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752 Part 4 Functional Materials

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Part 4 2

754 Part 4 Functional Materials

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Part 4 2

755

Magnetic Mat

4.3. Magnetic Materials

Magnetic materials consist of a wide variety of

metals and oxides. Their effective properties

are given by a combination of two property

categories: intrinsic properties which are the

atomic moment per atom p

, Curie temperature

, magnetocrystalline anisotropy coefﬁcients K

and magnetostriction coefﬁcients λ

; and extrinsic

properties which are essentially their coercivity H

and their magnetisation M or magnetic Induction J

as a function of the applied magnetic ﬁeld H.

Moreover, the effective properties are depending

decisively on the microstructural features, texture

and, in most cases, on the external geometric

dimensions such as thickness or shape of the

magnetic part. In some cases non-magnetic

inorganic and organic compounds serve as binders

or magnetic insulators in multiphase or composite

magnetic materials.

4.3.1 Basic Magnetic Properties.................... 755

4.3.1.1 Atomic Moment ...................... 755

4.3.1.2 Magnetocrystalline Anisotropy .. 756

4.3.1.3 Magnetostriction ..................... 757

4.3.2 Soft Magnetic Alloys............................ 758

4.3.2.1 Low Carbon Steels ................... 758

4.3.2.2 Fe-based Sintered

and Composite Soft Magnetic

Materials................................ 759

4.3.2.3 Iron–Silicon Alloys................... 763

4.3.2.4 Nickel–Iron-Based Alloys ......... 769

4.3.2.5 Iron–Cobalt Alloys ................... 772

4.3.2.6 Amorphous Metallic Alloys........ 772

4.3.2.7 Nanocrystalline Soft Magnetic

Alloys .................................... 776

4.3.2.8 Invar and Elinvar Alloys ........... 780

4.3.3 Hard Magnetic Alloys .......................... 794

4.3.3.1 Fe–Co–Cr ............................... 795

4.3.3.2 Fe–Co–V ................................ 797

4.3.3.3 Fe–Ni–Al–Co, Alnico ................ 798

4.3.3.4 Fe–Nd–B................................ 800

4.3.3.5 Co–Sm ................................... 803

4.3.3.6 Mn–Al–C ................................ 810

4.3.4 Magnetic Oxides ................................. 811

4.3.4.1 Soft Magnetic Ferrites .............. 811

4.3.4.2 Hard Magnetic Ferrites ............. 813

References .................................................. 814

4.3.1 Basic Magnetic Properties

Basic magnetic properties of metallic systems and ma-

terials are treated by Gignoux in [3.1]. Extensive data

on magnetic properties of metals can be found in [3.2].

Magnetic properties of ferrites are treated by Guillot

in [3.3]. Extensive data on magnetic and other prop-

erties of oxides and related compounds can be found

in [3.4] and [3.5].

4.3.1.1 Atomic Moment

The suitability of a metal or oxide to be used as

a magnetic material is determined by its mean atomic

moment (p

). For metals the Bethe–Slater–Pauling

curves, Fig. 4.3-1, indicate how p

depends on the av-

erage number (n) of 3d and 4s electrons per atom, and

on the crystal structure, i. e., face-centered cubic (fcc)

or body-centered cubic (bcc) structure. Alloys based

on Fe, Co, and Ni are most suitable from this point

of view, corresponding to their actual use. The char-

acteristic temperature dependence of the spontaneous

magnetization I

(T ), shown for Fe in Fig. 4.3-2, the

Curie temperature T

and the spontaneous magnetiza-

tion at room temperature I

(see Table 4.3-1), are the

ensuing properties.

Part 4 3

756 Part 4 Functional Materials

2.0

1.5

1.0

0.5

8.5 9.0 9.5 10.0 10.5

2.5

2.0

1.5

1.0

0.5

7.0 7.5 8.0 8.5 9.0

FeCo

FeNi

CoMn

CoCr

CoNi

NiMn

NiV

NiCr

NiCu

CoCr

CoMn

CoNi

FeCo

FeNi

NiCr

NiCu

NiMn

NiV

FeCo

FeCr

FeMn

FeNi

FeV

FeCr

FeV

FeMn

FeNi

FeCo

–

(

)

–

(

)

Fig. 4.3-1a,b Bethe–Slater–Pauling relation indicating the

dependence of the mean magnetic moment per atom p

the average number n of 3d and 4s electrons per atom for bi-

nary alloys with

(a) fcc structure and (b) bcc structure [3.6]

1.0

0.8

0.6

0.4

0.2

0 0.2 0.4 0.6 0.8 1.0

T/T

(T)/I

(T=0)

bcc

Fig. 4.3-2 Reduced spontaneous magnetization I

(T )/I

(T = 0) vs. reduced temperature T/T

for Fe [3.6]

4.3.1.2 Magnetocrystalline Anisotropy

Since the magnetic moment arises from the exchange

coupling of neighboring ions, it is also, coupled to

their positions in the crystal structures. Basically this

is the origin of the magnetocrystalline anisotropy which

plays a major role as an intrinsic property for the op-

timization of both soft and hard magnetic materials

because it determines the crystallographic direction and

relative magnitude of easy magnetization. As an ex-

ample, Fig. 4.3-3a shows the magnetization curves for

a single crystal of Fe in the three major crystallo-

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0 100 200 300 400 500

–2

–4

0 200 400 600 800 1000 1200

I (T)

H (A/m)

(100)

(110)

(111)

Medium

(110)

Hard

(111)

Ease

(100)

, 10K

(× 10

) (erg cm

–3

)

T(Κ)

10K

Fig. 4.3-3a,b Magnetization curves of an Fe single crystal

indicting the typical characteristics of

(a) magneto-

crystalline anisotropy and

(b) the temperature dependence

of the magnetocrystalline anisotropy constants K

Fe [3.6]

Part 4 3.1

Magnetic Materials 3.1 Basic Magnetic Properties 757

Table 4.3-1 Curie temperatures and intrinsic magnetic properties at room temperature

Element T

100

111

0001

1010

(K) (T) (10

−3

) (10

−3

) (10

−3

) (10

−6

) (10

−6

) (10

−6

) (10

−6

) (10

−6

)

Fe, bcc 1044 2.15 4.81 0.012 −0.012 22.5 −18.8 − − −4

Co, hcp 1388 1.62 41 120 − − − −4 −22 −71

Ni, fcc 624 0.55 −0.57 −0.23 0 −46 −24.3 − − −34

graphic directions of the body-centered cubic crystal

structure.

The anisotropy constants K

, K

, ... are deﬁned

for cubic lattices, such as Fe and Ni, by expressing the

free energy of the crystal anisotropy per unit volume as

= K

S +K

P + K

SP +... ,

with

S =α

+α

and P = α

where α

, α

,andα

are the direction cosines of the

angle between the magnetization vector and the crystal-

lographic axes. Corresponding deﬁnitions pertain to the

anisotropy constants for other crystal lattices.

In practice it can be important to know not only

the room temperature value of the magnetocrystalline

anisotropy constants K

but also their temperature de-

pendence, which is shown for Fe in Fig. 4.3-3b. For

many technical considerations it sufﬁces to take the

dominating anisotropy constant K

into account.

4.3.1.3 Magnetostriction

Magnetostriction is the intrinsic magnetic property

which relates spontaneous lattice strains to magnetiza-

tion. It is treated extensively by Cullen et al. in [3.3].

As a crystal property magnetostriction is purely intrin-

sic. The phenomenon of macroscopic magnetostrictive

strains of a single or polycrystalline sample is due to the

presence of magnetic domains whose reorientation oc-

curs under the inﬂuence of magnetic ﬁelds or applied

stresses and, thus, is a secondary property which has to

be distinguished.

Magnetostriction plays a role in determining a num-

ber of different effects:

•

As a major factor of inﬂuence on the coercivity of

soft magnetic materials because it determines the

magnitude of interaction of internal stresses of ma-

terials with the movement of magnetic domain walls.

〈

〈111

〈

〈100

〈

〈110

–5

–10

–15

–20

0 0.4 0.8 1.2 1.6 2.0 2.4

(× 10

–6

)

I(T)

Fig. 4.3-4 Dependence of the magnetostrictive elongation

on the magnetization intensity in three different crystallo-

graphic directions of Fe single crystals according to two

different sources (open and closed circles) [3.7]

These boundaries are associated with strains them-

selves unless the material is free of magnetostriction

altogether. This is practically impossible because

the components of this property vary with the ap-

plied magnetic ﬁeld, as shown for the example of Fe

in Fig. 4.3-4. Moreover, they vary with temperature

and alloy composition.

•

As a decisive variable determining the properties of

invar and elinvar alloys (Sect. 4.3.2.8).

•

As a property of anomalously high magnitude in

cubic Laves phase compounds of rare earth metals

such as Fe

(Tb

0.3

0.7

), which are the basis of mag-

netostrictive materials serving as magnetostrictive

transducers and sensors [3.3].

Part 4 3.1

758 Part 4 Functional Materials

4.3.2 Soft Magnetic Alloys

The basic suitability of a metal or alloy as a soft mag-

netic material is provided if its Curie temperature T

and

saturation polarization I

at room temperature are sufﬁ-

ciently high. The main goal in developing soft magnetic

materials is to reduce the magnetocrystalline anisotropy

constants K

, in particular K

, and the magnetostriction

constants λ

, to a minimum. This leads to a mini-

mum energy requirement for magnetization reversal.

The appropriate combination of the intrinsic magnetic

properties can be achieved by alloying additions and,

in some cases, by annealing treatments which induce

atomic ordering and, thus, an additional variation of K

and/or λ

. Surveys and data of soft magnetic alloys are

given in [3.8].

Table 4.3-2 Standard IEC speciﬁcation for non-alloyed magnetic steel sheet. The conventional designation of the different grades

(ﬁrst column) comprises the following order: (1) 100 times the maximum speciﬁed loss (W kg

−1

)at1.5 T; (2) 100 times the

nominal sheet thickness in (mm); (3) the characteristic letter “D”; (4) one tenth of the frequency in Hz at which the magnetic

properties are speciﬁed. The materials are delivered in the semi-processed state. The magnetic properties apply to test specimens

heat-treated according to manufacturer’s speciﬁcations

Grade Nominal Maximum speciﬁc total loss for Minimum induction in a direct or alter- Stacking Conventional

thickness peak induction (W kg

−1

) nating ﬁeld at ﬁeld strength given (T) factor density

(mm) 1.5Tat 1.0Tat 1.5Tat at 2500 at 5000 at 10 000 (kg dm

−3

)

at 50 Hz at 50 Hz at 60 Hz A/m A/m A/m

660-50-D5 0.50 6.60 2.80 8.38 1.60 1.70 1.80 0.97 7.85

890-50-D5 0.50 8.90 3.70 11.30 1.58 1.68 1.79 0.97 7.85

1050-50-D5 0.50 10.50 4.30 13.34 1.55 1.65 1.78 0.97 7.85

800-65-D5 0.65 8.00 3.30 10.16 1.60 1.70 1.80 0.97 7.85

1000-65-D5 0.65 10.00 4.20 12.70 1.58 1.68 1.79 0.97 7.85

1200-65-D5 0.65 12.00 5.00 15.24 1.55 1.65 1.78 0.97 7.85

Table 4.3-3 Standard IEC speciﬁctaion for cold rolled magnetic alloyed steel strip delivered in the semi-processed state. The

conventional designation of the different grades comprises the following order (ﬁrst column): (1) 100 times the maximum speciﬁed

loss at 1.5 T peak induction in (W kg

−1

); (2) 100 times the nominal strip thickness, in (mm); (3) the characteristic letter “E”;

(4) one tenth of the frequency in Hz, at which the magnetic properties are speciﬁed. the magnetic properties apply to test specimens

subjected to a reference heat treatment

Grade Nominal Reference Maximum speciﬁc total Minimum induction in a direct or Conventional

thickness treatment loss for peak induction alternating ﬁeld at ﬁeld strength given (T) density

(mm) temperature (W kg

−1

) (10

kg m

−3

)

(

◦

C) 1.5T 1.0T 2500 Am

−1

5000 Am

−1

10 000 Am

−1

340-50-E5 0.50 840 3.40 1.40 1.52 1.62 1.73 7.65

390-50-E5 0.50 840 3.90 1.60 1.54 1.64 1.75 7.70

450-50-E5 0.50 790 4.50 1.90 1.55 1.65 1.76 7.75

560-50-E5 0.50 790 5.60 2.40 1.56 1.66 1.77 7.80

4.3.2.1 Low Carbon Steels

Low carbon steels are the most widespread magnetic

metallic materials for use in electric motors and in-

ductive components such as transformers, chokes, and

a variety of other AC applications which require high

magnetic induction at moderate to low losses. This is

mainly due to the high intrinsic saturation polarization

of the base element Fe, J

= 2.15 T, and to the low cost

of mass produced steels.

Main processing effects on achieving materials with

a high relative permeability is the minimization of the

formation of particles (mainly carbides and sulﬁdes)

which may impede domain boundary motion, and induc-

Part 4 3.2

Magnetic Materials 3.2 Soft Magnetic Alloys 759

ing a texture – by suitable combinations of deformation

and recrystallization – with a preponderance of 100

and 110 components, while suppressing the 111 and

211components, such that the operating induction can

be aligned most closely to the easiest direction of magne-

tization 100. More details are given by Rastogi in [3.9].

Tables 4.3-2 and 4.3-3 show characteristic data of non-

alloyed magnetic steel sheet and cold rolled magnetic

alloyed steel strip, respectively.

4.3.2.2 Fe-based Sintered and Composite

Soft Magnetic Materials

Iron-based sintered and composite soft magnetic mater-

ials are treated and listed extensively in [3.10]. Iron and

Fe based alloys are used as sintered soft magnetic ma-

terials because of the particular advantages of powder

metallurgical processing in providing net-shaped parts

economically. The sintering process serves to achieve

diffusion-bondingof the powder particles with auniform

distribution of the alloying elements. The metallic bond

and degree of particle contact determine the magnetic

properties in each alloy system.

The operating frequency in an application is limited

by the resistivity of the material, which is increased be-

yond that of pure and dense Fe, primarily by varying

the type and concentration of alloying elements. Den-

sity and crystal structure have a major impact on the

magnetic properties, but only a minor effect on the re-

sistivity. The sintered materials have a resistivity ranging

from 10 to 80 µΩ cm and are applicable in DC and very

Table 4.3-4 Magnetic properties of sintered Fe products in relation to density [3.10]

Density  Sintering conditions Induction at Coercitivity Remanence Max. rel. permeability

(gcm

−3

) temp. (

◦

C),atm. 1200 A m

−1

(T) H

(A m

−1

) B

(T) µ

max

6.6 1120, DA 0.90 170

0.78

1700

6.6 1120, H

/Vac. 0.95 140

0.82

1800

6.6 1260, H

/Vac. 1.05 120

0.85

2800

6.9 1120, DA 1.05 170

0.90

2100

6.9 1120, H

/Vac. 1.05 140

0.97

2300

6.9 1260, H

/Vac. 1.20 120

1.0

3300

7.2 1120, DA 1.20 170

1.05

2700

7.2 1120, H

/Vac. 1.20 140

1.10

2900

7.2 1260, H

/Vac. 1.30 120

1.15

3800

7.4 1.25 136 1.20 3500

7.4 1.30 112 1.30 5500

7.6 1.50 80 1.40 6000

Measured from a maximum applied magnetic ﬁeld strength of 1200 A/m.

low frequency ﬁelds. The sintered materials comprise

Fe and Fe

−

P, Fe

−

Si, Fe

−

P, Fe

−

P, Fe

−

Ni,

−

Cr, and Fe

−

Co alloys. Characteristic data are listed

in Tables 4.3-4 to 4.3-11 [3.10].

It is useful to note that the evaluation of a large num-

ber of test data of sintered soft magnetic materials yields

consistent empirical relations. For sintered Fe products

these are:

[T]=4.47 −10.38 ,

[T]=3.87 −17.23 ,

[A/m]=11.47L

−0.59

ρ[µΩ cm]=−4.34 +44.77 ,

and

max

= 0.21L

0.68

×10

where  = density (g cm

−3

)andL = grain diameter

(average intercept length) (µm).

Dust core materials consist of Fe or Fe alloy particles

which are insolated by an inorganic high resistivity bar-

rier. They are applied in the 1 kHz to 1 MHz range. These

are to be distinguished from soft magnetic Fe composite

materials, which consist of pure Fe particles separated

by an insolating organic barrier, providing a medium

to high bulk resistance. Compositions and magnetic

properties of Fe based composite materials are listed in

Tables 4.3-12 and 4.3-13. These materials are applicable

in the frequency range from 50 Hz to 1 kHz.

Part 4 3.2

760 Part 4 Functional Materials

Table 4.3-5 Magnetic properties of sintered Fe–0.8 wt% P products in relation to density [3.10]

Density  Sintering conditions Induction at Coercitivity Remanence Max. rel. permeability

(gcm

−3

) temp. (

◦

C),atm. 1200 A m

−1

(T) H

(Am

−1

) B

(T) µ

max

6.8 1120, DA 1.05 120

1.00

3500

7.0 1120, H

/Vac. 1.20 100

1.05

4000

7.2 1260, H

/Vac. 1.25 95

1.15

4000

7.0 1120, DA 1.20 120

1.10

4000

7.2 1120, H

/Vac. 1.25 100

1.15

4500

7.4 1260, H

/Vac. 1.30 95

1.20

4500

7.0 1120, DA 1.25 120

1.20

4500

7.2 1120, H

/Vac. 1.30 100

1.30

5000

7.4 1260, H

/Vac. 1.35 95

1.25

5000

Measured from a maximum applied magnetic ﬁeld strength of 1200 A/m.

Table 4.3-6 Magnetic properties of sintered Fe–3 wt% Si products in relation to density

[3.10]

Density  Sintering conditions Coercitivity Remanence Sat. induction Max. rel. permeability

(gcm

−3

) temp. (

◦

C), time, atm. H

(Am

−1

) B

(T) B

(T) µ

max

7.3 64 1.15 1.90 8000

7.5 48 1.25 2.00 9500

7.2 1250, 30 min, H

80 1.0 4300

7.01 1120, 60 min, H

117

2800

7.19 1200, 60 min, H

4200

7.40 1200, 60 min, H

1.25 5600

7.43 1300, 60 min, H

8400

7.55 1371, DA

51 1.21 1.50

7.55 1371, DA

57 1.07 1.45

Measured according to ASTM A 596

Conventional compacting at 600MPa

Warm compacted at 600 MPa

Deﬁned as coercive force i. e. magnetized to a ﬁeld strength well below saturation

Formed by MIM

Table 4.3-7 Magnetic properties of sintered Fe

−

P in relation to density

[3.10]

Density  Sintering conditions Coercitivity Remanence Sat. induction Max. rel. permeability

(gcm

−3

) temp. (

◦

C),atm. H

(Am

−1

) B

(T) B

(T) µ

max

7.3

1.30

1.90

10 800

7.55

2.00

12 500

7.3

1250 30 min, H

1.1

6100

6.8

1120 30 min, H

100

0.6

2200

Measured according to ASTM A 596

Fe/3 wt% Si/0.45 wt% P

Fe/2 wt% Si/0.45 wt% P

Fe/4 wt% Si/0.45 wt% P

Part 4 3.2

Magnetic Materials 3.2 Soft Magnetic Alloys 761

Table 4.3-8 Magnetic properties of sintered Fe

−

P in relation to density [3.10]

Density  Sintering temp. Coercitivity Remanence Max. rel. permeability

(gcm

−3

) (

◦

C), time, atm. H

(Am

−1

) B

(T) µ

max

7.2

1120 30 min, H

1.1

4800

7.4

1250 30 min, H

1.0

9700

Fe/5 wt% Sn/0.45 wt% P

Fe/5 wt% Sn/0.5wt%P

Table 4.3-9 Magnetic properties of sintered Fe

−

Ni in relation to density

[3.10]

Density  Sintering Coercitivity Remanence Sat. induction Max. rel. permeability

(gcm

−3

) temp. (

◦

C),timeatm. H

(Am

−1

) B

(T) B

(T) µ

max

8.0

0.25

1.55

6000

8.0

0.85

1.60

30 000

8.5

0.40

0.80

74 900

6.99

1260, H

/Vac. 20

0.75

6.99

0.76

7800

7.30

1260, H

/Vac. 19

0.90

7.30

0.85

8700

7.50

1260, H

/Vac. 16

0.94

21 000

7.50

0.90

9100

7.4

1250, 30 min, H

0.8

13 000

7.66 1371, DA

16 0.42 1.27

Measured according to ASTM A 596

Fe/35–40 wt% Ni

Fe/45–50 wt% Ni

Fe/72–82 wt% Ni/3–5 wt% Mo

Fe/47–50 wt% Ni

Formed by MIM

Table 4.3-10 Magnetic properties of sintered Fe

−

Cr in relation to density

[3.10]

Density  Coercitivity Remanence Sat. induction Max. rel. permeability

(gcm

−3

) H

(Am

−1

) B

(T) B

(T) µ

max

7.1

200

0.50

1200

7.45

100

1.70

2500

7.35

100

1.55

1900

Measured according to ASTM A 596

Fe/16–18 wt% Cr/0.5–1.5wt%Mo

Fe/12 wt% Cr/0.2 wt% Ni/0.7wt%Si

Fe/17 wt% Cr/0.9 wt% Mo/0.2 wt% Ni/0.8 wt% Si

Part 4 3.2