V. Soft & Hard Magnetic Materials

V. Soft & Hard Magnetic Materials

(1) Introduction

(2) Soft Magnetic Materials

(3) Hard Magnetic Materials

(1) INTRODUCTION

 Classification

Hard magnets : H

> ~10 kA/m (~100 Oe), Soft magnets : H

< ~1 kA/m (~10 Oe)

Originally for iron & steel (mechanically hard -> high H

, mechanically soft -> low H

)

 Applications

Soft magnets : Mostly for electrical circuits for an amplification of the magnetic flux General requirements : high permeability(μ), low coercivity(H

), low hysteresis loss (W

) Hard magnets : An energy storage device as permanent magnets generating a magnetic field

General requirements : high coercivity(H

), high remanence(M

), high magnetic energy

{(BH)max, W

}

 AC Losses

W_tot = W_H + W_ec + W_a

Where, W_H = a hystereses loss, W_ec = an eddy current loss, and W_a = an anomalous loss W_H : the energy loss per unit volume in one cycle = the area inside a B-H loop

Energy W dissipated in a toroidal core over one cycle = the integral of the power loss over a period:

W_H =

Ampere's law and Faraday's law, V(t) = – dφ/dt = – AdB/dt W_H = iA∮H(t)dB : DC hysteresis loss

W_ec : the power loss due to a current induced by ac field (dB/dt )

Classical eddy-current loss : the power loss per unit volume at low frequency for a uniform magnetization

W_ec  B_max²d²v²^-1

Eddy-current loss due to wall motion : W_ec  W_AB/d, where W_AB is wall traveling distance during a half-cycle

W_a : excessive measured loss over the classical loss due to a inhomogeneous magnetization change



t

i t V t dt

0

( ) ( )

(1) INTRODUCTION

 Operation of Permanent Magnets

- Demagnetization curve : useful to decide the suitability of a permanent magnet for particular applications - Energy product = BH = μ₀MH (see Fig. 13.2, 13.3 in Jiles)

Maximum energy product (BH)max: maximum amount of useful work that can be performed by the magnet - Load line: a line due to demagnetizing effect

H_d = – {N_d/μ₀(1 – N_d)}B - Optimum operation condition

For a given application (i.e., a given shape), the most appropriate material is the one

with the largest value of BH along the load line.

For a given material, its shape should be made for its load line to pass through (BH)max to optimize its performance.

(1) INTRODUCTION

- Since the flux density B is dominated by the contribution from M, permeability μ is expected to be maximized

when anisotropic (K

≠ 0)

polycrystalline materials are textured.

B = μ

(H + M) ≈ μ

M : soft magnets - The magnetization process

for a Fe single crystal

(see Fig. 10.1 in O’Handley)

(2) Soft Magnetic Materials

(2) Soft Magnetic Materials

 Applications

i) DC Applications

① Electromagnets (Typically ~2.0 Tesla) ② Relays : Magnetic switches & control devices - Requirements : high μ, low H_c, high M_s(or B_s) - Requirements : low H_c, high μ, low B_r

- Typical Materials - Typical Materials

Soft iron (low-carbon steels, <0.05%C) for pole pieces Fe-Ni alloy (Permalloy) with Ni > 35%

μ_r= 10,000, H_c ~ 80 A/m (1 Oe), M_s = 1.7×10⁶A/m 2V- Permendur Major impurities(wt%)

0.02%C, 0.035%Mn, 0.025%S, 0.015% P, 0.002%Si Removal of impurities in hydrogen atmosphere

μ_r~ 100,000, H_c ~ 4 A/m (0.05 Oe), Co-Fe alloys

35%Co-Fe: large M_s at room temp. for pole tips M_s ~ 1.95×10⁶A/m

50%Co-Fe: larger M_s (Pemendur alloy) 2%V-49%Co-49%Fe (2V- Permendur)

If melted & magnetically annealed, called, "supermendur"

 Applications

ii) AC Applications

① Transformers ③ Magnetic Shielding Materials

- Requirements : low W_H, high μ, high M_s(or B_s), (Shielding apparatus from stray magnetic fields) low conductivity (σ): to reduce eddy current loss (W_ec) - Typical Materials

- Typical Materials Permalloy (Fe-Ni alloys)

Fe, Ni, Co + (P, Si, B) Mumetal (Cu-addition)

Grain-oriented Si-Fe alloys: reduce σ to σ/4 5%Cu-75%Ni-Fe

→ ~10% decrease in Ms is not serious 2%Cr-5%Cu-77%Ni-Fe Ni-Fe alloy (Permalloy)

Amorphous metal: rapid quenching ④ High Frequency Applications Metglas alloys: Metglas 2605: Fe₈₀B₂₀ - Typical Materials

Metglas 2615: Fe₈₀P₁₆C₃B Soft ferrites

Metglas 2826: Fe₄₀Ni₄₀P₁₄B₆ Mn-Zn ferrite (up to 500 kHz)

Metglas 2826A: Fe₃₂Ni₃₆Cr₁₄P₁₂B₆ μ_i = 1,000-2,000, H_c< 1Oe, ρ = 20~100Ωcm Metglas 2826B: Fe₂₉Ni₄₉P₁₄B₆Si₂ Ni-Zn ferrite (up to 100 MHz)

(Fe_xCo_1-x)₇₅Si₁₅B₁₀ μ_i = 10-1,000, H_c ~ several Oe, ρ = 10⁵Ωcm (Fe_xNi_1-x)₇₈Si₈B₁₄ Garnets for microwave devices

② Motor & Generators YIG, RIG (R : Rare Earth elements)

- Typical Materials

Non-oriented Si-Fe alloys, called, "electrical steel"

(2) Soft Magnetic Materials

- Magnetic steels: the most common application as cores in power and distribution transformers - Energy loss in these transformers : magnetic core loss + pure Joule heating loss in the copper coils

- Sources of the core loss

(1) loss due to eddy currents induced in the core by the uniform changes in B (2) microscopic eddy currents localized near moving domain walls

(3) acoustic losses due to magnetostrictive deformation of the core under changing flux in the so- called supplementary domain structure (90^o walls, closure domains)

- To minimize core loss

decreasing lamination thickness increasing resistivity

decreasing domain size decreasing magnetostriction - To minimize the coil loss (= i²R)

higher remanence

lower magnetic anisotropy

better crystallographic alignment low coil resistance

 Iron and Magnetic Steels

(2) Soft Magnetic Materials

Pure Fe (Major impurities (see Table 10.1)) - very high B_s (= 2.2 T)

- relatively small magnetocrystalline anisotropy, K₁ = + 4.8×10⁴ J/m³ - small magnetostriction constants, λ₁₀₀ = + 21×10^-6, λ₁₁₁= – 20×10^-6 To increase resistivity

- The addition of selected impurities to Fe : Si, Al,...

(see Fig. 10.2)

- Fe-Si phase diagram (see Fig 10.3)

- Variation of physical properties of Fe with Si content (see Fig. 10.4)

- Comparison of physical properties of pure Fe with those of 3%Si-Fe alloys (See Table 10.2)

To lower the core loss for motors and generators - Si addition to Fe (see Fig. 10.5, 10. 6)

- The effects on core loss of increasing texture and permeability (Fig. 10.7) - Control of grain size (see Fig. 10.8)

- Refinement of domain structure in textured Si-Fe

Achieving a small out-of-plane orientation of the [001] easy axis. (see Fig 10.9) Increasing the number of domain walls by laser scribing the surface of steel Iron and Silicon Steels

(2) Soft Magnetic Materials

Variation of physical properties of Fe with Si content (see Fig. 10.4) The core loss : Si addition to Fe (see Fig. 10.6)

Iron and Silicon Steels (continued)

(2) Soft Magnetic Materials

The effects on core loss of increasing texture and permeability (Fig. 10.7)

Goss or cube-on-edge texture: rolled sheet containing a random number of {110} planes and the [001] direction predominantly along the roll direction after annealing at 800^oC, resulting in a low field magnetization along the field (roll) direction

Control of grain size (see Fig. 10.8)

If too large, there are fewer domain walls and micro-eddy-current loss is high.

If too small, the internal stresses and abundant grain boundary pinning sites increase the loss.

Iron and Silicon Steels (continued)

(2) Soft Magnetic Materials

Iron and Silicon Steels (continued) Refinement of domain structure in textured Si-Fe

Achieving a small out-of-plane orientation of the [001] easy axis. (see Fig 10.9) Increasing the number of domain walls by laser scribing the surface of steel

(2) Soft Magnetic Materials

The paths of the zero anisotropy and magnetostriction lines in Fe_1-x-ySi_xAl_y (see Fig. 10.10) The composition of sendust : 10% Si, 5% Al, 85% Fe

The permeability peaks near this zero-anisotropy and zero-magnetostriction composition (see Fig 10.11) Application : some magnetic recording heads (because of mechanical hardness and magnetic softness) Sendust : named by researchers at Tohoku Univ., Japan because it can be used in powder of dust form

(2) Soft Magnetic Materials

- Three major Fe-Ni compositions

78% Ni-Fe permalloys (e.g., Supermally, Mumetal, Hi-mu 80) Both magnetostriction and magnetocrystalline anisotropy pass through zero near this composition.

Application : devices for the highest initial permeability 65% Ni-Fe permalloys (e.g., A alloy, 1040 alloy)

Strong response to field annealing while maintaining K₁≈ 0 50% Ni-Fe permalloy (e.g, Deltamax)

Higher flux density (B_s = 1.6 T) as well as their responsiveness to field annealing, which gives a very square loop

- Variation of M_s, T_c, K, and λ with Ni content in the FCC Fe-Ni alloys (see Fig. 10.13)

- Zero-magnetostriction compositions (homework)

 Fe-Ni Alloys (Permalloys)

(2) Soft Magnetic Materials

Magnetic properties of BCC Fe-Co alloys (see Fig. 10.17)

- Very high saturation induction (B_s ≈ 24 kG)

- Relatively low magnetic anisotropy: K₁ (disordered) ≈ - 1×10⁵J/m³ and K₁ (ordered) ≈ 0 - Substantial magnetostriction: λ₁₀₀ = +150×10^-6, λ₁₁₁= 25×10^-6

polycrystalline average, λ_s≈ 60×10^-6

- The anisotropy (including stress-induced) sets the upper limit for the permeability

the lower limit for the coercivity

- The primary factor determining the technical magnetic properties : grain size

- Order-disorder transformation to CsCl structure (below 730℃): the anisotropy, magnetostriction, and mechanical properties depend strongly on annealing and on cooling rates.

- The addition of V

(V-permendur or Supermendur: Fe₄₉Co₄₉V₂) (see Table 10.3)

- Applications: transformers and generators on aircraft power systems

 Fe-Co Alloys (Permendur)

(2) Soft Magnetic Materials

- Without long-range order, amorphous alloys rapidly quenched from the melt have no magnetocrystalline anisotropy; short- range order

- Amorphous metallic alloys based on transition metals can show a very easy magnetization process.

- Sources of anisotropy in amorphous alloys: magnetoelastic, thermomagnetic, and slip-induced anisotropy - High electrical resistivity (120-150μΩ・cm) compared to Si-Fe and Fe-Ni alloys (30-50μΩ・cm)

 attractive for high-frequency operation

- Metalloid atoms: B, P, Si, and so on are needed to stabilize the glassy state.

-The discovery of high permeability in ferromagnetic amorphous alloys based on Fe-P-C in 1964 by Duwez and Lin High-Induction Amorphous Alloys

- Lower magnetostriction in amorphous alloys compared to crystalline Fe-Co alloys : (FeCo)₈₀B₂₀ amorphous alloys compared to crystalline Fe-Co alloys (see Fig. 10.17b)

less sensitive to stress-induced anisotropy

Inherently high values of electrical resistivity and yield stress - Commercial high-induction amorphous Fe-B alloys (B_s≈ 16 kG)

- Core loss of selected amorphous and crystalline alloys (see Fig 10.18) Other Amorphous Alloys

Key factors for controlling soft magnetic properties : stress and magnetostriction coefficient - Co_xFe_1-xB₂₀amorphous alloys (see Fig. 10.20)

- Fe-Co-Ni amorphous alloys (see Fig. 10.21)

- Important λ_s= 0 compositions in (FeCoNi)_100-xTE_x(TE = Zr, Ta, Nb , or Hf) (see Fig. 10. 22)

 Amorphous Alloys

(2) Soft Magnetic Materials

 Soft Ferrites

Spinel ferrites

Mn-Zn ferrite (see Fig. 10.23(a))

- Compositional dependence of crystal anisotropy and magnetostriction constants (see Fig. 10.24) - Polycrystalline samples : highest permeability when λ₁₀₀= 0 in a K₁ > 0 field (easy axis [100])

or when K₁ < 0 field (easy axis [111]) and small λ₁₁₁ (see Fig. 10.25)

- Variation of magnetostriction and permeability for the (MnZnFe)-Fe₂O₃ system (see Fig. 10.25) - Variation of permeability and magnetostriction for the (MnZnFe)-Fe₂O₃ system (see Fig. 10.26) - Variation of permeability and anisotropy with temperature for Mn_0.31Zn_0.11Fe_1.06O_y(see Fig. 10.27) Ni-Zn ferrite (see Fig. 10.23(b))

- Dependence of permeability and magnetostriction on Fe₂O₃ content (see Fig. 10.28) Microwave ferrites

Garnets : YIG, RIG Hexagonal ferrites

(2) Soft Magnetic Materials

 Soft Ferrites (continued)

Mn-Zn ferrite (see Fig. 10.23(a)) Ni-Zn ferrite (see Fig. 10.23(b))

(2) Soft Magnetic Materials

- Requirements

A strong net magnetization : large B_r

A stable magnetization in the presence of external fields : large H_c

A high energy product BH : the materials characteristics of a permanent magnet are most efficiently used at the point of (BH)_max

- Applications

motors, generators, loudspeakers, bearings, fasteners, and actuators - Definition of coercivity

For fields opposing the direction of magnetization of a hard magnet, a smaller external field is required to give B = 0 than to give M = 0.

BH_c : the B-H loop coercivity

iH_c : the intrinsic M-H loop coercivity

iH_c>_BH_c

(see Fig. 13.1)

(3) Hard Magnetic Materials

- Comparison of second quadrant M-H loops

for some commercial permanent magnets (see Fig. 13.4) 1 MGOe = 1/4π erg/cm³ = 10^-4/4π kJ/m³

(3) Hard Magnetic Materials

- Three factors causing _iH_cto fall short of its maximum value (1) a dispersion in easy-axis(grain) orientations

(2) the presence of mobile domain walls

(3) exchange coupling between single-domain particles

- Major factors in the design of different permanent magnet materials (1) optimizing K_u (by crystallography, chemistry, and/or particle shape)

(2) maximizing B_r by introducing texture (preferred orientation) into the grain structure

(3) eliminating domain walls (by making single-domain particles) or pinning domain wall motion (by introducing certain defects)

(4) minimizing exchange coupling between single-domain particles (nonmagnetic grain boundaries)

- Early Permanent Magnets

lodestone : impure form of iron oxide (mostly magnetite Fe₃O₄ with fine regions of γ-Fe₂O₃) Impure metallic iron : C (see Fig 13.5)

Tungsten steel (7-8% W), Co-Mo and Co-Cr steels

Slowly cooled FeCo alloy through the order-disorder transformation temperature (800℃)

(3) Hard Magnetic Materials

 AlNICO & FeCrCo Magnets

Based on Co-addition to Fe₂NiAl (intermetallic Heusler compound, called Michima alloys)

 Hexagonal Ferrites and Other Oxide Magnets

Based on MO・6Fe₂O₃(M = Ba, Sr, and Pb) have the magnetoplumbite structure (see Fig. 13.15-20 and Table 13.2)

 Rare Earth-Transition Metal Intermetallics

Rare-Earth Intermetallics based on Nd₂Fe₁₄B₁

(1) Large uniaxial magnetic anisotropy (K_u = + 5×10⁶ J/m³) of this tetragonal phase

(2) The large magnetization (B_s = 1.6 T) owing to the ferromagnetic coupling between the Fe and Nd moments

(3) The stability of the 2-14-1 phase allowing development of a composite microstructure characterized by the 2-14-1 grains separated by nonmagnetic B-rich and Nd-rich phases, which tend to decouple the magnetic grains

 Other Permanent Magnets

CoPt

FePt and FePd alloys MnAlC magnets

(3) Hard Magnetic Materials

 AlNICO Magnets

(3) Hard Magnetic Materials

 Hexagonal Ferrites and Other Oxide Magnets

(3) Hard Magnetic Materials

 Rare Earth-Transition Metal Intermetallics (see Table 13.4 and Figs. 13.21-25)

Cobalt/Rare-Earth Magnets

(see Fig. 13.26-32 and Table 13.5) : RCo₅, R₂Co₁₇

(3) Hard Magnetic Materials

 Rare Earth-Transition Metal Intermetallics

Rare-Earth Intermetallics based on Nd₂Fe₁₄B₁ (see Figs. 13.33-38)

(3) Hard Magnetic Materials

 Summary

(3) Hard Magnetic Materials