Magnetic Properties of Materials PDF

Magnetic Properties of Materials 1. Background: A substance is composed of many numbers of atoms. The magnetic property of materials is due to the motion of electrons in orbits of atoms. The electrons have two types of motions: (i) revolutionary or orbital motion, and (ii) rotational motion...

Magnetic Properties of Materials 1. Background: A substance is composed of many numbers of atoms. The magnetic property of materials is due to the motion of electrons in orbits of atoms. The electrons have two types of motions: (i) revolutionary or orbital motion, and (ii) rotational motion giving rise to spin. Each electron revolving round the nucleus has a magnetic moment due to its orbital motion (𝜇 ) and a magnetic moment due to spin (𝜇 ). The net magnetic moment of the magnet is the vector sum of these two magnetic moments of all the electrons, 𝜇 = 𝜇 + 𝜇. In each atom, the electrons are in continuous motions round the nucleus in their respective fixed permissible orbits. These electrons form current loops that produce the magnetic field of their own like circular current carrying conductors. In many materials, these currents are randomly oriented and cancel the effect of each other thereby no magnetic field is produced. However, when an external magnetic field (called magnetizing field) is applied, these currents loops get oriented in a specific direction. Therefore, the respective material is said to be magnetized. 2. Few definitions: a. Intensity of magnetization (I): Consider a magnetic material consisting of atoms having magnetic moments and suppose the material has a net magnetic moment 𝑀 in a volume 𝑉. The intensity of magnetization then can be defined as the net dipole moment per unit volume. i.e. 𝐼= It is a vector quantity and its unit is ampere per meter (Am ). For a bar magnet of length of length 2𝑙 and cross-sectional area 𝐴, the above expression becomes For a bar magnet × Magnetic moment (𝑀)= 𝑚 × 2𝑙 𝐼= = × where 𝑚 is pole strength of the magnet. b. Magnetic permeability (𝝁): The magnetic permeability of a medium is the ratio of the magnetic field or flux density (𝐵) inside the material or medium to the magnetizing field intensity (𝐻). i.e. 𝜇= 1 It is the degree to which a magnetic field can penetrate a given medium or how permeable is the material for the passage of magnetic field lines through it. c. Relative permeability (𝝁𝒓 ): The ratio of the permeability of a material to that of free space is called the relative permeability. i.e. 𝜇 = where 𝜇 = 4𝜋 × 10 TmA and 𝜇 is a unitless quantity. d. Magnetic susceptibility (𝝌): It is defined as the ratio of intensity of magnetization (𝐼) to the magnetizing field intensity (𝐻). i.e. 𝜒= It measures how susceptible or easily and strongly a material is magnetized by 𝐻. It is unitless quantity. 3. Relation between 𝝁𝒓 and 𝝌: Consider a material (iron rod) is placed inside a uniform magnetic field (𝐵 ), such as inside a long solenoid as shown in Figure 1. The applied magnetic field magnetizes the material and aligns the dipoles along the field direction thereby producing a magnetic field 𝐵 of their own. Therefore, at any point in the medium, the magnetic field 𝐵 is the sum of the applied field 𝐵 and the field produced by the dipoles 𝐵. i.e. 𝐵 =𝐵 +𝐵 (1) Figure 1: An iron rod being magnetized by placing inside a current carrying solenoid. The magnetization field 𝐵 can be related to the intensity of magnetization (𝐼) as 𝐵 = 𝜇 𝐼, 𝜇 being the permeability of free space. Since 𝐵 and 𝐼 are parallel to each other, Eq. (1) becomes 𝐵 =𝐵 +𝜇 𝐼 (2) The magnetic field due to solenoid carrying current 𝐼 is 𝐵 = 𝜇 𝑛𝐼 , 𝑛 being number of turns per unit length of the solenoid. The magnetizing field intensity 𝐻 is related to the field due to the conduction current in the wire as 𝐻 = 𝑛𝐼 and hence 𝐵 = 𝜇 𝑛𝐼 = 𝜇 𝐻. Therefore, 𝐵 =𝜇 𝐻+𝜇 𝐼 (3) 2  𝐵 = 𝜇 (𝐻 + 𝐼) = 𝜇 (𝐻 + 𝜒𝐻) ∵ 𝜒 = , 𝜒 = magnetic susceptibility = 𝜇 (1 + 𝜒) 𝜇 = 𝜇 (1 + 𝜒) = (1 + 𝜒) 𝜇 = (1 + 𝜒) (4) where 𝜇 is called the relative permeability of the medium. Eq. (4) is the required relation between 𝜇 and 𝜒. 4. Classification of magnetic materials: An iron piece is strongly attracted by a bar magnet whereas other materials are weakly attracted and some are repelled by it. These responses of materials to the magnetic field of a bar magnet can be used to classify the magnetic materials into three classes. They are: a. Diamagnetic material: The substances which are feebly magnetized in the direction opposite to the applied magnetic field are called diamagnetic materials. Therefore, they are weakly repelled by the magnets. e.g.: bismuth, copper, water, alcohol, mercury, etc. The magnetic moment of atoms of a diamagnetic material is zero. But when they are placed in an external field, they acquire induced dipole moments which are in opposite direction to the applied field. Hence, the magnetization in a diamagnetic material always opposes the applied field. Some properties: i. They are repelled by magnets. ii. They move from a stronger to weaker field region. iii. When a diamagnetic rod is freely suspended in a magnetic field, it slowly turns to set at right angle to the applied field. iv. Since they are magnetized in a direction opposite to the applied field, they have small value for intensity of magnetization (𝐼). v. They always have negative values of magnetic susceptibility (−𝜒) in the range −10 to −10. vi. The relative permeability of these materials is slightly less than 1 in the order of 0.99990 to 0.99999 for solids and liquids. vii. These materials are independent of temperatures. b. Paramagnetic material: 3 The materials which are feebly attracted by a magnet are called paramagnetic materials. They are weakly magnetized in the direction of the applied magnetizing field. e.g.: aluminium, chromium, oxygen, manganese, etc. Their atoms have permanent magnetic moments which interact weakly with each other and randomly orient in different directions in absence of external magnetic field. When an external field is applied, their atomic moments align in the direction of field. The magnetic field inside it is the sum of the applied field and the induced filed due to magnetization. Some properties: i. They are feebly attracted by magnets and hence they move from weaker to stronger magnetic field region. ii. When a paramagnetic rod is freely suspended in a magnetic field, it aligns along the filed direction. iii. They are found in solid, liquid and gas. iv. They have small but positive value of intensity of magnetization as they are weakly magnetized in the same direction to the applied field. v. The relative permeability for these materials has value of nearly unity ranging from 1.00001 to 1.003 at room temperature. Therefore, the magnetic lined of force inside the material placed in a magnetic field is more than that outside it, i.e., the field inside the material is greater than that outside it. vi. The magnetic susceptibility of the material is small and positive. vii. They are temperature dependent and obey Curie law. Curie law: When the temperatures of the paramagnetic material increased, the thermal motion of atoms increases which tends to disturb the alignment of the magnetic moments and randomize them. As a result of which the intensity of magnetization decreases with increasing temperature. Therefore, the magnetic susceptibility is inversely proportional to the absolute temperature and the intensity of magnetization is 𝐼= where 𝐶 is a constant called Curie constant whose value is different for different materials. The relation was first discovered by Pierre Curie in 1895 and is called Curie law. It can be expressed as 𝜒= where 𝜒 is magnetic susceptibility. 4  c. Ferromagnetic material: The materials which are strongly attracted by a magnet are called ferromagnetic materials. They are highly magnetized in a magnetic field. e.g.: iron, nickel and cobalt and their alloys, such as alnico. Gadolinium and dysprosium are ferromagnetic at low temperature and compounds, such as CrO2 used in magnetic tape recordings are also ferromagnetic materials though neither chromium nor oxygen are ferromagnetic. Some properties: i. They are highly attracted by magnets. ii. They move from weaker to stronger field. iii. When a ferromagnetic rod is freely suspended in a magnetic field, it quickly turns along the field direction. iv. As they are magnetized in the direction of applied field, they have positive and very high value of intensity of magnetization. v. The relative permeability is very high of the order of 1000 to 100,000. vi. The magnetic susceptibility is positive and very high and varies with the applied field. vii. They are highly temperature dependent and follow Curie law 𝜒= below saturation temperature. The alignment of atomic moments in a ferromagnetic material is disturbed with increase in temperature. The temperature at which a material becomes paramagnetic is called Curie temperature, 𝑇. The ferromagnetic property is found only in solids, not in liquids and gases. 5. Domain theory of ferromagnetism: Magnetic domains (a) Absence of field (b) Weak field (c) Strong field Figure 2: Magnetic domains in ferromagnetic substance. There exist permanent atomic magnetic moments in ferromagnetic substances. There appear strong interactions among these neighbouring atomic moments and they align in a specific direction or parallel to each other in a small region in absence of external magnetic field (Figure 2(a)). The small regions having a specific orientation of atomic magnetic moments are called magnetic domains. Thus, a ferromagnetic substance is composed of several magnetic domains. Due to the 5 random magnetization of domains, they cancel the effect of each other and net magnetic moment of the substance is zero. When the substance is placed in an external field, the domains tend to orient in the direction or parallel to the field. As the result of which the domains boundaries shift; the domain having orientation along the field directions grow up and those having orientation in other directions shrink (Figure 2(b, c)). As the external applied field is made stronger, the domains having magnetic moments not aligned with the field become very small and when the domains fully align to the applied field direction, the material attains magnetic saturation. In this case, the material possesses certain magnetic moment. If the applied field is then removed, the domain walls do not move completely back to their original positions and the material retains a magnetization in the direction of the applied field. The thermal motion at room temperature is not sufficient enough to break up the specific orientation of the dipole moments. 6. Hysteresis Figure 3: Hysteresis loop of ferromagnetic material. Consider a ferromagnetic material like an iron rod is placed in an external magnetic field 𝐵 (= 𝐻). A magnetic field 𝐵 is developed in the material due to the application of 𝐻 and the plot of 𝐵 versus 𝐻 is shown in Figure 3. It can be observed that when 𝐻 is increased from zero, the magnetization and the total field 𝐵 in the material also increases along the curve OA and reaches the maximum value 𝐵 at A. The rod attains saturation as on further increasing 𝐻, there is no change in 𝐵. This happens when all the magnetic moments in the rod align along 𝐻. 6 When the field 𝐻 is gradually decreased and brought back to zero, the field 𝐵 does not retrace its original path but follows the curve AR and the material remains magnetized with a value of 𝐵. When 𝐻 is reversed, the magnetic moments in the material reorient until 𝐵 reaches to zero at point C. On further increasing 𝐻 in the reverse direction, the sample reaches to the saturation at point D in opposite direction and on returning 𝐻 to zero, the material is permanently magnetized at E. When the field 𝐻 is further increased in original direction, curve DEFA is traced as (Figure 3). The loop shows that the magnetization (𝐵) of the material lags behind the applied magnetic field 𝐻 when it is taken through a complete magnetization cycle. This tendency is called hysteresis and the closed curve ARCDEFA is called the hysteresis loop. Therefore, it can be stated that the permeability 𝜇 of a ferromagnetic material is not constant but varies with 𝐻 and history of the material. At points R and E, the material is magnetized even though applied field is zero. The magnetic field 𝐵 that remains after the material has been saturated when 𝐻 has been reduced to zero is called the remanance or retentivity of the material. This is represented by OR or OE and it is what makes the iron rod a permanent magnet. The reverse field (𝐻 ) needed to reduce 𝐵 to zero is called coercivity and it represents how difficult it is to destroy magnetization in the iron. Hysteresis loss: In the process of magnetization of the material through a cycle, energy is dissipated as heat and its temperature increases. The area of hysteresis loop is proportional to the energy dissipated per unit volume of the material during each magnetization cycle. This loss in thermal energy is called hysteresis loss and this occurs due to the orientation of the atomic moments in one direction and their reorientation in opposite direction in a magnetization cycle. (a) (b) Figure 4: Hysteresis loss of (a) steel and (b) soft iron core. 7 The shape and size of hysteresis loop is characteristic of each material. A broad hysteresis loop with high values of retentivity and coercive force is characteristic of a suitable material for a permanent magnet as a greater work must be done to change its magnetization. This property is observed in steel and hence it is used to make permanent magnets. However, a material having narrow hysteresis loop is suitable for transformer cores which undergoes many cycles of magnetization. Soft iron has smaller hysteresis loop and so it is used in transformer core as the loss of energy is less and the efficiency of transformer is higher. For the materials to be magnetically hard, they should have large value of 𝐻 as shown in Figure 4(a). The larger value of 𝐻 shows that the stronger external field (𝐻) is required to demagnetized the material. These types of materials are suitable for making permanent magnets to be used in speakers and moving coil-meters. The materials having smaller values of 𝐻 , such as iron are magnetically soft and have smaller hysteresis loop as shown in Figure 4(b). The smaller area of loop indicates that heat dissipation is minimum. Therefore, iron is useful in transformers, electromagnets, magnetic tapes and compact diskettes. 8