New techniques and results in the measurement of magnetostriction

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Submitted on 1 Jan 1951

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New techniques and results in the measurement of

magnetostriction

J.E. Goldman

To cite this version:

NEW

TECHNIQUES

AND RESULTS IN THE MEASUREMENT OF MAGNETOSTRICTION

By

J. E. GOLDMAN,

Westinghouse

Research Laboratories and

_Carnegie

Institute of

_Technology.

Sommaire. - L’auteur décrit la nouvelle

technique qu’il a élaborée pour la mesure des magnéto-strictions linéaires et _cubiques et _qui est _applicable aussi bien aux cristaux _{uniques qu’aux} matériaux

polycristallins. Il donne les résultats des mesures des constantes de _{magnétostriction} pour les alliages

fer-silicium et pour un très petit cristal _unique d’un _{alliage fer-cobalt,} ainsi _{que pour différentes} substances polycristallines. Les données relatives au cristal fer-cobalt ont conduit à _une nouvelle théorie de l’origine de _{l’anisotropie magnétique} de l’alnico V, qui est brièvement discutée. Enfin,

l’auteur _{indique rapidement} une relation entre la _{magnétostriction} eL la transformation ordre-désordre.

JOURNAL

19;)J,

Introduction. --

In 1947

[11,

the writer

_proposed

the use of electrical resistance strain _gauges for the measurement of

_{magnetostriction.}

This method off ers certain notable

_advantages

which will 1Je ennumerated below. Since that

time,

the

tech-nique

of measurement has been

refined,

the accuracy and _range

_improved;

this has made

_possible

measu-rements on materials and

_sample

_geometries

not

previously

amenable to accurate measurement. This paper will be devoted to a

_description

of the

method of measurement and a _{survey of} some

of the more recent results obtained as

_part

of a

program for the

_study

of

_{magnetostrictive}

pheno-mena initiated in the writer’s

_laboratory

and more

recently

continued in a _program under the writer’s direction at

_Carnegie

Institut of

_Technology

_[2].

The measurements on

single crystals

of iron-silicon

are

_part

of an

_unpublished

dissertation

_by

W. J.

Carr,

Jr. at the latter institution with the

_cooperation

of Prof. Smoluchowski.

Experimental Technique.

-- Electrical

resis-tance _{strain gauges}

_operate

on the

_principle

that

if a thin wire is stretched its resistance will

_undergo

a

_change

_proportional

to the

_degree

of strain. The constant of

_{proportionality}

is termed the _gauge

factor,

i.e.

and _{may vary} from i to i

depending

_upon the

material, the

_magnitude

of the stress and other

factors. In our

_experiments

we have used

commer-cial

_Type

A _gauges manufactured in the United States

_by

the Baldwin Locomotive Works. These gauges are of advance

₍₆₀

cu,

fio

ni)

wire and at

the

_magnitude

of

_magnetic

fields

used,

the

magneto-resistive effect in this material is either

_negligible

or small

_enough

so that it can be

_compensated

for without

_unduly

_impairing

_{the accuracy. In}

practice

the gauge is bonded to the

_sample

with

a cellulose-acetate cement. Commercial _gauges as

small as I.5 mm in

_length

are available

_permitting

the measurement of

_{magnetostriction}

on

_single

crystals

or other

_samples

as small as 3 mm in

diameter.

Measurements of the

_change

of resistance of the active _gauge are made with a conventional DC

Wheatstone

_bridge

in which all the arms of the

bridge

are made up of

_equivalent

_gauges that are

bonded to

_non-magnetic

material but with a

coeffi-cient of thermal

_{expansion closely matching}

that of the material under test thus

_eliminating

errors

due to ambient

_temperature

variations. The detector is a sensitive DC

_amplifier

which has

_{a y5}

c

_chopper

in the

_input,

_{a 75}

c narrow-band

_amplifier

and a

synchronous

commutator at the

_output.

The

_output

signal

is recorded on a o-5 mA recorder. Full scale deflection on the recorder can be obtained with an

_{input signal}

of jo-7 V. A schematic circuit

diagram

is shown in

_{figure i.}

The

_constancy

of the _gauge factor and the behavior of the bond at _{very low}

_positive

and

_negative

strains

_(expansion

and

_contraction)

were checked

by measuring

the known elastic moduli of metal

samples

using

this method. The

_system

is

_readly

calibrated in terms of strain

_by

_introducing

a

known

_change

in resistance in the active arm of the

_bridge

and

_noting

the deflection of the

_recording

milliammeter. With this

_arrangement

and with drift as well as

_pick-up

reduced to a minimum a

strain

_sensitivity

of the order of 2 x I o- 8 : mm scale

deflection can be obtained.

472

This method of measurement has the

_following,

noteworthy

advantages :

1. It can be

_applied

to the measurement of

magnetostriction

on

_samples

of a

_variety

of

_shapes

and

_geometries

_{including extremely}

small

_single

crystals

that do not

_permit

of

_ready

measurement

by

other methods.

2. In the case of thin laminated

_samples,

errors

due to

_bending

can be eliminated

_{by applying}

gauges on both sides of

_sample

and

_connecting

them in series.

3.

_Regions

over .which strain measurements are made are small so that variables such as end effects,

shearing

stresses and

_{non-uniformity}

are eliminated.

Fig. I. - Circuit

diagram of the magnetostriction measuring apparatus.

-4. The effects of

_temperature

variations and other ambient variables are eliminated.

_Adequate

sensitivity

and

_stability

are available so that mea-surements can be made when the

_sample

has attained thermal

_equilibrium

thus

_minimizing

errors

_resulting

from

_temperature

effects in the

_sample

due to

magnetocaloric

effect and other

_{magnetothermal}

eff ects.

5. A closed

_{magnetic path}

may be

used,

thus

assuring

a

_greater

_uniformity

of flux distribution

and

_eliminating

_possible

erros due to form effect. 6.

_Finally,

and

_perhaps

most

_significant,

measu-rements are _very

_readily

made in two

_{perpendicular}

directions thus

_eliminating

to a

_great

extent the

uncertainty

in the

_knowledge

of the

_demagnetized

state and errors in the

_{interpretation}

of results due to the

_possible

non-randomness in

_crystal

orientation

or in the initial distribution of domain directions. In the case of the

_{single crystal}

measurements the

sample

is

_always

saturated and

_only

the direction of

M3

is varied with

_respect

to the direction of strain measurement.

Moreover,

by measuring

the strain

_{simultaneously}

_parallel

and transverse to the direction of

_{magnetization,}

the _volume

magne-tostriction _{is very}

_easily

_separated

from the

longi-tudinal

_{magnetostriction,}

if one assumes that no

first order volume

_change

_accompanies

the latter. In this connection it _{may be}

_pointed

out that we

have

_recently

_adopted

this

_technique

for the measu-rement of volume

_{magnetostriction.}

Measurements on

_Single

_Crystals.

--

Quan-titative data on the behavior of the

_{magnetostriction}

constants of

_alloys

as a function of

_composition

are available

_only

in the case of the iron-nickel

alloys

[3]

and a few isolated cases

_[4]

where

_large

single crystals

have been made. In such cases as

the iron-cobalt

_alloys,

it is

_quite

difficult to obtain sizeable

_{single crystals}

and hence the

_significant

single crystal

magnetostriction

data is not avai-lable.

_Using

the above described

_technique

we have made measurements on a

_{single crystal}

of a 3o _per 100 cobalt-iron

_alloy

in the from of an

oblate

_spheroid

3.5 mm in diameter and o.3 mm in

thickness

_[5].

The

_plane

of the

_crystal

was

ascer-tained

_{by taking}

a back-reflection

_X-ray

_picture

and

found to be

_{approximately}

_(411).

_{A very fine} strain _gauge with active dimensions

approxi-mately

I.~ mm2 was bonded onto the

crystal

in such a _way that the direction-cosines of the _gauge axis

relative to the cubic axes are

_{(0.93 I,}

_{o .21).}

The

_crystal

was

_placed

in a

_magnetic

field

of lj

ooo Oe

and the

_change

in strain in the above fixed direction was measured as a function of the

_angle

made

_by

this direction

with

the direction of the field. The results

are

_plotted

in

_figure

2.

Using

the relation

given by

Al

Fig. 2. -

in

direction of gauge VS angle

between M~ and gauge.

Becker

_[6]

for the

_{magnetostriction}

of a cubic

_single

crystal

as a function of the direction-cosines of the direction of strain measurement and the direc-tion of

_{magnetization,}

we have obtained for the

_single

crystal

constants

and domain

_orientation)

in excellent

_agreement

with values obtained on a

sample

of this

_composition

measured in our

labo-ratory

in such a _way as to eliminate the

_uncertainty

in

_knowledge

of the initial domain distribution and in

_agreement

with the value

_{given by}

Snoek

_[7].

c _Kaya and Takaki

x _Webster

A Honda and _Mosiya,7a

Fig. 3. - Single crystal magnetostriction constants

of Fe-Si alloys (after Carr); and

.H, = z ~,~Iu

The

_availability

of such data has

_{become, indeed}

helpful

in

_interpreting

the mechanism of some

reactions

_{taking place}

in

_{magnetic alloys.}

The writer in collaboration with Smoluchowski in some

as

_yet

_unpublished

work has endeavored to

_explain

the mechanism of nucleation in Alnico V on this basis. It is

_proposed

that the

_precipitate

in this

alloy

is a

_phase

rich in iron and cobalt of the

approxi-mate

_composition

3o _per i oo Co. This is

compatible

with the

_hypothesis

of

_Bradley

and

_Taylor

_[8]

and with the observations of Geisler

_[9]

and fits the known

_optimum

_composition

of Alnico V if one

assumes that cobalt when added to the FeNiAl

system

simply

behaves like iron. The measured low

_{niagnetostriction}

of such a

_phase

in the

_[100]

suggests

that nuclei whose

_[100]

axes make a small

angle

with the _{matrix grow}

_{preferentially}

and the

magnetic

anisotropy

of the

_alloy

results from the

crystalline anisotropy

of the

_precipitate.

This data is also of further interest in

_{making possible}

a

quantitative

interpretation

of the effect of a

_magnetic,

field

_{applied during recrystallization}

_{upon the}

recrystallized

texture

_{reported by}

Smoluchowski and Turner

_[10].

Recently,

Carr

_[11]

has made measurements of the

_{single crystal magnetostriction}

constants of iron-silicon

_alloys

as a function of silicon content. His results are shown in

_figure

.3. These results

are also of

_great

theoretical

_{interest, for,}

_comparison

of the data with other

_systems

such as Fe-Al

_bring

out _{the very}

_significant

difference in the behavior of the

_magnetic

shells

_{during alloying}

and is the

subject

of a

_separate

treatment.

Moreover,

as

will be shown

below,

this data makes

_possible

a more

_quantitative

evaluation of the distribution

of domain directions in

_{polycrystalline}

media. Measurements on

_{Polycrystalline}

Materials.

- 1. A1 aterials with

Preleri

ed

Crystal

Orientation.

-Information on the distribution of domain directions

in a

_{polycrystalline}

material can be obtained

by

means of

_{magnetostriction}

measurements. A

_good

example

is afforded

_by

the data on

polycrystalline

materials

_having

a

_preferred

_grain

orientation. The

magnetostriction

vs. B curve for oriented 3.25 per I o0

silicon steel

_(Hipersil)

is shown in

_figure

l.

From

Fig. ~. - Magnetostriction in Hipersil in rolling direction.

Carr’s data shown in

_figure

3 we know the actual value of the

_{single crystal}

constants for this compo-sition. A check on the

_{compatibility}

of the measu-rements is afforded

_by

_noting

the measurement of the

_{magnetostriction}

as measured with the

_sample

magnetized

transverse to the direction of

_rolling

as shown in

_figure

5. The orientation of the crys-tallites in the material is as shown

_{schematically}

in

_figure

6. Thus one would

_expect

that when

magnetized

transverse to the

_rolling

direction the

magnetostriction

would be

_positive

until all the domains are

_magnetized

at 45°

to the direction of

B,

b

measurement, i.e.

_14.000

_gauss as observed.

V2

At this

_juncture

the material should behave

substan-tially

as a

single crystal

so that the

_{magnetostriction}

resulting

from

_turning

the direction of

magnetiza-tion from the

_[100]

to the direction of the field i.e.

_[110],

is

_{[6] :}

_~20134.0

x 10-0 in

_good

agreement

with

(Al l)

/50.000

-

474

the

_anisotropy

in the distribution of _{domains among} the six

_possible

_{easy initial directions.}

Fig. 5. -

Magnetostriction in _Hipersil transverse to _rolling direction.

The

_{negative magnetostriction}

at low inductions is associated with the laminar character of the

sample

and is

_interpreted

as

being

due to the extra

magnetostatic

energy if there is a

_component

of

magnetization

normal to the

_plane

of the sheet.

Fig. 6. - Orientation of crystals in Hipersil.

Thus if the

_crystal

makes a small

_angle

with the

_plane

of the

sheet,

then

_during

the

_steep

_portion

of the

magnetization

curve when

_{magnetization proceeds}

almost

_{exclusively by}

means of i 8oo

_boundary

displacements

there would result a

_component

of

magnetization

normal to the

sheet;

accordingly,

there are some " reverse " _goo

displacements

in

which domains

_{initially magnetized}

_antiparallel

to the field

_change

their

directions

by

goo

to neutralize the normal

_component.

This is

_analogous

to Stewart’s

_{interpretation}

of the

_negative

effect of tensile stress on

_{magnetization}

i n the same

_alloy

_[12].

A similar effect is observed in a _{5o per} 100 Fe-Co

alloy

with

_preferred

_grain

orientation as shown in

figure

7. The

negative

strain at low inductions does not _appear when the

_preferred

_grain

orientation is not

_pronounced.

2.

_{Magnetostriction}

and Order-Disorder. -

Gold-man and Smoluchowski

[13]

first discovered a

relationship

between

_{magnetostriction}

and the state of order of an

_alloy.

The

original

measurements were made on an

_alloy

of Fe-Co

_by

the

technique

Fig. 7.-

_{l- VS.B}

from demagnetized state for 50 % Fe-Co

alloy vith some preferred orientation.

described above. A theoretical

_{interpretation}

was

given

for the effect in terms of the

_{dipole-dipole}

interaction treatment of Becker. This

_required

certain

_assumptions

as to the character of the atomic moment in an

_alloy.

Our

original

ideas

Fig. 8. -

Magnetostriction of _{polycristalline} Iron-aluminium alloys.

have since been

_amplified

_by

Smoluchowski and form the basis for some of the ideas

presented

in

his paper elsewhere in this

meeting.

The writer has also extended the measurements of

magneto-striction as a function of order to

_Ni3Fe

(per-malloy)

[14]

where an increase

_by

a factor of two is observed in the

_{magnetostriction}

on

ordering;

and in the Fe-Al

_system

_{[ 1 ~~.}

The data on Fe-Al

are shown in

_figure

8. The

_single

_crystal

constants of Carr have also been found to be sensitive to thermal

_{treatment-probably}

due to a variation

pro-perties

of these three

_systems

to thermal treatment is due

_primarily

to _{the very}

_{large changes}

in

magneto-striction that are

_produced..

Remarque

de Street. - I should like to ask

Dr Goldman for further information on two

_points

of

_experimental

_{technique. Firstly,}

is there _any

disadvantage

in

_using

A. C.

_bridge

methods

_compared

with the method described i.e.

_using

a D. C.

_supply

and a "

chopped "

D. C.

_{amplifier ? Secondly,}

in his measurements has it been found _necessary to calibrate the resistance strain _gauges in situ or is it found sufficient to

_accept

_{the gauge factor} in accurate measurements ? I should like also to know if Dr Goldman has been able to make _any measurements on reversible

_{magnetostriction,}

i . e. the

_alternating

strain

_{produced by}

an

_alternating

field

_applied

at different

_points

on the

_hysteresis

cycle.

It would _{appear that his form of}

_apparatus

would be

_extremely

useful for such measurements.

Réponse

de M. Goldman. - We feel _{we can} obtain

lower noise level with D. C. than with A. C. As to the

calibration,

in the initial

_stages

of

_development

of this method we checked the _gauge factor

_given

hy

the manufacturer

_{by measuring}

the modulus of

_elasticity

in standard

_samples.

In

_general,

we have found the manufacturer’s data to be

_quite

accurate

_making

a

_regular

check of the _gauge factor unnecessary.

Remarque

de M. Weil. - Nous _avons utilis6

des 11 strain _gauges "

pour des mesures de

magneto-striction, A

diff6rentes

_temperatures

et dans des

champs

6lev6s

₍₁₅

ooo

_Oe),

notamment dans 1’etude

du ferrite de cobalt

_(~’.

R. A cad.

_{Sc., 1950,}

231,

224).

Remarque

de AI. Hoselitz. - We have also been

using

strain gauges for

_{magnetostriction}

measure-ments and the _{results obtained with strain gauges} have been the same as those obtained with our

opticai

lever method. In our

experiments

we were

able to use an

optical

lever in fields up to 5 ooo Oe.

REFERENCES.

[1] GOLDMAN J. E. - Phys. Rev., 1947, 72, 529.

[2] Supported by ONR.

[3] LICHTENBERGER F.2014 Ann. Physik, 1932, 15, 45. [4] SHTURKIN D. A. - C. R. Acad.

Sc., U. R. S. S., 1947, 58, No. 4, 581.

[5] The Fe-Co crystal was very kindly loaned to us _by Prof. L. W. Mc Keehan of Yale University and is

part of the set used _by J. W. Shih for the measurement of crystal anisotropy. Phys. Rev., 1934, 46, 139.

[6] BECKER-DORING. 2014 Ferromagnetismus, Berlin, Julius Springer, 1939, p. 275.

[7] SNOEK J. L. - New Developments in Ferromagnetic

Materials, Elsevier, 1947, p. 15.

[8] BRADLEY A. J. and TAYLOR. 2014 Nature, 1937, 140, 1012.

[9] GEISLER A. H., to be published. We are indebted to

Dr Geisler for _making available to us a _manuscript of _{his paper} in advance of _publication.

[10] SMOLUCHOWSKI R. and TURNER R. W. 2014 J. Appl. Phys., 1949, 20, 745.

[11] CARR W. J. Jr. 2014

Dissertation, Carnegie Institute of

Technology, 1950. [12] STEWART K. H. 2014

Physica, 1949, 15, 235.

[13] GOLDMAN J. E. and SMOLUCHOWSKI R. 2014

Phys. Rev., 1949, 75, 140.

[14] GOLDMAN J. E. - Phys. Rev., 1949, 76, 470; J. Appl.

Phys., 1949, 20, 1131.

[15] GOLDMAN J. E., STANLEY J. K. and HASSEL W., to be