The density of dislocations in compressed copper

THE L.

DENSITY M.

OF DISLOCATIONS

CLAREBROUGH,

M.

E.

IN COMPRESSED

HARGREAVES

and

G.

COPPER* W.

WEST?

The changes in stored energy, macroscopic density and electrical resistivity associated with the amlealing of deformed copper have been measured. Three independent estimates of the density of dislocations in the deformed material are obtained by combining these results with the best available theoretical values for the energy, density and resistivity changes associated with dislocations. The estimates from the energy and density measurements are in good agreement; but those from the resistivity measurements are approximately sixty times greater. This discrepancy may be due to the presence of stacking faults in the deformed copper. LA DENSITE

DES

DISLOCATIONS

DANS

LE CUIVRE

APRES

COMPRESSION

Les auteurs ont mesure les modifications d’energie, de densite macroscopique et de resistivite electrique resultant du recuit de cuivre deform& 11s obtienuent trois estimations distinct& de la densite des dislocations dans le metal deform6 en combinant leurs mesures avec les valeurs theoriques disponibles pour la variation d’energie, de densite et de r&istivite liees aux dislocations. Les calculs s’appuyant sur les mesures energetiques et densitometriques sont en bon accord avec la theorie, mais pour les mesures de resistivite les resultats sont approximativement soixante fois trop grands. Cette difference est due probablement it la presence de defauts d’empilement dams le cuivre deform& DIE

VERSETZUNGSDICHTE

IN GESTAUCHTEM

KUPFER

Die beim Anlassen von verformtem Kupfer auftretenden linderungen der aufgespeicherten Energie, der makroskopischen Dichte und des elektrischen Widerstandes wurden gemessen. Durch Kombination dieser Ergebnisse mit den besten verfiigbaren theoretischen Werten fur die Energie der Versetzungen, sowie die von diesen hervorgerufenen Dichte- und Widerstandsanderungen erhalt man drei voneinander unabhangige Abschatzungen fiir die Versetzungsdichte des verformten Materials. Die abgeschiitzten Werte aus den Energie- und Dichtemessungen stimmen gut iiberein, diejenigen aus den Widerstandsmessungen sind jedoch etwa sechzigmal grosser. Diese Diskrepanz hiingt wahrscheinlich mit dem Forhandensein von Stapelfehlern in verformtem Kupfer susammen.

1.

INTRODUCTION

energy is released over a small range of temperatme

The density of dislocations in a deformed metal may be estimated annealing

from the changes

in the stored energy,

and electrical

resistivity.

which occur macroscopic

during density

In order to compare

in a single peak

papers(ip2T3) have

measurements showed

calculations

discrepancies

locations these

and

from

However,

the the in

such

nickel. density

These of dis-

measurements nickel,

the

of

stored

energy is released over a wide range of temperature and the density and electrical resistivity change in two stages. Further, vacancies are present diEicult

to

choose

since there is evidence in the deformed nickel unequivocally

the

changes

that it is in

properties that must be attributed to the dislocations. The present paper reports measurements of stored energy, macroscopic density and electrical resistivity made on pure copper.

For this material,

* Received May 13, 1957. t Division of Tribophysios, Melbourne, Australia. ACTA METALLURGICA,

C.S.I.R.O.,

the stored

University

VOL. 5, DECEMBER

changes in

such

reported

for

between

as calculated

properties.

already

to recrystallization

with distinct

density and electrical resistivity. 2.

estimates it is essential that they be made from measurements on specimens of identical material. Previous

corresponding

and this peak is associated

1957

of

Commercial

was used.

EXPERIMENTAL

O.F.H.C.

Specimens,

copper

long, were annealed in vacuum then

compressed

described

(99.98

per cent Cu)

IQ in. in diameter

to various

previously.(2)

and 5 in.

for 1 hr at 600°C and

extents

Specimens

in the manner were

cut

and

machined from the compressed cylinders, those for the measurements previously,(l)

of density being the same size as used i.e.

19 in. long and 2 in. in diameter,

and those for the measurements being2in.

x

tin.

x

of electrical resistivity

&in.

The measurements of stored energy, density, and electrical resistivity were made in the manner described in previous publications.(lp2T4) The disadvantages of the annealing procedure used for the measurements of density on nickel(l) were largely overcome by heating the specimens in a stainless steel tube filled with pure nitrogen rather than in an evacuated tube. 738

silica

L.

M.

CLAREBROUGH,

M.

E.

HARGREAVES

AND

G. W.

WEST:

COMPRESSED

COPPER

739

If the changes in stored energy, density and electrical resistivity all result from a decrease in the number of dislocations

during recrystallization,

dent estimates locations

in the deformed

mation.

three indepen-

can be made of the density material

of dis-

for each defor-

These estimates are listed in Table 2 and are

all based on the assumption and screw dislocations. density from

of equal numbers of edge

In calculating

the dislocation

the energy measurements

it has been

assumed that the edge and screw dislocations have energies of 5 x 1O-4 ergs cm-l and 3.3 x 1O-4 ergs cm-l respectively.‘@ For the density measurements Temperature

FIQ. 1. Power difference (AP), increment in electrical resistivity (Ap) and fractional change in density (AD/D) as functions of temperature for copper deformed 55 per cent in compression and heated at G”C/min.

3.

The

results

deformed 6’C/min

RESULTS

of the

measurements

on

55 per cent in compression

specimens

and heated at

are shown in Fig. 1. The results in each case

are the mean of separate measurements on two identical specimens. Practically all the stored energy is released in a single peak and sudden changes in density and electrical resistivity occur in the corresponding

range of temperature.

specimens

deformed

compression Fig.

1.

The results for the

30 per cent and ‘70 per cent in

are similar in form to those shown

For all deformations

in

the peak in the AP

curve and the sudden changes in density and electrical resistivity Table

correspond

to recrystallization.

change in density

change in electrical resistivity the release of energy. 4.

(AD/D) and the

( Ap) which accompany

DISCUSSION

In the present experiments

the various properties

have been measured on specimens of identical material so that a correlation

of the results should be possible.

The values obtained

for the changes in density

and

electrical resistivity are in agreement with the results of Smart, Smith and Phillips(5) for oxygen-free pure copper. TABLE 1. Stored energy, fractional change in density and increment in electrical resistivity for copper deformed in compression

_

Deformation % compression

S W/g)

30 55 70

0.095 0.128 0.148

as was done for nickel,“) causes

dislocation

the

same

that

change

in

density as a row of vacancies

of the same length and

that

not

screw

dislocations

change in density.

do

contribute

For the measurements

resistivity

the

dislocation

line/cm2 has been used.(‘)

value

of

0.4 x lo-l4

to

the

of electrical ,uQ cm per

It can be seen from Table 2 that there are large discrepancies between the various estimates. In fact, the estimates in the three columns are approximately in the proportion 1 : 6 : 60. A similar factor of 6 was reported previously for nickel.(l) The discrepancy

between the first two estimates can

be removed by using the more recent estimates of Stehle and Seeger(@ for the density change associated with

a dislocation.

They

density change associated

have

shown

that

the

with a screw dislocation

copper in not negligible but is equivalent

in

to between

one and two times the change that would result from a

1 lists the total energy stored (8) together

with the fractional

it has been assumed, an edge

AD

Ap (yfi cm)

D 0.91 x IO-4 1.38 x 10-4 1.93 x 10-d

0.022 0.030 0.037

=

row of vacancies estimate

that

dislocation

of the same length.

the density

change

Further,

is rather greater than that due to a screw

dislocation.

On this basis, in considering

dislocations

could be considered

density

density,

all

to cause a change in

equal to twice that resulting

vacancies

they

due to an edge

of the same length.

from a row of

Then the estimates

given in Table 2 for the dislocation

densities calculated

from the density measurements

would be reduced by a

factor of 4 and the discrepancy

eliminated.

The large discrepancy from the measurements TABLE 2. Density

Deformation o/o compression

30 55 70

Dislocation density from energy measurements lines (cm-1)

8.5 x 10’0 1.1 x 10” 1.3 x 10”

between the results obtained of stored energy and electrical of dislocations

, /

Dislocation density from density measurements lines (cm-2)

4 x 10” 6 x 10’1 8 x 10”

in copper

i Dislocation 1 density from electrical ~ resistivity

/

5 x 10’2 7 x 10’2 9 x 10’2 _.-._

740

ACTA

METALLURGICA,

resistivity has been discussed in detail by Koehler(g) for copper and Boas (3)for nickel and attributed to the presence of stacking faults. However, the effect of a stacking fault on resistivity is still a controversial question and no further discussion will be entered into here. ACKNOWLEDGMENTS We we grateful to both these author8 for allowing us to see their manuscripts prior to publication. Note added in proof: Since writing the above we have received notice of two other relevant calculations. Firstly Dr. W. A. Warrison1o has calculated the resistivity change due to a dislocation with a hollow core and has found that the change may be an order of magnitude higher than previously supposed. Secondly Dr. W. 11. LomeP has used a different method from that of Stehle and Seeger to

VOL.

5,

1957

calculate the density change due to a dislocation and reached a similar result to theirs. REFERENCES 1. I;. M. CL~REBROUUH, M. E. HARGREAVES and G. W. WEST Phil. Mag. 1, 528 (1956). 2. L. M. CLAREBROVOH. M. E. HARGREAVESand G. W. WEST .&oc. Roy. Soo. A zS!$ 252 (1955). 3. W. BOAS Conference rtt Lake Placid. DislocatZonsand ~~h~n~~ Properties of Crystal (1956). 4. L. I& CL~BROU~H, M. E. HAROXEAVES,D. MICHELL wd G. W. WEST Ppoc. Roy. Sot. A 215, 507 (1952). 5. 5. S. SMART, A. A. SMITH and A. J. PHILLIPS XmTt-3. Amer. Inst. Min. (Metall.) Engrs. 148, 272 (1941). 6. A. H. COTTRELL Dislocations and Plastic Flow inCry&al.~ p. 38. Clarendon Press, Oxford (1953). 7. S. C. HUNTER and F. R. N. NABARRO PTOC. Roy. Soo. A 220, 542 (1953). 8. W. STEHLErendA. SEEOER 2. Phys. 146, 217 (1956). 9. J. S. KOEELER Impwitim mu8 I~~T~e~~o~ p. 162. American Society of Metals (1955)+ IO, W. A. HARRISON Resistivity due to dislomtions ir+ copper. To be published. 11. W. M. LOMER Density change of a crystal containing dislocations. To be published.