with the lowest applied field) for the <100> directions and with the highest applied field in the <111> directions. The <111> directions are said to be the hard directions for magnetization in BCC iron. For FCC nickel the easy

Figure 3





directions of magnetization are the <111> directions and the <100> the hard directions; the hard directions for FCC nickel are just the opposite as those for BCC iron.

For polycrystalline ferromagnetic materilas such as iron and nickel, grains at different orientations will reach saturation magnetization at different field strengths. Grains whose orientations are in the easy direction of magnetization will saturate at low applied fields, while grains oriented in the hard directions must rotate their resultant monent in the direction of the applied field and thus will reach saturation under much higher fields. The work done to rotate all the domains because of this anisotropy is called the magnetocrystalline anisotropy energy.

Domain wall energy:

Figure 4A domain wall is the boundary between two domains whose overall magnetic moments are at

different orientations and is analogous to a grain boundary where crystal orientation changes from one grain to another. In contrast to a grain boundary at which grains change orientaion abruptly and which is about 3 atoms wide, a domain change orientation gradually with a domain boundary being about 300 atoms wide. Figure 4 a shows a schematic drawing which takes place gradually across the boundary.

The reason for the large width of a domain wall is due to a balance between two forces: exchange and magnetocrystalline anisotropy. When there is only a small difference in orientation between the dipoles Figure 4 a, the exchange forces between the dipoles are minimized and the exchange energy is reduced (Figure 4 b). Thus, the exchange forces will tend to widen the domain wall. However, the wider the wall is , the greater will be the number of dipoles forced to lie in directions different from those of easy magnetization, and the magnetocrystalline anisotropy energy will be increased ( Figure 4 b). Thus, the equilibrium wall width will be reached at the width where the sum of the exchange and magnetocrystalline anisotropy energies is a minimum ( Figure 4 b).

Magnetostrictive energy:When a ferromagnetic material is magnetized, its dimensions change slightly, and the sample

being magnetized either expands or contracts in the direction of magnetization (Fig. 5). This magnetically induced reversible elastic strain (Δl/l) is called magnetostriction and is of the order of 10-6. The energy due to the mechanical stresses created by magnetostriction is called magnetostrictive energy. For iron , the magnetostriction is positive at low fields and negative at high fields (Fig. 5).





The cause of magnetostriction is attributed to the change in bond length between the atoms in a ferromagnetic metal when their electron-spin dipole moments are rotated into alignment during magnetization. The fields of the dipoles may attract or repel each other, leading to the contraction or expansion of the metal during magnetization. In summary, the domain structure formed in ferromagnetic material is determined by the various contributions of exchange, magnetostatic, magneto-crystalline anisotropic, domain wall, and magnetostrictive energies to its total magnetic energy. The equilibrium or most stable configuration is that for

Figure 5which the total magnetic energy is the lowest.

Magnetic hysteresis:

Hysteresis occurs in many fields of science. Perhaps the primary example is of magnetic materials ( ferromagnetic and ferrites) where the input variable H (magnetic field) and response variable B (magnetic induction) are traditionally chosen. For such a choice of conjugate variables, the area of the hysteresis loop takes on a special significance, namely the conversion of energy per unit volume to heat per cycle. When an external magnetic field is applied to a ferromagnet, the atomic dipoles align themselves with the external field. Even when the external field is removed, part of the alignment will be retained: the material has become magnetized.

Magnetic hysteresis is defined as the lagging of magnetic induction (B) or magnetization (M) behind the magnetic field (H).

A family of B-H loops for grain-oriented electrical steel (BR denotes

remanence and HC is the coercivity) is shown in Figure 6. The relationship between magnetic field strength (H) and magnetic flux density (B) is not linear in such materials. If the relationship between the two is plotted for increasing levels of field strength, it will follow a curve up to a point where further increases in magnetic field strength will result in no further change in flux density. This condition is called magnetic saturation.

If the magnetic field is now reduced linearly, the plotted relationship will follow a different

Figure 6





curve back towards zero field strength at which point it will be offset from the original curve by an amount called the remanent flux density or remanence(BR ).

If this relationship is plotted for all strengths of applied magnetic field the result is a sort of S- shaped loop. The 'thickness' of the middle bit of the S describes the amount of hysteresis, related to the coercivity of the material.

Its practical effects might be, for example, to cause a relay to be slow to release due to the remaining magnetic field continuing to attract the armature when the applied electric current to the operating coil is removed.

Hysteresis loop: magnetization (M) as function of magnetic field strength (H)

This curve for a particular material influences the design of a magnetic circuit.

This is also a very important effect in magnetic tape and other magnetic storage media like hard disks. In these materials it would seem obvious to have one polarity represent a bit, say north for 1 and south for 0. However, to change the storage from one to the other, the hysteresis effect requires the knowledge of what was already there, because the needed field will be different in each case. In order to avoid this problem, recording systems first overdrive the entire system into a known state using a process known as bias. Analog magnetic recording also uses this technique. Different materials require different biasing, which is why there is a

Figure 7

selector for this on the front of most cassette recorders.

In order to minimize this effect and the energy losses associated with it, ferromagnetic substances with low coercivity and low hysteresis loss are used, like permalloy.

In many applications small hysteresis loops are driven around points in the B-H plane. Loops near the origin have a higher µr. The smaller loops the more they have a soft magnetic (lengthy) shape. As a special case, a damped AC field demagnetizes any material.B-H product:

` The product of the flux density (B) and field strength (H) of a permanent magnet at any point of the demagnetization curve is a measure of the total energy stored in the external field of the magnet per unit volume of the permanent magnetic material producing the field. The maximum value of the product of B and H is called the maximum energy product, (BH)MAX and is a measure of the maximum amount of useful work that can be performed by the magnet. (BH)MAX is used as a figure of merit for permanent magnetic materials (Fig.8). The SI unit for the energy product BH is kJm-3. Basically, the maximum energy product of a hard magnetic material is the area occuppied by the largest rectangle that can be inscribed in the second quadrant of the hysteresis

loop of the Figure 8





material. The (BH)MAX value of a hard magnetic material may be a few tens. For example, Alnico 1, with 12% Al, 21% Ni, 5% Co, 2% Cu, 60% Fe the (BH)MAX value is 11.0 kJm-3 whereas rare-earth-Co, with 25.5% Sm, 8% Cu, 15% Fe, 1.5% Zr, 50% Co has a value of 240 kJm-3.

Check your understanding:

1. State true or false: The magnetic moment of a solid is the vector sum of the magnetic moments of its constituent atoms.

2. Choose the correct answer: The permanent magnetic moment of an atom is dependent on the quantum numbers: A) n and l; B) ml and ms ; C) l and ms.

3. Choose the correct answer: An element can form a strongly magnetic solid only if its atoms have: A) an incomplete valence shell; B) an incomplete inner shell; C) a vacant inner shell

4. Choose the correct answer: A ferromagnetic material is one in which: A) one constituent is iron; B) the constituents are transition metal oxides; C) the atomic magnetic moments are parallel; D) the atomic magnetic moments are antiparallel and unequal.

5. Choose the correct answer: The Curie temperature is the temperature at which: A) the saturation intensity of magnetization becomes zero; B) the domains become entirely randomly magnetized; C) the atomic magnetic moment disappears.

6. Choose the correct answer: Within each magnetic domain in a ferromagnet all the atomic magnetic moments are : A) antiparallel; B) demagnetized; C) parallel; D) random.

7. State true or false: A piece of material has no net magnetic moment. It can only therefore be composed of domains magnetized in different directions.

8. State true or false: A piece of magnetic material has a net magnetic moment when no field is applied. It must therefore be ferromagnetic.

9. Choose the correct answer: If the domain walls in a magnetic material can be easily moved the material displays: A) high permeability; B) high flux density; C) permanent magnetic behaviour.

10. Choose the correct answer: Magnetic recording tape is most commonly made from: A) small particles of iron; B) silicon-iron; C) ferric oxide.

11. Choose the correct answer: Permanent magnets are sometimes made by the aggregation of particles which are: A) smaller than a magnetic domain width; B) non-magnetic particles in a magnetic bonding medium; C) smaller than a domain wall thickness.

12. Explain ferromagnetism.

13. Discuss domain theory of magnetism.

14. Define hysteresis.15. Discuss the importance of BH product.

Summary

On completion of this topic you have learned

1. Ferromagnetism.2. Domain theory of Ferromagnetism.3. Magnetic Hysteresis.4. BH product or energy product.

Activity

1. Find the reason for the different shape and size of the hysteresis loops for ferromagnetic materials.





Suggested Reading

1. “Foundations of materials science and engineering-William F. Smith, McGrawHill.2. “Engineering Physics-II” by P.K.Palanisamy.3. http://en.wikipedia.org/wiki/Hysteresis.

Answers to CYU.

1. True2. B3. B4. C5. A6. C7. False8. False9. A10. C11. C12. Answer is in page 113. Answer is in page 2-514. Answer is in page 515. Answer is in page 6




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