The quenching-in of lattice defects in gold-cadmium

THE

QUENCHING-IN

OF LATTICE M.

S.

DEFECTS

IN GOLD-CADMIUM*

WECHSLERt

When B Au-Cd is quenched from a high temperature, a large increase in resistivity results. The amount of quenched-in resistivity was measured as a function of quench temperature and an energy of formation of 0.38 eV was obtained for the associated defects. The isothermal annealing of the quenched-in resistivity w&4 studied at a number of temperatures. The process appears to have an incubation period and an activation energy for motion of 0.58 eV. Possible explanations are discussed; the quen~h~g-~ of lattice vacancies is considered to be the most likely source of the effect. On the b&s of Jongenburger’s theoretical estimates of the resistivity arising from vacancies in gold, it is estimated that about 0.7% vacancies are frozen in after quenching from 450°C. LE GEL DES D&FAUTS

RGTICULAIRES

DANS

L’OR-CADMIUM

Lorsque Au-Cd est trempQ B partir d’une temperature BlevBs,on remarque un accroissement important de la r&istivit& Le pourcentage de r&sistivitbapr&strempe a &B mesure en fonction de la temperature de trempe et une Bnergiede formation de 0,38 eV a BtBobtenue pour les defauts associb. On a Btudibri dil%rentes temp&atures le revenu isotherme de la r&istivite ap&s trempe. Le pro&d6 semble montrer une pbriode d’incubation et avoir une Qnergied’activation de mouvement de 0,58 eV. L’auteur d&cute les interpr&ations possibles: le gel des lacunes semble 6tre la source la plus probable de cet effet. En se rapportant aux estimations th&oriquesde Jongenburger SUPla r&istivitb due aux lacunes dans I’or, on peut admettre que 0,7% des lacunes sont gel&s par trempe iLpartir de 450°C. DAS ~INFRIE~~N

VON GITTERFEH~ERN

IN GOLD-CAD~UM

Wenn B-Au-Cd van hoher Temperatur abgeschreckt wird, ergibt sich sine starke Wide~tandsz~ahmen. Die Griisse des “eingefrorenen Widerstands” wurde in Abhiingigkeit von der Absch~cktem~ratur gemessen. Daraus erh< man eine BiIdungsenergie van 0,38 eV fiir die massgebenden Fehlstellen. Ausserdem wurde bei verschiedenen Temperaturen die Erholung des eingefrorenen Widerstands bei isothermem Anlassen untersucht. Der Vorgang scheint mit einer Inkubationszeit und einer WanderungsAktivierungsenergie von 0,58 eV abzulaufen. Miigliche Erkllrungen fiir diese Erscheinung werdan diskutiert; als ihre wahrscheinlichsteUrsache wird das Einfrieren von Gitterleerstellen angesehen. Auf Grund der theoretisohen Abschiitzung von Jongenburger fiir den Widerstand von Leerstellen in Gold wird geschiitzt, dass naoh Rbschrecken von 450°C etwa 0,7% Leerstellen eingefroren sind.

1. INTRODUCTION

In order to study the effects of lattice defects on the properties of crystalline solids, experiments are performed on materials that contain a larger concentration of defects than would be present in thermal equilibrium. By observing the kind and extent of changes caused by excess defect concentrations, much can be learned of the nature of the defects. Two methods for producing an excess number of defects are by plastic deformation and bombardment with charged particles, neutrons, or electromagnetic radiation. A third method, and the one with which this pa.per is concerned, is to quench the solid from a high ~mperature. If the quenching is performed sufficiently rapidly, it is possible to retain the larger concentration of defects characteristio of thermal equilibrium at, the temperature from which the solid is quenched (the “quench temperature”). It has been found(l) that quenching produces an unusually large increase in the electrical resistivity * Received November 14, 1955; revised version August 6, 1956. t Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee. ACTA

~~TALLURGI~A,

VOL.

5, XARCH

1957

of Au-Cd. This paper describes an investigation of this effect. In a later section we shall be concerned with the origin of the quenched-in increase in resistivity in Au-Cd. In view of the fact that the Au-Cd system is relatively little known, it is appropriate to examine briefly what has been reported concerning the constitution of Au-Cd alloys near the equi-atomic composition. Two points are of particukr interest. The first of these is the 8-p transition at 337% as shown in Hansen,c2) and the second is the extent to which the alloy is less ordered at temperatures near the melting-point than at lower temperat,ures, say below 1OO’C. The p (Cs-Cl st.ruct,~~re)to p’ (o~horhombic) tra,nsit*ionthat appears on Mansen’s phase diagram at 267°C is derived from the work of Olander. illander(3) made electrolytic-ceil measurements of the e.m.f. of Au-Cd against pure cadmium, which indicated a phase transition at 267°C in the neighboring p + y’ region. From the magnitudes of calculated integral molar entropies, he deduced that the transition was in the ,8 phase to t’he left (lower cadmium content) of the two-phase region and not in the y’ phase to the right. In a subsequent 150

WECHSLER:

THE

QUENCHING-IN

OF

X-ray investigation, Olanderc*) found that filings of the 47.5 at. per cent Cd alloy quenched from 220°C and 430°C both indicated an orthorhombic structure, whereas an at-temperature exposure between 400°C and 450% gave a Cs-Cl struoture. These observations were regarded to indicate that the /L@’ tradition is not impeded by quenching, and to support the conclusion from electrolytic cell measurements that the transition is at 267°C. However, no at-temperature X-ray measurements were made at temperatures below 267°C. Later investigations have indicated that, had this been done, it would have been found that the orthorhombic structure does not become the equilibrium phase until much lower temperatures are reached. Bystrom and Almin(@ found from attemperature X-ray photographs that the cubic to o~horhombic transition is at 85 IJc 15°C. Moreover, they determined the transition d~atometriGally; in this ease the transition temperature was estimated to be 64 -& 6°C. The transformation temperature has also been determined by resistivity measurements.(*? 6, These indicate that the cubic to orthorhombic transformation takes place in the 47.5 at. per cent Cd alloy at about 60°C and the reverse transformation at about 8O’C. Furthermore, a detailed analysis of the crystallography of the phase change has been given. (‘) Another low-temperature m~ifi~tion has been reported for alloys closer to t,he 50-50 composition and the crystal structure has been specified as tetragonal, although a complete identification has not yet been made. Resistivity measurement& Q indicate the transition temperature for the cubic to tetragonal transformation to be 30% and the temperature of the reverse transformation to vary from 40 to 55%, depending upon thermal history. tilander’s 267’C transition has been regarded as an order-disorder transition,(Q) but MuldaweroO) has pointed out that electrical-resistance measurements in the region of 267% give no ~di~ation of any change taking place. This observation wa,s also made several years ago by the present author. Equilibrium-resistance measurements were made on two 47.5 at. per cent Cd samples in the temperature range from 20°C to 34O”C, and, in this case also, no evidence was found for a transition point at 267°C. olander, in his original paper,c3) calculated from the entropy in excess of that expected for perfect order that only 0.5o,i, of the atoms are misplaced at 450°C. This would correspond to an order parameter of 0.98. On the other hand, Kubasche~ski(ll) has determ~ed from ~alo~rnet~ri~ measurements that the entropy of meIting of b Au-Cd is the same as

LATTICE

DEFECTS

IN

GOLD-CADMIUM

151

the sum of the entropies of melting of the pure components, and from this he concludes that the alloy is disordered at the melting-point. An at-temperature X-ray diffractometer investigation was made at this laboratory* on /I Au-Cdin the telnperature range from 40°C to 600°C (approximately 25 degrees below the melting-point). The direct 110 and 200 reflections and the superstructure 160 reflection were observed. There was no evidence of the formation of a new phase, and even at 600°C a definite superstructure reflection was obtained. However, no attempt was made to study in a quantitative way the variation of integrated intensities with temperature, and thus no measure of the temperature-dependence of the order parameter was obt,ained. As the matter now stands, it seems rea.sonable to regard the fi Au-Cd phase as the equilibrium structure from below 100% t.o the melting-point, with a fairly high degree of order persisting to temperatures near the melting-point, as is apparently the case in Au-Zn.(rz) However, the details of the Au-Cd equilibrium diagram in this composition range are by no means settled, and further experimental work should be done. 2. SPECIMENS

AND

EXPERIMENTAL

METHOD

Most of the resistivity measurements described below were made on three samples of nominal composition 49 at. per cent cadmium. The minimum purities of the base materials as supplied by the manufacturer were 99.97% for the gold and 99.95% for the cadmium. Sample A was prepared by homogenizing and casting in an evacuated quartz tube, and samples B and C were homogenized and cast in a graphite mold contained within an evacuated quartz carrier. The mold was designed to produce rod-shaped samples containing short projections or nibs perpendicular to the axis of the rod. Both samples were lowered slowly through a temperature gradient in the Bridgman manner and annealed approximately one day fifty degrees below the meIting-post; this was followed by a furnace-cool. Voltage contacts were made to sample A by means of spring-loaded knife-edges and to the nibs on samples B and C by a sleeve and set-screw arrangement. The diameters of the samples were roughly one-eighth inch. Kelvin bridges were used to measure resistance. Measurements on sample A were made relative to an external standard resistance and on samples B and C relative to an untreated Au-Cd comparison * The author wishes to thank M. A. Bredig and R. D. Ellison of this Irdboratoryfor their advice and coflaborat.ion.

152

ACTA

METALLURGICA,

sample of the same dimensions and composit,ion. After quenching, samples B and C were placed alongside the comparison sample in a small holder and the holder was placed in a stirred oil-bath whose temperature was kept constant to within 022°C. In this way, a small bridge yoke could be used, resulting in a shortening of the time necessary for the treated sample to come to the temperature of the oil-bath. Furthermore, since the thermal coefficient of resistance was very nearly the same for the treated and comparison samples, the effect of thermal fluctuations in the oil-bath was cancelled out. In addition, the resistance of the comparison sample was measured as a function of temperature relative to an external standard in order that the absolute resistivity could be calculated. The quenching was carried out by holding the sample in a salt bath at the quench temperature and then rapidly removing the sample from the salt bath and plunging it into water at 40°C. In most cases, the time of hold in the salt bath was one minute. As is described below, longer holding times were found to give no increase in the quenchedin resistivity. In order to measure the quenching rate, experiments were performed on a sample of approximately the same size, shape, and composition (7j-in. rod, 49 at. per cent Cd) as the resistivity Chromel-alumel thermocouples samples. were attached to the sample and the thermocouple voltage during quenching was fed to a high-speed oscillo~aph or to a cathode-ray oscilloscope. The oscillograph charts or photographs of the oscilloscope screen presented a record of the time-temperature curve. The thermocouples were attached in two ways. In the first case, 30-gage chrome1 and alumel wires were individually spot-welded to the surface of the sample at a point midway along the length; the distance between the two-spot welds was approximately equal to the thickness of the wire. In the second case, short lengths of S&gage chrome1 and alumel wires were spot-welded end to end and a 1%mil-diameter transverse hole was drilled completely through the sample at a point midway along its length passing across and perpendicular to the axis. The thermocouple wires were insulated near the weld with quartz capillary tubing and the thermocouple was pulled through the hole in the sample so that the bead at the weld was at a point near the axis. The hole and bead size were such that good thermal contact was achieved betweeen the thermocouple bead and the wall of the hole. A small amount of cement was applied at both ends of the hole and the ends of the 3%gage wires were

VOL.

5,

1957

spot-welded to 30-gage duplex chromel-alumel thermocouple wire. The sample was quenched from approximately 450°C in the same manner as the resistivity samples. It was found as a result of a number of runs that the temperature decreases from 450% to 200°C in about 12 msec for a point on the surface and in about 85 msec for a point near the axis. Furthermore, about 0.6 see elapse from the time t.he sample is removed from the salt bath to the time it is immersed in the water, and during this time the temperature decreases about 6%. The quench temperatures presented below refer to the salt-bath temperature without correction for this the results are not changed decrease. However, significantly if this correction is made. Under slow‘cool conditions, the cubic to tetragonal transformation temperature was observed to be about 30°C for all samples. Care was taken to maintain the samples in the cubic phase at all times during the course of the heat treatments and measurements. Two types of experiments were carried out. In the first of these, the amount of quenched-in resistivity was measured as a function of the quench temperature from which the energy of formation of the quenched-in defect was calculated. In the second experiment, the isothermal relaxation from the quenched to the slowcooled value was measured at a number of temperatures. fn this way, the activation energy for movement of the defect was determined. 3. RESULTS

The effect of quenching ,8 Au-Cd alloys is to increase the resistivity by amounts that increase with rising quench temperature. The magnitude of the quenched-in resistivity is quite high; for example quenching from 450°C (approximately 175% below the melting-point) produces a change of the order of 1 ,uG-cm. A similar quenching experiment on pure gold(ra* r4) produced an increase of 0.01 $&cm with a quenching rate of about IO5 deglsec. Fig. 1 is a sem~oga~thmic plot of the quenched-in resistivity versus reciprocal absolute temperature of quench for samples A and B. The energy of formation sF calculated from the slope of the curve is 0.39 & 0.02 eV for sample A and 0.38 f 0.01 eV for sample B. The magnitude of the quenched-in resistivity was approximately the same for the two samples. The highest quench temperature used was 551 “C. However, the quenched-in resistivity for this measurement fell below t,he straight line determined by the other points by an amount outside the experimon~l error. This may be an i~ldication that at this temperature the rate of approach to

WECHSLER:

THE

T. Temperature 300

E 500

QUENCHING-IN

400

+, reciprocal

OF OC 200

quench temperature

FOG. 1. The change

in resistivity upon quenching versus reciprocal quench temperature for samples A and B. The temperature of measurement was 40°C and the annealed resistivity was 8.5 #&xn.

equilibrium is so great that it is impossible, with the quenching rate that was used, to quench in any more than, say, 1.5 micro-ohm-cm. This point was not used in the calculation of the least-squares straight line through the experimental points. Fig. 2 shows the results of a similar experiment on sample C, where, in addition, the effect of increasing the time of hold in the salt bath prior to quenching wits investigated. Holding times as long as 10 min were found to give no significant change in the amount of the quenched-in resistivity. Therefore it was concluded that 1 min is sufficient to establish equilibrium conditions at the quench temperature. The measurements on sample C give an energy of

LATTICE

DEFECTS

IN

GOLD-CADMIUM

153

formation of 0.37 f 0.01 eV. All the measurements were made at 4O”C, a temperature sufficiently low that negligible relaxation took place after quenching before fhe measurement was made. The annealing kinetics of the relaxation process that takes the alloy from the quenched to the slowcooled state was observed at a number of temperatures from 50°C to 90°C. In these runs the quench temperature was kept constant at 450°C. The time necessary for placing the sample in t,he sample holder before immersion into the constant-temperature bath was approximately 3 min. For samples B and C, the time after quench was corrected for the time spent before the sample was at temperature in the oil-bath, using the activation energy for motion calculated from the data on sample A. This correction was a small one. The shape of a typical relaxation curve is shown in Fig. 3. It is interesting that the process starts slowly; the curve apparently meets the time zero axis with zero slope. The final resistivity upon completion of the relaxation process was found to be equal to within 0.5% to the slow-cool value, i.e. the value obtained upon anneal at a high temperature followed by furnaceFurthermore, the change in resistivity cooling. upon quench from 450°C was reproducible to within lo/,. The fraction, j, of the quenched-in resistivity remaining at time t is given by

f(t) =

P(t)Pi -

ff Pf

7; temperature

f+ reciprocal quench temperature

OK-1

FIG. 2. The change in resistivity upon quenching versus reciprocal quench temperature for sample C. The temperature of measurement was 40°C and the annealed resistivity was 8.5 ,&-cm. The numbers refer t,o time of hold in minutes at the quench temperature.

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METALLURGICA,

VOL.

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195’7

lation along the abscissa. Therefore, if we consider any two of the relaxation curves for a given sample, the ratios of the times corresponding to the same value off are nearly the same for alI f. The extent to which this is true was determined in the following way. For each sample, the curve at a temperature T, near the center of the range of annealing temperatures was chosen as the standard curve. Ratios of the times corresponding to f values from 0.9 to 0.1 in 0.1 increments were taken for each curve with respect to its standard curve. The average of the nine ratios thus obtained was calculated for each of these pairs of curves. It was found that the I I I I 380 300 200 100 average deviation of the individual ratios from the min Annealing time avera,ge ratio was at most only a few per cent of the FIG. 3. Typical isothermal relaxation curve; sample 3 at average value itself. The constancy of this ratio, 61*1”C after quenching from 450°C. calledo5) the ‘“time-scale adjustment factor,” indicates where pi and pF are the initial and final resisti~Tities that there is a single relaxation time 7 ch~rac~risti~ respectively. In Figs. 4, 5, and 6, f is plotted versus of the annealing tempera,ture and that the annealing log annealing time for reIaxation at different temdepends upon t and 7 only in the combination t/T. peratures. An interesting feature of these annealing The time-scale adjustment factor, T(T)/T(!Z’&, is a curves is that they can be superimposed by trans- measure of the relative “jump time” of the unit 1.0

0.3

0.7

0.6 0 66+‘C A 79+=t 0 749oc - l 69.S’c * 6OSf’c

t

I-

i-

Annealing time

FIG. 4. Isothermd

relaxation CWVBS for sample A after quenching from 450%.

WECHSLER:

THE

QUENCHING-IN

OF

LSTTICE

DEFECTS

IN

GOLD-CADMIUM

155

.f

E

I

_L

ti rt: 03

ACTA

156 Tempemture

+,r&procal FIG.

7.

METALLURGICA, ec

annealing temperature%-’

Time-scale adjustment factor versus reciproea~ anneahg temperature.

process responsible for the relaxation. The activation energy for motion E& may be determined by plotting this factor versus reciprocal annealing temperature. Fig. 7 shows that, for the range of temperatures over which the annealing was carried out, the activation energy for motion may be given as 0.58 --J:0.05 eV. On the assumption that the activation energy for motion is constant over the whole range from the anneating ~rn~ratu~s to the quench ~mperatures, we may make a rough calculation of the time at the annealing temperature equivalent to the time spent during the quenching process. This calculation consists essentially of an integration under the curve of temperature versus time during the quench with 1 1 a weighting factor of exp EM - - - , where TA k ( T.4 Ti is the annealing temperature. From the observed cooling curve from 450% for a point on the axis of the sample, it was found that the time spent during the quenching is equivalent t-o about 10 min at 75%. Since the effective cooling rate for the entire sample is greater than that for a point on the axis, and since the annealing curves indicate little relaxation in 10 min at 75”C, it would appear that the quench is sufficiently fast to freeze in the situation characteristic of the quench temperature. This is consistent with the linearity of the curves shown in Figs. 1 and 2. 4. DISCUSSION In this section we inquire into the types of defects capable of being frozen in upon quenching and likely to be responsible for the noneq~lib~um effects observed. Also some a.dditional experiments are

VOL.

5,

1957

discussed that appear to facilitate a choice among the several possible explanations. We direct our attention first to the question of quenching stresses. These are the result of unequal thermal contraction of the surface and interior portions of the sample. The resulting plastic deformation could be accompanied by an increase in resistivity which anneals out upon isothermal hold. However, it would seem unlikely that quenching stresses sufficiently large to cause the observed effects could be induced in samples of diameters as small as Q in. Furthermore, temperatures as low as 60°C would not be expected to anneal out the effects of plastic deformation in times as short as several hundred minutes. However to test the idea still further, a I-mil Au-Cd foil of approximately the same composition as the rods was quenched from 450°C. The resistivity of the foil increased 0.81 ,us?,-cm, and upon annealing at 75*C a relaxation curve quite similar to those shown in Figs. 4,5, and 6 was obtained. It would seem virtually impossible for a thin foil to sustain quenching stresses capable of producing effects of this magnitude. It is well known that, in the case of alloys that undergo an order-disorder transformation, a large increase in resistivity can be induced by quenching. In such cases the less-ordered structure characteristic of the high temperature is frozen in and ordering takes place upon isothermal hold which reduces the resistivity to its slow-cool value. In the case of p-brass, however, despite the fact that it disorders at 465”C, it has been found”“) that the rate of approach to equilibrium order is so great that it is impossible to freeze in the less-ordered state. Thus in order to observe ordering effects upon quenching, it is necessary that the degree of order at the quench temperature be significantly less than at the temperature of measurement and that the rate of approach to equilibrium be not too great. The at-temperature X-ray spectrometer measurements on Au-Cd filings mentioned ea,rlier were performed to test the first of these two ideas. The composition of the filings was approximately 45.5 at. per cent Cd. The CuXc(-100 superstructure reflection was followed as a function of temperature in addition to several of the direct reflections. During the course of the measurements, the sample was surrounded by an atmosphere of helium. No attempt was made to make quantitative measurements of the intensities of the reflections or of the degree of order. Rowever, a definite superstructure reflection was obtained at 6OO”C, only about 25°C below the melting-point. This would indicate that the degree of order-is high at lower t,emperatures, say 45O”C, from which

WECHSLER:

considerable

quenching

Unfortunately, a function

THE

the

QUENCHING-IN

were

effects

long-range-order

of ~mperature

OF

observed.

parameter

of

ordering

on

density

and

X-ray-

lattice

parameter has been observed in a number In the case of #I-brass, Matsuda(r7) of materials. made dilatometric measurements that showed an incrense in length

upon

going from

the disordered

state,

have

an increase

reported

somewhat direction observed and

the

the

other

would

and

Keating

the ordered and

in lattice

greater than 0.10/b.

to

Warren(i@

parameter

of

Changes in the same

and of the same magnitude have been for Cu,Au.‘ls) Thus when the disordered

state is quenched lattice

in, the density parameter

hand,

certainly

is abnormally

abnormally

while

the

presence

lower

the

density

increase the average

interatomic

low

high.

On

of

vacancies

and

therefore

spacing,

the effect

on X-ray lattice parameter is in the other direction. This can be seen as follows. A vacancy can be introduced from

into

a lattice

a cry&a1

by

removing

site and placing

The effect on the density

an

atom

it on the surface.

is to produce

a decrease

corresponding to an increase in volume of one atomic volume minus the contraction of the lattice about the vacant site. However, an X-ray lattice parameter determination planar

is based on the measurement

spacing

and

the contraction

therefore

of the lattice

is only

of inter-

sensitive

to

and not to the fact

that an atom is missing from the lattice position. Thus, if a large number of vacancies are frozen in by quenching,

a decrease in lattice parameter

should

be apparent. density and X-ray lattice paramater* me~llrements on /? Au-Cd in the annealed and the quenched

state were made in this laboratory

and it was found that both these quantities upon quenching from 450°C.

decrease

It can be seen from Fig. 1 that quenching from 450°C increases the resistivity by 1 $&cm. In the absence of theoretical information to this alloy, a rough concentra.tion

that applies more directly estimate of the vacancy

corresponding

to

1 ,u!&cm

can

be

obtained by applying Jongenburger’Gr) result for pure gold, 1.5 ,&?-cm/at. per cent vacancies. This yields a vncancy concentration of about 0.67% vacancies. The equilibrium concentration of vacancies * The co-operation of M. C. Wittels, G. E. Klein, and F. A. Sherrill in making the lattice-parameter measurements is greatly appreciated. 3

IN

157

GOLD-CADMIUM

can be expressed as

(1)

has not yet been measured

for Au-Cd and therefore it is not known quantitatively

effect

DEFECTS

as

to what extent there is less order at the quench temperature than at the temperature of measurement. The

LATTICE

where X, energy

is the entropy

of formation

An-Cd.

The number

of formation

and Ed the

(= 0.38 eV)

of a vacancy

of vacancies

quenched-in

in may

be oonsidered to be much larger than the equilibrium number

at the temperature

of measurement.

We

find corresponding to c = 0.0067 at a temperature of 450°C that X,/k = 1.1. Zener@) has pointed out that X, should be positive freedom

of

movement

The theoretical values part,

they

from

near

0.3 to 2.5.

refer to f.c.c. to

because of the greater

atoms

a vacancy.

calculations(23* 2p*25) of X,/k

that range

expected

of

be

metals,

greatly

yield

For the most

but they

dependent

are not

upon

crystal

Thus the result that X,/k G 1 reported

structure.

here is not inconsistent with the values deduced from theoretical considerations. The fraction of vacancies

at

the

melting-post

calculated

from

equation (1) turns out to be about 0.02. We may compare these results with those obtained in

quenching

known

to

be

and Rosewell

experiments

on

disordered.

Nowick

materials and

that

are

Sladek(s@

and Nowickt27) have studied the effect

of quenching on a Ag-Zn alloys, using st,ress-relaxation techniques.

The

times

and

temperatures

for

the

removal of the effects of the quenching were approximately t.he same as those observed for Au-Cd. They obtained

the values eF = 0.51 eV and Ed = 0.86 eV

for the 30 at. per cent Zn alloy26, and E* = 0.51 eV and Ebb = 0.81 eV for 33.5 at. per cent Zn2?, to be compared

with

our

v;Llues of

Ed

0.38 eV

=-

and

e&f = 0.58 eV for Au-Cd. It is interesting that the ratio eF/eM is approximately the sa.me for the two alloys.

The value assigned to SF/k

Sladek

is

also approximately

experiments Rroom,

on

Stacey,

a-brass

have

by Nowick

unity. been

performed

and Westwood.c2s)

and

Quenching

They

by

obtained

a value of 0.34 eV for Ed. Thus the results reported here for Au-Cd are quite similar to those obtained on materials

for which

the question

of order does

not arise. On the basis of the quenching in of lattice vacancies, the question arises as to what type of vacancy is being measured, In an ordered binary alloy, the concentration of vacancies of both given by an expression of the type C=C,[exp

(---s>

where the subscripts stituents.

Thus,

types should

be

+exp(-$_)I

1 and 2 refer to the two eon-

assuming

that

the

two

types

of

ACTA

158

vacancies produce ap~roxima~ly resistivity,

we would expect

METALLURGICA,

the same additional

good straight-line

plots

VOL.

5,

1957

J. H. Crawford and R. E. Jamison of this laboratory, for

helpful

criticism,

and

R.

Kernohan

J. M. Williams

one predominates,

the apparatus and the making of measurements.

in which

energy that is measured. that even if the difference were such as to produce a straight

line,

temperature

case it is the smaller

However, it can be seen between the two energies maximum

this departure

range

departure

is so slight

ZOO-500°C

as

to

from in the

be scarcely

observable by measurements of this type. il;o positive identi~~ation of the defect responsible for the changes

in resistivity

upon

quenching

can

be made at this time, but in summary

it might be

said that, the evidence

in favor

an explanation involving

points

strongly

in terms of vacancies

ordering.

This is indicated

of

rather than one by the observed

decreases in both density and X-ray lattice parameter upon

quenching,

those

obtained

by the similarity with

tc Ag-Zn

of the results to

and Cu-Zn,

and

by

the preliminary observation that p Au-Cd is ordered at. t,emperntures close t,o the melting-point. The c(~ncentration large.

The

vacancies

of vacancies presence

affords

of

appears such

a bet;ter

to be unusualI>

a large

opportunit,~

number to

of

isolate

their effects from t,hose caused by other defects. This should lead to a better understanding of the mechanism

by which vacancies

alter the propert,ies

of solids. ACKNOWLEDGMENTS

I should operation

like to acknowledge of T. A. Read,

the advice

who suggested

and co-

the problem

and guided

the investigation in its early stages at and D. S. Billington, who Columbia University; ma,de its ~ontinI]a~tion at ORAL possible. 1 should also like to t,hank A. S. Nowick of Yale University, J. S. Koehler of the University of Illinois, and

for assistance

H.

in Figs. I and 2 if the two energies were equal or if

in the setting

and up of

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15. Ifi.

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