The thermal effects associated with magnetization processes

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The thermal effects associated with magnetization

processes

L.F. Bates

To cite this version:

THE THERMAL EFFECTS ASSOCIATED WITH MAGNETIZATION PROCESSES

By

L.

_{F. BATES,}

Professor

_University

of

_Nottingham.

Sommaire. - On donne

un résumé des études expérimentales sur les _{phénomènes thermiques qui} accompagnent l’aimantation dans les _{champs faibles et moyens, faites par} plusieurs auteurs pendant les vingt-cinq dernières années et aussi une _description des recherches à ce _{sujet poursuivies} à Nottin-gham dans les dix dernières années. Plusieurs des résultats expérimentaux importants sont décrits et

discutés avec l’aide d’une théorie _{donnée par MM. Stoner et} Rhodes. On donne une description des

essais pour reconstruire les courbes expérimentales du _dégagement de chaleur par le nickel

polycristallin à _partir des résultats des _expériences sur les autres propriétés du métal.

LE JOURNAL DE PHYSIQUE 19,

1. Historical Introduction. -- The heat which

is liberated or absorbed in successive

_stages

as one

magnetizes

and

demagnetizes

a

_piece

of

ferro-magnetic

material in low and moderate fields has

.

recently

been the

_subject

of several

_experimental

’

investigations

in

America,

England

and

_Japan.

Many

years ago,

Ewing pointed

out that in order to raise the

_temperature

of a

_specimen

of

_reasonably

pure iron

by

10 _{C it would be necessary} to take it

through

some

_!t.ooo

_{complete cycles}

of

magnetiza-tion

_using

fields sufficient to

_produce

the

_degree

of saturation

usually

referred to as technical

satu-ration,

i. e. fields of the order of a few hundred oersteds.

_{Consequently,}

it is

_only

within recent years that

precise

measurements have been made

on the heat

_changes

which occur in any

_single

restricted

_portion

of one of these

_cycles.

Adelsberger [Ig27]

appears to have been the first to

_attempt

the

_problem.

He measured the

changes

in

_temperature

of a hard steel

_rod,

chosen

for its

_{comparatively large}

effects,

by

means of

four

_{thermocouples}

attached to the rod. His

specimen

was mounted inside a Dewar

flask,

and

_by

using

a sensitive

_galvanometer

he attained a

sensi-tivity

of between

₃₆₄

and

₉₈₆

_{ergs :} cm3 : mm deflec-tion. He confirmed to an _{accuracy of o.65 per 100}

Warburg’s

law [1881]

which states that the area

of a

hysteresis

_{loop (I,}

_H),

is a measure of the

energy wasted in _ergs cm3 :

_cycle.

He was the first to obtain curves

_having

the

_general

_shape

now familiar in this

_work,

which show that as a

steel is

_demagnetized

from its saturation

_intensity

of

_{magnetization,}

it cools in a characteristic manner.

Another hard

steel,

K. S.

_magnet

steel,

was

shortly

afterwards examined

_by

Constant

using

a similar method with the very low

sensi-tivity

of

_~E~

ooo _{ergs : cm3 :} mm

_deflection,

and he found no

cooling

effects at all. A very

high

sensi-tivity,

8 ~

ergs : cm3 : mm

_deflection,

was achieved

by

Ellwood

_{[ 1 92 9] ,}

_using

i o 2

_{thermocouples}

in

series. His method could not be

_{generally adopted}

because it

_required

104

specimen

bars and 102 _copper

bars,

arranged

alternately

and connected in series with alternate

_pieces

_{of copper and} constantan to form the

_{thermocouples.}

The whole

_arrangement

was

_{packed together}

in the

_shape

of a

_{large ellipsoid}

of

revolution,

with a

_major

axis 60 cm and a minor

axis

3.4

cm

_long,

and

_placed

within an evacuated

vessel surrounded

_by

a

water-jacket;

but,

even with these

_precautions,

the zero of his

_measuring

instru-ment drifted a

_great

deal. In

_spite

of the

_great

sensitivity,

Ellwood’s results appear to be of little

value,

for his

_specimen

bars were so

_packed

in rice

flour that

_{magnetostriction}

_changes

of dimensions could not

_freely

take

_place,

and his results were

thereby .greatly

affected.

Miss Townsend

_[1935]

made the obvious

impro-vement of

_attaching

all the

_{thermocouples}

to a

single

rod

_specimen,

and attained a

_sensitivity

of 63o _{ergs : cm3 :} mm deflection when

_using

60

ther-mocouples

in series. Miss Townsend was the first to use a _pure

_{ferromagnetic}

metal, nickel,

and she

pointed

out the

_necessity

of

_allowing

the

_specimen

to

_expand

and contract

_{freely during}

the

measu-rements.

_Hardy

and

_{Quimby [Ig38]}

_{used pure}

specimens

of iron or nickel some 3o cm

long

and i mm

in

diameter,

with

_{5 7.}

_{thermocouples}

connected in series to a

_{galvanometer.}

The

_appropriate

junctions

were attached to the

_specimen

with

insulating

cement, and

_Hardy

and

_Quimby

were

the first to make serious

_attempts

to avoid errors

due to unwanted

_{magnetostriction}

stresses. The

galvanometer

deflections were

_amplified

_by

a

photo-electric

_device,

_giving

a final

_sensitivity

of between

T4o

and 220 _{ergs : cm3 :} mm. Their results

_usually

compare’

favourably

with those of latter workers. The Ellwood

_technique

was followed

_by

_Honda,

Okubo

and Hironé

_[rg2g]

and was

_greatly

extended

by

Okamura

_[tig36].

The latter

_investigated

iron,

cobalt,

and nickel-iron

_{alloys, using}

as _many as

48

specimen

bars in some cases, and between 3 I

and

_{l~~ thermocouples.}

The

_specimen

bars were

arranged aiternately

with nickel-silver

rods,

the

"

hot " and " cold "

_{thermojunctions being}

on the

specimen

and nickel-silver

rods,

respectively.

The whole

_arrangement

was enclosed in a vacuum

vessel. The

_general

_shapes

of the

_experimental

curves so obtained are similar to those obtained

by

later

workers,

and we shall refer below to Oka-mura’s

_interesting

_attempts

to allocate the observed thermal

_changes

to reversible and to irreversible processes.

In order to calibrate the

_measuring

_system,

many of the above workers relied on the correctness

of

_Warburg’s

law,

while some heated the

_specimen

by

passing

a small direct current

_through

it for a

short,

known interval of time.

2. Recent

_{experiments. -}

Since

_1938,

inves-tigations

of these _energy

_changes

have been carried out in

_{England, [Bates}

and

others,

1941,

1 g43,

1947,

1948,

1949]) using

a method which differs from those

so far described in that the

_{thermojunctions}

are

arranged

in

_parallel,

and each is

joined

in series to its own

_primary

on a

_transformer,

the

_secondary

winding

of the transformer

_being

connected to a

sensitive

galvanometer

of

_{long period.}

The

arran-gement

may be

appreciated by referring

to

figure

1, where I~

_represents

the

_{ferromagnetic}

rod under examination. The " hot "

_{thermojunctions}

of two

_{copper-constantan}

_{thermocouples}

are

_directly

attached to

R, while

the two " cold "

_junctions

are

close to the rod but not in contact with it. The short

portions

of metal between the full circles which

represent

the

_{thermojunctions}

are of

constantan;

the remainder of the circuit is of _copper.

The

_{primary windings}

on the transformer are as

identical as

_possible,

and care is taken to make the total resistance of each

_thermocouple

circuit the same. When the

_temperature

of the rod R

changes quickly,

that of the hot

_junctions

likewise

changes,

while that of the cold

_junctions

remains

unchanged. Consequently,

a current flows in each

primary winding,

the

_magnetic

flux

_through

the

secondary winding changes

and a ballistic deflection of the

_galvanometer

occurs. We assume that each

primary

current

_quickly

reaches its maximum

value and then remains constant until the ballistic

reading

is recorded. The

_galvanometer

thereafter returns to its zero.

Usually,

20

_{thermojunctions}

are

_employed,

and the hot

_junctions

are in direct electrical contact with the

_specimen.

Each

junction

may be attached

to R

_by

an ebonite collar with

_grub

screw, or

_simply

by

means of cotton

_thread,

the latter method

being

much

_preferred,

as

_{magnetostriction}

_changes

of dimensions can more

_easily

take

_place.

The

specimen

is about

Qo

cm

_long

and about

₄

mm in

diameter,

and is mounted

_vertically

inside a water-cooled

solenoid;

the vertical

component

of the earth’s

_magnetic

field is neutralised. A chosen

r . - New method of measuring

srnall changes of _temperature.

number of resistances are

placed

in

parallel

with

the

solenoid,

so that the

_magnetizing

_{field may be} varied in

_steps.

By comparison

with the common

method of

_placing

resistance in series with the

solenoid,

the

_parallel

connection has the

_advantage

that the time constant of the solenoid circuit is

large.

In order still further to increase this

constant,

and so

_prevent

the

_{establishment}

of

_large

_eddy

currents in the

_specimen,

a choke coil of low resistance

and self-inductance of some two _{henries is}

perma-nently

connected in series with the solenoid. If necessary, the

specimen

can be

_{longitudinally}

stretched

_by

means of a

_steelyard.

In addition to the two methods of calibration

_by

Warburg’s

law and

_by

direct current

_{heating already}

mentioned,

a third and _{very useful method is} now

available.

_{Referring again}

to

_figure

_I, we see that if the thread S is

_{pulled quickly,}

the left side of the wood

_strip

is lowered and the mass

_W

is

sud-denly suspended

from the lower end of the

_specimen.

Consequently,

the latter

_experiences

a sudden fall in

_temperature,

as shown

_by

Joule

_{[ 1884],}

and this fall may be calculated. We now have the

advan-tage

that we _may calculate

_directly

the

_quantity

of heat

_3Q

in _{ergs :} cm3, or the

_{corresponding}

given

by 3Q =

--- where

a. is the coefficient

of linear

_expansion

of the

_specimen,

A its area of

cross-section and T absolute

_temperature.

If the

specimen

is in any wise bent or deformed it is

neces-sary to pass a small

_alternating

current

_through

the

_specimen

for a

_short,

known interval of time and to calculate the

_change

in

_temperature

from the electrical data.

_Alternating

current must be used

as the

_{thermojunctions}

are in direct contact with the rod.

_Fortunately,

the current _{necessary is} too small to

_{produce thermo-magnetic changes}

in the

_specimen.

In _many

_experiments

a

_{specially-constructed}

galvanometer

with

_{electromagnetic}

field control

was

_used,

but a commercial

_instrument,

with its

permanent magnet

suitably

weakened,

is now

employed.

The scale is

_placed

about 8 m distant

from the mirror

_and

viewed with a

good telescope,

and it is _easy to read deflections to 0.1 mm with accuracy. The

sensitivity usually

lies between 35o to 600 _{ergs :} cm3 : mm, and it is

_frequently

checked

by reversing

a small direct current

_through

a

pri-mary

winding

on the transformer.

In work

prior

to

_{I g38,}

difficulties and errors arose from the use of

_{composite specimens, through}

rigid mounting

of the

_specimen

and the

thermo-junctions,

prolonged

temperature

drifts of the

galvanometer

zero,

_heating

due to

_eddy

currents and lack of check methods of calibration. In the

newer

_work,

_{many of} these difficulties and errors

have been overcome, but certain

_important

sources

of error must be mentioned.

First,

eddy

currents must be

_kept

small. This is

difficult,

particularly

when

_specimens

_{of pure iron}

are

_used,

but a

_simple

method has been found for

calculating

and

_allowing

for

_eddy

current

effects,

provided

that the total heat

dissipated

in a

_complete

hysteresis cycle

can be measured and

_compared

. with that calculated from

Warburg’s

law.

Any

difference

_D,

must be due to

_eddy

current

_heating

and we sum the

_quantity

over a

_complete

cycle,

where

_(~B1),

is the

_change

in

_magnetic

induc-tion in a

_given

_step,

and we write

where k is a _constant, so that we _may

_readily

cal-culate

Secondly,

there

_always

exists a

_stray

field around the solenoid and this is

_picked

_up

_by

the

thermo-couple

leads,

so that

_{spurious galvanometer}

deflec-tions are

_produced

when the solenoid field is

_changed.

Fortunately,

such deflections are much more

_rapid

or "

jerky

"

than the true thermal

deflections,

and

one _may first reduce

_them,

_by

careful

_twinning

and

_symmetrical

_mounting

of the

_thermocouple

leads,

and then eliminate them

_by

means of a com- 1

pensating

coil connected in series with a

_primary

winding

on the transformer. 1

3.

_Experimental

results. ~---- Before

presenting

the main

_body

of

_experimental

results it is

_helpful

to bear in mind the

_following

treatment which has been _{followed in many}

_{publications.}

When the

_{magnetization}

of a

_specimen

increases

_by

_dI,

the _energy

_supplied

to each cm3 is taken to be H

_dI,

and we _may write

so

_that,

on

_integrating,

we have

Now,

we measure the thermal

_change

_dQ

corres-ponding

to the

_change

dI

_by

the

_experiments

described

_above;

_{consequently, by plotting}

the

curves HdI,

I

and dQ,

I it is

_suggested

that we

may deduce the form of the

E-l,

.I curve and so

follow the

_changes

_{in the internal energy of the}

specimen

around a

_{hysteresis cycle.}

It thus appears

to be more convenient to _{express the}

_experimental

results in terms of I rather than of

H,

but we shall see below that for

_comparison

with certain

theories,

_ Fig. 2.

--- Annealed Armco iron.

it _may be more

_expedient

to express them in terms of H. It will also be shown later that the assump-tion that HdI is _{the energy}

_supplied

to each cm3 is

incorrect, and that the

expression HdB

should be

4R

used instead.

pure metals

iron,

nickel and

cobalt,

commencing

with the metals in the annealed state and

_following

the course of events as we

_magnetize

each

_specimen,

starting

from the

_{fully demagnetized}

state. The latter state is not

_{unambiguously}

_defined,

and for

our _{purposes it} is the state which is attained

_by

carefully demagnetizing

the rod

_{specimen hy}

alter-nating

field which is

_slowly

and

_carefully

reduced to zero.

In

_figure

2 are

_given

the

virgin

or initial

magnetiza-tion curves for a

_specimen

of annealed armco

_iron,

gg.8g

per Ioo _pure. In this

figure

and in those

to

_follow,

where not otherwise

stated,

the full line

_gives

_{the dQ,}

I curve, while the dotted and

the broken lines

_give

the fHdI-fdQ,

I and

the H dI,

I curves

_{respectively.}

The difficulties of

_making

measurements with pure iron are _very

great,

because of

_{huge eddy}

current effects and vibrational

_{disturbances,}

and the

_special

_difficulty

of

_compensating

for the induction effect had not been

_{fully appreciated}

when this

_figure

was obtained.

Fig. 3.- Annealed, unstrained nickel : virgin curve.

It is safe to state,

however,

that

_only

_very

_slight

thermal

_changes

occur over a

_large

_range of fields

changes,

but

_eventually

there occurs a definite

heating, undoubtedly

due to the well-known

magneto-caloric effect which was so well studied in France

by

Weiss and Forrer.

’

We are on rather more certain

_ground

when we

consider the

_virgin

curve for nickel

_gg.3l

_per I o0

pure, shown in

figure

:3. This was obtained

_by

taking

special

precautions

to eliminate induction effects. The material was

_extremely

soft and had

to be handled with care. There is no doubt in this case that there is a well-marked

_cooling,

followed

by

a

_{magneto-caloric heating,}

due to intradomain

magnetization

changes.

Similar features are shown in the

_virgin

curve

for

cobalt,

per Ioo _pure,

_figure

_{4. Here,}

it is

Fig. 4. -

Virgin curves for annealed cobalt.

obvious that fields even as

_high

as 5oo Oe do not suffice

_to

_produce

a rise in

_temperature

of the

specimen by

the

_{magneto-caloric}

_effect,

but one

is confident

that,

if

_higher

fields were

_applied,

the

d

_Q,

I curve would turn

_upwards.

Many

of the above features are

_reproduced

in

the

_following

curves for closed

_{hysteresis cycles.}

It _{is necessary} to draw attention to the fact that in each of the

_figures

_{which follow space has} been saved

_by

_{plotting only}

one half of

the dQ,

1

curves, etc. since the

_{remaining portion}

_{may be} obtained from the

_{plotted portion by}

suitable

displacement

and rotation. For

_convenience,

we

always

start

_{demagnetization}

from the left side of the

_figure.

In

_{figure 5}

are

_reproduced

the results for the annealed armco iron described above. It is

_thought

that

_{the f dQ, I}

curve is

_typical

of a _pure

_{ferromagnetic}

metal in an unstrained state and

_{initially subjected}

is directed to the

_pronounced

initial

_cooling

and

subsequent

rise in

_temperature.

It looks as if a

portion

of the curve had been _{folded back upon}

. Fig. 5. -- Annealed Armco iron (Hm - _58).

itself. In the case of

iron,

this

phenomenon

occurs

in rather low

fields,

and it is more or less

_completely

Fig. 6. -

Annealed Armco iron cycle C(Rm = _365.

masked

_by

the coarser _energy scale when we use

high

fields,

as in

_figure

_6,

where the

_dQ,

I curve

shows an initial

_cooling

followed

_by

a

_long,

almost

flat,

portion

and a final rise in

_temperature.

In order to obtain a similar effect in the case of

annealed nickel it is _necessary to use maximum

fields

_exceeding

35o Oe. A

_typical

set of results is

_given

in

_figure

_{7, which should be}

_compared

Fig. 7. - Annealed unstained nickel.

with

_figure

3 for the same

_specimen.

We shall

see below how the

_{extraordinarily}

well defined

valleys

in this curve _{may be made} to

_disappear

by straining

the

_specimen.

In

_comparison,

the results for annealed cobalt are

_{disappointing,}

because we have not been able to

_{apply sufficiently}

strong fields,

and

_figure

8

_{corresponds only}

to the

dome-shaped

portion

of the

_previous

_figure.

Fig. 8. - _{Annealed cobalt}

(H,,, = 35o).

There is one feature of

_general

interest about all these curves. The curve of

ET,

I

_always

reaches a

minimum at

the

remanent

_point

indicated

_by

I,~ ’

(or 7yem)

on the 7 axis. In the cases of both iron and nickel measurements in the

_region

of

1r

were

often difficult. It was felt

that,

in the case of

_iron,

at _any

rate,

the occurrence of accidental vibrations

would

_explain

the

_apparent

_{discontinuity;}

_but,

from the more

_rigorous

examination of nickel it is

now

_thought

that such effects are

_really

due to

pronounced

magnetostriction changes

which take

place

in these

_regions.

Turning

now to the curves for strained

materials,

we first have

figure

g for unannealed

(hard-drawn)

armco iron of the same

_compostion

as that of

_figures

2

number

_against

each curve

_represents

a

_longitudinal

stress,

expressed

in

_{kg :}

_mm2,

which was

_applied

to the

_specimen

for three hours and then removed.

Fig. g. - Unannealed iron. Maximum field 4oo Oe.

Fig. o. - Nickel after stress.

Although

the

_magnetic

data do not

_thereby

suff er very

great

changes,

considerable

_changes

in

the dQ,

I

curves are observed. The curves are

_sharply

divided into two

_types,

_namely

those taken befure and those taken after the

_application

of the

_yield

point

tension. One sees here the

_striking

disappea-rance of the

_{deep valleys}

characteristic of the

uns-trained material and the final

_development

of a curve

which is

_typical

of hard-drawn

_nickel,

and of which many

examples

may be found in the literature. These curves must _not, of course, be confused

with those which are obtained when the

_longitudinal

stress is

_applied

_thoughout

the course of the thermal

measurements. In the latter case, for extreme

tensions,

there is never _any

_sign

of

_cooling,

and the

curves have the appearance of some obtained for

hard

_steels,

which show

_merely

a

_heating

for the

field range between the two coercive

_points.

The

magnetic

data are then _very

_greatly

modified;

I

Fig. I I. - Unannealed cobalt _(H", = _351).

indeed,

the

_{hysteresis cycle}

for nickel under extreme tension is

_practically

a

_straight

line much inclined

too the I axis.

Moreover,

the mathematical

sta-tement, with which this discussion

_opened,

is now

incomplete,

since work is done with or

_against

the

_applied

extension F as the

_{specimen elongates}

magnetostrictively.

The extra term F dl which is to be

_added,

_complicates

the

_analysis

_{very much.} Some results for unannealed cobalt

are

_given

in

figure

In. The

dome-shape

is now more

pro-nounced. It _may be well to remember that cobalt is

_peculiar

in that the cast,

quenched

material is

frequently

in the form _{of face-centred-cubic}

crys-tals,

while cobalt annealed in vacuo and cooled

slowly

possesses

hexagonal

crystal

structure,

although

a

_specimen

with

_{purely hexagonal}

structure is most

unlikely.

The

_{magnetostrictive}

_properties

of the two kinds of material are shown in the literature

longitudinal

measurements for us, found

practically

no difference in our

_{specimens. X-ray}

_examination,

kindly

made

_by

Dr L.

_Lipson,

showed that the hard-drawn material was

_{mainly hexagonal}

with a

_slight

amount of cubic

_phase

_present,

and that

Fig. 12. -

Alloy 5 _(Hill = _37o).

there was some evidence of

_{slight preferred}

orien-tation ;

while the annealed material showed no

evidence of

_preferred

orientation.

But,

in

fact,

the annealed and unannealed

_specimens

were

nothing

like as diverse in

_crystal

structure as one

might

have

_imagined

from the thermal data.

Fig, z 3. -

42 Ni, 58 Fe alloy.

Only

a few of the measurements made with

ferro-magnetic alloys

can be mentioned here. In

_general,

they

are often characterised

_by

low saturation and

insignificant hysteresis properties.

For

_example,

a nickel-silicon

_{alloy, containing}

_g4.85

_per 100

Ni,

0.1

_{Cu, o.4 Fe,}

o.o5

C, 4.o Si,

0.6

NIn,

gave the results shown in

_figure

12, while an

_alloy

of

₄₂

_per 100

Ni and 58 _{Fe gave}

_figure

z 3.

_{Unfortunately,}

we

cannot make as much use of the

_great

_quantity

of _{data collected for many}

_alloys

as we would

_like,

since we do not know the _way in which their

_specific

saturation

_{magnetizations}

_vary with

_temperature

etc. In _many cases, the

ET

I curve exhibits a

maximum,

in contrast _{with pure}

metals,

which show a mini-mum at I = I,.. This is

definitely

so for

_cycles

with

high

values of but some

_queerly

sha-ped

ET,

I curves are sometimes obtained for

_cycles

with low values of

_Hma,.

For

_example,

for the

alloy

which is the

_subject

of

_figure

I3, a

_cycle

with

Hmax =

52 _{Oe gave} a

_Elf,

I curve with a

subsidiary

maximum at I =

I,.,

and a more

pro-nounced maximum on the other side of the I axis.

4.

_{Interpretation}

of results. - When _one

seeks to

_explain

the

_foregoing

results in terms of basic

_concepts,

one is somewhat hindered because there is no

_adequate

method of

_{distinguishing}

between irreversible and reversible thermal

_changes

in the several

_parts

of a

_{hysteresis cycle.}

_Thus,

if we make a

_change

from H to H ₊ dH

and,

accor-dingly, postulate

that we communicate a

_quantity

of energy H dI to each cm.3 of a

_specimen,

we observe a thermal

_{change dQ}

which is in

_general

made up

of two

_parts,

an irreversible

_portion

and a

reversible

_{portion dQr}

where

_dQ

= +

dQ,...

We cannot estimate these two

_quantitites

_{by making}

the

_change

in the reverse manner from H ~- dH to

H,

because the

_change

in

_{magnetization}

will not now be of the same

_magnitude

as before. We

can,

_perhaps,

with

great

good

fortune,

hope

to reduce the field from H + dH in such a manner

that we do

_produce

an exact

_change

in

magnetiza-tion

_equal

to -

dI,

and so observe a new thermal

change dQ’ given

by

dQ’

=

w

dQ.

But,

adequate experiments

on these lines have not

_yet

been made.

Okamura, indeed,

attempted

such an

experimental analysis

in his

work,

but the individual

field

_changes,

or

_steps,

which he made were far too

big,

and one cannot

_accept

_{many of his deductions.} There are _{two ways in which work may}

_usefully

be done with the available

_experimental

results. We may either

attempt

to

_interpret

the

_Q,I

or

_Q,H

curves in terms of fundamental theoretical

_concepts,

or we _may

_attempt

to calculate curves from

avai-lable

_magnetic

and thermoelastic data etc. and compare the curves so calculated with

_experimental

ones. The first

_procedure

was followed

_by

Stoner and Rhodes

_[1949]?

while the second was followed

by

Bates and Davis

_{[1 g5o].}

Stoner and Rhodes made a careful examination of all _{the processes involved and} the

_{corresponding}

contributions to the thermal measurements. The most

_important

feature of their work is the

emphasis

which it

_places

on the Weiss and Forrer

magneto-caloric

_effect,

for

_{they pointed}

out that this effect must not be overlooked even in low fields. In fact,

it _may be

_particularly

_important

in the case of

liberated par cme

_{by 3Q’,}

Stoner and Rhodes _express their main results in the form

where a

= T

dl° ,

and b

= T dK; K

is an

ani-I0

dT

K

dT

sotropy

constant, which measures the variations of

potential

energy of the

system

as a function of the orientation of the intrinsic

_{magnetization,}

_Io,

with

_respect

to the

_crystalline

axis. The first term

on the

_right-hand

side of the above

_equation

repre-sents the contribution due to

_changes

in the intrinsic

magnetization

of the

_domains,

and the second term the contribution due to domain vector rotations.

Hence,

for the

_{adequate testing}

of this

_theory,

dlo dK

we need data for

1,,

d7,,

K and

dT. Effects

due

to internal stresses and reversible

_boundary

move-ments could be taken into account

_by

modification of the

_{coefficient b,}

while the formation of new

domain boundaries

_might

be taken into account

by

modification of a.

Fig. 14. -

Magnetocaloric effect in annealed Armco iron. Values of b" calculated form the theory of Stoner and

Rhodes.

Let us now subtract from the observed heat

changes

those irreversible as well as reversible

heat

_changes

which we _may

reasonably

attribute

to

_changes

in

_spontaneous

_{magnetization.}

We thus obtain the statement

Here, b"

formally

corresponds

to

b,

but it is

_placed

within the

_integral

_sign

in case it is a variable

coefficient which has to be calculated from the

experimental

results.

_{Henc° , b " =}

₁₁

dT ’

or

,

if we wish to make clear what we do with

A f H dl

,

the

_experimental

results.

It should therefore be

_possible

to find how b" ‘’

varies over a

_hysteresis

_{cycle, remembering}

that we should

_expect

it to be

_equal

to the calculated value of b. Of course, one cannot

_expect

exact

agreement

between b" and

b,

because we do not

know b

_exactly,

we cannot

_separate

reversible

and irreversible heat

_changes,

and we do not know how to allow for the effects of internal stresses. For the latter _purpose, we

_should,

of course, need an

accurate measurement of the variation of the

magnetostriction

of the material with

_temperature.

But,

b’r would be

_expected

to

_change

_{discontinuously}

in

_regions

where _{irreversible processes} are

marked,

as, for

_example,

in the

_region

between the coercive

points

in a

_cycle.

In the

_following

table are

_given

values of b and b" which are now

_available,

_many

of them calculated

_by

Stoner and Rhodes:

TABLE. Values

_of

b arcd b".

1. Hardv and Ouimly; 2. Bates and Harrison; 3. Bates and _Healey; 4. Bates and weston; 5. Bates and Davis : 6. Davis: 7. Bates and Edmondson.

The curves for

iron,

nickel and cobalt taken from the paper

by

Stoner and Rhodes are

_given

of iron and nickel between b and b" is

_really

_striking

in many cases in the

_table,

but comment must be made on the value

_-1.~

I for b" obtained from the

results for a

_cycle

with annealed nickel with a

maximum field of

4oo Oe,

where the 11

folding

back " behaviour was recorded for the first time.

Fig. 15. -

Magnetocaloric effect in annealed cobalt. Values of b" calculated form the theory of Stoner and Rhodes.

Stoner and Rhodes appear to

_regard

this

pheno-menon as

_accidental,

_but,

_many

_experiments

in

Nottingham

have

_proved

its

_reality,

and it is believed that it would be found with _{all pure}

_{ferromagnetic}

metals if fields

_adequate

for its

_production

were

used.

_Figure

16 obtained

_by

Davis,

show how

Fig. 16. -

Annealed, unstrained nickel : values of b", calculated form the theory of Stoner and Rhodes.

difficult it is to deduce

precise

values for b’ from results _{obtained with very}

_carefully

annealed

specimens

of nickel. °

The fact that the values of b" for cobalt are

greater

for the unannealed than for the annealed metal may be due either to a difference in the

behaviours of the

_{magnetostriction}

with

tempera-ture or to _{the presence of different amounts of cubic}

phase

in the two

_specimens.

But,

it is certain that in the case of cobalt we have not

_applied

fields

sufficiently

great

to

_produce

the "

_{folding-back"}

effect.

There is one further

_point

of interest. If the

curves of b" are

_plotted

as functions of

.~,

instead of

H,

they

certainly

do not

_give

the

_impression

that b" is a true constant.

_For,

in the

_b",

H curves,

the

_hysteresis

_changes

are concentrated around

the axis of

_{ordinates; whereas,}

in the

_b’,

I curves

they

are

_spread

over the full _range of

I,

and it is

accordingly impossible

to deduce a

_single

definite numerical value of b" from them. This is clear from

_figure

_{I 7} for

_heavily

strained

nickel;

the

figure

for annealed nickel is even more

_complex.

Fig. i.

Let us now turn to the second method of

_dealing

with the

_experimental

results and see whether a

mathematical statment can be derived which will

permit

us to calculate the form which the

_Q,

I curves

_ought

to take. For this we need the

I,

H and

_{magnetostriction}

data and a

_knowledge

of the

magnetocaloric

effect for each

_specimen.

Our

busi-ness is to calculate the total

_quantity

of energy

put

into the solenoid and

_specimen

_system

_{for any} chosen

_step

in solenoid current. From this _energy

we are to subtract work done on or

_by

the

_specimen

in all ways known to us. The difference should

then _appear as an actual increase or decrease of

thermal energy and hence

_give

a

_change

of

tempe-rature of the

_specimen.

We must,

therefore,

consider

_separately

_changes

in the

_magnetic,

thermal,

magnetocrystallic

and

_{strain-energy}

_{contributions,}

knowing

that the sum of these

_energies

must be a

minimum when the field is

_steady.

Dealing

first with the work done in

magnetiza-tion,

we start with the

specimen

in the condition

_H,

I,

which is then

_changed

to H +

dH, I

-~-

dI,

so

causing

a total _energy

_change

where «u is the

_specific

heat of the

_specimen

in constant field. We are here in some

_slight

diffi-culty,

because we cannot at

_present

_{prove that}

we _may

_regard

the eff ect as a linear function of ~~I when the

_specimen

is

_unsaturated,

_although

that is a

reasonable

_assumption.

We now come to _energy

_changes

associated with the

_{magnetostriction}

_changes

of dimensions. In order to _{make any progress,} we must assume that

the internal stress is

_isotropic,

and we will assume it

equal

to o-z

_{dynes :}

_sq. cm

_{acting parallel}

and perpen-dicular to the axis of the

_specimen.

Then,

if for

example

the

_longitudinal

and transverse

magneto-striction constants are

_{I-I and hn}

we shall have a

quan-tity

of work

_equal

to + 2

i,,t]

_{ergs :} cm3. A

word is _{necessary about} the

_sign

of this work. It is

_{clearly independent}

of the sense of the

magnetiza-tion,

and

also,

of whether the

_{magnetostriction}

happens

to be

_positive

or

_negative.

This means

that it is zero when there is no

_{magnetostriction,}

but is

_positive

whenever there is a

_{magnetostrictive}

change

in dimensions.

Fig. 18.

In the case of well-annealed

specimens

there

will,

in

_addition,

be a contribution on account of

_crystal

anisotropy.

We have no data which will enable us to calculate this contribution.

_F6rtunately,

we know that it must be

_negligible

in

_comparison

with the effects due to internal strain in

_heavily

strained

_specimens.

To suin

_up,

for the

_change

f rom H to =H + dH

we have the

_following

statement for the heat liberated : cm3 in the

_specimen

or, if we take the saturation condition as our initial

standard _state, the statement,

enables us to calculate the _{toal thermal energy}

change

between

- Hma’(

and _{any other value} of the field. This statement has been used

_by

Mr J. H. Davis in

_calculating

the curves of

_figures

18 and _{i ()}

for annealed and

_heavily

strained nickel. In

passing,

let us note that no account has been taken of work

_against

_{the pressure of the}

_atmosphere

during

magnetostrictive

changes

of dimensions

or of work done in

raising

or

_lowering

the

thermo-couple

attachments on the

_{specimen; fortunately,}

such work is small.

Fig. 19.

In these

_ligures

the values of

-2013

were

_readily

4R

obtained from the

magnetic

data,

and the values of were obtained from

_equation

_[4]

_using

the

ligures

for

(2013)

H

calculated

_by

Stoner from the

H

measurements of Weiss and Forrer. Values of 0"1

were calculated

_by

Kersten’s reversible work method. The

_{longitudinal magnetostriction}

data were

_kindly

striction data are difficult to

obtain,

and the effects of strain on them do not _appear to have been stu-died. We therefore used some rather

incomplete

data

by

Fricke it is clear that

_attempts

must be made to

_put

this matter on a more

satis-factory

basis.

However,

for

_present

_purposes, the _{data may} be used

with,

perhaps,

some reserve, for the effects of transverse

_{magnetostriction}

are

small.

In

_{figure 18}

are

_given

the

_{experimental virgin}

_{Q, H}

curves for pure annealed and

heavily

strained

nickel

_together

with the curves calculated

according

to

_{equation (5).}

The

_agreement

between the two

curves for the stressed

specimen

is very

good

when one considers that the calculated curve is based on

the difference of four

_quantities,

of which three are

large,

and the values etc., are not known

H

with

_certainty

for the actual

_specimen

used. The lack of

_agreement

between the calculated and

experimental

values for the annealed

_specimen

is

undoubtedly

due to the effect of

_crystal

_anisotropy.

The calculated and observed curves for the

400

Oe

cycle,

shown in

_figure

_{I g,} are remarkable for the

close

_agreement

for the

_heavily

strained

_specimen,

and _{for the way in which the} calculated curve for the annealed

_specimen

follows the

_{general shape}

of the

_experimental

curve. The sudden

_cooling

for small

_positive

values of

H,

_{reported by}

Bates and Harrison and

_by

Bates and

_Healey

and

_thought

by

these workers to be a

_spurious

effect,

is

_clearly

seen in the calculated curves, and is the result of

magnetostrictive changes.

5. Conclusion. - In the

_preceding

pages has been

_given

a

_fairly

_{comprehensive}

statement of the

_body

of

_experimental

data now available on

the thermal

_changes

_accompanying

_{magnetization}

in low and moderate fields. The main results may be summarised as follows :

-1. There is a

_similarity

in the thermal

_changes

for initial

_{magnetization}

_{for the pure}

_{ferromagnetic}

metals,

initial

_{cooling being}

followed

_by

the well-established

_{magnetocaloric}

_heating;

2. There appears a "

_folding

back " effect in the

curves of thermal

_changes

for a

_cycle

of

magnetiza-tion,

in accordance with the

_phenomena

observed in the

_virgin

curves;

3. There are

_relatively

enormous effects on the

thermal curves

_produced

_by

internal strain in the

case of

nickel;

4. There are

_interesting

differences between the

behaviour of

_alloys

and those _{of pure metals.} There are, of course, many omissions from the

experimental

data. we should like to make

mea-surements on

_{single crystals,}

on cobalt and other

high coercivity

materials at

_higher

fields,

to find

the effects of internal strain on the behaviour of

iron, and,

for

_example,

on

_rolled

transformer sheet

material, before and after heat treatment. We would like to know whether there is a "

folding

back " effect in the latter

material,

and whether such an

_effect,

and others described

_here,

_might

account for the well-known 11

_discrepancy

loss "

therein;

experiments

are now in _progress on several

of these lines.

An

_attempt

has been made to

_interpret

some of

the

_experimental

results in terms of fundamental

magnetic

concepts.

This has thrown into bold relief the

_importance

of the

_{magnetocaloric}

effect,

so well established for

_high

fields,

in the low and moderate fields

_employed

here. It has also stressed °

the

_importance

of the variation of the

_crystal

anisotropy

constant w4th

_temperature,

and the need for the collection of data on this and on the

variation of the intrinsic

_{magnetization}

with

tem-perature,

if a _proper assessment of the

_experimental

facts is to be made.

An

_attempt

has also been made to deduce thermal behaviour from the available

_magnetic

data and those

on the

_{magnetocaloric}

and

magnetostriction

phe-nomena. This has been

_remarkably

successful

in the case of nickel under severe internal

strain,

but less so with well annealed

materials,

where

the effects of

_{crystal anisotropy}

are

_important,

unknown and difficult to estimate.

A une

_question

de M.

Néel,

M. Stoner

_répond.

-Pour comparer la th6orie a

Inexperience,

on

_opere

de la maniere suivante.

_Apres

avoir soustrait les effets dus aux variations de 1’aimantation

spon-tanée,

qu’il

est

_possible

de calculer avec assez de

certitude,

on _{compare la valeur de b}

_quasi

th6o-rique

_deduit

de K et de

fK,

en

_imaginant

_{que les}

dT

changements

proviennent

des rotations dans le

champ

magn6to-cristallin ),

avec la valeur effec-tive b"

_provenant

des

_exp6riences.

Pour des 6chan-tillons bien

recuits,

il _y a bon accord entre les valeurs de b et de

_{b ",}

dans les

_champs

_moyens et

_grands.

Naturellement,

il

_n’y

a _pas accord dans les

_champs

faibles par suite des

_changements

irr6versibles

qu’on

ne

_peut

_{pas traiter par la}

thermodynamique

ordinaire. L’allure des courbes de b’ met bien en

evidence les

_changements

irr6versibles.

_{D’ailleurs,}

on ne

_peut

pas calculer b avec

_{precision quand}

il _y

a des tensions internes en 1’absence de donn6es

sur 6

_(interne),

I. et on aura ces

reci-sions,

il sera

_possible

de determiner le caractere des

_changements

le

_long

de la courbe d’aiman-tation

_{(c’est-a-dire}

orientation des

_spins,

rotations,

changements

irreversibles),

en consid6rant la

Remauque

de M. Kurti. -- 11 _me semblerait

avantageux

de mesurer les

_engagements

de chaleur a basse

_temperature.

D’une

_part

les variations de

temperature

seront

_{plus grandes}

a cause de la

peti-tesse des chaleurs

_specifiques,

d’autre

_part,

comme

les

_d6gagements

r6versibles doivent

_d6croltre,

il sera

_plus

facile de

_s6parer

les

_phenomenes

rever-sibles des irréversibles.

Réponse

de Ski. Bates. -- Les _mesures à basse

temperature presentent

certainement une

_grande

importance,

mais il

_n’y

en a _pas eu encore de faites

jusqu’ici

a

ma, connaissance.

11 est a craindre que les fluctuations de

_temperature

soient alors

s6ricuses,

avec le

_dispositif

_que

_j’ai

d6crit.

Remarque

de M. Stoner,. - I)es _mesures a basse

temperature

presenteraient

certainement

_beaucoup

d’int6r6t,

mais il serait

_pr6f6rable

de bien connaitre d’abord les

_phenomenes

a la

_temperature

ordinaire ou les

_exp6riences

sont en outre

_plus

faciles. Nous n’avons pas trouve de méthode libre

d’objections

pour

s6parer

les

_ph6nom6nes

r6versibles et irr6ver-sibles. Nous faisons actuellement a Leeds

_(M.

Tebble et ses

_{collaborateurs)}

des

_{exp6riences qui complètent}

celles de M. Bates. Nous mesurons 1’effet Barkhausen

ainsi que la

susceptibilit6

reversible en fonction de

la

_temperature.

Nous

_esp6rons

ainsi

_{pouvoir analyser}

d’une manière

_{plus complete}

les courbes

_{magnétiques.}

REFERENCES.

ADELSBERGEH U. - Ann.

Physik, Leipzig, 1927, 83, 184. BATES L. F. - J.

Physique

Rad.,

1949, 10, 353.

BATES L. F. and WESTON J. C. 2014 Proc. Phys. Soc., 1941,

53, 5.

BATES L. F. and EDMONDSON A. S. 2014 Proc. Phys. Soc.,

1947, 59, 329.

BATES L. F. and HARRISON E. G. 2014 Proc. Phys. Soc., 1948,

60, 213.

BATES L. F. and HEALEY D. R. 2014 Proc. Phys. Soc., 1943,

55, 188.

BATES L. F. and DAVIS J. H.2014 Proc. _{Phys. Soc., 1950, 63} A, 1265.

CONSTANT F. W. 2014 Phys. Rev., 1928, 82, 486.

ELLWOOD W. B. -

Phys. Rev., 1929, 36, 1066. HARDY T. C. and QUIMBY L. -

Phys. Rev., 1938, 54, 217. HONDA K.,

ÔKUBO

J. et HIRONÉ T. - Sci.

Rep. Tôhoku

Univ., 1929, 18, 408. OKAMURA T. - Sci.

Rep. Tôhoku _{Univ., 1936, 24, 744.} STONER E. C. and RHODES P. 2014 Phil.

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