20.2 - Paramagnetism • Paramagnetism permanent dipole...

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Unformatted text preview: Paramagnetism • Paramagnetism: permanent dipole moment in some solids due to incomplete cancellation of e- spin or orbital magnetic moments random orientation of magnetic moments in absence of applied field zero net magnetism dipoles free to rotate…preferentially align with external field, but no mutual interaction between adjacent dipoles Applied Magnetic Field (H) aligned (2) Paramagnetic random No Applied Magnetic Field (H = 0) Adapted from Fig. 20.5(b), Callister 7e. μr >1 susceptibility = small, +ve, i.e. B-field is greater than in vacuum magnetization exists only when ext. H-field applied Chapter 20 - 21 Ferromagnetism • Ferromagnetism: some metallic materials - permanent magnetic moment - large & permanent magnetizations e.g. transition metals Fe, Co, Ni & rare earth Gd permanent magnetic moments due to uncanceled e- spins coupling interactions (not fully understood) cause net spin magnetic moments of adjacent atoms to align, even in absence of ext. H-field Applied Magnetic Field (H) aligned (3) Ferromagnetic Ferrimagnetic aligned No Applied Magnetic Field (H = 0) Adapted from Fig. 20.7, Callister 7e. susceptibility as high as 106, +ve, i.e. B-field much greater than in vacuum mutual e- spin alignment exists over large vol. regions - domains Chapter 20 - 22 Q: Why spontaneous magnetization? A: Positive interaction energy, i.e. attractive force between adjacent e- spins Consider it as a reverse domino effect. One electron lines up with the field and pulls the adjacent electron into alignment with it, until all the electrons in a given domain are lined up with the field Chapter 20 - 23 Ferromagnetism (Cont.) • Ferromagnetism: when all magnetic dipoles mutually aligned with external field: • saturation magnetization (Ms) • max possible magnetization corresponding saturation flux density (Bs) magnitude of saturation magnetization (Ms): Ms = net magnetic moment of each atom x # atoms present Net magnetic moment per atom: Metal Fe Co Ni # Bohr Magnetons/atom 2.22 1.72 0.60 Check out Example Problem 20.1, pp. W27 Chapter 20 - 24 Summary: Magnetic Moments for 3 Types none opposing (2) Paramagnetic random aligned (3) Ferromagnetic Ferrimagnetic aligned Applied Magnetic Field (H) aligned No Applied Magnetic Field (H = 0) (1) Diamagnetic Adapted from Fig. 20.5(a), Callister 7e. Adapted from Fig. 20.5(b), Callister 7e. Adapted from Fig. 20.7, Callister 7e. Chapter 20 - 25 Ferrimagnetism • Ferrimagnetism: some ceramics exhibit permanent magnetization - ferrimagnetism similar macroscopically to ferromagnetism, but different origin of net magnetic moment Ferrites, e.g. Fe3O4, cubic structure inverse spinel structure Consider Fe3O4 as: Fe2+O2- + (Fe3+)2(O2-)3 i.e. containing +2 and +3 valence state Fe ions: 4 Bohr magnetons/ion Fe2+ 5 Bohr magnetons/ion Fe3+ O2- ions magnetically neutral Fe2+ ions in octahedral positions Half Fe3+ ions in octahedral positions, but half also in tetrahedral positions Spin moments of all Fe3+ cancel out Magnetic moments of all Fe2+ aligned in same direction, thus responsible for net magnetization Chapter 20 - 26 Ferrimagnetism (Cont) Ms = net magnetic moment of each Fe2+ ion x # Fe2+ ions present How do we make other cubic ferrites? Substitute some Fe2+ w. metallic ions with different # Bohr magnetons e.g. Ni2+ (2), Mn2+ (5), Co2+ (3), Cu2+ (1) Vary composition ferrites with different magnetic properties See Design Example 20.1 Chapter 20 - 27 Effect of Temperature Increasing Temp. of a solid: Increases thermal vibration of atoms… Magnetic dipoles free to rotate, so what will happen if T increases? • atoms will tend to randomize directions or magnetic moments Ferro/Ferri-magnetic materials: • thermal atomic vibrations counteract coupling forces between adjacent magnetic dipoles… • decreases Ms • Ms = max. at 0 K • As T inc. Ms drops to Zero abruptly… – Tc = Curie Temp. Chapter 20 - 28 Saturation Magnetization vs. Temp. Above Tc, ferro- and ferrimagnetic materials = paramagnetic Chapter 20 - 29 Q. What is the Curie temperature or critical temperature Tc a measure of? A. The strength of interaction/coupling between adjacent electrons Think of Tc as a magnetic “melting point”. Above it, all the spins are randomly oriented and act like ducks on a pond that are not interacting. i.e. they respond to H independently. Below Tc the e- spins align and out of chaos comes order. In the same way that below Tm, order comes out of chaos… crystallinity Chapter 20 - 30 Magnetic Domains • Ferri- and Ferromagnetic Materials below Tc: small volume regions w. mutual alignment of magnetic dipole moments in same direction - Domains Each domain is magnetized to its Ms Adjacent domains aligned differently, separated by domain walls Grains in polycrystalline materials may comprise >1 domain Chapter 20 - 31 B-H Behavior - Ferro/Ferrimagnetic Mat’ls. • Relation bet. flux density B and field intensity H non- linear: – As the applied field (H) increases the magnetic moments align progressively with H Bs (Ms) Magnetic Induction (B, Tesla) H H H H H • “Domains” with aligned magnetic moment grow at expense of poorly aligned ones! Adapted from Fig. 20.13, Callister 7e. (Fig. 20.13 adapted from O.H. Wyatt and D. DewHughes, Metals, Ceramics, and Polymers, Cambridge University Press, 1974.) 0 H=0 Applied Magnetic Field (H, A-t/m) Chapter 20 - 32 Another View of Same Thing Chapter 20 - 33 Chapter 20 - 34 Hysteresis & Permanent Magnets • Process: B 3. Remove H, alignment stays! - permanent magnet! 4. Coercivity, HC - negative H needed to demagnetize! 2. Apply H, cause alignment Adapted from Fig. 20.14, Callister 7e. Applied Magnetic Field (H) 1. initial (unmagnetized state) Chapter 20 - 35 Hysteresis & Permanent Magnets Chapter 20 - 36 Hard vs. Soft Magnets Adapted from Fig. 20.19, Callister 7e. (Fig. 20.19 from K.M. Ralls, T.H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, John Wiley and Sons, Inc., 1976.) Hard Hard: large coercivity – good for perm. magnets – add particles/voids to make domain walls hard to move (e.g. tungsten steel: Hc = 5900 A-turn/m) Soft • Hard B Applied Magnetic Field (H) Soft: small coercivity – good for elec. motors – (e.g., commercial iron 99.95 Fe) Chapter 20 - 37 Hard vs. Soft Magnets Area within loop = magnetic energy loss/unit vol. of material per magnet’n./demagnet’n. cycle…heat gen. within sample Chapter 20 - 38 Hard vs. Soft Magnets Soft Hard (Permanent) Hysteresis Loop area small (thin & narrow) large (broad &~ square) Initial Permeability (μi) High Low Saturation Flux (Bs) Low High Remanence (Br) Low High Coercivity (Hc) Low High (BH)max Low High Example Application Transformer cores, motors, dynamos Loudspeakers Chapter 20 - 39 Energy Product (BHmax) (BH)max = area of largest B-H rectangle in 2nd quadrant of B-H curve: Units - kJ/m3 or (MGOe), where 1 MGOe = 7.96 kJ/m3 Represents energy required to demagnetize perm. magnet. Chapter 20 - 40 Hard Magnetic Materials • Conventional: – (BH)max of 2-80 kJ/m3 – magnetic steels, C-Ni-Fe (“cunife”), Al-Ni-Co alloys (“alnico”), hexagonal ferrites (BaO-6Fe2O3) • High Energy: – (BH)max >80 kJ/m3 – intermetallics such as SmCo5, Nd2Fe14B – often made via P/M techniques Chapter 20 - 41 Magnetic Storage • Information stored by magnetizing a material • Head can... – apply magnetic field H & align domains (i.e., magnetize the medium) – detect a change in the magnetization of the Image of hard drive courtesy Martin Chen. Reprinted with medium permission from International Business Machines Corp. Recording Medium Recording head Adapted from Fig. 20.23, Callister 7e. (Fig. 20.23 from J.U. Lemke, MRS Bulletin, Vol. XV, No. 3, p. 31, 1990.) • Two media types: - Particulate: needle-shaped -Fe2O3. +/- mag. moment along axis. (tape, floppy) Adapted from Fig. 20.24, Callister 7e. (Fig. 20.24 courtesy P. Rayner and N.L. Head, IBM Corporation.) - Thin Film: CoPtCr or CoCrTa alloy. Domains are ~ 10 - 50 nm! (hard drive) Adapted from Fig. 20.25(a), ~2.5 μm ~120 nm Callister 7e. (Fig. 20.25(a) from M.R. Kim, S. Guruswamy, and K.E. Johnson, J. Appl. Phys., Vol. 74 (7), p. 4646, 1993. ) Chapter 20 - 42 Inductive Read-Write Head • Head structure: – – – – coil around magnetic core small gap in core signal in core gen. field in gap field magnetizes small area of disk – magnetization remains…data stored – use same head to retrieve data – amplify signal… Chapter 20 - 43 Fe2O3 Magnetic Disk • Disk structure: – needle-like Fe2O3 or CrO2 – bonded to polymer film (tapes) or metallic disk (hard drive) – particles aligned w. long axes parallel to motion past readwrite head – each particle = single domain, can be magnetized w. magnetic moment along axis – Two possible states: – saturation magnetization in one direction (1) – saturation magnetization in opposite direction (0) Chapter 20 - 44 Summary • A magnetic field (H) can be produced by: – passing a current through a coil (H = NI/L) • Magnetic Induction (B): – occurs when a material is subjected to a magnetic field – is a change in magnetic moment from UNPAIRED electrons • Types of material response to a field include: – Ferro- or Ferrimagnetic (large magnetic induction) – Paramagnetic (poor magnetic induction) – Diamagnetic (opposing magnetic moment) • Hard magnets: large coercivity • Soft magnets: small coercivity • Magnetic storage media: – particulate -Fe2O3 in polymeric film (tape or floppy) – thin-film CoPtCr or CoCrTa on glass disk (hard drive) Chapter 20 - 45 FROM HERE ON OPTIONAL Chapter 20 - 46 Chapter 20 - 47 Superconductivity Hg Copper (normal) 4.2 K Adapted from Fig. 20.26, Callister 7e. • Tc = temperature below which material is superconductive – critical temperature – 1-20 K for S/C metals/alloys; up to >100 K for complex oxide ceramics (YBaCuO) Chapter 20 - 48 Limits of Superconductivity • ~26 metals + 100’s of alloys & compounds • Unfortunately, not this simple: Jc = critical current density if J > Jc not superconducting Hc = critical magnetic field if H > Hc not superconducting Hc= Ho (1- (T/Tc)2) Adapted from Fig. 20.27, Callister 7e. Chapter 20 - 49 Advances in Superconductivity • Research area stagnant for many years: – everyone assumed Tc,max was ~23 K – Many theories said you couldn’t go higher • 1987- new results published for Tc > 30 K – ceramics of form Ba1-xKxBiO3-y – started enormous race: • Y Ba2Cu3O7-x Tc = 90 K • Tl2Ba2Ca2Cu3Ox Tc = 122 K • tricky to make since oxidation state is quite important • Values now stabilized at ~120 K Chapter 20 - 50 Meissner Effect • Superconductors expel magnetic fields normal superconductor Adapted from Fig. 20.28, Callister 7e. • This is why a superconductor will float above a magnet Chapter 20 - 51 Current Flow in Superconductors • Type I current only in outer skin - so amount of current limited • Type II current flows within wire Type I M Type II complete diamagnetism HC1 HC mixed state HC2 H normal Chapter 20 - 52 Superconducting Materials CuO2 planes X Cu O Cu X X X Ba Y Ba linear chains X X X (001) planes X YBa2Cu3O7 Vacancies (X) provide electron coupling between CuO2 planes. Chapter 20 - 53 ...
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