W Morris Jr University of California Berkeley MSE 200A Fall 2017 Magnetism in

W morris jr university of california berkeley mse

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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Magnetism in Valence Metals Diamagnetism (Cu, Au, Zn, Hg) Magnetic ( Lorenz ) force eddy currents m of current loop opposes B χ < 0 but small (except in superconductors) Band paramagnetism (Al) Electron moment ( m B ) preferentially aligns with B Increases electrons with parallel spins χ > 0 but small N(E) N(E) E E band paramagnetism I m = IA n A B F = -e( v x B) diamagnetism
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Sc: 3d 1 4s 2 Ti: 3d 2 4s 2 V: 3d 3 4s 2 Cr: 3d 5 4s 1 Mn: 3d 5 4s 2 Fe: 3d 6 4s 2 Co: 3d 7 4s 2 Ni: 3d 8 4s 2 Cu: 3d 10 4s 1 m = 1 m B m = 2 m B m = 3 m B m = 5 m B m = 5 m B m = 4 m B m = 3 m B m = 2 m B m = 0 Core Magnetism: Transition Metals
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Core Magnetism High temperature : Spins disordered paramagnetism Low Temperature (T < T c ) Spins align = ferromagnetism Elements: Fe, Ni, Co, Gd, Dy Alloys and compounds: AlNiCo, FeCrCo, SmCo 5 , Fe 14 Nd 2 B Like spins alternate = antiferromagnetism Unlike spins alternate = ferrimagnetism Compounds: Fe 3 O 4 (lodestone, magnetite), CrO 3 , SrFe 2 O 3 Ferromagnetic (and ferrimagnetic) materials have engineering applications Ferromagnetism antiferromagnetism ferrimagnetism M = 0 M = (n/2)( m 1 - m 2 ) M = n m
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Ferromagnetism is Uncommon
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Ferromagnetism Ferromagnetism occurs by mutation at T c ( Curie T ) Energy is minimized by ordering spins into domains Net moment, M , would cause external field, increase energy Magnetic domains cancel so that M = 0 Natural ferromagnetism does not produce a net magnetic field M T T c paramagnetic ferromagnetic
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Ferromagnetism To magnetize a ferromagnet, impose H Domains move to align M and H Defects impede domain motion Moment ( M r ) retained when H removed Magnetic properties M s = saturation magnetization All spins aligned with field M r = remanent magnetization Useful moment of permanent magnet H c = coercive force Field required to erase moment Area inside curv e = magnetic hysteresis Governs energy lost in magnetic cycle H M H H c M s M r
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J.W. Morris, Jr. University of California, Berkeley MSE 200A Fall, 2017 Hard Magnets: High Field Strong natural magnet : maximize M s AlNiCo - M s ~ 1.0 T Sm(Co,Fe,Cu,Zr) 8 M s ~ 1.2 T Fe 14 Nd 2 B M s ~ 1.3 T Microstructural obstacles: maximize M r /M s Fine domain size Grain size Particle size (free particle or embedded precipitate) Defects and non-magnetic inclusions M s M r H c domain motion orientation M M H = M
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J.W. Morris, Jr.
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  • Fall '08
  • Staff
  • Magnetism, Magnetic Field, University of California, J.W. Morris

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