Moulson A.J., Herbert J.M. Electroceramics: Materials, Properties, Applications

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The garnet family has been highly developed and is widely exploited in

microwave engineering, in part because of its generally excellent dielectric

properties. This stems directly from the fact that all the iron is normally in the

state and thus no electron hopping is possible. The host material is YIG

which has M

values in the range 140–8 kA m

(4pM

¼ 1800–100 G). To

improve the temperature insensitivity of M

around room temperature Gd

ions

are substituted for Y

(Fig. 9.16). The composition of garnets can be designed

to enable them to handle high microwave power. For example an X-band three-

port circulator operating at a peak power of about 200 kW (average power,

200 W) exploits the garnet Y

2.1

0.9

¼980 kA m

;4pM

¼ 1230 G).

Garnets are also exploited in the construction of latching ferrite phase shifters

because they can be tailored to optimum performance with respect to low

insertion loss, temperature-insensitive M

, high remanence, low coercivity and

high power-handling capability. A square hysteresis loop is a requirement,

and this is inﬂuenced by microstructure as the optimum squareness ratio

occurs for dense pore-free material with a narrow distribution of grain size.

A garnet developed for a phased-array radar system has the composition

2.66

0.34

4.22

0.677

0.09

and a good microstructure, as shown in

Fig. 9.58.

542 MAGNETIC CERAMICS

Fig. 9.58 Microstructure of Y

2.66

0.34

4.22

0.68

0.09

. (Courtesy of C.D. Greskovich

and G.G. Palmer.)

TEAMFLY

Team-Fly

9.5.6 Permanent magnets

As discussed in Section 9.3.2, permanent magnet materials are required to give a

maximum ﬂux in the surrounding medium for a minimum volume of material

and to be resistant to demagnetization. Suitability of a material for a particular

application is judged by its B

, H

and (BH)

max

values, which are given in Table

9.3 for some of the principal hard magnetic materials. Permanent magnets can be

found in a wide range of applications including consumer, industrial, electronic,

automotive and medical equipment. The outstanding magnetic properties of the

rare earth variety make it ideally suited to high performance applications, for

example motors for computer disc drives and parts for medical technology where

the high cost of the magnet material can readily be absorbed.

There are many applications for which the magnetic properties of the ferrites

are quite adequate and this, coupled with their relatvely low cost, has assured

them of a large and sustainable market, for the foreseeable future, at least. They

have higher coercive ﬁelds than those for the mass-produced metal magnet types

and this allows them to be made into shapes (e.g. d.c. motor ﬁeld magnets)

involving high demagnetizing ﬁelds.

APPLICATIONS 543

Fig. 9.59 Hard ferrite components: (a) windscreeen wiper motor and ferrite segments; (b)

loudspeaker and ﬁeld magnets; (c) hard ferrite–polymer composites. (Perspective size

distortion; identiﬁcation letters are the same actual size.)

An important market is for the ﬁeld magnets in small d.c. motors for which the

shape demands high coercivity. Automotive applications for small motors

include the windscreen wiper (see Fig. 9.59(a)) and air-blower, window lift, and

pumps for fuel, ABS and power-steering. Similar motors are used in washing

machines and general kitchen appliances and also for portable tools. Another

important application is for ‘stepping’ motors which convert electrical impulses

into incremental mechanical movements for clocks, copying and fax machines

and medical equipment.

Generally speaking the higher quality hard ferrites are based upon Sr-

hexaferrite and those for less demanding applications on the cheaper Ba-

hexaferrite.

Ferrite magnets are used in the form of ﬂat toroids in moving coil

loudspeakers (Fig. 9.59(b)), and large pieces for magnetic separators for mineral

beneﬁciation and water ﬁlters.

Small pieces ﬁnd many diverse applications, for example in toys, door latches,

display boards, TV tube correction magnets, etc., and the plastic composite

variety is best known as a refrigerator door seal (Fig. 9.59(c)).

Problems

1. Derive an expression for the Bohr magneton and calculate its value.

A particular crystal has a cubic unit cell of side 1 nm. Each cell has an associated

induced magnetic moment of 10

for an applied ﬁeld of 10

. Calculate the

susceptibility and oﬀer an opinion as to whether the material is diamagnetic,

paramagnetic or ferromagnetic. [Answers: w ¼9.3  10

7

; diamagnetic]

2. Calculate the magnetic moment of an isolated Fe

ion and also that associated with

an Fe

ion in magnetite. Explain why they are diﬀerent.

The saturation magnetization of magnetite is 5.210

and the unit cell is of

side 837 pm. Assuming the inverse spinel structure, estimate the magnetic moment

(in Bohr magnetons) of the Fe

ion. [Answers: 6.7 m

and 4 m

; 4.11 m

]

3. Calculate the spin-only magnetic moments of Ni

,Zn

and Fe

Nickel ferrite (NiOFe

) and zinc ferrite (ZnOFe

) have the inverse and

normal spinel structures respectively. The two compounds form mixed ferrites.

Assuming that the magnetic coupling between ions is the same as in magnetite and

that the orbital angular momenta are quenched, calculate the magnetic moment (in

Bohr magnetons) per formula unit of nickel ferrite and Zn

0.25

0.75

. [Answers:

2 m

,0m

and 5 m

;2m

and 4 m

]

4. A soft ferrite with complex relative permeability m*

¼ 2000  7j is in the form of a

toroid of cross-sectional area 0.5 cm

and inner radius 3 cm. A primary winding

544 MAGNETIC CERAMICS

comprising 200 turns and a secondary winding of 100 turns are wound uniformly on

the toroid. Calculate the r.m.s. value of the e.m.f. generated across the secondary

winding when a sinusoidally varying current of frequency 50 Hz and amplitude 2 A is

passed through the primary.

Calculate the eﬀective permeability and loss tangent of the ferrite and the e.m.f.

when a 0.1 mm gap is introduced into the toroid.

Consider the implications of the results of the calculations for the manufacture

of soft ferrites for high-quality inductors. [Answers: 5.23 V; 1033, 1.8610

and

2.7 V]

5. A disc, 2 cm in diameter and 5 mm thick, magnetized normal to its faces and

manufactured from a ferrite with B

¼ 0.3 T and H

¼ 200 kA m

is required.

Comment on the practical feasibility of the requirement. Assuming the ferrite

composition to be ﬁxed, what steps might be taken to realize the requirement?

[Answer: H

¼ 238 kA m

]

6. Draw a block diagram illustrating the fabrication route for a ferrite-loaded plastic

suitable for a refrigerator door seal.

7. Derive an expression for the angular frequency of the precessional motion of an

electron situated in a magnetic ﬁeld.

8. The ferrimagnetic resonance phenomenon in a ceramic ferrite in the form of a strip

706562 mm is to be exploited in a particular microwave device, with the static ﬁeld

applied along the length of the strip. If the design frequency is 2 GHz and the

coercive ﬁeld for the ferrite is 100 A m

, what limiting value is placed on the

saturation magnetization?

It is anticipated that, because the device is to be used at high microwave power

levels, there is the risk of the onset of spin waves. How might the microstructure of

the ferrite be designed to reduce this risk? Suggest a fabrication route suitable for

achieving the objective. [Answer: M

556.7 kA m

]

9. A 1 GHz plane-polarized electromagnetic wave passes down a microwave ferrite

rod 50 mm long situated in a uniform magnetic ﬁeld parallel to the axis of the

rod. The magnetic ﬁeld strength is adjusted so that the relative permeability

values for the right and left circularly polarized components of the wave are 6

and 4 respectively. Calculate the angle through which the plane of polarization of

the wave is rotated on travelling the length of the rod. The relative permittivity of

the ferrite for both waves is 16 (velocity of light in a vacuum, 3610

[Answer: 548]

10. Explain why it is that magnetic domain structures in a thin magnetic garnet layer can

be visualized in a polarizing microscope and how the various structures can be

exploited. Describe two routes for fabricating such layers.

PROBLEMS 545

Bibliography

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546 MAGNETIC CERAMICS

INDEX

Accelerometer 386

Acceptor 23, 34

doped BaTiO

39, 41

Acoustic

impedance 374

matching 374

Activation energy 45

Activity 200

Actuators, see piezoelectric

Ageing

ferrites 527

ferroelectrics 78, 256, 318

piezoelectric 357

sensors 216

Aggregates – agglomerates 97, 98, 101

segregation of 104

Aliovalent substituents 23, 314

Alkoxides 450

Alumina 116, 276

applications 283

b-aluminas 187

conduction 280

properties 277, 283

substrates 286