HAL Id: jpa-00217285
https://hal.archives-ouvertes.fr/jpa-00217285
Submitted on 1 Jan 1977
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
DECOMPOSITION KINETICS IN Al-6.8 AT % Zn
G. Laslaz, P. Guyot, G. Kostorz
To cite this version:
DECOMPOSITION KINETICS IN
A1-6.8
AT
%
Zn
G. LASLAZ
Centre de Recherches P.U.K., 38340 Voreppe, France P. GUYOT
L.T.P.C.M. (LA 29), Institut National Polytechnique, B.P. 44,38401 St-Martin d7Heres, France and G. l<OSTOliZ
Institut Laue-Langevin, 38042 Grenoble, France
RBsumC. -La dtmixtion aprks trempe de la solution solide binaire AI-6,8 at % Zn a Ctk ttudike par microscopie tlectronique et diffusion des neutrons aux petits, angle;& a suivi 1a.cinttique de formation des zones de Guinier-Preston B diverses tempkratures de vieillissement
B
l'intkrieur de la lacune de miscibilitt. Bien que la vitesse de dtmixtion augmente rapidement avec le taux de sur- saturation, une transition spinodale abrupte n'est pas observte. Les resultats sont finalement comparks avec la thkorie classique et avec des modkles microscopiques rtcents.Abstract. - The decomposition after quench of the binary solid solution A1-6.8 at % Zn has been studied by transmission electron rnieroscopy and neutron small angle scattering. The kinetics of formation of the Guinier-Preston zones has been followed at various aging temperatures inside the miscibility gap. Although the rate of decomposition increases rapidly with the degree of super- saturation no sharp spinodal transition is observed. The results are finally compared with the classical theory and with recent microscopic models.
1. Introduction. - The decomposition kinetics of a binary solid solution can presently be described by two different theoretical approaches : one, which is essentially macroscopic, uses the concept of a coarse- grained free energy (Cahn [l], Hilliard [2], Langer [3]) ;
the other makes a microscopic description of the system in terms of reactions and diffusion of clusters (Binder and Stauffer [4]) and is tested by Monte Carlo simulations [5-61.
The first approach or classical theory leads to a singularity at a spinodal curve which separates
metastable from unstable states. Taking into account
fluctuations [3] and the non linear terms [7] in the diffusion equation which governs the evolution to- wards the equilibrium state, rounds off the spinodal singularity and makes gradual: the kinetics transition at the spinodal temperature.
The kinetic I'sing models of the second approach do not evidence any spinodal transition, although the simulations apparently show metastable states when the supersaturation is small [8] and confirm the ideas used in the standard nucleation theory.
In this work we have tried to clarify this problem of the existence of a spinodal transition in the classical AlZn alloy, using two experimental techniques, trans-
-
mission electron microscopy (T.E.M.) 'and neutron
small angle scattering (S.A.S.). T.E.M. and S.A.S. are indeed complementary : T.E.M. has the obvious advantage to image the clusters but overlapp effects cause some problems in evaluating high cluster densities ; S.A.S. gives the Fourier transform of the spatial correlation function of the alloy which can be directly compared with the structure factor predicted by the various theories.
The kinetics of decomposition of the AI-6.8 at
%
Zn alloy is followed after quench to various temperatures inside the miscibility gap (( solid-solution-
Guinier-Preston zones D, i.e. below 1530 [9]. There is some
uncertainty concerning the critical temperature Tc because of the formation of a transition phase ak :
Tc = 225 OC for 25 at
%
Zn [9], T, = 331 OC for 40 at Zn [10]. In any case our composition is fully asym- metrical with respect to the center of the gap.2. Experimental procedure. - For the T.E.M. Exa- minations polycristalline specimens are first homo- genized at 350 OC, slowly cooled at 240 OC and then aged at T, = 1330C, 1100C and 80OC; for 110 and
80 DC, the specimens are kept 30 S. at 135 OC before
aging at T, : such a quench is necessary to catch the first stages of the decomposition which rate increases
DECOMPOSITION KINETICS IN AI-6,8 AT % Zn C7-407 quickly when Ta decreases [ll]. Thin foils are made
after different aging times at Ta and quench to
-
20 OC. The neutron S. A.S. experiments are performedin-situ on the D1 1 spectrometer of the high flux reactor
of I.L.L. Grenoble. After homogenization at 350 OC a set of disks is directly transferred into a furnace at
T, centered on the neutron beam axis. The S.A.S. spectra are recorded at time intervals ranging from
min to 40 min, On Ta' the neu- FIG. 2, -Aging at 110 OC,
a) t = 10 min. b) t = 60 min. c)
tron wavelengths and the multidetector position, t = 220 min. G = 550.000. scattering ranges
2 X 10-'
A-l
Qe
13 X 10-'A-'
and
4 X 10-3
A-'
<
Q<
2 X I O - ~A-'
have been explored.As the scattering patterns had a radial symmetry around the incident beam, averages for constant Q have been calculated. Ta has been choosen equal to 133, 129, 122, 116 and 108 OC.
3. Results. - 3.1 TEM STUDY. - The micro- graphs of figures 1 and 2 illustrate two aging sequences at 133 and 110 OC. The complete results are described in detail in [l l]. The main features are as follows :
(i) At 133 OC, about one hour after quench must ellapse before any zinc rich cluster can be resolved in the microscope (- 10 A). This waiting time decreases when Ta decreases
(c
5 min at 110 OC, < 2 min at 80 .C).(ii) Spherical clusters (G. P. zones) are then resolv- ed : at 133 OC their density and size increase with aging time t, with a broad size distribution ; the density is about 3 X 1015 cm-3 after 300 min and the
size of the biggest zones increases like At 110 OC and 80 OC, the zone density stays roughly constant and equal to 7 X 10'' cm-3 and 10'8-10'9
respectively.
(iii) ~ s t w a l d ripening is next observed after
-
800 min at 133 OC, N 220 min at l l0 OC and-
10 min at 80 OC.(iv) The spherical G. P. zones transform pro- gressively into ellipsoidal zones and ( 11 1 ) platelets of the rhombohe'dral a; phase ; at 133 OC the first a;
precipitates appear after about 400 min, when the zone diameter is 80
A.
3.2 NEUTRON SAS STUDY. - The evolution of the scattered intensity I as a function of Q = 4 .n sin 8/1 (where 2 8 is the full scattering angle and 1 the incident wave length) is shown on figures 3 to 6 for increasing aging times at the different aging temperatures. For 133 and 129 OC I is indicated in bounts per S., and not in cross-section units dC/dQ, the calibration having not been performed for this two temperatures; the cor- respondence is approximately 400 counts for
at 129 OC and 800 counts for dZ/dQ = 10-2 cm-'
at 133 OC.
We notice the following features :
(i) All scattering profiles show an increase of I for Q
5
2 X 10-'W - l .
This effect is observed systema-tically for A1 and A1 alloys and is attributed to either surface imperfections or grain-boundary effects 112- 131. We presently attribute this increase primarily to a
FIG. 4. -Scattered intensity at 116 O C . Time in min. 1 = 6.7 A. FIG. 6. -Scattered intensity at 133 OC. Time in hrs. 1 = 8.13 A.
D = 2.563 m. D = 5.563 m. The dotted lines are the corrected curves for t 2 6 hrs.
FIG. 5. - Scattered intensity at 129 O C . Time in min. 1 = 6.7 A.
D = 5.563 m.
heterogeneous precipitation at grain boundaries, which can be observed in T.E.M. ,This scattering contribution-hasAen however considerably reduc-
ed with respect to our previous SAS experiments [l41 ,by increasing the specimen grain size. It is clear that this effect is particularly inconvenient at high tempe- ratures and low aging times where a possible scattering ring,-if any, is necessarily at low angles (see below) ;
&erefore we have attempted to correct the scattering curves at 133 OC for this effect by subtracting from each profile the first recorded scattering clirve (i.e.
t = 30 min), see figure 6.
(ii) For all temperature the scattered intensity
increases with aging time in the whole explored Q range and shows the appearance of a maximum :
for T, 129 OC, this evolution is quite :clear. At 133 OC the above correction is necessary to reveal the maximum for t
c
10 hrs, but its presence is unquestionable at longer aging times as shown fort = 23 hrs without correction in figure 7.
(iii) As a function of aging time, the position Q, of the maximum is slowly shifted towards smaller scatter- ing angles (figure 8). One point at 122 DC from an incomplete series has been included.
4. Discussion and conclusion,
-
It can first be checked that T.E.M. and S.A.S..give coherent results for the cluster size and cluster densities :DECOMPOSITION KINETICS IN AI-6,8 AT % Zn C7-409
FIG. 7. - Scattered intensity for t = 23 hrs at 133 O C . 1 = 18.6 A
D = 5.563 m.
10 20 30 40 50 60 70 tm,(lO&lls"~) Q max
1o"a-l
FIG. 8.
-
Maximum position vs aging time at different T,.(see also [14]) ; moreover S.A.S. gives R, in good agreement with T.E.M.
(ii) The zone density
Nv
can be estimated from Q, by N,-
(Qm/2 7 ~ ) ~ ; this leads toat 133 OC, and
Nv
= 5 X 1017 cm-3 at 108 OC, ingood agreement with the values given in
3
3.1. Furthermore the Ostwald ripening which appears the sooner the lower T,(4
3.1, iii), is fully confirmed by S.A.S., as demonstrated by the shift of Q, towards low angles, figure 8. Combining R, and N, with the zone composition given by the miscibility gap, one finds that the rate of decomposition varies considera- bly as a function of T, : at 108 OC, the decomposition is complete after about 100 min, whereas at 133 O C ,the alloy is still far from completely decomposed after l0 hours.
Further comments can be made about the S.A.S. profiles :
(i) The time evolution of the scattered intensity is qualitatively the same from 133 to 108 O C , in contra-
diction with [15]. In particular a scattering ring is also visible at 129 and 133 OC. No abrupt change of kinetics is observed around a spinodal temperature, which, according to [l 51 is located at 129
+
2 OC. Nevertheless the rate of decomposition increases rapidly with the degree of supersaturation (i.e. when the temperature decreases).(ii) The classical linear theory [l, 21 is not followed, even in the early stages of decomposition : there is no exponential law of Zvs. time at low temperatures, there is a shift of Q, and if a cross-over exists at a value Q, beyond our range of Q values, Q, 1: 2- 3 Q, would be required. But this is indeed not surprising for the asymmetrical composition, of our alloy. Similarly we find that a scaling of the scattered intensity, as predicted by the Langer theory [l61 is not possible.
(iii) According to the Ising models [S-61 the time evolution of Q, and I, should follow the relations
Q, a(t
+
10)-" and I, a(t+
10)n", with an average zone size ( R ) atm. For A1-20 at.%
Zn; the predicted values of the exponents are : a' = 0.2, a". = 0.7,m = 0.63-0.36 at Ta/Tc = 0.6, and they decrease as Ta increases. A first inspection (for Q,) of figures 8 and 9 (for l,) shows that power laws are followed
l 1
l0 2b 5b 100 200 360 t,"
between 108 OC (Ta/Tc = 0.63) ( l ) and
with 0.1
<
a' 0.3, 0.8<
a"<
3 and m = 0.75 at 133 OC (2). It appears therefore that the exponents aremore sensitive to Ta (or the supersaturation) than predicted by the simulations and in addition vary in reverse direction with Ta. This desagreement could have several reasons : our quench is not perfect, there is a transformation of the G. P. zones in phase
a;, both types of clusters introduce an elastic strain
( l ) Taking T, = 331 oC.
(') In fact S.A.S. gives R, c(t0.75 and R, #
<
R ), because it favours the large zones.which is not taken into account in the simulations ;
furthermore the size of the Ising lattices is limited, the aging times of the experiments and the simulations at high Ta are different, and the alloy concentration differs, too.
To conclude, the mode of decomposition of Al- 6.8 at
%
Zn seems to be the same inside and close to the miscibility gap, although the rate of formation of the G. P. zones increases quickly as the aging temperature decreases. Ostwald ripening appears sooner when the temperature is low. Power laws for the position and height of the peak of scattered inten- sity are followed, in favour of computer simulations or microscopic theories, but a closer comparison between identical systems remains to be done.References
[l] CAHN, J. W., Acta Met. 9 (1961) 795. [g] ANANTHARAMAN, T. R., SATYANARAYANA, K. G., Scripta
[2] HILLIARD, J . E., Phase Transformation. Ed. Aaronson H.I. Met. 7 (1973) 189.
(ASM Metals Park, Ohio) 1970. 1101 MURAKAMI, M., KAWANO. 0.. MURAKAMI. Y.. J. Inst. Metals
[3] LANCER, J. S., Ann. Phys. 65 (1971) 53.
[4] BINDER, K., STAUFFER, D., Adv. Phys. 25 (1976) 343. [5] RAO, M., KALOS, M. H., LEBOWITZ, J. L., MARRO, J., Phys.
Rev. B 13 (1976) 4328.
[6] SUR, A., LEBOWITZ, J. L., MARRO, J., KALOS, M. H., Phys. Rev. B 15 (1977) 3014.
. . . .
99 (1971) 160.
[l11 LASLAZ, G., GUYOT, P., Acta Met. 25 (1977) 277.
[l21 KOSTORZ, G., 2. Metalk. 67 (1976) 704.
[l31 TAGLAUER, E., Phys. Status Solidi 29 (1968) 259. [l41 LASLAZ, G., KOSTORZ, G., ROTH, M., GUYOT, P.,
WART, R. J., Phys. Status Solidi (a) 41 (1977). 1151 NAUDON. A.. ALAIN. J.. in collab. with DELAEOND. J..
.
.
, , , , , ,[7] DE FONTAINE, D., Ultrahe-grain metals (Syracuse Univ. QUA, A., MIMAULT, J., Scripta Met. 8 (1975) 1105. Press N.Y.) 1970 93. [l61 LANGER, J. S., BAR-ON, M,, MILLER, H. D., Phys. Rev. A
