INTERDIFFUSION IN DILUTE ALUMINIUM-COPPER SOLID SOLUTIONSt

J. B. 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 concentration-

distance curves obtained showed that interdiffusion was independent of concentration within the range

o-o.5 wt. y0 copper.

The activation energy calculated from the slope of a log, 5 versus T-i plot was 31.12 5 1.54 kcal/g j-o.43

and the frequency factor so 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 DILUEE D’ALUMINIUM ET DE CUIVRE

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 d’activation calculee a partir de la pente de la droite log, 0” en fonction de T-1 est de 31,12 :t

+0,43 I,54 Kcal/gr et le facteur de frequence 0, est &gal a 0,29 _o,17 cm2/sec.

L’auteur conclut que ces valeurs sont intimement liees it la diffusion de traceurs de cuivre dans

l’aluminium.

INTERDIFFUSION BE1 VERDUNNTEN FESTEN 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-’ berechnet, war

+0.43 31.12 & 1.54 kcal/g und der Frequenzfaktor o”, war 0.29 _. l7 cm2/sec. Diese Werte sind denen fiir

die Diffusion von Kupfer als Spurenelement in Aluminium sehr iihnlich.

INTRODUCTION

Interdiffusion of copper in aluminium has previously

been studied’1-5) at initial copper concentrations of

between 2 and 33 per cent. Of this work, the most

reliable appears to be that of Beerwaldc2) who, by

spectrographic analysis of slices through a clamped

couple with a 2 per cent copper core, obtained values

of 31 .I kcal/g atom for the activation energy and

concentrations was liable to be inaccurate due to the

difficulty in measuring tangents at such concentrations.

In addition, the use of core concentrations greater

than the solid solubility limit may have led to some

interference by precipitated second phase. Accord-

ingly, a study of diffusion in aluminium-copper solid

solutions was undertaken to obtain consistent and

reliable data.

0.177 cm2/sec for frequency factor 6, (recalculated EXPERIMENTAL TECHNIQUE

from a least squares analysis of Beerwald’s results).

There was no indication of any variation of diffusion The reliability of diffusion data is extremely sensi-

rate with concentration. Later workers(3*4) however, tive to variations in experimental technique, and

have suggested that the diffusion rates do, in fact, therefore special precautions were taken in this work

to ensure accurate results. Diffusion couples prepared vary with copper concentration.

Furthermore, a recent review of the previous work by roll bonding super-purity aluminium cladding to an

on the diffusion of solute elements in aluminium(@ has cc aluminium-coppers solid solution core were annealed

shown that much of the data cannot be considered under controlled atmosphere and temperature. The

reliable, owing to the insensitive analysis methods couples were then sliced parallel to the interface and th

used. Results illustrating compositional dependence e slices analysed to determine concentration-

distance curves. of diffusion were inconsistent. Composition-distance

curves were analysed mainly graphically by the area- 1. Bonding method

tangent method to produce data, which at low Rolling was selected as the bonding method,

t Received August 4, 1960. because it is the most practical and also has the

$ Aluminum Laboratories Ltd. Banbury, Oxon. § 99.997 per cent aluminium and 99.98 per cent copper.

ACTA METALLURGICA, VOL. 9, JUNE 1961 563

564 ACTA METALLURGICA, VOL. 9, 1961

advantage that oxide films at the interface are broken

up and distributed over a much larger area. Any

inverse segregation in the core was removed by

scalping prior to the homogenization treatment of 1

week at 450°C. The oxide film built up during this

treatment was removed by mechanical polishing prior

to cladding, so that the oxide would be minimized.

Polished super-purity aluminium plate was then

strapped to each side of the core and the composite

sandwich preheated for 1 hr at 450°C before hot

rolling. The total amount of deformation during

cladding was 70 per cent and the final thickness of

the couple # in. Diffusion couples 2 in. in diam-

eter were then cut from a longitudinal central strip

of the sandwich in the region where the interface was

flattest.

Experiments to determine the effect on diffusion

of dispersion of the oxide film at the interface were

carried out on a couple rolled to & in., i.e. in which

the oxide was spread over four times the area of the

3 in. couples. Similar diffusion parameters were

obtained from each material and it was therefore

concluded that oxide present at the interface did not

significantly interfere with diffusion.

2. Diffusion annealing

Duplicate couples contained in recrystallized alu-

mina sheaths were annealed in vacua at each of the

following temperatures: 635°C for ~15 hr, 610°C

for ~25 hr, 575°C for ~53 hr, 540°C for ~118 hr and

505°C for 280 hr, the times calculated from Beerwald’s

diffusion parameters ~1 to give approximately the

same amount of diffusion in each case. The couples

were then quenched into ice-cold water.

3. Slicing technique

Annealed couples were carefully aligned in a lathe

so that slices would be removed parallel to the inter-

face. The specimens were then reduced in diameter

by 0.125 in. to remove material influenced by surface

diffusion. Consecutive slices (0.001 in. thickness)

were subsequently machined parallel to the interface

of each diffusion couple to a distance just greater

than half its thickness. The individual slices were

directed by means of an air blast down a Perspex

chute into separate envelopes, great care being taken

to prevent contamination 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 the thickness of material removed at each cut.

4. Analysis methods

Analysis of the slices was carried out principally

by a spectrophotometric methodt7) using bis-cyclo-

hexanone reagent for concentrations from 0.5 per

cent down to 0.01 per cent copper and by radio-

activation analysis from 0.05 per cent copper to

zero.(s) Excellent agreement was evident between

the results obtained by both methods of analysis in

the region of overlap. The reproducibility of the

combined analysis method was checked by taking

two selections of thirty slices from the same couple

and calculating a diffusion coefficient from each one.

There was no significant difference between the diffu-

sion coefficients obtained from each set.

RESULTS

1. Calculation of diflusion parameters

The ideal diffusion curve, derived from Picks

second law

6C _ 6% y$=Dx2 (1)

(where C = concentration, t = time, I% = distance),

in which the interdiffusion coefficient b does not vary

with concentration, is symmetrical under the particu-

lar boundary conditions applicable to this work.*

Its solution under these particular conditions is

given by:

where C (wt. ‘%) is the concentration at distance

x cm from the interface, C, is the initial concentration,

b the interdiffusion coeficient (cm2/sec), t is the time

in seconds and 3, an integration variable. The second

term in the bracket is usually denoted by erf x/22,/(b).

Correcting for the small amount of copper present as

an impurity in the cladding, then the concentrations

C and C, are modified as C - c and C,, - c, respec-

tively. Inserting these in equation (2) and rearrang-

ing, one can write :

i (3)

where c is the concentration of copper in the cladding,

and + is the rearranged concentration term.

If the experimental data are consistent with the

above equation, a plot on arithmetic probability

paper of x against the concentration term 4 is linear

and vice versa. The slope obtained is inversely

proportional to the square root of the diffusion

coefficient, i.e.

dX 1

@ - K 22/(B) (4)

* (1) C = C, for z > 0, and C = 0 for z < 0 when t = 0. (2) For t > 0, C = Co/2 at z = 0.

MURPHY:

O.S?

0.4 -

6 t

uo 0.3-

.S

5

pm2 - : (a>

0.1 -

INTERDIFFUSION IN Al-Cu SOLID AOLUTIOSS

APPROXIMATE POSITION OF

0 SPECTROPHOTOMEtRlC ANALYSES

0 RADIOCHEMICAL ANALYSES

363

20 40 60 80 100 120 140 160 DISTANCE - 0.001 ins.

0.2 I 2 5 IO 20 40 60 80 90 95 98 99.5

(

C - Cmin. CtlGx.Crnin. x 100

FIG. 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

core. (b) Probability plot for same specimen.

where K is a constant depending on the scale of the

probability paper used and

&K$ldj 2 ( 1 4 tclx .

(5)

All the concentration-distance data obtained in

the present experiments gave straight lines when

plotted on probability paper (see Fig. l), and the

resultant interdiffusion coefficients were thus inde-

pendent of copper concentration between 0 and

0.5 wt. %.

2. Correction for diflusion which occurred prior to

diffusion anneal

Concentration-distance curves for as-rolled couples

(i.e. no diffusion anneal) showed that some diffusion

had occurred before and/or during rolling and accord-

ingly a correction was made to the coefficients ob-

tained in subsequent experiments. The amount of

diffusion which occurred in this manner was equivalent

to some diffusion occurring at each annealing tempera-

ture, and a time correction was therefore made as

follows : For as-rolled specimens,

(6)

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

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, and the corrected

time (t + t,) used to recalculate the interdiffusion

566 ACTA METALLURGICA, VOL. 9, 1961

coefficient. The correction decreased the experimental

values by approximately 2 per cent in each case.

Further substitution of the recalculated b in expres-

sion (6) did not give a significant difference between

the first and second approximations.

3. Sources of error

The sources of error to which measured diffusion

parameters are subject may be divided into two main

groups, viz. experimental errors (impurities, grain

boundary diffusion, temperature control, chemical

analyses, slicing methods, measurement of distance)

and computational errors (i.e. fitting linear probability

plots to data and measurement of slopes).

It is well known that small amounts of impurities

can affect diffusion rates but there is little information

concerning the magnitude of their effect at any

particular level of impurity. The present experiments

were carried out with the purest materials available

at the time, viz. 99.997 per cent super-purity alumin-

ium and 99.98 per cent OFHC copper. Future

experiments using zone refined materials should reveal

the effect of very small quantities of impurity on

diffusion rates.

In order to obviate the effects of grain boundary

diffusion the annealing temperatures used were

greater than 0.75 T,“K, where T, is the melting

point. However, an initial plot of the logarithm of

the interdiffusion coefficient against the reciprocal

of the absolute temperature suggested that the values

of d obtained at 505°C were slightly high, and be-

cause of the possibility of grain boundary diffusion

these values were, therefore, omitted from the data

used to calculate the activation energy and frequency

factor.

The grain size of all the couples used was of the

order 2000-3000 ,LA. Temperature control during the

annealing period was better than f 1°C for each

annealing temperature as measured by a platinum-

platinum rhodium thermocouple.

Possible errors in chemical analyses were checked

by analysing a number of replicate samples at

different levels of copper: the standard deviation of

analyses at 0.5 per cent and 0.1 per cent copper was

0.003 per cent. Below the 0.1 per cent copper level,

the accuracy of the spectrophotometer method

tended to fall.

Special precautions were taken to ensure that slices

were removed from the specimen parallel to the inter-

face, since misorientation of slicing would decrease

the slope of the concentration-distance curves and

hence reduce the calculated diffusion coefficients.

The thickness.of each slice was measured by means

of a dial gauge calibrated in units of lop4 in. Statisti-

cal analysis of fifty repeat readings carried out at the

same position on a specimen surface showed that the

standard deviation was 1.5 x 10e4 in. so that 95

per cent of all readings would be accurate to f3 x

10e4 in. No significant breaks were evident in any of

the concentration-distance curves, and it was therefore

concluded that there were no appreciable single errors

in the distance measurements.

TEMPERATURE - *C.

40-

IO -

S-

4 II

I I , II.5 I2 125

‘/T’C 8 IO4

FIa. 2. Variation of interdiffusion coefficient with temperature.

0

NURPHY: I~TE~DIF~USIO~ IN Al-Cu SOLID SOLUTIONS 567

DISCUSSION

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

the frequency factor & (limits quoted are for 95 per cent confidence, Q and log,& assumed to be normally distributed). The largest difference between duplicate results at any one temperature was wit~hin 8 per cent (575OC) whilst the best agreement was within 0.1 per cent (610’~~.

TEMPEO4luRE oc

A comparison between the present results and those of previous workers is shown in Fig. 3, which gives the relationship between interdiffusion coefficient and

the reciprocal temperat~e. It is evident that,, regardless of core composition, the results are well within an order of magnitude of each other. Beer- wald’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

very similar activation energy. Hilliard et CZZ.(O) have suggested that Beerwald’s resultso for the alumin- ium-zinc system are some 15 per cent low on t,he average, due to the use of a clamped couple in which contact between the core and sink may not be as good as in rolled couples. It is likely therefore that the difference in bonding methods accounts for his low results in the aluminium-copper system.

The form of the concentration-distance curves and

635 600 sso 500 40 41 I T

RESULTS

MEHL, RWINES 4ND

-t’CW DEN STONEN(3)

,(b*9b % CORE)

BRICK 4ND WLLlPd’~

(EVTECTiC CORE)

’ ‘\

‘\

FIG. 3. Comparison between previous data and present results.

568 ACTA METALLURGICA, VOL. 9, 1961

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*h concentration 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 self- diffusion 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

coJ&enta. ometimes referred to as partial chemical diffusion

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 YA 6 log Yn

6 log NA = S log NB

the interdiffusion coefficient may therefore be ex- pressed 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 aluminium- zinc system using the form:

b(X) = (X&* + X,DA*)m

where B(X) is the interdiffusion coefficient at com- position (X) and where m is the thermodynamic factor :

i

6 1% YA 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: INTERDIFFUSION IN Al-Cu SOLID SOLUTIONS 569

Mr. M. A. Reynolds and Mr. J. P. Bates for assistance 8. H. BAKER and R. A. HINE, Aluminium Laboratories Ltd.,

with the experimental work and chemical analyses, Banbury, unpublished work.

9. J. E. HILLI~RD, B. L. AVERBACH and M. COHEN, Acta respectively. The author also thanks Aluminium Met. 7, 86 (1959).

Laboratories Limited, Banbury for permission to 10. A. BEERWALD, 2. Electmchem. 45, ‘793 (1939). 11. T. FEDERIGHI, Phil. Mug. 4, 502 (1959).

publish this paper. 12. J. J. SPOKAS and C. P. SLIGHTER, Phys. Rev. 113, 1462

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