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Magnetic Materials

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Basic Magnetic Quantities Magnetic Induction or Magnetic Flux Density B Units: N C -1 m -1 s = Tesla (T) = Wb m -2

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2006: UNESCO Nikola Tesla Year 150 th birth Anniversary of Nikola Tesla AC vs. DC

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Ampere’s law in free space i B 0 = permeability of free space = 4 10 -7 T m A -1 = 4 10 -7 H m -1

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Magnetic dipole moment m i Area=A m=iA Units: A m 2

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Magnetization M of a solid A solid may have internal magnetic dipole moments due to electrons Magnetic dipole moment per unit volume of a solid is called magnetization Units: A m 2 /m 3 = A m -1

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Ampere’s law in a solid i B0B0 H: magnetic field intensity or field strength Units: A m -1

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In free space Inside a solid 16.1 16.3 16.2 = permeability of solid, H m -1 relative permeability of solid, dimensionless

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: magnetic susceptibility of the solid Types of magnetic solid Dimensionless diamagnetic-10 -5 superconductor paramagnetic +10 -3 ferromagnetic (universal) +10 3 -10 5 16.4

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Origin of permanent magnetic moments in solids: 1. orbital magnetic moment of electrons 2. spin magnetic moment of electrons 3. spin magnetic moment of nucleus We will consider only spin magnetic moment of electrons

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Bohr magneton B The magnetic moment due to spin of a single electron is called the Bohr magneton B B = 9.273 x 10 -24 A m 2 Net moment of two electrons of opposite spins = 0

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Unpaired electrons give rise to paramagnetism in alkali metals Na 3s 1 Net magnetic moment 1 B Fe 3d 6 4s 2 4 B atomcrystal 2.2 B Co 3d 7 4s 2 3 B 1.7 B Ni 3d 8 4s 2 2 B 0.6 B

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Example 16.1 The saturation magnetization of bcc Fe is 1750 kA m -1. Determine the magnetic moment per Fe atom in the crystal. a=2.87 ÅV = a 3 = 2.87 3 x10 -30 Magnetic moment per atom = 1750 x 1000 x 2.87 3 x 10 -30 x 1/2 = 2.068x10 -23 A m 2 = 2.2 B

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Ferromagnetic, ferrimagnetic and antiferromagnetic materials Due to quantum mechanical interaction the magnetic moment of neighbouring atoms are aligned parallel or antiparallel to each other. ferromagneticAnti- ferromagnetic Ferri- magnetic

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ferromagnetic Fe, Co, Ni, Gd Element TiCrMnFeCoNi 1.121.181.471.631.821.98 E exchange interaction = E unmagnetized -E magnetized 1.5-2.0 Heusler Alloys: Cu 2 MnSn, Cu 2 MnAl Ferromagnetic alloys made of non-ferromagnetic elements

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Thermal energy can randomize the spin FerromagneticParamagnetic T curie heat Fe1043 KCo1400 KNi631 K Gd298 KCu 2 MnAl710 K

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Ferrimagnetic materials Ferrites M 2+ : Fe 2+, Zn 2+, Ni 2+, Mg 2+, Co 2+, Ba 2+, Mn 2+, Crystal structure: Inverse spinel See last paragraph (small print) of Section 5.4

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Crystal structure: Inverse spinel Ferrites O 2+ FCC packing 4 O 2+ 8 THV 4 OHV Antiferromagnetic coupling Fe 3+ M 2+ Net moment due to M 2+ ions only.

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If Fe is ferromagnetic with atomic magnetic moments perfectly aligned due to positive exchange interaction then why do we have Fe which is not a magnet? Answer by Pierre Ernest Weiss (1907) Existence of domains known as Weiss domains

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Domain walls are regions of high energy (0.002 Jm -2 ) due to moment misalignment. Then why do the exist? Ans: Fig. 16.3

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Randomly aligned domains 1. decrease the manetostatic energy in the field outside the magnet 2. increase the domain wall energy inside the magnet A magnet will attain a domain structure which minimizes the overall energy

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16.3 B never saturates M saturates The value of B at the saturation of M is called the saturation induction (~ 1 T)

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Two ways for aligning of magnetic domains: 1.Growth of favorably oriented domains (initially) 2.Rotation of domains (finally) Initial permeability Saturation induction

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The hysteresis Loop Fig. 16.4 B r residual induction H c coercive field Area = hysteresis loss

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Soft magnetic materials High initial permeability Low hysteresis loss Low eddy current losses For application requiring high frequency reversal of direction of magnetization Eg. Tape head Problem 16.11

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Easily moving domain walls Low impurity, low non magnetic inclusions, low dislocation density low second phase precipitate Soft magnetic materials For low hysteresis loss ( frequency) For low eddy current loss ( frequency 2 ) Material: high resistivity Design: Lamination Choose: Pure, single phase, well-annealed material of high resistivity

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Table 16.1 Material Init. Rel.HysteresisSaturation Resistivity Perm.Loss (Jm -3) Induction (T) (10 -6 m) Com. Fe 250 500 2.2 0.1 Fe-4%Si 500 100 2.0 0.6 Fe-Si oriented 1500 90 2.0 0.6 Permalloy 2700 120 1.6 0.55 (45%Ni) Supermalloy 100,000 21 0.8 0.65 (79%Ni, 5%Mo) Ni-Zn Ferrite 200-1000 35 0.4 1 Mn-Zn Ferrite 2000 40 0.3 1

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Magnetic anisotropy Fig. 16.5 easy direction hard direction Iron single crystal Polycrystal: attempt to align easy direction in all grains Preferred orientation or texture By rolling and recrystallization By solidification By sintering ferrite powder in magnetic field

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Fe-4% Si alloy for low frequency transformers Wt% Si resistivity BsBs T DBTT Si enhances resistivity: low eddy current losses More than 4 wt% Si will make it too brittle

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L+ T Stable liquid log t TmTm glass Metallic Glass Fe + 15-25%(Si, B, C) High solute High resistivity Low eddy current loss AmorphousIsotropicNo hard direction AmorphousNo grain boundary Easy domain wall movement Low eddy current loss

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50 HzFe-4wt% Si K HzPermalloy, Supermalloy MHzFerrites

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Hard magnetic materials For permanent magnets Motors, headphones High B r, high H c B r H c = energy product Martensitic high carbon steels (B r H c =3.58 kJm 3 ) Alnico alloys: directionally solidified and annealed in a magnetic field (B r H c =5.85 kJm3) Mechanically hard c Magnetically hard Large M phase as elongated particle in low M matrix

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Elongated Single Domain (ESD) magnets Long particles, thickness < domain wall thickness Each particle a single domain No domain growth possible only rotation Ferrite: BaO 6 Fe 2 O 3 (Br Hc=48-144 kJm 3 ) Co-Rare Earths (Sm, Pr) (Br Hc=200 kJm 3 ) Nd 2 Fe 14 B (Br Hc=400 kJm 3 )

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For true understanding comprehension of detail is imperative. Since such detail is well nigh infinite our knowledge is always superficial and imperfect. Duc Franccois de la Rochefoucald (1613-1680)

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