In this article we will discuss about:- 1. Principal Ferromagnetic Elements 2. Ferromagnetism 3. Magnetic Domains 4. Magnetisation 5. Properties of Ferromagnetic Materials 6. Spontaneous Magnetisation in Ferromagnetic Materials 7. Magnetic Anisotropy 8. Magnetostriction.
Principal Ferromagnetic Elements:
The principal ferromagnetic elements are discussed below:
1. Iron:
It has the highest susceptibility comparatively. This property added with low cost makes iron most suitable for commercial purposes.
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Its magnetic properties are considerably affected by the presence of traces of carbon, oxygen and nitrogen, therefore, these undesirable elements should be reduced to the possible attainable limits. High purity means high permeability and reduced hysteresis loss. Its permeability is to the tune of 2,000.
It is also one of the important ferromagnetic elements. When it is heated, it remains ferromagnetic upto 395°C and beyond that its gets converted to paramagnetic.
Its properties as ferromagnetic material are considerably improved when alloyed with iron and cobalt. Its permeability is 300.
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Its permeability is 250 and increases with the temperature upto 300°C. It loses its magnetic properties at about 1130°C.
When in pure state it does not prove to be an important ferromagnetic material.
Its cost is adequately high.
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The only elements which are strongly ferromagnetic at normal temperatures are iron, cobalt and nickel. In Fig. 8.3 are shown typical normal-induction curves of annealed samples of iron, nickel and cobalt of comparatively high purity. These curves are given only for the purpose of general comparison and should not be considered as representing critical values.
Small variations in the degree of purity or in the annealing procedure lead to substantial differences in normal induction. The iron has greatest permeability, and this factor coupled with its low cost makes it the only element of commercial importance by itself.
Ferromagnetism:
The outstanding characteristic of a ferromagnetic material is that it is very strongly attracted by the magnet. Importance of iron as a magnetic material has led to the name ferromagnetism. Magnetic properties even exist in the absence of applied magnetic field.
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Ferromagnetism arises out of the electronic structure within the atoms. According to Pauli exclusion principle, not more than two electrons can occupy each energy level of an isolated atom and the same holds true for atoms in a crystal structure. The two electrons having the same energy levels have “spins” in opposite direction, and since each spinning electron can be considered equivalent to a moving charge, each electron acts as an extremely small magnet having north and south poles.
A material having even number of electrons in general has as many electrons spinning in one direction as in the other and the sum total effect is magnetically neutral in structure. In case of a material with unfilled subvalence shell, more electrons spin in one direction than in other resulting in a net magnetic moment. In materials like a-iron, cobalt and nickel, these moments are quite strong and atoms are sufficiently close together so that there is spontaneous magnetic alignment of adjacent atoms. These conditions cause ferromagnetism.
Magnetic Domains:
A specimen of ferromagnetic material, according to Weiss, consists of a large number of regions or domains which are permanently magnetised. The atomic moments in the individual domains are all aligned parallel to one another at temperatures far below the Curie point. Each domain is magnetically saturated and has a net magnetic moment.
However, the direction of the permanent magnetisation varies from domain to domain, and consequently the resultant magnetisation may be zero, or nearly zero. Above the Curie temperature, the domains may disrupt and the material may lose its ferromagnetic properties.
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The domains exist in single crystals as well as in polycrystalline samples. The domains are separated by domain walls in which the spin direction gradually changes from the preferred direction of one domain to the preferred direction of the neighbouring domain. A schematic arrangement of the domains with zero resultant magnetic moment is shown in Fig. 8.6 (a).
When an external field H is applied, say in horizontal direction, the domains having parallel orientation of spontaneous magnetisation grow in size at the expense of other domains that are magnetised in other directions by virtue of a motion of domain walls. This condition is shown in Fig. 8.6 (b).
The motion of domain walls can be considered as stealing of the neighbouring dipoles from other domains and aligning them in the direction of the external field so that the preferred domain increases in size. As the external field is increased progressively, a stage is reached when the whole material becomes one single domain giving rise to saturation of the magnetisation. Thus the hysteresis results due to motion of domain walls and also due to domain rotation to some extent.
The spontaneous magnetisation takes place in a material in certain preferred directions. When an external field is applied in an arbitrary direction, some domains which are easy to rotate, orient themselves in the direction of the field and become nearly immobile.
The coercive force needed to neutralise the spontaneous magnetisation in a ferromagnetic material, can be interpreted in terms of the mobility of the domain walls. The mobility of domain walls depends on the impurities in the material lattice imperfections etc. Thus it is possible to design a material by adding or subtracting impurities to obtain a desired value of coercive force.
The domain structure of a material can be observed under a powerful microscope by spreading a colloidal suspension of iron particles on nicely prepared surface of the material. These particles are attracted towards the domain boundaries where the magnetisation is quite large. This technique of observing the domain structure is known as the “magnetic powder technique.”
Magnetisation:
A ferromagnetic substance is unmagnetised when the domains are oriented at random. In such a situation there is no m.m.f. across the specimen, and it does not produce any magnetic field outside itself. Thus B and H are equal to zero.
Consider a toroidal solenoid wound on a non-magnetic core, such as shown in Fig. 8.7. If the flux density is measured on the centre line of the toroid, the relationship between B and H is given by the straight line OA in Fig. 8.8. If now the space within the toroid is filled with an unmagnetised ferromagnetic material, the well-known magnetisation curve OBCDE, is obtained.
The magnetisation curve has many names being referred to as- B-H curve, the magnetic saturation curve, the virgin curve, or simply the saturation curve.
The increase in flux density, B, in ferromagnetic material occurs when the magnetic field acting on the domains orients them in the direction of the field, so that the m.m.f. of each domain, or elementary magnet, is in such a direction as to increase the flux produced by the external field.
The straight part of the curve, BC, is traced out because the domains, influenced by a field, easily turn into these directions of magnetisation that have a component in the direction of magnetising force. As the magnetising force increases, the domains are with great difficulty oriented into the exact direction of the field.
This gives the rounded part of the curve, CD, commonly known, as the knee. The knee is not usually a very well-defined point, except in certain special materials. As the applied current is further increased, the magnetisation curve ultimately attains the slope DE, equal to that of airline OA. The material is said to be saturated.
The difference in flux between the saturation curve and the airline, OA at any magnetising force, is due to the contribution of the magnetic material. This flux is known as the intrinsic flux and gives a true measure of magnetic properties than does the total flux, especially at very high m.m.fs. The point at which the intrinsic flux density curve becomes horizontal gives the ‘intrinsic saturation’.
Properties of Ferromagnetic Materials:
The properties of ferromagnetic materials are divided into two distinct and separate ranges in such a way that the properties above a particular temperature are quite different from the properties below that temperature. This temperature is known as ferromagnetic Curie temperature and is designated by θf.
The two cases considered below are:
Case I: When T < θf
Case II: When T < θf
Case I: When T > θf:
When the temperature is above Curie temperature, θf the properties of ferromagnetic materials are similar to those of paramagnetic materials. Thus a ferromagnetic material possesses a very small susceptibility and hence very small magnetisation above θf. In this temperature region, the susceptibility depends upon temperature according to a law called Curie-Weiss law and the susceptibility is expected to decrease with increase in temperature.
The Curie-Weiss law states that-
It has been observed that eqn. (8.10) is not true for temperature T very close to θf because then the quantity (T – θ) may become negative which is not true for ferromagnetic materials.
Fig. 8.9 shows a plot between inverse of susceptibility (i.e., 1 / X) and temperature T.
The following points are worth noting:
a. In the vicinity of θf, the variation of 1 / X is non-linear.
b. The paramagnetic Curie temperature 0 of the material may be determined from the curve by extrapolating the straight-line portion of the curve towards the temperature axis as shown by the dotted line in Fig. 8.9.
c. A ferromagnetic material differs from a paramagnetic material in the fact that for the latter θ = 0.
The curve of Fig. 8.9 shows that θ > θf. However, the difference (θ – θf) is small, being 20 K to 70 K for the iron group of elements. (Example: For iron- θ = 1093 K and 1043 K).
Case 11: When T < θf:
When the temperature of the material is below θf it exhibits normal behaviour and follows the well-known hysteresis curve shown in Fig. 8.10.
Considering the material to be virgin, the flux starts building up from the origin as the value of the magnetising force H is increased from zero. In this range B is nearly proportional to H giving rise to constant permeability of the material. This permeability is called the initial permeability since there is no hysteresis in this region.
When H is further increased, the rate of increase of B falls and ultimately becomes zero and the flux density B reaches a maximum value or saturation (BM).
When the value of H is reduced from saturation value to zero, the reduction of flux does not follow the same path but is quite slow and as H becomes zero, there remains a certain amount of flux in the material called the remanent flux density Br, as shown in Fig. 8.10.
The material remains magnetised even in the absence of an external force and is said to be spontaneously magnetised. This magnetization corresponding to Br is Mr = Br / μ0. The spontaneous magnetization is the most important characteristic of ferromagnetic materials.
In order to reduce the remanent flux B, to zero, it is necessary to apply H in the reverse direction and the amount – Hc required to make Br zero is called the coercive force; its value varies over wide range and can be controlled by alloying the ferromagnetic material by other materials.
Spontaneous Magnetisation in Ferromagnetic Materials:
It has been seen that ferromagnetic materials exhibit spontaneous magnetisation below their Curie temperatures.
The explanation of the above phenomenon in terms of atomic properties may be given by considering the following examples:
Let the magnitude of remanent flux density of permanent magnet be of the order of say 1 Wb/m2. Since H = 0, the magnetisation Mr = Br / μ0 = 106 Amp/m. Also the magnetic dipoles moments in an atom are of the order of 1 Bohr magneton, i.e., ≃ 10-23 amp-m2.
Thus there must be at least 1029 atoms per cubic metre, all atomic dipoles being lined up parallel to each other, in order to provide the required magnetisation. Usually the number of atoms per cubic metre volume of a solid is approximately of the order of 1029. Thus the observed value of Mr indicates parallel alignment of essentially all the dipoles in the material.
In ferromagnetic materials, according to Weiss, the internal field seen by a given dipole is equal to the applied field plus a contribution from the neighbouring dipoles which tend to align it in the same direction as its neighbours.
Mathematically it may be expressed as:
Hi = H + γM … (8.11)
where, Hi = Internal field,
H = The applied field, and
γM = A measure of tendency of environment to align a particular dipole parallel to the magnetisation already existing.
The factor γ is called the internal field constant and shows the interaction which takes place between the poles. This hypothesis is used to explain the spontaneous magnetisation and is in consistent with Curie-Weiss law.
Fig. 8.11 shows the variation of spontaneous magnetisation with temperatures in low temperature range.
M = Magnetisation,
Msat = Saturation value of magnetisation,
T = Temperature, and
θ = Paramagnetic Curie temperature.
Magnetic Anisotropy:
It has been observed that in single crystal magnetic materials such as iron, the magnetic properties depend on the direction in which they are measured, i.e., iron exhibits preferred directions of magnetisation. When external field is absent, the spontaneous magnetisation takes up a specific direction with respect to crystal axis. In iron there are six equivalent preferred easy directions, one of the cube edges. This phenomenon is called as magnetocrystalline anisotropy.
Fig. 8.12 shows the magnetisation curves in different directions of an iron single crystal.
The various crystals of some polycrystalline materials are oriented more or less at random, and the properties in different directions are not greatly different. In several materials, which undergo specific treatment such as cold rolling, some regularity in the distribution of orientations, makes the magnetic properties of the material markedly anisotropic.
This is called ‘induced anisotropy’ and is of considerable practical importance. Thin films of Ni-Fe alloy deposited on to a substrate by evaporation in vacuum with magnetic field applied in the plane of the substrate, have subsequently easy direction for spontaneous magnetisation as the original field direction. Thin magnetic films are used as storage elements in the computers.
Uniaxial anisotropy can be induced in bulk materials by the following three methods:
1. Cold Working (particularly cold rolling) – uniaxial anisotropy is induced in the direction of rolling.
2. Magnetic Annealing – heat treatment of a material in a magnetic field produces a uniaxial anisotropy, related to field direction.
3. Magnetic Quenching – material is cooled in the presence of a magnetic field, through the Curie temperature, leading to a uniaxial anisotropy either parallel or perpendicular to the field direction.
Magnetostriction:
When a ferromagnetic material is magnetised small changes in dimensions occur, the effect being known as ‘magnetostriction’.
The magnetostriction may be of the following three types:
1. Longitudinal Magnetostriction – It is the change in length in the direction of magnetisation. This change may be increase or decrease in length.
2. Transverse Magnetostriction – It is the change in dimension, perpendicular to magnetisation direction.
3. Volume Magnetostriction – It is the change in volume resulting from the above two effects.
A characteristic showing the magnetostriction of some given material is the magnetostriction constant λ (Joule magnetostriction) defined by the following equation:
λ = δl / l … (8.12)
where δl = extension (or contraction) of a specimen I in the direction of an applied field of strength H when the field strength is raised from zero to a value causing technical saturation. (Change in length, δl refers to Joule effects).
The value of λ is generally not greater than 30 x 10-6.
Curves are shown in Fig. 8.13 (a), (b), (c) for single-crystal specimens cut and magnetised in the same directions as those given in Fig. 8.14. In nickel and cobalt the crystals contract for any direction of magnetisation. Iron is however more complicated. There is an extension for direction A and a contraction for direction C, while in direction B the iron first extends and then contracts.
Since a domain of iron is normally saturated in a cube-edge direction it may be concluded from Fig. 8.13 (a) that the crystal lattice of the domain is slightly deformed from a cubical form by an extension in one direction of about 20 parts in a million.
Therefore, during the magnetisation process in a single crystal of iron readjustments in the crystal lattice must occur throughout the specimen as the domain magnetisation vectors change direction. Such movements cause changes in internal stresses in the material. If the required movements are small the material is more easily magnetised. The magnetic permeability is therefore, related to the magnitude of the magnetostriction, which is one of the important factors determining magnetic properties.
The converse of the magnetostriction effect, the ‘Villari effect’ is also observed in the magnetic materials, whereby a longitudinal deformation leads to a change in permeability in the direction of applied strain. In general, material which extends on magnetisation will have its permeability raised by a tensile strain, whereas for a negative X material, an externally applied pull reduces the permeability.
Applications of Magnetostriction:
Magnetostriction has been largely the theoretical interest and of limited practical applications.
There have been some applications of magnetostriction to high frequency oscillators and to generators of super sound.
Magnetostriction is also used for underwater sound projectors and sound detectors.
The magnetic permeability is related to magnetostriction and for high permeability materials application, an effort is made to keep the magnetostriction as small as possible.