Lattice defects in a copper-aluminum alloy

LATTICE

DEFECTS

IN A COPPER-ALUMINUM

M. S. WECHSLER

ALLOY*

and R. H. KERNOHANt

Static (at-~m~rature) resistivity measurements and meas~ements after sir-cooling and waterquenching indicate an excess resistivity contribution at temperatures above ZOO’Cin &-Al (15 at. y/oAl) single crystals. From the static measurements, the energy of formation of the configuration responsible for the excess resistivity is determined to be about 0.2 eV. Annealing experiments after quenching from 450% were conducted, from which the activation energy for motion was evaluated. These experiments are correlated with a previous investigation of the effect of neutron irradiation on &-Al alloys, and a discussion is given in terms of short-range ordering and the annealing of lattice vacancies. SUR LES DEFAUTS

DE RESEAU DANS UN ALLIAGE

~IVR~-ALUMINIU~~

Des mesures de resistivitc a la m&me temperature (statique) et des mesures aprirsrefroidissement a I’air et apres trempe fournissent des valeurs en exces a des temperatures au-dessus de 200” C, pour des monocristaux de cuivre-xluminium (15 at. O/eAl). A partir de mesures statiques, l’energie de formation de la configuration responsable de ces valeurs a Ate trouvee de l’ordre de 0,2 eV. Des recuits apres trempe a 450°C ant permis d’evaluer l’energie d’activation du mouvement. Ces experiences sent en relation avec une etude precedents sur l’influence de l’irradiation des neutrons dans les alliages &-Al et la discussion se base sur l’ordre it petit,%distance et la restauration des Iacunes du &seau. GITTERFEHLSTELLEN

IN EINER

KUPFER-ALUMINIUM-LEGIERUNG

Stat&he Widerstandsmessungen (bei der betreffenden Temperatur) und Messungen nach Luft)abkiihlung und Absehrecken in Wasser ergeben an Cu-Al(15 At.% Al)-Einkristallen bei Temperaturen oberhalb 200°C einen zusatzlichen Widerstandbeitrag. Durch die statischen Messungen wurde die Bild~~~nergie der fur den Zusatzwide~tand verantwortlichen Ko~guration zu etwa 02 eV bestimmt. Nach Abschrecken von 45O*C wurden Erholungsvemuche durchgefiihrt, aus denen die Aktivierungsenergie fiir die Wanderung bset,immt wurde. Dime Experimente hangen mit einer friiheren Untersuchung i_iberdie Wirkung von Neutronenbcstrahlung auf Cu-Al-Legierungen zusammen. Sie werden mit Hilfe van Vorstellungen iiber eine Nahordnungseinstellung und die Erholung van Gitterleerstellen diskut,iert.

1. INTRODUCTION

decrease in resistivity.

In a previous paper,(i) the effect of neutron irradiation on a-solid-solution

&-Al

The nature of this metasta-

bility is difficult to ascertain on the basis of resistivity

alloys was described.

measurements

near room temperature, is observed. The magnitude

alone, but several suggestions

When the alloys are irradiated

made.(i)

a decrease in resistivity

less than the equilibrium

One possibility

may be

is that the alloy initially has amount

of order.

In this

of the decrease is larger for alloys of higher Al content

case, we must specify that the order is local, since no

(0.18 $2 em for the 15 at.% Al alloy) and no decrease

superlattice

in resistivity

may then be thought

is observed

for pure Cu.

The process

that brings about the decrease in resistivity alloys

is very

likely

diffusion-controlled,

for the since

which

no

than

will set in,

triggers

or accelerates

atomic

to introduce movements

takes place

for the unirradiated

The irradiation lattice

vacancies

so that

short-

at a lower temperature alloy.

This

short-range

ordering is assumed to result in the observed decrease in resistivity. An explanation in terms of short-range ordering has been given(sys) for similar irradiation

In a general way, the alloy may be considered to be in a metastable state in its original condition. Then, the irradiation

enhance

range ordering

decrease takes place upon irradiation at -120°C. However, if the sample is warmed above -50°C the decrease in following irradiation at -120°C, resistivity

is present in these alloys.

effects on Cu-Zn.

An alternative

explanation

is that

the metastability arises from the retention of a nonequilibrium concentration of lattice vacancies in the

a diffusion-

controlled process by which the material proceeds toward thermodynamic equilibrium, withan attendant

original preparation of the alloy. In this event, the neutron bombardment may introduce special sites at which the annihilation of the excess vacancies takes

* Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee. Received October 22, 1958. T Oak Ridge National Laboratory is operated by Union Carbide corporation for the U.S. Atomic Energy Commission.

place more readily than in the absence of the irradiation. The annealing out of the excess vacancies is

ACTA METALLURGICA,

VOL. 7, SEPTEMBER

1959

accompanied

599

by the observed

decrease in resistivity.

600

ACT&4 METALLURGICA,

VOL. 7, 1950

which show the effect of an additional contribution to the resistivity above 200°C. From these measurements, a value of eF was deduced. Secondly, experiments were performed in which excess resistivities were retained upon air-cooling and boater-queuc~ng from temperatures above 200°C. In addition, annealing experiments after quench~llg are described from which &*Iwas determined. 2. EXPERIMENTAL DETAILS The alloy was prepared by the Metallurgy Division at ORNL by vacuum melting and casting. The base constituents were electrolytic Cu of 99.92 OJO purity and Al of 99.99% purity. All samples contained 150 & 0.5 art.% Al and received an initial an~lea.liIl~treatment, consisting of holding several hours at 750°C followed by cooling at a rate of about lli*C/hr to room The above discussion suggests that a non”equilibrium defect st~ueture* is inadvertently retained in ten~perat~e. With the exception of a few quenchill~ the original preparation of the alloy, despite the slow experiments on 56 mil Cu-Al wire (Fig. 6), a11of the measurements were made on rod-shaped single cooling that is employed. The circumstances that crystals, + in. diam., containing short nibs t,hat served give rise to this situation are illustrated schematically in Fig. 1. If it were possible to maintain equilibrium as voltage contacts. The single crystals were prepared during cooling, the p vs. T dependence would follow by re-melting the alloy material in a split graphite the solid ourve. At temperatures above T,, the defects mold and lowering through a temperature gradient in are in equilibrium in sufficient quantity to make a a vacuum furnace. The 56 mil wire was prepared by si~ni~~ant contribution to the resistivity. At temswaging and drawing a portion of the same alloy stock perature T, this contribution is given by AC. Rowas was used far the single crystals. Voltage contacts ever, under actual conditions, the atomic mob~ities were applied by spot-welding short sections of the may be so low at a temperature T, that, upon cooling alloy wire transversely on the sample wire. below T,,%he defects characteristic of this temperatures The resistivity ~n~surements were made by the are frozen into the lattice. The contribution to the double-potentiometer method, using a Rubicon sixresistivity of this non-equilibrium eon~guration is dial thermo-free ~otentiolnete~. For the at-temperaindicated by BC. The decrease in resistivity that takes ture measurements, the sample was kept in an inert place upon neutron irradiation(l) near room temperaatmosphere inside a wire-wound t’ube furnace. The ture is 0.1s $2 cm for Cu-Al (15 at. “/ Al). Regarding temperature was measured using thermocouples adjsthis decrease as that necessary to bring the sample to cent to but not in oontact with the samples. For the thermal equilibrium, we may take BC = 0.18 pfz cm experiments on the effect of air-cooling or quenching, for this alloy. Upon cooling below Tz, the resistivity the samples were held in a s&-bath controlled at the follows the curve Iabelled “observed”‘. Thus, in order appropriate temperatures. The air-cooling was done for the rete~~tion of a non-equilibrium ~on~gu~ation in still air at room temperature and the quenchi~lg to take place upon slow cooling, a temperature T, was done by quickly removing the sample from the salt must exist at which the equilibrium eonce~ltration of bath and immersing it in water at room temperature. defects is significant and yet the atomic mobilities are For the annealing measurements after quenching, the low. This implies that the energy of formation, Ed, samples were placed in a constant-temperature silicone of the defect must be low and the activation energy oil bath and the resistivity measurements were made for motion, Fan, must be high. The experiments in situ. described in this paper indicate that these conditions A high-speed oscillograph was used to measure the are met in the 15 at.% Al &-AX allo*y. The temperacooling rates during the air-cooling and during quenchture IE’,is as low as 200°C. This is found to be the case ing of bhe single crystals. A co&ant current was from two types of experiments, In the &st instance, passed through the sample during the cooling and the static {at-temperature) measure~nents were made, voltage across the nibs of the sample was fed to the os~illo~aph. The current was too low to cause B * In this paper, the term “defect” is u,sedloosely to include measurable increase in the sample temperature CU-Al departure fram equilibrium order.

WECHSLER

ANT) KERNOHAN:

wire of the same composition

LATTICE

DEFECTS

as the sample was used to

IN

quadratic

A

COPPER-ALUMINUM

extrapolation

ALLOY

is used.

601

The positive devia-

make the voltage contacts in order to reduce thermal

tion of the observed

resistivity

e.m.f.‘s.

from the extrapolated

line suggests that lattice defects

The procedure

quenching actual

for the air-cooling

closely approximated

measurements.

and the

that used during the

In this way,

a trace

of the

resistance of the sample versus time during the cooling was obtained from which the temperature-time

curve

come

into

equilibrium

ten seconds

curve

was linear during

corresponding

to a rate of 8”C/sec

50 set were required to reach 200°C. ing, the maximum the temperature

the first

cooling reached

and

For the quench-

rate was 4500”C/sec 200°C

in about

and

0.09

sec.

The temperature of the sample decreased about 10°C during the time necessary to transfer it from the salt bath

to the

quenching

water.

No

correction

made for this decrease in temperature. the response

characteristics

To insure that

of the oscillograph

not being exceeded, a bare thermocouple In this case, the observed The

quenching

approximately

were

was quenched.

cooling rate was lO@C/sec.

characteristics the

was

same

reported

as those

here

measured

are by

a

different technique on another material4 using samples of the same size and shape and the same quenching procedure.

200°C

and

If the formation

200°C

cause

this excess

Ap = A exp (-ep/kT) where A is independent the excess l/T

resistivity

(1)

of the temperature

is the energy of formation

of the defect.

is plotted

in Fig. 3 (open circles).

an

of the defect

is a single, thermally-activated process, resistivity is expected to be of the form

T and eF

Accordingly,

on a log scale vs.

The points between 320

and 660°C satisfy equation (1) with the value &R = 0.19 eV, but at lower temperatures the open circles fall lower than is predicted energy of formation. the Introduction,

by equation

However,

(1) using this

as was discussed

it may be deduced

in

from the effect

of neutron irradiation on this alloy(i) that, at temperatures above T, = 200°C (Fig. l), the equilibrium excess resistivity

is not given by the observed

excess

resistivity

Fig.

where

(AB,

BC = 0.18 pfi cm.

1) but

by

AB + BC

When the Ap values determined

from Fig. 2 are increased by 0.18 ,& cm (filled circles, Fig. 3), it is found that equation the

3. RESULTS

above

increase in resistivity.

could be deduced. Upon cooling from 45O”C, the cooling rates were as follow-s. For the air-cooling, the temperature-time

values above

entire

formation

range

(1) is satisfied over

of temperatures.

!l’he energy

of

in this case is F~ = 0.15 eV.

3.1. Static measurements For the static (at-temperature)

measurements,

runs were made, the first extending second to 664°C. less than A”C/hr. The temperature room

temperature

Fig.

2 represents

two

to 404°C and the

The heating and cooling rates were The results are shown dependence

and 200°C. the

in Fig. 2.

appears linear between The dashed

extrapolation

of

line in

the

least

3.2. Measurements It

was

resistivity

upon air-cooling

mentioned

earlier

upon neutron

air-cooling,

between

factor of more than 103.

quadratic

extrapolation

of these points

slightly from the linear extrapolation described

below

do not

change

A

where the cooling-rate

differs only

and the results

significantly

if the

decrease in may indicate

hr). If this is the case, we would expect larger amounts of excess resistivity to be retained upon

measured

and 200°C.

the

that a non-equilibrium concentration of defects is retained in the alloy, even after slow cooling (~15”C/

squares straight line through the points of Run No. 1 room temperature

that

bombardment

x

600

5.0

is greater

TEMPERATURE (“C) 400 300

500

by a

200

,

j 0

* RUN NO. 1. DECREASING

T

2 g

1.0

$

0.5G

L B :: 0.10 w ;-

0.05 1.0

1.1

1.2

1.3

1.4

1.5

f , RECIPROCAL FIG. 3. Excess K TEMPERATURE

FIG. 2.LResistivity

vs. temperature,

(‘C)

Cu-Al

(15 at. y0 Al).

1.6

1.7

1.8

TEMPERATURE

1.9

2.0

2.1 (X1(

(‘K-‘)

resistivity vs. reciprocal absolute temperature, G-AI (15 at.% Al). poalc refers to the extrapolated values in Fig. 2. The value 0.18 pa cm is the decrease in resistivity observed upon neutron irradiation near room temperature (ref. 1).

602

ACTA

METALLURGICA,

VOL.

1 I

I

I

-100

0

100

L

-0.05 -200

I

I

I

I

200

300

400

500

T,TEMPERAT”RE

I

of air-cooling

ment are seen. higher

and

0

is illustrated

temperatures

100

300

200

400

c TEMPERATURE

in Fig. 4,

annealing

experi-

The sample was held for 30 min at

higher

SAMPLE PREVIOUSLY o IRRADIATED FOR 3 o WEEKS AT -,ZO*C AND ANNEALED AT 0°C o

ii

l”Cl

where the results of an isochronal

1959

-0,

cioo

FIG. 4. Air-cooling experiment. Excess resistivity as a function of holding temperature, Cu-Al (15 at.% Al). All measurements were made at -196°C. The sample w&s held 30 min at each temperature. For temperatures above room temperature, the sample was air-cooled to room temperature and then placed in liquid nitrogen for measurement.

The effect

r )I

’

7,

and

returned

to

- 196°C for measurement between each anneal. Above

FIG. 5. Air-cooling experiment on a Cu-Al (15 at.% Al) sample previously irradiated for three weeks at -120°C and annealed at 0°C. All measurements at 0°C.

whether

the measurements

-196°C.

are made at 0°C or at

Also, the similarity

between Figs. 4 and 5

suggests that the effect of the irradiation is dissipated when the temperature

is raised above

This is further indicated

ments from C to D, where the annealing temperature The resistivity levels off when the cooling is done from temperatures below 200°C at a

value above the original resistivity. resistivities

upon holding between 150 and 200°C. But when the samples are cooled in air from above 2OO”C, the resistivity increases. However, the increase in resistivity retained upon air-cooling continues only to about

310°C.

When

the air-cooling

is carried

out

200°C.

is decreased.

shows a slight tendency

to decrease

about

by the sequence of measure-

room temperature, the samples were cooled in air before placing them in the liquid nitrogen. Fig. 4 for the resistivity

500

PCI

induced

Thus, the lower

by the irradiation

covered upon decreasing

the temperature

are not reonce again

below 200°C. The effect of reducing

the time of hold

at each

temperature is shown by the sequence of points from E to F in Fig. 5. The resistivity at 0°C upon air-cool-

from a temperature above 31O”C, the retained resistivity decreases again. Upon air-cooling from 5OO”C,

ing from 310°C was the same for the five-minute

the resistivity

annealing

at -196%

is only slightly higher than

The data shown in Fig. 5 illustrate some additional aspects of this type of experiment. bombarded

and then annealed at 0°C. resistivity

to lie about

This sample had

by neutrons This treatment

at -120°C caused the

0.065 ,L& cm below its pre-

irradiation value, as has been described earlier.(i) Two isochronal annealing runs, similar to the one illustrated in Fig. 4, were carried out on the irradiated sample.

In this

hold.

temperature,

case, however,

the measurements

than for the two-hour

holds

(point

is done from temperatures

the result of

to equilibrium

below about 250°C.

holds

F as compared

with point D, Fig. 5). This is apparently

at tem-

When the air-cooling

above

31O”C, essentially

the same curve is traced for the points obtained five-minute

the

we find that the resistivity

the slowness of the approach peratures

hold

But, upon decreasing

levels off at a higher value for the five-minute

the original value.

been previously

as for the two-hour

with

holds at each temperat’ure (points G to H)

as for those with two-hour

holds.

were made at 0°C. Furthermore,

for the first run, the

3.3. Quenching measurements

time of hold at each temperature

was two hours and,

It is to be expected that larger amounts of excess resistivity are retained in the crystal as a result of the greater cooling rates used in the quenching experiments. This is shown to be the case in Fig. 6 where the quenched-in resistivity is compared with the

for the second run, it was five minutes. An increase in resistivity was observed upon air-cooling from temperatures up to about 31O”C, and, upon aircooling from above 31O”C, the resistivity at 0°C decreased again (points A to B). Thus, the behavior above 200°C is quite similar to that shown in Fig. 4 and indicates that the same results are obtained

resistivity retained upon excess resistivity deduced ments.

air-cooling and with the from the static measure-

It is seen that a maximum

of about 0.5 ,& cm

WECHSLER

AND

KERNOHAN:

LATTICE

DEFECTS

IN

A

COPPER-ALUMINUM

this temperature tivity

was stopped

was reached.

ALLOY

603

before the final resis-

For purposes

of calenlation,

the

final value for the anneal at 45°C was taken to be the value measured at this temperature

0.9

F

For all the annealing

u i

lated corresponding

0.8

completion

i -07 2 5 $ 0.6

before quenching.

runs, a parameter f was calcuto the fractional

departure

from

of the annealing process, where

Y n 0.5

and p, pi, and pf are the resistivity

% 304 E

initial

resistivity

immediately

the

final resistivity,

0.2

for

specified

01

plotted

after

at time t, the quenching,

and

In Fig. 7, f is plotted as a function of the annealing time. The times

co.3 d

respectively.

fractional

amounts

to a log scale in Fig.

of

annealing

arre

8 vs. the reciprocal

0 I

I

I

300 400 T, TEMPERATURE (W

200

100

,

500

600

FIG. 6. Excess resistivity vs. temperature measured by the static method, by air-coo&grand by water-quenching. &-Al (15 at.96 Al).

is retained upon quenching with a maximum

from 450°C as compared

of about 0.2 ,uUacm upon air-cooling

from 310°C. There appears to be no difference in the quenching results for the 56 mil wire as compared with those

for the one-eighth

sistivity

begins to be apparent

200°C for both air-cooling the temperature

The excess re-

upon heat-treating

and quenching.

at which

begin to indicate resistivity.

kinetics

at

t

102

i0

i, TIME

an additional

quenching from 450°C. The magnitude of the quenched-in resistivity was about 0.45 @2 cm. G-AI (15 at.% Al).

This is also

contribution

105

to4

(0’

(mm)

FICA 7. Normalized isothermal annealing curves after

TEMPERATURE

the static measurements

The static measurements

{Fig. 2) are t*hose plotted The

inch rods.

0

(“Cl

to the

for Run No. 2

in Fig. 6.

of the annealing

of the resistivity

retained upon quenching from 450°C were also studied. Refore

quenching,

measured

the resistivity

in the annealed

of the sample was

condition

at a number

of

temperatures between -196°C and 300°C. The total amount of quenched-in resistivity was determined by measuring

the

after quenching.

resistivity

at

-19ci°C

immediately

Then the sample was placed in the

annealing bath at temperatures

between 45 and 1OO’C

and the resistivity was measured in situ as a function of time at the annealing t.emperature. The resistivity

;: c

5

c

2 102

had begun to decrease by the time the first measurement was made,

but the measurements

at --L96’C

could be used to deduce the initial quenched value, pi, at the annealing temperature. The annealing process appeared to be close to completion when the measurements were discontinued for the runs at 62 to 100°C. In each case, it was found that the final value was slightly (about 0.04 ,ufi cm) lower than the resistivity determined prior to the quenching. The decrease at 45’C was exceedingly

slow and the run at

4 2.6

2.7

:.a

‘/T ,RECIPROCAL

2.9 ANNEALING

3.0

3.1

TEMPERATURE

3.2

(xW3)

(OK-‘)

FIG. 8. Activation energy curves for annealing after quenching from 45O’C. CL-Al (15 at.% Al).

ACTA

604

annealing

temperature.

METALLURGICB,

It is seen that the relation

satisfied,

increases

and

as the

the

process

(2)

activation

goes

on.

energy, The

Em,

activation

energy is plotted vs. f in Fig. 9. The activation energy increases linearly with the fractional amount of completion of the annealing process until the process is about 0.4 from completion. At this point, eM appears to increase somewhat more sharply. final value at f = 0 is about 1.2 eV. The Ed curve

obtained

upon

annealing

The vs.

after irradiation

f

at

-120°C

(ref. 1) is also shown in Fig. 9. The irradiation lowers Ed considerably in the early stages of the annealing.

In fact, the curve appears to extrapolate

7,

1959

normal resistivity. exists.

r = r,, exp (&,/kT) is well

VOL.

It is here that the chief difficulty

In the work of Meechan and Eggleston(5)

pure Cu and Au, a quadratic

extrapolation

resistivity observed at lower temperatures was used. The excess resistivity determined in this way was found to obey quite closely the Arrhenius dependence of equation (1). However, it was pointed out by Nicholas’Q that there is little theoretical justification for the use of such an extrapolation

and other possi-

bilities were suggested to explain the apparent anomalous resistivity not involve

at the higher temperatures

the assumption

Nevertheless,

that did

of defect concentrations.

in a later paper, Jongenburgerc’)

showed

fhat an analysis of previous data on the thermal expansion of Cu and Zu agrees closely with the results of Meechan and Eggleston.

In Jongenburger’s

analy-

0 at the start of the process. The curve for the irradiation case in Fig. 9 shows no sudden increase

sis, the data was fitted at the lower temperatures

in eLWat the low f values and E~+~ = 1.0 eV at the completion of the process.

extrapolation

t0

Ew

=

In the static method lattice

defects

temperatures, temperatures

of deducing

the presence

that come into equilibrium the resistivity is considered

of

at higher

observed

at the higher

to consist

of the super-

position of the normal resistivity and the contribution made by the defects. In order to carry out the separation

of

these

resistivity,

two

contributions

it is necessary

both a straight line and a Griineisen

to

the

observed

to assume values for the

r

1

of

these

in

the

region was used to determine Little

4. DISCUSSION

on

of the

difference

extrapolat,ions

by Jongenburger lower ments

higher

temperature

the normal resistivity.

in the results for the two types was found.

to

curve and the

of

It was also pointed

out

that higher excess resistivities

and

values are obtained from static measureon pure gold than are obtained by quench-

Ed

ing,(S-11) In t’he present investigation,

an attempt

was made

to determine whether the data obtained for the static measurements

(Fig. 2) is better fitted by assuming an

excess resistivity contribution given by equation (I) or by assuming the existence of higher order terms in the temperature Calculations

dependence

were

made*

of the normal resistivity. to

determine

the

least

squares fit of the data of Run No. 2, Fig. 2, to the following

f

two expressions p=A+

BT+Gexp(--B/T)

(3)

and p=a+bT+eT2$-dT3 each of which contains four The results were inconclusive, error associated

0

t ‘NEALING AN

I

with equation

less than that for equation AFTE?_QUE FROM 450-C

:NC

I

0 ANNEALIKG AFTER IRRADIATION AT -120°C (REF 4I

tion corresponding

(4) adjustable constants. in that the standard (3) was only slightly

(4). The energy of forma-

to 0 in equation

(3) was 0.16 eV.

However, the uncertainty as to whether equation (3) or equation (4) is applicable is largely dispelled by the results of the quenching and air-cooling experiments (Fig. 6). Since all measurements for these experiments are made at the same temperature, the additional

FIG. 9. F, vs. f for annealing after quenching from 450°C and after Irradiation for three weeks at - 120°C. f represents fractional departure from completion of the process. Cu-AI (15 at.% Al).

* We are indebted to N. M. Dismuke and A. H. Culkowski for carrying out the calculations on the ORNL ORACLE computer.

WECHSLER

resistivity

KERNOHAN:

AND

at temperatures

DEFECTS

above 200°C must be due

to the presence

of defects

the temperature

dependence

(equation

3) rather than

of the normal resistivity

(equation 4). The energy of formation observe for Cu-Al(15

LATTICE

of about

0.2 eV that we

at.% Al) is quite low compared

IN

expected.

of the interaction

and a divalent

in

a-brass,

burger”’ and 0.90 eV reported by Meechan and Eggleston(5) for pure Cu. It has been observed

activation

that the energy of formation

in alloys is

Quenching

experiments

on 70130 a-brass have been reported(12’ that indicate an energy of formation

of 0.34 eV.

of the quenching of an Au-Cd composition, obtained

values

of

respectively.

surements(i4y15) have

to

(e,/kT)

relaxation,

measurements

on quenched

to the 14).

and

However,

quench-annealing energy for motion,

with such a low value for eE‘,

smce sR-eiGI was found to be significantly 0.19 eV.

value

of the composite activation

for the activation

Ed, were not consistent

time

was found to be propor-

eR,

greater than

Thercbfore, it was concluded(14) that the true

value of eff was more reliably 0.51 eV. The above-mentioned

a large

given by eR -

~~~

=

in Cu

atom gives a value of less

vacancy-solute

interaction equality

is

of the

energies for Cu and Zn in the alloy

determined

by tracer diffusion

On the assumption

as

measurements.(l*)

that the excess

resistivity

is

due to vacancy concentrations, we may calculate approximate values for the entropy of formation of a vacancy

in the alloy and the concentration

of vacan-

cies at the melting point. The concentration, considered to be given by the usual expression cr, = exp (S,/k

mea-

The relaxation

1, reference

measurements

were

by Alfred and

between a vacancy

with the approximate

and density(i3’

corresponding

F~ = 0.19 eV (see Fig. for

0.28 eV

performed Zn).

after quenching

exp

equilibrium energy

and

Stress relaxation

been

alloys (near 30 at.%

immediately tional

0.38 eV

as a result of resistivityt4’

measurements, Ag-Zn

Also, in the case

alloy near the 50 at. y0

impurity

605

than 0.1 eV. Furthermore, as is pointed out by Lome@) in connection with the similar situation inconsistent

previously

ALLOY

For example, the calculation

Marcho’)

with the values of about 0.70 eV reported by Jongen-

lower than for pure metals.

A COPPER-ALUMINUM

-

e,lkT)

(5)

where S, is the entropy of formation. the

data

shown

calculation

in Fig.

regarded

3 and

with

= -2.1.

caution,

On the basis of

Jongenburger’sos)

of 1.3 pfi cm per at.%

Cu, we find that S,/k

cv, is

vacancies for pure

This result should be

since theoretical

considera-

tions(s0-23’ predict a positive

entropy

a vacancy

This arises because

in pure metals.

atoms neighboring freedom vibration

of motion,

a vacancy

acquire

which lowers

and raises the entropy.

of formation

of the

an additional

the frequency

of

If this is the case in

the alloy, it is unlikely that the negative entropy that we calculate is related to an error in the factor 1.3 ,& cm per at.% vacancies, since this quantity

results on alloys

would have to be reduced by a factor of about ten to

chiefly in terms of the quench-

ing and annealing of lattice vacancies, although in the

make our calculations yield S,T/k = 0. However, the calculated value for X,/k is fairly sensitive to the

case of the quenching

measured value of cl, and, corresponding

have been interpreted

terms of short-range shall

first

discuss

vacancies. formation

The

quenching

of cr-brass(i2’ an explanation

our

results

theoretical

in terms

basis

for

of

the

in

to the same

We

Ap values at 450°C as are shown in Fig. 3, eR must be

lattice

raised to about 0.31 eV to give S,/k = 0. On the other hand, it may be that atomic oscillations are

order was also considered.

smaller

energy of a vacancy in an alloy as compared

more restricted

in the neighborhood

of a vacancy

in

with that in the pure metal is discussed by Lomer.06) It is pointed out that an interaction may exist be-

alloys, leading to a negative entropy of formation. This might be expected to be the case if there were

tween

a strong solute-vacancy

vacancies

and solute

atoms

that

causes the

interaction.

From equation

energy to form a vacancy in the alloy to be reduced from that in the pure metal by an amount that

(5) we find also that the vacancy concentration at the melting point (1040°C) is 2.1%. This is a factor of

corresponds

approximately

“binding

to the energy of this interaction.

energy”

is expected

to be relatively

the case of a large solute atom such as Al.

This large in

Neverthe-

less, as in the case of a-brass,(i6’ certain difficulties must be reconciled. One such difficulty is the magnitude of the binding energy. The energy of formation of vacancies in pure Cu has been reported to be 0.70 eV(‘) and 0.90 eV.c5) If we use the value 0.8 eV for pure Cu and 0.2 eV for Cu-AI, we must predict 0.6 eV for the binding energy. This is larger than is 2

and Nowick’24’

five greater than that estimated from stress-relaxation

by Li

measurements

on a Cu-Al alloy of similar composition. An interesting aspect of the results of our quenching experiments is that, when the quenching temperature exceeds 45O”C, the amount of retained resistivity begins once again to decrease. Similarly, for air-cooling experiments the maximum retained resistivity is obtained at 310°C. These observations indicate that the annealing-out of the excess resistivity occurs more

ACTA

606

rapidly for higher quenching T,

> 45O”C, the

METALLURGIC-~,

temperatures

annealing

rate

( Ts).

becomes

For

so high

VOL.

7,

1959

where 2 = 12, v z 1Or3 see-l, and exp (8,/k) s 1. For the vacancies that are being annihilated when the

relative to the cooling rate that the excess resistivity

process is half over, we find that nJ = 5 x 104 jumps,

characteristic

using eM = 0.88 eV forf

of

450°C

cannot

be

retained.

The

of

vacancy

jumps

= 0.5 (Fig. 9). This number

is significantly

less than

that

cooling rate for the air-cooling is a factor of about 500 smaller than for the quenching, so that for the

obtained

air-cooling

ments on pure metals. For example, Pearson and Brad-

ture.

this effect takes place at a lower tempera-

A similar effect was observed

of pure gold. annealing

in the quenching

Bauerle and Koehlercs) found that the

was much more rapid for higher quenching

temperatures, equation

although in this case no departure from

(1) was noted for the highest T,

quenching

experiments

on

pure

used.

gold

were

The inter-

pretedfz5) vacancies.

in terms of the quenching-in of lattice It was suggested that the reduction in

annealing

time for higher T,

number

of divacancies

activation

measure-

shaw estimate that nJ is of the order of IO9 or lOlo jumps for Au,@) Pt,(2*’ and A1.(2s) On the other hand, from 5

x

lo4 to lo6 jumps

are estimated

for Ag-Zn

(approximately 30 at. o/0 Zn) as a8 result of stress relaxation measurements. (r4*15) It may be that n, is characteristically smaller for solid solution alloys than for pure metals, although further work needs to be done

to test this point.

calculated

If nJ in equation

(6) is

for values of 7 and ~,u corresponding

to

aggregates

Divacancies’26)

and certain

for f = 0.9 and decreases with decreasing values off.

groups(27)* are expected to have lower

A decrease in the number of jumps as the annealing

energies for motion

Furthermore,

of quench-annealing

or other vacancy

at higher temperatures. larger vacancy

was due to the larger

as a result

clustering

of

than single vaca.ncies.

the

multiple

vacancies

other values off, it is found that nJ = 2 x lo6 jumps

proceeds

is to be expected,

the vacancies

if the clusters formed by

that anneal early in the process act as

may take place in the early stages of the annealing.

sinks

These clusters may serve as sinks at which single vacancies are annihilated. Thus, the multiple vacan-

remains the same if the clusters are considered to collapse and form dislocation loops, since these loops

cies formed

at higher temperatures

may

cause the

for those

that

anneal

may then serve as vacancy

later.

sinks.

The

argument

Such dislocation

entire annealing process to be accelerated. This effect should be particularly important for the quenching

loops have been seen in the electron microscope for quenched aluminun~.(30) At the outset of the anneal-

and air-cooling

ing,

experiments

high initial concentration multiple

vacancies

on Cu-AI, because of the of vacancies.

In fact, the may

only pre-existing dislocations would serve as The necessary dislocation density, d, may be

cause the annealing to be sufficiently rapid during the

calculated from nJ on the assumption that each site on a dislocation line constitutes a point where vacan-

cooling to prevent the retention of vacancies characteristic of these temperatures. This would give rise to

cies may be annihilated. Then, annihilation sites per cm3 is d/a,

the maximum

lattice

parameter.

lattice

sites

quenching

at the higher temperatures

sinks.

in the Ap vs. T curves in Fig. 6 for

and air-cooling.

The annealing measurements

after quenching

from

450°C show that e,1I increases as the annealing proceeds. This behavior also suggests that there is more than one annealing entity and that the predominant motion shifts during the course of the annealing from the defects having lower activation energies for motion to those having higher energies. The average number of vacancy

jumps, nJ, that a vacancy

is annihilated data.

may be estimated

For annealing

makes before it

from the annealing

at a constant

temperature,

the

number of jumps is given by nJ = TF

(6)

where 7 is the time for the annealing and P is the jump rate.

I? may be written P = Zv exp (X,/k)

exp (-&,/kT)

(7)

* The authors are indebted to A. K. Seeger for the opportunity to see reference 27 in advance of publication.

on

the

jumps

per

average is

to

the number of where a, is the

Since the total number of cm3 is of the order of ao-3, only one jump in every da,2

an annihilation

site,

whereby

nJ =

l/das2.

Early in the annealing process (f = 0.9), we find nJ = 2 x lo6 from which we deduce a dislocation density of about 5 X 10s dislocations per ems. This appears to be a reasonable

value for an upper limit

(since d (f = 0.9) > d (f = 1.0)) to t,he concentration of pre-existing annealing

dislocations.

were to continue

But, if the subsequent to be at dislocations,

the

concentration of dislocations would have to increase rapidly. For example, at f = 0.5, nJ = 5 x 104 jumps, which corresponds to a dislocation density of about 2 x lOlo dislocations per cm2. It should be mentioned that the use of the observed activation energies (Fig. 9) in equations (6) and (7) to calculate nJ is based on the assumption that the observed .sM’s are indeed the energies with which defects annealing at a given stage of the process move.

Whether

this

WECHSLER

assumption

LATTICE

KERNOHAN:

AND

DEFECTS

is correct depends upon the details of the

activation

energy

sinks. In an alloy

spectrum

containing

and the distribution a solute

concentration

15 at.%, it is unlikely that the equilibrium arrangement is a completely random one. recent

measurements

X-ray

diffuse

in this

scattering

neutron-irradiated

of

atomic Indeed,

Laboratory(31)

from

of

of the

an annealed

and

a

single crystal of Cu-Al

have indi-

cated that the alloy contains a significant

amount of

short-range

order.

It

is important,

therefore,

to

consider the possibility that the extra resistivity at temperatures above 200°C is due to a decrease in the equilibrium

short-range

order.

Unfortunately,

theoreticalinformation(12~32)isavailable relation between short-range order resistivity. to the

Also, resistivity

conclusion

that

measurements

an increase

little

concerning the and electrical have led

in short-range

order increases the resistivity of Cu3Au(33) and decreases the resistivity atomic

of Cu-Zn.(34)

rearrangements

occur by a vacancy

Nevertheless,

during

mechanism,

process

the kinetics of order-

ing are governed by the concentrations of vacancies.

since the

the ordering

and mobilities

Therefore, much of the above discussion

concerning the quench-annealing measurements applies also to the case of ordering. On this basis, an interesting possibility

presents itself for an explanation

of the maxima in the quenching and air-cooling in Fig. 6. It may be that, although

curves

the major effect

of the quenching is to retain lesser amounts of shortrange order, vacancies are also quenched in at the higher temperatures. accelerate tendency

the ordering to maintain

The additional reaction, equilibrium

vacancies

may

so that there is a short-range

order

during the cooling from higher temperatures. ACKNOWLEDGMENTS

The advice and co-operation

of D. S. Billington and

other members of the Solid State Division are greatly appreciated.

We wish also to thank H. B. Huntington,

IN

A COPPER-ALUMINUM

J. H. Crawford,

ALLOY

Jr., and D. K. Holmes

607

for helpful

discussions. Kind assistance was furnished by J. E. Thomas in the making of measurements and by F. A. Sherrill, J. A. Milko and J. B. Flynn in the prepa.ration of the samples. REFERENCES 1. 11. S. WECHSLER and R. H. KERNOAAN, J. Phys.Chem. Solids. 7, 307 (1958). 2. D.B. ROSENBLATT,R.SMOLIJCHOWSKI~~~ G.J.DIENEs, J. AppZ. Phys. 28, 1044 (1955). 3. A. C. DAMASK, J. Phys. Chem. Solids 4, 177 (1958). 4. M. S. WECHSLER, A&cl Met. 5, 150 (1957). 5. C. J. MEECHAN and R. R. EGGLESTON, Acta Met. 2, 680 (1954). 6. J. F. NICHOLAS, Acta Met. 3, 411 (1955). 7. P. JONGENBIJRGER, Phus. Rev. 106. 66 (1957). 8. J.E. BAKJERLE and J. ~.KOEBLER; Phys. Rkv. 107,1493

(1957). 9. F. J. BRADSHAW and S. PEARSON, Phil. Msg. 2,37!) (1957). 10. J. W. KAUFFMAN and J. S. KOEHLEIL, Phys. Rev. 97, 555

(1955). 11. B.G. LAZAREV~~~O.N.OVCHARENKO, Dokl.Akad.Xauk. S.S.S.R. 100. 875 (1955). Phws. 3. 26 (1954). 12. See T. BROOM. Ad&ace 13. W. J. STURM'~II~ M. S. ~EC&L.ER~ J. AppZ. Phys. 29, 15OQ (19.57). SLADEK, ActaMet. 1, 131 (1953). 14. A.S. Now~c~andR.J. and 9. S. NOWICK, Trans. Amer. Inst. 15. A. E. RO~WELL Min. (Met&) Engrs. 197, 1259 (1953). 16. W. M. LOMER, Institute of Metab Monwgruph No. 23, p. 79. London (1957). 17. L. C. R. AI,FRED and N. H. MARCH, PhiE. Xtrg. 2, 985 (1957). 18. J. HINO,C.TO~IZUKA~~~C.WERT, ActuMet.5,41(1957). 19. P. JONGENBURGER, Appl. Sci. Res. B 3, 237 (1953). 20. C. ZENER, J. Appl. Phys. 22, 372 (1951). 21. A. D. LECLAIRE, Acta Met. 1, 438 (1!)53). 22. H. BROOKS, Impurities and Imperfections, 11. 1. American Society for Metals, Cleveland (1955). and E. S. WAJDA,Phys. 23. H.B. HUNTINGTON,G.A.SHIRN Rev. 99, 1085 (1955). 24. C. Y. LI and A. S. NOWICK, Phys. Rev. 103, 294 (1956). 25. J. 8. KOEHLER, F. SEITZ and J. E. BAUERLE, Phys. Rev. 107, 1499 (1957). 26. J. H. BARTLETT and G. J. DIENES, Phys. Rev. 89, 848 (1953). 27. A. K. SEEGER, Ser. V, Proceedings of the Second International Conference on the Peaceful Uses of Atomic Energy, 1958. Pergamon Press, New York. 28. F.J. BRADSHAW~~~S.PEARSON, PhiLMag. l,Sl2( 1956). 29. F.J. BRADSHAW~~~S.PEARSON, PhiZ.Mag.2,570 (1957). and K. H. 30. P. B. HIRSCH, J. SILCOX, R. E. SMALLMAN WESTMACOTT, Phil. Mag. 3, 897 (1958). 31. B. S. BORIE, private communication. 32. J. B. GIBSON, J. Phys. Chem. Solids 1, 27 (1956). 33. A. C. DAMASK, J. Phys. Chem. Solids 1, 23 (1956). 34. A. C. DA~~ASK, J. AppZ. Phys. 27, 610 (1956).