Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

1. Engineering 45 MagneticProperties Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Learning Goals – Magnetic Props • How to measure magnetic properties • Atom-scale sources of magnetism • How to Classify Magnetic Materials

3. Properties of Solid Materials • Mechanical: Characteristics of materials displayed when forces and or torques are applied to them. • Physical: Characteristics of materials that relate to the interaction of materials with various forms of energy. • Chemical: Material characteristics that relate to the structure of a material. • Dimensional: Size, shape, and finish

4. Material Properties Chemical Physical Mechanical Dimensional Composition Melting Point Tensile properties Standard Shapes Microstructure Thermal Toughness Standard Sizes Phases Magnetic Ductility Surface Texture Grain Size Electrical Fatigue Stability Corrosion Optical Hardness Mfg. Tolerances Crystallinity Acoustic Creep Molecular Weight Gravimetric Compression Flammability

5. Magnetic Field Strength B • Consider a Tightly Coiled Wire Carrying an Electric Current, I • This SOLENOID Configuration Generates a Magnetic Field with Strength, H I L • N  Number of Coils (turns) • I  Current (Amps) • L  Coil Length (m) • where

6. Magnetic Field Strength cont B • H has the unusual Units of Amp-Turns per Meter (A/m) • H induces Magnetic Flux, B as I L Think: C = ε(A/L) • where • µ  the Magnetic PERMEABILITY (Henry per meter, or H/m) • Units for B = Tesla • 1 Tesla = 1 Amp-Henry

7. Magnetization B I • B = µH applies to the General Case where some Material Occupies the Center of the Coil • BaseLine Case → Coil in a VACUUM L • µ0 is a Universal Constant • µ0 = 1.257x10-6 H/m

8. The Presence of Material in the Coil-Core Changes the Magnetic Flux The Intensity of the Materal-Filled Coil Relative to the Baseline B = Magnetic Induction inside the material current I Magnetization cont.

9. Alternatively Describe the Magnetic Field Strengthening by Magnetization cont.2 • m is A Unitless Material Property • So B • Where M  MAGNETIZATION • A Material Property • Units → Amp/m • Define Magnetic SUSCEPTIBILITY • Then µr vs m

10. magnetic moments electron electron spin nucleus Magnetic Susceptibility Origins • Measures the response of electrons to an Electric field • Electrons Produce Electric Fields Due to • Orbit about a the Nucleus (a tiny current) • Electron Spin (recall spin-↑ & spin-↓) • The Magnetic Analog to the Electronic charge, q, is the Bohr Magneton: • µB = 9.27x10-24 J/Tesla

11. Types of Magnetism • Magnetism arises from e- Orbit & Spin • NET MAGNETIC MOMENT = Sum of all individual Magnetic moments from both Orbit & Spin • The Form of the Magnetic Sums Yields Three Types of Magnetism • DiaMagnetism • DECREASES B • ParaMagnetism • Weakly Enhances B • FerroMagnetism • STONGLY Enhances B

12. The 3 Types of Magnetism permeability of a vacuum: (1.26 x 10-6 Henrys/m) (3) ferromagnetic e.g. Fe3O4, NiFe2O4 ferrimagnetic e.g. ferrite(), Co, Ni, Gd 6 c ( as large as 10 ) -4 c (2) ( ~ 10 ) paramagnetic e.g., Al, Cr, Mo, Na, Ti, Zr c vacuum ( = 0) -5 (1) c diamagnetic ( ~ −10 ) e.g., Al O , Cu, Au, Si, Ag, Zn 2 3 Magnetic induction B (tesla) Strength of applied magnetic field (H) (ampere-turns/m)

13. DiaMagnetism • NonPermanent and Weak • m ~–10-5 (recall Ni  600) • Exists Only When H-Field Applied • Atoms have NO permanent Magnetic DiPoles • When Field Applied, the Generated Dipoles COUNTER the Field → B<B0 Thus • ur <1 (i.e., a %-age) • m <0m (i.e., NEGATIVE)

14. ParaMagnetism • Each Atom DOES Possess a Permanent DiPole • Atomic Dipoles are RANDOMLY Arranged •  A “Chunk” of Material has NO Net Macroscopic Magnetism • However, Dipoles Do Align to an Applied Field, Strengthening it • Yields a Small & Positive m: 10-5 -10-3

15. FerroMagnetism • Material is Magnetic, Even withOUT an Applied H-Field • Relatively Rare in Nature • Large Susceptibility Caused by Parallel Alignment of Domains due to Coupled Spin Moments of UnPaired Electrons • Yeilds Large & Positive m: 102 -105 • Recall Field Strength Eqn

16. Magnetization vs H • M for Ferromagnetics is a Function of the Applied Field, H • As H increases, B approaches a Maximum Value • i.e., the Magnetization SATURATES • Msat for FerroMags • Where • nB  Bohr Magnetons per atom • µB  Bohr Mageton Value • N  atomic Density

17. AntiFerroMagnetism • Atoms Contain a Permanent DiPole,but There are equal Quantities of Oppositely Directed Dipoles • Therefore, the magnetic field cancels out and the material appears to behave in the same way as a paramagnetic material • Dipoles will Align somewhat to an Applied Field thus • Yields a Small & Positive m: 10-5 -10-3 • Similar to Paramagnetics

18. FerriMagnetism • Arises in Ceramics Where The Oxidant (the metal) Exists in More than One Valence State • Example = Ferrite (Lodestone), Fe3O4 • Fe Exists in Two Valence States: +2 & +3 • The Fe DiValent:TriValent Ratio = 1:2 • Note that The Divalent & TriValent Iron Ions have Bohr Magneton Ratios of 4 & 5 respectively • O2- ions are Magnetically Neutral

19. X X X X X X FerriMagnetism cont • The Atoms in LodestoneArrange in AXtal Structure that can be Represented as • Note that Magnetic SpinMoments for the TRIVALENT ions Cancel • This Leaves a Net Ferrimagnetic Form due to the DiValent Fe2+ ions

20. Magnet Types Summarized

21. Even though electronic exchange forces in ferromagnets are very large, thermal energy eventually overcomes the exchange and produces a randomizing effect. This occurs at a particular temperature called the Curie temperature (TC). Below the Curie temperature, the ferromagnet is ordered Above TC the FerroMagnet is DISordered. The saturation magnetization goes to zero at the Curie temperature. (ºC) Temperature Affects

22. In Ferr(o/i)Magnetic Materials ThereExist Small PHYSICAL volumes ofWell Aligned Magnetic Dipoles called DOMAINS The Domains are MicroScopic, and,in polyXtal Materials a Grain Maycontain More than one Domain The Magnitude of M for a Macroscopic Piece of Material is the VECTOR sum of all Magnetization for all Domains This is a VOLUME-Weighted Integration Magnetic Domains

23. Magnetization vs H Revisited • For Ferr(o/i)Magnetics as H↑ the Overall Dipole Alignment becomes Stronger. • In other Words, The Favorably-Aligned Domains GROW at the Expense of the less favorably Aligned Domains • Thus Domain Structure can overcome Grain (Physical) Structure B sat H H H induction (B) Magnetic H H 0 Applied Mag Field (H) H = 0 • c.f. cool photos ontext pg W19

24. B Applied H Field Permanent Magnets • Permanent Magnets Exhibit Hysteresis in their B-H Curves Due to B-Lags in the Aligning & Unaligning processes • An Outline of the Process • Apply H, Cause Domain Alignment & Growth • Bring H to Zero, some Alignment remains (Remnance, Br). Have Permanent Magnet • Initial (Unmagnetized) State • To Reach B=0 Must Apply NEGATIVE H (Coercivity, HC) Magnet is Still Perm.

25. Soft & Hard Magnet Materials • The Area within the B-H Curve is Proportional to Energy Absorbed bythe Permanent Magnet • This will be Dissipated as Heat • “Soft” Materials Have Small Hysteresis Areas, but Lower Magnetizations • Good for Devices Where High H-Field Reversal Rates and hence Heat dissipation is as issue; e.g., Electric Motors • “Hard” have Large Hysteresis Areas, but Higher Remnance • The High Remnance, and resistance to demagnetization, Makes Hard Materials well suited for Permanent Magnet applications

26. Consider a Hard Material Hysteresis Curve at right The Area Under the Curve has units of Energy Density: B-H Energy Density • (BH)max as measured in the 2nd Quadrant is the Industry Standard metric for Resistance by a PM to Demagnetization • PM material Microstructure is adjusted to impede Domain Wall motion, enhancing(BH)max • Now Mult by m2/m2: 

27. Application  Magnetic Storage Tape recording medium recording head • Information is stored by magnetizing material. • Head can... --apply magnetic field H & align domains (i.e., magnetize the medium). --detect a change in the magnetization of the medium. Simulation of hard drive courtesy Martin Chen. Reprinted with permission from International Business Machines Corporation. Adapted from Fig. 20.18, Callister 6e. (Fig. 20.18 from J.U. Lemke, MRS Bulletin, Vol. XV, No. 3, p. 31, 1990.) • Two media types: --Particulate: needle-shaped g-Fe2O3. +/- mag. moment along axis. (tape, floppy) --Thin film: CoPtCr or CoCrTa alloy. Domains are ~ 10-30nm! (hard drive) Adapted from Fig. 20.20(a), Callister 6e. (Fig. 20.20(a) from M.R. Kim, S. Guruswamy, and K.E. Johnson, J. Appl. Phys., Vol. 74 (7), p. 4646, 1993. ) Adapted from Fig. 20.19, Callister 6e. (Fig. 20.19 courtesy P. Rayner and N.L. Head, IBM Corporation.) 9

28. Summary  Magnetics • A magnetic field can be produced by • Running a current through a coil • Magnetic induction • Occurs When A Material Is Subjected To A Magnetic Field • Is A Change In Magnetic Moment From Electrons • Types of material-response to a Mag-field are • Ferri- Or Ferro-magnetic (Large Magnetic Induction) • Paramagnetic (Poor Magnetic Induction) • Diamagnetic (Opposing Magnetic Moment)

29. Summary cont. • HARD magnets → LARGE Coercivity. • SOFT magnets → SMALL Coercivity. • Magnetic storage media: • Particulate g-Fe2O3 in Polymeric Film (Tape Or Floppy) • Thin Film CoPtCr or CoCrTa On Glass or Aluminum Disk (Hard Drive)

30. WhiteBoard Work - Magnetics A bar of an Fe-Si Allow has B-H characteristics shown at Left. A bar of this Material inserted into a wire coil 0.2 m long, and having 60 turns, thru which passes a current of 100 mA. 1.35 For This arrangement: (a) What is the B-Field within the bar? (b) At this magnetic field find: 1) The Permeability 2) The Relative Permeability 3) The Susceptibility 4) The Magnetization • Remember the 1.35 Tesla Value