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MAGNETIC MATERIALS : Characteristic Magnetic Permeability

µ = B/H (H / m)

µ₀ → Permeability of free space i.e.

µ₀ → 4π × 10^–7 H/m

µ_r → Relative permeability of a medium

Magnetic dipole moment 

 = Current (Area of cross section of current loop)

nˆ → Unit vector normal to the surface
 = IAnˆ ;  (A – m²)

Magnetization :

Magnetization is defined as magnetic dipole moment per unit volume

M = NP_m – (A/m)
Where,

N → Number of magnetic dipole per unit volume.
Type

Susceptibility X_m

X_m V_s T relation

Diamagnetic Negative and small T independent

Example : Atoms of material have closed shells, (–10^–6)
Organic materials, e.g. may polymers; covalent Negative and large solids e.g. Si, Ge, diamond; some ionic solids, e.g., (–1)
Below a critical alkali-solids : some metals Cu, Ag, Au. temperature

Superconductor

Paramagnetic Positive and small Independent of T Example : Due to the alignment of spins of conductor     (10^–5 – 10^–4) electrons. Alkali and transition metals.

Positive and small Materials in which the constituent atoms have a          (10^–5)

Curie or Curie Weiss law permanent magnetic moment, e.g., gaseous and liquid

oxygen; ferromagnets (Cr), and ferrimagnets (Fe₃O₄)

Curie - Weiss law at high temperature

Ferromagnetic :

Positive and very Ferromagnetic below and Example : May possess a large permanent large paramagnetic above the magne-tization even in the absence of an applied Curie temperature. field. Some transition and rare earth metals,

X_m→ ∞ 

Fe, Co, Ni, Gd, Dy.

Antiferromagnetic:

Positive and small Antiferromagnetic below Example : Mainly salts and oxides of transition and paramagnetic above metals, e.g. MnO, NiO, MnF₂, and some transition the Neel temperature X_m metals, α – Cr, M_n decrease

Ferromagnetic Positive and very large Ferrimagnetic below and Example : May posses a large permanent paramagnetic above the magnetization even in the absence of an applied Curie temperature X_m→ ∞ field. Ferrites.

Atomic Unit of Magnetic Moment-Bohr Magnetron 

Bohr magnetron =   

Where, h → Planck’s constant
m → Mass of electron
e → Charge of electron

Total magnetic dipole moment in influence of magnetic field B is given by

Where, P_mi → Induced orbital magnetic – dipole moment

Relation Between magnetic Flux Density and Magnetization

 
Also 

Where, x _m = µ_r - 1
X_m → Magnetic susceptibility

Diamagnetic Materials :

Diamagnetic materials are composed of atoms that do not have any associated intrinsic magnetic moment but possess only weak induced magnetic moments.
Existence of diamagnetism is exhibited by rejection of H-line of external field. They are repelled by a magnet. Heating will destroy diamagnetism.

• The diamagnetism arises due to circulating charge in orbits therefore all the materials exhibit diamagnetism 
• The diamagnetic materials have – ve and very small magnetic susceptibility 
• The diamagnetic material are repelled by the magnetic field 
• These material moves from higher intensity to lower intensity in magnetic fields
•   Magnetic susceptibility is independent of magnetic flux density and temperature

Examples of Diamagnetic

Cu, Ag, Au, AI₂O₃, diamond Nickel.

Origine of Magnetic Dipole Moment

There are three mechanism of angular momentum of charge in atoms which causes the magnetic dipole moments. 

• orbital Angular Momentum of Electron 
• Spin angular momentum of electron 
• Nuclear spin angular momentum

Note:
1. The electron spin magnetic moment is more than orbital magnetic moment
2. The nuclear spin magnetic moment is very small as compared to orbital magnetic moment because of heavy mass of nuclear.

Paramagnetic Materials:

In paramagnetic materials like Mg, AI, V, Cr, Mo, W, the interaction between atoms having net spins is zero. The spins of the various atoms in the metal are randomly oriented and have a low net magnetization of about one-millionth (10^–6) that of ferromagnetic material. The low magnetism is again reduced as temperature increases (because randomization of atomic magnets, causes zero residual magnetism).

In some materials the permanent magnetic dipole moments of individual atoms is not acted upon each other. Therefore dipoles are randomly distributed and net magnetization of the material is zero. Such materials are called paramagnetic materials.
 

Alignment of Dipoles

Note:

1. As temperature increases the thermal agitation among the individual dipole moments also increases.
2. When an external magnetic field is applied all the dipole moments get aligned in same direction parallel to each other. But with increases is temperature thermal agitation causes disalignment of dipoles again.
3. Magnetic susceptibility of paramagnetic material is a small an positive (10^–3).

4. Magnetic susceptibility of paramagnetic materials is more than diamagnetic materials.

5. paramagnetic materials are attracted by the external magnetic field. These material move from low intensity to high intensity of field.
6. Curie Law i.e. Variation of (X_m) paramagnetic
X = C/T

Where, C → Curie constant

T⁰ → K

7. Some paramagnetic materials follow Curie-weiss Law

C → Curie constant

θ → Curie temperature

Example : Fe₂O₃, MnSO₄, FeSO₄, NiSO₄

FERROMAGNETIC MATERIALS :
Ferromagnetism involves an electrostatic interaction between adjacent atoms that affects the alignment of the resultant electron spins of the atom.
If the interaction is positive, the spins are aligned parallel to one another and their magnetic are additive and ferromagnetism results.

The properties of ferromagnetic element are explained on the basis of existence of domains of atomic magnet with the resultant magnetic moment vector which is different for different domains in helterSkelter directions. These domain vectors undergo orientation towards the direction of applied field.
Magnetization increase with the strength of applied field.

B_S = Saturation value
B_R = Residual value
H_C = Coercive H-fields
B – H Curve area = Energy loss per cycle of magnets.

Magnetization reaches saturation value at Bs. If H is reduced to zero, the aligned domains contribute to residual magnetism which cannot be reduced to zero unless opposite H-Field is increased to HC. H is called coercive force. Each cycle of magnetization results in Hystersis loss equal to the area of B-H loop.
Iron/cobalt/nickel are strong ferromagnetic materials.

If the temperature is increase above Curie temperature, T_C they behave as paramagnetic weak materials. T_C is different for Fe, Co and Ni.

Due to large Hystersis loss of energy, ferromagnetic cores (For transformer action) cannot e used for frequencies above 4 kHz. It is ferrite core which can be used for high frequencies from 10 kHz to 10 MHz, etc. 

• Ferromagnetic materials have all the dipole moment aligned parallel to each other even in the absence of external magnetic field 
• The magnetic susceptibility of ferromagnetic materials is positive and very large. 
• These materials consists of the elements with partly filled inner electron cells. 
• The Iron group is an example of Ferromagnetic materials
  The Ferromagnetic materials exhibit spontaneous magnetization only up to a critical temperature called curie temperature these material behave paramagnetic materials above the Curie temperature and follow curie-weiss Law.

 Example : Co, Fe, Ni, Gd, Dy

Ferromagnetic materials are oxides of metals with iron like MoFe₂ O₃, where M is a bivalent metal i.e. Fe, Cu, Mn, etc., whose structure is of the spinel family.
A spinel like (MgAI₂O₄) is a compound whose Al (trivalent) atoms and Mg atoms occupy tetrahedral sites in an FCC oxygen lattice. (Other trivalent and divalent metal iron may be used in place of Al and Mg).
Curie temperature of these materials is given by

Co → 1393
Fe → 1043
Ni → 631
Gd → 289
Dy → 105

Behavior of Ferromagnetic Materials Below Curie Temperature

Magnetic susceptibility of ferromagnetic materials increases with increase in temperature, for temperature less than curie temperature.
 

The material exhibit B – H curve at temperature below curie temperature

When a fresh ferromagnetic is subjected to external magnetic field, it follows OAB of the BH curve as shown in figure.
When the external magnetic field is removed, the materials remains magnetized permanently and this remaining magnetic flux density is called “Residual Magnetism”.

Co-Ercive Field The magnetic field required to be applied continuously in opposite direction to reduce the resident magnetism to zero.

Spontaneous Magnetization Below the curie temperature a ferromagnetic material remains magnetised permanently even if external applied field is removed.

 The property of ferromagnetic materials is called spontaneous magnetization Spontaneous Magnetization

Where, Br → Residual magnetic flux density

Molecular Field of Magnetic Materials and Internal Field :

γ → Internal field constant
 → Molecular magnetic field
 → Magnetisation

Behaviour of Ferromagnetic Materials Above Curie Temperature

As the temperature increases above the curie temperature, the internal field of the material is not sufficient to maintain the parallel alignment of magnetic dipole moments are randomly distributed above curie temperature and materials behave like paramagnetic materials.
Above the curie temperature the materials follow curie-weiss law.

Note: Molecular field is mainly responsible for alignment of dipoles in one direction.

Ferro Magnetic Materials :

The ferromagnetic materials in demagnetized state are divided into a number of small regions, the dipole moments in each of these regions are alliged in same direction but the direction of alignment varies from one region to another. These regions are called “Ferromagnetic Domains”. And wall separating “Ferromagnetic Domains” is called “Domains Wall”.

Note : Material used in transformer should have low Hystersis and high permeability

Ferroelectric Material :

When a Ferro electrical materials is subjected to external field it gets polarized and it remains polarized even external field is removed. The direction of polarization can be changed by applying external field in opposite direction. The Ferroelectric material exhibit spontaneous polarization. When a fresh material is subjected to external electric field, if follows the path OAB of Hystersis characteristic as shown below 

when external electric field is removed, the material retain some polarization as shown in figure this polarization is called residual polarization

Where, OC → Residual polarization

Coercive Field 

This is the electric field required to be applied in opposite direction to reduce the residual polarization to zero. The Ferroelectric material exhibit spontaneous polarization only up to a critical temperature called curie temperature.
After curie temperature, the material stops behaving like ferroelectric material and it starts behaving like piezo-electric material

Notes: Above curie temperature, the Hystersis loop merges into a straight line.

Condition for Spontaneous Polarization

α → Polarisability
γ → Internal field constant
N → No of dipoles/volume.

Expression for Curie-Eeiss Law

The ferroelectric materials above the curie temperature follows a law called curie-welss law.
Polarization of materials is changes with temperature hence orientational polarization and it is given by

C → Curie constant
θ → Curie temperature

Note:
1. In case of ferroelectric material relative dielectric constant increases with increase in temperature when temperature of material is less than curie temperature.
2. In Ferro-electric material polarization is not a unique function of the electric field.

Examples of Ferro-electric Materials
1. BaTiO₃.
2. CaTiO₃.
3. PbTiO₃.
4. Rochelle’s salt.
5. Potassium dihydrogen phosphate (KDP).
6. Ammonium dihydrogen phosphate (ADP).
7. Lead Zirconate. (Pb Zr O₃)

Note: All the ferroelectric mate rials are pyroelectric.
All the pyroelectric materials are Piezoelectric but reverse is not true.
Anti Ferroelectric Materials 

• These are the materials which do not possess permanent dipoles moment because of geometry of spontaneous polarization. 
• The neighbouring dipoles are aligned in antiparallel to each other. 
• The antiferroelectric materials looses their antiferroelectric property above a critical temperature called curie temperature.

Antiforroelectric materials            curie temperature

1. Lead Zirconate (PbZrO₃)             233°C  

2. Sodium niobate NaNbO₃             638°C

3. ADP                                             125°C

FERRITES (Ferrimagnetic Materials)

Special Characteristic of Ferrites In Ferrites nearly all of the valence electrons are tied up in bonds with neighboring atoms. Thus their conductivity is less and hence unable to generate Eddy Current (unlike ferro-metals) and also damper mechanical and electrical vibrations. Only thing is that ferrites have weak magnetic moments p1/4[ of ferromagnetic materials. But ferrites have  Hysteresis loops very much rectangular in shape. i.e. large saturation magnetization Hence they are very much suited for core materials for high frequency transformers.

Figure show small loop area of ferrimagnetic materials. Switch rate is fast as required for high frequency applications.

Curie-Weiss Law of Ferromagnetism

Magnetic susceptibility,   

This is termed is curie-weiss law.
Curie law alone indicates that below Curie temperature (T < θ), X becomes negative (i.e. paramagnetic would become diamagnetic). But for most paramagnetic, Curie temperature is very low and T < θ situation rarely can arise

• The dipole moments in these materials are alligned in antiparallel but net magnetization is not zero and therefore materials possesses a net magnetic moment. This net magnetization disappears above a critical temperature called. “Curie temperature”.  The Ferrimagnetic materials have high dc resistivity and hence these materials are preferred for constriction of magnetic core at microwave and high frequencies. At these frequencies, the eddy current losses in ferrites are lower than the ferromagnetic materials.

Note: Resistivity of ferries are more than Ferromagnetic materials.

Electric and Magnetic Characteristic of Ferrites

1. High resistivity
2. Low dielectric losses
3. High permeability
4. High curie temperature
5. Mechanically hard and Brittle

Application of Ferrites : 

1. For permanent magnets, these ferrites are called Hard Ferrites and have High resistivity and high coercive force.
Example: Barium and strauntium ferrites. These ferrites have high uniaxial anisotropy
2. For transformer and inductor cores these are called soft ferrites. These ferrites have, high permeability, low coercive force, low eddy current losses and are able to operate up to 10 Mhz Example : Mn, Zn, NiZn.
3. For data storage : The ferrites having rectangular Hystersis loop can be used for construction of magnetic memory core.

Example : Mn - Mg, Mn - Cu, Li - Ni Ferrites
4. For Microwave component : At microwave frequencies, 1 to 100 GHz, the E.M. waves interact with spin magnetic oments of materials, and the process which takes place is called Faraday’s Rotation.
Example : Mn Fe₂ O₄, Ni Fe₂ O₄, Co Fe₂ O₄

Soft Magnetic Materials The magnetic materials in which direction of magnetization can be altered easily by an applied magnetic field are called, soft magnetic materials. Such materials have high permeability, low coercive force, low Hystersis and eddy current loss

Application 

These materials are used as core of the transformer machines and magnetic memory core.
Example : Alloys of iron. Ni - Fe Alloy with 30 – 80% Ni, Ferrites, Iron with silicon, Si, 4-5% content  is used for construction of transformer core, used at low frequencies. Iron with nickel contents is used for high frequencies. Ferrites can also be used at high frequencies.

Soft Materials	Application
1. Silicon Steel

 Hard Magnetic Materials 

• Hard magnetic materials retain a considerable amount of magnetic energy after the magnetizing force has been removed. 
• These materials are difficult to demagnetise, such materials are also called permanent magnetic materials.

Characteristics of hard Magnetic Materials 
1. High permeability
2. High curie temperature
3. High coercive force
4. Good residual magnetism

Hard Magnetic Materials	Uses
Carbon Steel
Tungsten Steel