- Email: [email protected]
On the decay of vacancies in aluminium-copper alloys measured by an internal friction method
ON THE DECAY OF VACANCIES IN ALUMINIUM-COPPER ALLOYS MEASURED BY AN INTERNAL FRICTION METHO.D* K. M. ENTWISTLEt
Changes of internal friction at low frequenciesduring isothermal ageing at 73°C of Al-4 wt.% copper wires are interpreted in terms of a migrating internal friction peak due to stress-induced ordering of copper atoms. If the vacancy decay follows a second order rate curve, it is deduced that the relaxation time z will vary with ageing time f as t = za + Bt. Where fi is a constant and to is the as-quenched value oft. This relation fits the 73°C data fairly well but the deduced value oft, exceeds that expected from resistivity data on pure aluminium by two orders of magnitude, which may be explained by inefficient quenching. The existence of interaction between indium atoms and vacancies is deduced from preliminary experiments in which indium addition to an AlA wt.% copper alloy modifies the decrement time curve following quenching. UTILISATION
DE MESURES DE FRICTION INTERNE DES LACUNES DANS LES ALLIAGES
POUR L’ETUDE DE LA DISPARITION CUIVRE - ALUMINIUM
Les auteurs ont Btudie les modifications de friction interne a basse frtquence qui se manifestent pendant le vieillissement isotherme a 73°C de fils de cuivre a 4% en poids d’A1, et attribuent ces modifications au deplacement dun pit de friction interne, d&placement du a un rearrangement des atomes de cuivre. Si la disparition des lacunes ob6it a une loi du second ordre, les auteurs deduisent que le temps de relaxation 7 variera en fonction du temps suivant la loi: 7 = Ta + Br. oti l3 est une constante, et oh T. est la valeur de r immediatement apres la trempe. Cette relation explique dune mani&re satisfaisante les faits experimentaux obtenus a 73”C, mais la valeur de T, qu’elle perment de d&luire est sup&ieure (de deux ordres de grandeur) a celle que donnent des mesures de resistivite sur aluminium pur; cette discordance peut s’expliquer par une trempe incompl8te. Partant d’experiences preliminaires au tours desquelles ils ont observe qu’une addition d’indium a un alliage de cuivre a 4% en poids d’Al modifiait la courbe d’evolution du decrement aprbs trempe, les auteurs concluent & l’existence dune interaction entre les atomes d’indium et les lacunes. UBER
DAS
AUSI-IEILEN
VON LEERSTELLEN IN ALUMINIUM-KUPFER-LEGIERUNGEN, GEMESSEN DURCH DIE INNERE REIBUNG
Veriinderungen der inneren Reibung bei niedrigen Frequenzen w&rend isothermen Alterns bei 73°C von Drlhten aus Al-4 Gew. % Cu werden zuriickgefuhrt auf ein wanderndes Maximum der inneren Reibung, dem spannungsbedingte Ordnung der Kupferatome zugrundeliegt. Wenn das Ausheilen der Leerstellen einer Reaktion zweiter Ordnung folgt, muB die Relaxationszeit 7 von der Alterungszeit t abhtingen gemiil3 7 = Za + gr. wo l3 eine Konstante und 7a der Wert von r unmittelbar nach dem _4bschrecken ist. Diese Beziehung gibt die Messungen bei 73°C ziemlich gut wieder; der daraus hergeleitete Wert von 7, ist jedoch zwei GriiBenordnungen hiiher, als man nach Widerstandsmessungen an reinem Aluminium erwarten wiirde. Das erklilrt sich vielleicht durch unvollkommenes Abschrecken. Die Existenz einer Wechselwirkung zwischen Indium-atomen und Leerstellen wird hergeleitet aus vorlaufigen Experimenten, in denen die Hinzuftigung von Indium zu einer Legierung Al-4 Gew.% Cu die Zeitabhilngigkeit des Dekrements nach Abschrecken andert.
INTRODUCTION The interpretation of the results of an investigation of the effect of a third element, specifically indium or magnesium, on the rate of quench-age hardening of an aluminium-copper alloy required more precise information than was currently available on the decay _~~. __--* Paper 6 presented
at the Conference on Internal Friction held on 10 and 11 July, 1961, at Cornell University. t Department of Metallurgy, University of Manchester, Manchester 13. ACTA METALLURGICA,
VOL. 10, APRIL
of the concentration of quenched-in vacancies in these alloys. There follows an account of some preliminary experiments which were carried out to explore the proposal that these data might be obtained by internal friction measurements. EXPERIMENTAL
OBSERVATIONS
ON Al-4
wt.%
Cu
Berry and Nowick(1,2) have reported that quenched and reverted Al-4 wt.% copper wires show an internal friction peak at about 185°C for a vibration frequency
1962
12861
ENTWISTLE: PAPER 6 OF INTERNAL
of 2 c/s. They put forward convincing evidence that this peak arises from the stress-induced ordering of the copper atoms in solution in the al~~ium lattice. Freshly-quenched wires which were rapidly heated to temperatures below 185°C gave initial damping values above the curve for the reverted material. These observations are confirmed by our results shown in Fig. 1.
5min
0
50
of 223’C
100 Temp.,
150
200
YZ
FIG. 1. o the decrement-temperaturecurve of 0.035 in. diameter Al-4 wt. % Cu wire, water quenched from 535OC, heated over 2 min to 223’C, left for 5 min at 223°C and then cooled at SO”C/hr. x the damping of freshly quenched wires approximately four minutes after attaining the indicated temperature.
The internal friction measurements were made on wires 0.035 in. (0.89 mm) diameter by a conventional torsion pendulum in which the only novel feature was the design of the specimen; this had a-in. diameter ends cast on in a eutectic AI-Cu alloy giving a reproducible and loss-free grip without the need to deform the ends of the wire plastically. The full curve in Fig. 1 is the damping measured at 0.57 c/s during cooling from 223’C of an Al-4 wt.% Cu specimen which had been quenched from 535”C, heated rapidly to 223°C and left there for about 5 min before cooling. The cooling rate through the damping peak was about SO”C/hr. The crosses represent the damping values measured after about 4 min at the indicated temperature; prior to this the specimens bad been quenched from 535”C, aged for about 4 mm at room temperature and heated over about 1 min to the temperature of measurement. Berry suggests that the high damping of the freshlyquenched wires is explained by a reduction of the relaxation time of the copper atoms by the quenched-in concentration of vacancies. This depresses the damping peak temperature for a given vibration frequency. As the vacancy concentration decays to its equilibrium value, the relaxation time will rise and the peak will migrate upwards along the temperature axis. If this
FRICTION
281
CONPRRENCE
is so then isothermal measurement of internal friction as a function of time at a temperature between those of the as-quenched peak and the equ~ib~um peak should show a maximum at the instant at which the peak temperature passes through the temperature of measurement. Since the peak is of anelastic origin, the time to maximum damping in such an experiment will be longer for lower frequencies of vibration, therefore, in principle, isothermal measurements of internal friction at a number of different frequencies should reveal the variation of relaxation time, and therefore of vacancy concentration, during ageing. Information of this kind as been obtained for silver-zinc solid solutions by Nowick and Sladek(3), and by Roswell and Nowick’4) using anelastic creep recovery. In the present alloy system the relaxation strength (2.5~ 10W3) makes the anelastic strains too small to allow accurate measurements by this method; it is for this reason that the internal friction method was explored. Figure 2 shows the result of an unsuccessful attempt to detect a peak in the decrement-time curve for Al-4 wt.% Cu specimens quenched from 535°C and aged 3
\
l
x 0
i
0.265Elstc 0.570 c/set 1 quenched
535.C
0 104
oqemg me.
mm
PIG. 2. The variation of decrement with time at 73% of Al-4 wt.% Cu wires quenched from 535°C. The wires rested at 20°C for about 5 min after quenching and before heating over about 1 mm to 73°C. ‘at 73°C. The specimens were at room tempera~re
for about 4 min after quenching. The damping is seen to fall with time. Only the time-dependent component is shown; the background damping (between 0.7 and 4.0~ 10m3dependent on frequency) which the specimen attained after about 1000 min has been subtracted from the measured values. The three curves shown were measured each at a different frequency (0.265,0.57 and 1.80 c/s) and it is clear that the damping of the specimen at a given instant always increases as the frequency falls. This behaviour is consistent with the existence
ACTA
288
METALLURGICA.
of the ordering peak at a temperature which is always above the temperature of measurement, either because it migrates very rapidly or because the peak in the as-quenched state is above 73°C. We enquire more closely into these possibilities in the discussion. The effect of ageing temperature on the decrementtime curve is shown in Fig. 3 which gives results for 52, 73 and 111°C. Again no maximum is evident. The full lines in Fig. 3 are theoretical curves which will be discussed later.
VOL. IO,1962
K=&exp
--& [
B1
where E, is the jump enthalpy. K, will be a constant if the vacancies make a fixed number of jumps in their lifetime at a given vacancy concentration. The resistivity data for aluminium were made at temperatures below those of the present measurements; we therefore use equation (2) to extrapolate Federighi’s 0°C data to higher temperatures and assume that K,, does not change. The extrapolation requires a knowledge of E,, which varies with quenching temperature. We take here a value of 0.46 eV which is close to Panseri and Federighi’s value for a quenching temperature of 520°C. If this is combined with 0.79 eV for the formation enthalpy of vacancies, E,, then E,+E, = 1.25 eV which agrees well with 1.22 f 0.06 eV measured by Berry for the activation energy for stressinduced migration of copper in aluminium with an equilibrium concentration of vacancies. This agreement would be expected if copper-vacancy interaction is small. If t’ is the time at which C/C, = Q at T = T,
FIG. 3. The effect of ageing temperature on the variation of decrement with time following quenching from 535°C. Frequency 0.57 c/s. The full lines are the calculated curves using equations (7) and (9) for temperatures of 52, 73 and 1ll’C; the curve showing the peak is that for 111°C.
then
t’=-.-=
1
1
-_
._
and
DISCUSSION It
is helpful to compute the expected damping behaviour of the quenched Al-Cu alloy on the assumption that the copper atoms have zero binding energy with vacancies so that the vacancy formation energy and jump rates are identical to those in pure aluminium. Panseri and Federighi’s (5)resistivity data on quenched aluminium were obtained under quenching conditions similar to those used in the present experiments. Their resistivity decay curves below lOO”C, together with those of de Sorbo and Turnbull@) for lower quenching temperatures, can be shown to follow a second order rate curve in the initial stages. This implies that the vacancy concentration C varies with time, t, as c=
G 1 + KCJ
(1)
where Cc is the concentration at t = 0 and K is a rate constant, which will vary with temperature, T,, as
where S, is the formation entropy (S,/kw1) and TQ is the quenching temperature. Now taking the measured value of t’ = 2.5 min at T, = 273°K for To = 793°K (= 520°C - the effective quenching temperature for an actual temperature of 535°C) we deduce &exp
2 0
= 1013.08min-l .
The relaxation time z for stress-induced ordering at any instant when the vacancy concentration is C is 1 -_= azvC
t
exp
dG, [ kT, 1
where AG,, the jump free energy = E,-TaS,. For the equilibrium concentration of vacancies temperature T,
I
at
ENTWIWLE:
PAPER 6 OF INTERNAL
1
(5)
from Berry’s measurements. We put the second order rate relation for vacancy decay in equation (4) and get the following relation giving t as a function of ageing time
-
I
+exp[ -&]exp[ = _ __ ~____~--~-___-___
t
1 +K,exp(+)exp[
-- +-] ..___
z=t,+K,exp
289
CONFERENCE
The table confirms that if the vacancy concentratiofi in the alloy equals that in similarly treated pure aluminium then a maximum in the decrement-time curve should be attained after about 9 min at any ageing temperature between 50 and 110°C. If this were the case it would have been detected in the present experiments. It should be noted that the approximately constant value of the time to peak damping in Table 1 1 results from the fact that tQ < - ; this means that cc)
-&]exp[-$Jr.
This equation can be simplified by introducing the relaxation time zg for the freshly quenched specimen.
then
FRICTION
(7)
This equation shows that dtldt is independent of T, and T,, except in so far as these affect K,. Peak damping will be attained when oz = 1 that is when 0
the calculated as-quenched peak temperature (-4°C) is always well below T,, but although an increase of T, increases the temperature difference between T, and the as-quenched peak, the more rapid peak migration at the higher temperature compensates for this togive conditions for peak damping in a time which is approximately constant. These considerations lead to the conclusion that the decrement-time curve will vary with T, only for values of T, near to the asquenched peak temperature. Turning now to the results of Fig. 2 we take the damping values at the three frequencies after ageing for 4 min at 73°C and fit through them a decrement frequency curve of the form 6 = 26,,
-
W-r
1 +Co2t2 Table 1 gives the computed times to peak damping using the vacancy data for aluminium in equation (8). The vacancy concentration at the peak, C,, is expressed in terms of C,, C, is also given in terms of the equilibrium concentration C,. Strictly, equation (1) cannot apply for long times since it predicts C = 0 at t + co rather than the equilibrium concentration C,; however Table 1 shows that C, is always at least 100 C, so equation (1) can be used with only small error. TABLE 1
~_
.__ 1
rim~~~n~ti~P~ -. __
?
/ Tq(sec)
1
9.13
92.3
10-6.24
0.0030
73
9.20
&
10-X60
0.0012
111
9.25
iii;
lo-!w
o.ooo25
___-
______ TQ = 793’K:
where 6,, = 4x 10-3, the estimated peak height of Fig. 1. The fit is shown in Fig. 4 and gives z= 1.115 sec. A repetition of the procedure for data after ageing
~_~ Ej = 0.46 eV; ;
-_
Ef = 0.79 eV;
.=:
FIG. 4. Decrement-frequency curves of a single relaxation time fitted through the measured damping values at three frequencies on quenched Al4 Cu wires. o Aged 4.min at 73°C; l Aged 40 min at 73’C. The lower value of the frequency of the fitted peak for 40 min ageing indicates that T rises as ageing proceeds.
ACTA METALLURGICA,
290
for 40 min gives t = 3.67 set, confirming that r rises during ageing as expected. If these two values oft lie on a line of the form given by equation (6) we find t = 0.83+0.072 t.
(10)
If, therefore, this treatment of the results is valid rQ is 0,83 set which is greater thani= 0.279. This 0 means that the as-quenched peak temperature is above the ageing temperature of 73°C (it is at 99°C if we assume E, = 0.46 eV) and therefore no peak would be evident’ at 73°C at frequencies above 1/0.83x 27~ = 0.19 c/s. Unfortunately, damping measurements at frequencies of this order must inevitably be timeconsuming. Using equation (10) we can calculate S as a function of time by substituting for t in equation (9). If also Ef , where Ej = 0.46 eV we assume zQvaries as exp __ I kT, I we can compute corresponding curves for other ageing temperatures. The results of such calculations are shown in Fig. 3 where the derived curves are compared with the measured values at 52, 73 and 111°C. The fit is good for the 73°C curve, confirming that the second order rate equation is a fair representation of the decay process. The agreement is fair at 52°C but is poor at 1ll”C, where a peak is predicted but not observed. It may be unfair to apply equation (1) at 111°C. It is instructive to compare the deduced relaxation times for the binary alloy at 73°C t = 0.83 + 0.072 t with that expected from the vacancy data for aluminium t = 0.0012 + 0.030 t. dtfdt is of the same order in the two cases, which implies a comparable number of vacancy jumps before annihilation. The extrapolated value of to for the binary alloy is longer than that expected from vacancy data on pure aluminium. This is most likely to be explained by the effective quenching temperature being below that at which the specimen was in fact solution treated; if I/r0 = 10X4e6see-l, E, = 0.79 eV and Ej = 0.46 eV we require a value of T4 = 390°C to explain the extrapolated value of zg. We can dismiss an alternative explanation of the high values of r, that they arise from vacancy decay during the period
Vol. 10, 1962
of about 5 min at room temperature immediately after quenching. If we use the fact, implied in equation (7) that dz/dt is independent of T,, together with an assumed value of Ef = 0.46 eV so that t~CoC/t730C = 16, then it is computed that ageing for 5 min at 20°C increases rat 73°C from 0.81 to 0.83 sec. Vacancy decay during 5 min at room temperature following quenching does not, therefore, cause a significant increase of relaxation time. It is claimed, in conclusion, therefore that Fig. 2 confirms Berry’s view that the temperature of the copper ordering peak is depressed by quenched-in vacancies. However, unambiguous vacancy data can be obtained from this effect only if the unstable peak is located experimentally, and the present exploratory measurements show that the required experimental conditions will not easily be attained. The as-quenched values of the relaxation time appear to be lower than those to be expected from the accepted value of the formation energy of vacancies in pure aluminium and this fact demands that vibration frequencies below 0.1 c/s will be required to detect the migrating peak. Under these experimental conditions the decrement values must be measured from a small fractional fall of vibration ampIitude, since only in this way can a sufficient number of points be recorded in the short interval before the peak passes through the temperature of measurement. MEASUREMENTS
ON AN Al-Cu-In SPECIMEN
Iridium, in concentrations of the order of 0.01 at.% reduces the rate of G.P. 1 zone formation in aluminium-copper alloys. A possible explanation of this is that indium-vacancy interaction reduces the concentration of vacancies in the vicinity of the zone-forming copper atoms. If th.is is so, then indium should also increase the relaxation time for stress-induced ordering of the copper atoms. The results in Fig. 5 indicate that this may well be so; we compare there the decrement-time curves at 73°C of quenched Al-4 wt.% Cu and Al-4 wt.% Cu-0.058 wt.‘% In specinens. The ternary alloy shows time-dependent damping which is also frequency-sensitive, but at any instant the damping values are lower than those for the binary alloy containing no indium. This would be expected if indium accelerated the upward migration of the temperature of the copper ordering peak. The alternative explanation, that indium accelerates the rate of fall of the peak height, is not acceptable since at this
ENTWISTLE:
PAPER 6 OF INTERNAL
temperature iridium reduces the rate of zone formation and, therefore, the rate of removal of copper from solution. Figure 6 shows what is thought to be the copper ordering peak in the Al-Cu-In alloy. The corresponding curve for the binary Al-Cu alloy from Fig. 1 is shown dotted for comparison. Both peaks occur at about the same temperature and in both cases the vacancy concentration at the peak temperature is
\\
AI Cu
x
\
In .. .
,.
FRICTION
CONFERENCE
291
cantly influence the equilibrium concentration of vacancies in the vicinity of the copper atoms at this temperature. The reduced height of the peak in the ternary specimen may result frcm the effect of indium in accelerating the removal of copper atcms from solution to form 0’ precipitate. 7
. AI4CuO58In ---AI 4Cu
1
I I
I
I
I
I
,.
, I
1
.
0
2 tog
aqetng
time.
3 man
FIG. 5. Comparison between the variation of decrement with time at 73°C for Al-4 wt. % C&O.058 wt. % In wires (full lines) and Al-4 wt. % Cu (dotted) both quenched from 530°C.
likely to be the equilibrium value; it is, therefore, concluded that the relaxation time for ordering of the copper atoms is unaffected by the presence of indium at 175°C and, therefore, that indiumdoes not signifi-
1
50
,.’
.
100 Teme.
150
200
“C
FIG. 6. Damping-temperature curves at 0.57 c/s of 0.035 in. dia. wires of Al-4 wt. % Cu-O.058 wt. % In and Al-4 wt. % 0.1 quenched from 530% heated to 223°C for about 5 min and cooled at SO”C/hr. REFERENCES B. S. BERRY and A. S. NOWICK, N.A.C.A. Tech. Note 4225 (1958). B. S. BERRY,Actu Met. 9, 98 (1961). A. S. NOWICK and R. J. SLADEK, Actu Met. 1,131 (1953). A. E. ROSWELL and A. S. NOV&K, J. Metals, I?.Y. 5, 1259 (1953). C. PAN~ERIand T. FEDERIGHI, Phil. Mag. 3, 1223 (1958). W. DE SORBO and D. TURNBULL, Acta Met. 7, 83 (1959).
Changes of internal friction at low frequenciesduring isothermal ageing at 73°C of Al-4 wt.% copper wires are interpreted in terms of a migrating internal friction peak due to stress-induced ordering of copper atoms. If the vacancy decay follows a second order rate curve, it is deduced that the relaxation time z will vary with ageing time f as t = za + Bt. Where fi is a constant and to is the as-quenched value oft. This relation fits the 73°C data fairly well but the deduced value oft, exceeds that expected from resistivity data on pure aluminium by two orders of magnitude, which may be explained by inefficient quenching. The existence of interaction between indium atoms and vacancies is deduced from preliminary experiments in which indium addition to an AlA wt.% copper alloy modifies the decrement time curve following quenching. UTILISATION
DE MESURES DE FRICTION INTERNE DES LACUNES DANS LES ALLIAGES
POUR L’ETUDE DE LA DISPARITION CUIVRE - ALUMINIUM
Les auteurs ont Btudie les modifications de friction interne a basse frtquence qui se manifestent pendant le vieillissement isotherme a 73°C de fils de cuivre a 4% en poids d’A1, et attribuent ces modifications au deplacement dun pit de friction interne, d&placement du a un rearrangement des atomes de cuivre. Si la disparition des lacunes ob6it a une loi du second ordre, les auteurs deduisent que le temps de relaxation 7 variera en fonction du temps suivant la loi: 7 = Ta + Br. oti l3 est une constante, et oh T. est la valeur de r immediatement apres la trempe. Cette relation explique dune mani&re satisfaisante les faits experimentaux obtenus a 73”C, mais la valeur de T, qu’elle perment de d&luire est sup&ieure (de deux ordres de grandeur) a celle que donnent des mesures de resistivite sur aluminium pur; cette discordance peut s’expliquer par une trempe incompl8te. Partant d’experiences preliminaires au tours desquelles ils ont observe qu’une addition d’indium a un alliage de cuivre a 4% en poids d’Al modifiait la courbe d’evolution du decrement aprbs trempe, les auteurs concluent & l’existence dune interaction entre les atomes d’indium et les lacunes. UBER
DAS
AUSI-IEILEN
VON LEERSTELLEN IN ALUMINIUM-KUPFER-LEGIERUNGEN, GEMESSEN DURCH DIE INNERE REIBUNG
Veriinderungen der inneren Reibung bei niedrigen Frequenzen w&rend isothermen Alterns bei 73°C von Drlhten aus Al-4 Gew. % Cu werden zuriickgefuhrt auf ein wanderndes Maximum der inneren Reibung, dem spannungsbedingte Ordnung der Kupferatome zugrundeliegt. Wenn das Ausheilen der Leerstellen einer Reaktion zweiter Ordnung folgt, muB die Relaxationszeit 7 von der Alterungszeit t abhtingen gemiil3 7 = Za + gr. wo l3 eine Konstante und 7a der Wert von r unmittelbar nach dem _4bschrecken ist. Diese Beziehung gibt die Messungen bei 73°C ziemlich gut wieder; der daraus hergeleitete Wert von 7, ist jedoch zwei GriiBenordnungen hiiher, als man nach Widerstandsmessungen an reinem Aluminium erwarten wiirde. Das erklilrt sich vielleicht durch unvollkommenes Abschrecken. Die Existenz einer Wechselwirkung zwischen Indium-atomen und Leerstellen wird hergeleitet aus vorlaufigen Experimenten, in denen die Hinzuftigung von Indium zu einer Legierung Al-4 Gew.% Cu die Zeitabhilngigkeit des Dekrements nach Abschrecken andert.
INTRODUCTION The interpretation of the results of an investigation of the effect of a third element, specifically indium or magnesium, on the rate of quench-age hardening of an aluminium-copper alloy required more precise information than was currently available on the decay _~~. __--* Paper 6 presented
at the Conference on Internal Friction held on 10 and 11 July, 1961, at Cornell University. t Department of Metallurgy, University of Manchester, Manchester 13. ACTA METALLURGICA,
VOL. 10, APRIL
of the concentration of quenched-in vacancies in these alloys. There follows an account of some preliminary experiments which were carried out to explore the proposal that these data might be obtained by internal friction measurements. EXPERIMENTAL
OBSERVATIONS
ON Al-4
wt.%
Cu
Berry and Nowick(1,2) have reported that quenched and reverted Al-4 wt.% copper wires show an internal friction peak at about 185°C for a vibration frequency
1962
12861
ENTWISTLE: PAPER 6 OF INTERNAL
of 2 c/s. They put forward convincing evidence that this peak arises from the stress-induced ordering of the copper atoms in solution in the al~~ium lattice. Freshly-quenched wires which were rapidly heated to temperatures below 185°C gave initial damping values above the curve for the reverted material. These observations are confirmed by our results shown in Fig. 1.
5min
0
50
of 223’C
100 Temp.,
150
200
YZ
FIG. 1. o the decrement-temperaturecurve of 0.035 in. diameter Al-4 wt. % Cu wire, water quenched from 535OC, heated over 2 min to 223’C, left for 5 min at 223°C and then cooled at SO”C/hr. x the damping of freshly quenched wires approximately four minutes after attaining the indicated temperature.
The internal friction measurements were made on wires 0.035 in. (0.89 mm) diameter by a conventional torsion pendulum in which the only novel feature was the design of the specimen; this had a-in. diameter ends cast on in a eutectic AI-Cu alloy giving a reproducible and loss-free grip without the need to deform the ends of the wire plastically. The full curve in Fig. 1 is the damping measured at 0.57 c/s during cooling from 223’C of an Al-4 wt.% Cu specimen which had been quenched from 535”C, heated rapidly to 223°C and left there for about 5 min before cooling. The cooling rate through the damping peak was about SO”C/hr. The crosses represent the damping values measured after about 4 min at the indicated temperature; prior to this the specimens bad been quenched from 535”C, aged for about 4 mm at room temperature and heated over about 1 min to the temperature of measurement. Berry suggests that the high damping of the freshlyquenched wires is explained by a reduction of the relaxation time of the copper atoms by the quenched-in concentration of vacancies. This depresses the damping peak temperature for a given vibration frequency. As the vacancy concentration decays to its equilibrium value, the relaxation time will rise and the peak will migrate upwards along the temperature axis. If this
FRICTION
281
CONPRRENCE
is so then isothermal measurement of internal friction as a function of time at a temperature between those of the as-quenched peak and the equ~ib~um peak should show a maximum at the instant at which the peak temperature passes through the temperature of measurement. Since the peak is of anelastic origin, the time to maximum damping in such an experiment will be longer for lower frequencies of vibration, therefore, in principle, isothermal measurements of internal friction at a number of different frequencies should reveal the variation of relaxation time, and therefore of vacancy concentration, during ageing. Information of this kind as been obtained for silver-zinc solid solutions by Nowick and Sladek(3), and by Roswell and Nowick’4) using anelastic creep recovery. In the present alloy system the relaxation strength (2.5~ 10W3) makes the anelastic strains too small to allow accurate measurements by this method; it is for this reason that the internal friction method was explored. Figure 2 shows the result of an unsuccessful attempt to detect a peak in the decrement-time curve for Al-4 wt.% Cu specimens quenched from 535°C and aged 3
\
l
x 0
i
0.265Elstc 0.570 c/set 1 quenched
535.C
0 104
oqemg me.
mm
PIG. 2. The variation of decrement with time at 73% of Al-4 wt.% Cu wires quenched from 535°C. The wires rested at 20°C for about 5 min after quenching and before heating over about 1 mm to 73°C. ‘at 73°C. The specimens were at room tempera~re
for about 4 min after quenching. The damping is seen to fall with time. Only the time-dependent component is shown; the background damping (between 0.7 and 4.0~ 10m3dependent on frequency) which the specimen attained after about 1000 min has been subtracted from the measured values. The three curves shown were measured each at a different frequency (0.265,0.57 and 1.80 c/s) and it is clear that the damping of the specimen at a given instant always increases as the frequency falls. This behaviour is consistent with the existence
ACTA
288
METALLURGICA.
of the ordering peak at a temperature which is always above the temperature of measurement, either because it migrates very rapidly or because the peak in the as-quenched state is above 73°C. We enquire more closely into these possibilities in the discussion. The effect of ageing temperature on the decrementtime curve is shown in Fig. 3 which gives results for 52, 73 and 111°C. Again no maximum is evident. The full lines in Fig. 3 are theoretical curves which will be discussed later.
VOL. IO,1962
K=&exp
--& [
B1
where E, is the jump enthalpy. K, will be a constant if the vacancies make a fixed number of jumps in their lifetime at a given vacancy concentration. The resistivity data for aluminium were made at temperatures below those of the present measurements; we therefore use equation (2) to extrapolate Federighi’s 0°C data to higher temperatures and assume that K,, does not change. The extrapolation requires a knowledge of E,, which varies with quenching temperature. We take here a value of 0.46 eV which is close to Panseri and Federighi’s value for a quenching temperature of 520°C. If this is combined with 0.79 eV for the formation enthalpy of vacancies, E,, then E,+E, = 1.25 eV which agrees well with 1.22 f 0.06 eV measured by Berry for the activation energy for stressinduced migration of copper in aluminium with an equilibrium concentration of vacancies. This agreement would be expected if copper-vacancy interaction is small. If t’ is the time at which C/C, = Q at T = T,
FIG. 3. The effect of ageing temperature on the variation of decrement with time following quenching from 535°C. Frequency 0.57 c/s. The full lines are the calculated curves using equations (7) and (9) for temperatures of 52, 73 and 1ll’C; the curve showing the peak is that for 111°C.
then
t’=-.-=
1
1
-_
._
and
DISCUSSION It
is helpful to compute the expected damping behaviour of the quenched Al-Cu alloy on the assumption that the copper atoms have zero binding energy with vacancies so that the vacancy formation energy and jump rates are identical to those in pure aluminium. Panseri and Federighi’s (5)resistivity data on quenched aluminium were obtained under quenching conditions similar to those used in the present experiments. Their resistivity decay curves below lOO”C, together with those of de Sorbo and Turnbull@) for lower quenching temperatures, can be shown to follow a second order rate curve in the initial stages. This implies that the vacancy concentration C varies with time, t, as c=
G 1 + KCJ
(1)
where Cc is the concentration at t = 0 and K is a rate constant, which will vary with temperature, T,, as
where S, is the formation entropy (S,/kw1) and TQ is the quenching temperature. Now taking the measured value of t’ = 2.5 min at T, = 273°K for To = 793°K (= 520°C - the effective quenching temperature for an actual temperature of 535°C) we deduce &exp
2 0
= 1013.08min-l .
The relaxation time z for stress-induced ordering at any instant when the vacancy concentration is C is 1 -_= azvC
t
exp
dG, [ kT, 1
where AG,, the jump free energy = E,-TaS,. For the equilibrium concentration of vacancies temperature T,
I
at
ENTWIWLE:
PAPER 6 OF INTERNAL
1
(5)
from Berry’s measurements. We put the second order rate relation for vacancy decay in equation (4) and get the following relation giving t as a function of ageing time
-
I
+exp[ -&]exp[ = _ __ ~____~--~-___-___
t
1 +K,exp(+)exp[
-- +-] ..___
z=t,+K,exp
289
CONFERENCE
The table confirms that if the vacancy concentratiofi in the alloy equals that in similarly treated pure aluminium then a maximum in the decrement-time curve should be attained after about 9 min at any ageing temperature between 50 and 110°C. If this were the case it would have been detected in the present experiments. It should be noted that the approximately constant value of the time to peak damping in Table 1 1 results from the fact that tQ < - ; this means that cc)
-&]exp[-$Jr.
This equation can be simplified by introducing the relaxation time zg for the freshly quenched specimen.
then
FRICTION
(7)
This equation shows that dtldt is independent of T, and T,, except in so far as these affect K,. Peak damping will be attained when oz = 1 that is when 0
the calculated as-quenched peak temperature (-4°C) is always well below T,, but although an increase of T, increases the temperature difference between T, and the as-quenched peak, the more rapid peak migration at the higher temperature compensates for this togive conditions for peak damping in a time which is approximately constant. These considerations lead to the conclusion that the decrement-time curve will vary with T, only for values of T, near to the asquenched peak temperature. Turning now to the results of Fig. 2 we take the damping values at the three frequencies after ageing for 4 min at 73°C and fit through them a decrement frequency curve of the form 6 = 26,,
-
W-r
1 +Co2t2 Table 1 gives the computed times to peak damping using the vacancy data for aluminium in equation (8). The vacancy concentration at the peak, C,, is expressed in terms of C,, C, is also given in terms of the equilibrium concentration C,. Strictly, equation (1) cannot apply for long times since it predicts C = 0 at t + co rather than the equilibrium concentration C,; however Table 1 shows that C, is always at least 100 C, so equation (1) can be used with only small error. TABLE 1
~_
.__ 1
rim~~~n~ti~P~ -. __
?
/ Tq(sec)
1
9.13
92.3
10-6.24
0.0030
73
9.20
&
10-X60
0.0012
111
9.25
iii;
lo-!w
o.ooo25
___-
______ TQ = 793’K:
where 6,, = 4x 10-3, the estimated peak height of Fig. 1. The fit is shown in Fig. 4 and gives z= 1.115 sec. A repetition of the procedure for data after ageing
~_~ Ej = 0.46 eV; ;
-_
Ef = 0.79 eV;
.=:
FIG. 4. Decrement-frequency curves of a single relaxation time fitted through the measured damping values at three frequencies on quenched Al4 Cu wires. o Aged 4.min at 73°C; l Aged 40 min at 73’C. The lower value of the frequency of the fitted peak for 40 min ageing indicates that T rises as ageing proceeds.
ACTA METALLURGICA,
290
for 40 min gives t = 3.67 set, confirming that r rises during ageing as expected. If these two values oft lie on a line of the form given by equation (6) we find t = 0.83+0.072 t.
(10)
If, therefore, this treatment of the results is valid rQ is 0,83 set which is greater thani= 0.279. This 0 means that the as-quenched peak temperature is above the ageing temperature of 73°C (it is at 99°C if we assume E, = 0.46 eV) and therefore no peak would be evident’ at 73°C at frequencies above 1/0.83x 27~ = 0.19 c/s. Unfortunately, damping measurements at frequencies of this order must inevitably be timeconsuming. Using equation (10) we can calculate S as a function of time by substituting for t in equation (9). If also Ef , where Ej = 0.46 eV we assume zQvaries as exp __ I kT, I we can compute corresponding curves for other ageing temperatures. The results of such calculations are shown in Fig. 3 where the derived curves are compared with the measured values at 52, 73 and 111°C. The fit is good for the 73°C curve, confirming that the second order rate equation is a fair representation of the decay process. The agreement is fair at 52°C but is poor at 1ll”C, where a peak is predicted but not observed. It may be unfair to apply equation (1) at 111°C. It is instructive to compare the deduced relaxation times for the binary alloy at 73°C t = 0.83 + 0.072 t with that expected from the vacancy data for aluminium t = 0.0012 + 0.030 t. dtfdt is of the same order in the two cases, which implies a comparable number of vacancy jumps before annihilation. The extrapolated value of to for the binary alloy is longer than that expected from vacancy data on pure aluminium. This is most likely to be explained by the effective quenching temperature being below that at which the specimen was in fact solution treated; if I/r0 = 10X4e6see-l, E, = 0.79 eV and Ej = 0.46 eV we require a value of T4 = 390°C to explain the extrapolated value of zg. We can dismiss an alternative explanation of the high values of r, that they arise from vacancy decay during the period
Vol. 10, 1962
of about 5 min at room temperature immediately after quenching. If we use the fact, implied in equation (7) that dz/dt is independent of T,, together with an assumed value of Ef = 0.46 eV so that t~CoC/t730C = 16, then it is computed that ageing for 5 min at 20°C increases rat 73°C from 0.81 to 0.83 sec. Vacancy decay during 5 min at room temperature following quenching does not, therefore, cause a significant increase of relaxation time. It is claimed, in conclusion, therefore that Fig. 2 confirms Berry’s view that the temperature of the copper ordering peak is depressed by quenched-in vacancies. However, unambiguous vacancy data can be obtained from this effect only if the unstable peak is located experimentally, and the present exploratory measurements show that the required experimental conditions will not easily be attained. The as-quenched values of the relaxation time appear to be lower than those to be expected from the accepted value of the formation energy of vacancies in pure aluminium and this fact demands that vibration frequencies below 0.1 c/s will be required to detect the migrating peak. Under these experimental conditions the decrement values must be measured from a small fractional fall of vibration ampIitude, since only in this way can a sufficient number of points be recorded in the short interval before the peak passes through the temperature of measurement. MEASUREMENTS
ON AN Al-Cu-In SPECIMEN
Iridium, in concentrations of the order of 0.01 at.% reduces the rate of G.P. 1 zone formation in aluminium-copper alloys. A possible explanation of this is that indium-vacancy interaction reduces the concentration of vacancies in the vicinity of the zone-forming copper atoms. If th.is is so, then indium should also increase the relaxation time for stress-induced ordering of the copper atoms. The results in Fig. 5 indicate that this may well be so; we compare there the decrement-time curves at 73°C of quenched Al-4 wt.% Cu and Al-4 wt.% Cu-0.058 wt.‘% In specinens. The ternary alloy shows time-dependent damping which is also frequency-sensitive, but at any instant the damping values are lower than those for the binary alloy containing no indium. This would be expected if indium accelerated the upward migration of the temperature of the copper ordering peak. The alternative explanation, that indium accelerates the rate of fall of the peak height, is not acceptable since at this
ENTWISTLE:
PAPER 6 OF INTERNAL
temperature iridium reduces the rate of zone formation and, therefore, the rate of removal of copper from solution. Figure 6 shows what is thought to be the copper ordering peak in the Al-Cu-In alloy. The corresponding curve for the binary Al-Cu alloy from Fig. 1 is shown dotted for comparison. Both peaks occur at about the same temperature and in both cases the vacancy concentration at the peak temperature is
\\
AI Cu
x
\
In .. .
,.
FRICTION
CONFERENCE
291
cantly influence the equilibrium concentration of vacancies in the vicinity of the copper atoms at this temperature. The reduced height of the peak in the ternary specimen may result frcm the effect of indium in accelerating the removal of copper atcms from solution to form 0’ precipitate. 7
. AI4CuO58In ---AI 4Cu
1
I I
I
I
I
I
,.
, I
1
.
0
2 tog
aqetng
time.
3 man
FIG. 5. Comparison between the variation of decrement with time at 73°C for Al-4 wt. % C&O.058 wt. % In wires (full lines) and Al-4 wt. % Cu (dotted) both quenched from 530°C.
likely to be the equilibrium value; it is, therefore, concluded that the relaxation time for ordering of the copper atoms is unaffected by the presence of indium at 175°C and, therefore, that indiumdoes not signifi-
1
50
,.’
.
100 Teme.
150
200
“C
FIG. 6. Damping-temperature curves at 0.57 c/s of 0.035 in. dia. wires of Al-4 wt. % Cu-O.058 wt. % In and Al-4 wt. % 0.1 quenched from 530% heated to 223°C for about 5 min and cooled at SO”C/hr. REFERENCES B. S. BERRY and A. S. NOWICK, N.A.C.A. Tech. Note 4225 (1958). B. S. BERRY,Actu Met. 9, 98 (1961). A. S. NOWICK and R. J. SLADEK, Actu Met. 1,131 (1953). A. E. ROSWELL and A. S. NOV&K, J. Metals, I?.Y. 5, 1259 (1953). C. PAN~ERIand T. FEDERIGHI, Phil. Mag. 3, 1223 (1958). W. DE SORBO and D. TURNBULL, Acta Met. 7, 83 (1959).