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' 1962

NBS MONOGRAPH 47

Basic Magnetic Quantities and

the Measurement of the Magnetic

Properties of Materials

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3,

1901, as amended by Congress in Public Law 619, 1950. These include the development and

maintenance of the national standards of measurement and the provision of means and methods

for making measurements consistent with these standards; the determination of physical constants

and properties of materials; the development of methods and instrmnents for testing materials,

devices, and structures; advisory services to government agencies on scientific and technical problems; invention and development of devices to serve special needs of the Government; and the

development of standard practices, codes, and specifications. The work includes basic and applied

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various consultation and information services. Research projects are also performed for other

government agencies when the work relates to and supplements the basic program of the Bureau

or when the Bureau's unique competence is required. The scope of activities is suggested by the

listing of divisions and sections on the inside of the back cover.

Publications

The results of the Bureau's research are published either in the Bureau's own series of publications or in the journals of professional and scientific societies. The Bureau itself publishes three

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four separate sections, presents complete scientific and technical papers; the Technical News

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A complete listing of the Bureau's publications can be found in National Bureau of Standards

Circular 460, Publications of the National Bureau of Standards, 1901 to June 1947 ($1.25), and

the Supplement to National Bureau of Standards Circular 460, July 1947 to June 1957 ($1.50),

and Miscellaneous Publication 240, July 1957 to June 1960 (Includes Titles of Papers Published in

Outside Journals 1950 to 1959) ($2.25); available from the Superintendent of Documents, Government Printing Office, Washington, D.C.
UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astln, Director

Basic Magnetic Quantities and

the Measurement of the Magnetic

Properties of Materials

Raymond L. Sanford and Irvin L. Cooler

National Bureau of Standards Monograph 47

Issued May 21, 1962

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 30 cents
Preface

Since 1909 when the first NBS Circular on Magnetic Testing was issued,

successive revisions have been prepared in order to keep up to date with the

development of new magnetic materials and methods of testing. Since the

last circular, C 456, Magnetic Testing, was issued in 1946 the importance of

magnetic materials and testing methods has greatly increased. In view of the

many requests for information regarding magnetic quantities, materials, and

testing methods, the present revision and extension of the previous circular has

been prepared. It supersedes Circular C 456, Magnetic Testing.

II
Contents

Preface

1. Introduction

2. Magnetic quantities and units ; 2.1. Systems of units—dimensions

2.2. Basic quantities

I a. Magnetic induction, B

; b. Magnetizing force, H

2.3. Magnetic constant, r„

2.4. Derived quantities

a. Magnetic flux, 4> b. Magnetomotive force,

c. Magnetic reluctance,^

I 6 Magnetic characteristics of materials

I 3.1. Magnetic permeability

3.2. Magnetic susceptibility

3.3. Classification of materials

3.4. Magnetic hysteresis and normal in- duction

3.5. Core loss

4. Measurement of static magnetic fields

4.1. General principles

4.2. Pivoted coil 4.3. Pivoted magnet

4.4. Ballistic methods

a. Ballistic galvanometer

b. Intercomparison of mutual inductors

and calibration of test coils 4.5. Rotating test coil 4.6. Bismuth spiral

4.7. Hall effect

4.8. Saturable core

4.9. Nuclear magnetic resonance

Page Page

11 5. Tests with direct current 12

5.1. Testing of materials 12

1 5.2. Ring method 14

5.3. Straight bar and solenoid 15

1 5.4. Permeameters 17

1 a. MH permeameter 17

2 b. High-H permeameter 18

2 c. Fahy Simplex permeameter 19

2 5.5. Tests of low permeability materials 21

2 5.6. Magnetic susceptibility 21

3 5.7. Magnetic standards 23

3 5.8. Limits of accuracy 23

3 5.9. Requirements of standard specimens for 4 • d-c permeameters 24

5.10. General precautions 24

4 6. Tests with alternating currents 24

4 6.1. Core loss and a-c permeability at power

5 frequencies 24

5 a. Voltmeter-wattmeter methods 25

b. Bridge methods 27

6 6.2. A-C Measurements at higher than power

7 frequencies 29

7. Typical magnetic properties of materials 30

L 7.1. Solid core materials 30

L 7.2. Electrical sheet and strip 30

i 7.3. Special-purpose materials 31 ° 7.4. Ferrites 32

Q 7.5. Permanent-magnet materials 33

a. Quench-hardened alloys 33

b. Precipitation-hardening alloys 33

|V c. Work-hardened alloys 34

. . d. Ceramic magnet materials 35

-.^ e. Powder magnets 35

j2 7.6. Feebly magnetic materials 35

12 8. References 35

III

Basic Magnetic Quantities and the Measurement of the Magnetic

Properties of Materials

R. L. Sanford and I. L. Cooter

This paper gives general information regarding the two basic quantities, magnetic

induction, B, and magnetizing force, H, and also the magnetic constant (often designated

by the symbols and yuo). Information is also given regarding the magnetic properties

of various materials and methods and apparatus commonly used in the Magnetic Measurements Section for measuring these properties by means of reversed direct current or alter- nating currents of low frequency. Magnetic measurements peculiar to high frequencies are not discussed. In view of the gradual adoption of the rationalized mksa system of units,

this system is included as well as the classical cgs electromagnetic system.

1. Introduction

The work of the Magnetic Measurements Section of the National Bureau of Standards includes

(1) testing of specially prepared test specimens intended for use as standards for checking magnetic

testing apparatus (2) investigation and development of magnetic testing apparatus (3) calibration

of mutual inductors, test coils, and instruments for

measuring magnetic fields, and (4) investigations

in the field of magnetics such as studies of phenomena associated with nuclear magnetic resonance or

the selection and testing of materials suitable to be

used as standards of nuignetic susceptibilit^^

This monograph gives general information

regarding magnetic quantities and units, the magnetic characteristics of various materials, and

methods and apparatus commonly used in the

Magnetic Measurements Section for magnetic

testing.

2. Magnetic Quantities and Units

2.1. Systems of Units—Dimensions

For many years magnetic quantities have been

expressed in the cgs electromagnetic ^ system of

units. In this system the centimeter, gram, and

second are taken to be the basic units in which the

concepts length, mass, and time respectively are expressed. A three-dimensional system lacks the

"resolving power" necessary to distinguish between the magnetic quantities denoted by the

symbols B and H. The ratio between these two

quantities in empty space, or /xq, is arbitrarily

assigned the value unity in this system and therefore /xj, or fio is usually omitted from the equations

without affecting the numerical values.

Another system based on the meter, kilogram,

and second as the units of length, mass, and time

respectively has been adopted by the International

Electrotechnical Commission (lEC) and is rapidly

gaining favor. It seems likely that this system

eventually will replace the cgs system. In this

system the ratio ol B to FI in empty space is not

unity and consequently it cannot be ignored. A

fourth dimension in addition to length, mass, and

time is required to characterize magnetic and elecI There are two other cgs systems, namely the electrostatic system and the

gaussian system, but in this monograph cgs means cgs eloetromagnetle

unless otherwise specified.

trical quantities in this system. It must be electric or magnetic in nature. The lEC has chosen

electric current, /, as the fourth dimension.

When the four dimensions LMTI are applied to

magnetic quantities the distinction between B and

H is clearly evident.

At the same time that the lEC adopted the

mksa (Giorgi) system of units a further step was

taken, namely, "rationalization." The object of

rationalization is to transfer the factor 47r from

linear equations to those having circular symmetry. In the rationalized system, the ratio of

B to H in empty space,^ r,„ is 47r X 10"' h/m.

By applying four dimensions to quaTitities in the

cgs electromagnetic system (wliich is not inherently

three-dimensional, as is ordinarily assumed) additional "resolving power" can be gained, the distinction between B and H then becomes cloai-ly

evident and nuitual consistency between the two

systems of units is brought about. Tlio symbols

L, ]\{, T, and / denoting lengtli, mass, time, and

current respectively may be applied to either

system.^

- Since this is a true definitional constant, whereas the symbol n denotes

relatic)iishi|is usually not constant, the symbol T„ is used instead o! n, or

II, to avoid confusion.

3 Many writers consider Q ((luantity of electricity) to be a more simple

concept than current and use it as the fourth dimension. The dimensions

then are LMTQ.

i

1
2.2. Basic Quantities

Symbol

There are two basic magnetic quantities and "

a constant from which all other magnetic quanti- B

ties are derived. They are magnetic induction,

B (often called flux density), magnetizing force ^ or magnetizing field, H (also called magnetic e_ field strength or magnetic intensity), and the «- magnetic constant T^.

ogs

gauss

dyne

abampere

centimeter

volt

square centimeter

second

mksa (Giorgl)

tesla newton

ampere

meter

volt

square meter

second

a. Magnetic Induction, B

A current-carrying conductor in a magnetic

field experiences a mechanical force, the magnitude

of which depends upon the magnitude of the cur- rent and the field, the length of the conductor

and its orientation in the field. This dependence

on direction and magnitude identifies the field as a vector field. Its direction is considered to be

the direction of the conductor for which the mechanical force is zero. The quantity measured by

the mechanical force experienced by a currentcarrying conductor in a magnetic field is called

magnetic induction, B.

If a linear conductor is perpendicular to the

direction of the field and the field is uniform along

its length

where

and

B=F/Il

5=magnetic induction

mechanical force

/= current

/=length of the conductor.

There is another phenomenon by which the pres- ence of a magnetic field can be detected and its

magnitude determined. If a conducting loop or

coil is placed in a magnetic field and the strength

of the field is varied, the orientation of the coU

in the field is changed or the coil is removed from

the field, an electromotive force will be induced

in the coil during the change. At any instant

while a change is taking place

e=Na dB/dt

where e= instantaneous induced emf

A^= number of turns in the coil a =average area of the turns

5=magnetic induction

t=t\me.

Provided that B is uniform over the area a, the

total change in induction, AB, in a given time is

AB edt.

The units for the cgs and mksa (Giorgi) systems

are as follows:

The dimension * of magnetic induction is [B]=MT-U-K

b. Magnetizing Force, H

In view of the general acceptance of the concept

that the magnetic behavior of materials is due to

the presence within them of electrons in motion

(spins or rotations) it is reasonable to conclude

that magnetism is simply one of the manifestations

of an electric current. Magnetic induction at a given point must therefore be due to the influence

of electric currents. The magnetizing influence of an electric current is proportional to its magnitude

and depends upon its geometrical configuration, i The measure of the ability of an electric current to

| produce magnetic induction at a given point is called the magnetizing force (magnetic field

strength or magnetic intensity), H.

At the middle of a very long uniformly wound j solenoid

H=KNI/l

where ^Z'= magnetizing force

K=?i constant depending on the system

of units

7V=number of turns

/= current

/= axial length of the solenoid.

The units for the two systems are as follows:

Symbol cgs mksa (Giorgi) H oersted Ampere-turn per meter

1turn

ampere

meter

K 4x

N turn

/

I abampere

centimeter

The dimension of magnetizing force is

[H]=L-'I.

2.3. Magnetic Constant, Tm

The magnetic constant for any system of units

is the proportionality factor in the expression re- lating the mechanical force between two currents

* The square brackets in a dimensional ec[uatioii denote "the dimension of."

2
to their intensities and geometrical configurations.

In differential form this may be written

where

is the magnetic constant

dF is the element of force of a current element

Iidli on another current element

I2dl2 at a distance r.

face, the product of the induction, B, by the area,

A, is the magnetic flux.

(t>=BA

where

</)= magnetic flux

5=magnetic induction uniformly distributed and

normal to the plane of the surface of which

.4= area.

If the induction is not uniformly distributed over

the area, the surface integral of the normal component of B over the area is the magnetic flux

Ti is a unit vector in the direction from li to I2

n is a dimensionless factor which is unity in

unrationalized systems and 47r in rationalized systems.

The magnetic constant is also equal to tke ratio of

the magnetic induction, B, to the corresponding

magnetizing force, H, in a vacuum. For this reason it is often called the permeability of space

(or vacuum) and denoted by the symbol n„ or y.^. Since the symbol m, with or without subscripts is used to denote several different relationships between B and H which in general are not constant,

the symbol is used to denote the magnetic constant. The value of Tm determines the system of

units employed. In the classical cgs system the

value of Tm is unity and it is a numeric. In the

rationalized mksa (Giorgi) system its value is 4xX10~'^ and the dimension is LMT~^I~^ (henries

per meter).

2,4. Derived Quantities

The principal derived quantities are associated

with the idea of a magnetic circuit, somewhat, but

not exactly, analogous to an electric circuit. It is a magnetic structure which may contain one or more airgaps or other "nonmagnetic" materials

and designed to contain certain continuous lines

of magnetic induction. Ideally, none of the

induction would escape from the circuit. However, since there is no insulator for magnetism,

this ideal condition is rarely if ever realized. The

magnetic flux which escapes from a magnetic circuit is called leakageflux or simply magnetic leakage.

a. Magnetic Flux, <t>

Given a plane surface or cross section within the

boundaries of which there is a uniformly distributed field of magnetic induction, B everywhere

having a direction normal to the plane of the surwhere

and

*=JjB.dA

(/)= magnetic fiux

5=Magnetic induction

dA=eLn element of area.

It is important to note that although both B and

A are vectors, 0 is a scalar and cannot have

direction.

The units in the cgs and rationalized mksa

systems are

The dimension of magnetic flux is

b. Magnetomotive Force,

^

In a magnetic circuit, the line integral of the

magnetizing force around the circuit is called the

magnetomotive force. It is proportional to the

total ampere-turns linked with the circuit.

^=KNI

where

magnetomotive force

A'^= number of turns

/=current

and

K=a constant depending on the system of units.

The units for the two systems are

3
Symbol

N

/

K

mksa

Table 1. Magnetic quantities and units

ampere-turn

turn

ampere

1

The dimension of magnetomotive force is ] =/.

c. Magnetic Reluctance, P?

Tiie magnetic flux resulting from a given

magnetomotive force acting on a magnetic circuit

is determined by the magnetic reluctance of

the circuit. Thus

where

0=flux

^=magnetomotive force.

,^=magnetic reluctance.

The units are

and

Quantity and

cgs Unit ^ Name of To convert cgsem values dimension

(mksa)

Symbol

Name Equation

rationalized mksa unit

to rational- ized mksa

values, multiply by

Induction B gauss ^'11 tesla 10-*

(I in abamperes)

(wcber/m*)

Magnetizing

force i -1/ H oersted

(7 inamperes)

3TT1 TlPrP- turn per meter103 79.58

47r

Magnetic

Constant r„ 47rX10-' = 12.57X10-7 LMT-U-'- (in vacuum)

Flux zmr-n-'

0 maxwell ,^jjB,A weber 10-8

Magnetomotive

ForceJ

Reluctance PI

gilbert or C 2/' = mi ampereturn10/47r=0.7958

10»/4ir

Normal per- meability M B 47rX10-' = 12.57X10-'

LMT-"-I-2

Relative Per- meability

(dimension loss)

Mr C)

Susceptibility

(dimension less)

k 47r = I2.57

The dimension of reluctance is \R\=L~'^M'''^T'^P

3. Magnetic Characteristics of Materials

3.1. Magnetic Permeability

» In this table, "cgs unit" refers to the unrationalized cgs electromagnetic system.

Magnetic permeability, denoted by a symbol

H, with or without certain subscripts, is a term

used to express various relationships between

magnetic induction, 5, and magnetizing force, H,

in a material under specified conditions. The

simplest relationship is the ratio of induction to

the corresponding magnetizing force.

This is usually called absolute permeability or simply the permeability. The term has a specific

significance, however, only under certain definite

conditions. For certain types of material the

ratio is constant, not depending upon the degree

of magnetization. For other materials the ratio

depends upon the induction. If the corresponding

values of B and H are determined by a standardized normal procedure (to be described later) the

5 Previous to 1930 the cgs unit of reluctance was called the oersted, but

the International Electrotechnical Commission, in 1930 adopted the name

oersted for the cgs unit of magnetizing force, leaving the unit of reluctance without a name.

ratio of B to H is called the normal permeability.

This is generally denoted by the symbol /x, without subscripts. It relates only to points on the

normal induction curve. The symbol \i with

various subscripts denotes either the normal

permeability at specified values of i? or 2? or the ratio of certain changes in B to the corre- sponding changes in H. In this discussion, the

term permeability (symbol \i) denotes normal

permeability.

Permeability has the dimension

-2 {ix\=LMT-''I

in the rationalized mksa system.

The symbol denotes the quantity called

relative permeability. It is the ratio of the permeability of a material to that of space (or vacuum).

Or it may be defined as the ratio of the permeability of a material to the magnetic constant.

Since this is the ratio of two quantities having

the same dimensions, //^ is seen to be a dimension-
less ratio and its value is independent of the

system of units. The absolute permeability is the relative permeability multiplied by the value

of Tm pertinent to the system of units employed.

In the cgs system, the value of is unity so that

the numerical value of the absolute permeability

in this system is the same as that of the relative

permeability. It is for this reason that in the

cgs system the normal permeability is considered

also to be a dimensiordess ratio which leads to

the conclusion that B and H are quantities of

the same kind.

3.2. Magnetic Susceptibility

The magnetic induction, B, in a material due

to a magnetizing force, H, is made up of two

components, that induced in the space alone,

TmH, and that due to the magnetization ^ of the

specimen, 5,. That is B=1\H+Bt.

The ratio of these two components is called the

magnetic susceptibility, k

k=B,/T^H

since

B,=B-T„H

k=B,/T„H= (B/T^H) - 1 = - 1

This differs from susceptibility in the classical

cgsem system by the factor 47r because in the

cgsem system in which rm=l, the equations are customarily written

B=H+4:tJ

J= {B-H)/4Tr

and

k=JlH= iB-H)/4:rH= (m- l)/47r.

J is called intensity of magnetization and has

the dimensions of magnetic induction. The

ratio of J to H, therefore, has the dimensions of

permeability although susceptibility is actually a dimensionless constant. However, in the cgsem

system only three dimensions are employed, B

and H are considered to be quantities of the same

kind, and is a dimensionless ratio. Inthemksa

system as has been previously noted is not

unity and therefore in vacuum B is not equal to

H, their ratio is not unity and so neither the

values nor the dimension of can be ignored as

the}^ are in the classical cgsem system.

Susceptibility is used to characterize materials

whose permeability differs from unity by only a very small amount. The susceptibility of a material divided by its density, p, is called its mass susceptibility, X.

' » The component due to the magnetization of the specimen is called the

intrinsic induction, 7?,-. \m

x=k/p

The mass susceptibility multiplied by the atomic

weight A is called atomic susceptibility, x^.

3.3. Classification of Materials [32]

The magnetic properties of materials result from

the motions of electric charges within them. The

motions are either rotation in orbits or spins about

the axis of the charges. These motions constitute

equivalent electric currents and therefore produce

magnetic fields. The field-producing eft'ect of an

orbit or spin is called its magnetic moment. It is a vector whose direction is that of the axis of spin

or of the normal to the plane of the orbit and whose

magnitude is the product of the equivalent current

and the area enclosed by its path. The magnetic

moment of a magnetized body is the vector sum

of its internal moments. Dimensionally, [m\ =UI

where m is the magnetic moment.

In the past, materials have been classified as diamagnetic, paramagnetic, or ferromagnetic.

However, two other classes are now recognized,

namely, antiferromagnetic and ferrimagnetic. The

magnetic properties of a single atom depend upon

the relative locations and directions of spins of its

electrons. The spin of the nucleus and orbital

motion of the electrons constitute such small parts

of the magnetic moment that they can generally

be neglected. The moments of two electrons in

the same orbit or shell whose spins are in opposite

directions mutually cancel. An atom has a permanent magnetic moment if there is an excess of

spins in one direction.

The magnetic properties of materials composed

of associated atoms depend upon the arrangement

of the atoms with respect to each other. This

determines the kind of interactions between their

magnetic moments. The forces of interaction

(also called exchange forces) are functions of the

ratio of the distance between atoms to the diameter

of the orbit or shell in which the uncompensated

spins are located.

Diamagnetic materials have no permanent magnetic moment. However, moments are induced

by the influence of a magnetic field. The induced

moments have a direction opposite to that of the

inducing field. Consequently the relative permeability is less than unity. The diamagnetic

susceptibility is negative. The diamagnetic susceptibility is very small, not more than a few parts

in a million, and usually independent of temperature and applied magnetic field. It is probably'

present in all materials but usually masked by

other larger effects.

Paramagnetic materials have a permanent magnetic moment but the interatomic spacing is so great that there is negligible atomic interaction.

The relative permeability is greater than imity so the susceptibility is positive. Although the eft'ect

is greater than the diamagnetic effect, it is still

5
very small, not more than a few parts in a hundred

thousand. There are two kinds of paramagnetism

called strong and weak. Except for high fields of

the order of 10* gausses (1 tesla) or higher the

strong paramagnetic susceptibility is constant

with field at a given temperature but varies inversely with temperature at a given field. Weak

paramagnetism is due to the effect of conduction

electrons in conducting metals and is practically

independent of temperature.

Ferromagnetic materials have a relative permeability greater than unity and generally very

high. The permeability is not constant but depends upon the degree of magnetization. Ferromagnetic materials exhibit hysteresis, that is, the induction corresponding to a given magnetizing force depends upon previous magnetic history.

Furthermore, the intrinsic induction approaches a limiting or saturation value as the magnetizing

force is increased indefinitely. Ferromagnetism

has sometimes been called a special case of paramagnetism but in view of the differences in the

processes involved, it should not be so classified.

Ferromagnetic materials are temperaturesensitive and when the material is heated, the

temperature at which it is transformed from the

ferromagnetic condition to the paramagnetic

condition is called the Curie temperature.

In ferromagnetic materials, the interatomic

distances compared to the diameter of the orbit or shell in which the uncompensated spins are located are such that neighboring atoms have

their magnetic moments alined parallel and in

the same direction. This is called positive

interaction. Not all of the moments in a body are oriented in the same direction. Instead, they are

lined up in groups called domains which act as magnetic entities. Each domain is spontaneously

magnetized to saturation but because they are oriented in various directions the resultant

magnetization in any direction may be anything

from zero to the saturation value at which all domains would be oriented in the direction of the

applied field.

Antijerromagnetic materials are those whose

interatomic distances are less than the critical

value so that the magnetic moments of neighboring

atoms line up parallel to each other but in opposite

directions, that is, antiparallel. The susceptibility of these materials is so low that they might

easily be mistaken for paramagnetic materials.

The experimentally distinguishable characteristic

is that the susceptibility increases instead of

decreasing as the temperature is raised until the

thermal agitation destroys the interaction.

Above this temperature the material becomes

paramagnetic. This is analogous to the Curie

point in ferromagnetic materials but is called the

Neel point for this class of materials.

Ferrimagnetic materials are those in which

unequal magnetic moments are lined up antiparallel to each other leaving a net permanent

moment. Permeabilities are of the same order of

magnitude as those of ferromagnetic materials

but are lower than they would be if all the atomic

moments were parallel and in the same direction.^ ' Under ordinary conditions the magnetic charac- f teristics of ferrimagnetic materials are quite | similar to those of ferromagnetic materials. '

i 3.4. Magnetic Hysteresis and Normal

Induction

| One of the important characteristics of

| ferromagnetic materials is the phenomenon of

' magnetic hysteresis. This phenomenon is illustrated in figure 1. If a demagnetized specimen

is subjected to the influence of a magnetizing force,

H, which is increased from zero to higher and

higher values, the magnetic induction, B, also

increases but not linearly with H. This is shown

by a curve oabcd. This nonlinearity is another of

the characteristics of ferromagnetic material.

B

Figure 1. Normal induction curve and hysteresis loops.

If the increase in H is stopped at a point such as , b and then decreased, the induction does not

[ retrace the original curve in reverse order but lags

behind it as indicated by the curve b, Br, He, etc. This lag is called magnetic hysteresis. The point j where the magnetizing force is zero is called the

j residual induction, Br. The negative magnetizing ; force at which the induction becomes zero is called ; the coercive force, He. The closed curve starting

^ from b through Br, He, etc. back again to b is called a hysteresis loop. The loop does not always close

at the first reversal of the magnetizing force but

will close after enough reversals have been made,

j ' There is a technically important class of m&terial called ferrites. The

atomic interactions in these miiteri<iis is mainly antiferromagnetic but there

is a net magnetic moment which gives them ferromagnetic characteristics. 1 The ferrites are ceramic bodies having extremely high electrical resistivity , which makes them particularly valuable for use at high frequencies. '

6
If the limits of H in each direction are equal, the

limits of B in the two directions will also be equal

!i and the material is said to be in a symmetrically

' cyclic condition. The induction at the tip of such

a loop is called the normal induction. The ratio

of B to H at this point is called the normal

permeability fi=B/H.

It is easy to see that the size of a hysteresis loop

for a given material depends upon the value of

induction at its tip. The normal induction curve,

I oabcd, is the locus of the tips of a family of cyclically

' symmetrical hysteresis loops.

The normal induction curve usually consists of

three distinct stages. In stage I the rate of

increase of B as H is increased is comparatively

small. The steep part of the curve represents

stage II of the magnetization. In this stage, a small increase in H produces a relatively large

increase in B. In stage III the rate of increase of

B is again small. In this stage the intrinsic induction, Bi, asymptotically approaches a limiting

value which is called the saturation induction, Bs.

For this reason, stage III is sometimes called the

saturation range. Magnetic saturation is another

I of the distinguishing characteristics of ferro-

^ magnetic materials.

The magnetizing force and induction at the tip

of a hysteresis loop are denoted by the symbols

Hm and B„„ respectively. As B^ is carried

higher and higher in the saturation range there

I comes a time when further increase does not proi duce any further increase in B^ and He. The

! maximum values of these quantities are called

retentivity, Brs, and coercivity, Hcs, respectively.

4. Measurement of

4.1. General Principles

There are two aspects of a basic phenomenon by

which magnetic fields can be measured. They

are (1) the mechanical force experienced by a cur- rent-carrying conductor in a magnetic field or (2)

the electromotive force induced in a conducting

loop (test coil) when the magnetic induction encii-cled by or linked with the loop is changing,

either because the induction is varying or because

the loop is moving with respect to the induction.

It is important to note that the quantity measured

I by either method is by definition magnetic induction, B. Magnetizing force, H, is calculated in

terms of either electric current and its geometry

or a measured value of B divided by the magnetic

constant, r„. In the cgs system, is unity so there is no numerical difference between B and

H. Consequently, it is general practice in certain

cases to measure B and call it H. In the niksa

system, Tm is not unity so it must be taken into

account in determining the value of i? in a mag-

, netic field.

I There are several additional methods by which

magnetic fields can be measured. These are (1)

change in electrical resistance due to a magnetic

For permanent-magnet materials, the important

part of the hysteresis loop is that portion in the

second quadrant between the residual induction

point, Br, and the coercive force point. He. This

is called the demagnetization curve. Points on

this curve are designated by the coordinates B^ and

Hg. The product of Ba and Ha for any point on

the demagnetization curve represents the energy

external to the magnet which could be maintained

under ideal conditions. A curve obtained by

plotting the products of the corresponding coordinates Ba and Ha as abscissas against the induction

Ba as ordinates is called the energy-product curve. The maximum value of the energy-product,

(BaHa)m is a good criterion of the relative quality

of permanent magnet materials.

3.5. Core Loss

When materials are subjected to alternating

magnetic fields, as in the cores of transformers, a

certain amount of energy is expended which can- not be recovered but is dissipated in the form of

heat. This loss of energy is called core loss.

Core loss is made up of two major components,

hysteresis and eddy currents.^ The hysteresis

loss depends upon the area of the hysteresis loop

and the frequency of alternations. The eddy

currents are induced in the core by the alternating

magnetic flux and depend not only upon the frequency and maximum induction but also upon the

electrical resistivity of the material, the thickness

of the laminations, and the insulation between

them.

Static Magnetic Fields

field, (2) the Hall effect, (3) behavior of saturable

magnetic cores in a magnetic field, (4) optical

effects, and (5) nuclear magnetic resonance." The

measurement of a magnetic field in terms of the

mechanical force experienced by a currentcarrying conductor is, of course, basic. However,

accurate measurements by this method, although

simple in principle, require somewhat elaborate

apparatus and very careful experimental px'Ocedure. Such apparatus is not commonly available. A pivoted-coil arrangement is similar in

principle and often used on account of its con- venience if high accuracy is not required.

4.2. Pivoted Coil

A pivoted (or suspended) coil is essentially an

inversion of the well-known d'Arsonval type of

instrument. In the d'Arsonval instrument the

coil is located in the constant field of a permanent

magnet and its deflection against the restoring

force of a spring or suspension is a measure of

the current in the coil. The inversion consists

« A third coin[)onont, may ho observed at. frcquoneies, but at lower

frequencies it is usually neRliKible eompared with the tolal loss. "The methods commonly used in the field of terrestrial luaKiietisni arc not described in detail but only such methods as lind application iirimarily

in connection with the testing of materials are considered.

7
in substituting the field to be measured for the

field of the permanent magnet. The coil, preferably without the usual iron cylinder within it, is mounted in a fixture so that it can be placed in

proper position in the field to be measured.

There are three different methods of making the

measurements. The most convenient is employed

in a commercially available instrument. Bv

this method, the current necessary to produce a certain standard deflection is observed by means

of a milliammeter connected in series with the

coil and the adjustmg resistors. Since the current

is inversely proportional to the field, the milliammeter is calibrated in terms of the field strength

in gausses. It would also be possible to observe

the deflection of the coil due to a standard current

or to measure the torque required to bring the

deflection back to zero. The first mentioned

method is most convenient. The presence of an

iron core inside the moving coil is objectionable

because it distorts the field being measured.

One limitation of this type of instrument is that for accurate results the field must be uniform

throughout the volume occupied by the coil so that fields of small extent cannot be accurately

measured.

4.3. Pivoted Magnet

The pivoted coil has two disadvantages. It is too large to go into small spaces such as the gap

in the magnetic circuit of a d'Arsonval instrument. Also it requires connections to a source

of current. The development of permanent

magnet materials having extremely high coer- civity has made it possible to produce an instrument by which magnetic fields can be measured

in terms of the torque on a very small magnet.

This instrument, called a gaussmeter, consists

of a light-weight shaft pivoted at each end and

supported between jewels. A small cylindrical

Silmanal magnet is mounted on the shaft near

its lower end. At the other end is a hair spring

for measuring the torque and a pointer which

moves over a scale, calibrated in gausses. The

magnet is about an eighth of an inch long in the

direction of the shaft. It is magnetized in a direction perpendicular to the axis of the shaft.

The moving system is enclosed in a thin-walled

protective tube which extends perpendicularly

from the back of a case which houses the scale

and pointer. The pointer is mounted on the

shaft in a direction parallel to the magnetic

axis of the magnet so that when the pointer reads

zero on the scale it also indicates the direction

of the field in which the magnet is located. To

measure the strength of the field, the instrument

is rotated about the axis of the probe until the

scale reading is a maximum. The axis of the

magnet is then at right angles to the direction

of the field and the scale reading shows its value

in gausses. It is important to avoid exposing

the magnet to a field greater than 5,000 gausses

as the magnets cannot be stabilized for higher

fields and therefore the calibration would be

affected.

Alternating fields and fields greater than 5,000

gausses can be measured by a modified form of the

instrument in which the Silmanal magnet is re- placed by a cobalt-plated surface on soft iron.

By this system, the general direction of the field can be determined, but not its polarity.

The gaussmeter is regularly furnished with

probes either 1% in. or 5 in. long and diameters of

0.052 in. or 0.090 in.

4.4. Ballistic Methods

Ballistic methods are so called because they

employ a ballistic galvanometer. In making a measurement, a test coil connected to a ballistic

galvanometer is placed in the field with its axis in

the direction of the field and the deflection of the

galvanometer is noted when the test coil is either

suddenly removed from the field or rotated 180°

| about its diameter.'" This produces an impulsive

current in the galvanometer circuit which is | proportional to the total change in linkage between

the field and the test coil.

a. Ballistic Galvanometer

Tlie ballistic galvanometer commonly used for

magnetic measurements is a moving-coil instrument of the d'Arsonval type.'' It is an instrument

for integrating electrical impulses of short duration. The coil is usualh^ suspended but some

pivoted-coil instruments are also in use. The

moment of inertia of the coil is high and the

restoring force due to the suspension or spring is low so that the natural period on open circuit is long, usually of the order of 20 sec or more. The

behavior of the galvanometer is controlled mainly

by the amount of resistance in its circuit. This

determines the amount of electromagnetic damping due to the current induced in the coil as it moves in the field of the permanent magnet. The

damping due to air friction is usually negligible

compared to the electromagnetic damping.

If the external resistance has a certain critical , value, the return of the coil to its zero position after i a deflection occurs in a minimum of time without ; oscillation. This is called critical damping. The

j external resistance for critical damping is an j important characteristic of a ballistic galvanometer.

If the external resistance is greater than the i critical value, the return to zero after an impulse ! is by a series of oscillations of continually decreas- ; ing amplitude. The galvanometer is then said to i be underdamped.

If the external resistance is less than the

j critical value, the galvanometer is overdamped. i The maximum deflection for a sudden impulse

comes sooner than when critically damped but

1" If the field arises from an electromagnet the field may be reversed by

reversinp the current in the magnetizing coil.

11 For an excellent detailed discussion of the theory and operation of the

ballistic galvanometer see Harris, Electrical Measurements, pp. 301-341, Wilev, 1952.

8
the return to zero is slow. For magnetic measurements, the balhstic galvanometer is usually used

in the overdamped condition. Some operators,

however, like to have the galvanometer critically

damped or very slightly underdamped. Under

this condition it is necessary that the impulse be

complete before the coil has moved appreciably

from its zero position. Otherwise, if the impulse

is prolonged, the integration will not be complete

and the reading will be low.

For measurements of magnetic fields it is usually possible to produce sudden brief impulses but

in the testing of ferromagnetic materials, the impulses are likely to be of such long duration that

it is necessary to use a very heavil}^ overdamped

galvanometer if good accuracy is to be obtained.

As a rule, the intrinsic sensitivity of a ballistic

galvanometer is sufficiently high to permit an in- crease in damping by shunting the galvanometer

as shown in figure 2. The figure shows alternative

methods of connecting a ballistic galvanometer to a test coil. The choice of methods is a matter of

taste. In both diagrams TC is the test coil, RS

is a series resistor for adjusting the sensitivity, and

RP is a resistor connected in parallel with the

galvanometer when the key ^K" is closed on the lower

contact. In diagram A the galvanometer can be

short-circuited by closing K on the upper contact.

This will stop the motion of the coil almost instantly if it is swinging. In diagram B the resistor RC is permanently connected to the galvanometer and so adjusted that when key K is open the galvanometer is critically damped.

This allows the galvanometer coil to return to its zero position after a deflection in minimum time

without oscillation.'^ Some operators omit RP

when this connection is used.

If the restoring force could be made zero, the

only control of the galvanometer deflection would

be the electromagnetic damping.'^ The motion

of the galvanometer coil would then follow the

change in flux linkage in the test coil exactly and

the final deflection would not be influenced by the

time taken by the change. An instrument whose

torsional restraint is so small that this condition

is closely approximated is called a fluxmeter. As

a rule, however, it is more convenieiit to have a suspension or spring stiff enough to give a fairly

stable zero. A galvanometer which is sufficiently

overdamped to approach the performance of a

true fluxmeter is said to have fluxmeter characteristics.

If the circuit of a galvanometer with a weak

suspension or spring is not free of temperature

gradients or contacts between dissimilar metals,

thermal electromotive forces may be very troublesome by causing an unsteady zero and spurious

deflections. Also, it is desirable to have a method

for setting the galvanometer exactly on zero quickly and easily. Figure 3 is a diagram of a

'2 In practice the resistance is often adjusted so tliat tlie galvanometer is slightly underdamped and will pass beyond zero once before coming to rest. This makes it possible to be sure that the coil is swinging freely between tho

pole pieces without friction.

13 Except for a slight amount of air damping which usually is negligible.

RS

RS

Figure 2. Connections for ballistic galvanometer.

-wvi ^

Tc: :zs

Figure 3. Zero adjuster and thermal emf compensator.

device which has been found to be very useful.

Two slide-wire resistors are connected in parallel

to a small dry cell through a high resistance. The

two sliders are connected to opposite ends of a

resistor of low value which is mserted in the galvanometer circuit. Contact ZS has a detent so that it can always be set at the same position.

To compensate for thermal emfs, the slider TC is set so that the galvanometer does not drift wlien

contact ZS is on the detent. To set the zero, contact ZS is moved one way or the other till the

galvanometer reads zero. It is then quickly re- turned to its neutral position. The galvanometer

is calibrated by means of a mutual inductoi- of

known value whose secondary winding (in fig. 4)

is connected permanently in series witli the test

coil.'^ It is often convenient to adjust the seiisi-

" If necessary, to avoid tho possible effects of stray fields, a nonindiictive

resistance equal to that of the secondary coil may be substituted for the coil after calibration.

9
Rp;

Figure 4. Calibration circuit for ballistic galvanometer.

tivity so that the scale is direct reading in terms

of induction thus avoiding the necessity of multiplying the reading by an odd-valued scale constant

to obtain the value of the field in specified units.

The calibrating current which must be switched

in the primary of the mutual inductor is calculated

by the formula

KBoN

where

/c=current

7^= a constant dependent upon the system of units

i?= induction

aA''= area-turns of the test coil

i,„=mutual inductance.

In the cgs system Ic is in amperes, B is in gausses,

aN is in cm^-turns, Lm is in henries, and K is 10~*. In the mksa system Ic is in amperes, B is in teslas, aN is in m^-turns, Lm is in henries, and

K is unity.

If the field is to be measured by withdrawing

the test coil, the resistance in the galvanometer

circuit is adjusted so that when Ic is suddenly

reduced to zero the deflection is 10 cm. If the

field is to be measured by flipping the coil through

180° or by reversing the fleld, the galvanometer

is adjusted to read 10 cm when Ic is reversed.

If the value of H is desired, it is only necessary

to divide the observed value of i? by r,„. In the

cgs system r,„ is unity so that H is numerically

the same as B. In the mksa system is 4irX 10"'' so that it is not possible as it is in the cgs system

simply to measure B and call it H.

b. Intercomparison of Mutual Inductors and

Calibration of Test Coils

At the National Bureau of Standards the standard of mutual inductance is one built with considerable care for use in determining the unit of

resistance. The value of mutual inductance has

been computed in terms of the dimensions of

the inductor and is known to a few parts in a million. Since ballistic magnetic measurements are

carried out with direct currents, the working standards of mutual inductance are calibrated by comparison with the primary standard using a directFiGURE 5. Diagram of connections.

current method somewhat similar to one proposed

by Maxwell [1].^^ A diagram of connections is shown in figure 5. Lmi and L„a are the mutual

inductors to be compared, i^i must have the

greater value. The primary windings are con- nected in series to the battery, B, through the

reversing switch, S, the rheostat, C, and the ammeter, A. The secondary windings are connected

so as to oppose each other. Ri and R2 are adjustable precision resistors. It is important that the

ballistic galvanometer, @, be connected as indicated because if it is connected between points

E and G leakage currents might give trouble unless

the insulation between coils in the inductors is practically perfect. A measurement is carried out

as follows. With switch St, closed Ri is set at

some convenient value and the primary current

is set at a value not exceeding the current-carrying

capacity of the primary windings of the inductors.

R2 is then adjusted so that upon reversal of the

primary current by switch S there is no residual

deflection of the galvanometer. If the self-induct- ances of the secondary windings of the two inductors are not equal there may be a small double

kick but this is generally not troublesome. When

balance is obtained, the value of 1^2 is

T —T ^1

Si? is the total resistance of the secondary circuit

of Lmi including Ri, R2, the secondary winding of

Lmi, and all the leads. The excess over i?i-f-^2 is determined by setting Ri and R2 to zero, opening

switch Si, and measuring the resistance of the rest

of the circuit by means of a Wheatstone bridge

connected across Si,. Correction for the resistance

of the leads to the bridge can be made by measuring

their resistance with switch Sj, closed. The usual

precautions should be taken against the effect of

stray fields. Leads should be t wisted and the two inductors should be located at some distance from each

other and so oriented that no interaction between

the primary of one inductor and the secondary of

'» Figures in brackets indicate tlie literature references on page 33.

10 i
the other can be observed. Some errors may

result from capacitance betweea the primary and

secondary circuits. This can be minimized by

i repeating the observations after reversing the

connections of the primary of one inductor and

the secondary of the other and averaging the

results.

It is usually not feasible to calculate the value

of area-turns of a test coil with a satisfactory

degree of accuracy, especially if it has more than

one layer. It is much better to determine the

value experimentally. If a test coil is placed at

the middle of a long slender solenoid whose pitch

of winding is uniform and accurately known, its

area-turns can be calculated from the mutual

inductance between the solenoid and test coil

and the induction per unit current in the solenoid.

The mutual inductance can be determined by the

method described above. It is important that

the axis of the test coil be alined with that of

the solenoid. The error due to lack of alinement

is proportional to 1 —cos d where 6 is the angle

between the two axes. If the angle is less than

2.5°, the error from this source will not exceed

0.1 percent.

The value of area-turns is calculated from the

equation {aN)=KLJC

where

aN= area-turns

iif= a constant depending on the system of units

Xm=the mutual inductance

(7= the value of induction per ampere in the

solenoid.

In the cgs system, K is 10^ is in henries, and

C is in gausses per ampere. Area is then in square

centimeters. In the mksa system K is unity,

Ln is in henries, C is in teslas per ampere, and area

is in square meters.

If a coil whose area-turns value is to be determined is too large to insert in an available solenoid

or has a handle which cannot be detached, the

calibration field may be obtained by means of a Helmholtz arrangement. This consists of two

identical very short coaxial coils, the axial distance

between them being equal to their radius. This

produces a very uniform field along about the

middle third of the axis between the coils. If a

is the radius in centimeters, N is the number of

turns in each coil, and i is the current in amperes,

the magnetizing force at the midpoint between

the two coils isH= /^,2x3/2 oersteds.

(?)

This reduces to

0.899lA^i , H= , oersteds. a

To convert to ampere turns per meter (mksa

units) multiply by 10V4ir= 79.58. If coils having

very small values of area-turns are to be tested

this can be done in the field between the poles of

an electromagnet. The field must be uniform

over the area of the test coil and measured by a standard method. Since it is generally not

feasible to reverse the current in the electromagnet,

the reading must be made either upon suddenly

removing the coil from the field or preferably by

rotating it through 180° about an axis which is perpendicular to the direction of the field.

4.5. Rotating Test Coil

A continuously rotating test coil can be used

to measure magnetic fields. The coil is rotated

at constant speed about a diameter. It is con- nected through a commutator or cam-operated

reversing switch to a d-c instrument which indicates the average voltage induced in the coil.

If the reversal comes at the time when the a-c voltage induced in the coil is zero, the reading

on the instrument will be a maximum and will

be proportional to the magnetic field. Commercial

instruments operating on this principle have the

rotating coil at the end of a long shaft which has

at its other end a SAnichronous motor. The shaft

has to be long enough to avoid errors due to stray

fields from the motor. The accuracy of the

measurement depends directly upon the accuracy

with which the frequency of the power source is controlled. The apparatus is generally calibrated

by observations in known fields.

4.6. Bismuth Spiral [2] One of the so-called secondary efl^ects which is utilized to measure magnetic fields is the change

in electrical resistance of a conductor when it is subjected to the influence of a transverse magnetic

fiekl. Most metals show this effect, but only in

bismuth is it sufficiently large to be of practical

value for the measurement of magnetic fields.

The bismuth spu'al is made of small insulated

bismuth wire wound bifilarly in a fiat spiral, all the turns being in one plane. The ends are usually

soldered to heavy copper leads. The spiral is held in place and protected from mechanical

damage by thin discs of mica which are fastened

to the copper leads. The diameters of the spirals

range from 0.5 to 2.0 cm and they are ordinarily

about a millimeter thick overall. It is essential

that the bismuth be of very high purity. Otlierwise, anomalous and uncertain results will be

obtained. The major difficulty encountered in

the use of a bismuth spiral is that it has two

temperature coefficients; not only does bismuth

have the ordinary temperature coefficient in the

absence of a magnetic field but also the change in

resistance due to a magnetic field depends upon

the temperature. If proportional change in re- sistance is plotted against the value of magnetic

field, the curve is not linear below about 5,000

gausses. Above this value the curve is practically

11
linear but the projection of the linear part does not

pass through zero. Bismuth spirals are not much used at present

but the principle might be useful for some

applications.

4.7. Hall Effect

The Hall effect furnishes a very convenient

means for the measurement of magnetic fields.

Instruments are available which utilize this principle. It can be very simply stated as follows.

If a thin strip or film of metal, usually bismuth,

indium antimonide, or indium arsenide, has a current in it, two points can be found at opposite

ends of a line approximately at right angles to the

current which will be at the same electrical

potential if no magnetic field is acting. If a magnetic field is applied at right angles to the

plane of the strip a difference of potential appears

between the two points. This difference of potential is proportional to the intensity of the magnetic

field. In practical instruments a-c is used so that

the emf produced by the action of a magnetic

field can be amplified and thus provide increased

sensitivity. Calibration is carried out in magnetic

fields of known value.

4.8. Saturable Core

A saturable core is one which reaches practical

saturation under the influence of a relatively low

magnetic field. Thus a very small change in the

effective magnetizing force will produce a large

change in the inductance of a coil containing a satm'able core. This principle is used for the

measurement of magnetic fields. This is done by

energizing a coil containing a satm'able core with

alternating current. The frequency is usually a few kilocycles per second. If a steady magnetizing field such as that of the earth is also present,

there will be induced in the circuit a second

harmonic component. This second harmonic

voltage is proportional to the intensity of the

superposed steady field. The steady field is determined in either of two ways. The amplified

second harmonic voltage may be filtered out and

measured or the steady field may be neutralized

5. Tests With

5.1. Testing of Materials

General Principles. The principal object of

testing ferromagnetic materials by d-c methods is to obtain data from which normal induction curves and hysteresis loops can be plotted. This is done

either by using suitably shaped specimens such as rings which constitute the entire metallic part of

the magnetic circuit or by means of permeameters.

16 Several devices using this principle are described in the book, Saturating Core Devices, by L. R. Crow, The Scientific Publishing Company, Vincennes, Indiana.

by means of direct current in a coil surrounding the > core. When this is done, the second harmonic ' I voltage disappears. The value of the field is then ! i calculated in terms of the direct current, and the ; 1 turns and dimensions of the coil. This is the more ! | precise method because variations in the amplifier |

i only change the sensitivity with which the balance |

( can be made. If the second harmonic voltage is i i measured dkectly, the apparatus must be call- ^

( brated in fields of known values. |

i

4.9. Nuclear Magnetic Resonance '

'

Nuclear magnetic resonance is another phenom- | i enon by which it is possible to measure homo- ! i geneous magnetic fields with very high accuracy. I The measurement is based on the equation i

2-Kv='YpB I or transposing, j

i

In this equation B is the field in gausses, v is the t resonance frequency in cycles per second and 7p is ^ a quantity called the gyromagnetic ratio. The

gyromagnetic ratio 7^ is the ratio of the magnetic > moment of a nucleus to its angular momentum. I

' The measurement is made by immersing a i

i sample of material containing nuclei, whose gyro- \ magnetic ratio is known, in the steady field to be |

I ineasured. The sample is then subjected by means 1

'

of a surrounding coil to an alternating magnetic {

i field at right angles to the steady field. The I

' frequency of the alternating field is adjusted to be • i equal to the resonance frequency of the nuclei in i

\ the sample. At this frequency which is directly |

I proportional to the intensity of the steady field | there is an absorption of energy from the exciting

circuit. This is generally observed by means of a 1 cathode ray oscilloscope. B is then calculated,

using the equation i

i

I B=— gausses " 1 ,

where v is the resonance frequency and 7^ is the | gyromagnetic ratio. |

1

Direct Currents ! A permeameter is a magnetic circuit provided |

' with magnetizing and test windings in which a i

'

test specimen can be inserted so as to compose a i . part of the circuit. Since there is no material

f which acts as an insulator with respect to mag- ;,

' netism, the magnetic circuit must be arranged so i

'

as to produce the greatest possible uniformity in

[ the distribution of magnetic induction across the ; section and along the length of that part of the ,

' specimen directly involved in the test. Several I

' permeameters have been developed which differ ,

'

1' To convert from gausses (cgs) to teslas (mlcsa) multiply by 1 X 10-*.

12
from each other in form of magnetic cu'cuit and

j method of determining corresponding vahies of

H and B. In the Koepsel [3] and Esterhnc [4] permeameters. tlie ends of the specimen are clamped between iron poh> pieces reseinbHng those

of a d'Ai'sonval insti'ument but much hirger. The

magnetizing winding surrounds the specimen.

Compensating coils in series with the main magnetizing winding are mounted on the pole pieces.

Their function is to compensate for the magnetic

reluctance of the pole pieces. In the Koepsel

apparatus there is a regular d'Arsonval movingcoil whose pointer gives an indication of the

value and du-ection of B in the specimen when

there is a current of fixed value in the coil. Values

of H are estimated in terms of the current in the

magnetizing winding. In the Esterline apparatus,

the d'Arsonval coil is replaced by a rotating armature. When this armature is driven at a constant

speed the induced voltage is taken to be a measure of B in the specimen. Neither of these

permeameters is capable of very high accuracy

and neither is at present in common use.

I Other permeameters have been developed by

1 DuBois [5], Hughes [6], Picou [7], Ihovici [8], Niwa [9], and Burrows [10]. The Burrows permeameter is based on the principle of so distributing the magnetomotive force around the

magnetic circuit that there is negligible magnetic

I leakage, at least from the specimen under test. It

I was for many years accepted as the standard

apparatus for d-c magnetic testing. However,

the operation of this apparatus is tedious and

time-consuming and is unduly sensitive to nonuniformity in magnetic properties along the

length of the specimen. Also, it requires two

similar specimens. The MH permeameter [11]

was developed with the object of eliminating or jninimizing these drawbacks and has been adopted

by the Magnetic Measurements Section as the

standard method for d-c magnetic testing in the

I'ange of magnetizing force up to 300 oersteds

(approximately 24 X 10^ ainp-turns/m) . The Fahy

Simplex permeameter [12] has been in general use

for many years for tests in the same range of

magnetizing force and for this reason is used for

testing when so requested. The advent of very

hard magnetic materials requiring the use of very

high magnetizing forces for testing led to the

1 development and adoption of the High-H permeameter [13] for magnetizing forces up to 5,000

oersteds (approximately 40X10"' amp-turns/m).

These three methods, the MH, High-H, and

Fahy Simplex permeameters, are called ballistic

methods because a ballistic galvanometer is employed in the measurements.

In ballistic tests, values of B are obtained in

terms of the deflection of a ballistic galvanometer

connected to a test coil (B-coil) surrounding the

specimen. The deflection is proportional to the

change in the induction linkecl with the test coil.

If the change is simply a reversal in direction,

then the induction is one half of the observed

change. There are two ways in which values of

H may be determined. One way is to calculate

it in terms of the current-turns per unit length

at a given section of the magnetic circuit. This

is tlie method employed in the testing of ]-ing

specimens and in tlie Burrows permeameter.

The other way is to determine B in the air at a

suitable location and calculate the value of H

from the equation

H-=BIT„,.

Since r„j = l in the cgsem system, it has become

general practice to determine B^^ and call it H.

This does not lead to a numerical error in the

cgsem system. It has also become general practice

to call the coils by which this determination is made //-coils. If H is calculated in terms of

current the magnetic circuit and magnetizing

windings nmst be so arranged that there is no

magnetic leakage from the part of the specimen

over which the i?-coil extends and the n:iagnetizing

winding nmst be uniformly distributed over the

same portion of the specimen. This is the

principle involved in the Burrows permeameter

and approximated in the ring test. If H is determined ballistically, it is not neces- sary that the magnetizing winding surround the

section of the specimen surrounded by the Bcoil but the magnetic circuit must be so arranged

that the field of induction in the region adjacent

to the specimen occupied by the 7/-coil is uniform

oi' if not it must be possible to extrapolate to the

surface of the specimen. This is the underlying

principle of the MH and High-H permeameters.'^

In ballistic tests, as described earlier, the galvanometer is calibrated by means of a nuitual

inductor whose secondary winding is part of the

galvanometer circuit. Excepting during calibration, the secondary winding may be replaced

l)y a noninductive resistor having the same

resistance. This is to avoid errors which might

be caused by pickup from other parts of the

circuit.

It is customaiy to adjust the sensitivity of the

galvanometer so that the scale is direct -reading

in terms of induction or magnetizing foi'ce. Thus, in the cgs system, the magnetic induction

on reversal may be 1,000 gausses/cm of deflection or the magnetizing force may be 1, 10, or 100

oersteds/cm. By this procedure the necessity

of multiplying the scale reading by an odd-valued

factor is avoided. If H is measured in terms of

current in the magnetizing whiding, oidy the

calibration for B needs to be made.

The calibrating current for a selected value of

B is given by the equation

r KBAN

'» Any (lULUitily dotermincd in li'rms of an induced emf in a tosi coil is

bti defiiiilion 11 and not H.

' 19 The Fahy Simplex peiinouinclci oiioratcs on a somewhat difteroni pi iii- ciplc and is described later.

13

627047—62
where

/r= calibrating current in amperes

i^=a constant depending upon the system of

units.

jB=the selected value of induction ^= the cross sectional area of the specimen

A^= number of turns in the test coil

L„, = mutual inductance in henries.

In tlie cgs system K is 10"*, B is in gausses, and

A is in square centimeters.

In the mksa system, K is unity, B is in teslas,

and A is in square meters.

In calibrating for a selected value of H the

equation becomes

KTMaN

L

where

/c= calibrating current in amperes

K — ?L constant depending upon the system of

units.

r,„ = the magnetic constant

H=i\\e selected value of magnetizing force

aA7^= area-turns of the test coil

X,„=mutual inductance in henries.

In the cgs system K is 10"'^ r„, is unity, H is the selected value of magnetizing force in oersteds,

and aN is the area-turns of the test coil in cm--

turns.

In the mksa system, is unity, r„, is 47rX10"',

H is the selected value of magnetizing foj'ce in

ampere-turns per meter, and aN is area-turns in

m^-tui'ns.

Since the caliljration is usually made by J'eversal

of the calibrating current, care must be taken

when measuring changes in induction or magnetizing force as in the detei'mination of points on

the hysteresis loop to multiply the readings by 2. Because the area of the B-qo\\ is larger than that

of the specimen, a correction must be made to the

observed value of B to account for the "air"

flux existing in the space between the coil and the

specimen. Thus the induction, B, is

B^Bot,s-kT,,H

where

-Bobs =observed value of B (for specimen of area A)

a =area of the test coil

A=area of the specimen

r^^the magnetic constant

H=the magnetizing force.

In the cgs sj^stem, B is in gausses, r„ is unity

and H is in oersteds. In the mksa system, B is in teslas, r,„ is 47rX10~'^ and H is in ampere-turns

per meter.

^ is a numeric and has the same value in either

system.

In making observations of normal induction, I the specimen should first be demagnetized to I eliminate latent polarization due to previous \ magnetization. This is done by subjecting it to

j the influence of reversals of magnetizing force of

| gradually decreasing magnitude starting from a peak value well into the third stage of niagnetiza- i tion. The frequency of reversal should be low

enough so that induced eddy currents will not

j interfere with the demagnetizing process. About

Ic/s has been found satisfactory for the average I case. If the specimen does not compose the i entire magnetic circuit and has a small cross j section compared with the rest, it may be neces- i sary to demagnetize the rest of the magnetic

| circuit using a larger specimen and then to repeat i the process with the smaller specimen in place. I After demagnetization, the :iiagnetizing current } is set at the value corresponding to the lowest- i point desired and reversed several times until I successive readings of the induction are the same. | The specimen is then in a symmetrically cyclic i condition and the observed induction is the normal j induction. The corresponding magnetizing force '

is then determined either by taking a ballistic

deflection or b_y observing the magnetizing current | according to the type of apparatus being used, i Additional points on the nonnal induction curve | are determined in the same way. Demagnetiza- ! tion need not be repeated if each point so deter- ] mined is higher than any preceding one. It is tlie practice of some observers to start with the ; highest point and then to demagnetize from each | point to the next lower one. This is sometimes ! preferable, especialh' if the specimen is likely to j be heated unduly. i If points on a hysteresis loop are to be determined, cyclic condition is first obtained by several

reversals of tlie magnetizing current corresponding

to the tip of the loop and the resulting values of

B and H observed. The current is then suddenly

reduced in value by inserting additional resistance i in the magnetizing circuit. For points on the

negative side of the H-axis, the current is simultaneously reversed and reduced. The observed

changes in B and H are subtracted from the

values at the tip and the results thus obtained are

' taken to be the coordinates of the required point | on the hysteresis loop.

j The process is repeated for other points, care >, being taken to reestablish cyclic condition at the \ tip before each observation. ! In setting up apparatus for ballistic testing, it

is important to twist the conductors in both i, primary and secondary circuits and so to locate i the nmtual inductor with reference to the rest of ; the apparatus as to prevent errors due to stray

j fields.

j

5.2. Ring Method

I Although a ring would appear to be the ideal , form of specimen for magnetic testing, it has

certain disadvantages which should always be

14
taken into account. The principal advantage is the absence of airgaps and end effects.

In the cgs system, H is calculated using the

equation

0.4 A^/

D

where

magnetizing force in oersteds

A'^= number of turns in winding

/= current in amperes

/^=mean diameter of the ring in cm.

To convert to rationalized mksa units (ampereturns per meter) multiply by 1000/47r = 79.58.

This calculation is suffi.ciently accurate for most

purposes provided that the mean diameter of the

ring is large compared to its radial width. Since

the outer circumference of the ring is greater than

the inner circumference, the turns per unit length

are less on the outside than on the inside and

consequently the magnetizing force is not uniform

across the section. Table 2 shows the ratio of the

average value of H to that at the mean radius in

rings of either circular or rectangular cross section.

For difference no greater than 1 percent, a ratio

of at least 10 of mean diameter to radial width is usualb^ recommended.

Table 2. Ratio of average, value of H lo value at mean

radius in rings of rectangular and circular sections [IS]

Ratio of diameter to radial tliickness

Rectangular Circular

2 1.0986

1.0397

1.0216 1.0137

1. 0094

1. 0069

1.0052

1.0033

1.0009

1. 0718

1. 0294

1. 0163

1 . 0102

1. 0070

1.00.52

1. 0040

1.0025

1.0007

3 - - 4

5G

8

10

19

It is not safe to assume, however, that siniply

making the ratio 10 or more assures accurate

results. Errors may also result from irregularity

in winding or from noimniform magnetic properties

along the circumference of the ring. Irregularity

in winding can be minimized by the exercise of

extreme care in winding or by the use of a winding

machine. However, errors due to nonuniformity

in the specimen which can neither be calculated nor conveniently determined experimentally may be

large and therefore, the use of ring specimens as reference standards for checking the accuracy of

other methods is not recommended. The method

is also limited to low magnetizing forces which can

be applied without producing excessive heating.

In spite of the disadvantages of the ring specimen for measurements of high accuracy or for

standardizing purposes, this form of specimen is widely used in production testing for quality control or the development of new matei'ials, notably

the ferrites. Its use has been greatly facilitated

in recent years by the development of a machine

by which extremely uniform windings can be

rapidly applied. The secondary winding is applied first so as to minimize the effect of air-flux

between coil and specimen.

A diagram of connections for the ring test is shown in figure 6. Current is derived from the

battery, B, controlled by the resistors R and R'

,

and measured by the ammeter A or some more

precise method for measuring current. The cur- rent can be reversed by switch C or reduced by

opening switch C" , ov I'eversed and reduced by

operating both switches simultaneously. If

switch D is closed upward the current is in the

magnetizing coil M. If D is closed downwards,

the current will be in the primary winding, P, of

the calibrating inductor.

The secondary or test winding, T, is coimected

in series with the secondary winding of the inductor and the series resistor, RS, and the parallel

resistor, RP, as shown. The ballistic galvanometer is connected through the key k across the

resistor RP.

The procedure for making a test is described on

p. 13 et seq.

5.3. Straight Bar and Solenoid

It is possible to make ballistic tests with a

straight specimen of uniform cross section magnetized in a solenoid. In this case, the deterniination of the magnetic induction at the midsection of the bar offers no particular difficulty.

The principal problem lies in the determination of

the magnetizing force. This arises from the fact

that the magnetic circuit comprises not only the

bar but also the air-space in which the lines of

Figure 6. Connections for the ring list.

15
Table 3. Demagnetizing coefficient and factor

Z>=ratio of length to diameter

10-. 15.. 20..

30..

40-.

50-.

B0-.

70-.

80..

100.

150.

200.

H=H'- NI

Ellipsoid N

0. 2549

. 1350 .0848

.0432

.0266

.0181 .0132

. 0101 .0080

. 0054

. 0()2()

. 0010

.Mann [14] N

0. 2560

. 1400

. 0898

.0460

. 0274

.0183

.0131

. 0099

. 0(»78

. 0052

. (11)25 .0015

0. 0203

.0111

. 00714

. 00366

.00218

. 00146

. 00104

. 00080

. 00062

. 0(M141

. 00020 .00012

Du Bnis [15] N

0. 2160

. 1206

. 0775

.0393

. 0238

. 0162

.0118

. (1089

. 0069

. (1045

. 0020

.0011

0. 0172

.0096

. (1062

. 00313

. 00189

. (10129

. (10094

. 00071

. (10055

. 00036

. (10016

. 00009

Shuddemagen [16] N

0. 2000

. 1040

. 0655

. (1335

. 0206

. 0139

.0101

. 0077

. 0061

. (1041

. 0020

.0012

Db

(1. 0159

.0083

.0052

. 00267

. 00164

.00110

. 00080

. 00061

. 00049

. 00033

. 00016

. 00009

Equation »

N

0. 2512

. 1235

. (1747

. 0367

. 0222

. 0150

. 0109

. 0083

. 0066

. 0045

. 0022

.0013

Db

0. 0200

.0098

. 0059

. (10292

. 00176

.00119

. 00087

. 00066

. (10052

. (10035

. 00017

.00011

> IogioW=1.15-1.75 logioX) logio2>s=0.05-1.75 log,o/3 Note: The above values of A^and Db are calculated for cgsem system of units.

intiuction extend from one en(i of the bar to the

other. Thus the total magnetomotive force is not

confined to the space within the solenoid and con- sequently the magnetizing force available for the

bar is less than would be calculated in terms of

the ampere-turns per unit length in the solenoid.

Classical theory attributes this diminution to the

effect of fictitious poles near the ends of the specimen and therefore the effect has been called a "demagnetizing" effect. The effect is expressed by

the equation

H=Wwhere

H=the effective magnetizing force

H' =the apparent magnetizing force

DB=th.e demagnetizing coefficient

-Bj= intrinsic induction

r;„=the magnetic constant.

In the cgs system, r,„ is 1. In the rationalized

mksa system, r^,; is 47rX10~''.

Except for ellipsoids of revolution, Db cannot be

calcidated but must be determined experimentally.

It has been found that the demagnetizing coefficient

is practically constant up to about the top of the

second stage of magnetization. Above this the

value decreases with increased induction. Within

the linear range, the value for bars of circular sec- tion is a function of the ratio of the length to diameter of the specimen ^° but published tables

by different experimenters are not in perfect

agi'eement.

According to Bozorth [32], the demagnetizing

factor depends not only upon the dimensional

ratio but also upon the permeability. He also

For sections other than circular, the diameter is taken to the. diami't.er of the circle which has the same area a.s that of the bar.

gives graphs by which apparent permeability can

be converted to true permeability or vice versa. Most of the tables available at the present writing

are given in terms of "intensity of magnetization"

rather than in terms of 7?,;. The equation commonly given is H=H'-NI

where H and IF are the true and applied magnetizing force respectively, is the demagnetizing

factor, and / is tlie "intensity of magnetization."

Tlie intensity of magnetization as imderstood here

is Bj/^ir so that

N^AttDb.

Table 3 shows some publislied values of the

demagnetizing factors together with equations

which practically average the values given by

Mann [14], DuBois [15], and Shuddemagen [16].

These equations provide a means for estimating

the demagnetizing factor for intermediate values

of the dimensional ratio.

The diagi-am of connections shown in figure 6

for the ring test is substantially right for the solenoid test. The only changes required are to take

M to be the solenoid winding and T to represent

the test coil at the middle of the test bar. In calculating the applied magnetizing force H', if the

solenoid is very long compared to its mean diameter and if tlie cgs system of units is used, the

equation is

//' = 0.47r n I

where

i/' =applied magnetizing force in oersteds

«=number of turns per cm

/= current in amperes.

If the solenoid is relatively short, a more nearly

accurate value can be obtained by using the

I

16
equation

where

[ /= length of the solenoid in cm

and

r/ = raean diameter of the winding in cm . A more accurate value for multilayer coils can be

obtained by calculating each layer separately and

adding the results. To convert from oersteds to

rationalized mksa units, multiply by 1000/47r=

79.58.

Unless the test coil is wound directly upon the

specimen its area should bo determined and the

standard air-flux correction should be applied to

the observed value of B. (See p. 14.)

On account of the difficulty of obtaining accurate values of the demagnetizing factor this

method is not capable of high accuracy but for

some purposes it may be the most convenient for

straight specimens if approximate restilts are good enough.

5.4. Permeameters

a. MH Permeameter

I The MH permeameter [11] was designed with

j the purpose of producing au instrument which

I would not have the disadvantages inherent in

the Burrows permeameter but would have comparable accuracy. It should also be an absolute

instrument in the sense that its constants can be

determined from its own dimensions and therefore

do not have to be calibrated by reference to any

other permeameter. The JMH permeameter fulfils

these essential requirements. In addition, it has

the advantages that it requires only a single

specimen and is more simple and rapid to operate

than the Burrows permeameter. Furthermore, it

is much less sensitive to the effect of nonuniform

magnetic properties along the length of the

specimen. It is also used for ordinary magnetic

testing within its proper range; that is, up to

300 oersteds or 24X10* amp-turns per meter.

The permeameter is shown in figure 7. The

magnetic circuit is made of laminated electrical

sheet of armature grade. The laminated structure reduces the effect of eddy currents induced

in the circuit by the changes in ffux incident to

the testing procedure. The specimen and the

synunetrical U-shaped yokes which span it rest

on two end pieces supported by Bakelite blocks.

The yokes are recessed so as to make good contact

with the end pieces and the ends of the specimen

in such a way that no clamping is required. This

eliminates mechanical strain in the specimen.

The symmetrical yokes promote a uniform distribution of magnetic induction across the section

of the specimen and along its length. The disMH is ii designation lor "iiicdiuni //."

Figure 7. MH permeameter.

Figure 8. Test coil assembli/ for MH permeameter.

tribution is also improved by auxiliary windings

around the ends of the A^okes and the end pieces.

These are connected m series with the main

magnetizing coil which surrounds the specimen.

The proper number of tmiis in these auxiliary

coils depends upon the magnetic jiroperties of the

yokes and end pieces and is determined experimentally for each instrument. The preferred

length of test specimen is 28 cm but specimens as short as 24 cm can be used if necessary.

The test-coil assembly is shown in figure 8. This assembly is held in place within the magnetizing coil by two Bakelite rings. A platform

extending between these rings serves to hold the

5-coil in place and to support ffexible specmiens

such as strips of electrical sheet so as to prevent

errors due to mechanical strain.

A 100-turn 5-coil extends over the middle 3 cm

of the specimen. Just above it, but not surrounding the specimen, is a compensating coil adjusted

to have the same value of area-turns as the 5-coil.

This coil is connected in series opposing the Bcoil so that the reading of the galvanometer upon

reversal of the magnetizing current is proportional to the intrinsic induction, B;. Thus the

usual air-flux correction is not required. If

desired, the total induction, B, can be obtained

simply by adding to the observed value of Bt the

value of TmH. In the cgs system r,„=]. In the

mksa system, r,„=47rX10~^ The i?-coil is able

to accommodate specimens as large as 1X3 cm in cross section.

The ^Z^-coil system is also shown in the figure 8. It consists of two rectangular coils with nearly

identical values of area-turns mounted on a turnla hie below the specimen. The upp(>r coil extends

into a recess in the supporting phitforni so as to

17
WWVWVX • ^AAAA/W^/^

R R'

RB,:

RPt

b h

:rh<.

•sh

G AH H'

--VWA/V- Rr Figure 9. Connections for the MH permeameter.

come close to the surface of the specimen. The

turntable can be rotated through 180° about a

vertical axis by means of a rack and pinion arrangement operated by an iroTi-clad solenoid and

plunger located far enough away from the magnetic circuit to avoid interference. The lower

coil has the larger value of area-turns and is adjusted to equality of effective value of area- turns by means of a noninductive shunting

resistor. If the two coils are connected in series

opposing and rotated the reading of the galvanometer will be proportional to the gradient of the

magnetic field. A reading taken by means of

the upper coil alone together with the gradient

permits extrapolation to the surface of the specimen and thus the determination of the magnetizing force acting on the specimen.

The use of rotating coils (flip coils) has some

advantages over a fixed-coil system, especially

when determining points on a hysteresis loop.

With fixed i?-coils, it is necessary to calculate

values of Hd for a point on the loop in terms of

the difference between two large quantities.

With the flip coils the value of is determined

directly with suitable sensitivity and observations can be repeated without the necessity of reestablishing a symmetrically magnetized condition.

The Burrows criterion for perfect demagnetization is that the induction for a given low magnetizing force shall be a maximum. This is not

feasible to apply experimentally. With the flip

coils, it is only necessary to observe whether or not the magnetizing force corresponding to a given low magnetizing current has the same

absolute value regardless of the direction of the

current. If there is a difference, the presence of

residual magnetization is indicated. The demagnetizing procedure should then be repeated.

Taking into consideration all the possible sources of error inherent in the apparatus, it is estimated that by the exercise of great care in

taking the readings and averaging several readings

for each point, values of induction are accurate

to within about 0.5 percent. Values of magnetizing force will come within the same accuracy

or 0.05 oersted, whicliever is larger. For routine

tests, values of either induction or magnetizing

force accurate to within 1 percent should be

obtained without difficulty.

Figure 9 is a diagram of connections for the

MH permeameter.

Battery E furnishes the magnetizing current

which is controlled by resistors R and /?' and

measured by ammeter A or by a standard shunt

and potentiometer. With switch D closed upward tlie current is in the primary winding P of

tlie calibrating inductor L^- If it is closed downward, the magnetizing winding is energized.

With selector switch F closed on b, the 5-coil

B is connected to the galvanometer circuit

through the calibrating resistor EBg. If F is closed on h, the i^-coils are in the galvanometer

circuit through the calibrating resistor EHg. The

selector switch, G, determines whether the upper

coil, u, alone is in the circuit or the coils u and

I are connected in series opposing. Resistor sh

is for adjusting the effective area turns of coil

I to be equal to the area-turns of coil u. Rc,

noninductive resistor, is to compensate for the

resistance of coil / so that the resistance of the

galvanometer circuit will be the same whether

one or two coils are connected.

It should be noted that for a spechnen which is magnetically nonuniform along its length, the

values of B and H obtained by the MH permeameter relate only to the part of the specimen

linked with the i?-coil.

b. High-H Permeameter

The High-H permeameter [13] shown in figure

10 is used for testing "hard" magnetic materials

at magnetizing forces up to 5,000 oersteds

18
Figure 10. High-H permeameter.

(40X10* amp. turns/meter). Since only a short

length of the specimen is included in the test,

it is possible to apply the high magnetizing forces

without appreciable heating. The magnetic circuit is made of laminated electrical sheet of

armature grade. The specimen, of rectangular

cross section, is held in pole pieces extending

between two U-shaped yokes. The construction

of the pole pieces is indicated in the sketch of

figure 11. They have longitudinal channels into

which filler pieces are fitted as shown. The

specimen is located in the space between the

bottom of the channel and the filler. The distance between pole pieces, or gap lengtii, is adjustable; and scales are provided to indicate

the gap length up to 10 cm, which is the maxinmm

generally used. The filler pieces are fastened at

their outer ends to heavy brass plates which are clamped to the ends of the pole pieces so as to

keep the fillers parallel with the bottom of the

channels. The main magnetizing coils surround

the pole pieces and auxiliary coils are wound on

the yokes.

Two similar i^-coils are mounted one above tlie other on a vertical shaft below the specimen.

They can be rotated 180° by means of a small

motor through beveled gears and a long horizontal

shaft. The lower coil has a slightly greater value

of area-turns than the upper coil and is adjusted

to have the same effective value by a noniiiductive

shunt. If the two coils are connected to the

galvanometer in series, opposing, and rotated

through 180° from a position such that their axes

are parallel to the direction of the field, the

deflection is proportional to the radial gradient

of the field. If the axis of the upper coil is set to be the same distance below the surface of the

Figure 11. Pole pieces of the high-H permeameter.

specimen as the distance between the axes of the

coils this gradient can be used directly to extrapolate the value obtained by the upper coil alone

to the surface of the specimen.

In order to keep the air correction small,

individual 5-coils are wound on tiiin brass forms

to fit specimens of various sizes. The coils are

5 nun long and usually have 25 tui-iis. Relatively short specimens can be used but for

specimens 5 cm or less in length, it is better to

butt the ends against the pole pieces rather than

to attempt to insert them in the regular way.

It is estimated that for magnetizing forces from

100 to 5,000 oersteds (8X10=* to 40X10* ampturns/meter) it is possible under favorable conditions to obtain values of either induction or magnetizing force which will be accurate within

0.5 percent. Under ordinary conditions of routine

testing, the errors probably do not exceed 1 percent.

The wiring diagram shown in figure 9 applies

also to the High-H permeameter if it is understood that the magnetizing coil, M, is on the pole

pieces instead of over the specimen.

c. Fahy Simplex Permeameter

For several years, the Fahy Simplex permeameter [12] has been in use in many laboratories for

routine magnetic testing. Since this permeameter

tends to give average values of the properties

of a nonuniform specimen, agreement with another

permeameter which includes only a relatively

short section in the test should be expected only

for a uniform specimen. Unless a specimen has

been checked for imiformity, it is safer to assume

that it is nonuniform, and lack of agreement

should not be interpreted as an ei'i'or of eithcM'

permeameter.

For checking other Faliy Simplex permeameters,

the Magnetic Measurements Section has cahbrat(>(l

one by reference to a stanchird pefmeanieter

using uniform bai's as standards. This instrument is used as a working st anda rd and constitutes

a i)ia('tical means of making the clieck.

19
Figure 12. Magnetic circuit of Fahy Simplex permeameter.

The magnetic circuit, of the Fahy Simplex

periBeameter is indicated in the sketch of figure 12. The yoke, Y, is made of laminated silicon sheet.

Two soft iron blocks, H, make contact with the

ends of the specimen. Clamps hold these blocks

and the specimen in place against the pole pieces

of the yoke as shown. The magnetizing winding

is wound on the yoke. The i>'-coil for measuring

the nuxgnetic induction has 100 turns uniformly

wound on a brass form which surrounds the

specimen and extends over its whole length

between the pole pieces. For determining the

magnetizing force, a unifonnly wound H-co\\ of

many turns on a straight nonmagnetic form

extends horizontally between the upper ends of

the //-blocks.

In oi'der to gain the advantages of "flip coils"

for the determination of magnetizing force,

especially for points on the hysteresis loop, the

NBS instrument was modified by providing a means of rotating the //-coils through 180° about

a vertical axis. The modified instrument is shown in figure 13. The //-blocks had to be

lengthened slightly so that the //-coil could clear

the magnetizing coil but experiment showed that

this did not affect tiie accuracy of the results.

As previously stated, the flip coil arrangement

inakes it possible to determine values of Ha on the

hysteresis loop with adequate sensitivity and to

repeat the observation without the necessity of

repeating the process of producing a symmetrically

cyclic condition for each repetition of the observation. It also provides a convenient and positive

indication of proper demagnetization. Demagnetization has been complete if for a very small

magnetizing force, the values of H are equal for

reversals with the magnetizing current in either

direction.

The Fahy Simplex permeameter is not an

absolute instrument. It requires calibration by

reference to an absolute instrument which is taken to be a standard; if it were not for the

inevitable magnetic leakage, the theory of the

instrument would be comparatively simple. The

Figure 13. Modified Fahy Simplex permeameter.

1 //-coil is assumed to indicate the difference of

| magnetic potential between the ends of the

//-blocks. These blocks then in effect transfer ' the ends of the coil to the ends of the specimen. I On account of leakage, however, the actual

situation is not quite so simple. Experiment ' has shown that if the actual value of area-turns , in the //-coil is used in calculating H, the value ' thus obtained is not correct.

The single-yoke arrangement leads to a nonuniform distribution of mduction both along the

length and across the section of the specimen.

Also, since the magnetizing coil is on the yoke

rather than on the specimen, some of the leakage

j flux is linked with the //-coil. The reluctance of | the //-blocks should also be taken into consideration. In view of all of the potential sources of

| error inherent in the design, it was somewhat [ surprising to find that a simple correction pro- [ portional to the observed magnetizing force

| would bring the results practically in line with | the results obtained with an absolute instrument

if uniform specimens are used in the intercom- ' parison. This correction is most conveniently

applied by assigning to the //-coil a value of

what might be called the "effective" area-turns

j which is somewhat different from the measured I value. It has been found that if the specimen i is laminated, the maximum number of strips for

which reasonable accuracy can be obtained is

| ten. The error is apparently a function of the

number of air gaps between the pole pieces and

the //-blocks. _i With so many factors involved, it is not feasible ! to give a precise estimate of the accuracy obtained but in general, under normal conditions,

j values of either B or H for normal induction may i, reasonably be expected to be accurate within 2

percent. For the determination of coercive force, | another phenomenon must be taken into con- ; sideration. It has been found that when the i average induction as indicated by the 5-coil is I zero, the B in the part of the specimen next to , the pole pieces has already reached a negative

value while the outer part next to the //-blocks is !

20
still positive. Since the 7?-blocks are in contact

with this outer part, the value of He will be low.

The error depends upon the slope of the hysteresis loop at the He point. If it were vertical,

there would be no error. As a rule, the slope is less and consequently the error is greater the

higher the value of He.

The Fahy Simplex permeameter has found

favor primarily on account of its easy manipulation and the requirement of only a single specimen.

Its accuracy is probably within the range of

uniformity of most magnetic materials.

The wiring diagram is like that of figure 9

except that coil I and resistor sh are omitted and

the magnetizing coil M is on the yoke instead of over the specimen.

5.5. Tests of Low-Permeability Materials

Materials having a permeability only slightly

in excess of unity are generally tested in a straight

solenoid. Since the intrinsic induction for such

materials is very low, the correction for selfdemagnetization is small and can be neglected

without appreciable error in the value of magnetizing force calculated in terms of the current.

In order to obtain a satisfactory degree of precision in the determination of the intrinsic induction it is necessary to balance out the direct

effect of the magnetizing field. This can be done

by connecting the secondary of a mutual inductor

of variable value in series-opposition with the

test coil which usually has several hundred turns

The primary of the inductor is connected in

series with the solenoid. The mutual mductor is adjusted so that, with no specimen in the testcoil, there is no deflection of the ballistic galvanomter upon reversal of the magnetizing current

The galvanometer can then be used at its maximum sensitivity. When a specimen is inserted

within the test coil and the magnetizing current

is reversed, the galvanometer deflection is proportional to the intrinsic induction. The galvanometer is calibrated by means of a standard

mutual inductor in the usual way.

In the Fahy Low-Mu permeameter [17] a somewhat different arrangement is employed. Two

similar test coils are used. The specimen is inserted in one coil and the other constitutes a compensating coil to balance out the effect of the

magnetizing force on the main test coil. The

compensating coil has a value of area-turns somewhat greater than that of the other coil. In order

to balance the system with no specimen present,

the compensating coil is shunted with a resistor

whose value is adjusted so that, with no specimen

in the test coil, no deflection of the galvanometer

results from a reversal of the magnetizing current.

Then when a specimen is inserted in the test coil

and the magnetizing current is reversed, the re- sulting deflection is proportional to the intrinsic

induction. The galvanometer is calibrated in the

usual way by means of a standard mutual inductor.

5.6. Magnetic Susceptibility

The measurement of magnetic susceptibility re- quires the use of much more sensitive apparatus

than is needed for the measurement of ferromagnetic properties. Just as in the measurement of

magnetic fields, there are only two basic methods

for the determination of magnetic susceptibility.

One is the measurement of the mmute mechanical

forces experienced by a body in a nonuniform

niagnetic field. The other is by means of induction methods. For precise measurements, the

force methods are more commonly used.

The principal methods in use by the Magnetic

Measurements Section are known as the Gouy

method [18], the Faraday method [19], and the

Thorpe and Senftle method [20].

TV

FiGUBE 14. Gouy apparatus.

The Gouy apparatus is illustrated by the diagram of figure 14. A cylindrical speciiiien, ,s, of

uniform cross section, A, is hung from a sensitive

balance with its axis vertical. The lower end is located in the uniform part of the magnetic field

between the poles, P, of a powerful electromagnet,

and usually above the center line of the pole

pieces. The specimen should be long enough to

bring its upper end into a much weaker field. Tlie

force due to the application of the magnetic field

is measured by the balance. The magnetic susceptibility is then calculated by using the equation

22

Transposing,

2T„J

" Note: In t!ic cliissical casom sy.stcm of units, the oqu'ition is iisn:illv uivon

as f=lcAiHi'—H2^-j/2. This oqiiution is (liincnsionally inlioinogonoo'ns l)nt gives the same numerical lesults as tlie oilier because in this system r„ is unity and there is no numerical distinction between li and //.

21
cgsem mksa

(rationalized)

^=volunie susceptibility

/=force dynes newtons

rm=magnetic constant 1 47rX10~^

^=area of specimen cm^

i?i= field at lower end gausses teslas

52=field at upper end gausses teslas.

The use of rationalized units yields values of

magnetic susceptibility which are 47r times the

values obtained by the use of unrationalized

units. (See pp. 4-5). The Magnetic Measurements Section generally uses the nuclear magnetic

resonance method (see pp. 12-13) for measuring Bi

and a pivoted magnet instrument for measuring

Bo. (In the classical cgsem system, it is customar}^

to measure B and call it H.) The Gouy apparatus

at NBS is equipped for measurements at temperatures as low as that of licjuid hydrogen.

The Faraday method is adapted to measure- ments of magnetic susceptibility of specimens too

small for the Gouy method. A small sample of

magnetically isotropic material experiences no

mechanical force when placed in a uniform magnetic field. However, if there is a gradient in the

field, a force will be experienced. In this case

mxBdB/dy^

r

Transposing,

mBdB/dy

where

cgsem mksa

(rationalized)

x==mass susceptibility (see pp. 5-6)

r —: magnetic constant 1 4xX10-'

: mechanical force denies newtons

m— mass grams kilograms

B= magnetic field gausses teslas

y= distance cm m.

Here as with the Gouy method, the values in a

rationalized s^-stem are 47r times those in an

unrationalized system.

Measurements with this method on an absolute

basis are attended with some difficulty. The

apparatus is generallj' calibrated by the use of

-3 The force is giycn as f=mxHdHidti when the classical cgsem system of units is used. This equation is dimensionally inhomogeneous but gives rise to no numerical error because r„ is unity and no distinction is made between B and H in the classical cgsem system.

standard samples of known susceptibility. The

standard must be of the same size and shape as the specimen to be tested and located in the same

position in the nonuniform field.

T

I FiGUEE 15. Vertical beam Faraday apparahis.

|

1 The apparatus is shown diagrammatically in j figure 15. The specimen, S, is mounted at the , lower end of a quartz beam, and a permanent magnet, M, is mounted near the upper end. The i beam is supported by a horizontal berylliumj copper wire near the midpoint; the specimen is ; carefully positioned between the pole pieces in

the region where the product of the field by the

field gradient is constant over the volume of the ; specimen. Measurements are made by applying '

a field and then restoring the beam to its original

position hj means of a torque exerted on the

permanent magnet by a current in the solenoid, u.

' The position of the beam is indicated by observing

the tip,T, with a telescope and scale. , The Thorpe and Senftle method, described by

Thorpe and Senftle [20], is generally used for ; measuring small samples of material. The method I is illustrated in the diagram of figure 16. A

quartz spring supports the specimen initially in a

position between the poles of the magnet and

slightly below the center of the pole faces. After

the deflection of the spring, due to the application

22
FiGUKE 16. Quartz Helix magnetic susceptibility balance.

of the field, has been observed for this position,

the magnet is lowered to a new position and

another observation of the deflection is made.

This procedure is repeated for several selected

positions of the magnet until there is no observable change in deflection when the magnet is moved to a lower position. From the proper

integration of the curve of displacement of the

sample versus the distance of the magnet from

the sample, the maximum value of the magnetic

field between the poles of the magnet, the mass of

the sample, and the elastic constant of the quartz

spring, it is possible to calculate the magnetic mass

susceptibility of the sample by the equation

'"'-'-'max

where

X=mass susceptibility

A=area under the curve

elastic constant of the quartz spring

magnetic constant

m=mass of the sample

5=the maximum field of the magnet.

Since

m=Kh/g

where

/!,= measured static deflection of the quartz

spring

and

g =acceleration due to gravity,

The induction methods most generally used are a-c bridge or balance methods and the vibration

magnetometer.^^ These methods involve the inducing of voltage in a coil as a result of changing

flux linkages due to the applied field or a position

change of the coil or sample. These methods

have the advantages that they use uniform magnetic fields and cover a larger range of susceptibilities than the force methods; however they

usually require a standard material for calibration

purposes.

5.7. Magnetic Standards

In view of the natiu'e of the magnetic units, it is obviously not feasible to realize them in concrete

form. The calibration of magnetic testing apparatus is carried out in terms of the electrical units by

the use of standard shunts, potentiometers (or

ammeters), and mutual inductors. The basic

standards are (1) a mutual inductor so designed

that its value can be calculated from its dimensions

(2) a standard resistor, and (3) a standard cell. These basic standards are used to calibrate working standards and these working standards in turn

are used for the calibration of the measuring circuits. For the intercomparison and standardization of permeameters it is necessary to make use

of carefully selected and prepared test speciniens

whose magnetic properties are accurately determined by some standard method. It may perhaps

be proper to refer to such test specimens as magnetic standards.

The preparation and maintenance of standards

of magnetic susceptibility present some difficult

problems. The material must be of high purity

(ferromagnetic impurities are particularly troublesome) and means must be provided to prevent

contamination during handling or storage. Questions of stability and temperature effects are also

important. Standards of susceptibility are requhed

for the calibration of apparatus with which it is difficult or impossible to obtain absolute results.

The Magnetic Measurements Section has a continuing program for the investigation of standard

materials such as water, benzene, nickel chloride,

and hydrated ferrous ammonium sulfate (Mohr's

salt) and the improvement of methods of preparations and measurement of standards specimens.

5.8. Limits of Accuracy

The problem of magnetic testing consists in

determining simultaneous values of magnetic

2' Masnctochcmistry—P. W. Solvvood Iiitciscicnco I'lil'lislioi's.

23 A Vibratinp Sample Mimiioloiiii'lor by M. V. Frederick—IRE Ti;ins- aption on Instrumentalion 1-9, No. 2 (Sept. 1960).

23
induction and magnetizing force. It is relatively

easy to obtain fairly accurate values of induction,

but the accurate determination of the corresponding magnetizing force is more difficult. It is only by the exercise of great care in the selection of

test specimens and manipulation of the testing

apparatus that an acciu'acy of 1 percent can be

attained. The influence of the quality and condition of the test specimen is of great importance,

especially in the standardization of permeameters

because inaccuracies really arising from the condition of the specimen itself should not be charged

to the testing apparatus.

5.9. Requirements of Standard Specimens

for D-C Permeameters

Specimens to be used as standards for the

calibration or intercomparison of permeameters

should be chosen and prepared with the following

points in view: (1) magnetic uniformity along

the length, (2) metallurgical stability, and (3)

uniformity of section.

If the specimen varies in permeability along

its length, errors are introduced in the measure- ments which cannot be calculated or eliminated

by compensation, and which may be of considerable magnitude. It is possible to have errors due to this cause alone which amount to 25

percent or more. Moreover, various methods are

sensitive to this influence in varying degrees.

It is obvious, therefore, that such specimens

should not be used for the intercomparison or standardization of testing apparatus. Various

methods for the determination of the degree of

uniformity of magnetic-test specimens have been

proposed [21], but probably the most satisfactory

one is to prepare a specimen much longer than

is required for the final form and to make measure- ments at suitable intervals along its length. If

the results of these measurements are in agreement, then the specimen is, from this pomt of

view, satisfactory to use as a standard.

It is well known that specimens of steel freshly

heat-treated are not metallurgically stable; that

is, changes in internal structure or condition may

go on for some time. These changes are accompanied by corresponding changes in magnetic

properties. It is necessary, therefore, to make

sure that specimens to be used as magnetic

standards are metallurgically stable. This can

be accomplished by either natural or artificial

aging.

It is quite obvious that irregularity in cross section along the length of a specimen would

have an effect similar to that of a variation in

magnetic permeability. For this reason, it is important that care should be used in preparing

the specimen to maintain a uniform cross section.

5.10. General Precautions

In the calibration and use of magnetic standards,

it is necessary to avoid (1) mechanical strain, (2)

variations in temperature, and (3) mechanical

vibration.

Mechanical strain influences the magnetic

properties of materials to a marked degree. It is important, therefore, in the calibration and use

of magnetic standards that they be clamped

without bending. The effect of bending is particularly noticeable in materials of high permeability and in the steep part of the magnetization

curve. The effect of variations in temperature is not

negligible [22], and care should be taken that

standards be not heated during the course of a

test. The temperature coefficient is not constant

and varies for different materials or even for the

same material with different heat treatments.

Mechanical vibration should be avoided in

magnetic testing. It has a tendency to increase

the apparent permeability and to decrease the

hysteresis. This is generally not a serious factor,

but for work of high accuracy, it should be considered and the specimens protected from ex- cessive vibration.

6. Tests With Alternating Currents

6.1. Core Loss and A-C Permeability at Power

Frequencies

Magnetic tests with alternating currents are extensively employed by producers and users of

magnetic core materials in connection with quality

control and for obtaining design data. These

tests are generally made by methods specifled by

the American Society for Testing Materials.

Since magnetic materials are continually being

improved and new and better methods of testing are being developed, the specifications require

frequent revision in which the Magnetic Measurements Section cooperates. For this reason, it is neither necessary nor desirable to give detailed

descriptions of the current standard methods.

The general principles are presented here but for

specific details, the reader is referred to the latest

Standards on Magnetic Materials issued by the

ASTM[23]._

The principal objects of testing with alternating

currents are to determine core loss, a-c permeability, and incremental permeability of laminated

magnetic core materials. The test specimens

usually consist of strips of flat-rolled material

assembled in the form of a square magnetic

circuit inserted in four solenoids which are permanently mounted on a suitable base. Each of

the solenoids has two uniformly distributed

windings. The corresponding windings of the

four coils are connected in series to form primary

and second windings having an equal number of

24
turns. The primaiy winding carries the magnetizing current. The secondaiy winding is used to

energize vohmeters and the voltage coil of a wattmeter (if used). A third winding may be

required in certain types of tests. The set of

coils mounted on a base is generally called an

Epstein frame.

Since flat-rolled core material has directional

properties, half of the specimen strips are generally

cut with their long dimension in the direction of

rolling and half in a direction at right angles to

the direction of rolling. Certain materials with

oriented grain structure may have the strips all cut in the direction of rolling. When the strips are cut "half and half" they are so assembled that

strips on opposite sides of the square are cut in

the same direction.

There are two principal types of testing methods

in which the Epstein frame is used, voltmeterwattmeter methods, and bridge methods.

a. Voltmeter-Wattmeter Methods

The basic diagram of connections for these

methods is shown in figure 17. The a-c source should deliver as nearly a sinusoidal voltage as

possible with a minimum amount of distortion

when fully loaded. The current is controlled

preferably by means of a suitable autotransformer

rather than by series reactance. Excessive re- sistance or inductance in the circuit causes an

undesirable amount of distortion in the wave

form. Connected in series with the primary

winding, P, of the test frame are: an anmieter, A,

of low internal impedance, the primary winding of

a calibrated mutual inductor, L^, the current coils

of a wattmeter, W, designed specially for measurements at very low power factors and the primary

winding of a compensating mutual inductor, L^c

(if used).

The secondary winding of the compensating

inductor, L^c (when used) is connected in series

opposition to the secondary winding, S, of the test frame. When the selector switch Sw is closed

downward, the rms-reading voltmeter, rms Vm,

the average-reading voltmeter,^*' Av Vm, and the

potential coil of the wattmeter, W, are connected

in parallel to the secondary winding S of the test frame through the secondary winding of the compensating inductor, Lmc- The 50-cm Epstein test requires a specimen consisting of 10 kg (22 lb) of

material cut into strips 50 cm (lO'^Ke in) long and

3 cm {V/U in.) wide. This relatively large sample

previously was required in order to obtain a fau^

average result for material which was not very uniform even throughout a single sheet. The strips are assembled in the test frame with butt joints at

the corners, which are clamped to maintain a low

magnetic reluctance at the joints. Improved

manufacturing techniques now permit the use of

much smaller samples and the 25-cm Epstein test^'' requiring only 2 kg (4.4 lb) is now standard.

28 This is an instrument whose moving system responds to the average

value of the rectified alternating current. " Tests are often made on smaller specimens but the 2 kg sample is stand- ard at present.

Sw

RMS

Vm Av. Vm

Figure 17. Diagram of connections for Epstein tests hy

the voltmeter-wattrneter methods at power frequencies.

In carrying out tests using the 25-cni Epstein

frame, a better joint at the corners than the butt

joint used in the 50-cm apparatus is required on

account of the shorter magnetic circuit. A doublelap joint has been adopted. This requires strips at

least 28 cm (IIK2 in.) long. Strips up to 50 cm

(IQ^Ke in.) long can be used if necessary. The

width of the strips is the same as in the 50-cm test,

i.e., 3 cm (l^fe in.).

The sample is first weighed and then inserted in

the test frame in four equal groups in such a way

that at each corner the strips of adjacent groups

successively overlap and groups at opposite sides

of the square are cut in the same direction. No

insulation other than the natural oxide is used

between strips except in the case of oxide-free material. The corners may be clamped to reduce the

magnetic reluctance but it must be done carefully so as not to introduce excessive mechanical strain

in the strips.

The apparatus is then connected to the a-c

source and the current is adjusted so that the

voltage of the secondary coil of the test frame as indicated by the average-reading voltmeter cor- responds to the desired maximum induction in the

specimen. This voltage is given by the equation

where

10«

£'ave= average voltage

Bn =maximum induction in gausses

A =cross-sectional area of the specimen,

cm^ = number of turns in secondary coU

/ =frequency in cycles per second

(If B is in teslas and a is in m^ the factor 10^ is not

needed.)

The cross-sectional area of the specimen is determined from the mass, density, and lengtli of the

strips

where

. m

^^4l5

^=area in cm^

m={]\Q mass in grams

I =length of a strip in cm

5 = density in g/cml

25
The density for most of the conventional materials is assumed from their chemical composition.

For other materials, the density must be determined experimentally. For silicon-iron alloys the

values range from 7.55 to 7.85 depending upon the

silicon content. (See table 4.) Densities of

nickel-iron alloys vary from 7.85 to 8.90. (See

table 5.)

Table 4. Silicon-iron alloys

Silicon content range Assumed density

Percent

0 to 0. 5 7. 85

0. 5 to 2.

7. 75

2, 0 to 3.

7. 65

3. 5 to 5.7. 55

Table 5. Iron-nickel alloys

determined from straight lines joining points give

Nickel Density

Percent glcm^

0 7. 85 30 8.00

50 8.26

80 8.64

100 8.90

After the frequency and voltage have been properly adjusted, the wattmeter is read. The value

obtained includes not only the total loss in the

core but also the losses in the instruments con- nected to the secondary winding of the test frame.

The loss in each instrument is &/R where E is the

rms voltage and R is the ohmic resistance of the

instrument.

If the wave-form distortion as indicated by the

form factor,^, differs from 1.111 (form factor of a

sine wave) by more than 1 percent, it is necessary

to make a correction to the observed value of the

core loss to account for the fact that whereas the

hysteresis component of the total loss is a function

of the average voltage, the eddy-current component is a function of the rms voltage [24].

If the cross-sectional area of the specimen is much less than that of the secondary coil of the

test frame, a correction must be made for the extra

induced voltage due to the air flux. This correc- tion can be calculated from the equation

E„

where

4:NfT^H,ia-A)

10»

£0=average voltage due to air flux

A7^= number of turns in secondary coil

/=frequency in cycles per second

magnetic constant=l

a =area of secondary coil in cm^

^=area of specimen in cm^

Hp=pesik magnetizing force in oersteds.

If the mksa system of units is emploj^ed, the equation becomes

Ea=4.NJV^Hj,(a-A)

in which

£"0= average voltage due to air flux

r^=47rX10-^

Hp=peak magnetizing force in amp-turns/m

and areas are in m^.

In the cgs system, the peak magnetizing force

is calculated by using the equation

OAttNIj,

la where

^Z'p=peak value of magnetizing

force in oersteds

A''= number of turns in primary winding

/p=peak current, amperes

Za= assumed length of the magnetic circuit =94

cm.

In the mksa system, Hj, is in ampere-turns/

meter and la is in meters (0.94 meter) and the

equation is Up——J—

The peak value of the magnetizing force. Hp, is determined in terms of the peak current and the

number of turns per unit length in the magnetizing

wmdmg, P. The peak current is proportional to

the average voltage induced in the secondary

winding of the mutual inductor, Lm

Ip —KEaveThe factor K is determined b}^ observing the

average voltage induced by a sinusoidal current

of known value.

The a-c permeability is taken to be the ratio of

the maximum induction to the peak value of

magnetizing force. It is convenient to compensate for the extra voltage due to air flux by means of the compensating

mutual inductor {Lmc in the diagram) . The mutual

inductance is adjusted to be equal to that between

the primary and secondary windings of the test frame (no specimen inserted). If this is done, the

indicated induction is the intrinsic induction, Bt,

in the specimen.

The specific core loss is calculated by dividing

the corrected value of total watts by the "active

weight" of the specimen. The active weight is

mil

where

mi =active weight in kg

m=weight in kg =assumed length of magnetic circuit = length of strips.

= 94 cm

26
b. Bridge Methods

Generally, core loss and a-c permeability are determined by the voltmeter-wattmeter method.

In many cases, however, there are certain advantages, such as increased sensitivity and greater

frequency range, in making these measurements

by a bridge method. For measurements at low

inductions (not over 1,000 gausses or 0.10 tesla)

and at high frequencies, the bridge methods have

been used successfully for several years. More

recently, however, bridge circuits have been developed by which measurements may be made at

higher inductions. The ASTM [23] has approved

as standard a modified Hay bridge for use in

measurements at inductions up to 10 or 12 kilogausses in nonoriented steels or 16 to 18 kilogausses

in oriented silicon steels. For measurement at

higher inductions, the distortion in the wave form

of the exciting currents is considerable and it has

been found necessar}^ to use special techniques

[25] in order to obtain accurate results with bridge

methods.

Figure 18 is a diagram of a modified Hay bridge

currently approved as standard by the ASTM

[23]. The assumed equivalent impedance of the

coil containing the test specimen is shown in the

diagram at the right. The inductance of the coil

alone without the specimen, Ly,, and its resistance,

Bw, are considered to be in series as shown. They

are balanced by the capacitance C4 and the resistance respectively. Ordinarily the inductance

of the coil alone is so small that it is negligible and

C'y, need not be used.

The apparent additional resistance, ^i, due to

the core loss and the inductance, Zi, due to the

permeability of the test material are considered

to be in parallel. They are balanced by the

resistance, Rd, and the capacitance Ct,. Ra and Rc

are fixed resistors whose product is equal to the

product of the impedances of the other two arms

of the bridge. Since Rc carries the total exciting

current it must have such current-carrying capacity that it will not be heated excessively.

Z> is a detector, tuned to the fundamental frequency of the voltage supply. This detector

should have a high impedance and high sensitivity

to the fundamental frequency. Previously, vibration galvanometers have been employed for this

purpose, but they have been almost entirely

replaced by electronic devices of various kinds.

The a-c source is connected to the bridge

through an isolating transformer. In the arrangement recommended by the ASTM, this transformer has a tapped secondary for convenience in

selecting the proper range of voltage to be applied.

The primary is fed from an autotransformer con- nected to the generator. This provides the fine

control of the applied voltage. Other arrangements may be employed provided that there is isolation between the source and the bridge and

the series resistance is not used to control the

current. Resistance tends to distort the wave

form of the induced voltage and may lead to

excessive errors. [25]

For incremental values, the d-c magnetizing

current may be supplied to the secondary winding,

^^2. The average a-c voltage is then read across the primary winding, A^i. The IR drop in this

winding causes a slight error but this is usually

negligible. The d-c source must furnish a steady

current. A storage batter}^ is ordinarily the best

Equivalent Impedance

of Test Frame

Figure 18. ModiHed Hay Bridge.

27
source as rectified a-c requires a great deal of

filtering. The d-c circuit contains a series inductor

of at least 10 h when carrying maximum current.

This is to limit the a-c current in the d-c circuit

to a negligible value.

The maximum induction in the specimen is indicated by a voltmeter connected to the secondary winding A''2 of the test frame. The voltmeter,

Vave, indicates the average voltage. The maximum induction in terms of average voltage in cgs

units is

E^y,=4. BANJXIOwhere

-Eave= average volts

5=maximum induction, gausses (if the air-flux

compensating inductor is used, B is the

intrinsic induction, Bi)

yl=area of specimen, cm^

A7"=number of turns in winding

/=frequency, cycles per second.

In mksa units,

i?= induction in teslas

^=area in m^

and the factor 10~^ is omitted. The other factors

remain the same. The rms value of the exciting current can be

determined by connecting the rms-reading voltmeter across the resistor Rc as indicated.

As in d-c testing, the first step, especiallj^ if measm'ements are to be made at low values of

induction, is to demagnetize the specimen. This

is accomplished by first setting switch -$'2 so as to

take Rc out of the circuit and opening switch S3 and

then with switch Si closed, setting the a-c source

to zero and connecting it to the bridge. The

voltage is then raised until the average voltmeter

indicates that a maximum induction of the order

of 14 kilogausses has been reached. The current

is then gradually and steadily decreased until the

indicated induction is somewhat lower than the

lowest at which a measurement is to be made. If

this pohit is below about 1,000 gausses (0.100

teslas) it will be necessary to take into account the

drift in values which takes place immediately

after demagnetization. This drift is rapid during

the first few seconds but the rate of change

decreases as time goes on. For this reason, if reproducible results are to be obtained, a standard

procedure must be followed. For the best

reproducibility, it is necessary to wait several

hours after demagnetization before making the

test. This would be very inconvenient in most

2^ According to ASTM specifleations, the scale of this instrument is cali- brated in terms of average volts multiplied by 1.111, the form factor of a pure

sine wave. This may be confusing in some instances, especially when an

rms-reading voltmeter and average-reading voltmeter are used together to determine the form factor.

cases. Fortunately, it has been found that a

satisfactory degree of agreement can be obtained

if balance is reached about 3 min after demagnetization. If the test induction is higher than 1,000

gausses (0.100 teslas) the drift is not observed.

Rw and Cw (if used) are preset according to the

equations

-r, , RaRc

R

and

w

Cw— Lw (C in farads).

RaRc

These balance the resistance, Rw, and the inductance, Lw, of the test winding, N (specimen not

inserted) , thus avoiding the necessity of calculating

the effect of Rw and LwSince Rc must carry the total exciting current

and the voltage drop across it must be less than

10 percent of that across the test winding to avoid

excessive distortion of the wave form, its proper

value will depend upon the range of inductions

at which measurements are to be made. Ordinarily, 1,000 ohms is used for the lowest range

(10 to 50 gausses), 100 ohms is used for the

medium range (50 to 500 gausses) and 10 ohms

for the higher range (500 to 10,000 gausses). The

resistor Ra may be set so as to make permeability

direct-reading in terms of d or core loss may be

direct-reading in terms of Rt,. Directions for

setting may be found in the ASTM specifications.

Readings are made as follows. With switch S2

set to connect Rc into the circuit and switches

Si, S3, and »S'4 closed, the applied voltage is raised

to the point at which the desired induction as indicated by the average-reading voltmeter is reached. Balance is then obtained by successively

adjusting R^ and until the detector shows a minimum reading. The balance equations are

as follows

and

where

Li =inductance due to the permeability of the

test material, henries;

and

7?i=increased apparent resistance due to core loss

in the test material, ohms.

In the cgs system

and since

10«li

Li =RaRcC'b

28
it follows that

In these equations

fe= effective a-c permeability of the test

material

Zi =assumed effective length of the magnetic

circuit =94 cm

A^i =number of turns in the primary winding.

In the mksa system, the equation is RaRcCill

where

Zi =assumed effective length in meters =0.94

and

.A=area in square meters.

Areas are determined from the length, mass, and

density of the strips.

Core loss, Pc, is calculated from the observed

values of Ri and Ei

Rl RaRc

The specific core loss f

is

p —±_£

nil

where mi is the active mass as indicated above.

Reactive or quadrature power is

Pn _ E,'^ E,'

OiLi wC\RaRc

the unit is called the var. The specific value is Pg/nii where mi is the effective mass, determined

as shown above.

Incremental values of permeability and core

loss are determined in the order of increasingvalues of biasing magnetizing force. Direct

current is supplied to the secondary winding and

adjusted to the required value and reversed several

times to establish a cyclic condition in the specimen. The a-c is then applied and the bridge is adjusted and readings taken as described above.

The d-c magnetizing force is calculated as follows

In the cgs system, the biasing or d-c magnetizing

force is

where

ZZ^6=biasing magnetizing force, oersteds

Ia-c =d-c current, amperes

/i =assumed length of the magnetic circuit, cm.

In the mksa system

where

and

Ia-c= d-c current, amperes

li is in meters

Ht, is then ampere-turns per meter.

For incremental tests, the average-reading voltmeter is connected to the primary winding A^^i. For this test values of incremental induction, Ba

are limited to not more than 1,000 gausses (0.1000

tesla).

6.2. A-C Measurements at Higher Than Power

Frequencies

Magnetic materials have been developed which

are particularly useful at high frequencies on

account of their extremely high electrical resist- ance. They are ceramic materials called ferrites.

Magnetic tests of these materials are usually made

on specimens in the form of small rings. Although

the Hay bridge can be adapted to make measure- ments at the higher frequencies, it has the disadvantage that each ring must be wound

individually. In order to obviate this difficulty,

Haas [26] has developed a radiofrequency

permeameter similar in principle to an instrument

developed earlier for power frequencies by Kelsall

[27]. It is shown diagrammatically in figure 19.

The radiofrequency permeameter consists es- sentially of a transformer. The primary is wound

on a powdered ring core. The secondary consists

of a central conducting tube over which the ring

specimen can be placed. The one-turn secondary

is completed by a coaxial outside cylinder and end

plates which form a single short-circuited turn

which is linked with both the primary core and the

specimen as shown in the equivalent circuit. The

top plate is removable for insertion of the test specimen. Measurements are made of the input

Cover Plate

I

, . yyI

Specimen

• Primary Core

Primary Winding

Primary Core

Primary Winding

Single Turn Secondary

— Cover Plate

Specimen

Figure 19. Radio frequsncy pcnneameter.

29
impedance of the primary winding with no

specimen and the secondary open-circuited, with

the secondary circuit closed but no specimen, and

with the secondary circuit closed and a specimen

in place. These measurements can be made with

a 9-meter or an impedance bridge. From the

values thus obtained, initial values of complex

permeability and losses can be computed. Details

of the measurements and computations can be

obtained from the original paper [26].

7. Typical Magnetic Properties of Materials

Magnetic materials are used under a great

variety of conditions both for cores and for permanent magnets. In order to meet many of these

special requirements, it is frequently necessary to

"tailor make" the material. This may require

"special" alloying elements, heat-treating temperatures and procedure, and special mechanical

working. In general, however, the metallic magnetic materials employed in practice are alloys

mainly composed of one or more of the ferromagnetic metals, iron, nickel, and cobalt. Other

elements are always present, either as undesired

impurities or as alloying elements added for the

purpose of producing certain desired characteristics. In figure 20 are shown typical normal

induction curves of annealed samples of iron,

nickel, and cobalt of comparatively high purity.

These curves are given only for the purpose of

general comparison and should not be considered

as representing critical values. Small variations

in the degree of pm-ity or in the annealing procedure lead to substantial differences in normal

induction.

Magnetic materials employed in commercial

practice may be considered under the following

six classifications: (1) solid core materials; (2)

electrical sheet or strip; (3) special alloys; (4)

ferrites; (5) permanent-magnet materials; and

(6) feebly magnetic materials. In view of the

rapid and continued progress in the development

of magnetic materials, it is only feasible to give

data characteristic of several of the materials

commercially available at present. These data

indicate merely the range of properties obtainable

20

to 15

<O

m

CO

If

Nl

50 100 OERSTEDS

150 200

FiGUEE 20. Typical norml induction curves of annealed

samples of iron, nickel and cobalt.

in the various classes of material and should not

be considered as critical, since considerable variation from these values will be found in practice.

7.1. Solid Core Materials

These materials are used for the cores of directcurrent electromagnets, relays, field frames of

d-c machines, etc. The principal requirement is high permeability particularly at relatively high

inductions. For the majority of uses, it is desirable that the coercive force and hysteresis be

low. The principal materials employed are soft

iron, low-carbon steel, cast iron, and an alloy of

approximately 49 percent of cobalt, 49 percent

of iron, and 2 percent of vanadium known as Permendur or Supermendur. Permendur is characterized by very high permeability in the upper

part of the normal induction curve and a saturation

induction approximately 10 percent greater than

that of pure iron. Its cost is relatively high,

however, and its use is limited in general to pole

tips in which a very high induction is required.

Several varieties of soft iron are available, such as Armco iron, Norway iron, and Swedish charcoal

iron. These irons are especially refined to reduce

impurities and to make as pure iron as is commercially feasible. A typical composition is 99.91

percent of iron, 0.02 percent of carbon, with small

percentages of manganese, phosphorous, and

sulfur. Low-carbon steel should not have more

than 0.0 to 0.2 percent carbon and should contain

only the usual small amounts of the ordinary

impurities. Cast iron has a relatively low permeability and is used principally in field frames

when cost is of primary importance and extra

weight is not objectionable. Cast iron is high in

carbon (about 3%) and also contains about 3

percent of silicon and varying percentages of

phosphorous, manganese, and sulfur.

The best magnetic properties for these materials

are obtained by a suitable annealing treatment

after machining and fabrication processes have

been completed. The properties of cast iron can be greatly improved by malleabilizing, a process

that converts a large part of the carbon to the

amorphous form.

Typical normal induction curves for solid core materials are given in figure 21.

7.2. Electrical Sheet and Strip

The term electrical sheet (or strip) is commercially used to designate iron-silicon alloys

produced in sheet or strip form and used as core

30
25

20

_l

5

0

Fe1;o

SOFT

CAST

RON

STEEL

MALLEI CAST 1 BLE RON

-"^ CAST 1 RON

Y

0 50 100 150 200

H, OERSTEDS

Figure 21. Typical normal induction curves for solid core materials.

materials in alternating-current apparatus such

as transformers, motors, electromagnets, or relays.

The principal requirements are high permeability,

low hysteresis, and high electrical resistivity. The

several grades differ mainly with respect to their

silicon content, which ranges from 0.5 percent to

approximately 5 percent. Alloys containing the

higher percentages of silicon are practically nonaging; that is, the permeability and losses do not

change appreciably with time. The required

magnetic properties are produced by annealing.

By a suitable combination of cold-rolling and

heat treatment, electrical sheet may be produced

in which the majority of the crystals are given a favorable orientation. Such material has considerably better magnetic properties in the preferred

direction than ordinary grades, their maximum

permeability is approximately twice as high and

they have much lower core losses combined with

higher permeability at high induction than

ordinary grades. Figure 22 shows typical normal

induction curves for two grades of electrical sheet

and oriented-grain material. The improvement

in the oriented-grain material is particularly

conspicuous in the upper part of the normal

induction curve. The different grades of electrical sheet and strip are usually sold on the basis of guaranteed maximum values of total core loss, as determined in

accordance with the specifications of the American

Society for Testing Materials [23]. The common

designations of the various grades are armature,

electrical, motor, dynamo, and transformer. The

transformer grades are further subdivided into

classes denoted by numerals corresponding to the

core loss under standard conditions. Armature,

electrical, and motor grades are used principally

in small motors, a-c magnets and starting trans20

CD 5

ORIENTED GRAIhJ

LOW SILICON

HIGH S LI C 0 N

0 5 10 15 20

H, OERSTEDS

Figure 22. Typical normal induction curves for electrical

sheet.

formers. The dynamo grade is used in highefficiency rotating machines and small transformers. The transformer grades are used in

power and radio transformers.

7.3. Special-Purpose Materials

For certain applications, special alloys and other

materials have been developed which, after proper

fabrication and heat treatment, have superior

properties in certain ranges of magnetization. For

instance, alloys of nickel and iron with possible

small percentages of molybdenum or chromium

have very high values of initial and maximum

permeability. Alloys of this class which may

have from 70 to 80 percent of nickel are called

Permalloys. Special attention to the purity of

the constituents, the manufacture, fabrication, and

heat treatment has resulted in an alloy of nickel,

iron, molybdenum, and manganese that has a maximum permeability greater than one million.

This alloy when commercially prepared and rolled

into thin tapes (0.001 to 0.004 in. thick) has a maximum d-c permeability between 300,000 and

900,000. An alloy of 50 percent nickel and 50

percent iron is called Hipernik. Another alloy

having a small percentage of copper in its composition is called Mumetal. The characteristics of

these alloys differ in detail but in general they have

high initial and maximum permeability, low

hysteresis, and low saturation values. The alloy,

Supermendur, of 49 percent of iron, 49 percent of

cobalt and 2 percent of vanadium has high

permeability which persists at higher values of

induction than the nickel-iron allo3^s. Typical permeability curves for several specialpurpose alloys are given in figure 23 and figure 24.

A certain alloy of nickel, cobalt, and iron after

suitable lieat treatment has very nearly constant

permeability for inductions below 1,000 gausses

and is called Perminvar. The 50-50- nickel- iron

31
125000

100000

>-t 75000

CL

25000

\ RMALLOY

H 1 PE R N 1

>v MUM E TAL

0 2500 5000 7500 10000

B, GAUSSES

Figure 23. Typical permeability curves for special purpose

alloys I.

alloy can also be heat-treated so as to have similar

characteristics.

Many of the above described alloys are rolled

into thin tape (as thin as 0.0001 in.) and spirally

wound cores are prepared from the tape. This

permits the designer to make use of their directional properties as well as to use them at much

higher frequencies by decreasing eddy-current

effects.

Another series of magnetic alloys of copper,

nickel, and iron is temperature-sensitive having an

approximately linear relation between permeability and temperature. These are called Thermalloys. The principal use is in the compensation of

watt-hour meters for temperature variations.

They are also used in certain types of thermal

relays.

Although chemical composition and impurities

are very important in the preparation of a magnetic alloy, experience has shown that with the

same chemical composition a wide variety of

magnetic properties can be obtained by varying

the mechanical working and type of heat treatment. This is very strildng in the nickel-iron and

iron-silicon alloys and has led to the development

of materials having a practically rectangular

hysteresis loop. These are of great importance in

the field of electronics.

7.4. Ferrites

Ferrites are nonmetallic ceramic materials

whose extraordinarily high electrical resistivity is especially useful for high-frequency" applications.

They are finding increasing use in applications

such as electronic computers, antenna rods,

isolators, and magneto-strictive devices. They

are made of iron oxide combined with certain biFiGUKE 24. Typical permeability curves for special purpose I alloys II. I

valent oxides, hydroxides, or carbonates of metals

| such as manganese, cobalt, nickel, copper, zinc, or , magnesium. The process of manufacture is sim- ] ilar to that of other high-grade ceramic materials,

j The powdered materials, which must be of high

| purity and proper particle size, are mixed in | suitable proportions, pressed or extruded to the

desired shapes, and fired. This procedure produces

j chemical compounds of the metallic oxides. , These materials are often called "soft" ferrites i to distinguish them from certain ceramic materials

used for the manufacture of permanent magnets.

In common with other ceramics, the}" are mechan- I ically hard and brittle and require special tools for

cutting or grinding. Also, since they require no

| critical materials, ihey are relatively low in cost.

| Although the saturation inductioii of the soft

j ferrites is not high, this is not important because ! they are generally used at low inductions. Their '

relative initial permeabilities (100 to 1,500) are i, very good for the high frequencies involved. The I principal disadvantage of the ferrites is their low ; Curie points which range from 100 to 500 °C.

j This is important if they are to operate at temperj atures much higher than room temperature.

Typical magnetic properties of some ferrites at

| room temperature are shown in figure 25. In

figure 26 is shown the temperature dependence of ! magnesium-manganese ferrite.

32
m" 2000

1 \ \ \ r

FERRITES

6 8 10 H , oersteds Figure 25. Typical normal induction curves for "soft"

ferrites.

7.5. Permanent-Magnet Materials

Although it is possible to make permanent

magnets of almost any kind of steel that is capable

of being hardened hy heat treatment, it is best to use materials especially produced for the purpose.

Magnets made from other types of material are

likely to be inferior in quality or unnecessarily

expensive. Before the development of the special

magnet steels, magnets were generally made of

plain high-carbon tool steel. This type of steel

is relatively inexpensive, but its magnetic properties are so greatly inferior to those of the special

steels that now it is practically never used for

making permanent magnets.

Permanent-magnet materials may be grouped

in five classes as follows: (a) Quench-hardened

alloys; (b) precipitation-hardened alloys; (c)

work-hardened materials; (d) ceramics; and (e)

iron-powder compacts. Figure 27 shows typical

demagnetization curves for several permanentmagnet materials.

a. Quench-Hardened Alloys

Tungsten, chromium, and cobalt magnet steels

have been in use for many years. Prior to the

first world war, tungsten steel was the standard

high-grade permanent-magnet material. The

optimum tungsten content is between 5 and 6 percent, with about 0.6 percent of carbon. During

World War I, when tungsten was scarce, chromium

magnet steel was developed and extensively used

in this country. There are two principal grades,

one containing about 1 percent of chromium and

0.6 percent of carbon, and the other containing

about 3.5 percent of chromium and 0.9 percent of

carbon. The 3.5-percent chromium steel is used

in many applications. Shortly after World War

10 H, oersteds Figure 26. Temperature dependence of a magnesium-manganese ferrite.

I, the Japanese metallurgist Honda announced the

development of a new permanent-magnet steel

having cobalt as the principal alloying element,

which he named KS magnet steel. This steel also

contained substantial percentages of tungsten,

chromium, and molybdenum. The coercive force

of this material is about four times as great as that

of the tungsten or chromium magnet steels. This

development stimulated further investigations

which led to the commercial production of several

types of cobalt magnet steel having various percentages of cobalt. High-cobalt magnet steels

have from 35 to 41 percent of cobalt, and lowcobalt steels have from 8 to 9 percent. These

steels also have tungsten and chromium in addition to the cobalt. An intermediate cobalt steel

has 17 percent of cobalt and about 9 percent of

chromium. Tungsten is sometimes substituted

for part of the chromium.

The quench-hardened alloys can be forged and

machined from the ingot.

b. Precipitation-Hardening Alloys

The most important permanent-magnet materials are of the precipitation-hardening variety.

This group includes the Alnico, Cunife, Cunico,

and Vicalloy. The process of hardening in these

alloys is related to the change from a single phase

at high temperature into two new phases when the

temperature is lowered beyond a certain value.

The fact that high values of coercive force can be

obtained with alloys containing no carbon was

anounced in 1932 by Seljesater and Rogers [28]

in the United States, Koster [29] in Germany, and

Mishiina [30] in Japan. These precipitationhardening permanent-magnet alloys contained

aluminum, nickel, and iron. Although the residual induction was relatively low, the coercive force

33
was so high, about 475 oersteds, that new applications of permanent magnets were made possible.

Further investigation showed that the addition of

cobalt to the alummum, nickel, and iron could

increase both the residual induction and coercive

force. There are more than twenty different commercial varieties called Alnico having coercive

force values ranging from 400 to 1,100 oersteds

and maximum energy products from 1.2X10^ to

approximately 7 X lO** gauss-oersteds. The Al-NiCo-Fe alloys are very hard and brittle, so that they

cannot be formed by the usual methods of forging

and machining but must be either cast or molded

in powder form and then sintered. Final finishing

is done by grinding.

Other alloys that belong to the precipitationhardening group, however, are unusual for high

coercive force permanent-magnet material in that

they are so ductile that they can be formed readily

by rolling or drawing and can be drawn to fine

wires before the final heat treatment [31]. Cunife, Cunico, Silmanal, and Vicalloy are alloys of this

type.

The platinum alloys have very high values of

coercive force but their low residual induction and

high cost limit their usefulness.

c. Work-Hardened Alloys

Several ordinarily "nonmagnetic" alloys of iron

may become ferromagnetic after cold working due

to a phase change in the material. Stainless steel

(18% chromium, 8% nickel) is "nonmagnetic" at

room temperature after being rapidly cooled from

1,200 °C in the usual process of manufacture.

However, if it is hardened by cold working such as

34
drawing through a reducing die it may develop

properties such that it makes an acceptable permanent-magnet material at room temperature. If

this work-hardened alloy is then reheated to a high temperature and cooled slowly it regains its

original nonmagnetic condition at room temperature. Another alloy that shows this property

contains 45 percent iron, 15 percent Ni, and 40

percent Cu. Nesbitt [32] has measured a co- ercive force of 240 oersteds and a residual induction

of 4,400 gausses in wire of this composition which

after quenching from 1,000 °C, was then cold

drawn from 0.026 to 0.006 in. Increasing the

percentage of iron to 60 percent, decreasing the

percentage of copper to 25 percent, with 15 percent nickel produced an alloy that after similar

treatment as above resulted in a coercive force of

170 oersteds and residual induction of 11,000

gausses.

d. Ceramic Magnet Materials

A commercial development in permanent-magnet materials which is increasing in importance

each year is the barium ferrite or ceramic permanent-magnet material. This is a chemical compound and has mechanical characteristics similar

to other ceramics. They are hard, brittle, have

a lower density than metals, and extremely high

electrical resistivity. The basic ingredients are barium carbonate and iron oxide. These materials in powdered form are compressed in dies

under high pressure to the required shape. This

compacted material is then sintered at a high

temperature. This process produces a material

which has an He of approximately 2,000 oersteds, a B, of approximately 2,000 gausses, and a demagnetization curve which is practically a straight

line. Further improvements in ceramic materials

have resulted in a higlily-oriented barium-iron

oxide whose magnetic properties, on a weight basis, are almost equal to those of Alnico V. The co- ercive force is approximately 2,000 oersteds, the

residual induction 4,000 gausses, and the energy

product is 3.5 times that of the unoriented variety.

At right angles to the direction of grain orientation, however, this material exhibits negligible

permanent-magnet properties and has a permeability of only approximately 1.0.

e. Powder Magnets

Although pure iron is usually regarded as a

high-permeability or "magnetically soft" material

yet theory has predicted and experiments have

proved that compacts of pure iron powders may

produce very good permanent magnets. Powder

magnets have been produced of iron and iron

alloys (such as 70% iron and 30% cobalt) (Permet)

with particle size of about 10"^ cm diameter with

He up to 500 oersteds and energy product of

1.5X10® gauss-oersteds. The permanent-magnet

properties result from the discrete small particles

of a single phase instead of from the presence of

two or more phases as in most other metallic

permanent-magnet material. Further experimental work with particle size and shape and processes

of manufacture have produced, in the laboratory,

magnets with energy products comparable to

those of Alnico V and theoretical considerations

predict even higher values.

Manganese-bismuth permanent magnets also

belong to this group. This material is an anisotropic aggregate of crystals of the intermetallic

compound manganese bismuthide (Mn Bi) and is a product of powder metallurgy. Manganese

bismuthide is prepared from the chemical action

between molten bismuth and powdered manganese

when heated to approximately 700 °C in an inert

atmosphere of argon or helium. Cooling is ac- complished in such a manner as to produce

ciystallization of the compound. Laboratoryproduced material may have a residual induction

of approximately 4,800 gausses and a coercive

force of 3,600 oersteds with energy product values

as high as 5X10® gauss-oersteds.

Powder metallurgy has also produced sintered

Alnico magnets. These magnets have greater

mechanical strength and more uniform magnetic

properties than the cast variety at the expense of a slight decrease in the magnetic properties.

Magnet materials prepared from metal oxides

such as cobalt ferrites and Vectolite have been

made and used for many years; however, they

have been practically superseded by the barium

ferrites.

7.6. Feebly Magnetic Materials

It is occasionally desirable to use metallic

materials for tools or parts of equipment which

require practically nonmagnetic materials. Oxygen-free, high-conductivity copper, copperberyllium alloy, and pure aluminum are often

used where mechanical strength is not required.

Aluminum-bronze, nickel-copper, stainless steels,

and manganese steels can be used if a permeability not exceeding 1.10 is permissible. In

using such a material, it should be kept in mind

that even when the bulk material is sufficiently

nonmagnetic, mechanical working, surface con- tamination or temperature effects may make it unsatisfactory.

8. References

[1] Gray, Absolute measurements in electricity and magnetism, 2d Ed. p. 535, MacMillan Co., London

(1921).

[2] George S. Smith, Use of bismuth bridge magnetic

fluxmeter for ac fields, Trans AIEE 58, p. 52 (1939).

George S. Smith, A new magnetic fluxmeter, Trans

AIEE 56, p. 441 (1937).

[3] A. Koepsel, Apparat zur bestimmung der magnetischen eigenschaften des eisens in absoluten mass und director ablesung, ETZ. 15, p. 214 (Apr. 12,

1894). C. W. Burrows, An experimental study of the koci)scl

permeameter, BS Sci. Pap. 11, 101 (1914) S228.

35
[4] R.. B. Treat and J. W. Esterline, A new magnetic

testing apparatus, Elec. World 30, 696 (1897).

[5] H. E. J. G. Du Bois, Magnetic circuits and their

measurements, Electrician 27, 634 (1891).

[6] E. Hughes, ' A magnetic bridge for testing straight

specimens, Proc. Phys. Soc. (London) 37, 233

(1925).

[7] R. V. Picou, Permeametre universal, Bui. Soc. Int. des Elec. [2] 2, 828, (1902).

[8] A Iliovici, Sur un nouveau permeametre universal,

Bui. Soc. Int. des. Elec. [3] 3, 581 (1913).

[9] Y. Niwa, A null method for testing magnetic properties of materials, Researches Electrotech. Lab.

(Tokyo) No. 142 (1924).

[10] C. W. Burrows, The determination of the magnetic

induction in straight bars, Bui. BS 6, 31 (1909)

S117.

[11] R. L. Sanford and P. H. Winter, A permeameter for magnetic testing at magnetizing forces up to 300

cersteds, J. Research NBS, 45, (Julv, 1950)

RP2109.

[12] F. P. Fahv, A permeameter for general magnetic

analysis, "Chem. and Met. Eng., 19, 339 (1918). R. L. Sanford, Performance of the Fahv simplex per- meameter, BS J. Research 4, 703 (1930) RP174.

[13] R. L. Sanford and E. G. Bennett, An apparatus for magnetic testing at magnetizing forces up to 5,000 oersteds, J. Research NBS 23, 415 (1939)

RP1242.

[14] C. R. Mann, Phvs. Rev. 3, 359 (1896).

[15] H. Du Bois, Wied Ann. 7, 942 (1902).

[16] C. L. B. Shuddemagen, Proc. Am. Acad. Arts Sci. 43,

185, (1907).

[17] The Fahy low-mu permeameter for measuring low

permeabilitv, Iron Age 130, 330 (1932).

[18] L. G. Gouy, Compt. rend. 109, 935 (1889).

[19] M. Faraday, Experimental researches Vol. Ill,

Taylor and Francis, London, pp. 27 and 497 (1855).

[20] Arthur Thorpe and Frank E. Senftle, Absolute method

of measuring magnetic susceptibility. Rev. Sci. Inst. 30, No. 11, 1006-1008, (Nov. 1959).

[21] R. L. Sanford, Determination of the degree of uni- i formity of bars for magnetic standards, Bui. BS ! 14, 1 (1916) S295.

I [22] R. L. Sanford, Temperature coefficient of magnetic ; permeability within the working range, Bui. BS 12, '

1 (1915) S245.

[23] See latest edition ASTM Standards—Metals—Test

Methods.

[24] G. Camilli, A flux voltmeter for magnetic tests, Trans- i actions AIEE XLV, pp. 721-728 (1926). ! [25] I. L. Cooter and W. P. Harris, Investigation of an , alternating-current bridge for the measurement of core losses in ferromagnetic materials at high flux ' densities, J. Research NBS 57, No. 2, (Aug. 1956) i RP 2699. I W. P. Harris and I. L. Cooter, Improved bridge I method for the measurement of core losses in ferroj magnetic materials at high flux densities, J. Re- i search NBS 60, No. 5, (May, 1958) RP2865.

j [26] Peter H. Haas, a radio-frequency permeameter, J. | Research NBS 51, No. 5, (Nov. 1953) RP2454. I [27] G. A. Kelsall, Permeameter for alternating-current | measurements at small magnetizing forces:, J. Opt. I Soc. Am. and Rev. Sci. Instr. 8 (Feb., 1924). I

[28] K. S. Seljesater and B. A. Rogers, Magnetic and me- | chanical hardness of dispersion-hardened iron alloys. I Trans. Am. Soc. Steel Treating 19, 553 (1932). '

| [29] W. Koster, Dauermagnetwerkstoffe auf der grundlage , der auscheidungs hartung, Stahl U. Eisen 53, 849

(1933). I

[30] Mishima, Magnetic properties of iron-nickel-alumi- I num allovs. Ohm (July, 1932) abstracted in Iron

Age 130, 346 (1932).

[31] I. L. Cooter and R. E. Mundy, Cunife wire magnets

of small size, J. Research NBS 59, No. 6, (Dec.

1957) RP2808.

[32] Richard M. Bozorth, Ferromagnetism, D. Van

Nostrand Co., Inc. p. 401 (1951).

36

U.S. GOVERNMENT PRINTING 0FFICE:1962
U.S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineering in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the front

cover. WASHINGTON, D.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. High Voltage.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering

Metrology. Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standard

Reference Materials. Applied Analjrtical Research. Crystal Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion Controls. Crystal Chemistry.

Polymers. Macromolecules: Synthesis and Structmre. Polymer Chemistry. Polymer Physics. Polymer Characterization. Polymer Evaluation and Testing. Polymer Standards and Research. Dental Research.

Metallurgy. Engineering Metallurgy. Microscopy and Diffraction. Metal Reactions. Metal Physics. Electrolysis and Metal Deposition.

Inorganic Solids. Engineering Ceramics. Glass. Solid State Chemistry. Crystal Growth. Physical Properties

Constitution and Microstructure. Crystallography.

Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials.

Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Metallic Building Materials.

Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics.

Operations Research.

Data Processing Systems. Components and Techniques. Computer Technology. Measurements Automation.

Engineering Applications. Systems Analysis.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Solid State Physics. Electron Physics. Atomic

Physics.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation.

Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy.

Molecular Kinetics. Mass Spectrometry.

OflBce of Weights and Measures.

BOULDER, COLO.

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Cryogenic

Technical Services.

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research.

Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services. Vertical Soundings Research.

Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Standards. High Frequency Electrical Standards. Radio Broadcast Service. Radio and Microwave

Materials. Atomic Frequency and Time Interval Standards. Electronic Calibration Center. Millimeter-Wave

Research. Microwave Circuit Standards.

Radio Systems. Applied Electromagnetic Theory. High Frequency and Very High Frequency Research. Modulation Research. Antenna Research. Navigation Systems.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics Ionosphere and E.xosphere

Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.

Radio Physics.

Circuit Standards.