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Interdiffusion in dilute aluminium-copper solid solutions
INTERDIFFUSION
IN DILUTE
ALUMINIUM-COPPER J. B.
SOLID
SOLUTIONSt
MURPHY:
A study has been made of the interdiffusion of copper from an tc solid solution into aluminium with special attention to minimizing experimental and computational errors. The form of the concentrationdistance curves obtained showed that interdiffusion was independent of concentration within the range o-o.5
wt. y0 copper.
The activation
energy calculated
and the frequency factor so
from the slope of a log, 5 versus T-i plot was 31.12 5 1.54 kcal/g j-o.43 was 0.29 _. l7 cm*/sec. It is concluded that the data obtained are closely
related to the tracer diffusion of copper in aluminium. INTERDIFFUSION DANS UNE SOLUTION SOLIDE D’ALUMINIUM ET DE CUIVRE
DILUEE
L’auteur a Btudie, avec des precautions speciales pour minimiser les erreurs experimentales et les erreurs de mesure, l’interdiffusion du cuivre a partir d’une solution solide cc-aluminium-cuivre dans l’aluminium. La forme de la courbe dormant la concentration en fonction de la distance montre que l’interdiffusion est independante de la concentration dans un domaine variant de 0 a 0.5% en poids de cuivre. L’energie I,54 Kcal/gr
d’activation
calculee a partir de la pente de la droite log, 0” en fonction de T-1 est de 31,12 +0,43 est &gal a 0,29 _o,17 cm2/sec.
:t
et le facteur de frequence 0,
L’auteur conclut l’aluminium.
que ces valeurs
INTERDIFFUSION
BE1
sont intimement
VERDUNNTEN
liees it la diffusion
FESTEN
de traceurs
de cuivre
dans
BLUMIKIUI\I-KUPFER-LOSUNGEN
Die Interdiffusion van Kupfer aus einer festen cc-L&sung in Aluminium wurde untersucht; dabei wurde besonderer Wert darauf gelegt, experimentelle und Berechnungsfehler miiglichst klein zu halten. Die Form der Kurven Konzentration gegen Entfernung zeigte, daR die Interdiffusion im Bereich O-O.5 Gew. yc Kupfer unabhiingig von der Konzentration war. Die Aktivierungsenergie,
wie man sie aus der Steigung der Kurve log, 5 gegen T-’ +0.43 & 1.54 kcal/g und der Frequenzfaktor o”, war 0.29 _. l7 cm2/sec. Diese Werte
31.12
die Diffusion von Kupfer
als Spurenelement
in Aluminium
INTRODUCTION
Interdiffusion been studied’1-5) between reliable
at initial
copper
2 and 33 per cent. appears
spectrographic
has previously
concentrations
analysis
of slices through
who,
of 31 .I kcal/g 0.177 cm2/sec
atom
for the activation
for frequency
factor
from a least squares analysis There was no indication rate with concentration. have suggested
6,
by
interference solutions
and
of any variation
of diffusion
tive
second
was undertaken
to obtain
to
variations
of the data cannot
Accordsolid
consistent
to ensure accurate results.
work
ccaluminium-coppers
has
under controlled
be considered
data is extremely
in experimental
and
sensi-
technique,
and
were taken in this work Diffusion couples prepared
by roll bonding super-purity
on the diffusion of solute elements in aluminium(@
phase.
TECHNIQUE
of diffusion
therefore special precautions
rates do, in fact,
a recent review of the previous
shown that much
by precipitated
The reliability
vary with copper concentration. Furthermore,
greater
limit may have led to some
EXPERIMENTAL
results).
Later workers(3*4) however,
that the diffusion
the use of core concentrations
reliable data.
(recalculated
of Beerwald’s
due to the
ingly, a study of diffusion in aluminium-copper
values
energy
In addition,
than the solid solubility
a clamped
couple with a 2 per cent copper core, obtained
was liable to be inaccurate
difficulty in measuring tangents at such concentrations.
of
Of this work, the most
to be that of Beerwaldc2)
sind denen fiir
sehr iihnlich.
concentrations
of copper in aluminium
war
berechnet,
aluminium cladding to an
solid solution core were annealed
atmosphere
and temperature.
The
reliable, owing to the insensitive analysis methods used. Results illustrating compositional dependence
couples were then sliced parallel to the interface and th e slices analysed to determine concentrationdistance curves.
of diffusion were inconsistent. Composition-distance curves were analysed mainly graphically by the areatangent method to produce data, which at low
1. Bonding method Rolling because
t
Received August 4, 1960. $ Aluminum Laboratories Ltd. Banbury,
ACTA
METALLURGICA,
VOL.
9,
Oxon.
JUNE
1961
§ 99.997 563
was
selected
it is the most
as
the
practical
per cent aluminium
bonding
method,
and also has the
and 99.98 per cent copper.
ACTA
564
advantage
METALLURGICA,
that oxide films at the interface are broken
up and distributed
over
inverse
in
segregation
a much the
larger area.
core
was
Any
removed
by
VOL.
9,
1961
by a spectrophotometric hexanone
reagent
cent down activation
treatment
polishing prior
the results obtained
be minimized.
the region
was removed
to cladding, Polished
super-purity
strapped
by mechanical
so that the oxide
would
aluminium
plate
was
then
to each side of the core and the composite
sandwich
preheated
1 hr at 450°C of
was 70 per cent and the final thickness Diffusion
deformation
hot
cladding
# in.
amount
before
The
the couple
total
for
rolling.
couples
during of
combined
central
strip
of the sandwich
in the region where the interface was
flattest. Experiments
to determine
analysis
two selections
of the oxide film at the interface
couples.
obtained
Similar
from
concluded
each
diffusion
material
did not
interfere with diffusion.
2. Diffusion
obtained
couples
contained
temperatures:
in recrystallized for ~15
hr, 610°C
hr, 540°C for ~118
parameters ~1 to
hr and
of diffusion
give
approximately
in each case.
into ice-cold
the
The couples
water.
couples were carefully
so that slices would be removed face.
The specimens
aligned in a lathe
parallel to the inter-
were then reduced
in diameter by surface
diffusion.
thickness)
Consecutive
of each diffusion than
slices
machined couple
half its thickness.
directed
(0.001
in.
parallel to the interface
to a distance The individual
by means of an air blast down
chute into separate envelopes, to prevent
contamination
just greater slices were a Perspex
great care being taken
of one slice with preceding
slices. A dial gauge, calibrated in 0.0001 in. and mounted parallel to and just above the lathe axis, measured cut. 4. Analysis Analysis
from each one.
between the diffu-
ideal
parameters
diffusion
curve,
derived
from
Picks
second law _ 6%
6C
(1)
y$=Dx2
(where
C = concentration,
in which the interdiffusion with concentration, lar boundary
t = time, coefficient
is symmetrical
conditions under
these
I%= distance), b does not vary
under the particu-
applicable
to this work.*
particular
where
conditions
is
C (wt. ‘%) is the
the thickness
of material
b the interdiffusion
coeficient
removed
at each
distance
variable.
The second
term in the bracket is usually denoted by erf x/22,/(b). in the cladding,
C and C, are modified tively.
of copper present as
then the concentrations
as C -
c and C,, -
Inserting these in equation
c, respec-
(2) and rearrang-
ing, one can write : (3)
i where c is the concentration and + is the rearranged If the experimental above
equation,
of copper in the cladding,
concentration
term.
data are consistent
a plot
on
arithmetic
paper of x against the concentration
with the probability
term 4 is linear
and vice versa. The slope obtained is inversely proportional to the square root of the diffusion coefficient, i.e. 1
dX
@ out principally
at
(cm2/sec), t is the time
in seconds and 3, an integration
methods of the slices was carried
concentration
x cm from the interface, C, is the initial concentration,
Correcting for the small amount
by 0.125 in. to remove material influenced were subsequently
coefficient
RESULTS
an impurity
3. Slicing technique Annealed
by taking
alu-
505°C for 280 hr, the times calculated from Beerwald’s
were then quenched
was checked
in
of the
in vacua at each of the
635°C
hr, 575°C for ~53
same amount
of analysis
given by:
mina sheaths were annealed
diffusion
to
between
from each set.
Calculation of diflusion
1.
Its solution
annealing
Duplicate following
were
and it was therefore
that oxide present at the interface
significantly
for ~25
parameters
copper
slices from the same couple
a diffusion
sion coefficients
cent
reproducibility
There was no significant difference
were
the oxide was spread over four times the area of the
per
was evident
The
method
0.5 per
and by radio-
by both methods
of thirty
and calculating
The the effect on diffusion
0.05
of overlap.
carried out on a couple rolled to & in., i.e. in which 3 in.
from
from
copper
agreement
2 in. in diam-
eter were then cut from a longitudinal
of dispersion
analysis Excellent
using bis-cyclo-
concentrations
to 0.01 per cent
scalping prior to the homogenization treatment of 1 week at 450°C. The oxide film built up during this
zero.(s)
methodt7)
for
*
-
K 22/(B)
(1) C = C, for z > 0, and C = 0 for z < 0 when t = (2) For t > 0, C = Co/2 at z = 0.
(4) 0.
INTERDIFFUSION
MURPHY:
IN
Al-Cu
SOLID
AOLUTIOSS
363
O.S? APPROXIMATE POSITION OF 0.4 6 t uo 0.3-
0
SPECTROPHOTOMEtRlC
0
RADIOCHEMICAL
ANALYSES
ANALYSES
.S 5 pm2 :
-
(a>
0.1 -
20
0.2
I
60 80 DISTANCE -
40
2
IO
5
20 (
0.001
40 C - Cmin. CtlGx.Crnin.
100 ins.
60
120
80
140
90
95
160
98
99.5
x 100
1. (a) Concentration-distance curve for specimen annealed at 610°C for 25 hr 32 min showing slight decrease in copper content towards centre of (b) Probability plot for same specimen. core.
FIG.
where K is a constant probability
depending
on the scale of the
ingly a correction tained
paper used and
was made to the coefficients
in subsequent
experiments.
The amount
obof
diffusion which occurred in this manner was equivalent &K$ldj 4 All
the
experiments
on probability interdiffusion
pendent
of
copper
gave paper
resultant
(5)
tclx ( 1 .
concentration-distance
the present plotted
2 data straight (see Fig.
coefficients
concentration
obtained lines l),
in
ture, and a time correction
was therefore
made as
follows : For as-rolled specimens,
when
and the
(6)
were thus indebetween
0
and
where t,. is a time increment
due to diffusion
during
and before rolling and where d#dx is the slope of the probability plot of the as-rolled specimen. Thus, for
0.5 wt. %. 2. Correction for diffusion anneal
to some diffusion occurring at each annealing tempera-
diflusion
Concentration-distance
which
occurred
curves for as-rolled
prior
to
couples
(i.e. no diffusion anneal) showed that some diffusion had occurred before and/or during rolling and accord-
each interdiffusion
coefficient
obtained
at the various
temperatures, substitution in the above expression gave an approximate value oft, which was then added to the diffusion annealing time, time (t + t,) used to recalculate
and the corrected the interdiffusion
ACTA
566
coefficient. values
METALLURGICA,
Further substitution
2 per cent in each
of the recalculated
sion (6) did not give a significant
3. Sources of error parameters groups,
viz.
boundary analyses,
diffusion
are subject may be divided into two main experimental errors (impurities, grain
diffusion,
temperature
slicing methods,
and computational
control,
measurement
concerning
the
magnitude
of distance)
their
were carried out with the purest materials and
99.98
experiments the effect
per
cent
OFHC
small
quantities
any
number
accuracy
analyses
of
were checked
replicate
samples
at
the standard
deviation
of
Below the 0.1 per cent copper level, of
the
Special precautions face,
spectrophotometer
method
were taken to ensure that slices
since misorientation
of slicing
would
the slope of the concentration-distance
Future
hence reduce the calculated The thickness.of
on
diffusion
decrease
curves
and
coefficients.
each slice was measured by means
of a dial gauge calibrated
diffusion rates.
in units of lop4 in. Statisti-
cal analysis of fifty repeat readings carried out at the
In order to obviate diffusion
a
were removed from the specimen parallel to the inter-
alumin-
of impurity
each
by a platinum-
tended to fall.
using zone refined materials should reveal of very
as measured
errors in chemical
analysing
the
available
copper.
during the
f 1°C for
than
analyses at 0.5 per cent and 0.1 per cent copper was
The present experiments
at the time, viz. 99.997 per cent super-purity ium
at
better
used was of the
control
rhodium thermocouple.
0.003 per cent.
effect
was
different levels of copper:
of slopes).
of
temperature
by
It is well known that small amounts of impurities can affect diffusion rates but there is little information particular level of impurity.
annealing Possible
errors (i.e. fitting linear probability
plots to data and measurement
period
platinum
chemical
,LA. Temperature
annealing
diffusion
from the data
energy and frequency
factor. The grain size of all the couples order 2000-3000
of error to which measured
omitted
used to calculate the activation
between
the first and second approximations.
The sources
of grain boundary
these values were, therefore,
case.
b in expres-
difference
9, 1961
cause of the possibility
The correction decreased the experimental
by approximately
VOL.
the
the effects of grain boundary
annealing
greater
than
0.75
point.
However,
the interdiffusion
where
T,“K, an initial
coefficient
of the absolute temperature of d obtained
temperatures T,
used
standard
is the melting
plot of the logarithm against
same position
were
the
was
per cent of all readings
of
10e4 in. No significant
reciprocal
concluded
high, and be-
surface showed that the
1.5 x 10e4 in. so that would be accurate
-
*C.
0
40-
IO -
S4 II
I II.5
, 125
I I2 ‘/T’C
FIa. 2. Variation of interdiffusion
8 IO4
coefficient
with
95 x
curves, and it was therefore
that there were no appreciable
in the distance measurements.
TEMPERATURE
to f3
breaks were evident in any of
the concentration-distance
suggested that the values
at 505°C were slightly
on a specimen
deviation
temperature.
single errors
NURPHY:
I~TE~DIF~USIO~
IN Al-Cu
SOLID
SOLUTIONS
567
DISCUSSION
the reciprocal temperat~e. It is evident that,, regardless of core composition, the results are well within an order of magnitude of each other. Beerwald’sc2) results for a core concentration of 2 per cent give lower values of b which lie, however, on a line parallel to the present results and accordingly give a the frequency factor & (limits quoted are for 95 very similar activation energy. Hilliard et CZZ.(O) have per cent confidence, Q and log,& assumed to be suggested that Beerwald’s resultso for the aluminnormally distributed). The largest difference between ium-zinc system are some 15 per cent low on t,he duplicate results at any one temperature was wit~hin average, due to the use of a clamped couple in which 8 per cent (575OC) whilst the best agreement was contact between the core and sink may not be as within 0.1 per cent (610’~~. good as in rolled couples. It is likely therefore that A comparison between the present results and those the difference in bonding methods accounts for his of previous workers is shown in Fig. 3, which gives low results in the aluminium-copper system. the relationship between interdiffusion coefficient and The form of the concentration-distance curves and
Figure 2 illustrates the variation of interdiffusion coefficient with temperature. The slope of the line provides a value of 31.12 f 1.54 kcal/g atom for the 0.43 activation energy Q, and 0.29 & o 17 cm2/sec for
TEMPEO4luRE 635
600 I
sso
oc 500
T
41
40
RESULTS
MEHL, -t’CW
RWINES DEN
,(b*9b
BRICK
4ND
(EVTECTiC
%
CORE)
WLLlPd’~ CORE) ’
‘\ ‘\
FIG.
4ND
STONEN(3)
3. Comparison between previous data and present results.
ACTA
568
METALLURGICA,
their linear probability plots indicates that within the range O-O.5 per cent copper interdiffusion does not depend on copper concentration. This result is contrary to the conclusions drawn from some previous worlr(3,5) which showed concentration-dependence of zi; the core compositions used, however, were high and t)he graphical met,hods used to evaluate b were not very accurate at low concentrations. It is possible, of course, that within the range O-O.5 per cent copper t,he variation of b wit*hconcentration is not significant, but may become so over a greater composition range. Future work using 2 per cent and 4 per cent copper cores should enable the extent of concentration dependence to be determined. The value of the activation energy obtained agrees closely with the value of 30.6 & 1.15 kcal/g atom suggested by Federighicll) for the energy of selfdiffusion of aluminium, and may be compared with the vaIue of 32.2 kcal/g atom suggested by Spokas and Slich~r(lz) from nuclear magnetic resonance experiments. Federighi’s value was determined from studies of annealing out of vacancies in super-purity aluminium. The validity of the vacancy mechanism of volume diffusion in substitutional solid solutions has now been fairly well established and recent experiments by Dienes and Damask support this view. These investigators found that diffusion rates in iron were enhanced by neutron bombardment, i.e. by the introduction of additional vacancies. The theory of diffusion in dilute substitutional solid solutions is, however, by no means fully developed, and there has been much discussion of the physical interpretation of interdiffusion coefficients and frequency factors in relation to the atomic jumps which constitute diffusion. In a chemical diffusion experiment, the parameter measured is the interdiffusion coefficient 4, which measures the rate of flow relative to a surface defined so that equal numbers of atoms of each species diffuse in opposite directions across it. Darken(15) has proposed that in a binary system the interdiffusion ~oe~~ient is a function of the individual diffusion coefficients? DA and D, as follows : l? = NADB f NnDA where NA and NB are the respective atomic fractions, and DA and DB specify the respective rates of flow of A and 3 atoms relative to the lattice planes. Furthermore the individual coefficients DA and DB ometimes referred to
coJ&enta.
as partial chemical diffusion
VOL.
9, 1961
are related to the self- (tracer) diffusion coefficients
DA* by t,he form:
where yA is the activity coefficient of A. Using t’he Gibbs-Duhem relationship for a binary system : 6 log Yn 6 log YA 6 log NA = S log NB the interdiffusion coefficient may therefore be expressed in terms of the tracer diffusion coeff!cients: is = (N,L),*
+ NBD_**)
i
The above relationships are based on the validity of assumptions that lattice parameter changes were negligible, that a non-defective lattice was fully maintained by complete shrinkage and that expansion and shrinkage occurred only along the diffusion direction. SeitzPJ’) and Le Claire(“8)have shown theoretically that Darken’s equations cannot be expected to hold in general for diffusion by a vacancy mechanism, since the part played by vacancies is omitted in Darken’s treatment, although they would be valid if the vacancy concentration was everywhere in equilibrium. Experimentally, however, calculations of DA* and DB* using the above equations seem reasonably satisfactory and recently, Hilliard et uZ.@) have discussed self- and interdi~usion in the aluminiumzinc system using the form: b(X)
= (X&*
+ X,DA*)m
where B(X) is the interdiffusion coefficient at composition (X) and where m is the thermodynamic factor :
6 1%YA
i
1+-----. 6 1% x-4 1
If, in the case of the present results, a value of unity for the factor m over the range O-0.005 atom fraction of copper in aluminium is assumed, then: fi = (0.995RCU* + 0.005D,1*). Since the Dal* term is small compared with b, the present results effectively describe the tracer diffusion of copper in a dilute aluminium-copper solid solution in which there is no chemical gradient. ACKNOWLEDGMENTS
The author wishes to thank Mr. A. D. Le Claire and Mr. G. E. 0. Tucker for valuable disoussions, and
MURPHY:
Mr. M. A. Reynolds with
the
Laboratories
The
IN
and Mr. J. P. Bates for assistance
experimental
respectively.
INTERDIFFUSION
work
author
Limited,
and also
Banbury
chemical thanks for
analyses,
Aluminium
permission
to
publish this paper. REFERENCES 1. R. M. BRICK and A. PHILLIPS, Trans. Amer. Inst. Min. (Metall.) Engrs 124, 331 (1937). 2. A. BEERWALD,2. Electrochem. 45, 789 (1939). 3. R. F. MEHL, F. N. RHINES and K. A. VON DEN STEINEN, iWet& & Alloys 13, 41 (1941). 4. H. B~~CKLE,2. Electrochem. 49, 238 (1943). 5. H. BUCKLEand A. KEIL, M&au et Corros. 24, 59 (1949). 6. J. W. H. CLARE., Metallurgia, Manchr. 57, 344 (1958). 7. J. F. BATES, Aluminium Laboratories Ltd., Banbury, unpublished work.
8.
Al-Cu
SOLID
SOLUTIONS
569
H. BAKERand R. A. HINE, Aluminium Laboratories Ltd.,
Banbury, unpublished work.
9. J. E. HILLI~RD, B. L. AVERBACH and M. COHEN, Acta
Met. 7, 86 (1959).
10. A. BEERWALD,2. Electmchem. 45, ‘793 (1939). 11. T. FEDERIGHI,Phil. Mug. 4, 502 (1959). 12. J. J. SPOKAS and C. P. SLIGHTER,Phys. Rev. 113, 1462 (1959). 13. W. M. LOXER, Symposium on Vacancies and Other Point Defects in Metals. Monagr. Ser. Inst. Met& No. 23 (1957). 14. G. J. DIENES and A. C. DAMASK,J. AppZ. Phys. 29, 1713
(1958).
15. L. S. DARKEN, Trans. Amer. Inst. Min. (Metall.) 176, 184 (1948). 16. F. SEITZ, Phys. Rev. 74, 1513 (1948). 17. F. SEITZ, Actu Cryat. 3, 355 (1950). 18. A. D. LE CLAIRE,Progr. Met. Phys. 4, 320 (1953).
Engrr
IN DILUTE
ALUMINIUM-COPPER J. B.
SOLID
SOLUTIONSt
MURPHY:
A study has been made of the interdiffusion of copper from an tc solid solution into aluminium with special attention to minimizing experimental and computational errors. The form of the concentrationdistance curves obtained showed that interdiffusion was independent of concentration within the range o-o.5
wt. y0 copper.
The activation
energy calculated
and the frequency factor so
from the slope of a log, 5 versus T-i plot was 31.12 5 1.54 kcal/g j-o.43 was 0.29 _. l7 cm*/sec. It is concluded that the data obtained are closely
related to the tracer diffusion of copper in aluminium. INTERDIFFUSION DANS UNE SOLUTION SOLIDE D’ALUMINIUM ET DE CUIVRE
DILUEE
L’auteur a Btudie, avec des precautions speciales pour minimiser les erreurs experimentales et les erreurs de mesure, l’interdiffusion du cuivre a partir d’une solution solide cc-aluminium-cuivre dans l’aluminium. La forme de la courbe dormant la concentration en fonction de la distance montre que l’interdiffusion est independante de la concentration dans un domaine variant de 0 a 0.5% en poids de cuivre. L’energie I,54 Kcal/gr
d’activation
calculee a partir de la pente de la droite log, 0” en fonction de T-1 est de 31,12 +0,43 est &gal a 0,29 _o,17 cm2/sec.
:t
et le facteur de frequence 0,
L’auteur conclut l’aluminium.
que ces valeurs
INTERDIFFUSION
BE1
sont intimement
VERDUNNTEN
liees it la diffusion
FESTEN
de traceurs
de cuivre
dans
BLUMIKIUI\I-KUPFER-LOSUNGEN
Die Interdiffusion van Kupfer aus einer festen cc-L&sung in Aluminium wurde untersucht; dabei wurde besonderer Wert darauf gelegt, experimentelle und Berechnungsfehler miiglichst klein zu halten. Die Form der Kurven Konzentration gegen Entfernung zeigte, daR die Interdiffusion im Bereich O-O.5 Gew. yc Kupfer unabhiingig von der Konzentration war. Die Aktivierungsenergie,
wie man sie aus der Steigung der Kurve log, 5 gegen T-’ +0.43 & 1.54 kcal/g und der Frequenzfaktor o”, war 0.29 _. l7 cm2/sec. Diese Werte
31.12
die Diffusion von Kupfer
als Spurenelement
in Aluminium
INTRODUCTION
Interdiffusion been studied’1-5) between reliable
at initial
copper
2 and 33 per cent. appears
spectrographic
has previously
concentrations
analysis
of slices through
who,
of 31 .I kcal/g 0.177 cm2/sec
atom
for the activation
for frequency
factor
from a least squares analysis There was no indication rate with concentration. have suggested
6,
by
interference solutions
and
of any variation
of diffusion
tive
second
was undertaken
to obtain
to
variations
of the data cannot
Accordsolid
consistent
to ensure accurate results.
work
ccaluminium-coppers
has
under controlled
be considered
data is extremely
in experimental
and
sensi-
technique,
and
were taken in this work Diffusion couples prepared
by roll bonding super-purity
on the diffusion of solute elements in aluminium(@
phase.
TECHNIQUE
of diffusion
therefore special precautions
rates do, in fact,
a recent review of the previous
shown that much
by precipitated
The reliability
vary with copper concentration. Furthermore,
greater
limit may have led to some
EXPERIMENTAL
results).
Later workers(3*4) however,
that the diffusion
the use of core concentrations
reliable data.
(recalculated
of Beerwald’s
due to the
ingly, a study of diffusion in aluminium-copper
values
energy
In addition,
than the solid solubility
a clamped
couple with a 2 per cent copper core, obtained
was liable to be inaccurate
difficulty in measuring tangents at such concentrations.
of
Of this work, the most
to be that of Beerwaldc2)
sind denen fiir
sehr iihnlich.
concentrations
of copper in aluminium
war
berechnet,
aluminium cladding to an
solid solution core were annealed
atmosphere
and temperature.
The
reliable, owing to the insensitive analysis methods used. Results illustrating compositional dependence
couples were then sliced parallel to the interface and th e slices analysed to determine concentrationdistance curves.
of diffusion were inconsistent. Composition-distance curves were analysed mainly graphically by the areatangent method to produce data, which at low
1. Bonding method Rolling because
t
Received August 4, 1960. $ Aluminum Laboratories Ltd. Banbury,
ACTA
METALLURGICA,
VOL.
9,
Oxon.
JUNE
1961
§ 99.997 563
was
selected
it is the most
as
the
practical
per cent aluminium
bonding
method,
and also has the
and 99.98 per cent copper.
ACTA
564
advantage
METALLURGICA,
that oxide films at the interface are broken
up and distributed
over
inverse
in
segregation
a much the
larger area.
core
was
Any
removed
by
VOL.
9,
1961
by a spectrophotometric hexanone
reagent
cent down activation
treatment
polishing prior
the results obtained
be minimized.
the region
was removed
to cladding, Polished
super-purity
strapped
by mechanical
so that the oxide
would
aluminium
plate
was
then
to each side of the core and the composite
sandwich
preheated
1 hr at 450°C of
was 70 per cent and the final thickness Diffusion
deformation
hot
cladding
# in.
amount
before
The
the couple
total
for
rolling.
couples
during of
combined
central
strip
of the sandwich
in the region where the interface was
flattest. Experiments
to determine
analysis
two selections
of the oxide film at the interface
couples.
obtained
Similar
from
concluded
each
diffusion
material
did not
interfere with diffusion.
2. Diffusion
obtained
couples
contained
temperatures:
in recrystallized for ~15
hr, 610°C
hr, 540°C for ~118
parameters ~1 to
hr and
of diffusion
give
approximately
in each case.
into ice-cold
the
The couples
water.
couples were carefully
so that slices would be removed face.
The specimens
aligned in a lathe
parallel to the inter-
were then reduced
in diameter by surface
diffusion.
thickness)
Consecutive
of each diffusion than
slices
machined couple
half its thickness.
directed
(0.001
in.
parallel to the interface
to a distance The individual
by means of an air blast down
chute into separate envelopes, to prevent
contamination
just greater slices were a Perspex
great care being taken
of one slice with preceding
slices. A dial gauge, calibrated in 0.0001 in. and mounted parallel to and just above the lathe axis, measured cut. 4. Analysis Analysis
from each one.
between the diffu-
ideal
parameters
diffusion
curve,
derived
from
Picks
second law _ 6%
6C
(1)
y$=Dx2
(where
C = concentration,
in which the interdiffusion with concentration, lar boundary
t = time, coefficient
is symmetrical
conditions under
these
I%= distance), b does not vary
under the particu-
applicable
to this work.*
particular
where
conditions
is
C (wt. ‘%) is the
the thickness
of material
b the interdiffusion
coeficient
removed
at each
distance
variable.
The second
term in the bracket is usually denoted by erf x/22,/(b). in the cladding,
C and C, are modified tively.
of copper present as
then the concentrations
as C -
c and C,, -
Inserting these in equation
c, respec-
(2) and rearrang-
ing, one can write : (3)
i where c is the concentration and + is the rearranged If the experimental above
equation,
of copper in the cladding,
concentration
term.
data are consistent
a plot
on
arithmetic
paper of x against the concentration
with the probability
term 4 is linear
and vice versa. The slope obtained is inversely proportional to the square root of the diffusion coefficient, i.e. 1
dX
@ out principally
at
(cm2/sec), t is the time
in seconds and 3, an integration
methods of the slices was carried
concentration
x cm from the interface, C, is the initial concentration,
Correcting for the small amount
by 0.125 in. to remove material influenced were subsequently
coefficient
RESULTS
an impurity
3. Slicing technique Annealed
by taking
alu-
505°C for 280 hr, the times calculated from Beerwald’s
were then quenched
was checked
in
of the
in vacua at each of the
635°C
hr, 575°C for ~53
same amount
of analysis
given by:
mina sheaths were annealed
diffusion
to
between
from each set.
Calculation of diflusion
1.
Its solution
annealing
Duplicate following
were
and it was therefore
that oxide present at the interface
significantly
for ~25
parameters
copper
slices from the same couple
a diffusion
sion coefficients
cent
reproducibility
There was no significant difference
were
the oxide was spread over four times the area of the
per
was evident
The
method
0.5 per
and by radio-
by both methods
of thirty
and calculating
The the effect on diffusion
0.05
of overlap.
carried out on a couple rolled to & in., i.e. in which 3 in.
from
from
copper
agreement
2 in. in diam-
eter were then cut from a longitudinal
of dispersion
analysis Excellent
using bis-cyclo-
concentrations
to 0.01 per cent
scalping prior to the homogenization treatment of 1 week at 450°C. The oxide film built up during this
zero.(s)
methodt7)
for
*
-
K 22/(B)
(1) C = C, for z > 0, and C = 0 for z < 0 when t = (2) For t > 0, C = Co/2 at z = 0.
(4) 0.
INTERDIFFUSION
MURPHY:
IN
Al-Cu
SOLID
AOLUTIOSS
363
O.S? APPROXIMATE POSITION OF 0.4 6 t uo 0.3-
0
SPECTROPHOTOMEtRlC
0
RADIOCHEMICAL
ANALYSES
ANALYSES
.S 5 pm2 :
-
(a>
0.1 -
20
0.2
I
60 80 DISTANCE -
40
2
IO
5
20 (
0.001
40 C - Cmin. CtlGx.Crnin.
100 ins.
60
120
80
140
90
95
160
98
99.5
x 100
1. (a) Concentration-distance curve for specimen annealed at 610°C for 25 hr 32 min showing slight decrease in copper content towards centre of (b) Probability plot for same specimen. core.
FIG.
where K is a constant probability
depending
on the scale of the
ingly a correction tained
paper used and
was made to the coefficients
in subsequent
experiments.
The amount
obof
diffusion which occurred in this manner was equivalent &K$ldj 4 All
the
experiments
on probability interdiffusion
pendent
of
copper
gave paper
resultant
(5)
tclx ( 1 .
concentration-distance
the present plotted
2 data straight (see Fig.
coefficients
concentration
obtained lines l),
in
ture, and a time correction
was therefore
made as
follows : For as-rolled specimens,
when
and the
(6)
were thus indebetween
0
and
where t,. is a time increment
due to diffusion
during
and before rolling and where d#dx is the slope of the probability plot of the as-rolled specimen. Thus, for
0.5 wt. %. 2. Correction for diffusion anneal
to some diffusion occurring at each annealing tempera-
diflusion
Concentration-distance
which
occurred
curves for as-rolled
prior
to
couples
(i.e. no diffusion anneal) showed that some diffusion had occurred before and/or during rolling and accord-
each interdiffusion
coefficient
obtained
at the various
temperatures, substitution in the above expression gave an approximate value oft, which was then added to the diffusion annealing time, time (t + t,) used to recalculate
and the corrected the interdiffusion
ACTA
566
coefficient. values
METALLURGICA,
Further substitution
2 per cent in each
of the recalculated
sion (6) did not give a significant
3. Sources of error parameters groups,
viz.
boundary analyses,
diffusion
are subject may be divided into two main experimental errors (impurities, grain
diffusion,
temperature
slicing methods,
and computational
control,
measurement
concerning
the
magnitude
of distance)
their
were carried out with the purest materials and
99.98
experiments the effect
per
cent
OFHC
small
quantities
any
number
accuracy
analyses
of
were checked
replicate
samples
at
the standard
deviation
of
Below the 0.1 per cent copper level, of
the
Special precautions face,
spectrophotometer
method
were taken to ensure that slices
since misorientation
of slicing
would
the slope of the concentration-distance
Future
hence reduce the calculated The thickness.of
on
diffusion
decrease
curves
and
coefficients.
each slice was measured by means
of a dial gauge calibrated
diffusion rates.
in units of lop4 in. Statisti-
cal analysis of fifty repeat readings carried out at the
In order to obviate diffusion
a
were removed from the specimen parallel to the inter-
alumin-
of impurity
each
by a platinum-
tended to fall.
using zone refined materials should reveal of very
as measured
errors in chemical
analysing
the
available
copper.
during the
f 1°C for
than
analyses at 0.5 per cent and 0.1 per cent copper was
The present experiments
at the time, viz. 99.997 per cent super-purity ium
at
better
used was of the
control
rhodium thermocouple.
0.003 per cent.
effect
was
different levels of copper:
of slopes).
of
temperature
by
It is well known that small amounts of impurities can affect diffusion rates but there is little information particular level of impurity.
annealing Possible
errors (i.e. fitting linear probability
plots to data and measurement
period
platinum
chemical
,LA. Temperature
annealing
diffusion
from the data
energy and frequency
factor. The grain size of all the couples order 2000-3000
of error to which measured
omitted
used to calculate the activation
between
the first and second approximations.
The sources
of grain boundary
these values were, therefore,
case.
b in expres-
difference
9, 1961
cause of the possibility
The correction decreased the experimental
by approximately
VOL.
the
the effects of grain boundary
annealing
greater
than
0.75
point.
However,
the interdiffusion
where
T,“K, an initial
coefficient
of the absolute temperature of d obtained
temperatures T,
used
standard
is the melting
plot of the logarithm against
same position
were
the
was
per cent of all readings
of
10e4 in. No significant
reciprocal
concluded
high, and be-
surface showed that the
1.5 x 10e4 in. so that would be accurate
-
*C.
0
40-
IO -
S4 II
I II.5
, 125
I I2 ‘/T’C
FIa. 2. Variation of interdiffusion
8 IO4
coefficient
with
95 x
curves, and it was therefore
that there were no appreciable
in the distance measurements.
TEMPERATURE
to f3
breaks were evident in any of
the concentration-distance
suggested that the values
at 505°C were slightly
on a specimen
deviation
temperature.
single errors
NURPHY:
I~TE~DIF~USIO~
IN Al-Cu
SOLID
SOLUTIONS
567
DISCUSSION
the reciprocal temperat~e. It is evident that,, regardless of core composition, the results are well within an order of magnitude of each other. Beerwald’sc2) results for a core concentration of 2 per cent give lower values of b which lie, however, on a line parallel to the present results and accordingly give a the frequency factor & (limits quoted are for 95 very similar activation energy. Hilliard et CZZ.(O) have per cent confidence, Q and log,& assumed to be suggested that Beerwald’s resultso for the aluminnormally distributed). The largest difference between ium-zinc system are some 15 per cent low on t,he duplicate results at any one temperature was wit~hin average, due to the use of a clamped couple in which 8 per cent (575OC) whilst the best agreement was contact between the core and sink may not be as within 0.1 per cent (610’~~. good as in rolled couples. It is likely therefore that A comparison between the present results and those the difference in bonding methods accounts for his of previous workers is shown in Fig. 3, which gives low results in the aluminium-copper system. the relationship between interdiffusion coefficient and The form of the concentration-distance curves and
Figure 2 illustrates the variation of interdiffusion coefficient with temperature. The slope of the line provides a value of 31.12 f 1.54 kcal/g atom for the 0.43 activation energy Q, and 0.29 & o 17 cm2/sec for
TEMPEO4luRE 635
600 I
sso
oc 500
T
41
40
RESULTS
MEHL, -t’CW
RWINES DEN
,(b*9b
BRICK
4ND
(EVTECTiC
%
CORE)
WLLlPd’~ CORE) ’
‘\ ‘\
FIG.
4ND
STONEN(3)
3. Comparison between previous data and present results.
ACTA
568
METALLURGICA,
their linear probability plots indicates that within the range O-O.5 per cent copper interdiffusion does not depend on copper concentration. This result is contrary to the conclusions drawn from some previous worlr(3,5) which showed concentration-dependence of zi; the core compositions used, however, were high and t)he graphical met,hods used to evaluate b were not very accurate at low concentrations. It is possible, of course, that within the range O-O.5 per cent copper t,he variation of b wit*hconcentration is not significant, but may become so over a greater composition range. Future work using 2 per cent and 4 per cent copper cores should enable the extent of concentration dependence to be determined. The value of the activation energy obtained agrees closely with the value of 30.6 & 1.15 kcal/g atom suggested by Federighicll) for the energy of selfdiffusion of aluminium, and may be compared with the vaIue of 32.2 kcal/g atom suggested by Spokas and Slich~r(lz) from nuclear magnetic resonance experiments. Federighi’s value was determined from studies of annealing out of vacancies in super-purity aluminium. The validity of the vacancy mechanism of volume diffusion in substitutional solid solutions has now been fairly well established and recent experiments by Dienes and Damask support this view. These investigators found that diffusion rates in iron were enhanced by neutron bombardment, i.e. by the introduction of additional vacancies. The theory of diffusion in dilute substitutional solid solutions is, however, by no means fully developed, and there has been much discussion of the physical interpretation of interdiffusion coefficients and frequency factors in relation to the atomic jumps which constitute diffusion. In a chemical diffusion experiment, the parameter measured is the interdiffusion coefficient 4, which measures the rate of flow relative to a surface defined so that equal numbers of atoms of each species diffuse in opposite directions across it. Darken(15) has proposed that in a binary system the interdiffusion ~oe~~ient is a function of the individual diffusion coefficients? DA and D, as follows : l? = NADB f NnDA where NA and NB are the respective atomic fractions, and DA and DB specify the respective rates of flow of A and 3 atoms relative to the lattice planes. Furthermore the individual coefficients DA and DB ometimes referred to
coJ&enta.
as partial chemical diffusion
VOL.
9, 1961
are related to the self- (tracer) diffusion coefficients
DA* by t,he form:
where yA is the activity coefficient of A. Using t’he Gibbs-Duhem relationship for a binary system : 6 log Yn 6 log YA 6 log NA = S log NB the interdiffusion coefficient may therefore be expressed in terms of the tracer diffusion coeff!cients: is = (N,L),*
+ NBD_**)
i
The above relationships are based on the validity of assumptions that lattice parameter changes were negligible, that a non-defective lattice was fully maintained by complete shrinkage and that expansion and shrinkage occurred only along the diffusion direction. SeitzPJ’) and Le Claire(“8)have shown theoretically that Darken’s equations cannot be expected to hold in general for diffusion by a vacancy mechanism, since the part played by vacancies is omitted in Darken’s treatment, although they would be valid if the vacancy concentration was everywhere in equilibrium. Experimentally, however, calculations of DA* and DB* using the above equations seem reasonably satisfactory and recently, Hilliard et uZ.@) have discussed self- and interdi~usion in the aluminiumzinc system using the form: b(X)
= (X&*
+ X,DA*)m
where B(X) is the interdiffusion coefficient at composition (X) and where m is the thermodynamic factor :
6 1%YA
i
1+-----. 6 1% x-4 1
If, in the case of the present results, a value of unity for the factor m over the range O-0.005 atom fraction of copper in aluminium is assumed, then: fi = (0.995RCU* + 0.005D,1*). Since the Dal* term is small compared with b, the present results effectively describe the tracer diffusion of copper in a dilute aluminium-copper solid solution in which there is no chemical gradient. ACKNOWLEDGMENTS
The author wishes to thank Mr. A. D. Le Claire and Mr. G. E. 0. Tucker for valuable disoussions, and
MURPHY:
Mr. M. A. Reynolds with
the
Laboratories
The
IN
and Mr. J. P. Bates for assistance
experimental
respectively.
INTERDIFFUSION
work
author
Limited,
and also
Banbury
chemical thanks for
analyses,
Aluminium
permission
to
publish this paper. REFERENCES 1. R. M. BRICK and A. PHILLIPS, Trans. Amer. Inst. Min. (Metall.) Engrs 124, 331 (1937). 2. A. BEERWALD,2. Electrochem. 45, 789 (1939). 3. R. F. MEHL, F. N. RHINES and K. A. VON DEN STEINEN, iWet& & Alloys 13, 41 (1941). 4. H. B~~CKLE,2. Electrochem. 49, 238 (1943). 5. H. BUCKLEand A. KEIL, M&au et Corros. 24, 59 (1949). 6. J. W. H. CLARE., Metallurgia, Manchr. 57, 344 (1958). 7. J. F. BATES, Aluminium Laboratories Ltd., Banbury, unpublished work.
8.
Al-Cu
SOLID
SOLUTIONS
569
H. BAKERand R. A. HINE, Aluminium Laboratories Ltd.,
Banbury, unpublished work.
9. J. E. HILLI~RD, B. L. AVERBACH and M. COHEN, Acta
Met. 7, 86 (1959).
10. A. BEERWALD,2. Electmchem. 45, ‘793 (1939). 11. T. FEDERIGHI,Phil. Mug. 4, 502 (1959). 12. J. J. SPOKAS and C. P. SLIGHTER,Phys. Rev. 113, 1462 (1959). 13. W. M. LOXER, Symposium on Vacancies and Other Point Defects in Metals. Monagr. Ser. Inst. Met& No. 23 (1957). 14. G. J. DIENES and A. C. DAMASK,J. AppZ. Phys. 29, 1713
(1958).
15. L. S. DARKEN, Trans. Amer. Inst. Min. (Metall.) 176, 184 (1948). 16. F. SEITZ, Phys. Rev. 74, 1513 (1948). 17. F. SEITZ, Actu Cryat. 3, 355 (1950). 18. A. D. LE CLAIRE,Progr. Met. Phys. 4, 320 (1953).
Engrr