# Magnetic Materials

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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. - PowerPoint PPT Presentation

### Text of Magnetic Materials

• Magnetic Materials

• Basic Magnetic QuantitiesMagnetic Induction or Magnetic Flux Density BUnits: N C-1 m-1 s = Tesla (T) = Wb m-2

• 2006: UNESCO Nikola Tesla Year150th birth Anniversary of Nikola TeslaAC vs. DC

• Amperes law in free spaceiB0= permeability of free space = 4 10-7 T m A-1 = 4 10-7 H m-1

• Magnetic dipole moment miArea=Am=iAUnits: A m2

• Magnetization M of a solidA solid may have internal magnetic dipole moments due to electronsMagnetic dipole moment per unit volume of a solid is called magnetizationUnits: A m2/m3 = A m-1

• Amperes law in a solidiB0H: magnetic field intensity or field strength Units: A m-1

• In free spaceInside a solid16.116.316.2 = permeability of solid, H m-1 relative permeability of solid, dimensionless

• : magnetic susceptibility of the solidTypes of magnetic solidDimensionlessdiamagnetic-10-5superconductor-1paramagnetic+10-3ferromagnetic(universal)+103-10516.4

• Origin of permanent magnetic moments in solids:1. orbital magnetic moment of electrons2. spin magnetic moment of electrons3. spin magnetic moment of nucleusWe will consider only spin magnetic moment of electrons

• Bohr magneton BThe magnetic moment due to spin of a single electron is called the Bohr magneton B B= 9.273 x 10-24 A m2Net moment of two electrons of opposite spins = 0

• Unpaired electrons give rise to paramagnetism in alkali metalsNa 3s1Net magnetic moment 1 B Fe 3d64s24 Batomcrystal2.2 BCo 3d74s23 B1.7 BNi 3d84s22 B0.6 B

• Example 16.1The saturation magnetization of bcc Fe is 1750 kA m-1. Determine the magnetic moment per Fe atom in the crystal.a=2.87 V = a3 = 2.873x10-30Magnetic moment per atom= 1750 x 1000 x 2.873 x 10-30 x 1/2= 2.068x10-23 A m2 = 2.2 B

• Ferromagnetic, ferrimagnetic and antiferromagnetic materialsDue to quantum mechanical interaction the magnetic moment of neighbouring atoms are aligned parallel or antiparallel to each other.ferromagneticAnti- ferromagneticFerri- magnetic

• ferromagneticFe, Co, Ni, GdElementTiCrMnFeCoNi1.121.181.471.631.821.98Eexchange interaction= Eunmagnetized-Emagnetized 1.5-2.0Heusler Alloys: Cu2MnSn, Cu2MnAlFerromagnetic alloys made of non-ferromagnetic elements

• Thermal energy can randomize the spinFerromagneticParamagneticTcurieheatFe1043 KCo1400 KNi631 K Gd298 KCu2MnAl710 K

• Ferrimagnetic materialsFerritesM2+: Fe2+, Zn2+, Ni2+, Mg2+, Co2+, Ba2+, Mn2+, Crystal structure: Inverse spinelSee last paragraph (small print) of Section 5.4

• Crystal structure: Inverse spinelFerritesO2+ FCC packing 4 O2+8 THV4 OHVAntiferromagnetic couplingFe3+Fe3+M2+Net moment due to M2+ ions only.

• 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

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

• Randomly aligned domains1. decrease the manetostatic energy in the field outside the magnet2. increase the domain wall energy inside the magnetA magnet will attain a domain structure which minimizes the overall energy

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

• Two ways for aligning of magnetic domains:Growth of favorably oriented domains (initially)Rotation of domains (finally)Initial permeabilitySaturation induction

• The hysteresis LoopFig. 16.4Brresidual inductionHccoercive fieldArea = hysteresis loss

• Soft magnetic materialsHigh initial permeability Low hysteresis lossLow eddy current lossesFor application requiring high frequency reversal of direction of magnetizationEg. Tape headProblem 16.11

• Easily moving domain wallsLow impurity, low non magnetic inclusions, low dislocation density low second phase precipitateSoft magnetic materialsFor low hysteresis loss ( frequency)For low eddy current loss ( frequency2)Material: high resistivityDesign: LaminationChoose: Pure, single phase, well-annealed material of high resistivity

• Table 16.1Material 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 0.6Permalloy 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 1Mn-Zn Ferrite 2000 40 0.3 1

• Magnetic anisotropy Fig. 16.5 easy direction hard directionIron single crystalPolycrystal: attempt to align easy direction in all grains Preferred orientation or textureBy rolling and recrystallizationBy solidification By sintering ferrite powder in magnetic field

• Fe-4% Si alloy for low frequency transformersWt% SiWt% SiresistivityBsTDBTTSi enhances resistivity: low eddy current lossesMore than 4 wt% Si will make it too brittle

• L+TStable liquidlog tTmglassMetallic Glass Fe + 15-25%(Si, B, C)High soluteHigh resistivityLow eddy current lossAmorphousIsotropicNo hard directionAmorphousNo grain boundaryEasy domain wall movementLow eddy current loss

• 50 HzFe-4wt% SiK HzPermalloy, SupermalloyMHzFerrites

• Hard magnetic materialsFor permanent magnetsMotors, headphonesHigh Br, high HcBr Hc = energy product Martensitic high carbon steels (Br Hc=3.58 kJm3) Alnico alloys: directionally solidified and annealed in a magnetic field (Br Hc=5.85 kJm3) Mechanically hardcMagnetically hardLarge M phase as elongated particle in low M matrix

• Elongated Single Domain (ESD) magnetsLong particles, thickness < domain wall thicknessEach particle a single domainNo domain growth possible only rotationFerrite: BaO 6 Fe2O3 (Br Hc=48-144 kJm3) Co-Rare Earths (Sm, Pr) (Br Hc=200 kJm3) Nd2 Fe14 B (Br Hc=400 kJm3)

• 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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