Precision density measurements on deformed Copper and Aluminum single crystals

PRECISION

DENSITY MEASUREMENTS ON DEFORMED AND ALUMINUM SINGLE CRYSTALS* M. J. HORDONt

COPPER

and B. L. AVERBACH:

Measurements of the fractional decrease of density were used to estimate the number of dislocations in annealed and plastically strained single crystals of high-purity copper and aluminum. An almost linear increase in dislocation density with shear strain was observed. Dislocation concentrations of the order of 101O/cmaafter shear stmins in the range 0.1-0.5 were calculated from precision density det,erminations, in good agreement with values obtained from X-ray measurements.

~~~SU~~S PREMISES DE DENSITE DES ~~O~OCRIST~~U~DEFO~~~S DE CUIVRE ET ALUMINIUM Des mesures de la di~ninutionfraction&e de densiti ont et& employees pour Bvaluer le nombre de dislocations dans des monoeristaux t&s puns de cuivre et d’ahnninium qui ont subi un traitement de revenu et une deformation plestique. On a observe une augmentation de la densite des dislocations qui et&itpresque lineaire avec la deformation de cisaillement. Des concentrations de dislocations de l’ordre degrandeur de 101~jcm2ont ete calcules apres des deformations de cisaillement de O,l-9,5 it partir de mesures p&&es de densite, ce qui a Qte en bon aocord avec les valeurs obtenues par rayons X. P~~~~ISIONSDICHTEMESSU~GEN

AN VERFORMT~N

EI~KRISTALL~N

AUS

KUPFER UND ALUMINIUM Aus Messungen der relativen Dichteabnahme wurde die Zahl der Versetzungen in ausgegliihten und plrastischgedehnten Einkris~llen aus Kupfer und Aluminium hoher Reinheit abgeschiztst. Es wurdc eine fast lineare Zunahme der Versetzungsdichte mit der Abgleitung beobachtet. Nach Abgleitungen im Bereioh von 0,I bis 0,5 wurden aus Pr~~ision~i~h~best~mungen Versetzungsdichten von der GroGlenordnung 101O/emeberechnet, die gut mit den Ergebnissen von r~ntgenographischen Messungen iibereinstimmen. 1. INTRODUCTION

A wide variety of experimental techniques has been available for the study of dislocation densities and spatial distributions in both annealed and in plastically strained crystals. In a previous paper@) (hereafter called Ref. l), estimates of dislocation density as a function of plastic strain were derived from doublecrystal X-ray rocking curve broadening for highpurity copper and aluminum single orystals. The present paper reports the results of precision hydrostatic density measurements on the same crystals in an effort to provide independent estimates of the dislocation density for comparison. Since the deformation was carried out at room temperature, the only defects considered stable enough to remain were line defects such as edge and screw dislocations. 2. EXPERIMENTAL PROCEDURE Cylindrical single crystals, 5 in. long by 5/S in. diameter, of high-purity copper and aluminum were * This paper is taken from a thesis submitted by M. J. Hordon in partial f~~llment of the requirements for the Sol?. degree in Metallurgy at the Massachusetts Institute of Technology. Received May 9, 1960; revised September 6, 1960. M~~o~;~~tt;ddress: The Alloyd Corporation, Cambridge, chiz;;artment

of Metallurgy, M.I.T.,

ACTA METALLURGICA, 6-w

PP 1

VOL.

Cambridge, Massa-

9, MARCH

1961

grown from the melt by the Bridgman technique. Flat tensile specimens with dimensions 1.5-2.5 in. in length, 0.375 in. in width and O.OSO-0.~00 in. in thickness in the gage section were prepared from these crystals with surfaces parallel to within -&!i” of the (Ill) and flOO>pl anes for copper and the (100) plane for aluminum, as reported in Ref. (1). Changes in density after plastic deformation were measured by a differential hydrostatic weighing technique similar to that of Be1S2). The apparatus consisted of a semimicro balance with a sensitivity of 1 x 10-s g. Specimen and standard crystals were suspended by platinum wires from the balance arms and were immersed in a weighing liquid of l-2 dibromopropane (p = 1960 g/ml) in turn contained in a water bath maintained at 25% f O.Ol”C. The temperature was controlled by a mercury thermoregulator and both weighing liquid and water bath were continuously stirred to ensure equilibrium heat distribution. Density changes were determined by a di~erential technique which involved weighing the test specimen as annealed and after deformation against an annealed standard in air and in the weighing liquid. The advantages of this method were that the temperature and variation of density with temperature of the weighing liquid did not have to be determined as long as the temperature was everywhere uniform, and errors due

247

ACTA

248

METALLURGICA,

Resolved

sheor

VOL.

stress

9, 1961

( kg/mm2)

jcj3K

Al

0.8 I

I

Resolved

sheor

I .o

0

I

stroin

y

0.8 -

.

.”

FIG. 1. Influence of applied shear stress and prior shear strain on hydrostatic density of copper and aluminum single crystals.

to a change in depth of immersion

of suspension wires

and changes in surface tension of the weighing liquid were cancelled

of the test specimen AP_

( W, -

the differential

W,)U d, do p (W, M -[---

where p is the absolute specimen

weight,

density

change

has been given as w

P --L M

-

~~

l-

(WI -

W,Y

( W, -

W,)%,

a0 WoY 4 -

specimen

density,

do is the density

weighing

M is the

(W, -

is negligible in this case, and a0 < do, equation

Wo)” (1) can

be simplified :

P

mize the weight difference (W, men and standard to

crystal

minimize

should be closely In the

differences.

present case, the crystals weighed about 10 g and were prepared

by etching

to have a weight

weighing in the

The results are shown in density

change Apjp is

difference \<

shear stress and shear strain values from tensile data in a manner reported

decrease nearly linearly as a function

of shear stress

and strain, and in the strain range studied, copper and aluminum resolved

showed

the same variation

shear strain.

Extrapolation

of Aplp with of the curve in

Fig. 1 to a shear strain y of 0.6 (tensile strain F N 0.3)

Clarebrough

W,)“, and the speci-

weights

volume

hydrostatic

in Ref. (1). As Fig. 1 shows, the density was found to

agreement

p (WI - WOY -. M do - a0

To reduce errors, M should be large in order to maxi-

matched

Resolved

were computed

gave -ApIp

AP _

DISCUSSION

were made after plastic deformation

Fig. 1 in which the fractional

of the weighing

Because

change

plotted against residual shear strain and applied shear

steps before and after straining,

in liquid and air, respectively.

AND

shear strain range 0.1-0.5.

1 (1)

density

of the density of copper and alumi-

num crystals by the differential

stress.

a0

of the relative

x 10-s.

3. RESULTS

Measurements technique

liquid, a, is the density of air, and Wnd, Wna denote the sequential

The accuracy

was about 51

out.

For this technique,

1

50 mg.

a value of about 1 x 10-4, in very good with the value of 0.9 x 1O-4 reported et uZ.(~) for copper deformed

by

30 per cent in

compression. Estimates

of dislocation

concentration

N were de-

rived from the decrease in crystalline density following the analysis of Stehle and Seegert4) using the expression

N = -APIP 2b2

HORDON

AVERBACH:

AND

PRECISION

DENSITY

MEASUREMENT

values are in good agreement 10n/cm2

calculated

from

et &.(a) for deformed

with the value of 1.1 x

the

changes

data

of Clarebrough

cooper.

4. CORRELATION

Estimates

249

OF RESULTS

of dislocation

in crystal

density

density

for

calculated

plastically

from

strained

copper and aluminum are compared in Table 1 along with values derived from X-ray rocking curve broadening measurements seen that

the

reported

X-ray

and

within a factor of 2; in

calculating

in Ref. (1).

density

thus the assumptions

dislocation

It can be

methods

densities

agreed involved

appear

fairly

reasonable. TABLE 1. ‘Density of dislocations in cold worked copper and aluminum single crystals Shear strain (y)

1 0. I

0

0.3

0.2 Resolved

shear

0.4

0.5 COppI

strain

FIG. 2. Dislocation densities calculated from hydra. static density measurements.

where

b is the

Burger’s

vector.

The

expression

assumes that the screw and edge components dislocations

are equal.

The volume

effect

defects such as vacancies can be reasonably since

vacancies

rapidly

would

be expected

after room temperature

to

of the of other

discounted anneal

deformation

out

of high-

___.-. 0.102 0.244 0.447 -~ __~_ 0.116 0.220 0.421

of dislocation

density

I

/

I x 10’0

1~

3 x 10’0 5 x 10’0

’

9 x 109

:

1 x 10’0 3 x 10’0 8 x 10’0

2 x 10’0 9 x 10”’

Aluminum

.~

7 x 109 2.5 x lo’* 4 x 10’0

* X-ray values of disloca,tion density taken from Ref. (1).

purity copper and aluminum. The resulting variation

Dislocation density IV (cm-1)

~~~ ~~~. ._.__

ACKNOWLEDGMENTS

with

that N varied linearly for copper in the linear harden-

The authors are grateful to the United States Atomic Energy Conlmission and to the M.I.T. Instru-

ing strain range (Stage II of the single crystal tensile

mentation

curve) whereas the curve for aluminum

Force for sponsoring

residual shear strain is shown in Fig. 2. It is apparent

linearity

in the strain range above 0.2 corresponding

to the region where cross slip occurred Ref. (I).

departed from

The linear portion

(Stage III) see

of the curve is described

by the expression

and

like also to acknowledge Dr. A. It. Rosenfield,

the

United

this investigation.

States

the advice and cooperation Professor

Air

They would

D. A. Thomas

of and

G. Langford. REFERENCES

N = Ky where the constant

Laboratory

(4)

K is approximately

for copper and 0.8 x 10n/cm2

1 x 10n/cm2

for aluminum.

These

I. M. J. HORTONandB. L. AVERBACH, Acts. Met. 9,237 (1961). 2. G. A. BELL, Aust. J. A&. Sci. 9, 236 (1958). 3. L. M. CL.AREBROUGH, M. E. H~RGREAVESand C. IV. WEST, Acta Met. 5, 738 (1957). 4. H. STEIKE and A. SEEOER,2. Php-. 149, 217 (1956).