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

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can be sintered in fully oxidizing atmospheres since their magnetic properties do

not depend on the presence of lower-valency ions such as Fe

or Mn

. Other

properties, including lattice dimensions, temperature coeﬃcients of magnetiza-

tion and expansion and magnetic anisotropy, can be tailored by adjustments to

composition. Garnets can be grown as single crystals, and thin ﬁlms of complex

composition, once the basis of ‘bubble’ memories, now attract considerable

interest for magneto-optical applications (see Section 9.5.4).

9.3 Properties In£uencing Magnetic Behaviour

9.3.1 Soft ferrites

Soft ferrites are used for the manufacture of inductor cores (pot cores) for

telecommunications, low-power transformers and high-ﬂux transformers such

as television line output transformers, and as television tube scanning yokes

(Fig. 9.17). The more important material characteristics for these and other

applications are now discussed with emphasis on the inﬂuence of composition

and microstructure. The review paper by A. Broese van Groenou et al. [9] and

the monograph by E.C. Snelling [10] are recommended to supplement the

discussion.

Initial permeability (m

)

High initial permeability is achieved through control of composition and

microstructure. It depends in a complex manner on high saturation magnetiza-

tion, low magnetic anisotropy and low magnetostriction. The magnetic

anisotropy falls oﬀ very rapidly as the saturation magnetization falls to a low

value near the Curie temperature, so that the net result is a peak in permeability

just below the Curie temperature followed by a steep fall to a value close to unity

as the magnetization falls to zero. Figure 9.18 shows the variation of m

with

temperature for MnZn and NiZn ferrites with a range of zinc contents; it also

illustrates the change in Curie temperature with zinc content mentioned earlier

(Section 9.2.1). The dependence of the permeability of the NiZn system on

frequency is discussed in Section 9.3.1. Magnetic anisotropy is low in the MnZn

ferrites and can be adjusted in the NiZn system by substituting small amounts of

cobalt for the nickel, since the anisotropy constant for cobalt ferrite is opposite in

sign to that of most ferrites (see Table (9.1).

Magnetostriction can be reduced by adjusting the sintering atmosphere during

the application of the maximum temperature and afterwards so that a small

amount of Fe

is formed, thus taking advantage of the opposite sign of the

magnetostriction constant for Fe

compared with that for most other ferrites

492 MAGNETIC CERAMICS

TEAMFLY

Team-Fly

PROPERTIES INFLUENCING MAGNETIC BEHAVIOUR 493

Fig. 9.17 Range of soft ferrite components: (i) TV scanning yoke (components kindly

supplied by Philips Components Ltd.); (ii) UR core and TV line output transformer; (iii) E

core for switched mode power supply; (iv) wide band transformer core; (v) core giving good

magnetic shielding; (vi) high Q (adjustable) ﬁlter core (cf. Fig. 9.48); (vii) precision ferrite

antenna for transponder; (viii) multilayer EMI suppressors; (ix) toroids for laser and radar

pulse applications; (x) typical EMI shields for cables. ((ii)–(x) Courtesy of ‘Ferroxcube UK’.)

(see Table 9.2). The introduction of Fe

has the disadvantage of lowering the

resistivity of the ferrite, but a high permeability can be obtained without

excessive penalty in this respect.

Because a major contribution to m

is from Bloch wall movements,

microstructure has a signiﬁcant inﬂuence. High magnetic anisotropy implies

high-energy walls readily ‘pinned’ by microstructural defects. Thus, for a high-

permeability polycrystalline ferrite, very mobile domain walls are required,

demanding in turn large defect-free grains coupled with low magnetic

anisotropy. Figures 9.19 and 9.20 illustrate the sensitivity of permeability to

grain size, and Fig. 9.21 shows how porosity leads to reduced permeability,

presumably because of domain wall pinning.

The loss factor (tan d)/m

The way in which magnetic loss in a material is expressed depends upon the

particular application. For example, in the case of pot cores, when currents are

small and hence the ﬂux density is also small (typically less than 1 mT), the loss

factor used is (tan d)/m

or its reciprocal m

Q where Q is the quality factor.

The loss factor is usually expressed in terms of three main contributions,

namely

tan d

ð9:31Þ

494 MAGNETIC CERAMICS

Fig. 9.18 The variation with temperature of the initial relative permeability m

for diﬀerent d

values in (a) Mn

17d

and (b) Ni

17d

(after [10]).

in which tan d

, tan d

and tan d

are the hysteresis, eddy current and ‘residual’

loss tangents. The processes contributing to residual loss are diﬃcult to identify

but include ferrimagnetic resonance and domain wall resonance (see below). In

low-current high-frequency applications of high-resistivity ferrites, when

hysteresis and eddy current losses are low, residual losses may dominate.

PROPERTIES INFLUENCING MAGNETIC BEHAVIOUR 495

Fig. 9.19 Microstructure of high permeability Mn–Zn ferrites with a range of grain sizes: (a)

¼ 6500; (b) m

¼ 10 000; (c) m

¼ 16 000; (d) m

¼ 21 500. (Courtesy of Philips Technical

Review.)

Fig. 9.20 Dependence of the initial relative permeability on grain size.

P.J. van der Zaag [11] discusses loss mechanisms in soft ferrites and shows that

a signiﬁcant contribution to residual losses over the frequency range 500 kHz to

10 MHz originates from domain wall motion in multi-domain grains. This is

evidenced by a predicted and observed decrease in ‘intragranular’ loss

accompanying a transition from two-domain to mono-domain grains as the

grain size is decreased in the range 0.2 to 5 mm).

It is shown (Section 9.1.4) that the loss factor is independent of gaps

introduced in the magnetic circuit. In the case of pot cores (Fig. 9.48), where air

gaps are introduced both intentionally and because of the imperfect join, the loss

factor is a particularly useful parameter.

In the case of ferrites operating at high amplitudes (e.g. above 10 mT) and in

the typical frequency range 15–100 kHz power is dissipated mainly through

hysteresis, although eddy current loss may also contribute signiﬁcantly. Losses in

materials intended for such high-power applications are usually expressed in

terms of power-loss density (Eq. (9.15)) measured directly from the alternating

voltage across the winding on a toroid, the in-phase component of the current

and the toroid volume.

Electrical resistivity

The resistivity r of an inductor core material is important because it determines

eddy current losses. In general room temperature resistivities of ferrites lie in the

range 10

710

O m, many orders of magnitude higher than that of the most

resistive of the ferromagnetic alloys (about 8610

O m). Typical resistivity–

temperature data for MnZn and NiZn ferrites are shown in Fig. 9.22. For both

496 MAGNETIC CERAMICS

Fig. 9.21 Dependence of the initial relative permeability on porosity: curve A,

0.5

; curve B, NiFe

(after [6]).

types the conductivity mechanism is believed to be electron hopping between

ions of the same type on equivalent lattice sites, e.g. Fe

$Fe

,Mn

$Mn

or Ni

$Ni

(see Section 2.6.2). In the ideal inverse spinel structures NiFe

and MnFe

there is no opportunity for hopping. However, as mentioned

above, in practice the structures are not ideal and ions of the same type but

diﬀering oxidation states do occur on equivalent lattice sites. In the case of

MnZn ferrite, for example, in order to maintain a major proportion of the Mn in

the Mn

state so as to achieve the required magnetic properties, sintering is

carried out in a slightly reducing atmosphere which carries with it the risk of

converting some of the Fe

to Fe

; this must be carefully controlled for

otherwise hopping conductivity could rise to an unacceptable level. In contrast,

the NiZn ferrite family can be ﬁred in air without oxidizing a signiﬁcant

proportion of Ni

to Ni

and ensuring that the concentration of Fe

negligible. Therefore the opportunity for electron hopping is very much lower

than in the case of the MnZn ferrites. As always, the chosen composition and

fabrication steps are a compromise to achieve optimum properties for particular

applications. The extent to which electrical conductivity is sensitive to

composition, ﬁring conditions and microstructure is illustrated by the following

examples.

Figure 9.23 shows electrical resistivity data for Ni

0.3

0.7

2+d

47x

in which d

measures the amount of iron over the normal stoichiometric amount. For d ¼ 0

PROPERTIES INFLUENCING MAGNETIC BEHAVIOUR 497

Fig. 9.22 Temperature dependence of the resistivity for NiZn and MnZn ferrites.

all iron is assumed to be in the Fe

state and so no hopping occurs. Positive d

implies the presence of some Fe

and the conditions for n-type electron hopping

(Fe

!Fe

). With negative d the charge balance can be restored by the

formation of Ni

; however, the conversion of Ni

to Ni

requires greater

energy than the conversion of Fe

to Fe

when d is positive. The charge

balance when d is negative may in part be maintained by the formation of oxygen

vacancies. In addition, the concentration of Ni ions is only one-seventh that of

Fe ions. The net result is a very large increase in resistivity when the iron content

is reduced (see Section 2.6.2).

The addition of cobalt to a nickel ferrite has been employed to increase

resistivity, as illustrated in Fig. 9.24. For an explanation it is necessary to

consider the third ionization potentials of chromium, iron, manganese, cobalt

and nickel, which increase in this order. The addition of cobalt tends to maintain

the iron in the Fe

state by virtue of the equilibrium

2þ

þ Co

3þ

¼ Fe

3þ

þ Co

2þ

Similarly the presence of Ni

is discouraged because of the equilibrium

3þ

þ Co

2þ

¼ Ni

2þ

þ Co

3þ

It appears that the small amounts of Co

and Co

which occur, probably on

equivalent lattice sites, have little eﬀect upon conductivity because of the large

hopping distances.

The importance of the rate of cooling from the sintering temperature is

apparent from the following data for a ferrite of composition Ni

0.4

0.6

After sintering in air at 1300 8C followed by rapid cooling, the resistivity was

10 O m. Analysis showed the FeO content to be 0.42%. When the same sample

was reheated and then cooled slowly, the FeO content was 0.07% and the

resistivity was more than 1000 O m. The explanation is that at high temperatures

is favoured and is quenched in by the rapid cooling. During slow cooling,

498 MAGNETIC CERAMICS

Fig. 9.23 Dependence of the resistivity of the ferrite Ni

0.3

0.7

2+d

47x

on the iron content.

PROPERTIES INFLUENCING MAGNETIC BEHAVIOUR 499

Fig. 9.25 Schematic diagram of a ferrite with semiconducting grains surrounded by

insulating grain boundaries.

Fig. 9.24 Dependence of the resistivity of the ferrite NiFe

1.9

on the cobalt content.

Fig. 9.26 Dependence of the resistivity of the ferrite Ni

0.4

0.6

on frequency.

reoxidation can occur, and the resulting lower Fe

content restricts the

opportunity for electron hopping.

Microstructure can also play an important role in determining electrical

resistivity. If the cooling rate is arranged so that, because of the high oxygen

diﬀusivity along grain boundaries compared with that in the single crystal, the

grain boundaries oxidize preferentially, it results in each semiconducting grain

being surrounded by a grain boundary region of relatively high resistance

(Fig. 9.25). This conﬁguration of zones of diﬀering conductivities can be

represented by an equivalent electrical circuit (see Section 2.7.5) comprising a

series connection of shunted capacitors, where one capacitor type represents the

grain and the other the grain boundary zone, and the shunts are the resistances of

the two regions. An analysis of the model predicts frequency dispersion of both

resistivity (Fig. 9.26) and permittivity (Fig. 9.27).

Another way of modifying the resistivity of the grain boundary region is to

add small amounts of CaO and SiO

. Figure 9.28 shows the eﬀect of such

additions on the resistivity and loss factor of a ferrite. Studies of the grain

boundary show that the Si and Ca ions substitute in the ferrite crystal lattice

close to the boundary, rendering the region insulating.

500 MAGNETIC CERAMICS

Fig. 9.27 Dependence of tan d and e

on frequency for the ferrite Ni

0.4

0.6

Permittivity (e

)

Above a frequency of 1 GHz the permittivity of MnZn ferrites is around 10, but

at 1 kHz it can reach values in the range 10

–10

. The dispersion is caused by the

relatively insulating grain boundaries referred to above. The same eﬀect occurs in

the NiZn ferrites, although to a less marked extent, and Fig. 9.27 shows the

frequency dispersion of e

and the dielectric loss tangent for the ferrite

0.4

0.6

. If an equivalent circuit is used, and reasonable values for the

resistivity, relative permittivity and dimensions are assigned to the grain and

grain boundary phases, a relaxation frequency of approximately 20 kHz is

estimated, which agrees quite well with experimental data.

Resonance e¡ects

The replacement of the MnZn ferrite family by the NiZn ferrites as the

application frequency rises is partly due to the higher resistivities of the NiZn

PROPERTIES INFLUENCING MAGNETIC BEHAVIOUR 501

Fig. 9.28 Inﬂuence of SiO

and CaO additions to the ferrite Mn

0.68

0.2

on (a)

resistivity (O m) and (b) loss factor ((tan d)/m

 10

6

) at 100 kHz (after [9]).