Nuclear magnetic resonance of Co69 nuclei in precipitated cobalt particles

NUCLEAR

MAGNETIC

s. NASU,~

RESONANCE

H.

YASUOKAJ

OF co59 NUCLEI PARTICLES * Y.

NAKAMURAf

IN PRECIPITATED

and

Y.

COBALT

MURAKAMI?

The Co60 nuclear magnetic resonance signals in precipitated Co-rich particles have been successfully observed by a transient (spin-echo) NMR method using heat-treated Cu-3.52 at. o/0Co alloy powders. The observed resonance spectra consist of a main intense sharp line and a week satellite line, and the resonance frequencies of both lines at 77°K are 217 - 219 MHz, depending on the heat treatment, and 198 MHz respectively. The resonance frequency of the main line indicated that the crystal structure of the precipitated particles is face centered cubic as has been expected. Careful measurements of the center frequency of the main line make it possible to discuss the internal pressure, acting on the precipitated particles, as a function of the effective particle size. The satellite line is attributed to the Co atoms located on the nearest neighbor sites of the Cu atoms dissolved in the precipitated particles. From the intensity ratio of the main line to the satellite line, the Cu concentration in precipitated particles has been estimated to be an extremely small value of 0.5% and is independent of the aging time and the particle size. This is probably the first report of the NMR study of the precipitated particles and the pulsed NMR technique is found to be one of the most effective methods to get microscopic and detailed informations of the precipitation phenomena. RESONANCE

MAGNETIQUE

NUCLEAIRE DES NOYAUX DE COBALT PRECIPITEES

CO”~ DANS

LES PARTICULES

Les signaux de resonance magnetique nucleaire du Co so dans les particules precipitees riches en Co ont et6 observes avec succes par RMN transitoire (echo de spin) sur des poudres de l’alliage Cu-3,52 at. ‘A Co ayant subi un traitement thermique. Les spins de resonance observes consistent en une raie principale fine et intense et une raie satellite faible, et les frequences de resonance de ces deux raies 8. 77°K sont respectivement 217 N 219 MHz (cette valeur dependant du traitement thermique) et 198 MHz. La frequence de resonance de la raie principale montre que la structure des particules precipitees est cubique faces cent&es comme prevu. Des mesures precises de la frequence centrale de la raie principale rendent possible une discussion relative a la pression interne agissant sur les particules pr&pitees. Cette pression serait fonction de la taille effective des particules. La raie satellite est attribu&e aux atomes de cobalt situ& sur les sites premiers voisins des atomes de cuivre dissous dans les particules precipitees. D’apres le rapport des intensites relatives a la raie principale et a la raie satellite, la concentration du ouivre dans les particules precipitees a et6 evaluBe 8, une valeur extremement faible, 0,5 %, et est independante du temps de vieillissement et de la taille des partioules. Cette etude des particules precipitees par RMN est probablement la premiere, et les auteurs trouvent que la methode par RMN pulsee est I’une des meilleures methodes pour obtenir des informations microscopiques detaillees sur les phenomenes de precipitation. KERNMAGNETISCHE

RESONANZ

VON Cos9-KERNEN

IN KOBALTAUSSCHEIDUNGEN

Die Signale der kernmagnetischen Resonanz (NMR) van Cosg m kobaltreichen Ausscheidungen wurden erfolgreich mit einter Spin-Echo-NMR-Methode an wiirmebehandeltem Cu-3,52 At. ‘A CoPulver beobachtet. Die beobachteten Resonanzspektren bestehen aus einer scharfen Hauptlinie und einer schwachen Satellitenlinie; die Resonanzfrequenzen beider Linien sind bei 77°K je nach Wiirmebehandlung 217 bis 219 MHz bzw. 198 MHz. Die Resonanzfrequenz der Hauptlinie deutet darauf hin, da13 die Ausscheidungen, wie erwartet, eine kubisch-fliichenzentrierte Struktur besitzen. Eine sorgfliltige Messung der Frequenz im Zentrum der Hauptlinie erlaubt eine Diskussion des auf die Ausscheidungen wirkenden inneren Druckes als Funktion der effektiven TeilchengrGBe. Die Satellitenlinie wird den Co-Atomen auf niichste-Nachbar-Plitzen zu den in der Ausscheidune ..,- geliisten Kunferatomen I zugeschrieben. Aus dem Intensitlitsverhiiltnis van Haupt- und Satellitenlinie wurde die Kupferkonzentration in den Aussoheidungen abgeschlltzt: sie ist sehr klein, etwa 0,5%, und unabhiingig van der Auslagerungszeit und TeilchenmoDe. Das ist wahrscheinlich der erste Bericht tiber NMR-Untersuchungen an Aussoheidungen und es zeigt sich, da9 die NMR-Method0 eine der effektivsten Methoden zur Gewinnung mikroskopischer und detaillierter Informationen iiber Ausscheidungsphiinomene ist.

1. INTRODUCTION

Since the first successful nuclear magnetic resonance (NMR)

observation

of Co5g nuclei in ferromagnetic

f.c.c. cobalt metal, the NMR of nuclei in magnetic atoms has become one of the most powerful methods * Received August 12, 1970. t Department of Metallurgy, Kyoto University, Kyoto, Japan. $ Department of Metal Science and Technology, Kyoto University, Kyoto, Japan. ACTA

METALLURGICA,

VOL.

19, JUNE

1971

for investigating

magnetic

NMR technique,

it becomes

and dynamic

characters

materials.(i)

Utilizing

the

possible to study static

of local

atomic

system

in

ferromagnetic particles not easily obtained by other methods. High precision measurements of the distribution of the frequency for resonance or the hyperfine field in metals and alloys are possible using the NMR technique. To estimate the accurate distribution of resonance frequencies is useful in order to 561

ACTA

562

discuss local environments

METALLURGICA,

of the resonant

nuclei in

Applying study

the NMR microscopic

In the final section,

nature

are many

alloy

and Cu-Ni-Co,

of

the

precipitated

systems,

such

Co-rich

particles

Among

these

matrix.

dilute Cu-Co alloys were attracted the

process

of

studied by other means atively simple.(2*3) The transmission

in

systems,

to our attention

has

been

electron

micrograph

as

because

extensively

and is believed

to be relof a Cu-Co

that in the early stage of the pre-

cipitation process the precipitated are entirely coherent with the spherical

2(a)

shape.(4s5)

Co-rich particles Cu matrix and

Increasing

the

period

of

conclusions

on the nature of

emerging

from

the NMR

sample preparation

and precipitation

of the

Co-rich Particles

precipitated

alloy

of the NMR technique,

precipitation

alloy foil showed

as Cu-Co,

results and inter-

2. EXPERIMENTS

suitable for the NMR studies

of the ferromagnetic

the first application

of

process.

from

alloy

Experimental

the precipitated particles studies are summarized.

particles in an alloy matrix for better understanding There

2.

are given in Section 3.

to the precipitation

the kinetics of the precipitation Au-Co

given in Section

to make it possible to

technique

it can be expected

the

19, 1971

pretations

metals and alloys. phenomena,

VOL.

Present NMR Cu-3.52

at. T’

prepared

from

copper

studies have been carried out using Co alloy

by induction

high purity

powders.

electrolytic

cobalt

melting

alumina

The and

alloy

was

oxygen-free

for several times

crucible

under

inert

in a

gas pro-

tection.

After the alloy ingots were filed, these alloy

powders

were mixed

with fine alumina

powders

to

avoid sintering during annealing at high temperatures. These samples were subsequently silica

tube

and

given

sealed in evacuated

a solution

hr at 1050°C and finally followed crushing in water.

treatment

for

by quenching

The subsequent

1

and

aging treatment

aging treatment, the particles become large and incoherent, changing their shapes to ellipsoids and,

was done in a silica tube at a constant

finally, the particle shape becomes an octahedron.

These alloy powders were sealed off in a glass tube and placed inside of the inner finger of a Dewar for the

These precipitated

Co particles in diameter ranging

from 20 to 1000 A are classified into three categories

NMR measurements.

by

by

their

magnetic

Particles

large

domains; tized

to

without

rotating

follows.@)

any domain the

(1) ferromagnetic

particles

of domain

particles entire

as

contain

these multi-domain

single-domain by

enough

by the motion

particles

properties

walls.

temperature

the

(3) Much

ation fluctuates thermally. technique

for studies

of magnetic and atomic properties in fine ferromagnetic particles, there now exist two distinct NMR studies; one is associated category

(l)]

particles. nuclei

and

However,

For the particles precipitated

domain

multi-domain

the

other

with

particles

the NMR signal associated walls

is

[the

single-domain with

almost

is

homogeneously

Cu-Co alloy, the coarsening equation particle size i is expressed by(s-ll) f3

-

PO3 =

valid

k

in

the

in the

of the average

. t,

(1)

where ?,, is the average particle radius at the onset of the coarsening and k is the rate constant. The

precipitated

evaluated short-time

aged

paremagnetic However,

particle

by analyzing

specimen

particles

size

in

Fig.

the magnetization which

contains

(40 N 100 A

even immediately

in

1

was

curve in a super-

diameter).

after quenching the speci-

unbelievably For this enhanced by the wall displacement.(l) reason, most of the NMR studies in ferromagnetic

men shows a euperparamagnetic behavior probably because of the existence of the clustering of Co solute

metals and alloys have been worked out using multi-

about 20 A in radius whose value was found to be nearly constant after aging for 1 min. The particle size obtained from the subsequent aging periods of more than 1 min increases gradually and is well expressed by equation (1). Assuming that the rate

domain signals

in

with

method(‘)

room

magnetic

changes

granumetry

at

powders ; this

particles whose diameter is below about 120 A.

In these

of the NMR

curve

using the same sample

smaller single-domain particles. In these so called superparamagnetic particles the direction of magnetizIn applications

The particle size was estimated magnetization

(2) Smaller

boundaries. moment.

measuring

are magne-

magnetization

magnetic

temperature

of 6OO”C, and then the tube was quenched into water.

particles. In the present study, the NMR were also observed in precipitated multi-

domain particles. In Section 2 are described the sample preparation and the determination of the precipitated Co-rich particle size. The transient NMR technique is also

atoms(i2J3) and its effective

size was estimated

to be

constant k is unchanged during the coarsening from superparamagnetic to multi-domain particles, the

NASU

NUCLEAR

et al.:

MAGNETIC

Aging

RESONANCE

Time

at

600°C

OF

Co59

NUCLEI

IN

583

Co

(min.)

Pm. 1. Average precipitated

particle size as a function of the aging time at 6OO’C for the Cu-3.52 at. % Co alloy. dotted line is the extrapolation of the observed line using equation (1).

The straight

particle

size even

after

should be expressed of

equation

occurs

(1).

at grain

long time

boundaries,

turns out naturally the discontinuous

aging

by the extrapolated If a discontinuous the

above

to be unreliable. precipitation

treatment

straight line precipitation assumption

100 p) that each alloy particle

calibrator

contains almost

2(b) Experimental

wave

(steady

state)

and the other

excitations

transient

(pulsed)

of nuclear excitations. on

what is the nature of observed signal, particularly

the

broadness of NMR lines. In alloy systems, however, the line width usually becomes broad due to many crystallographic planes,

transient

defectso*)

(e.g.

dislocations

NMR

method

and

disordered

lattices,

so on),, hence

is suitable

to their

the

NMR

signal detections. In the present experiments, therefore, the transient NMR method was utilized and the so called “spin-echo” The technique spins

in

nuclear signal was observed.

of transient

ferromagnetic

excitation

materials

is by

of nuclear now

well

established and has been fully described by many resonance workers. It consists of creating a nuclear spin-echo by applying two consecutive pulses of rf excitation to the sample and of measuring the amplitude of spin-echo signal as a function of resonance frequency across nuclear resonance

the inhomogeneously line. After adjusting

signal

the

echo

of the calibrator

amplitude,

produced

was externally

by

a

For

a

pulsed

standard

signal

put on, and the amplitude

signal was made equal to the ampli-

tude of the echo signal, both

being observed

on an

oscilloscope. The calibrator signal voltage was then taken as the amplitude of the nuclear signal at that frequency.

The

transverse

These two methods have different merit depending

faulted

of

the pulsed rf

echo signal.

calibration

voltage

accuracy

was

kept small enough so that the echo decay due to the

method of the pulsed NMR

For the observation of NMR signal, there are now two different types of technique; one is using conspins

frequency,

was tuned to a maximum

estimated to be less than 10 per cent. The separation between the rf pulses (6 psec) was

stage at 600°C.

technique

tinuous

a tuning circuit in which the sample

to a particular

measurements generator

no grain boundary. It seems, therefore, that after aging for 1 min, the precipitation process in Cu-3.52 at. % Co alloy is in a coarsening

frequency

of

particles, however, is very small and could be negligible, since the size of alloy powders is so small (of about

was placed,

alloy

The amount

in the present

system, including

broadened a receiver

relaxation

was negligible.

remove any change in exciting was kept constant

condition,

In

order

to

the rf level

and the pulse width at each point

was adjusted

in such a way that t’he echo signal The rf pulse field intensity becomes its maximum. was about 20 Oe and the rf pulse width of about 0.5 N 2.0 ,usec was used. A block diagram of the apparatus used in this study is illustrated in Fig. 2. For

low

temperature

measurements,

exposed-tip

liquid nitrogen and helium Dewars were used. The finger of the Dewar was fitted with the tuning samples coil

which

is coupled

to

a rf transmitter

and

a

receiver by low impedance cables. The alloy powders were sealed off in a glass tube and placed inside the finger of the Dewar.

The sample tube was about

10

mm in diameter for 77°K measurements and was about 7 mm in diameter for 4.2”K measurements in which the sample tube was filled by helium gas.

3.

EXPERIMENTAL

RESULTS

AND

INTERPRETATIONS

The Co5g NMR signals of precipitated Co-rich particles in Cu-3.52 at. % Co alloy have been observed at temperatures below 300°K. Since the essential

664

ACTA

i

METALLURGICA,

-

Pulse

1971

i --v-f 1 3 q

Pulse Oscillator

Amplifier

Generator

z k

19,

J-u-t

i

Pulse

VOL.

i 3

m

ri

Osi IIoscoDe

I

FIQ. 2. Block diegram of the pulsed NMR system. features

did

interpretation

not

change

with

was mostly

temperature,

the

made for the data taken

at 77’K. 3(a) Resonance frequencies The Cos9 spin-echo whose precipitated The

observed

intense

particle

sharp line (M)

consist

and a weak

broad satellite line (N).

Typical

of a main

and somewhat

spectra are shown in

more

than

155 min,

was observed

a satellite

frequency

(198 MHz at 77°K) than that of the main

at a much

The analysis of satellite lines observed

magnetic

size is larger than 100 A. spectra

aged

line N

line.

and spectra

signals were observed in samples

resonance

In samples resonance

dilute

lower frequency

Co alloys(15) indicated satellites

whose environments

lower

in ferro-

that

these

are due to the Co atoms

are perturbed

by an addition

of

impurities. It is necessary

to discuss the hyperfine

on the nuclei of Co atoms disturbed

Fig. 3 for alloys aged for 100 min, 10 hr and 1 week at

neighbor

600°C

the precipitated Co particles are assumed to give rise to the observed satellite resonance line.

after

solution

heat-treatments

respectively.

The observed spin-echo intensity increases with increasing aging period, since the number of CoS9 nuclei

contributing

the

spin-echo

in multi-

domain

particles

increases

period.

However,

in this figure the observed

intensity is normalized The main resonance frequency

increasing

at 217 MHz. peak has been observed

range between

for all aged samples.

with

signal

aging echo

since the Cu atoms

dissolved

in

The hyperfine field, H,, of a Co nucleus is generally represented as to be proportional to magnetization and to the magnetization by nearest neighbors.

its local produced

Then, the field acting on the Co

atom at the ith position is in a

217 and 219 MHz at 77°K

Since the observed

impurity,

field acting

by the nearest

Hz) = a - pi + b . 2 ,un.,,,

R’Vl

frequencies

are considerably lower than that of h.c.p. Co metal (227 MHz at 77”K’l)) and almost agree with that of pure f.c.c. Co metal (217 MHz(l)), the observed signal is attributed to the resonance in f.c.c. particles. The reason for the slightly higher frequencies will be discussed in a following section [3(b)] as arising from the internal stress. It follows, therefore, that the crystal structure of the precipitated particles is f.c.c.

where pi and ,uu,., are the moments

(2)

of the ith atom

and of each of the nearest neighbor atoms, respectively, and a and b are proportional constants which were determined empirically to be -39 and -7.3 KOe/,uB. The magnetic moment of the Co atoms on the nearest neighbor

sites of an impurity

= 1.7 + (dji/dc + 1.7)/12, P 12.12

is given by (3)

NASU

et al.:

NUCLEAR

RESONANCE

MAGNETIC

OF

Cosg NUCLEI

IN

Co

506

Once the resolved satellite line in the experimental spectrum

0

is assigned to a given configuration

of the

impurities, the intensity ratio, I, of the satellite line to the main line in a f.c.c. lattice, in which the

i

impurity

atoms

calculated

are randomly

distributed,

I = N/M

= 12(1 -

c)“c/(l

where c is the atomic concentration Aged for

atoms.

00

is easily

as

Here

we have

ignored

-

c)12,

(5)

of the Cu impurity the contribution

of

interfaces between precipitated particles and the alloy matrix to the resonance spectrum, since the Co

IO

atoms in the interface

region have so many impurity

atoms with various configurations

that the resonance

frequency of such atoms will be distributed widely. From the observed integrated intensity ratio, I, the concentration cipitated

of the Cu atoms dissolved

Co particles

is estimated

in the pre-

to be about 0.5 %.

This value of the Cu content in the small precipitated

190

180

200

Frequency

210

220

230

J

1Mc/sec)

Fm. 3. Co60 resonance (spin-echo) spectra in Cu-3.62 at.‘/, Co alloy samples aged at 600°C observed at 77°K. M:. main line arising from the pure f.c.c. Co. N: satellite line &sine from the Co atoms on the nearest neighbor sites of thz Cu impurity. A satellite line between 220 N 225 MHz observed in the 1 week aged sample, is attributed to stacking faults. The observed echo intensity was normalized at 217 MHz.

where dp/dc is the rate of decrease

of the average

particles is firstly estimated from the NMR technique. The present result is extremely small as compared to that expected

precipitation

process

cipitated

particle

H, = a * I-L

where p,, is the moment

(4)

+ 7~~ + ,G,&

of Co having no impurity

on

its nearest neighbor sites and so its value is 1.7 ,uB and !-&n. is the moment of the impurity. For the Co-Cu

alloys, dpldc was determined

to be

-2.25 ,L+/(CU atom) by Crengle(16) and the magnetic moment of Cu impurity atom, pi,,,, should be zero.

obey

the

particles is independent

of

the

usual

prephase

in

of the aging

period and the precipitated particle size, within the experimental error. This means that the stable phase in the first stage of aging.

As is seen in Fig. 3, another observed

week aged sample.

+ b(4 x P,.,

composition

not

It was also found that the copper concentration the precipitated

has been

lattice is written by

the

does

diagram, but almost pure f.c.c. Co particles precipitate initially from the matrix.

the nearest

in the f.c.c.

of the Cu

suggests that in the early stage of the

is precipitated

of an impurity

phase diagram,

This large difference

concentration

moment of the alloy with increasing impurity concentration. Then the field at the Co nucleus which is neighbors

from the equilibrium

i.e. 10% at 600”C.(17)

between

broader

220 -

satellite line

225 MHz

for

This line can be considered

1 &B

arising from co59 nuclei in stacking faults and agrees well

with

that

of

deformed

Co powders.04)

The

f.c.c. + h.c.p. transformation of the Co-rich particles in Cu matrix can be induced by heavy cold working.(lsJ9)

Therefore,

the NMR

technique

may be a

good tool for the study of the transformation precipitated

of these

particles.

Particle size dependence of the center frequency

Using equation (4), the value of hyperfine field of the Co nuclei which are the nearest neighbors of Cu

3(b)

impurity is estimated to be -199 KOe. This value agrees well with the hyperfine field of the observed satellite line. Consequently, it is concluded that the observed satellite line is due to the co59 resonance

frequency is slightly higher than that of the free f.c.c. cobalt metal and depends on the aging period and the particle size. The experimental results obtained at 77 and 4.2”K are shown in Fig. 4 where the upper

associated with the Co atoms which are on the nearest neighbor sites of the Cu impurity atoms dissolved in the precipitated particles.

abscissa indicating the particle size was obtained from the dotted straight line in Fig. 1. The pressure dependence of the Cos9 resonance

As mentioned

in a previous

section,

the

center

566

ACTA

METALLURGICA, Effective

150

,

Particle

200

19,

Diameter 300

I

I

VOL.

(WI

400

I

1971

500

I

600

801

I

I

I

$ : 77°K 4

$

I

I

I

: 4.2”K

1

I!lWl

I

1000

100 Aging

lime

at

10000

600°C

(min.)

FIQ. 4. Aging period and/or particle size dependence of the center frequency of the main line.

frequency

in f.c.c.

Co metal was studied(20*21) and it

was found that = $0.135

MHz/kbar.

(6)

These pressure studies of free f.c.c. Co metals suggest that the shift of the center frequency in Fig. 4 should be attributed particles.

to the internal stress acting on Then, using equation

(6), the

nuclear

magnetic

rich particles

The frequency

The

resonance

ing aging time from 100 to 300 min, and then reaches kbar.

value which is evaluated

The most interesting

feature

that after arriving at its maximum

to be about 12 of this study is

value the internal

precipitated

can be observed from Cu-Co

crystal

structure

weak

in Co-

alloy matrix.

consist of a main weak satellite line.

of the main line is about the same as

that of free f.c.c.

value of the pressure increases gradually

with increas-

result of this study is that the

resonance

The observed resonance spectra intense sharp line and a relatively

internal pressure on the particles can be easily estimated as a function of aging time. The estimated

the maximum

CONCLUSIONS

The most important

av/+

precipitated

4.

Co metal.

This implies

of the precipitated

satellite associated

line

that the

partiole is f.c.c.

is attributed

to

the

co59

with the Co atoms which are on

the nearest neighbor sites of the dissolved Cu atoms. From the intensity ratio of the main line to the satellite line, the Cu concentration particles

wss estimated

in precipitated

to be about

0.5%

Co

which is

stress is abruptly decreased at the particle size of about 300 A and becomes roughly independent of particle size. This abrupt decrease of the internal

surprisingly small as compared to that expected from the phase diagram. It is also found that the concentration

is independent

pressure may be attributed to the loss of full coherency between the precipitates and the Cu matrix. The

treatment,

that is, independent

electron

microscopic

observation

by

Tanner

and

Servi(s) and Phillips(4) indicated that the entire loss of coherency occurred at the particle size of 350 N 600 A in diameter and therefore these observations agree fairly well with the present results. It should nevertheless be emphasized that the present NMR detection of this effect is more sensitive than the electron microscopic observation.

of

the

period

of

aging

of the particle size.

Careful measurements of the particle size dependence of the center frequency of main line yield the maximum value of the internal stress, acting on the precipitated particles, of about 12 kbar. The stress is abruptly decreased at the particle size of about 300 A as a result of losing coherency cipitates and the Cu matrix.

between

the

A much weaker broad satellite line associated

prewith

Co5B nucleus in stacking faults was also observed in a

NASU

et al.:

NUCLEAR

long period aged sample at higher frequency the main line. We believe that

the present

RESONANCE

MAGNETIC

side of

work is probably

the

first example where NMR signal8 have been observed in precipitated

particles

and provides one of the most

accurate sources of new microscopic about precipitation phenomena.

information

ACKNOWLEDGEMENTS

The authors contributions

thank

Mr. T. Areki

throughout

this work.

for his various The authors

are

also indebted to Prof. 0. Kawano

for his interests and

discussions

for his help in the

and to Mr. T. Kubo

experiments. REFERENCES 1. A. M. PORTIS end R. H. LINDQTJIST,in Magnetism,

Vol. II Part A, edited by G. T. RADO and H. SUHL. Academic Press (1965). 2. A. KELLY and R. B. NICHOLSON, in Progress in Materials Science, Vol. 10, edited by B. CHALMERS. Pergamon Press (1961). 3. J. D. LIVINQSTON, Trans. Am. Inst. Min. Enqrs 215, 566

(1959).

OF

Cos8 NUCLEI

IN

Co

567

4. V. A. PHILLIPS, Trans. Am. Inst. Min. Ertgr8 280, 967 (1964). 5. L. E. TANNER and I. S. SERVI, Acta Met. 14,231 (1966). 6. C. P. BEAN and J. D. LIVINOSTON, J. appl. Phys. 30,120s

(1959).

7. J. J. BECKER, Trans. Am. Inst. Min. Enqrs 209,59 (1957). 8. J. D. LIVINUSTON, Tracts. Am. Inst. Min. Engrs 215, 566

(1959). \----I

G. W. GREENWOOD, Acta Met. 4, 243 (1956). J. M. L~FSHIFTZ and V. V. SLYOZOV, J. phys. Chem. Solids 19, 35 (1961). 11. C. WAQNER, 2. Elektrochem. 65, 581 (1961). 12. I. S. JACOBS and R. W. SCHMITT, Whys. Rec. 113, 459 (1959). 13. G. J. VAN DER BERG, J. VAN HERK and B. KNOOP, in Proceeding8 of the 10th International Conference on low

1::

Temperature Physics, Moscow, Vol. 4, p. 272 (1966). R. STREET, D. S. RODBELL and W. L. ROTE, Phys. Rev. 121, 84 (1961). S. KOBAYASHT, K. ASAYAMA and J. ITOR, J. phys. Sot. Japan 21,65 (1961). J. CRANOLE, Phil. Maq. 46, 525 (1955). M. HANSEN and K. ANDERKO, Constitution of Binary Alloys, Vol. 1. McGraw-Hill (1958). N. TAMAQAWA and T. MITUI, J. phys. Sot. Japan 20,1988 (1965). S. Ndsu,

Y.

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