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The production and annealing of point defects in β-CuZn
THE
PRODUCTION
AND
ANNEALING
M. J. KOCZAKllt,
OF POINT
H. HERMAN1
and
DEFECTS
IN /M~.&I*
A. C. DAMASK8
Ordered fl.brass was irradiated with 1.5 MeV electrons at 20°K and then annealed. Three prominent decay stages ocour at 40, 65 and 90°K with respective energies of about 0.03, 0.05 and 0.1 eV. These stages are similar to those which occur in pure metals and are therefore believed to arise from correlated interstitial-vacancy recombination. A stage occurs in the range of lOO-150°K which is believed to arise from either nncorrelated interstitial migration or from the release of trapped interstitials. A long decay stage begins at 159°K and continues until it joins the thermal equilibrium curve above room temperature. It has a varying activat,ion energy w&h about, 0.4 eV at 200°K. The annealing goes well below the pre-irradiat,ed value at 180°K and a similar effect is observed after irradiation at 78°K. This enhanced ordering is assigned to the vacancy. After quenching an unirradiat,ed sample to - 14”C, transferring quickly to liquid nitrogen and then annealing, two stages are seen; one from -50 to about 0°C with an activation energy of 0.45 & 0.05 eV and one in the range of IO-120°C with an activation energy ranging from 0.6 to 0.7 aV, the location of the latter stage depending upon the quench temperature. The lower temperature stage is assigned to the vacancy and the upper stage to vacancies trapped at antiphase domain boundaries. On the basis of these assignments it is understandable t)hat the high vacancy mobilit)y inhibits the retention of quenched-in disorder in this system. PRODUCTION
ET
RECUIT
DES
DEFAUTS
PONCTUELS
DANS
CuZn /?
Du laiton /j’ordonne a et& irradii? aux Plectrons de I,5 MeV a 20°K puis recuit. Trois stades de revenu pr~dominants se produisent a 40,65 et 90°K avec des energies respectives de 0,03,0,05 et. 0,l eV environ. Ces stades sont analogues a ceus qui apparaissent dam les m&aux purs et les auteurs supposent par consequent qu’ils sent dtis a la recombinaison co&lee interstitiel-aoune. Un stade se produit egalement dans le domaine 100-150”K, et il semble Btre dQ ou bien a la migration non eorrelee de I’intcrstitiel, ou bien a la liberation des int,erstitiels pieges. Un long stade de revenu commence a 150°K et continue jusqu’a ce qu’il rejoigne la courbe d’equilibre thermique au-dessus de la temperature ambianta. I1 a une Bnergie d’activation variable, avec 0,4 eV environ it 200°K. A 18O”K, le recuit conduit a des valeurs bien inferieures aux valeurs correspondantes avant irradiation, et un cffet analogue est observe apres irradia. tion a 78°K. Cette mise en ordre est attribueo aux lacunes. Apres trempe d’un echantillon non irradie jusqu’a - 14OC,transfert rapide dans l’azote liquide, puis recuit, deux stades apparaissent; l’un a partir de - 50°C jusqu’it environ 0°C avec une Bnergie d’aetivation de 0,45 f 0,05 eV, et l’autre dans le domaine de 10°C it 12O’C avec une (inergie d’act,ivat.ion sit&e ent,re 0.6 et 0,7 eV, la situation de ce dornier stade d~pendant de la temperature de trempe. Le premier stade cst attribue aux lacunes et le deuxieme aux lacunes piegees RUX front,ieres des domaines antiphases. I1 est done logiquc que la forte mobilite des latunes emp&he de retenir le desordre c&h par trempe dam cc systeme. DIE
ERZEUGUSG
UND
DAS
AUSHEILEN
VON
PUNKTFEHLERN
IN
1.CuZn
Geordnetes @-Mussing wurde mit 1,5 MeV-Elektronen bei 20°K bestrahlt und dann angelassen. Drei ausgepragte Erholungsstufen treten bei 40,65 und 90°K auf. Die zugehorigen Aktivierungsenergien sind etwa 0,03, 0,05 und 0,l eV. Diese Stufen sind den in reinen Metallen beobachteten Stufen ahnlich und es wird deshalb angenommen, da6 sie die Folge von korrelierten Zwischengitteratom-LeerstellenRekombinationon sind. Eine Stufe zwischen 100 und 150°K wird entweder der freien Wanderung dcr Zwisehengitteratame oder der Wanderung van Zwischengitt,eratomen, die sieh in diesem Tamperaturbereich van ~aft.stellen losrei0en, zugesohrieben. Eine breite Ausheilstufe beginnt bei 150°K und mtindet in die thermische Gleichgewichtskurve oberhalb Raumtemperatur. Ihre Aktivierungsenergie variiert und ist bei 200°K etwa 0,4 eV. Der Widerstand liegt weit unterhalb des Wertes dar unbestrahlten Probe bei 180°K und naeh 78”K-Bestrahlung wird ein ahnlichor Effekt beobachtet. Diese erhohte Ordnung wird der Leerstelle zugeschrieben. Eine unbestrehlte Probe wurde auf - 14OC abgesohreckt, schnell auf Stickstofftemperatur gebracht und dann angelassen. Zwei Stufen wurden beobaohtet: eine zwischen - 56°C und 0°C mit eincr Aktiviorungsenergie von 0,45 & 0,05 eV und eine zweite zwisohen 10 und 120°C mit einer Aktivierungsenergie von 0,6 bis 0,7 eV; die Lage der zweiten Stufe hangt von der Abschrecktemperatur ab. Die Stufe zwischen -50 und 0°C wird der Leerstelle zugeschrioben und die andere Stufe den an Antiphasengrenzen festgehaltencn Leerstellen. Aufgrund dieser Zuordnungen ist es verst~ndlieh, da13wegen der hohen Leerstellenbewegliehkeit die dureh Abschrecken erzeugt,e Unordnung in diesem System nicht erhahen bleibt..
1. INTRODUCTION
* Received August 13, 1979. Work supported by the U.S. Atomic Energy Commission and the National Science Foundation GK 1085 at the University of Pen~ylvania and GK 10009 at Stony Brook. The work was part of the requirements for the Ph.D. of M. J. K. at the University of Pennsylvania. t University of Pennsylvania, Philadelphia, Pa. and Brookhaven National Laboratory, Upton, N.Y. $ State University of New York at Stony Brook, N.Y. 9 Queens College of the City of New York, Flushing, N.Y. and Brookhaven National Laboratory, Upton, N.Y. Ij Now at: Department of Materials Science, State University of New York, Stony Brook, N.Y. ACTA
METALLURGI~A,
VOL.
19, APRIL
If the defect assists in diffusion and moves in an alloy which has not yet attained an equilibrium degree of order, then the defect may enhance the establishment of order. It has been shown by several investigators that such excess defects can yield greater degrees of order than are achievable by thermal means alone.c1*2) In the present study the annealing of point defects and their effect on the order in p-brass is reported. The ordered microstructure of &brass has been well characterized and the &--Cl crystal structure of the ordered alloy is a particularly interesting framework in reactions.
Defects in excess of the thermal equilibrium concentration are able to modify various solid state
1971
303
XCTA
304
which to study point defects. been examined
Although
by quenching,(3-5)
deformation,(‘)
METALL17RGICA,
@-brass has
irradiation@)
the point defect formation
and
VOL.
19,
1971
do not arise from changes in the chemical composition since all initial values were reproducible. For quenching,
and migra-
the specimens were gravity-dropped
The
size
(wire
diameter
=
into
not been completely
0.015 in.) provided for a fast quench while eliminating
understood.
a comparison
of annealing
and
irradiation
electron
ident’ification of vacancies
In the present’ work
following is made
of the temperature and interstitials
both quenching and
a tentative
range of migration
is given.
2. EXPERIMENTAL
The as-received
p-brass at.%
rod.
The electron
wt. % Zn) was in the The major
by spectrographic
analysis
were Mg, Fe
range from 47 to 50
in structure,
structure
and has an ordered
below the critical temperature,
460°C. This limited compositional the brittle nature
range, coupled with
of the alloy
and high zinc vapor
pressure, presents serious difficulties tion.
impurities
by weight.
Zn, is b.c.c.
in wire fabrica-
It was therefore necessary to grow single crystals
in order to facilitate Single
reduction
crystals
Bridgman
were
technique
operations.
grown
thermal
stresses.
were immediately
energy
irradiations
After
stored
a modified
procedure.
at
from
0.3
provides
to
3.0 MeV
The beam current was regulated 10-6-10-3
with
better than 6 KeV throughout
cent of the t’otal current,
National
electrons of an voltage
this range.
to better than 1 per
with a current
range
MeV for all irradiations, 1 pA/cm2.
density
of
At this current density the temperature
with a current
of
the samples during irradiation
did not exceed 20°K.
To assure a uniform electron dose along the electrical gage length, the electron beam was scanned vertically and horizontally.
The beam current was monitored Faraday
cup by an Elcor
current
used for the electron
irradia-
integrator.
The
The liquid
cryostat,
tions, was built by the Janis Research Company.
then encapsulated
cryostat
lo-”
torr.
through
tubes at a pressure
The rods were slowly
a temperature
gradient,
single crystal and bicrystal
drawn
(~1
yielding
of
in./hr)
6 in. long
rods.
No phase separation was detected by metallography or X-ray
studies and chemical
analysis
the starting materials.
from
Wires of 0.015 and 0.006 in.
diameter were drawn for the quenching tron irradiation
experiments,
and the elec-
respectively.
or liquid
nitrogen
irradiation employed portions
experiments,
liquid studies
nitrogen
A dummy
are less than the
size of the data points given in the figures. Annealing of small diameter wires of p-brass elevated However,
temperatures
was
The errors associated
measurements
by conduction
reported here
300”K,
with
-&O.Ol”K.
Cali-
sensors monitored and annealing.
Sosin and Neely(@
in which rods.
sapphire
metallizing
the sample
holder
In order to facilitate
inthe
samples to the sapphire, a
process
Corporation.
thermal contact
were cooled
in a manner similar to the design of
corporates
This
was performed process
provided
by
the good
between t’he sapphire and the speci-
men. 3. RESULTS (a)
Annealing following quenching 1. Isochronul annealing.
A plot of the as-quenched
resistivity (measured in liquid nitrogen) is shown in Fig. 1 where, for later discussion, the curve is divided into three regions. Region a shows an increase in resistivity
at
may result in a loss of zinc.
the changes in the resistivity
and platinum
and of
during the irradiations
The liquid
and for some
experiments.
specimen was always employed.
germanium
5
control
The wire specimens, 0.006 in. diameter,
Advac
temperatures. while
of the irradiation
with the resistivity
brated
between
temperature
the temperature
were used only for the electron
for the quenching
temperatures
automatic
The
so that samples can anneal at
soldering of the resistivity
A standard four-probe potentiometric circuit was employed with measurements carried out at liquid helium measurements
was designed
MO-Mn
(b) Electrical resistivity measurements
helium
given
of the wires
indicated no significant change in the composition
of
A. The electron energy energy used was 1.5
as-received bars were swaged to & in. diameter rods and in quartz
in
out at the
Brookhaven
This accelerator
range
regulation
were carried
Accelerator
from an isolated
using
in the following
from
liquid nitrogen.
Laborat,ory.
has a compositional
Cs-Cl-type
the samples
PROCEDURE
alloy (Cu-48.4
and Si, all 0.001%
arising
quenching
Dynamitron
of 4 in. diameter
determined
problems
(c) Electron irradiation
(a) Alloy fabrication form
water.
specimen
tion energies, as well as their relation to ordering, have
from
quench
where a maximum 2OO”C, the resistivity 3OO”C, region
temperatures
up to 2OO”C,
of 5 per cent is reached.
Above
drops off to about 2 per cent at
b, and
then
displays
a continuous
8
QUENCH TEMPERATURE, FIG. 1. Resistivity
*C
vs. quench temperature.
increase up to the highest temperature of 5OO”C, region c. This behavior is similar to that reported by Clark and Brown(a) and Harkcom and Martin.@) Annealing was studied following quenching from both above and below the critical temperature (460%) Figure 2 shows isochronal recovery curves after quenching from 500,435 and 400°C. A main recovery stage is observed between 20 and 75°C for the samples quenched from 5OO”C, and between 50 and 120°C for those quenched from below the critical temperature. The rate of recovery is seen to increase with increased quench temperature. In addition to the main stage, a small recovery stage is observed for all of the isochronal results between -50 and O”C, followed by a shallow minimum. It appears that the range of this early stage is independent of quench temperature in that it terminates around -10°C for all quenched samples. Comparison between water and brine quenching is also shown in Fig. 2 where it is seen that the faster brine quench yields a higher value of quenched-in resistivity, 14 vs. 11 per cent for the quench into water. The later increase in resistivity, which occurs beyond the main annealing stage in Fig. 2, can be identified with region a of Fig. 1. All four of the annealing curves merge at temperatures above 125’C, and it can therefore be concluded that equilibrium order is rapidIy achieved above 125°C. 2. I~o~~~~~l ~~~~~ng. Isothermal anne&lings were performed to determine the activation energy
and order of reaction of the major annealing stage shown in Fig. 2. Sets of these data were taken for different quench temperatures. For all quench temperatures the decay in the temperature range of 20120°C yielded an activation energy of 0.6 eV for quenches from above the critical temperature to 0.7 eV for quenches from below in agreement with the analyses of this decay by other techniques.(ss4) The order of the reaction was obtained in the following manner. It is assumed that the decay is a singlyactivated process which can be described by
where K, is the rate constant, y is the order-of-reaction and E is the activation energy for the process. This equation may be written as In
[
dnY-
- ---t--
- y In n + In [K, exp (--E/kT)]
(2)
where the expression In [K, exp (-E/l&“)] is constant for a given isothermal curve, and therefore the slope of a plot of In n vs. In [(-t&/d In t)/t] gives a value for the order-of-reaction, y. Isothermal annealing at 75% following quenching from 500°C is shown by the lower curve of Fig. 3. In this figure the normalized resistivity, which is plot,ted as the ordinate, is identified with n. It is seen that only the latter 40 per cent of the reaction is linear with an order of approximately unity. Isothermal annealing at 30°C following quenching
306
from
temperatures
between
yield
an activation
energy
100 and
d5O”C also An order-of-reaction was also determined, an example of which is shown by the upper curve of Fig. 3 for annealing at, 20°C after quenching from 175%. It is seen that, the entire process fits a straight line, yielding an order of a~proxin~ately m&y. of 0.65 -& 0.05 eV.
(b) Electron irradiation 1. Production of defects. An ordered condition was achieved prior to electron irradiation by amiealing at 500°C for 15 min followed by annealing at, 200°C for 15 min and then furnace cooling. The resistivity ratio ~~~*o=~~*.~o~of t,he wire was typically seven. Irradiatio~~swere carried out with an electron energy of 1.5 MeV, which is capable of displacing both copper and zinc atoms.‘g) The change of resistivity with dose for 1.5 MeV electrons near 20°K is 8.8 X 10e2’ near 78”K, it is 5.5 x 10e2’ 0cm/electrons/cm2; Rcm[electrons/cm 2. These values are comparable to the damage rates of pure metals, e.g. for copper near 10°K. the rate is 9 x lo-*7 ~cm~ele~trons~cmz for 1.5 MeV electrons.(iO) 2. Amealing spectrum following electron irradiation. Isochronal recovery in 10 min pulses following irradiation at 20°K to dose of 4.5 x 1017 electrons/ cm2 is shown in Fig. 4. Liquid helium was used as the measuring temperature up to liquid nitrogen t,emperature, then liquid nitrogen was used. The amiealing curve shows a number of substages below 100°K followed by a stage which begins at 100
-I -4
TEMPERATURE OC FIG.2. 10 min isochronal annealing after quenohing. C-guench from 500 to 25°C. n-quench from 500 to 14%. n-quench from 435 to 25°C. C-quench from 400 to 25°C.
0. IO _
O.Old 0.001
I
I
I
I
I
I
IllIll
0.10 - (dnldlntlt
Fro. 3. o-isothermal
IllIll
0.01
1.0
1
annealing at 20°C after quench from 1’75°C. A-isothermal 75°C rafterquench from 500°C.
annealing at
KOCZAK,
HERMAN
AND DAMASK:
POIX’T
DEFECTS
I?i
/j-Cu%n
307
80 60 z y
40
0 2
20
8
0 -20
25
50
75
100
125
150
FIG. 4. 40
and ends at 150°K.
This stage,
Above
150°K
defined
stages,
there
is a steady
185°K
the resistivity
value.
This “extra recovery”
not well
in all specimens. decrease
and it is important falls below
200
with
no
to note that at the pre-irradiated
is indicative
of enhanced
225
250
at 20°K
min isochrone aft,er electron irradiation
although
defined in Fig. 4, was reproducible
175 “K
TEMPERATURE,
a broad annealing stage from 120 to about 230°K
in
which the resistivity
again anneals to below the pre-
irradiated
value
resist,ivity
irradiation
at 20”K, Fig. 4. At 24O”K, the resistivity
increases 350°K.
of
as it did
following
and merges with the equilibrium Following
curve at
a 10 min isochronal pulse at 363’K,
ordering and was also seen in annealing curves follow-
the specimen was then annealed at 315°K and below.
ing irradiation
The solid curve without data points shows the values
at liquid
nitrogen
temperature.
The
point at which the plot crosses the zero of the recovery
of resistivity
axis was found
315”K,
to shift to lower annealing
tures with higher irradiation Two specimens electrons/cm2 times
irradiated
to a dose of 4.5 x 101’ annealed
both
the temperature The activation
curves
shift for a given
by
ing stage between 100
annealing
and
150°K
taken for the annealindicate has
an
that the activation
energy of about 0.15 eV near its midpoint
at 125°K
and about 0.25 eV near the end at 150°K.
The stage
which
energy
begins at 150°K
has an activation
about 0.3 eV at 175’K and 0.4 eV at 200°K. be noted that this type of activation is very crude when several overlapping involved
the resistivity
now
follows
the
plot
of
It should
energy analysis processes are
and, although errors cannot be assigned, the
above numbers represent only approximate
equilibrium
4. DISCUSSION
energies.
The following
annealing stages have been observed
after electron irradiation. (a) There are several annealing perature range of 20-100°K. nent stages at 40,65
stages in the tem-
The three most promi-
and 90°K have energies of about
0.03, 0.05 and 0.1 eV, respectively. (b) A stage is observed which
has an activation
in the range of lOO-150°K energy
at its midpoint
(c) A long continues curve.
annealing
stage begins
at 150°K
The activation
energy of this stage varies and
is about 0.3 eV at 175°K and 0.4 eV at 200°K. electrical
resistivity
of
this
stage
goes
temperature also results in the resistivity to below the pre-irradiated value.
curve shows
the equilibrium
a of Pig. 1.
The curve following
values
of
value
following
in region
The following
the irradiation shows
after quenching.
as given previously
and
until it begins to rise along the equilibrium
Annealing
1.35 x 10la electrons/cm2.
of
about 0.15 eV and near its end of 0.25 eV.
chronal anneal of ordered p-brass following irradiation
resistivity,
the It is
order.
near 78’K quenched-in
curve ;
clear that the irradiated specimen has now attained a condit,ion of equilibrium
pre-irradiated
The broken
It
for the irradiated
Figure 5 shows a comparison of two experiments. The solid curve with data points represents an isoto a dose of
below
to 30 min.
arises because of different samples.
stage.
to be 0.03, 0.15 and 0.1 eV,
100 and 250°K
specimen
displacement
times increased
and determining
energies of the three stages at 40, 65 Several cross-cuts
between
The activa-
steps were estimated
annealing
and 90°K are estimated respectively.
for pulse
change for several temperatures
with annealing
is seen that
of 10 and 40 min, respectively.
normalizing
stage
doses.
were isochronally
tion energies of the decay
tempera-
in
this
irradiation
temperature at liquid
The
below
the
range. nitrogen
decreasing
annealing stages have been observed
_%CTA
308
NETALLIJRGICA,
VOL.
TEMPERATURE, - 100 0
-
19,
1971
OC 100
2.5
8 X
Q?
i.
Q!? 0
-2.5
200
100
400
300
TEMPERATURE,
OK
FIG. 5. c-10 min isochrone following irradiation at 78°K. - isochrone of irradiated sample after it was annealed to 100°C. - - - equilibrium resistivity of unirradiated sample.
(d) An annealing
stage occurs
between
-50
and
being
annihilated
in a non-correlated
manner,
or
it could be equivalent
to stage II in metals.
that this annealing curve would extend to even lower
has
be
temperatures
content(12) and does not appear in very pure metals.
about 0°C.
From the shape of the curve, it appears
magnitude
if such quenches of this
stage
could
be made.
increases
with
The
increasing
been
shown
It is therefore interstitials
quench rate. (e) A small increase in resistivity
occurs after O”C,
to
believed
trapped
that comparable
dependent
upon
Stage II impurity
to arise from the release of
at impurities.
trapping
It is reasonable
occurs for the interstitials
and this is followred by a decrease which returns the
in P-brass and stage b above could be assigned to this
resistivity
mechanism.
to the equilibrium
occurs in the range of lo-75°C
curve.
This decrease
after quenching
from
If, however,
stage Ie of metals,
this stage is equivalent
then the equivalent
500°C and in the range of 75-120°C after quenching The activation energy for 435°C or below.
must occur during the long annealing after 150°C.
this stage varies from 0.6 eV for quenches from above
complete,
about
the critical temperature
introduced
by
from
below.
to 0.7 eV for quenches
from
When the quench is from the vicinity of 200°C
the reaction entire stage.
is essentially
first-order
throughout
As the quench temperature
the
is increased
At
150”K,
copper
stages
a and b are apparently
80 per cent of the extra resistivity the
80 per cent
irradiation
has
of the irradiation
annealed.
In
damage
has
annealed at the end of stage Ie at 55”K, and by 180°K only a few per cent of the remaining annealed.
only the latter part of the decay remains first-order.
when
to
of stage II
In contrast,
20 per cent has
in B-brass the resistivity
has
in (a) are remarkably similar to those observed in pure metals. In metals
returned to its original value by 180°K and then goes
these are categorized
B-brass which causes atomic interchange
The stages below 100°K grouped
Ie.
The proposal
as stage I with substages Ia to
by Corbett
stages Ia to Id correspond of interstitials
to vacancies
seems quite reasonable
et uZ.(~~)that the sub-
to the correlated is generally
annealing
accepted.
It
to give the same assignment
Therefore,
above
The stage in (b) between 100 and 150°K can then It could belong to Ie, have either of two assignments. are
150°K a defect moves in and thereby
increases the order. The mechanism of enhanced ordering can be considered either in terms of an interstitial model or vacancy
model.
The possibility
stitials must be considered
to the stages below 100°K in &brass.
the final substage in metals, in which interstitials
below it.
ments
have
been given
of ordering by inter-
since in pure copper argufor interstitial-type
defects
being responsible for all stages below 273°K. Electron irradiations near 78”K, where interstitial migration
KOCZAK,
HERMAN
occurs, revealed no ordering during irradiation. fact an interstitialcy
mechanism
If in
were responsible
for
ordering, it is likely that ordering would have occurred near 78’K.
Further, interstitialcy
the replacement the reverse.
formation
that the formation
energy.
of interstitial
Since it can be shown that the ratio formation
an interstitialcy
energies is similar in &brass,
ordering
mechanism
would
likely, because it would be energetically zinc interstitial
be un-
favorable for a
to replace a copper lattice atom, but Annealing of interstitials should there-
not the reverse.
fore proceed largely on the copper sublattice observed
ordering
Ordering
by
explanation
could
not be attributed
a single vacancy
and the to them.
is a more
plausible
seen by the comparison annealing
of the irradiation
curves,
part of the annealing has an activat’ion
Figs. 2 and 4.
energy of about 0.4 eV.
perature
annealing
after
quenching,
returns
A rough
stage d.
This
10 min at 250°K and
ordering
constant taken as lo-l3 see, E is the activation
energy
Bragg and Williams which maximizes
energy for the quenched-in 0.05 eV, which stage c.
in the
defect of stage d is 0.45 &
is comparable
to the latter
part of
Examination
of the photomicrographs by and Brown (14) shows that the antiphase
Cupschalk domain
boundaries
samples
quenched
are spaced from
above
If these are the vacancy
about critical
4,~ apart
in
temperature.
sinks this distance
corre-
sponds to about 10s jumps so the lower energy of 0.4 eV is probably defect, vacancy,
the better choice.
Since this quenched-in
because of its characteristics, the defect
which
orders
is probably the lattice
the
above
equilib-
with ordering under thermal ordering
energy
is 1.6-1.7 eV(“)
theory,
below
and, from the
the ordering
the ordering,
and
gained,
therefore
step should
energy per
have
A more reasonable
only about 0.2 eV can
a
thermal
about
model
equilibrium
1.4 eV associated
for stage e is that t,he
vacancies are already present in the alloy but trapped with
an energy
Brownu4*18) boundaries
of
about
pointed
out
0.2 eV. that
would act as vacancy
boundary
a vacancy
that
also
dislocation
loops
vacancies
breaks
it would
Cupschalk
antiphase
half the ordered
in an ordered show
region.
These
electronmicrographs
formed
Additional
and
domain
traps since at such a
only
by
the
near such boundaries
of this idea.
of
condensation
of
(14’ in confirmation
vacancies may be attached
to
the first layer with an energy which in a first approximation
reported
from
bond is about 0.03 eV. Thus, in an atomic interchange
thermodynamic
N is usually
The
energy of 0.65 &
energy. (16) The self diffusion
ordering
or
With these numbers the act’ivation
in.
with the re-establish-
for the equilibrium
the critical temperature
In
metals
can be quenched
rethat
energy should be about that for self diffusion less the
and N is the number of jumps to either annihilation well-annealed
that
of course,
small deviations
conditions,
to a trap in which the defect has a lower resistivity. range of 106-108.
mounting
suggest
t’he activation
0.05 eV is not consistent equilibrium
investigators
process, T,, is a
disorder
However,
from the relation
where 7 is the time for the annealing
curve
This implies,
of order from
rium.(r5)
the
is about 2 hr at room
of stage e and the fact that it
equilibrium
some short-range
bonds
(3)
design
first-order kinetics is consistent ment
309
so all quench effects would be annealed.
is occurring.
the energy for migrat,ion in this stage can be estimated
T = NT~ exp (E/kT)
/I-CuZn
experimental
to the
with it.
stage c,
IN
Both the magnitude
and the
estimate may be made of the energy of the low-temstage anneals in approximately
temperature,
ordering
The latter
curve after irradiation
present
can be
which favors the vacancy
DEFECTS
time of a sample for irradiation
be
at the present state of knowledge.
Further evidence quench
It has
energy of the zinc
in f.c.c. Cu,Zn is twice that of the copper
interstitial.d3)
in the
involves
This requires that copper and zinc inter-
stitials have a comparable interstitial
migration
of a copper atom by a zinc atom and
been estimated
POIXT
DAMASK:
AND
would
be the divacancy argument,
binding energy.
By
using the heats of forma-
tion, it can be shown that the energy per bond in ,$ brass is approximately the experimental in copper
the same as in copper.
value for divacancy
is reported
Since
binding energy
as 0.2 eV,(lg) the divacancy
binding energy should be about the same in b-brass. Therefore, t’he interpretation sufficient
vacancies
of stage e is that t,here are
present
in the alloy
which
are
trapped in the vicinity of the antiphase domain boundaries with a binding
energy to traps of 0.1-0.2
eV.
Since about 0.4 eV has been assigned as the vacancy migration
energy,
these vacancies
would be released
when thermal energy of about 0.6 eV is available. They would then be free to migrate and correct the
175°K following irradiation is also presumed to be the An ideal experiment would be the irradiavacancy.
short-range
tion and annealing of the alloy quenched
This would show if the stage cl quench step is a continua-
be created when a sample is heat treated above the critical temperature. Kuper et &.(17) have shown
tion of the stage c annealing or not.
that
from 500°C.
Unfortunately,
The
disorder which had been quenched
extra
above
vacancies
the
critical
in
the
traps
temperature
can
the
in. readily
average
self-diffusion energy of the copper and zinc atoms is only about 0.9 eV. This leads to a vacancy formation energy of 0.45 eV and an atomic fraction of vacancies of 1.5 X 10b3; vacancies bound to traps will form xvith even lower energy. The high mobility of both the free and the trapped vacancies in b-brass offers an explanation of why it is so difficult to quench in any significant amount of disorder. The authors are grateful to Dr. Norman Brown of the University of Pennsylvania for supplying the alloy used in this investigation.
1. A. C. DANASK, J. qqA. Phys. 27, 610 (1955). 2. A. C. DAMASK. in Stztdiavin Radiation Effects on Solids, Vol. II, edited by G. J. DIENES. Gordon and Breach (1967).
3. N. BROWN, Acta Met. ?, 210 (1959). 4. J. S. CLARKand N. BROWN, J. Phys. Chem. Solids 19, 291 (1961). 5. J. K. HARKCOMand 111.C. MARTIN,J. appl. Phys. 39,399 11968). 6. %L R.’ EGGLESTONand E‘. E. Bowofax. .7. appl. Phya. 24, 299 (1953). 7. 11. W. Ii. HONEYC~I~XBE and W. Boas, Amt. -7. scient. Res. Al, 192 (1948). 8. A. .SOSI~ and’ IF. H. NEELY, Rev. Gent. Iastrum. 32, 922 (1961). 9. F. SEITZ and J. KOEHLER, in So&l State Physics, Vol. 2, edited bv F. SEITZ and D. TURNRIILL. Academic Press (19:56). 10. CT.W. ISELER, H. I. DAU~SON.A. S. hfEH?iER and J. MI. KATTFF~LIAX, Ph.ys. Rev. 146,468 (196%). 11. .J. W. CORBETT,R. B. SMITH and R. M. WALKER, Phys. Rev. 114, 1452 (1959). 12. D. G MARTIN, Phil. Xq. 6, 839 (1961). 13. A. C. I~AMASK,AC&Z&fet. 13, 1104 (1965). 14. 8. G. CIXSCHALKand N. BROWN, Acta Met. 15,847 (1967). 15. S. IIDA, J. phys. S’oc. Japan. 10, (1955). 16. G. H. VINEYARD, P&a. Rev. 102, 981 (1956). 17. A. B. ICI-PER, D. LAZARUS, 5. 2%. MANICING and C. T. T~XIZUKA, Phys. Rev. 104, 1536 (1956). and X. BROWN, Acta Met. 16,657 (1968). 18. S. G. CUPSCHALK 19. A. SEEGER,V. GEROLD,KIN Poxa C~IIKand M. Rij~t~, Phys. Lett. 5, 107 (1963).
PRODUCTION
AND
ANNEALING
M. J. KOCZAKllt,
OF POINT
H. HERMAN1
and
DEFECTS
IN /M~.&I*
A. C. DAMASK8
Ordered fl.brass was irradiated with 1.5 MeV electrons at 20°K and then annealed. Three prominent decay stages ocour at 40, 65 and 90°K with respective energies of about 0.03, 0.05 and 0.1 eV. These stages are similar to those which occur in pure metals and are therefore believed to arise from correlated interstitial-vacancy recombination. A stage occurs in the range of lOO-150°K which is believed to arise from either nncorrelated interstitial migration or from the release of trapped interstitials. A long decay stage begins at 159°K and continues until it joins the thermal equilibrium curve above room temperature. It has a varying activat,ion energy w&h about, 0.4 eV at 200°K. The annealing goes well below the pre-irradiat,ed value at 180°K and a similar effect is observed after irradiation at 78°K. This enhanced ordering is assigned to the vacancy. After quenching an unirradiat,ed sample to - 14”C, transferring quickly to liquid nitrogen and then annealing, two stages are seen; one from -50 to about 0°C with an activation energy of 0.45 & 0.05 eV and one in the range of IO-120°C with an activation energy ranging from 0.6 to 0.7 aV, the location of the latter stage depending upon the quench temperature. The lower temperature stage is assigned to the vacancy and the upper stage to vacancies trapped at antiphase domain boundaries. On the basis of these assignments it is understandable t)hat the high vacancy mobilit)y inhibits the retention of quenched-in disorder in this system. PRODUCTION
ET
RECUIT
DES
DEFAUTS
PONCTUELS
DANS
CuZn /?
Du laiton /j’ordonne a et& irradii? aux Plectrons de I,5 MeV a 20°K puis recuit. Trois stades de revenu pr~dominants se produisent a 40,65 et 90°K avec des energies respectives de 0,03,0,05 et. 0,l eV environ. Ces stades sont analogues a ceus qui apparaissent dam les m&aux purs et les auteurs supposent par consequent qu’ils sent dtis a la recombinaison co&lee interstitiel-aoune. Un stade se produit egalement dans le domaine 100-150”K, et il semble Btre dQ ou bien a la migration non eorrelee de I’intcrstitiel, ou bien a la liberation des int,erstitiels pieges. Un long stade de revenu commence a 150°K et continue jusqu’a ce qu’il rejoigne la courbe d’equilibre thermique au-dessus de la temperature ambianta. I1 a une Bnergie d’activation variable, avec 0,4 eV environ it 200°K. A 18O”K, le recuit conduit a des valeurs bien inferieures aux valeurs correspondantes avant irradiation, et un cffet analogue est observe apres irradia. tion a 78°K. Cette mise en ordre est attribueo aux lacunes. Apres trempe d’un echantillon non irradie jusqu’a - 14OC,transfert rapide dans l’azote liquide, puis recuit, deux stades apparaissent; l’un a partir de - 50°C jusqu’it environ 0°C avec une Bnergie d’aetivation de 0,45 f 0,05 eV, et l’autre dans le domaine de 10°C it 12O’C avec une (inergie d’act,ivat.ion sit&e ent,re 0.6 et 0,7 eV, la situation de ce dornier stade d~pendant de la temperature de trempe. Le premier stade cst attribue aux lacunes et le deuxieme aux lacunes piegees RUX front,ieres des domaines antiphases. I1 est done logiquc que la forte mobilite des latunes emp&he de retenir le desordre c&h par trempe dam cc systeme. DIE
ERZEUGUSG
UND
DAS
AUSHEILEN
VON
PUNKTFEHLERN
IN
1.CuZn
Geordnetes @-Mussing wurde mit 1,5 MeV-Elektronen bei 20°K bestrahlt und dann angelassen. Drei ausgepragte Erholungsstufen treten bei 40,65 und 90°K auf. Die zugehorigen Aktivierungsenergien sind etwa 0,03, 0,05 und 0,l eV. Diese Stufen sind den in reinen Metallen beobachteten Stufen ahnlich und es wird deshalb angenommen, da6 sie die Folge von korrelierten Zwischengitteratom-LeerstellenRekombinationon sind. Eine Stufe zwischen 100 und 150°K wird entweder der freien Wanderung dcr Zwisehengitteratame oder der Wanderung van Zwischengitt,eratomen, die sieh in diesem Tamperaturbereich van ~aft.stellen losrei0en, zugesohrieben. Eine breite Ausheilstufe beginnt bei 150°K und mtindet in die thermische Gleichgewichtskurve oberhalb Raumtemperatur. Ihre Aktivierungsenergie variiert und ist bei 200°K etwa 0,4 eV. Der Widerstand liegt weit unterhalb des Wertes dar unbestrahlten Probe bei 180°K und naeh 78”K-Bestrahlung wird ein ahnlichor Effekt beobachtet. Diese erhohte Ordnung wird der Leerstelle zugeschrieben. Eine unbestrehlte Probe wurde auf - 14OC abgesohreckt, schnell auf Stickstofftemperatur gebracht und dann angelassen. Zwei Stufen wurden beobaohtet: eine zwischen - 56°C und 0°C mit eincr Aktiviorungsenergie von 0,45 & 0,05 eV und eine zweite zwisohen 10 und 120°C mit einer Aktivierungsenergie von 0,6 bis 0,7 eV; die Lage der zweiten Stufe hangt von der Abschrecktemperatur ab. Die Stufe zwischen -50 und 0°C wird der Leerstelle zugeschrioben und die andere Stufe den an Antiphasengrenzen festgehaltencn Leerstellen. Aufgrund dieser Zuordnungen ist es verst~ndlieh, da13wegen der hohen Leerstellenbewegliehkeit die dureh Abschrecken erzeugt,e Unordnung in diesem System nicht erhahen bleibt..
1. INTRODUCTION
* Received August 13, 1979. Work supported by the U.S. Atomic Energy Commission and the National Science Foundation GK 1085 at the University of Pen~ylvania and GK 10009 at Stony Brook. The work was part of the requirements for the Ph.D. of M. J. K. at the University of Pennsylvania. t University of Pennsylvania, Philadelphia, Pa. and Brookhaven National Laboratory, Upton, N.Y. $ State University of New York at Stony Brook, N.Y. 9 Queens College of the City of New York, Flushing, N.Y. and Brookhaven National Laboratory, Upton, N.Y. Ij Now at: Department of Materials Science, State University of New York, Stony Brook, N.Y. ACTA
METALLURGI~A,
VOL.
19, APRIL
If the defect assists in diffusion and moves in an alloy which has not yet attained an equilibrium degree of order, then the defect may enhance the establishment of order. It has been shown by several investigators that such excess defects can yield greater degrees of order than are achievable by thermal means alone.c1*2) In the present study the annealing of point defects and their effect on the order in p-brass is reported. The ordered microstructure of &brass has been well characterized and the &--Cl crystal structure of the ordered alloy is a particularly interesting framework in reactions.
Defects in excess of the thermal equilibrium concentration are able to modify various solid state
1971
303
XCTA
304
which to study point defects. been examined
Although
by quenching,(3-5)
deformation,(‘)
METALL17RGICA,
@-brass has
irradiation@)
the point defect formation
and
VOL.
19,
1971
do not arise from changes in the chemical composition since all initial values were reproducible. For quenching,
and migra-
the specimens were gravity-dropped
The
size
(wire
diameter
=
into
not been completely
0.015 in.) provided for a fast quench while eliminating
understood.
a comparison
of annealing
and
irradiation
electron
ident’ification of vacancies
In the present’ work
following is made
of the temperature and interstitials
both quenching and
a tentative
range of migration
is given.
2. EXPERIMENTAL
The as-received
p-brass at.%
rod.
The electron
wt. % Zn) was in the The major
by spectrographic
analysis
were Mg, Fe
range from 47 to 50
in structure,
structure
and has an ordered
below the critical temperature,
460°C. This limited compositional the brittle nature
range, coupled with
of the alloy
and high zinc vapor
pressure, presents serious difficulties tion.
impurities
by weight.
Zn, is b.c.c.
in wire fabrica-
It was therefore necessary to grow single crystals
in order to facilitate Single
reduction
crystals
Bridgman
were
technique
operations.
grown
thermal
stresses.
were immediately
energy
irradiations
After
stored
a modified
procedure.
at
from
0.3
provides
to
3.0 MeV
The beam current was regulated 10-6-10-3
with
better than 6 KeV throughout
cent of the t’otal current,
National
electrons of an voltage
this range.
to better than 1 per
with a current
range
MeV for all irradiations, 1 pA/cm2.
density
of
At this current density the temperature
with a current
of
the samples during irradiation
did not exceed 20°K.
To assure a uniform electron dose along the electrical gage length, the electron beam was scanned vertically and horizontally.
The beam current was monitored Faraday
cup by an Elcor
current
used for the electron
irradia-
integrator.
The
The liquid
cryostat,
tions, was built by the Janis Research Company.
then encapsulated
cryostat
lo-”
torr.
through
tubes at a pressure
The rods were slowly
a temperature
gradient,
single crystal and bicrystal
drawn
(~1
yielding
of
in./hr)
6 in. long
rods.
No phase separation was detected by metallography or X-ray
studies and chemical
analysis
the starting materials.
from
Wires of 0.015 and 0.006 in.
diameter were drawn for the quenching tron irradiation
experiments,
and the elec-
respectively.
or liquid
nitrogen
irradiation employed portions
experiments,
liquid studies
nitrogen
A dummy
are less than the
size of the data points given in the figures. Annealing of small diameter wires of p-brass elevated However,
temperatures
was
The errors associated
measurements
by conduction
reported here
300”K,
with
-&O.Ol”K.
Cali-
sensors monitored and annealing.
Sosin and Neely(@
in which rods.
sapphire
metallizing
the sample
holder
In order to facilitate
inthe
samples to the sapphire, a
process
Corporation.
thermal contact
were cooled
in a manner similar to the design of
corporates
This
was performed process
provided
by
the good
between t’he sapphire and the speci-
men. 3. RESULTS (a)
Annealing following quenching 1. Isochronul annealing.
A plot of the as-quenched
resistivity (measured in liquid nitrogen) is shown in Fig. 1 where, for later discussion, the curve is divided into three regions. Region a shows an increase in resistivity
at
may result in a loss of zinc.
the changes in the resistivity
and platinum
and of
during the irradiations
The liquid
and for some
experiments.
specimen was always employed.
germanium
5
control
The wire specimens, 0.006 in. diameter,
Advac
temperatures. while
of the irradiation
with the resistivity
brated
between
temperature
the temperature
were used only for the electron
for the quenching
temperatures
automatic
The
so that samples can anneal at
soldering of the resistivity
A standard four-probe potentiometric circuit was employed with measurements carried out at liquid helium measurements
was designed
MO-Mn
(b) Electrical resistivity measurements
helium
given
of the wires
indicated no significant change in the composition
of
A. The electron energy energy used was 1.5
as-received bars were swaged to & in. diameter rods and in quartz
in
out at the
Brookhaven
This accelerator
range
regulation
were carried
Accelerator
from an isolated
using
in the following
from
liquid nitrogen.
Laborat,ory.
has a compositional
Cs-Cl-type
the samples
PROCEDURE
alloy (Cu-48.4
and Si, all 0.001%
arising
quenching
Dynamitron
of 4 in. diameter
determined
problems
(c) Electron irradiation
(a) Alloy fabrication form
water.
specimen
tion energies, as well as their relation to ordering, have
from
quench
where a maximum 2OO”C, the resistivity 3OO”C, region
temperatures
up to 2OO”C,
of 5 per cent is reached.
Above
drops off to about 2 per cent at
b, and
then
displays
a continuous
8
QUENCH TEMPERATURE, FIG. 1. Resistivity
*C
vs. quench temperature.
increase up to the highest temperature of 5OO”C, region c. This behavior is similar to that reported by Clark and Brown(a) and Harkcom and Martin.@) Annealing was studied following quenching from both above and below the critical temperature (460%) Figure 2 shows isochronal recovery curves after quenching from 500,435 and 400°C. A main recovery stage is observed between 20 and 75°C for the samples quenched from 5OO”C, and between 50 and 120°C for those quenched from below the critical temperature. The rate of recovery is seen to increase with increased quench temperature. In addition to the main stage, a small recovery stage is observed for all of the isochronal results between -50 and O”C, followed by a shallow minimum. It appears that the range of this early stage is independent of quench temperature in that it terminates around -10°C for all quenched samples. Comparison between water and brine quenching is also shown in Fig. 2 where it is seen that the faster brine quench yields a higher value of quenched-in resistivity, 14 vs. 11 per cent for the quench into water. The later increase in resistivity, which occurs beyond the main annealing stage in Fig. 2, can be identified with region a of Fig. 1. All four of the annealing curves merge at temperatures above 125’C, and it can therefore be concluded that equilibrium order is rapidIy achieved above 125°C. 2. I~o~~~~~l ~~~~~ng. Isothermal anne&lings were performed to determine the activation energy
and order of reaction of the major annealing stage shown in Fig. 2. Sets of these data were taken for different quench temperatures. For all quench temperatures the decay in the temperature range of 20120°C yielded an activation energy of 0.6 eV for quenches from above the critical temperature to 0.7 eV for quenches from below in agreement with the analyses of this decay by other techniques.(ss4) The order of the reaction was obtained in the following manner. It is assumed that the decay is a singlyactivated process which can be described by
where K, is the rate constant, y is the order-of-reaction and E is the activation energy for the process. This equation may be written as In
[
dnY-
- ---t--
- y In n + In [K, exp (--E/kT)]
(2)
where the expression In [K, exp (-E/l&“)] is constant for a given isothermal curve, and therefore the slope of a plot of In n vs. In [(-t&/d In t)/t] gives a value for the order-of-reaction, y. Isothermal annealing at 75% following quenching from 500°C is shown by the lower curve of Fig. 3. In this figure the normalized resistivity, which is plot,ted as the ordinate, is identified with n. It is seen that only the latter 40 per cent of the reaction is linear with an order of approximately unity. Isothermal annealing at 30°C following quenching
306
from
temperatures
between
yield
an activation
energy
100 and
d5O”C also An order-of-reaction was also determined, an example of which is shown by the upper curve of Fig. 3 for annealing at, 20°C after quenching from 175%. It is seen that, the entire process fits a straight line, yielding an order of a~proxin~ately m&y. of 0.65 -& 0.05 eV.
(b) Electron irradiation 1. Production of defects. An ordered condition was achieved prior to electron irradiation by amiealing at 500°C for 15 min followed by annealing at, 200°C for 15 min and then furnace cooling. The resistivity ratio ~~~*o=~~*.~o~of t,he wire was typically seven. Irradiatio~~swere carried out with an electron energy of 1.5 MeV, which is capable of displacing both copper and zinc atoms.‘g) The change of resistivity with dose for 1.5 MeV electrons near 20°K is 8.8 X 10e2’ near 78”K, it is 5.5 x 10e2’ 0cm/electrons/cm2; Rcm[electrons/cm 2. These values are comparable to the damage rates of pure metals, e.g. for copper near 10°K. the rate is 9 x lo-*7 ~cm~ele~trons~cmz for 1.5 MeV electrons.(iO) 2. Amealing spectrum following electron irradiation. Isochronal recovery in 10 min pulses following irradiation at 20°K to dose of 4.5 x 1017 electrons/ cm2 is shown in Fig. 4. Liquid helium was used as the measuring temperature up to liquid nitrogen t,emperature, then liquid nitrogen was used. The amiealing curve shows a number of substages below 100°K followed by a stage which begins at 100
-I -4
TEMPERATURE OC FIG.2. 10 min isochronal annealing after quenohing. C-guench from 500 to 25°C. n-quench from 500 to 14%. n-quench from 435 to 25°C. C-quench from 400 to 25°C.
0. IO _
O.Old 0.001
I
I
I
I
I
I
IllIll
0.10 - (dnldlntlt
Fro. 3. o-isothermal
IllIll
0.01
1.0
1
annealing at 20°C after quench from 1’75°C. A-isothermal 75°C rafterquench from 500°C.
annealing at
KOCZAK,
HERMAN
AND DAMASK:
POIX’T
DEFECTS
I?i
/j-Cu%n
307
80 60 z y
40
0 2
20
8
0 -20
25
50
75
100
125
150
FIG. 4. 40
and ends at 150°K.
This stage,
Above
150°K
defined
stages,
there
is a steady
185°K
the resistivity
value.
This “extra recovery”
not well
in all specimens. decrease
and it is important falls below
200
with
no
to note that at the pre-irradiated
is indicative
of enhanced
225
250
at 20°K
min isochrone aft,er electron irradiation
although
defined in Fig. 4, was reproducible
175 “K
TEMPERATURE,
a broad annealing stage from 120 to about 230°K
in
which the resistivity
again anneals to below the pre-
irradiated
value
resist,ivity
irradiation
at 20”K, Fig. 4. At 24O”K, the resistivity
increases 350°K.
of
as it did
following
and merges with the equilibrium Following
curve at
a 10 min isochronal pulse at 363’K,
ordering and was also seen in annealing curves follow-
the specimen was then annealed at 315°K and below.
ing irradiation
The solid curve without data points shows the values
at liquid
nitrogen
temperature.
The
point at which the plot crosses the zero of the recovery
of resistivity
axis was found
315”K,
to shift to lower annealing
tures with higher irradiation Two specimens electrons/cm2 times
irradiated
to a dose of 4.5 x 101’ annealed
both
the temperature The activation
curves
shift for a given
by
ing stage between 100
annealing
and
150°K
taken for the annealindicate has
an
that the activation
energy of about 0.15 eV near its midpoint
at 125°K
and about 0.25 eV near the end at 150°K.
The stage
which
energy
begins at 150°K
has an activation
about 0.3 eV at 175’K and 0.4 eV at 200°K. be noted that this type of activation is very crude when several overlapping involved
the resistivity
now
follows
the
plot
of
It should
energy analysis processes are
and, although errors cannot be assigned, the
above numbers represent only approximate
equilibrium
4. DISCUSSION
energies.
The following
annealing stages have been observed
after electron irradiation. (a) There are several annealing perature range of 20-100°K. nent stages at 40,65
stages in the tem-
The three most promi-
and 90°K have energies of about
0.03, 0.05 and 0.1 eV, respectively. (b) A stage is observed which
has an activation
in the range of lOO-150°K energy
at its midpoint
(c) A long continues curve.
annealing
stage begins
at 150°K
The activation
energy of this stage varies and
is about 0.3 eV at 175°K and 0.4 eV at 200°K. electrical
resistivity
of
this
stage
goes
temperature also results in the resistivity to below the pre-irradiated value.
curve shows
the equilibrium
a of Pig. 1.
The curve following
values
of
value
following
in region
The following
the irradiation shows
after quenching.
as given previously
and
until it begins to rise along the equilibrium
Annealing
1.35 x 10la electrons/cm2.
of
about 0.15 eV and near its end of 0.25 eV.
chronal anneal of ordered p-brass following irradiation
resistivity,
the It is
order.
near 78’K quenched-in
curve ;
clear that the irradiated specimen has now attained a condit,ion of equilibrium
pre-irradiated
The broken
It
for the irradiated
Figure 5 shows a comparison of two experiments. The solid curve with data points represents an isoto a dose of
below
to 30 min.
arises because of different samples.
stage.
to be 0.03, 0.15 and 0.1 eV,
100 and 250°K
specimen
displacement
times increased
and determining
energies of the three stages at 40, 65 Several cross-cuts
between
The activa-
steps were estimated
annealing
and 90°K are estimated respectively.
for pulse
change for several temperatures
with annealing
is seen that
of 10 and 40 min, respectively.
normalizing
stage
doses.
were isochronally
tion energies of the decay
tempera-
in
this
irradiation
temperature at liquid
The
below
the
range. nitrogen
decreasing
annealing stages have been observed
_%CTA
308
NETALLIJRGICA,
VOL.
TEMPERATURE, - 100 0
-
19,
1971
OC 100
2.5
8 X
Q?
i.
Q!? 0
-2.5
200
100
400
300
TEMPERATURE,
OK
FIG. 5. c-10 min isochrone following irradiation at 78°K. - isochrone of irradiated sample after it was annealed to 100°C. - - - equilibrium resistivity of unirradiated sample.
(d) An annealing
stage occurs
between
-50
and
being
annihilated
in a non-correlated
manner,
or
it could be equivalent
to stage II in metals.
that this annealing curve would extend to even lower
has
be
temperatures
content(12) and does not appear in very pure metals.
about 0°C.
From the shape of the curve, it appears
magnitude
if such quenches of this
stage
could
be made.
increases
with
The
increasing
been
shown
It is therefore interstitials
quench rate. (e) A small increase in resistivity
occurs after O”C,
to
believed
trapped
that comparable
dependent
upon
Stage II impurity
to arise from the release of
at impurities.
trapping
It is reasonable
occurs for the interstitials
and this is followred by a decrease which returns the
in P-brass and stage b above could be assigned to this
resistivity
mechanism.
to the equilibrium
occurs in the range of lo-75°C
curve.
This decrease
after quenching
from
If, however,
stage Ie of metals,
this stage is equivalent
then the equivalent
500°C and in the range of 75-120°C after quenching The activation energy for 435°C or below.
must occur during the long annealing after 150°C.
this stage varies from 0.6 eV for quenches from above
complete,
about
the critical temperature
introduced
by
from
below.
to 0.7 eV for quenches
from
When the quench is from the vicinity of 200°C
the reaction entire stage.
is essentially
first-order
throughout
As the quench temperature
the
is increased
At
150”K,
copper
stages
a and b are apparently
80 per cent of the extra resistivity the
80 per cent
irradiation
has
of the irradiation
annealed.
In
damage
has
annealed at the end of stage Ie at 55”K, and by 180°K only a few per cent of the remaining annealed.
only the latter part of the decay remains first-order.
when
to
of stage II
In contrast,
20 per cent has
in B-brass the resistivity
has
in (a) are remarkably similar to those observed in pure metals. In metals
returned to its original value by 180°K and then goes
these are categorized
B-brass which causes atomic interchange
The stages below 100°K grouped
Ie.
The proposal
as stage I with substages Ia to
by Corbett
stages Ia to Id correspond of interstitials
to vacancies
seems quite reasonable
et uZ.(~~)that the sub-
to the correlated is generally
annealing
accepted.
It
to give the same assignment
Therefore,
above
The stage in (b) between 100 and 150°K can then It could belong to Ie, have either of two assignments. are
150°K a defect moves in and thereby
increases the order. The mechanism of enhanced ordering can be considered either in terms of an interstitial model or vacancy
model.
The possibility
stitials must be considered
to the stages below 100°K in &brass.
the final substage in metals, in which interstitials
below it.
ments
have
been given
of ordering by inter-
since in pure copper argufor interstitial-type
defects
being responsible for all stages below 273°K. Electron irradiations near 78”K, where interstitial migration
KOCZAK,
HERMAN
occurs, revealed no ordering during irradiation. fact an interstitialcy
mechanism
If in
were responsible
for
ordering, it is likely that ordering would have occurred near 78’K.
Further, interstitialcy
the replacement the reverse.
formation
that the formation
energy.
of interstitial
Since it can be shown that the ratio formation
an interstitialcy
energies is similar in &brass,
ordering
mechanism
would
likely, because it would be energetically zinc interstitial
be un-
favorable for a
to replace a copper lattice atom, but Annealing of interstitials should there-
not the reverse.
fore proceed largely on the copper sublattice observed
ordering
Ordering
by
explanation
could
not be attributed
a single vacancy
and the to them.
is a more
plausible
seen by the comparison annealing
of the irradiation
curves,
part of the annealing has an activat’ion
Figs. 2 and 4.
energy of about 0.4 eV.
perature
annealing
after
quenching,
returns
A rough
stage d.
This
10 min at 250°K and
ordering
constant taken as lo-l3 see, E is the activation
energy
Bragg and Williams which maximizes
energy for the quenched-in 0.05 eV, which stage c.
in the
defect of stage d is 0.45 &
is comparable
to the latter
part of
Examination
of the photomicrographs by and Brown (14) shows that the antiphase
Cupschalk domain
boundaries
samples
quenched
are spaced from
above
If these are the vacancy
about critical
4,~ apart
in
temperature.
sinks this distance
corre-
sponds to about 10s jumps so the lower energy of 0.4 eV is probably defect, vacancy,
the better choice.
Since this quenched-in
because of its characteristics, the defect
which
orders
is probably the lattice
the
above
equilib-
with ordering under thermal ordering
energy
is 1.6-1.7 eV(“)
theory,
below
and, from the
the ordering
the ordering,
and
gained,
therefore
step should
energy per
have
A more reasonable
only about 0.2 eV can
a
thermal
about
model
equilibrium
1.4 eV associated
for stage e is that t,he
vacancies are already present in the alloy but trapped with
an energy
Brownu4*18) boundaries
of
about
pointed
out
0.2 eV. that
would act as vacancy
boundary
a vacancy
that
also
dislocation
loops
vacancies
breaks
it would
Cupschalk
antiphase
half the ordered
in an ordered show
region.
These
electronmicrographs
formed
Additional
and
domain
traps since at such a
only
by
the
near such boundaries
of this idea.
of
condensation
of
(14’ in confirmation
vacancies may be attached
to
the first layer with an energy which in a first approximation
reported
from
bond is about 0.03 eV. Thus, in an atomic interchange
thermodynamic
N is usually
The
energy of 0.65 &
energy. (16) The self diffusion
ordering
or
With these numbers the act’ivation
in.
with the re-establish-
for the equilibrium
the critical temperature
In
metals
can be quenched
rethat
energy should be about that for self diffusion less the
and N is the number of jumps to either annihilation well-annealed
that
of course,
small deviations
conditions,
to a trap in which the defect has a lower resistivity. range of 106-108.
mounting
suggest
t’he activation
0.05 eV is not consistent equilibrium
investigators
process, T,, is a
disorder
However,
from the relation
where 7 is the time for the annealing
curve
This implies,
of order from
rium.(r5)
the
is about 2 hr at room
of stage e and the fact that it
equilibrium
some short-range
bonds
(3)
design
first-order kinetics is consistent ment
309
so all quench effects would be annealed.
is occurring.
the energy for migrat,ion in this stage can be estimated
T = NT~ exp (E/kT)
/I-CuZn
experimental
to the
with it.
stage c,
IN
Both the magnitude
and the
estimate may be made of the energy of the low-temstage anneals in approximately
temperature,
ordering
The latter
curve after irradiation
present
can be
which favors the vacancy
DEFECTS
time of a sample for irradiation
be
at the present state of knowledge.
Further evidence quench
It has
energy of the zinc
in f.c.c. Cu,Zn is twice that of the copper
interstitial.d3)
in the
involves
This requires that copper and zinc inter-
stitials have a comparable interstitial
migration
of a copper atom by a zinc atom and
been estimated
POIXT
DAMASK:
AND
would
be the divacancy argument,
binding energy.
By
using the heats of forma-
tion, it can be shown that the energy per bond in ,$ brass is approximately the experimental in copper
the same as in copper.
value for divacancy
is reported
Since
binding energy
as 0.2 eV,(lg) the divacancy
binding energy should be about the same in b-brass. Therefore, t’he interpretation sufficient
vacancies
of stage e is that t,here are
present
in the alloy
which
are
trapped in the vicinity of the antiphase domain boundaries with a binding
energy to traps of 0.1-0.2
eV.
Since about 0.4 eV has been assigned as the vacancy migration
energy,
these vacancies
would be released
when thermal energy of about 0.6 eV is available. They would then be free to migrate and correct the
175°K following irradiation is also presumed to be the An ideal experiment would be the irradiavacancy.
short-range
tion and annealing of the alloy quenched
This would show if the stage cl quench step is a continua-
be created when a sample is heat treated above the critical temperature. Kuper et &.(17) have shown
tion of the stage c annealing or not.
that
from 500°C.
Unfortunately,
The
disorder which had been quenched
extra
above
vacancies
the
critical
in
the
traps
temperature
can
the
in. readily
average
self-diffusion energy of the copper and zinc atoms is only about 0.9 eV. This leads to a vacancy formation energy of 0.45 eV and an atomic fraction of vacancies of 1.5 X 10b3; vacancies bound to traps will form xvith even lower energy. The high mobility of both the free and the trapped vacancies in b-brass offers an explanation of why it is so difficult to quench in any significant amount of disorder. The authors are grateful to Dr. Norman Brown of the University of Pennsylvania for supplying the alloy used in this investigation.
1. A. C. DANASK, J. qqA. Phys. 27, 610 (1955). 2. A. C. DAMASK. in Stztdiavin Radiation Effects on Solids, Vol. II, edited by G. J. DIENES. Gordon and Breach (1967).
3. N. BROWN, Acta Met. ?, 210 (1959). 4. J. S. CLARKand N. BROWN, J. Phys. Chem. Solids 19, 291 (1961). 5. J. K. HARKCOMand 111.C. MARTIN,J. appl. Phys. 39,399 11968). 6. %L R.’ EGGLESTONand E‘. E. Bowofax. .7. appl. Phya. 24, 299 (1953). 7. 11. W. Ii. HONEYC~I~XBE and W. Boas, Amt. -7. scient. Res. Al, 192 (1948). 8. A. .SOSI~ and’ IF. H. NEELY, Rev. Gent. Iastrum. 32, 922 (1961). 9. F. SEITZ and J. KOEHLER, in So&l State Physics, Vol. 2, edited bv F. SEITZ and D. TURNRIILL. Academic Press (19:56). 10. CT.W. ISELER, H. I. DAU~SON.A. S. hfEH?iER and J. MI. KATTFF~LIAX, Ph.ys. Rev. 146,468 (196%). 11. .J. W. CORBETT,R. B. SMITH and R. M. WALKER, Phys. Rev. 114, 1452 (1959). 12. D. G MARTIN, Phil. Xq. 6, 839 (1961). 13. A. C. I~AMASK,AC&Z&fet. 13, 1104 (1965). 14. 8. G. CIXSCHALKand N. BROWN, Acta Met. 15,847 (1967). 15. S. IIDA, J. phys. S’oc. Japan. 10, (1955). 16. G. H. VINEYARD, P&a. Rev. 102, 981 (1956). 17. A. B. ICI-PER, D. LAZARUS, 5. 2%. MANICING and C. T. T~XIZUKA, Phys. Rev. 104, 1536 (1956). and X. BROWN, Acta Met. 16,657 (1968). 18. S. G. CUPSCHALK 19. A. SEEGER,V. GEROLD,KIN Poxa C~IIKand M. Rij~t~, Phys. Lett. 5, 107 (1963).