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Magnetic Materials

Magnetic Materials. Basic Magnetic Quantities. Magnetic Induction or Magnetic Flux Density B. Units: N C -1 m -1 s = Tesla (T) = Wb m -2. 2006: UNESCO Nikola Tesla Year 150 th birth Anniversary of Nikola Tesla. AC vs. DC. Ampere’s law in free space.

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Magnetic Materials

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  1. Magnetic Materials

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

  3. 2006: UNESCO Nikola Tesla Year 150th birth Anniversary of Nikola Tesla AC vs. DC

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

  5. Magnetic dipole moment m m=iA Units: A m2 Area=A i

  6. 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 m2/m3 = A m-1

  7. Ampere’s law in a solid i B0 H: magnetic field intensity or field strength Units: A m-1

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

  9. 16.4 : magnetic susceptibility of the solid Dimensionless  Types of magnetic solid diamagnetic (universal) -10-5 superconductor -1 paramagnetic +10-3 ferromagnetic +103-105

  10. 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

  11. 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 m2 Net moment of two electrons of opposite spins = 0

  12. Unpaired electrons give rise to paramagnetism in alkali metals Net magnetic moment atom crystal Na 3s1 1 B 4 B 2.2 B Fe 3d64s2 3 B 1.7 B Co 3d74s2 Ni 3d84s2 0.6 B 2 B

  13. 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 Å V = a3 = 2.873x10-30 Magnetic moment per atom = 1750 x 1000 x 2.873 x 10-30 x 1/2 = 2.068x10-23 A m2 = 2.2 B

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

  15. Fe, Co, Ni, Gd ferromagnetic Eexchange interaction= Eunmagnetized-Emagnetized Element Ti Cr Mn Fe Co Ni 1.12 1.18 1.47 1.63 1.82 1.98 1.5-2.0 Heusler Alloys: Cu2MnSn, Cu2MnAl Ferromagnetic alloys made of non-ferromagnetic elements

  16. Thermal energy can randomize the spin Tcurie Ferromagnetic Paramagnetic heat Fe 1043 K Co 1400 K Ni 631 K Gd 298 K Cu2MnAl 710 K

  17. Ferrimagnetic materials Ferrites M2+: Fe2+, Zn2+, Ni2+, Mg2+, Co2+, Ba2+, Mn2+, Crystal structure: Inverse spinel See last paragraph (small print) of Section 5.4

  18. Ferrites Crystal structure: Inverse spinel O2+ FCC packing 8 THV Fe3+ 4 O2+ Antiferromagnetic coupling 4 OHV M2+ Fe3+ Net moment due to M2+ ions only.

  19. 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

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

  21. 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

  22. 16.3 B never saturates M saturates The value of B at the saturation of M is called the saturation induction (~ 1 T)

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

  24. The hysteresis Loop Br residual induction Hc coercive field Area = hysteresis loss Fig. 16.4

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

  26. Soft magnetic materials For low hysteresis loss (  frequency) Easily moving domain walls Low impurity, low non magnetic inclusions, low dislocation densitylow second phase precipitate For low eddy current loss (  frequency2) Material: high resistivity Design: Lamination Choose: Pure, single phase, well-annealed material of high resistivity

  27. Table 16.1 Material Init. Rel.Hysteresis Saturation 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

  28. Magnetic anisotropy Fig. 16.5 Iron single crystal <100> easy direction <111> hard direction 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

  29. Fe-4% Si alloy for low frequency transformers Si enhances resistivity: low eddy current losses resistivity More than 4 wt% Si will make it too brittle TDBTT Bs Wt% Si Wt% Si

  30. Metallic Glass Fe + 15-25%(Si, B, C) T Stable liquid Tm High solute L+ High resistivity glass Low eddy current loss log t Amorphous Isotropic No hard direction Amorphous No grain boundary Easy domain wall movement Low eddy current loss

  31. 50 Hz Fe-4wt% Si K Hz Permalloy, Supermalloy MHz Ferrites

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

  33. 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 Fe2O3 (Br Hc=48-144 kJm3) Co-Rare Earths (Sm, Pr) (Br Hc=200 kJm3) Nd2 Fe14 B (Br Hc=400 kJm3)

  34. 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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