Chapter 1 Magnetic Materials

Transcription

1 Chapter 1 Magnetic Materials Figures cited with the notation [RCO] Fig. X.Y are fro O Handley, Robert C. Modern Magnetic Materials: Principles and Applications. New York: Wiley-Interscience, Courtesy of John Wiley and Sons, Inc. Used with perission. Spring ter, 2004 Magnetic Materials

2 Bob O Handley This course is about agnetic aterials Understanding properties Fro ultidisciplinary perspectives: Physics, Cheistry, Electrical Engineering, Materials Science Selecting aterials for applications Designing aterials / properties for applications Materials science ( phase diagras, bonding) Cheical physics (electronic structure) Engineering new cobinations of aterials Spring ter, 2004 Magnetic Materials

3 Malaysia University of Science and Technology Progra: M.U.S.T. MIT Technology Developent Progra (TDP) working with Malaysia & Motorola to create elite private teaching and research university near Kuala Lupur, Malaysia Short courses, seinars, curriculu & research developent Graduate-level instruction, research Prof. Ridha Berriche in Malaysia Proote MUST-industry-governent ties MUST progra is distinct fro, but siilar in spirit, to Singapore/MIT, Argentina, back to early 60s, IIT, Kanpur (late Noran Dahl, Course II) Spring ter, 2004 Magnetic Materials

4 Magnetic Materials Ground rules A. Text Modern Magnetic Materials Principles and Applications, R.C. O Handley (Wiley, 2000); (Discounted at B. Grades Test (id ter) 20% Hoe works 20% Written assignent 40% Oral presentation 20% 05/11/04, 05/13/04 C. Lab exercises, easureents, basic properties and ore Spring ter, 2004 Magnetic Materials

5 Magnetic Materials Approach in text is inductive, Socratic INPUT fro you. A. Observations explanations, principles B. Free energy, iniization Doains, M-H Ch. 1-9 C. Applications to soft, hard, nanocrystalline aterials, transport, surfaces, agnetic recording Ch Read handouts, text; what do you find effective, what do you need? Suggest other topics for possible coverage? Spring ter, 2004 Magnetic Materials

6 Where are Magnetic Materials Used? Volue usage Iages reoved due to copyright considerations. Transforers and coputer disk drive. Dollar value [RCO] Fig Spring ter, 2004 Magnetic Materials

7 OBSERVATIONS OF MAGNETISM Field about wire [RCO] Fig. 1.1 Apére Solenoid [RCO] Fig. 1.2 Faraday [RCO] Fig. 1.3 We will ake these concepts quantitative and apply to aterials... Spring ter, 2004 Magnetic Materials

8 CONSTUTIVE RELATIONS Electric Polarization p =qd d q p P = P = χ E D = ε 0 E + P = ε 0 (1 + e p vol. χ e = n p )E = ε 0 ε r E ε E P Magnetic Polarization p = µ = agnetic oent, µ µ M = = n µ νol. M = agnetic oent density, or agnetization. Spring ter, 2004 Magnetic Materials

9 THREE MAGNETIC FIELDS: M, H, B 2 fields M = χh, χ is diensionless in MKS; M, H have sae units. H is field intensity, M is agnetization, oent density 3 rd field B = µ 0 (H + M ) = µ 0 (1 + χ) H = µ 0 µ H MKS r [B = H + 4 πm = (1 + 4 πχ)h ] cgs MAGNETIC POTENTIAL ENERGY: θ B µ U = µ B u = M B MKS µ H M H cgs [RCO] Fig. 1.4 Spring ter, 2004 Magnetic Materials

10 THREE MAGNETIC FIELDS, M, H, B Field source: Coupled fields: Maxwell Equations E = ρ ε B = 0 E = B t B = µ 0 J + µ 0 ε E t Faraday Apère B field lines do not eanate fro a agnetic charge Integral Forulas for source equations ρ = charge / volue, integrate over volue: E(x x )d 3 x = 1 ρ(x x )d 3 x, B d 3 ε 0 E Gauss Theore Gauss Theore E nda = 1 ρ(x x )d 3 x ε 0 Electric field lines eanate fro positive charge x = 0 B nda = 0 But there is no agnetic onopole source of B! Spring ter, 2004 Magnetic Materials B

11 Integral fors for COUPLED Maxwell Equations B = agnetic flux per unit area, and J = current per unit area, so integrate over area ( E) da = B da B da = µ Ý 0 J 0 da + µ 0 DdA t Stokes Theore E dl V = φ t Faraday s Law of induction: V = N B A N = No. of turns t B = φ A [RCO] Fig. A1.2 Stokes Theore B dl = µ 0 I Apère s Law: This is how agnetic fields are generated by currents. More on this Spring ter, 2004 Magnetic Materials

12 QUANTITATIVE current-field relations (Right-hand rules) FIELD OUTSIDE CURRENT-CARRYING WIRE B dl = µ 0 I [RCO] Fig. 1.6 B = µ 0 I 2πR for closed circular path 2πRB = µ 0 I (In a agnetic ediu, B includes icroscopic and acroscopic currents) I H = 2πR M H (H includes only acroscopic currents) φ B = A what area? Spring ter, 2004 Magnetic Materials

13 Alternate derivation: Integrate differential for in cylindrical coordinates: B R 1 [rb θ (r)]= µ 0 J r r (rbθ ) = µ 0 Jr dr r 0 RB θ (R) = µ 0JR 2 + C, 2 I J = 2 πr I B = µ 0 2πR +C C = 0 because B vanishes at R = µ 0 I dl r Biot-Savart for ore useful: db = 3 4π r dl I r Spring ter, 2004 Magnetic Materials

14 Filed inside Solenoid ( B) da = B dl = µ 0 J da = µ 0 NI sense of is RH rule, [RCO] Fig. 1.8 B NI out dl + B in dl = µ 0 NI B i = µ, H i = NI 0 l l, = 0 REVIEW N / l = # turns / length ( B)d 2 x = µ 0 Jd 2 x B dl = µ 0 J Field about wire B = µ 0 NI 2πR NI B = µ 0 Field inside solenoid Spring ter, 2004 Magnetic Materials

15 More on p, M. ORIGIN OF MAGNETISM IN MATTER Let s approxiate a aterial as a stack of electron orbits: Assue orbits are coplanar (M is saturated) and B = µ (H + M ) = µ 0 M 0 H ext = 0 Cobine solenoid equations with constitutive relation N M = vol. µ [RCO] Fig. 1.9 µ = IA = e ω πr 2 = 2 e B = µ NI = µ N µ µ = IA 0 0 l v Atoic agnetic 2 πr 0 v = 2E oents due to current 2π π r0 orbits ( l 0) Al (E 1s for hydrogen is 13.6 ev) Spring ter, 2004 Magnetic Materials

16 Nuerical consistency: er 0 er 0 2π 2 2 λ µ = v = λ = 2πr 0 in the Bohr odel e µ = = A 2 2 This is the Bohr agneton, µ Β, agnetic oent of one electron spin. A agnetic aterial has n = # / vol of these, so B = µ = 1.16T Observe: Fe: µ = 2.2 µ Β Ni: µ = 0.6 µ Β Spring ter, 2004 Magnetic Materials

17 Review B dl = µ 0 I µ 0 I B = 2πR Faraday s Law of B induction: V = N t A N = No. of turns NI B i = µ, H i = 0 l NI l, N / l = # turns / length Spring ter, 2004 Magnetic Materials

18 Review B = µ 0 (H + M ) = µ 0 (1 + χ) H = µ 0 µ H r (In a agnetic ediu, B includes icroscopic and acroscopic currents) M H Magnetic Polarization p = µ = agnetic oent, µ µ M = = n µ νol. M = agnetic oent density, or agnetization. µ = IA e µ = = A 2 2 NI N µ Fe: Β s = 2.2 Τ B = µ 0 = µ 0 l Al Ni: Β s = 0.6 Τ Spring ter, 2004 Magnetic Materials

19 Types of Magnetic Materials Weak Magnetis Ferroagnetis [RCO] Fig.1.11 [RCO] Fig Spring ter, 2004 Magnetic Materials

20 Magnetic Doains [RCO] Fig [RCO] Fig Calculate doain structures fro free energy expressions for shape, crystallography and stress Spring ter, 2004 Magnetic Materials

21 Technical Magnetis [RCO] Fig.1.14 Flux density: B = µh = µ 0 (H + M ) Pereability: µ = B H Magnetic Field: H = NI l Spring ter, 2004 Magnetic Materials

22 Suary Pereability: µ = B H Ferroagnetis Magnetic Field: Flux density: H = NI l B = µh = µ 0 (H M ) In vacuu: B = µ 0 H (Tesla) N M = vol. µ In aterial: B = µ 0 (H + M) = µ 0 (1+ χ)h = µh Spring ter, 2004 Magnetic Materials