A calorimetric determination of precipitate interfacial energies in two AlCu alloys

A CALORIMETRIC

DETERMINATION OF PRECIPITATE IN TWO Al-Cu ALLOYS* J. D. BOYDt

and

INTERFACIAL

ENERGIES

It. B. NICHOLSONj

An isothermal calorimeter has been used to determine the heat evolution during coarsening of the 0” and 0’ precipitates in an Al-4 o/0 Cu and an Al-4 o/oCu-0.1 0/o Cd alloy. The results can be correlated with the metallographic changes observed in the two alloys. The values of the mean specific interfacial enand 530 thalpy, FE, obtained are as follows: 1530 ergs cm-e (0’ in Al-Cu), 250 ergs om-2 (8’ in Al-Cu-Cd) ergs cm-2 maximum (0” in Al-Cu). The relative magnitudes of these figures are shown to be in good accord with the known precipitation and coarsening characteristics of the two alloys. However the absolute values are difficult to interpret in terms of the specific interfacial enthalpies of the two types of interface existing on the disc-shaped precipitates. DETERMINATION

CALORIMETRIQUE PRECIPITES

DES

DANS

DEUX

ENERGIES

INTERFACIALES

ALLIAGES

Al-Cu

DES

Un calorimbtre isotherme a BtB utilis6 pour determiner 1’6volution calorifique au tours du grossissement des pr&ipit&s 0’ et 0” dans les alliages Al-4% Cu et Al-4% Cu-1 yc Cd. Les rbsultats peuvent &re relies aux variations m&allographiques observ6es dans les deux alliages. Les valeurs de l’enthalpie interfaciale 1530 ergs cm-2 (0’ dans Al-Cu), 250 ergs cm-2 spbcifique moyenne 7~ obtenues sont les suivantes: (8’ dans Al-Cu-Cd) et 530 ergs cme2 maximum (8” dans Al-Cu). Les auteurs montrent que les amplitudes relatives de ces valeurs sont en bon accord avec les caract6ristiques de grossissement et de pr6cipitation connues pour les deux alliages. Cependant les valeurs absolues sont difficiles B interpreter St l’aide des enthalpies interfaciales specifiques des deux types d’interfaces existant sur les pr&ipit&+ en forme de disques. EINE

KALORIMETRISCHE BES’II;MMUNG DER GRENZFLACHENENERGIE AUSSCHEIDUNGEN IN ZWEI Al-Cu.LEGIERUNGEN

VON

Die WBrmeentwicklung w&hrend des VergrGberungsprozesses van fl”- und 0’-Ausscheidungen in den Legierungen Al4 ‘A Cu und Al-4 % Cu-0,l % Cd wurde mit einem isothermen Kalorimeter gemessen. Ein Zusammenhang zwischen diesan Ergebnissen und den metallographischen Veriinderungen in den beiden Legierungen konnte gefunden werden. Die gemessenen Werte der mittleren spezifischen Grenzfl&chenenthalpie yB sind: 1530 erg/cm2 (8’ in Al-Cu), 250 erg/cm2 (8’ in Al-Cu-Cd) und 530 erg/cm2 (MC&mum, 0” in Al-Cu). Die relativen Werte dieser Grenzfliiohenenthalpien sind in guter tybereinstimmung mit den bekannten Ausscheidungsund VergrGberungseigenschaften der beiden Legierungen. Die Absolutwerte kiinnen jedoch nur sehr schwer anhand der speziellen Grenzfliichenenthalpien der beiden, an den scheibenfi%migen Ausscheidungen existierenden GrenzflBchentypen interpretiert werden.

1. INTRODUCTION

The physical characteristics play an important metallurgy(l)

but it is only recently

be quantitatively specific

growth,

evaluated.

fracture,

One major parameter is

free

to theories

in the other, the specific interfacial

to

energy,

yF,

which

of recrystallization,

precipitate

nucleation

is

grain

and growth

and the strength of dispersed phase alloys. While indirect,

a number

have been developed

boundaries twin

of techniques,

in single phase

boundaries,c2)

there

both

direct

for measuring

materials,

and

e.g. grain or in

obtaining absolute values of yp for boundaries between

solution

the specific interfacial

enthalpy,

precipitates

Al-Cu

in

two

obtained

indirectly

nucleation(3,4) or particle

coarsening@-*)

but direct measurements

are experimentally

* Received February 5, 1971. This work was carried out at the Department of Metallurgy, University of Cambridge, England. Battelle Memorial Institute, t Metal Science Group, Columbus, Ohio. 2 Department of Metallurgy, University of Manchester, Manchester, England. ACTA

METALLURGICA,

VOL.

19, OCTOBER

1971

which

was based on one previously employed

by ,&strom(11J2)

to measure grain boundary

enthalpies,

and involved

the evolution of heat accompanying coarsening (“Ostwald ripening”) and change in interfacial

An independent metallographic study and conventional Lifshitz-Wagner analysis(13J4) of the

experiments difficult.

of

The technique

precipitate

by

one

contained a small addition of cadmium.

area.

been

yH, of the 0’ and 0”

alloys,

values

have

con-

This paper reports another calorimetric investigation in which an attempt was made to measure directly

relating this to the concomitant

yp

yH was

of alloys

(and hence varying inter-

when one phase is finely dispersed in the other. Some of

enthalpy,

calorimetry

with

effect),@)

facial areas) of two phases.(l’J)

measuring

material particularly

from

taining varying dispersions

yF for

has been less progress

different phases in a multi-phase

calculated

in one,

from the change in solubility

change in particle size (the Gibbs-Thomson

that techniques

to enable these characteristics

interfacial

fundamental

yF was calculated

role in many aspects of physical

have been developed the

Only two major papers exist in the literature:

of solid state interfaces

coarsening of the same precipitates in the same alloys was made during the course of this work and the results are given in another paper.(*) The present work has

the

evaluating necessary

1101

advantage

of

the interfacial

being

a direct

energy

for the coarsening

method

of

so that it is not

process

to follow

any

ACTA

1 II’_”

METALLURGICA,

particular law of coarsening (in fact the 0’ precipitate does not coarsen in accord with the Lifshitz-Wagner analysis’s)). On the other hand the experimental f~fficulties are much greater than in indirect methods. lt is well known that when precipitation from solid solution is complete, the precipitates coarsen such that their interfacial area decreases and their volume fraction is nearly constant. In fact the volume fraction increases slightly as a result of the GibbsThomson effect already mentioned. Thus, during ~oa~ening t,here is an evolntion of heat & = AH,I’,

- yH&

VOL.

19,

IO101

10101 t

Peripheral

t

r.OOll

1~001

n

~~~~~/_____

/__

-_lhj-

(1)

where & is the rate of heat evolution, AH, is the heat of solution of the precipitate while p+, and 8, are respectively the algebraic rates of change of the volume fraction and interfacial area of preoipitate per unit volume of alloy. Ideally the term AH,V, is neg~~bly small and the whole of the heat of evolution is due to the change in interfacial area whence the calculation of yli is straightforward. Alternatively a correction can be made if V,, is either measured or calculated from the rate of change of particle size via the Gibbs-Thomson equation assuming a value for specific interfacial free energy, yF. Clearly this procedure becomes less reliable as AHSvV becomes comparable in magnitude with y HA e. Aluminium-copper alloys are well-suited for experiments of this type because the volume fraction of precipitate is q&e large and exists in a finely dispersed form. In addition there is strong indirect evidence that the trace addit,ion of Cd causes a substantial change in the interfaeial energy so that experiments on alloys with and without Cd additions provide a useful check on the experimental method. The geometry of the 8” and 0’ precipitate are illustrated in Fig. 1 together wit’h the parameters used in this paper.

1971

__

D _._-..

-,

K=D/h

FIG. 1. The morphology

of 0” and 13’and definition of parameters wed in this paper.

measure a heat flow of 0.5 cal/hr with an accuracy of & 10 per cent. The change in interfacial area during coarsening was determined by transmission electron metallo~aphy. The electron microscopy specimens were prepared by cutting 0.3 mm thick slices from the calorimeter specimens by means of a spark-erosion machine, cutting 2.3 mm diameter discs from the slices, and thinning the discs by a 2-stage jetting and eleotropolishing process. (MJ’) True particle size distributions were obtained by measuring the diameter of particles viewed edge-on as in Fig. 2. When possible, measurements were made on dark-field micrographs taken using a precipitate reflection. Foil thicknesses were determined by me~uring the proje&ed widths of slip TABLE

.-.

Alloy 1 Alloy 2

1. Composition of alloys (wt. %)

cu

Ft?

3.95 4.00

0.0035 0.004 -.~-._

Cd ox

2. EXPERIMENTAL The material was supplied in the form of extruded rod.* The compositions and impurity contents of the alloys used are given in Table 1. ~ylind~cal specimens 2 in. long x 0.5 in. diameter were machined directly from the as-extruded rod. All specimens were given a solution treatment of 4 hr at 525% and quenched into wat~erat 20°C. An isothermal calorimeter, the construction of which has been described elsewhere,05) was used to measure the heat evolution during precipitation and coarsening as a continuous function of ageing time. The sensitivity of the calorimeter was sufficient to

* We are grateful Research Labor&xies, of this material.

to the British Aluminium Company Gerrsrd’s Cross, England for t,he supply

FIQ. 3. At-4%

Cu aged 20 hr at, 240-C, dark-fkkl micrograph,; = (002)0,.

BOYD

AKD NICHOLSOX:

INTERFACIAL

ENERGIES

IS

TWO

Al-Cu

ALLOYS

1103

traces, or the projected widths of precipitates that intersected both surfaces of the foil.(17,18) In order to obtain the true particle size distribution, it was necessary to correct the observed dist~bution for the bias produced by particles intersecting the foil surface. A typical corrected particle size distribution for 8’ is shown in Fig. 3. Hilliard(*9) has given a thorough discussion of the systematic errors that can arise in quantitative transmission microscopy, and the metallographic methods employed in the present work were based on his results.* A complete description of the correction procedure is given elsewhere(m) and an almost identical procedure has been published independently by Crompton et aZ.@l) 3. REStJLTS

3.1 6’ in Al-Cu The interfacial enthalpy yH for 8’ was determined by rne~u~g the heat evolution during ooaraen~g at 240°C. At this temperature 0’ nucleates directly from the K solid solution. Figure 4 shows the heat evolution as a function of ageing time t at 240°C. The data represent the results of 5 independent experiments, and the curve of best fit has been drawn through the experimental points. There is an initial rapid rate of heat evolution up to an ageing time, t = 8 hr due to precipitate formation, followed by a slow rate of heat evolution during coarsening until t = 20 hr when the reaction becomes too slow to detect. It is useful to compare this calorimeter result with the metallogra,phic study of 13’coarsening carried out

Ageing time, FIG.

ht

4. Rate of heat evolution at 240°C for solution treated and quenched specimens of Al-4 % Cu.

independently.@) The results are reproduced in Fig. 5 as the corrected mean particle diameter, D, plotted as ( D)3 against t. A tl@ law is approx~a~ly obeyed up to t cr’ 20 hr although coarsening does not appear to follow the Lifshitz-Wagner model.@) After t N 20 hr there is a sharp reduction in the coarsening rate. The metallo~ap~c results are thus in excellent agreement with the heat evolution measurements. There is

-

sot

-

-

4oc

3oc

B ‘0 x % _

200

% ‘5

-

-

1

100

FIG. 3. Distribution of 8’ diameters for Al4% 20 hr at 240°C.

Cu aged

* It should be noted, however, that there is an error in Hilliard’s paper. His equation (34) is correct but in the subsequent paragraph the expression for the number of particles of m&mum diameter should read: N(D)n-d,,, Ad = N(d) Ad/t.

x 0

I

IO

I 20

I 30

Ageing time,

1

40

hr

FIG. 5. Coarsening kinetics of ‘@ in Al-4% Al-4% Cu-0.1 o/oCd aged in 240°C.

Cu and

ACTA

1104

initially a large evolution formation

of

continues

8’

METALLURGICA,

of heat associated

from

solid

solution.

with the

This

until t e 8 hr when precipitation

plete and coarsening evolution

of heat

begins.

due

change

until

t e 20 hr when the sharp reduction in coarsening rate shown in Fig. 5 is clearly related to the cessation heat evolution As

(l),

the

to

the

particle

calculation size

of

A,

theoretical

e.g. of

where the contribution

although

much

(2) were

value calculated

from the

phase diagram(24) by a factor of about 5.

after electropolishing

of

stand proud of the

causing

particles

with

outside the foil to have anomalously large there is probably a systematic error in a

sizes ;

has

longer lost

calculated

than

whereas equation

(2) assumes perfect

All these errors would tend measured values of V,. An attempt magnitude

particle

size distribution

calculating number

to increase the to estimate the

of the first, error was made by determing from

V, by the method

of

particles

distribution

was

an oxide

size interval particularly

of

at

the small

factor of 2-3. lead to a large discrepancy size distributions particle

sizes (Fig. 3).

third moment

skewed towards

Hence

large

when calculating

of this distribution,

tail of the distribution

D could

in V, is that the particle

are strongly

the

the large diameter

is dominant,

and any error in

this tail will result in a very large error in Vv. Measurement)s of 0” particles view.

The

described

0” particles

later reinforce

this

are an order of magnitude

smaller than 8’ so that the problem of intersection with the foil surface is correspondingly reduced. In addition Gaussian. in every values.

the

size

distributions

are

more

nearly

The measured volume fractions for 0” were case within

20 per cent of the theoretical

for a

the

period

of the

calorimetric

parameter

A,

was against

tW3 in Fig. 6. The total beat evolved in the coarsening period t = 10-16 hr is 6.0 Cal/g mole, and the decrease in interfacial

area AA,

is 1.6 x lo4 cm-i.

Before using these figures to determine yH, we must ascertain the magnitude of the volume fraction change (1).

Because

of the inaccuracy

V, experimentally,

obtain p’, by measurement.

in

it was not possible to

Therefore the increase in V,

which takes place during coarsening must be estimated from the generalised

Gibbs-Thomson

CD = co exp

and

particle sizes but VUwas still found to be too high by a The reason why these errors in measuring

evidence

(3) and is plotted

a

due to Schei1.(25) The

in each

reduced,

replica

is other

in

for a given

The

determining

the

particles are slightly lens shaped and the periphery is often faceted

are given

from equation

parallel to the direction

discs.

there

times constant

coherency.(s6)

term in equation

beam;

to

when the flat interface of the precipitate

arising from measuring particles which are not exactly of the electron

ageing

These are effectively

measurements

centres

interface

change in the value of a for 8’ after ageing times very

from equation

appears to be due to a number

of the peripheral

of rf for various

The values of V, calculated

surface

2Rv,*

A, (which is only ~5 per cent of the total) is ignored and V,* = 0.046 for ageing at 240”C.(24) The measured

defined as the ratio of the diameter to the thickness.

causes : the 0’ particles frequently

A,, [the

(l)] using the formula:

D

precipitate where R is the mean aspect ratio of the precipitate

of D and the

value of Vu, I’,*, in calculating

Table 2.

This discrepancy

It is possible to minimise the

for

distributions,

for our

error in the measured

quantity required for equation

values

higher than the theoretical

strong evidence

error by using only the first moment

A,=-

using the expression:

metastable

provides

of a systematic

of

Fig. 3, were used to calculate the volume fraction precipitate

This comparison

noted on Fig. 4.

a preliminary

equation

1971

particle size distribution.

is com-

in A,

19,

interpretation

effect

There is then a small

to the

VOL.

c

where cD is the equilibrium

equation :cz7)

4y(Fp’Jf RTD ,

)

solubility

adjacent

to a

disc shaped particle of diameter D, c,, is the solubility adjacent

to an infinitely

large particle, y(F’) is the free

energy of the peripheral

interface

of the 8’ particle

(Fig. l), M is the molar volume of the precipitate and RT

has its usual meaning.

bound for the effect,

To obtain

phase

an upper

we take y$!‘) = 2000 ergs cm-s

giving a change of V, =: 5 x 10-5.

Then, if AH, =

7.3 kcal/g mole of copper, (24) the total heat evolution TABLE 2.

8”

Variation of

mean aspect ratio, with ageing time

in AI-Cu

Time at 165°C (hr)

0’ in Al-Cu

K,

of

8’ in Al-Cu-Cd

Time at 240°C

Time at 240°C (hr)

%?

(hr)

48

24

8

45

8

240

26

41 20 750

45 42 -lo*

49 22

* Taken from Weatherly

precipitates

z

and Kicholson.‘2B’

x 40 t:

BOYD

NICHOLSOX:

AND

INTERFACIAL

EXERGIES

addition

IN

(~0.1

wt.%)

the precipitation Specifically, promotes and

Al-Cu

it was found the

numerous

8’

that

particles

the

are

alters

alloys.(28-30)

trace

element

smaller

of 8”,

and

more

at all stages of ageing.

microscope

phenomenon’20)

significantly

of Al-Cu

of 0’ at the expense

in the ternary

electron

1105

ALLOYS

of cadmium

characteristics

the nucleation

that

recent

TWO

investigation

of

-4 this

has verified these results, and has also

shown that the trace addition causes the 19’coarsening rate

to

be

support

considerably

the suggestion

X-ray

evidence,

that

precipitate-matrix

reduced.@)

These

results

of Silcock

et aZ.,(30) based on

cadmium

segregates

interface

and reduces

to

the

the inter-

facial energy of 0’. In order to investigate

this trace-addition

effect,

yH for 8’ in the ternary alloy was measured directly by calorimetry,

and compared

binary alloy given above. identical 0

II I5

I IO

I

hr I 50

20

t,

during ageing of the ternary

240°C is shown in Fig. 7. The heat’ evolution

-l/3

-'/3 t,

to that discussed in detail previously.

heat evolution

I 0.3

I 0.4

0.5

with t’he results for the

The procedure adopted

was

The

alloy at curve for

I

hr

FIG. 6. Time variation of the interfacial area of 0’ in Al-4 % Cu and Al-4 % Cu-0.1 % Cd aged at 240°C.

from

this source

during

the period

t = 10-16 hr is

0.15 Cal/g mole which is only about 2 per cent of the measured

heat of coarsening

and

therefore

can

be

neglected. Thus

we can finally

evolution

equate

the

measured

heat

-Al-4%Cu-O.I%Cd

and, if the average density of the alloy is taken to be and

2.78 g cm-3

the

average

molecular

28.4 g/g mole, the average interfacial

weight

enthalpy,

Al -4%Cu

---

with the measured change in interfacial area is

yH, is

1530 ergs cm-2 (Table 3). The heat of formation

of 0’ from the supersaturated

solid solution, calorimetry precipitate

AH, can also be determined from the results, The total heat evolved during the

formation

and AH, is calculated to be 8.5

x

previously

been

4

lo3 Cal/g mole of Cu.

3.2 8’ in Al-Cu-Cd It, has

e~;Oa--=---rz_d_ 2

period is 134 Cal/g mole of alloy,

reported

that

a trace

6

6

IO

12

Ageing time,

14

16

18

Fro. 7. Rate of heat evolution at 240°C for a solutiontreated and quenched specimens of Al-4 % Cu-0.1 % Cd (the average heat-evolution curve for Al-4% Cu from Fig. 4 is also shown for comparison).

TABLE 3. Heat evolution measurements

Precipitate

Time interval,t (hr)

Change in interfacial area A& (cm-‘)

8’ in Al-Cu 0’ in Al-Cu-Cd 8” in Al-Cu

lo-16 lo-16 30-40

1.6 x lo4 4.8 x 104 3.0 x 104

20

hr

Heat evolved (cal g mole-l)

Correction for change in ?‘v (cal g mole-l) -

3.9

?

Average interfacial snthalpy TB (ergs cmmz) 1530 250 530 (max)

ACTA

1106

METALLURGICA,

VOL.

Ageing time, FIG.

8.

Rate of heat evolution

19,

hr

at 165’C for as-solution-treated

the binary aIloy is also reproduced in Fig. 7 for comparison. The two curves are similar during the precipitate formation stage as would be expected. However, during coarsening the rate of heat evolution from the ternary alloy is less than from the binary alloy, and is virtually zero after 16 hr. The metallographic data (Fig. 5) shows that the coarsening behaviour of 8’ in Al-Cu-Cd is qualitatively similar to that of 0’ in AI-Cu but that D and ?i(D)3/?&are smaller in the ternary. The considerable scatter in the data for the ternary is due to the fact that there is a nonuniform distribution of particle sizes up to 20 hr ageing time. The total heat evolved in the interval t = IO-16 hr is 3.0 Cal/g mole; the change in interfacial area is larger than in the binary due to the smaller initial values of D and is equal to 4.8 x lo4 cm-l. The change in volume fraction again eon tributes a negligible amount to the heat evolution and hence the calculated value of yH is 250 ergs cm-2 (Table 3).

1971

specimens of _&l-4% Cu.

the Gibbs-Thomson effect is correspondingly more important and the change of volume fraction is approximately an order of magnitude higher. The precise evaluation of the Gibbs-Thomson equation, and hence the magnitude of the correction, is sensitive to the value chosen for y(Fp),for example if’y’,p) = 300 ergs cmV2, the change in V, is 3.7 x lo4 and the

3.3 8” in AI-Cu The 0” precipitate in the binary alloy was studied by measuring the heat evolution during ageing at 165’C when the rate of transformation to 6’ is negligible. The calorimetry results are given in Fig. 8 (2 specimens), and the metallographic results in Fig. 9. The param. eter A, was calculated directly from the measured particle size distributions, since the values of V, determined from equation (2) agreed well with the theoretical value. The total heat evolution in the interval t = 30-40 hr is 3.9 Cal/g mole. However because of the smaher size of the 8” particles compared with 8’ considered earlier,

I 40

Ageing time.

1 80

I

I20

hr

Fra. 9. Cortrsening kinetics of 8” in Al-l,% 165°C.

Cu aged at

BOYD

AND NICHOLSON:

INTERFACIAL

corresponding heat evolution is 1.0 Cal/g mole. lf a larger value of yp(P) is chosen (for example Boyd and Nicholson(*) calculated yp(P) = 1580 ergs cm-2 although this value is very sensitive to the calculated diffusivity), the change in V.,,accounts for virtually all the heat evolution and the technique becomes unworkable. ln view of this problem, it is only valid to quote an upper bound for the value of TH by neglecting the change in V, entirely. Then fR = 530 ergs cm2 (max) as shown in Table 3. 4. DISCUSSION

4.1 Heat of ~0~~~0~of 8’ The value of 8.5 x 103 Cal/g mole Cu is a measure of the heat of formation of 8’ from the supersaturated K solid solution, and must be numerically equal to the heat of solution of 8’ in K. This quantity will be referred to as the heat of solution of 8’, AHS, and should not be confused with the heat of formation of 8’ from its constituent elements AH,. An Arrhenius plot of the 8’ me&stable phase boundary given by Borelius et &.(24)yields a value of 7.3 x lo3 cal/g mole Cu for the heat of solution of 0’. The heats of solution of G.P. zones and 8” have been calculated from the metastable pha,se boundaries determined by Beton and Rollason,@l) and the heat of solution of 0 has been calculated from the equilibrium phase boundary given by Borelius et QJ.(~~)All of these values are assembled in Table 4, and it is seen that the value of AH, for 8’ determined in the present work by direct calorimetric measurement is in fair agreement with the value calculated from the phase diagram. In addition the complete set of values shows a sensible progression from the first metastable precipitate to the equilibrium phase. 4.2 Experimental

accuracy in the coarsening experiments

Direct calorimetric measurement is a valid technique for determining interfacial enthalpy only if equation (1) represents a complete heat balance for the system. Before going on to discuss our results (which give larger values of the interfacial enthalpy than might be expected) it is important to consider other possible sources of heat which could lead to an erroneous result. Initially we should note that the TABLE 4. He&s of solution, AH~, of procipitdes

--

Precipitate .__ G.P. zones t: 0 6

A& (k cd/g mole Cu) 5.4 ::: 2:;

in Al-Cu

Reference 33: Present work :pl

ENERGIES

IS

TWO

Al-Cu

ALLOYS

1107

exact correlation between the evolution of a detectable amount of heat and rates of coarsening determined metallographically in both alloys is strong evidence that this process is the major source of heat. However other possible processes that would give rise to a heat of reaction are : 1. a change in the volume fraction of precipitate; 2. a change in the composition of the precipitate Ieading to a change in volume fraction of precipitate during coarsening; 3. precipitation at grain boundaries ; 4. grain growth; 5. a change in the dislocation structure of the specimen ; 6. oxidation of the specimen. Silcock et al.(32) found that the equilibrium volume fraction V of 8’ is formed after 6 hr ageing at 240°C which is in excellent agreement with our estimate of S-10 hr. The good agreement between the metallographic and calorimetric measurements in the present work is further evidence that the equilibrium V was formed in each case before the heats of coarsening were measured. No significant trend in V during coarsening was noted which might have indicated a change in precipitate composition. However, as already pointed out, the aoeuracy of calculation of V was poor. There is no theoretical reason to expect a change in precipitate composition without a change in phase and the best experimental support for the neglect of this possibility is the sharp drop in the rate of heat evolution at the same time as the reduction in the rate of coarsening of 8’. If a change in composition was making a substantial contribution to the heat evolution, this would certainly be an unlikely coincidence. The grains of the as solution treated specimens were mostly equiaxed with a mean grain diameter of 230 p. This is a suflloiently coarse grain size to make the total grain boundary area about 0.5 per cent of the precipitate interfacial area and hence it is justifiable to neglect any heat effects produced by small amounts of grain growth. Equally the volume fraction of grain boundary 8 is so small that even were it all to be precipitated during the coarsening period (which is certainly not the case) it would provide a negligible contribution to the heat output. The heat effect resulting from the annihilation of a dislocation ia 8 x lo-l2 Cal/cm length of dislocation.(B) Thus a reduction in the dislocation density correspending to about 1Orocm cm--a during coarsening would be necessary to produce a significant contribution to the heat output. This change is far greater than

ACTA

11ox

METALLCRGICS,

the minimum that would be detected metallographitally but, in fact, no change was observed. The specimen chamber of the calorimeter was not surrounded by an inert atmosphere, but it is unlikely that there was any oxidation of the specimen. At temperatures below 3OO”C, oxidation of aluminum virtually ceases after a few hours, when a certain thickness of oxide has formed,(34) (i.e. a logarithmic oxidation law is obeyed). After the solution treatment at ,525, no further oxidation is expected at 240°C. Thus we conclude that the major part! of the measured heat evolut’ion does, in fact, result from the coarsening process and its concomitant change in volume fraction resulting from the operation of the Gibbs-Thomson effect.

Following the work of Beoker,(35) Turnbull,c3@ Brook@‘) and Van de Merwe,@JQ) it is possible to make eal~ulations of both the “chemical” and “geometrical” contributions to the enthalpies of solid state interfaces. Typically these give values in the range lo-200 ergs cmP2 for coherent interfaces where there is no geometrical ~ont,ribution and 1~1~ ergs crne2 for semi-coherent and non-coherent interfaces.c2Q’ These values seem reasonable when compared wit.h accepted figures for surface energies and grain boundary energies in pure metals and the few figures available for interfaces between dissimilar solids.(2,40’

interfacial

enthalpy

We now consider the experimental results in the light of the discussion on experimental accuracy and the theoretical values of interfacial enthalpy. First, the raw values of 1/H may be assessed semi-quantitatively. If the r&,&e values in Table 3 are examined, it is seen that the effect of Cd is to reduce the interfacial enthalpy of 8’ by a factor of about 6 to a value comparable to that measured for the 0” precipitate. This is excellent experimental con~rmation of the role of Cd in reducing the interfacial energy which is well established in the literature on Al-Cu alloys.~28~Q)In addition, the closeness of the values of 1/H for 19’(Cd) and 0” is in good accord with their similar nucleation characteristics. It was mentioned earIier that the addition of Cd to Al-Cu alloys more or less eliminates the 0” stage and the modified 8’ precipitate is nucleated in as fine a dispersion as 8” in the pure alloy. Thus the relative values of qH give confidence that the calorimetric results are reliable and sensible and

VOL.

19,

19il

suggest that a more detailed comparison of theory and experiment is justified. In order to make this comparison, it is necessary to re-calculate the values of the average interfacial ent,halpy in terms of the specific interfaeial enthalpies of the peripheral and habit plane interfaces y>r’ and #) respectively. If the precipitates have a shape determined by the Wulff theorem, i.e. the total int.erfacial energy is a minimum, then yg’ = (~~3)~~ and yfl”) = $7,. The calculated values for the 8’ precipitates are given in Table 5, This exercise is not worth doing for 0” because of the unreliability of the values of yN mentioned earlier. Specific interfacial enthalpies, ykP) and yFJ, for the 0’ precipitate caloultlted from yR .~ ~(Hf y;pl”’ ia YE PrecipittEte {ergs omm2) (ergs CX-~) (ergs w-2) __~_ ,--21,620 510 0’ (Al-&) 1530 3500 83 8’ (Al-Cu-Cd) 250 ~.

TABLE

5.

These values are clearly very much larger than those suggested in Section 4.3 : by about an order of magnitude in the ease of ytf”’ and at least a factsor of 2 for GO’ If the assumption concerning the Wulff theorem YH is incorrect and the aspect ratio is affected by other factors, e.g. elastic strainenergy’s) or barriers to particle growth,(*l) the values of yelp) and yflH) will tend towards yhl. Boyd and Nicholson(s) have shown that the observed value of _fpmay depart substantially from that predicted by the Wulff theorem for a strained coherent precipitat#e as the particle size increases. The calculation is more difficult to make for EL partially coherent precipitate like i3’ but is certainly possible that g is strongly affected by elastic strains and this would reduce the values of ygj to a more sensible range. Some support, for this suggestion comes from the observation of Weatherly and Nicholson(26)(repe at ed in Table 2) that R changes from -42 to N 10 when the habit plane int,erface loses coherency. Nevertheless even the values of yH are still substantially higher than t’he values of yp for precipitatematrix interfaces quoted in the literature.(2*4Q) The discrepancy can hardly be accounted for by the entropic contribution to the enthalpy. The entropy of solid-vacuum and solid-solid interfaces is usually given as 0.5-1.0 ergs cm-2 “K-l (11~12*42*p3) so that at the t)emperatures of interest (400-5OO”K), the difference between the free energy and the enthalpy should only be 200400 ergs cm-2. Some measure of the expected interfacial free energy for 0’ can be obtained from its nucleation characteristics since the undercooling required for

BOYD

AND

homogeneous

nucleation

of a precipitate

on y,.(ss,ss)

Tw o cases

where these

reasonably well established y’ phase in Ni-Al interfacial

are the precipitation

and Co in Cu-Co.

free

energy

the undercooling

is ~20

the

formed.(46)

while

below

Therefore

homogeneous

In A1-Cu, the 8’

homogeneously

8” is

required

for

is at least 130°C and hence

the value of yE‘ is likely to be substantially 200 ergs cm-2.

above

this temperature

the undercooling

nucleation

and

nucleation

figures for Cu-Co

ergs cm-2 and -80°C.(41) cannot be nucleated

of the

ergs cm-2 (‘3~

required for homogeneous

0” solvus,

are

In the former the

is about 30”C.(45) The corresponding are ~200 precipitate

is dependent quantities

more than

This argument shows that although the

measured value of yIi = 1530 ergs cm-2 seems high, it may still be a fair indication present with theoretical tested

and

infancy.

of the real value.

calculations

experimental

At

still largely un-

measurements

in

their

it is not fruitful to speculate further. 5. CONCLUSIONS

1. An evolution of Al-Cu cipitate

alloys

of heat detected has been

coarsening

during the ageing

correlated

with the pre-

process.

2. By making certain assumptions

the evolution

of

heat can be used to calculate values of TH, the specific interfacial

enthalpy

of the precipitates.

The results

are 1530 ergs cm-2 for 8’ in Al-Cu, 250 ergs cm-2 for 8’ in Al-Cu-Cd

and 530 ergs cm-2 (max) for 0” in Al-Cu.

3. Qualitatively with the hypothesis

these results are in good agreement that Cd reduces the interfacial en-

ergy of 8’ and with the similar nucleation tics of 0” in Al-Cu

and the modified

4. In terms of absolute are higher than expected discrepancy

magnitude,

characteris-

8’ in Al-Cu-Cd. all the results

and some suggestions on this

have been made. ACKNOWLEDGEMENTS

One of the authors (J. D. B.) is grateful to the Master and Fellows of Churchill College, for financial support in the form of a research studentship. REFERENCES 1. R. C. GIFKINS (editor), Interfaces. Butterworths (1969). 2. E. D. HONDROS,Interfaces, edited by R. C. GIFKINS, p. 17. Butterworths (1967).3. J. C. FISHER, J. H. HOLLOMONand D. TURNBULL, Trans. metall. Sot. A.I.M.E. 185,691 (1949).

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