Magnetic Moments In Amorphous Palladium-

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Magnetic Moments In Amorphous Palladium-Cobalt-Silicon Alloys
Citation
Weiner, Martin Eric
(1968)
Magnetic Moments In Amorphous Palladium-Cobalt-Silicon Alloys.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/NZ2B-DN76.
Abstract
The magnetic moments of amorphous ternary alloys containing Pd,
Co and Si in atomic concentrations corresponding to Pd_(80-x)Co_xSi_(20) in
which x is 3, 5, 7, 9, 10 and 11, have been measured between 1.8 and
300°K and in magnetic fields up to 8.35 kOe. The alloys were obtained
by rapid quenching of a liquid droplet and their structures were
analyzed by X-ray diffraction. The measurements were made in a null-coil
pendulum magnetometer in which the temperature could be
varied continuously without immersing the sample in a cryogenic liquid.
The alloys containing 9 at.% Co or less obeyed Curie's Law over certain
temperature ranges, and had negligible permanent moments at room
temperature. Those containing 10 and 11 at.% Co followed Curie's Law
only above approximately 200°K and had significant permanent moments
at room temperature. For all alloys, the moments calculated from
Curie's Law were too high to be accounted for by the moments of individual
Co atoms. To explain these findings, a model based on the
existence of superparamagnetic clustering is proposed. The cluster
sizes calculated from the model are consistent with the rapid onset of
ferromagnetism in the alloys containing 10 and 11 at.% Co and with the
magnetic moments in an alloy containing 7 at.% Co heat treated in such
a manner as to contain a small amount of a crystalline phase. In
alloys containing 7 at.% Co or less, a maximum in the magnetization vs
temperature curve was observed around 10°K. This maximum was eliminated
by cooling the alloy in a magnetic field, and an explanation for
this observation is suggested.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
(Materials Science and Applied Mathematics)
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Minor Option:
Applied Mathematics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Duwez, Pol E.
Thesis Committee:
Unknown, Unknown
Defense Date:
15 May 1968
Record Number:
CaltechTHESIS:07222014-134811615
Persistent URL:
DOI:
10.7907/NZ2B-DN76
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MAGNETIC NOMENTS IN AMORPHOUS PALLADIUM-COBALT - SILICON ALLOYS

Thesis by
Martin Eric Weiner

In Partial Fulfillment of the Requirements

For the Deg ree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California
1968

(Submitted May 15, 1968)

ii.

ACKNOWLEIX;MENTS

I would like to thank Dr. Pol Dmvez for his encouragement,
suggestions , and personal interest in this work.

Dr. R. II. Willens

served as my research advisor for the year 1965-1966 and I would
like to thank him for his h e lp in the cons truction of the magnetomet e r,
his design of the variable temperature chamber, and his continued
interest in my work after leaving Caltech.

Gary Nix was responsible

for the design and construction of the automatic temperature controller
described in this thesis and assisted in taking experime ntal data.
I would like to express my appreciation to the U. S . Atomic
Energy Comnission for their financial support and the U.

s. National

Science Foundation and the U. S. Steel Corporation for Fellmvship aid.

iii.

ABSTRACT

The magnetic moments of amorphous ternary alloys containing Pd,
Co and Si in atomic concentrations corresponding to Pd

_xCoxsi 20 in

which xis 3, 5, 7, 9, 10 and 11, have been measured between 1.8 and
300°K and in magnetic fie ld s up to 8.35 kOe.

The alloys were obtained

by rapid quenching of a liquid droplet and their struct ur es were
analyzed by X-ray diffraction.

The measurements were made in a null -

coil pendulum magnetometer in which the t emperatur e could be
varied continuous ly without immersing the samp l e in a cryogenic liquid.
The alloy s containing 9 at.% Co or le ss ob eyed Curie's Law over certain
temp e rature ranges, and had negligible permanent moments at room
t emp e rature .

Those containing 10 and 11 at.% Co foll owed Curie ' s Law

only above approximately 200 K and had significant permanent moments
at room temperature.

For all alloys, the moments calculated from

Curie ' s Law were too high to be accounted fer by the moments of individual Co atoms.

To exp lain these findings, a model based on the

existence of superparamagnetic clustering i s proposed.

The c lu ster

sizes calculated f rom the mod e l are consistent with the rapid onset of
ferromagnetism in the alloys containing 10 and 11 at.% Co and with the
magnet ic moments in an alloy containing 7 at.% Co heat treated in such
a manner as to contain a small amount of a crysta lline phase .

alloy s containing 7 at.% Co or l ess , a maximum in the magnetization vs
t emperatur e curve was observed around 10°K.

This maximum was elimi -

nated b y cooling the alloy in a magnetic field, and an exp lanation for
this observation i s suggested.

iv.

TABLE OF CONTENTS

Part

Page

Introduction

II.

Experimental Proc edures
A.

Alloy Preparation and Structure De termination

Design and Performances of the Magnetometer

III.

Results

IV.

Discussion

Conclusions

References

Appendices
A.l.

A. 2 .

A. 3 .

A.4 .

References

INTRODUCTION

The e xis t e nce of ferromagnetism in amorphous solids ha s bee n
pr ed i cted theoretically.

In the mod e l u sed by Gubanov, (l) there i s

no long r a nge per i odic arrangement of atoms in a l attice , a nd only th e
exchange int egra l of n e i g h bor ing ferromagnetic atoms and the radial
distribution function of the structur e are t ake n into consideration .
F e rromag n etic amor phous a ll oys have b een obtained by two different
techniques .

By evaporat ing cobal t and gold on a substrate at liquid

nitroge n t emperature, Mader and Nowick( ) succe e ded i n deposit i ng
amorph o u s films as thick as about 600 A .
25 to 60 at .% Co t-ler e ferromagnetic.

The films containing from

By r apid qu ench ing fr om the

liquid s tat e , Ts u ei and Duwez( ) obtained amorphous ferromagnetic
alloys containing 68 at. % Pd , 12 at. % Co and 20 at.% Si.
This pa rticular a lloy has a r eman ence of about 0.1 G and a coer cive force of 466 Oe .

As ex plaine d in Ref .

( 3 ), the t e rnary Pd

-co

- si

amorphous a lloy is jus t one of a series of amorphous a lloys whose compositions can b e r e pr esented b y Pd

_x-Fx-si

in which F repr esent s any

of the thr ee f erroma gne tic e l ements Fe, Co, or Ni, a n d x i s the concentration of that e l ement .

The maximum values of x b e yond whi ch the

amorphous structure cannot b e obtained are approx i mate l y 5 at .% Fe,
12 at. % Co and 15 at. % Ni.

When no ferromagnetic e l ement i s present,

the binary amorphous alloy Pd

-si

i s di amagn e tic.

The main purpose

of the pr esent inves tiga tion was to study th e formation of localiz ed
magnetic moment s in the t ernary Pd-Co-Si alloys as a fun c tion of cobalt
content.

-2-

II.

EXPERIMENTAL PROCEDURES

Alloy Preparation and Structure De termination
The ternary palladium-cobalt-silicon alloys were prepared by in-

duction melting .

The three c l ements were of the following purities:

99 . 99% pure Pd from Engelhard Industries; spectrographic quality Co
from Johnson and Hatthey containing 10 ppm Si, 5 ppm Ni, 2 ppm Fe and
less than 2 ppm of other metallic impurities; transistor grade silicon
of at least 99.999% purity.

As explained in Ref.

(4), a strong exo-

thermic reaction takes place between Pd and Si and no reaction occurs
between the melt and the fused silica crucible .

Since the we ight

losses after melting were always less than 0.2%, no chemical analyses
wer e performed and all alloy compositions report e d are the nominal ones .
The amorphous structure in the Pd-Co-Si alloys was obtained by
rapid quenching from the liquid state .

The "piston and anvil"technique

described in Ref. (5) was used because rather l arge specimens (about
50 microns in thickness and 20 or more mm in diamet e r) can be obtained .
In their present state of developme nt, the techniques for rapid quenching from the liquid state do not always yield reproducible r es ults
because,as explai ned in Ref, (5), the actual rate of cooling can vary
within large l imits from specimen to specimen .

As a res ult of th ese

shortcoming s it is n ecessary to study the structure of every one of the
quenche d specime ns before proc eeding with the measurements of their
physical prop er ties .

In the pre sen t study, the structur e of the

-3-

quenched alloys should be "amorphous '', the Lerm amorphous being taken
in the sense that the alomic arrangement in Lhe solid, as deLermined
by various techniques such as X-ray diffraclion, eleclron diffraction
and electron microscopy is simi lar to thaL found in liquid alloys or in
solids generally classified as glasses .

The X-ray diffraclion patlern

of an amorphous Pd-Co-Si alloy is praclically identical with that of
an amorphous binary Pd

-si

alloy described in Ref.

(5).

It consisls

of four or fiv e very broad maxima and the analysis of such a pattern
lead s to a radial distribution function very similar to thaL found for
liquid s tructur es .( )

After many years of exper i ence in qu enching

liquid alloys into an amorphous structure, it has been found that \vhen
the qu enching conditions are not th e optimum ones, the X-ray diffracLion
patt ern of the quenched foil still shmvs th e same very broad peaks , but
a few weak but sharp Bragg r ef l ect ions are present.

This means that

most of the foil still consists of an amorphous phase, but i solated
crystals of an equilibrium (or in some cases a non-equilibrium)phase
are present .

The existence of this type of duplex structure in quenched

foils has been described in Ref. (5).

Experience ha s a l so shown that if

a quenched foil contains a small amount of a crystalline pha se , thi s
phase is likely to generate a sharp p eak at a Bragg angle located near
the maximum of the first very broad amorphous diffraction band.

The

pres ence of weak Bragg r ef lec Lions super imposed on the broad maximum due
to th e amorphous band

cannot be detected by the usual diffractometer

scanning u sing a rate meter

since w~ak diffraction peaks would be los t

-4within the noise limits.

An X-ray diffraction patt er n of each foil

studie d in this investigat ion \·7as Lherefore t aken \vith a diffractometer
equipped with a step-scanning mechanism so that int ens ity meas ur e ments
could be taken with a statistical accuracy of about 0.6% in steps of
0. 05° in 2e

\vi thin th e cr itical range of Bragg angles b e t\vee n 30 and

50° in 28 .

The total time requir ed for a full scanning of an amorphous

specimen \va s about 10 hours .

Thi s time wa s of cour se much shorler for

specimens for which a Bragg peak appeared on th e dif frac lion pa tt e rn
during sc anning .
During the course of this inves tigation it became advisable to
measure magnetic moments in alloys containing very sca ll amount s of a
crys talline pha se .

Since th e kine tics of crysLallization of amorphou s

Pd-Co- Si alloys i s not known, a f ew pre liminary ex p eriments we r e n eces sary to det e rmine what h eat tr ea tme nt would l ead to the onset of crystallization.

Amorphou s foil s were sea l ed in evacuated pyrex tubes and

heat ed for various l eng th s of time at 250, 300 and 32 5°C.

Aft e r a geing

at 325°C for 96 hours, weak Brag g r e flections were ob served in the
X-ray diffraction patt ern obtained by step scann ing .

A comparison

between th e diffraction patterns of the amorphou s and the partly crystalliz ed specimens is shown in Fig. 1.

The weak c rystalline peaks super-

imposed on th e amor phou s band are characteristic of one of several either
stable or metastable crystalline ph ases but the ir compl e t e identification would r e quir e a long and t ed ious study of crys tallization kine ti cs .
Since th e main purpose of these exper i men t s was to find out the effec t

Fig . 1.

X- ray diffraction patterns of amorphous (lower, smooth curve) and partly
crystallized alloys containing 7 at.% Co .

0~~--~--~--~--~--~--~--~--~--~--~--~--L---L-~L-~--~--~---L--~

z 3

~ 4r-

>- 5
(/)

Q)
....

-6-

of the presence of a small amount of crystalline phases on the magnetic
moments, a precise knowledge of the crystal structure of these phases
was no t r equired for int erpreting the results.
B.

Design and Performances of the Magnetometer
A wide variety of techniques have been employed for the measure-

ment of magnetic moments.

For metals, the most corrunonly used type of

magnetometer involves the measurement of the force exerted on a sample
located in a magnetic field.

One may either measure the for ce directly

or one can use a null technique in which the force i s counterb alanced
by inducing a magnetic moment in a coil located in the same field as
the; sample .

The null condition is that the magnetic moment of the coil

b e equal in magnitude but opposite in s i gn to that of the samp l e .
Force magnetometers may be divided into t\vO main groups .

One

cons i sts of those in which the magnetic force is vert ical (b a l ance t ype )
and the oth er of those in which it i s h or i zon t al (p endu lum t y pe ) .
One common balance type magnetometer was d esc rib ed by W.
Sucksmith . ( ),( )

He employed a rig id r od attached to a ring which

d ef l ected under the application of a vert i cal loa d .

Two mirrors were

mounted on the ring at positions calculated to g i ve maximum deflection
to a light b eam int ercepting both mirr ors.

The deflection was read by

a trave lling microscope and calibrated by applying a knmvn weight t o the
ba se of the ring.
stant H dH
dX f or

His e l ectromagnet h ad pole pieces tapered for con.

paramagnet~c

dH f or f er roma gnet~c
ones.
samp 1 es an d dX

His

method n ecessitates a guiding device to prevent lat era l motion of the

-7-

rigid rod.

Many other balance type magnetomelers have been described,

the basic difference among them being the force measuring device.
Lundqui st and Myers(S) described a strain gage measuring system.

Soule,

et a 1. (g) u sed a quartz beam microbalance and a null technique.

In the

latter, the beam \vas counterbalanced \vith a magnetic rod, and a solenoid
was used to increase or decrease the effective mass of the counterweight
to achieve a null.
Pendulum magnetometers have been described by Bozarth, et al. (lO)
and Jongenburger and Berghout.

(11)

Both employed a null technique with

compensation accomplished by passing current thrcugh a coil rigidly
attached to the pendulum ala posilion such that it was affected by the
same field as the sample.

Then under certain conditions described by

Jongenburger and Berghout, the moment induced in the coil \vill equal
that in th e samp l e ( aparl from a difference in sign ).
dH
dX should be constant over the entire coil.

In particular,

Bozarth, et al. used strain

gages for null detection and Jongenburger and Berghout used a differential transformer.

In an updating of th e apparatu s used by Bozarth,

et al., Shen1ood (l ) described the use of silicon strain gages and
suggested a technique for aligning the p endulum in the field with an
accuracy of the order of+ 0.1 degree.

This i s particularly important

in studies of anisotropy.
In comparison with other methods , force magnetometers have a number of advantages.

First of all, the moment measured is completely

independent of the geometry of the samp l e (except for demagnetizing
fields).

They are particularly desirable for measurements in metals

-8-

since a d.c. field is used and no eddy current problem arjses .

Perhaps

most significant is that they directly measure the force on a sample
located in a magnetic field .

Thus there is no ambiguity in the results

if the measurements are carried out properly.

One disadvantage of the

force method is that the force depends on the field applied and sensitivity is very lm·l for small fields.

Another disadvantage common to

any technique involving mechanical motion is the sensitivity to vibration and convection currents.
The major advantage of the pendulum type magnetometer over the
balance type is the fact that the gravitational force is perpendicular
to the magnetic force .

Since the latter is typically much smaller than

the weight of the moving section of the magnetometer, the balance type
involves the measurement of a small change in force at a high absolute
level .

In addition, the moving section of the magnetometer is normally

suspended in a small tube.

Thus, any temperature gradient would tend to

create vertical convection currents, affecting a balance system more
than a pendulum system .

This effect could be very serious near the

temperature of liquid helium, where a small change in temperature corresponds to a large change in pressure.

A further advantage lies i n

measurements on strongly ferromagnetic materials, which tend to be
attracted tmvard one of the pole pieces of the magnet .

A pendulum can be

constrained to a single axis of motion without any friction devices .
The magnetometer used for this investigation is of the horizontal
type using the null method.

An electrical detecting system was decided

upon because it is capable of a wide range of sensitivities and permits

-9-

the u se of pha se sensitive det ect ion.

Strain gages were u sed b ecau se

of the ir simplicity and compactness and b ecause the bending beam to which
they are bond ed provid es a n a Lural damping action .

Furthe rmor e , the

. .
.] .
(13)
d eve 1 opment o f· 1 ow temperaLurc coc ff· LcLcnt SL Leon straLn gages
enables measurements of much lmver strains than metal gages.

A counter-

weight sysLem \vas des i gned to overcome both the restor ing torque of the
bending beam and the ef[ecL of gravity to any extent des ired.

An analy-

sis of the entire strain gage-pendulum system is given in appendix A.l.
The basic features de s ir ed in the construction of the magnetometer
were:
1.

Control of the tempera ture of th e strain gages as well as
other critical electrical components .

Protection of the strain gages during assembly and during
changing of th e sample.

Easy assembly and disassembly of various parts .

Minimum pendulum mass.

Minimum magnetic moment of the components in the magnetic
field .

The use of an exchange gas to avoid immersing the pendulum
in a liquid, especially at its boiling po i nt.

A system for continuous temperat ur e control from 1.3°K to

Ability to adapt to a slightly modified standard Se lect-a-Stat
dewar manufactured by Sulfrian Cryogenics.

The tail section

-10-

of this mod el is demounlable and o ne constLucted in the
standard three wall fashion with a 1 1/2" outer diameter
wa s used .
The problems involved in the construction of the pendulum suppor t
( see Fig. 2) >vere t o provide a h eat path to lhe s train gages for temperatur e control, to align the stra in gage spring both verlically and with
the magnet , and to allmv sma ll final adjuslmenls to insure fr ee motion
of the pendulum.

The support was mach ined out of two pieces of copper .

The lower p a rt was machined first and all di mensions were measured accurat e l y to insure proper alignment and correcl pendulum l ength .

The s lot

milled for the strain gage spr ing >vas u sed as an alignment r eference .
Then the upper par t was machined, except for the bolt holes , and s ilv er
brazed to the l ower part with care taken to avoid d i stort ion.

After

bra zing , e i ght oversized bolt hol es were drilled u s ing a dividing head
chuck with th e centers of one pair of hol es in th e same plane as t h e
strain gage spring.

The oversized hol es allow the sma ll lat e r a l adjust-

ment s me ntione d above.

A s piral arrangement of 1/4" Cu tubing was soft

soldered to the top of the pendulum support as part of the water temperatur e control system ( see Appendix A.2 ).

To ins ure proper vertical

alignment of the p end ulum, pieces of drill rod were pressed into two of
the holes in the strain gage spr ing groove and the third was tapped to
allow fastening.

Thi s method of fasten ing permits g ood thermal cont ac t

b etween the spring and the pendulum support as well as easy disassembly.

The wires from the two strain gages and the pendulum coil were

-11ELECTRICAL WIRES

- COPPER

ALIGNMENT RING
(BRASS)
BRASS

BRAZE

LOCKING RING
(BRASS)

Cu PIPE
2Y.!" ID X .1875"

PENDULUM SUPPORT
(COPPER)

~ ---- Cu TUBE

1.505" ID X .060"

BRASS

SLOT FOR WIRES

10.225"
PIN S FOR ALL- SPECIMEN
CHAMBER WIRES

AI COUNTERWEIGHT TUBE
I" OD X .049"

STRAIN GAGE SPRING
( .005" PHOSPHOR BRONZE)

STAINLESS STEEL TUBE

.902 " I D X .049"

BRASS

DEWAR
(STAINLESS STEEL)

3MM OD
QUARTZ

Fig . 2 .

Drmving of upper sect ion of Pe ndulum, Pendu]um
Support, and Upper Spec imen Chamber .

-12-

sold e r e d to t e r ndn a ls n ear the top of the s trip.
na~ s

Wir es from th e termi-

the n l ead through grooves in the pendulum s upport to a cent er hole

and into a v acuum- tig ht connec tor box ( see Fig. 3).

These terminal s

assist in easy assembly and disassemb ly of the components of th e p e ndulum.
The s tr a in gage spr ing \vas machined fr om a piece of 0.005" thick
phosphor bronze which \vas gl u e d to a flat piece of aluminum \vith duco
c e ment.

Aft e r machining, the springs were eas ily removed with acetone .

The s ilicon strain gages wer e bonded to one of the springs by th e manufactur e r.

(Microsyste ms , Inc., Pasadena, California) .

At the bottom of the s pring i s an alumi num fitting, machined
from a single pi ece of aluminum.

The spring was attached to and aligned

with the fittings u s ing th e technique previously described for th e copp e r pendulum supp or t.

The count erwe i ght tub e was attach e d to this fit-

ting with thr ee scr e\vs, allowing easy access to the strain gages and
electrical c o nnec tions .(see Figs . 2 and 3) .
The n ext member of the pendulum assembly is an aluminum rod which
is screwed int o the aluminum fitting .
aluminum nut and a lock washer .

It i s locke d in place with an

The bottom of the rod was drill e d out

to a ccommodat e the quart z tube with a minimum of cl earance .
n ecessary to ins ur e vertical alignme nt of the pe ndulum.

Thi s was

Quartz was

us e d for the remainder of the p endulum b ecau se of its hig h modulu s (re lative to other nonme t a llic ma t eria l s ), low thermal conductivity, and
extremely l ow therma l expans ion.

The last of these i s particularly

-13-

ELECTRICAL
CONNECTOR BOX
(VACUUM TIGHT)

ALIGNMENT
RING

LOCKING
SCREW (3)

LOCATING PIN
BEARING
HOUSINGS

Fig. 3.

Pendulum Support and Re lat ed Equipment.

-14-

desirable s ince the position of the null-coil (and sample ) in the field
i s then independent of temperature.

The

quart~

tube wa s glued in pl ace

with du co cement ( easily dissolved) and the wir es w~re brought out
thr ough side h o l es as in Fig. 2.

The quart z tub e was attached to a

quartz coil form ( see Fig. 4) and the coi l wound by hand afterward .

The

l a tt er consists of about 100 turns of 32 gage nyclad copper magnet wir e .
Each l ayer was coated wi th G.E . No. 703 1 insulating varnish .

Thi s var-

ni s h p erforms quit e well in vacuum and at low temperatures .

The center

of the quartz tub e tvas u sed as a guide for the \vir es .

Thus , one may

have several quartz tubes available- e . g ., for various r anges of magn e tic moment or different samp l e s i zes - and instal l them in a s h ort
time with minimum di sassembly .

If the tubes are quit e stra i ght and

care i s taken in a ligning the axis of the coil with the ax i s of the mag n e t and with the s train gage s pring , only a minimum of adjustment i s
n ecessary .

Each tub e mus t b e recalibrated every time it i s r e ins t al l ed

in the instrument .
The counten1eight tub e was made from standard size aluminum tubing
(the aluminum fitting to whic h it was attached was d es i gned to accommodat e it).

A lathe was employed to obtain the corr ect l ength and to

square the ends .

The three scr etv holes were drilled in a milling machin e

u s ing a divid ing head chuck .
A locking ring was d es i gned to protect the s train gages .
machined f r om a pi ece of 1 1/2" brass rod .

It was

It contains thr ee set screw

holes and thr ee countersunk holes to accommodate the locking scr ews

-15-

PENDULUM
COIL
LINER FOR
MATCHING
LOCATING PIN

SAMPLE

Cu TUBING
(FOR STRAIN
GAGE
TEMPERATURE
CONTROU

GAS VALVE
(FOR SPECIMEN
TEMPERATURE

CONTROL)

Fig. 4.

Upper Specimen Chambe r and Pe n dul um Coil.

-16-

(s ec Figs. 2 and 3).

All six hol es were drilled using a dividing head

chuck to insure uniform distribution of mass and proper al i gnment for
the locking screws.

The locking screws were machined to the correct

l ength and their tips, Lo Lhe correct conical shape .

This insures that

the pendulum is still vertical in the locked condit i on.

A counterweight

could have been installed in a fashion similar to the locking ring, since
the specimen chamber was designed Lo accommodate such a countenveight.
However, the cenler of mass of the first pendulum conslructcd vJas
quite close to the bottom of the slrain gage spring and no counlcrwcight was needed to oblain good sensitivity .
The alignment ring (see Figs. 2 and 3) was designed to insure
alignment of the pendulum after each specimen ch ange.
from 3/4" thick flat brass to a 9" diameter.

It was machined

Then eight holes concen-

tric·with those on the top of the pendulum support were drilled in it.
Four of these were tapped to allow the pendulum support to be attach ed
to it and four were drilled to allow bolts to pass through.

During

final assembly the pendulum was adjusted as mentioned above and bolted
tightly to the alignment ring.

The alignment ring and pendulum suppor t

then effectively became a single unit.

This combination was then fas-

t ened with four bolts to the specimen chamber flange.

In order to

obtain precise alignment after a change of specimen, there are casehardened locating pins in the alignment ring and matching liners in the
specimen ch amber flange.

These insure position repeatability within

0.0007", which is well beyond that required.

To facililate changing of

-17samples, two h ousings containing line ar ball bearings \,Tcre attached to
the alignment ring.

These guide the pendulum assembly a long two case-

hard ened 1/2" steel rods ( see Fig . 5) .

To avo id tilling , there arc two

bearings on one side to allmv three-point support.

Huch of the mass of

the aligmnent ring served no purpose after machining and \vas milled
a\vay in order to lower the weight supported by the d e \•lar .
The upp er flange of the specimen chamber ( see Fig . 2) was machined
from 3/l~'' flat brass.

Four holes were drilled and tap ped in it to al l mv

fastening of the pendulum support - a lignment ring as semb ly.

The rest

of th e upper section of the chamber was made up of standard tubes and
pipes, as indicated in Fig. 2 .

These were cut to the proper length and

the two brass reducing fittings were machined from pie ces of brass rod .
The lmver flange of the upper section was made from 1/2" flat brass .
di sc ~

8 1/2" in diamet e r, was first machined.

Then h oles for six bolts

and for the two lmver support fittings for the steel guide rods ( see
Fig. 5) were drilled.

Next, all excess material was milled away .

The

entire assembly was then si lv er brazed and ch ecked on a lath e for concentricity .

Soft copper tubing, 1/4" in diameter, was \vound around the

copper parts of the specimen chamber and soft sold ered to it.

This

assembly constitutes a part of the temperatur e control sys tem for the
e l ectr i ca l components (s ee Appendix A.2).

In order to al low raising of

the pendulum, quick-disconnect couplings wer e installed in the water
lines of the temperatur e control system where necessary .
The l ower part of the specimen chamber consists of a variable

-18-

CASE-HARDENED
STEEL RODS

THERMOCOUPLE
REFERENCE
JUNCTION

FLOOD VALVE
(FOR SPECIMEN
TEMPERATURE
CONTROL)

Fig . 5.

INDUCTOR FOR
BRIDGE BALANCE
(THERMALLY
INSULATED)

Magnetometer in Closed (Operating) P osilion.

-19-

temperature chamber and a connec ti ng tub e

( see Fig. 6).

In order to

ins ur e a vacuum-tight seal between the connecting tube and the

de~-1ar,

a 3/8" brass disc ~-lith two 0-ring grooves and a cer~ter hole to allow
the connecling tube to pass Lhrough ~.,as machined ar.d positioned above
the neck of the dewar ( see Fig. 2).
those on the dewar flange.

It has six bolt hol es aligned with

Since the neck is not a\·a ilable for filling

the cryogenic storage chamber , the dewar was modified b y Lhe manufacturer to allow transfer thr ough a separate b ayonet coupling.
The connecting tube menlioned above aclual l y consists of several
sections joined by silver brazing .

There i s a thick -wall ed stainless

steel sec ti on at the top to a llow for an 0-ring seal and Lwo thinwalled sections joined b y a sta inl ess steel b e ll 0\,7S .

Thi s arrangement

provid es minimal h eat transfer and allm-1s for theru:al expansion·.

There

are two sections of copper wool attached to brass ri n gs which were in
turn soft soldered to the thin-\-7alled stainless steel tub e .

These lower

the amount of radiative h eat transfer to th e cryogenic bath and minimi ze
th e t emp e ra tur e gradient in the lm-1er part of th e specimen chamber .
The variable t emperature chamber is shmm in F i g . 6 .

The section

containing the doubl e thr ead was machined from a rod of OFHC copper.
The sides of the lm-1e r part of th e copper section were machined flat
to allow room for th e grooves joining th e two thr eads and to max i miz e
th e space available for the pendulum coil .

The coil must swing paralle l

to these flat sides and th e alignment problem was so lv e d by marking th e
dewa r and orienting it before matching th e holes o n the bottom of th e

-20-

STAINLESS STCEL
TUBE

ly4'oD x .o2a

~HELIAHC WELD
- 3MM OD
QUARTZ TUBE

......._INN ER CHAMBER OF DEWAR
(STAINLES S STEEL)

STAINLESS STEEL TUBE

%5'oD x .o2o
Ag BRAZE

INDIUM GASKET
STAINLESS STEEL TUBE

HELIARC WELD

~~~~·oD x .oos

INLET TUBE FOR
VARIABLE TEMP.
CONTROL
9 BRAZE

BRASS RING FOR
ELECT RICAL PIN S

OUTLET TUBE
AQ BRAZE

DOUBLE THREAD
~ POINT

AQ BRAZE

FLOODIN G
GROOVE TO JOIN
INLET TO OUTLET
Ag BRAZE

GROOVE FOR G E
THERMOMETER AND
THERMOCOUPLE
(FILLED WITH INDIUM)

Fig . 6.

Dra \lling of Lm11er Section of P e ndulum and Lm11er
Spec imen Chamber (Variab l e Temperatu re Chamber ).

-21-

upp er pa rt of the specimen chamber to those in th e de1,•ar flange.

Thus, ·

in th e final assemb ly, the str a in gage s pring , th e pendulum coil, and
th e va riab l e t emperature chamber arc s i multaneous ly aligned with the
magne t.

Aft er machining of th e OFHC copper r od was completed it was

lig htl y pr essed into a thin-walled copper tube .

Sinc e s lig ht mixing of

th e inle t and outlet gases ( see below) d oes not pose a probl em , the r e i s
no sea l b etween th e inl et and outlet threads.
and brazes i ndicated in Fig. 6 \vere made .

The n

th~

various we ld s

The next ste p was to check

concentricity on a lathe and to check for l eaks in th e variou s sect i ons .
Th e l a tt e r was done with a mass spectrome t er l eak detector sensitive
to h e lium.

The e ntir e assemb ly \vas then insta lle d in the d ewar (b efore

ins t a llation of the upp er section of the spec imen chamber ) and h e ld in
place with 12 bolt s via the s t a inl ess s t ee l flan ge s h own in Fig. 6.
n ecessary vacuum sea l was made \vi t h an indium gask e t.

The

Both the inlet

and outlet tub es shown in Fig . 6 follm..r a spiral path around th e spec ime n chamber above the var i able t emperat ur e section .

The outl et tube

wa s wrapped around and soft soldered to the s tainles s stee l connec ting
tub e jus t b e lmv th e flange in order t o lm..rer the temp erat ure g radi e nt
in th e s p ec ime n ch amber.

It then l eads throug h a vacuum- tig ht coupling

on top of th e d ewar to a n eedl e valve us e d to control the gas flow.
( see Fig. 4).
In op e r a tion, there are two t echniques for controlling th e t emp erature of th e variable t emperatur e chamber .

One method i s to open the

floo d valve and to allow the cryogen t o flm..r dmvn int o the flooding

-22-

chamber .

The valve is operated by pulling on a wire which passes

through th e pump-out port of the dewar.

It i s a standard spring-loaded

toggle valve \vhich was machined to allm..r it to fit in tbe smal l space
available and fitted Hith a teflon scat .

At the top, the wire i s

attached to a pi ece of drill rod \vhich s lid es through a vacuum tig ht
coupling.

A stainless stee l

tube was bent and positioned to guide the

wir e around th e 90° turn from the neck of the dewar to the pump-out
port ( sec Figs. 5 and 6).

Temperature control employing this valve is

u sed for measurements at a boiling point, measurements b c lm..r 4. 2°K,
and to aiel in lmvcr ing the temperature from one measuring !JOint to th e
n ext .

The second method for controlling temperature is used for all

other temperatures des ired .

In this method, a balance b etween a flmv of

gas through the doubl e thread and current through a heater is u sed .

The

h ea l er current i s supplied by an automatic temperature controller (sec
Append ix A.4) .

The gas flm..r is achieved by applying s light pressure to

th e cryogenic bath (normally only a 1 1/2 ps i safely release valve i s
u sed ) and opening th e needle valve mentioned above .

The h eater consists

of several turns of constantan wire wrapped around the variable t emperature chamber .

As in the case of the pendulum coil, G.E. No. 7031 insulat-

ing varnish was used.

Measurement of temperature is discus sed in

Append ix A . 4 .
In order to measure the level of cryogen in the inner chamber of
the dewar and of the liquid nitrogen in the chamber used for radiation
shielding, two three-position carbon resistor level indicators were

-23-

constructed.

The resistors had a nominal value of 3000 and were

attached to thin-,.,ralled stainless steel tubing.

Two 1 1/2 volt batter-

ies arc used as a source a[ pm..rcr and the current through the resistors
determines the level of the liquid.

In liquid nitrogen, the current

through a resistor is about 7 . 2 rna and in liquid helium, 0.8 rna .

the cryog en is not boiling too rapidly, the value of the current in each
case increases about 0.5 rna if the resistor is slightly above it.
After assembly of the various components of th e system , several
problems remained befor e making measurements.

First of all it was

necessary to check for noise in the electronics .
Appendix A . 2 .

This is discussed in

Next, it was necessary to align the pendulum.

Since the

magnetometer was not intended for experiments involving directionally
dependent magnetic moments, it was not cons idered necessary to attempt
a rotational alignment better than that achieved during assembly .
However, some lateral adjustment and slight Lilting of the de,.,rar were
necessary to obtain free motion of the pendulum .

To check the swing,

an impul se was given to the p endulum by turning the current to the pendulum coil on and off while the electromagnet was on.

Then the detector

signal prior to the variable time constant filter of the lock-in amplifier ( see Appendix A.2.) was observed on an oscilloscope.

When an

adjustment position was found such that the signal appeared as a clean
sinusoidal one, it was assumed that the pendulum was free of constraint.
Additional evidence for prop e r alignment of the pendulum was obtained
by observing that the det ector signa l follm..red the gradual appl ication

-24of a small fie] d smoothly in both dir ect ions , and by making sure that
th e p e ndulum r eturn e d t o the same position after r emoval o f

th e field .

Aft e r alignment, it wa s n ecessary to determine th e coil c urr e nt
r equir e d to overcome the moment of th e section of th e p e ndulum in th e
field .

Since s ampl es \vhose moment s are to be measur e d are wrapped in

a piece of Al foil, a piece of about the right mass (7 mg ) was inser t ed
into th e coil for th e d eter mination of this corr ec tion current.

This

null corr ec tion wa s measur e d as a function of fi e ld and t e mp era tur e
ov e r the range of op erat ion of the magne t ome t er .

The c o rrec tion \vas

found to be n eglig ibl e except b e low 10°K or for meas ur ement s on samp l es
with small moments .

The moment of impurity iron in th e copper wir e

forming the pe ndulum coil wa s assumed r es pons ibl e for most of the
correction b e lO\v 20°K.

The effect of th e Al foil \vas ch e cked at several

t e mpe r a tures and found to b e n eg ligible for most measurements.

The

pieces us e d we r e always cut f rom th e same lot and matched \vi thin 0. 5 mg.
The maximum total corr ec tion is 2 x 10affect most meas ur ement s .

emu and does not ser ious ly

For samples whe r e one wish es to use th e

maximum sen s itiv it y availabl e in th e magne tome t e r, it would be wise to
make a separa t e check of the correction curr e nt with the same piece
of Al fo il to be u sed with th e sample.

Both the field and the tempe ra-

ture should b e r e produc ed accurat e ly during th e mea s ur e me nt on the
sampl e .
The pe ndulum coil was calibrated by u s ing a piece of hig h purity
Ni foil.

The Ni wa s supplied by Johnson , Matth ey & Co., Limited.

Their

-25-

spectrographic analysis showed 8 part.:.; per million of Fe, 3 pp111 of Si
and less than l ppm of all other elements.

The nickel was scaled in an

evacuated quartz tube and annealed at l700°C for several hours.
then etched in nitric acid and \,rcighed on a microbalance.

It was

The current

required for a null was measured at 77°K and 4.2°K in a field of 8 . 35 kg.
The values of the corrected current at these temperatures were v7ithin
1/2 of 1?. of each other, as required, and the value given for 0°K(l )
was used for the calibration.

The result \vas

~(coil) = 3.93 x 10- 3 emu/milliamp .
To check the calibration, the susceptibility of pure Bi \vas measured at
room temperature.

The result was )( =

-1.348 x 10

-6

cgs/gram.

This

falls between two reported values and is considered accurate to about
1/2 of l 'i'o .

To insure that the field affecting the sample i s only due

to the applied field, it is necessary to calculate the field of the
pendulum coil .

The maximum coil current used is 1 00 rna .

Assuming a

solenoidal field and 100 turns/em, the field due to the current in the
pendulum coil is H = Ni/4rr ~ 0.8 Oersted , which is negligible.
The u ltimate sensitivity of the magnetometer in the configuration
described i s 4 x 10-

emu (about 1 microamp) with a field of 8.35 kOe.

It would not be particularly useful to attempt to increase it much further since extreme caution would then be required to eliminate i mpurities.
4 x 10

For example, 0.02 microgram of iron would have a moment of about

-6

emu .

For very weak specimens, it is better to usc a sample

-26of sufficient size to bring the moment within the ceasuring range of
th e instrument.

Since the magnetometer described has eas ily int erchange-

able pendulum parts, one could construct a quartz tube and coil assembly
with a capacity for larger masses .

The sample need not be inside the

coil, buL one must be sure that both the sample and the coil are influenced by the same field gradient.
For measuring the magnetic moments, the foils of the Pd-Co-Si
alloys were cut into small rectangular pieces (about 2 mm x 5 mm) so
thal they could be inserted into the pendulum coil.

These pieces were

wrapped in an aluminum foil (0.0005" thick) to hold them in position
in the pendulum coi l \vhile the pendulum was lmvered into the specimen
chamber .

The weights of all the a lloy specimens \•7ere determined before

and after measuring their magnetic moments.

The magnet i c moments of

all the samples were measured bct\·7een 4. 2°K and 300°K, and the magnetic
moments of the amorphous samples containing 3, 5, and 7 at . % Co as well
as the partly crystallized specimen containing 7 at.% Co were measured
at 1.8°K.

In addition, the effect of cooling in a 7.5 kOe field was

determined at 4.2°K and 1.8°K for the amorphous and partly crystallized
samples containing 7 at.% Co.

At each temperature and for each applied

field, the zero point of the lock-in amplifier ( see Appendix A.2) was
checked before and after the measurement .
occurred, the measurements were repeated.

I f any significant drift

-27III.

RESULTS

The magnetizations in a field of 8.35 kOe of the amorphous
specimens conlaining 3, 5 , 7, 9, 10, and 11 at . % Co arc shm·m in Fig. 7
as a function of temperature and in Fig. 8 as a function of 1/T.

The

results of the same measurements on the partly crystallized sample
containing 7 at.% Co arc plotted as a function of temperature and as
a function of 1/T in Fig. 9 and Fig. 10, respectively.

For the purpose

of comparison , the results obtained with the amorphous a lloy of the
same composition are reproduced in these figures.

Representative

curves of magnetization (in Bohr magnetons per Co atom) vs applied
field at 77°K and 300°K are shmvn in Fig. 11 for alloys containing 7
and 10 at.% Co.
The effect of cooling in a 7.5 kOe field on both the amorphous
and partly crystallized samples containing 7 al.% Co was to eliminate
almost entirely the low temperature maximum in the magnetization.

the amorphous sample the ratio of the magnetization in a field of

8.35 kOe at 1.8 K to that at

~-.2

K was changed from 0.81 to 0.94.

The

effect in the partly crystallized sample was to change the ratio from
0.87 to 0.99.

-..~...
_,.

...,CD

1.2

-u

.2
.I

0 1.0

1.4

1.6

1.8

2.0

Fig . 7.

120

140 160
T (°K)

180

200

220

240

P~gnet iza tion per Co atom of amorphous alloys in
a field of 8 . 35 kOe plotted vs temperature .

100

!"'\

Co 11 Pd 69 si 20

260 280 300

r-.)

\f)

.004 .008 .012

.6 ~I

:0 L

0 1.0

:t
........

- (I) 1.2

1.4

1.6

1.8

2.0

--<)

Magnetization per Co a tom of amorphous alloys in a
field of 8 . 35 kOe plott ed vs inverse temperature .

1/T (°K-1)

.020 .024 .028 .032 .036 .040 .044 .048 .052 .056 .060

Fig . 8 .

.016

Co 3 Pd77Si 20

Co 7 Pd 73 Si2o

Co II Pd 69 Si2o

\.0

()

-0

1.0

1.2

1.4

' 1.6

1.8

2.0

10 20

40
Fi g . 9 .

I 00

120

160

T (°K)

140

180 200

220

240

260

280 300

per Co atom of amorphous and part l y crysta ll i zed
alloys containi ng 7 at .% Co i n a field of 8 . 35 kOe plotted
vs temperature .

Y~gnet i zation

AMORPHOUS

PARTLY CRYSTALLIZED

1.2

0 1.0
........

:i..
........

1.4

1.6

1.8

2.0

Fig . 10.

.016

.032 .036 .040 .044 .048 .052 .056 .060

1/T(oK- 1 )

.020 .024 .028

Magnetization per Co atom of amorphous and partly crystallized alloys
containing 7 at.% Co in a field of 8 . 35 kOe plot ted v s inverse temperature.

.004 .008 .012

AMORPHOUS

t-'

l.V

b0 .6

--u

-.f

Fi g . 11.

H( KOe)

Repr esentat i ve curves of magnetization per Co atom of
amorphous alloys plotted vs applied field .

300°K

1.4,--r----r---r--r----r----r---.,..---'T------.

-33-

IV.

DISCUSSION

The variation of magnetization with temperature can g ive informat ion on whether or not a magnetic so lid follm..rs Curie ' s Law, in which
case a plot of magnetization vs 1/T should yield a straight line.

For

the amorphous Pd-Co-Si alloys, this is far from being the case although,
as shown in Fig . 8, these curves show a linear portion within certain
temperature ranges.

For low cobalt content (Pd

is from 4.2 to 300°K.

co si ) this range
3 20

It becomes smaller as th e cobalt content is

increased and is restricted to near room temperature (l/T<0 .006) for
alloys containing 11 at.% Co.

On the basis of Curie ' s Law, it is pos-

sible to calculate a moment per magnetic center .

To carry out such a

computation, it was assumed, as a first approximation,that the cobalt
atoms are sufficiently far apart and there i s only one magnetic center
per cobalt atom .

In this case the suscept ibility

X. can be expressed

by (15)

/'-. = N p

IJ.B/3kT +

X o

in which N i s the numb er of magnetic centers, p is the effective mome nt
per center, and ) (
without any Co .

i s the susceptib ility of the amorphous Pd-Si alloy

It i s assumed that the moments are due only to electron

spins so that p = g~S(S+l)I-L
as

un~ty.

and g = 2.

In the units used, 1-LB is taken

s·~n ee t h'~ s a 11 oy ~s
· d'~amagnet~c,
(l 6 )

Then the loca l moment is 1-L = g S.

~ 0 can be neglected.

-34The values of the moment

per cobalt atoms,

, calculated in

this manner are. shown in Fig. 12 as a function of cobalt content.

The

moments per Co atom for th e alloys containing 10 and 11 at .% Co do not
fall in line with those calculated for lower Co concentrations.

The

fact that these two alloys must have a different magnetic structure is
also illustrated by the int ercept of their magnetization vs 1/T curves
shown in Fig. 8.

These results would indicate that these two alloys arc

ferrom:ignetic at room temperature.

On the other hand , the curvature

of the magnetization vs temperature plots (see Fig . 7) is clearly
opposite to that expected for ferromagnetism.

Apparently, part of each

sample is paramagnetic and part ferromagnetic, and the relative amounts
of each are temperature dependent.

Such behavior makes a quantitative

analysis o f the magnetic moments of these two samples very difficult
and a qualit at ive discussion of the ir b e h av ior will be attempted at the
end of this section.
An important result related to the a lloys containing 9 at.% Co or
less is the rather large values obtained for the moment per atom of
cobalt,

~a'

shown in Fig. 12.

The l arge values of ~

clearly i mp ly that

there must be more than one Co atom per magne ti c center .

The extrapo -

l ations of the magnetization to 1/T = 0 in Fig . 8 for alloys containing
9 at . % Co or l ess are so smal l as to indicate a nearly negligible perman ent moment in these alloys .

Therefore , th e alloys containing 9 at . % Co

or l ess seem to b e superparamagnetic over at l east part of the temperature range inv est i gated .

Superparamagnetism was originally suggested as

an explanation for the magnetic behavior observed in certain two phase

10 ~

Fig . 12 .

:::t.

()

:::t.
........

--m 12 1

AT. /o Co

Moment per a tom of Co calculated f rom the slope of the linear portions of the
cr vs T-l curves assuming Curie ' s Law a nd one magnetic c enter per Co atom .

0 = PARTLY CRYSTALLIZED SAMPLE

0 = AMORPHOUS SAMPLES

(...)

-36-

alloys consisting of very

sn~ ll

fcrroQagnetic particles in a non-

magne lic matrix. (l ) The requirements for the ferromagnetic partic l es
are Lhal they be single domains and that thermal fluctuations of the
total sp in of a particl e overcome any tendency tmmrd bulk fer:romag netic phenomena such as rem'lnence and hysteres is.

As suggested by

Ishikawa, (lB) superparamagnelism may a l so be expected in magnetically
dill•.te sing}e phase alloys where superparamagnetic clu s ters result from
random fluctualions in composition.

The clusters are magnetically

i solatf'd hecause they are surrounded by non-magnetic atoms .

sing~.c

In such

phase system, one would nol expect a Langevin type d ependence

of magnetization on H/T since there is a range of cluster sizes.
· · (l 7 ) st1·11 h o ld s.
ever, ttLC
requ1rement
o f HI T superpos1t1on

How-

In thi s

context, the r e quireme nt of H/T superposition means thal magnetization
curve s must be temperature indep e nd e nt to Lhe extent that they superimpose when plotted vs H/T rather than vs H as in the usual magne tization curve .

Thus the existence of superparamagnetism may be confirmed

by 1) lack of remanence and 2 ) experimental v e rification of H/T superposition .
Plots showing H/T superposition have bee n made for samp l es containing 9, 7, and 5 at.% Co and are given in Fig. 13.

For these plots,

a value of cr
(Co) was obtained by extrapolations to zero applied
ao
field of the linear regions of magnet ization vs H curves .

One would

not expect thi s type of plot to be valid for either high concentrations
of Co or lm.,r temperatures, where s i gnificant c urvatur e occurs i'1 a plot
of mag netization vs field at a given temperature ( see Fig. 11).

One

0 = 228°K

.4 I-

.I f-

.2 f-

~0 .3 f-

::i..

f........

®......._

HIT (OefOK)

Co 5 Pd75Si2o

I ~

Plots showing H/T superposition for three of the
amorphous alloys.

Co 9 Pd 71 Si 20

Co 7 Pd 73 Si2o

0 = .295°K

0 = 126 °K
® = 224°K

X = 77°K

5AT.%

0 ®0

~08 8

Fig. 13 .

~ = 295°K

8 = 294°K

0 = 205°K

8 = 252 °K

8 .5 f-

0 = 127°K
® = 174°K

0 = II6°K
® = 158°K

7AT.%

SYMBOLS

X = 77°K

9 AT.%

77°K

.6 f-

100

110

120

-..J

-38-

important source of uncertainty for the H/T plots is the difficulty in
assigning a reliable value to the extrapolated value of a

(Co).

The

results shown in Fig. 13, however, seem to indicate that the H/T superposition is reasonably satisfied for alloys containing 9 at.% Co down
to about 116°K, and also satisfied for alloys containing 7 and 5 at.% Co
down to 77°K .

An interpretation of the results obtained at lower

temperature is very difficult because the remanence at these temperatures could not be measured accurately enough with the present magnetometer, which does not have a high enough sensitivity for low magnetic
fields.
In order to investigate the nature of the superparamagnetic
clusters in the amorphous Pd-Co-Si alloys, certain assumptions must be
made about atomic moments .

First of all, there is considerable evidence

that the moment of a Co atom in an alloy tends to be independent of its
environment.

For example, it was observed by Ehara(lg) in NMR measure-

ments that the resonant frequency of co

in dilute solutions of Co in

Pd was virtually the same as in bulk Co, indicating an unchanged Co
moment.

One would expect Fe to behave similarly to Co in its magnetic

properties, and Mossbauer measureme nts in an Fe-Pd solid solution( 0)
indicate that the moment at an Fe site is independent of field and ternperature. Thus, it appears reasonable to assume that the moment associated with a Co atom in the alloys studied is 1.7 ~B' as in bulk Co.
high magnetic moments calculated from the experimental data for the
amorphous alloys might be due to clusters of Co atoms.

There are

The

-39-

several reasons why one would not expecl large enough Co clusters Lo
explain the re su lls.

In the case of the alloy containing 9 at .% Co,

the calcu l ated ~a i s about 17 ~
(17/1. 7)

This would require a clu ster of

or about 100 Co atoms per cluster.

Such a numb er of cobalt

atoms in an amorphous matrix could crystallize into a n ucleus of crystalline cobalt about 10 A in diameter, and a coba] t crystalline phase \-!Ould
b e observed during the ear ly stages of crystallization of an amorphous
alloy.

Instead, among the first crystalline phases detect ed after

ageing an amorphous alloy conLaining 7 at.% Co for 96 hour s at 325° was
a solid solut ion of Co in Pd ( see Fig. 1).

The observed di ff racLion

peak corresponding to Lhe (111) reflection was at an ang l e corresponding
to a lattice parame ter of about 3.86 A, which is approximatE'ly that of a
Pd-Co solid so] ution containing 10 (±2) at.% Co . ( l)

If it is assumed

that during the early slage of crystallization a ll the silicon remains
in the amorphous matrix, the expected Pd t9 Co concentration in a Pd-Co
solid solution would be 9 . 6 aL . %, which agrees quite well with the X-ray
dif fract ion data .
Thus it appears quite c l ear that there must b e a magnet ic
moment associated with a Pd atom .
atom by the presence of a

A moment can be induced in a Pd

ferromagnct~c

atom such as Co.

(21)

However,

the particular Pd atoms which arc polarized and the moment to be
assigned to such atoms depends strongly on the a lloying elements .

The

possible polarization of Pd atoms in the amorphous alloys will now be
discussed.

In principle, the intercept at 0 at . % Co of th e curve of

vs at.% Co ( sec Fig. 12) would give the mome nt associated with an

-40-

isolat ed Co atom plus the moment of any pol arized Pd atoms.

The curve

in Fig. 12 is not accurate enough to obtain a pr ec i se value of th e
intercept, but it i s clear that such an intercept could not be much
above 1.7 ~B. which is the moment per Co atom.

On thi s basi s , along

with the fact that the amorphous alloy without Co (Pd

) is diamag-

netic, it is assumed that a magnetic moment may exist on a Pd atom
only if thi s atom has two or more Co n eares t neighbors.

The probabili-

ty of finding a Pd atom without any Co nearest neighbors can b e evaluated if it is accepted that, as shown by Crewdson,

(22)

the

atom~c

arrangement in an amorphous Pd-Si alloy (based on a study of the radial
distribution function) is such tha t a given Pd atom h as, on the average,
11.6 n earest neighbors of any of the two species.

If x is the atomic

fraction of cobalt in the alloy, the probability for a Pd atom to h ave
. hb ors ~. s (1 -x ) 1 1. 6 .
zero Co n e~g
boris 11.6x(l-x)

10 6
· .

The probability for one nearest neigh-

The r efore the fraction of Pd atoms with two or

more Co n eares t neighbors is given by

Since the re are

= 1 -

(l-x)

11 6
10 6
• - 11.6x(l-x)

0 8
· -x Pd atoms for each Co atout, the effective moment

per Co atom i s given by

~eff

0 . 8 -x
- - - . f.

A value of 1. 7 ~B for ~Co i s a r easonabl e assumption, but the value to
assign to ~Pd depends on severa l poss ible assumptions .
Bozarth, et al. ( l) suggest that their magnetic data on dilute

-41-

alloys of Co in Pd may be exp l ained by a model in which the 0.6 hol e
in the 4d band of Pd i s compleLely polarized for all n earest neighbors
of a Co atom and n early unpolarizccl for u1ore distant atoms .

By combin-

ing magneLization and neutron diffraction results on PdCo and Pd Co,
23
Cable,et a] . ( ) obtained ~Pd's of 0.35 ~B and 0 . 45 ~B' respeclively,
and a ~Co of 2.0 ~B ·

Similar work on PdFe and Pd Fe yielded ~F e ' s of

2.9 ~B and 3.0 ~B' r espect iv ely , and a ~Pd of 0.30 ~B.

Their values

for Pd Fe (ordered) were ~Fe= 3.0 ~B and ~Pd = 0.45 ~B. Pickart and
24
Nathans( ) al so made n eutron diffraction measurements on FcPd
(ordered) and obtained ~Fe= 2.73 ~Band ~Pd = 0 . 51 ~B ·

Ehara(lg) s ug-

gcsts a mod e l for CoPd solid solutions in which a Pel atom with one Co
nearest neighbor has a moment of 0.3 ~B and a Pel atom with two or more
n earest neighbors has a moment of 0.6 ~B (compl ete polarization).

obtains a fairly good fit to data obtained from saturation mag n etization measurements except for very low concentrations of Co.

For this

situation, h e suggests that deviations are due to contributions f rom
mor e distant Pd atoms.

Thus the proper choice of ~Pd to be applied to

a calculation of cluster s iz e is not easily mad e .

Experimental data

on crystalline solid solutions appear to suggest that Pd atoms arc
n ever fully polariz e d.

Furthermore, disordered solutions t e nd to hav e

a lmver ~Pd than ord e red phases.
cluster size for amorphous Pct
tion that ~Pel

For these rea sons , a calculation of

_xCoxsi

has b een made under the assump-

0.30 ~B and i s ind ependent of Co concentration.

The

values of f and ~eff calculaled under these assumptions are plolt ed in

-42-

Fig. 14 as a function of Co concentration.

As expected, the cxtrapo-

lations of the t'vo curves to zero concentration lead to approximately
0 and 1.7 ~B' respectively.
The average number of Co atoms per cluster is then obta ined
from the results of the magnetization vs T
is given by

-1

plots ( see Fig. 8)

and

N(Co)/cluster = (~a/~eff) , w~ere ~a= moment per atom of

Co obtained from Curie's Law by assuming one magnetic center per atom
of Co.

Note that the square must be t aken quantum mechanically, i . e .

= gS implies ~.L

g S (S+l).

By assuming Lha t g = 2, a curve repre-

sent ing the average number of Co atoms per cluster is obtained and i s
shovm in fig . 15.

It would be logical to expect the curve shown in

Fig . 15 to extrapolate to one Co atom per cluster .

Although additional

data on alloys containing from 1 to 3 at . % Co would be required to sub stantiate such an extrapolatjon, such a result is clearly a reasonable
poss ibility.
By heat treating one of the amorphous alloys at a temperature
lmv enough so that long range diffusion does not occur, one may hope
to obtain a classical superparamagnetic system in which there are
magnetic microcrystals in the amorphous alloy .

I f one knmvs the mag-

n et ic properties of the microcrystals, one can check the validity of
the cluster model.

From the X-ray diffraction pattern of an alloy

containing 7 at . % Co heat treated at 325°C for 96 hours ( see Fig . 1)
the dominant crystalline phase can be identified as a Co-Pd solid solution .

In a Co-Pd solid solution , one wou]d expect a Pd atom with just

.05

.101-

.151-

. 20~

.25~

.30

Fi g . 14 .

~""-..

AT. /o Co

f = FRACTION OF Pd ATOMS
POLAR IZED

MOMENT PE R ATOM
OF Co

}Left= EFFECTIVE MAGNETI C

The f rac tion of Pd a toms polariz ed (f) and the effect i ve moment per
Co a tom (~eff) plotted vs at .% Co .

::1..
.......

< l)

-!.8

-11.2 ::1..

~ 1.6 -en

--12.0

2.4

t_..)

.!:'-

15r

N(Co)
CLUSTER

201--

251-

301-

AT /o Co
The number of Co atoms per cluster plott ed vs at .% Co.

Fig . 15.

0 = PARTLY CRYSTALLIZED SAMPLE

0 = AMORPHOUS SAMPLES

-i

35~--~----~----~----~----~----~--~----~----~--~

;:..

1--

-45-

one or more nearest neighboring Co at01ns to be polarized ~.;rith a momPnt
of about 0.3 ~B·

In addition, the number of nearest neighbors become s

12 instead of 11.6.

Thus, proceeding in the manner uRed for the amor-

p h ous case , f -- 1 - (l-x)

= 0 . 602 .

If all Si is rejected, x

Then ~eff = 1 . 7 + 0.3 x

fore, N(Co)/cluster = 13.7.

= 0 . 096 yielding

· ~~~; 07 x 0 . 602 = 3.58.

0 8

There-

This falls very close to the value calcu-

lated for the amorphous sample and is believed to justify the cluster
model proposed .
In order to explain the magnetic moments of the amorphou s
alloys, a model based on superparamagnetism \.;ras proposed.

However,

pure superparam3gnetism exists only for those samples containing
9 at.% Co or less and above a certain temperature which depends on the
concentration of Co atoms .

The deviations from s up erparamagnctism

should be consistent with th e cluster model proposed, and thi s \.;rill
now be discussed.
At a concentration of about 9 at.% Co, it i s noted that th e
number of Co atoms per cluster rises rapidly.

Thu s , ferromagnetic

b ehavior should start to occur in this r egion ~ather s harply as a function of concentration .

This i s believed to be responsible for the posi-

tive extrapolation of the magnetization to 1 /T = 0 (Fig . 8) for alloys
containing 10 and 11 at.% Co.
room temperature.

These t\.;ro alloys are ferromagnetic at

However , fen.- omagnetic ordering is by no means com-

plete as shm.;rn by magnetization vs T curves ( sec Fig . . 7).

The curvature

for at least p art of each curve is opposite to that expected for normal

-46-

ferromagnetic behavior.

All this is quite consistent \-lith the super-

paranmgnetic model proposed above.

Since the cluster size calculated

changes rapidly with temperature for higher Co concentrations, one
should expect strongly concentration dependent transitions to fcrromagnetic behavior.

Hm-1ever, a portion of the clusters can stil l act

paramagnctically while the rest of the solid is ordered fcrromagnetically.
This would explain the curvature observed in the magnetization vs T
curves.

Further information would be obtained from magnetic measure-

ments above room temperature.
There arc two dominant features characteristic of the low ternperature behavior of amorphous alloys of Pd

_xCoxsi

First of all,

there is a deviation from linearity in all alloys in the magnetization
vs T

-1

curves (sec Fig. 8) (this is not seen in the curve for Pd

because the abscissa of the graph doesn't extend far enough) .

co si
3 20

The other

feature is that alloys containine 7 at . % Co or less show a maximum in
magnetization at a fixed field as a function of temperature.

The first

feature is strongly temperature dependent and the second i s not.

The

maximum is almost complete l y eliminated by cooling in a magnetic field.
As discussed previously, one cannot assume that ferromagnetic
ordering exists at the exact point of deviation from linearity in the
magnetization vs T

-1

curves.

Hmvever, a significant s lope in the mag-

nctization vs field curves (sec Fig . 11) pers i sts at the lm-1est temperatures in all samples at the maximum applied field available in the experiments, and the large deviation from linearity in the magnetization

-47-

vs T

-1

curves cannot be ascribed entirely to non-linear dependence of

magnetization on H/T.
must occur.

Thus some interaction between the clusters

If specific heat measurements could be made on the small

amount of material available from amorphous foils, considerable additional information could be gained~

It is, however, clear that the

onset of cluster interaction is quite tcmpr.rature dependent, cxpecially
ncar a concentration of 9 at.% Co.

This is in qualitative agreement

with the results obtained above for cluster size (sec Fig. 15), \-lhich
varies rapidly in this range of concentration.
The maximum in magnetization observed at l0\-7 temperatures may
be ascribed either to a form of antifcrromagnctic coupling bct\.,recn a
portion of the moments present or to a form of magnetocrystalline
anisotropy applicable to an amorphous alloy.

The elimination of a

maximum due to anisotropy by the use of cooling in a magnetic field is
analogous to the magnetic cooling of some types of permanent magnets.
That cooling in a magnetic field can eliminate a maximum due to anti.
(26)
ferromagnetic coupling has been shm.,rn by Nesb~tt, et al.
for the

compound Mn Tb.

It is not possible with the equipment available to

distinguish bctv7cen these t\-70 possible effects.

HmoJever, the effect

of cooling in a magnetic field clearly eliminates the possibility of
a drop in magnetization due to a change in atomic moments.

Antiferro-

magnetic ordering has been suggested as an explanation for the maxinrum
in magnetization observed in dilute alloys of Mn in Cu(
(28)
Au'

) and Fe in

but coollng in a magnetic field has no effect in these alloys.

-48-

Ano t h e r

type of trans ition to antiferromagnetism occurs in a lloys di s-

playing exch ange inver s i on such as F e-Rh al loys . (

In these alloys,

there i s a trans ition from a ferromagnetic state to an ant if erromag n e tic s t a l e as the t emperature i s lmvered.

Thi s i s in contr as t to

Mn-Cu and F e -Au dilut e alloys, which do not display tru e bulk ferromagnetism al any t emper ature .

Hmvever, in the case of Fe-Rh alloys,

the t empera ture of exchange invers ion i s very concentration dependent,
in contras t to amorphous Pd

_xCox s i

alloys .

Ve ry hig h puls e d fields

can e limina t e Lh e antiferromagnetic state in Fe-Rh alloys , but the
effec t of coo ling in a magnet i c field i s noL known.

High field,

hyst eres i s loop , thermal hysteres i s , h eat capaci ty, and l mv t emp e rature

(below 4.2 K) r es istivity measurements could b e u se ful in determining
the orig in of the maximum in magnetization.
pr e par e dilute alloys of the type Pd

_xF e x Si

It might also b e u seful to
20

.( )

ments on these alloys s how a maxi mum similar to Pd

If mag n et ic measure_xcoxsi

, Mossb auer

Effect me asurement s might be u seful in elucidat ing its orig in.

-49-

CONCLUSIONS

The magnetic moments of ternary amorphous Pd-Co-Si a lloys have
been studied.

The amount of Si was kept fixed at 20 at.% and Co was

substituted for Pd in amounts from 3 at . % to 11 at . %.

The results

of the study shmved that t:he magnetic moments depended strongly on
both composition and temperature.

Since Curie ' s LaH \vas follmved over

part of the temperature range for all of th e samples and since the local moments calculated from Curie ' s Law were much too high to be due to
atomic moments of individual Co atoms, a model based on superparamagnetism in a homogeneous system is proposed.

Both Co and Pd arc knoHn

to be magneticaJly active in a]loys but some assumptions about their
magnetic moments are necessary .

From the experimental data it appears

r easonable to assume that in the present alloys all the Co atoms have
a fixed moment of 1 .7 ~B (as in bulk Co) and that the Pd atoms which
have two or mor e Co nearest neighbors h ave a magnetic moment of 0.3 ~

From this statistical model an average size for a superparamagnetic
cluster was calculated.

From this calculation, it was deduced that the

clu ster s i ze increases very rapidly when the Co concentration reaches
about 9 at .%.

This i s pr ecisely the concentration beyond which ferro-

magnetism ( as determined by a positive i ntercept at 1/T = 0 in the
magnetization vs 1/T plots) ex i sts at room temperature.

Furthe~

experi-

mental evidence for the validity of the cluster model was provided
by experiments on a partly crysta llized alloy .

The main crystal line

-50-

phase was identified as a Pd-Co solid solution and, by using atomic
moments valid for this phase, a cluster size Has determined.

Although

the measured magnetic moments of the partly crystalline alloy were much
higher than those of the corresponding amorphous alloy, the calculated
cluster sizes Here very close .

The deviations from superparamagnetic

behavior observed at low·cr temperatures and higher concentrations of
Co may be ascribed to interactions between c]usters.

The type of inter-

action leading to a maximum in magnetization at lm.;r temperatures in
alloys containing 7 at.% or less cannot be determined precisely by the
experiments performed .

Calorimetric and resistivity measurements

might be of value for this purpose.
investigated

The clusters themselves might be

directly by the use of very high magnetic fie l ds or by

performing nuclear magnetic resonance me asureme nts on alloys containing
Pd

105

The effect of the Si concentration on the magnetic properties

is unknown and more information in this area might be obtained by varying the Si content.

Unfortunately, the range of silicon concentrations

within which these alloys can be quenched into an amorphous phase is
rather narrow (from 15 . 5 to about 23 at.%).

Thus, the experiments per-

formed ra i se a number of significant questions.

However, a fairly

crude model seems to have yielded quite consistent results in the amorphous ternary alloys with

two magnetically active species .

-51-

REFERENCES

A. I. Gubanov, Soviet Physics, Solid SLate, 2, 468 (1960).

S. Mader and A. S . Nowick, Applied

C. C. Tsuci and Pol Dmvez, J. Appl. Phys., 38, 4096 (1967).

Pol Du,vez, R. H. Willens, and R. C. CreHdson, J. Appl. Phys., 36,
2267 (1965).

Pol Duwez, Transactions of the ASM, 60, 607 (1967).

W. Sucksmith, Phil. Mag., 8, 158 (1929).

W. Sucksmith, Proc. Roy. Soc., 170, 551 (1939).

N. Lundquist and H. P. Myers, J. Sc i. lustrum. , 39, 154 (196 2).

D. E. Soule, C. W. Nezbeda, and A . W. Czanderna, Rev. Sci . Instr.,
35, 1504 (1964).

10.

R. M. Bozorth, H. J. Williams, and Dorothy E. Walsh, Phys. Rev.,
103, 572 (1956) .

11.

P. Jongenburger and C. W. Berghout, Appl. Sci. Res . Section B,
Vol. 7, 366 (1961).

12.

R. C. Sherwood, private communication.

13.

J . C. Sanchez and W. V. Wright, Instr. Soc . of America, Conference
Preprint, 37-SL61 (1961).

14.

R. M. Bozorth, Ferromagnetism, D. Van Nostrand Company, Inc.
p. 867.

15.

P. A . Wolff, P . W. Anderson, A . M. Clogston, B. T. Matthias,
M. Pe t er , and H. J. Williams, J. Appl. Phys., 33, 1173 (1962).

16.

R. H. Willens, private communication.

17.

C. P . Bean and J. D. Livingston , J. Appl. Phys., 30, 120S (1959).

18.

Y. I s hikawa, J. Appl. Phys., 35 (part 2), 1054 (1964).

19 .

Shaw Ehara, J. Phys. Soc . Japan, 19, 1313 (1964).

Physic~

Lett ers , 7, 57 (196 5) .

(19 51) ,

-52-

20.

P. P. Craig, R. C. Peris ho, R. Segna n, and W. A. St eyert, Phys.
Rev.,l38, Al460 (1965).

21.

R. M. Bozorth, P. A. Wolf f , D. D. Davis, V. B. Compton, and
J. H. Wernick, Phys . Rev., 122, 1157 (1961).

22.

R. C. Crewd s on, Ph.D. The s i s , California Ins titut e of Technology,
(1966) .

23.

J. W. Cabl e , E. 0. Wollan, W. C. Koehl er, and M. K. Wilkins on,
J. Appl. Phys., 33, 1340 (1962).

24.

S. J. Pickart and R. Nathans , J. Appl. Phys ., 33, 1336 (1962).

25.

H. Sato, A. Arrott, and R. Kikuchi, J. Phys. Chern. Solids, 10,
19 (1959).

26.

E. A. Nesbitt, H. J. Williams, J. H. Wernick and R. C. Sherwood,
J. Appl. Phys. , 34, 1347 (1963).

27.

A. W. Overhau ser, J. Phys. Chern. Solid s , 13, 71 (1960).

28.

R. Tournier andY. I shikawa, Phys ics Lett ers, 11, 280 (1964).

29.

J. Kouvel and C. Hart e lius, J. Appl. Phys., 33, 1343 (1962).

-53-

APPENDIX

A.l.

Analysis of the Strain Gage - Pendulum System
The moving section of the pendulum consists of a bending beam

which is fixed at the top and a rigid member v7hich is attached to the
bottom of the bending beam.

Silicon strain gages are bonded on both

sides of the bending beam and wired such that their outputs are additive.
For the purpose of this analysis, the rigid member is replaced by a
point mass positioned at its center of mass .

The magne tic forc e is also

assumed to be a point force applied at the bottom of the rigid member .
A diagram of the bending beam j_s shO\·J n in Fig. A.l.
Let x

= coordinate of point along the phosphor bronze spring and

y = coordinate of deflection.

The origin i s at the bottom of the spring.

The parameters involve d are :
E = modulus of elasticity

area moment of inertia

total mass of pendulum assumbly

force on coil (due to field)

L = coordinate of center of coil
L' = coordinate of top of beam

coordinate of center of mass

acceleration due to grav ity

Then by balancing torques, (l)

...

Fi g . A. l .

Diagram of the phosphor bronze s pring i ll~st=ating tl.e
coordinates used in the analy s is of t he sens i tivity of
the mag netometer .

PHOSPHOR BRONZE
SPRING

ASSUME
LOCALLY

.!"'--- (R + ~) d8

- ~ ----

'/ .[ 4-1
1\...

1"''

~?-/:/ Cl RCULAR

-~ t

\..~

-55where -L'< x < 0.

This is a first order linear differential equation

in~ whose solution is:( 2 )

~=-{ex;;[j fJ!l (R-+X)clx}j

x[~ (L + x)(exp{jif (R+ X)dxj}«x
where C is an arbitrary constant to be determined by the boundary
condition :

d)< x=-L"

-56-

From the boundary condition,

c'~-:;~ exp[~(R.-cl)
_ (L-R.) /2EIJ/fA(R;L~)
/tvlf
e du .
L{

~ =-~{1-exp{;JA{(R_-C/'-(R~x))}
~{exp[~(Rrx)jj(L-R)/~1@

~R+X) -JJI:f)'<--L')J)
.xl~j;j_!lt
e "( d u.
e ol
10

From Fig.

cA.

(6) it may be seen that the net change in length on

eith er s id e = t/2 dB where t

= thickness of the bend ing beam.

Ther efore

the strain is given by

The above value is the strain at a point.

In r e ality, strain gages have

a finit e active l e ngth which is difficult to obtain exactly.

The active

l ength in the gages used appear s t o b e l ess than J/8 inch so the u se of
a point strain in these calculations seems jus tifi ed.

- 57-

From the or i ginal differential equat i o n:

=-L (L+x.)- Mg (R~xJi4-.
dx'- EI
El
d.x
~ = -2~I(L<-x) ~ih_(R-+X)

~ {1- exp[~{(r<-L'/-(R.+ x.)j)

+{exp[jjry(R. xtj] (L-RJ;p;i

.jW:r (f<.+- X) L.{ 'A.
e du. -

f}_~ (R- L•') (.{ 2 } ]
e du. .

'{)

Assume that the strain gages measure the s l rain at x =

- L'

---

-58-

Numer ical calculation of sensitivity :

1/12 wt

width of phosphor bronze spring = 0.318 em

thickness = 0.0127 em

85.4 g

11 x 10

980 cm/sec

100.2 em

dynes/cm

L'= 2 . 54 em
R = 2 . 6 em - This Has obtained by finding the r:1ass and balance
point of the quartz rod plus coil and the counterweight tube plus locking ring and combining them in
a weight ed average .

magnetic field = 8 kOe

dH
dy

magnet ic fi eld gradient = 300 Oe/cm al H = 8 kOe.

dH
Both H and dy were measured directly with a Hall Eff ec t probe.
G.F. = gage factor for the silicon s train gages =
R = resistance .

G.F.

6R/R

100 from data supplied by the manufacturer.

m = magnetic moment

out

s .g.

= output voltage from strain gage bridge circuit.
=voltage across each strain gage= 0.5 volt.
-5

Thus, (a)

1.05 X 10

(b)

1.412 X 10

-7

where

-59-

(d)

47.45
l,ll~

(e)

=SO eu du

1.809

0.0~02

(f)=J eu

0.050

-L'

e:( - )

-1 . 05 X 10-S + 1.15 X 10-S

1.0 x 10

-6

dyne

-1

Since both gages are active:

out

= 2V

s . g.

R~ = 2V · (G. F. ) · g

_aut.

-4

volt/dyne

1 ~ (Energy) I =

= 1.0 x 10

I ~ (m · H) I

out = 3.0 x 10- 2 volt/emu= 30 mV/emu

The sensitivity was measured directly at H ~ 8 kOe by changing the
current in th e magnetometer coil by a known amount and observing the
change i n output voltage .

This measurement yielded:

out

tJ. m

10 mV
emu

Possible r easons for the discrepancy between measured and calculated
values are:
a)

The g lue used to attach the slrain gages to the phosphor
bronz e spring may signif icantl y affect both E and t .

-60-

The calculation involves a difference of two close numbers
so that it is very sensitive to certain parameters which
may not be known with sufficient accuracy .

Both the assumption of point strain a nd the point at which
the strain was calculated may be in error .

Various limiting cases:

-t
2EI

-1.05 x 10- 5 dyne -l

(L - - )

This yields an increase of a factor of 10 over the above
calculated value.

Thus, judic iou s attempts to reduce the

mass (without changing other paramet e rs) would b e useful .
b)

R = L, i.e . - all mass concentrat e d at the bottom of the
pendulum.

-tL'
2 EI

= -2.77 x 10

-7

dyne

-1

Thus , the calculated sens itivity was increased by a fac tor of 4
in moving th e center of mass

up~vard

toR = 2 . 6 em.

Let L - 2L
E:

= -2.3x l0 -6

Thus , doubling the pendulum length increases the sens itivit y by a
littl e more than a factor of 2.
do so

Since it would be difficult to

without increas ing Hg, there is probably little point i n

-61-

u sing a longer pendulum.
d)

Let R = - x.

This yields the same result as having zero mass .

This is easy to do and could become very worth\vhile if a magnet ometer coil with a very small mome nt were built .

The increase

in sensitivity will be offset some\vhat by a lessening in the
damping effect of the phosphor bronze spring and some experimcntation to determine an optimum R would be necessary.
e)

Let R go above -x .

exponential manner.

The sensitivity will increase in an
An absolute upper limit to R is determined

by the condition that a stable equilibrium exist when F = 0.
Calculation of critical stability:
Let F = restoring force in bending beam at x = 0 .
Mg ( RfJ-1-y) = FL ' by torque balance about top of b e nding beam .

E.Y
I = 21
dx x=o

1 FL ' 3
y(x=o) =- - - 3 EI
Mg [ R·l/2 -FL'EI

FL'1 -

3 EI

1. FL ' ]
3 EI

FL '

+ 2EL
MgL '

For the above numbers,

em
32 X 2.54 -1- 1.40x2
. 54

= 1. 69+0 . 56 = 2.25 em

Therefore, the maximum allm.;rable value for R is 2 .25 em above the

-62-

bottom of the phosphor bronz e spring.
A.2.

Measurement of Strain Gage Output
An a.c. bridge circuit utilizing a lock-in amplifier as a detec-

tor was judg ed to be the besL way to measure the strain .

By using the

strain gages as two adjacent arms of the bridge, the effect of temperatur e variations on bridge balance is less ened if the chara cteristics of
the slrain gages are similar .
In choos ing the bridge components; the major problems considered
were temperatur e and frequency stability.

In the former, it is of

course desirable that the temperalure coeff icient of impedance be small.
In the latter, it is desirable that the bridg e balance b e independenL
of frequency.

The final design chosen is shown in Fig. A.2.

The detector is a Princeton Applied Research model HR-8 lock-in
amplifier.
ment.

It is an almost ideal instrume nt for this type of measure-

Since detection is phase sens itive and since the output i s fed

into a variable time constant filter, both the effect of noise and
random S\vinging of the pendulum are greatly diminished.

Th e sensitivity

of the instrume nt is actually well beyond the level required, enabling
operation at a low oscillator output.

Two preamplifiers are available -

type A for high and type B for low input impedance.
employed for this bridge.

The latter was

Since the signal i s fed through a tuned

amplifier prior to cross-correlation with the oscillator output, analysis of noise as a function of frequency is very simple .
chosen for operation wa s 1 kc .

The frequency

The noise l evel at this frequency \vas

- 63-

GEN ERAL RADIO
T YPE 941 - A
TOROIDAL TRANSFORM ER 7

GENERAL RADIO
T YPE 13 11 - A
AUD IO OSC I L L ATOR

.cYO
nnnnnnnnr
,~.

VAR IABLE
INDUCTOR

0 t o .1.0.
DECADE
RES I STOR
0 to l D.
DECAD E
RES ISTOR
REFERENCE
S I GNAL

DETECTOR

GENERAL RAD IO
50 t o 11 00 pf
~---,,------' VARIABLE CAPACITOR

200 KD.
0 t o 50 KD.
VA RI AB L E
RES ISTOR
0 t o 1 KD.
VA R IABLE
RES I ST OR

S ILI CON
STRAIN GAG E
Fig . A . 2 .

Diagram of the e l ectr i ca l circuit u sed t o measure
th e strain in the phosphor bronze spr ing .

-64-

low and the input impedance not far above that recommended for the typ e
B preamplifier.
This type of circuit is very convenient since the transformer
itself serves as the r e quired two l egs of the bridge .

In addition, the

effect of lead wire capacitance on frequency stability is quit e small
in this type of bridge .

By placing g round at the center of the second -

ary on the transformer, l ead wire capacitances either have the effect of
being in para ll el with one winding on the transforme r
with the detector.

or in parallel

In the latter case, the impedance du e to the

capacitance is certainly high enough not to act as a load on the lockin amplifier .

In the forme r case, the transformer winding appears as

a short circuit to the capacitance so that it again has littl e effect .
Since the r eac tanc es of the two

se~ondary

windings on the trans-

forme r are not perf ect ly matched, an external e l ement is n ecessary to
achieve reactive balance .

If the element i s inductive , reactive bal-·

ance will be i ndependent of frequency .

The amount o f inductanc e neces-

sary was determined approximately by placing a variabl e inductor in
series with the transf ormer.

The amount n ecessary was about 450 IJ.h.

An inductor was th en wound on a l ength of 3 em pyrex tubing .

Two 200 IJ.h

windings were made and wired togethe r in an opposing sense to minimiz e
noise pick-up.

The n 40 IJ.h, 30 IJ.h, 20 IJ.h, and 10 IJ.h windings were made .

This yie l ds a r easonab le amount · of r eso lution without a larg e numb er of
winding s or a continuous system involving s liding contacts and th e ir
probl ems.

The pyrex tube \va s then centered in a large copper pipe (the

-65-

inductance of the windings applies when thry arc in the pipe).

This

reduces noise pick-up and enables control of temperature. (see bel0\-7).
After placing the two 200 ~h windings in series with the transformer, the amount of capacitance necessary to achieve reactive balance
was detcrminc·d.

For a capacitor in p.::trallcl \-lilh a r0sistor :

R(l 1 +

jwRC)
(wRC) 2

For reactive balance,
wb.L = Im(Z)

where b. L is the additional inductance required.

t. L

- R?.
s.g.

1 + (wR s . g. C)
where R

s.g .

Therefore,

i s the r esistance of a single strain gage.

An amount of

inductance close to that calculated was then added in ser i es.

For final

precision b a lancing, a high resolution 50-1100 ~~f air capacitor was
used.
The chief disadvantage of this type of bridge is that the copper
wire used in th e windings of the inductor and the transformer has nonnegligible resistance.

Since copper has a large thermal coefficient of

resistance, thi s type of bridge is temperature sensitive .

For this rea-

son, a system for controlling the t emperature of critical components
was built.

These components are the strain gages , the two series decade

-66-

resistors, the inductor, the transformer, and the oscillator.

All other

elements carry very little current and have only a small effect on balance.

Since it would be virtually impossible to control the temperature

of lead wires and conLacts, the former were nude as short as possible
using the heaviest gage available and the latter were good quality high
frequency connectors.
Copper plates and pipes with copper tubing soft soldered to them
were placed as close as possible to the critical components .

The system

for control ling temperature was constructed as in Fig. A.3.

The water

bath contains two copper coils (one for the system water and one for tap
water), a mechanical stirrer, a heater, and a thermistor.

The control

temperature is set close to and sl i ghtly above room temperature.
makes control simple and radiative l osses small .
necessary to reject heat from the oscillator .

This

The cooling water is

The controller is an on-

off type in which a thermistor controls a relay.

The

te~pera tur e

of the

water bath changes less than 0 . 1°C over a period of several hours.

aid in maintaining constant temperature , all the copper parts surrounding the critical components are wrapped with fiber glass insulation .
The copper parts used in the temperature control system also
help in shielding electronic components against noise .
magnetic shielding foils were used as well.

I.Jhere necessary,

The main sources of pick-

up were the transformer, ground loops, and loops in the bridge circuit.
The foils were found to be highly effective in eliminating noise pickup by the transformer.

Judicious efforts were made to eliminate or

Fig. A.3.

WATER BATH

TO
SYSTEM

---<>

FROM
SYSTEM

<---

CENTRIFUGAL
PUMP _ _ _ J

VALVE

Diagram of the water system used to control the temperature of the strain
gages and of the sensitive elements of the bridge (see Fig. A.2 ).

CONTROLLER

TO
HEATER

TO THERMISTOR

TANK TO
PROVIDE HEAD
FOR PUMP

Q'\

-....J

-68-

reduce the area of the t\-70 types of loops .
used near right angle connectors.

Shielding foils were also

By th ese techniques it was possible

to reduce the noi se level observed on the lock-in amplifier well belm-1
the desired operating sensitivity.
The final bridge assembly is reasonably free of drift and noise.
The capacitor used for fine balancing i s virtually never

change~,

indi-

cating exce llent stability of reactive elements and negligible effect
from any frequency drift.

The balance point of the resistive elements

changes in a fashion indicating that strain gage temperature control is
not always too good.

Since the strain gages are mount ed on a very thin

strip of phosphor bronze, the heat transfer is not sufficient .

Fu Lhermore

they are subject to convection currents caused by cooling of the bottom
of the pendulum .

The latter can b e el iminated by evacuating the cham)er

containing the pendulum.

In this case the heat transfer to the copper

pipe surrounding the strain gages is great ly reduced.

From experience

it was judged preferable to maintain a gas atmosphere at 10 lo 15 lb/in

pressure in the chamber.
A possible i mprovement would be to have the bridge elements very
close to the strain gages .

These e lements could consist of two wire-

wound non-inductive resistors chosen so that only external balancing
by means of variable parallel resistors is necessary.

Another possi-

bility i s to have a longer phosphor bronze spring and four strain gages
wired to double th e output of the above system .

A series resistor would

be necessary to bring the bridge close to balance.

Both of the above

-69-

arrangeme nts would eliminate l ead \.]ire problec.s .

I f the strain gages

were changed, balance could be reslored merel y by wiring in a s ingle
resistor of the appropriate value .

Some form of temperature control

would stil l be desirabl e but the bridge would he le ss Lemperalure sensi tive.

llowever, the chief limiting faclor in Ute enlire system appear s

to be the non-zero magnetic moment of the p endulum coil.

Measurcmenls

well inlo the range where this becomes s i gnificant can eas ily be made
with the system as described.
A.3.

Current Supply for the Pc>ndulum Coil
The current is supplied by a Princeton Applied Research model

TC-100.2BR Voltage/Current Reference Source.

In the current mode, 0 Lo

100 milliamps arc available and the r esolution is severa l orders of
magnitude better than required.
time is very fast.

Setting i s done digitally and reaction

It s digital sett ing feature eliminales th e need for

a separate pot entiometer to measure current.

The only drmvback of

digital setting i s that a stepwise change in current impart s an impul se
to the pendulum, affecting short t e rm stability .

H01vever with experience

and a roug h idea of what the current should be, this i s not a serious
problem.

The maximum current is fairly sma ll.

HoHever, operational a

higher current cou l d cause slight h eating , causing erroneous t emperature measurements .

For mater i als with strong moments , it is better to

reduc e the mass than to use a large coil current.
A . 4.

Mcasuremenl and Control of Specimen Temp era ture

For the range 1.3 K to 4.2 K, the vapor pressure above condensed

-70-

helium (inside the specimen chamber) serves as an indication of temperature and a manostat (a pressure control device) maintains a set temperature.

From 4.2°K to 77°K, the resistance of a germanium resistance

thermometer indicates temperature and a balance between a small flm-1 of
liquid helium and a 0-4 watt heater is used for control.

From 77 K to

300°K, a copper-constantan thermocouple indicates temperature and a
balance between a small flm-1 of liquid nitrogen and the heater is used
for control.
Current to the Ge resistance thermometer i s supplied by a 0-5
volt Kepco regulated power supply.

It is operated in the voltage mode

with a high resistance in series .

(In the current mode , the minimum

current i s 1 rna which is too large.)

Under these conditions , the cur-

rent is very nearly independent of the resistance of the ther mometer .
The current is determined by measuring the vo l tage across a General
Radio type 1441 lOOP standard resistor with a Leeds and Northrup type
K Potentiometer .

The voltage across the thermometer i s also measured

with the potentiometer and its resistance is thereby obtained.

The

temperature is found by comparison with a calibration made against
another crystal whose calibrat ion was supp l ied by the manufacturer.
All thermocouple wire connect ions are welded, and the l eads are
brought out of the dewar through g l ass-to-metal vacuum seals which
enable a wire to pass through.

The thermocouple voltage i s

IIE asured

with the t ype K potentiometer and compared with a reference table for
for copper-constantan thermocouples.

When it is known that the

-71-

measuring point is at the boiling point of nitrogen , the voltage reading
is very close to th e proper value and no additional calibration is
n ecessary .
The heater consists of conslantan wire wound around and atlached
to Lhe copper \"all of the specimen chamber.
ohms.

Its resistance is about 5

It was considered desirable to keep Lhe l ead wires sma l l to avoid

heal transfer, and the current is Lherefore l imited to 900 rna .

The

heater currenl is supplied by an automatic temperature contro ller .
Automatic temperature control is desirable for a number of reasons .
First of all , il enables the operalor to concentrate on making magnetic
measurements without frequently having to check and adjust the temperatur e .

Secondly, an automatic controller can reach a new se t point

without any attention from the operator .

Finally , the more stable the

temperature, the better the stab ility of the magnetomeler.

Since the

effective thermal mass of the specimen chamber is both smal l and highly
temperature dependent, proportional control as opposed to on-off control,
rapid response and variable sen sit ivity t o temperature fl u ctuations are
n ecessary .

A circuit diagram of the controller constructed i s given in

Fig. A. 4 .

In operation, the thermocouple voltage is fed into a Cohu

Kint c l model 1 12A D.C. amplifier .

The output i s compared with an adjust -

able voltage (corresponding to the desired temperature).

This difference

voltage i s then amplified and current is fed into the h eater in proportion to this difference voltage .

A nominal va lue of heater current may

be sel manually in order that the difference voltage be nearly zero at

Fig . A.4 .

BUFFER

-=
SET

TEMP

"'"'

270~

Diagram of the electrical circuit used for automatic control of the
temperature of the specimen chamber.

r~ i

+13

i"'"'"
5n

•8

-...J

-73-

Lhe des ired temperature.

Wilh experience, n ear ly critical damping

and Lempera lure conlrol to beller Lhan 0 . 1°C can be obtained.

-74-

REFERENCES

Charles 0. Harris , Inlrocluc lion Lo Slrcss Analysis, Th e Macmillan
Company (1959), p . 97 .

Harold Hay] and, Differentia] Equalions AppU eel in Science and
Engineering, D. Van Nostrand Company, Inc . (1957), p . 70.