Pergamon

Acta metall, mater. Vol. 42, No. 9, pp. 3035-3043, 1994 Copyright 1994 Elsevier Science Ltd

0956-7151(94)E0084-T Printed in Great Britain. All fights reserved 0956-7151/94 $7.00 + 0.00

NUCLEATION MECHANISM OF DISCONTINUOUS PRECIPITATION IN Mg-AI ALLOYS AND

RELATION WITH THE MORPHOLOGY

D. DULY I and Y. BRECHET z

tDepartment of Engineering, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, England and 2Laboratoire de Thermodynamique et Physico-Chimie M~tallurgiques, ENSEEG, B.P. 75,

38402 Saint Martin d'H&es, France

(Received I June 1993; in revised form 2 February 1994)

Abstract--The nucleation rate of discontinuous precipitation in Mg-AI has been measured as a function of temperature, initial grain size and solute content. From these measurements, it appears that at high temperatures (T/> 220C) all precipitation nodules nucleate via Fournelle and Clark's mechanism, whereas at lower temperatures (T ~ 140C), at least one of the mechanisms identified by Tu and Turnbull or Purdy and Lange is also active. The proportion of double seam nodules determined by optical microscopy decreases from more than 1/2 to 0 when the temperature increases. In the low temperature domain, this behaviour is in agreement with that predicted by Baumann, Williams and Michael.

Rtsumt---Le taux de germination de la prtcipitation discontinue dans les alliages Mg-A1 a 6t6 mesur6 pour difftrentes temptratures, tailles de grains initiales et teneurs en solutt. A partir de ces mesures, il apparait qu'~ haute temptrature (T/> 220C), tousles nodules de prtcipitation se forment suivant le mtcanisme de Fournelle et Clark alors qu'fi de plus basses temptratures (T ~ 140C), l'un des mtcanismes identifits par Tu et Turnbull et Purdy et Lange est 6galement actif. La proportion de nodules prtsentant une double courbure, dtterminte par microscopie optique, dtcrolt d'une valeur suptrieure A 1/2 jusqu'~ 0 lorsque la temptrature augmente. Dans le domaine des basses temperatures, ce comportement est en accord avec celui prtdit par Baumann, Williams et Michael.

1. INTRODUCTION 2. POSSIBLE MECHANISMS OF NUCLEATION

The relationship between discontinuous precipi- tation and heterogeneous grain boundary precipi- tation is still an open problem. In particular, the nucleation step of discontinuous precipitation in relation with grain boundary precipitation needs to be precised. The various possible nucleation mech- anisms have been clearly identified in numerous systems but the question of their relative importance, for a given system, depending on temperature and solute concentration needs some more extensive studies.

The scope of this paper is to investigate this problem for Mg-A1 alloys. The variation of the nucleation rate of discontinuous precipitation has been measured as a function of the temperature, the Ai content C O and the grain size diameter d. It is shown that it is possible to identify the domi- nant nucleation mechanism from this data and from a combined study of the morphology of precipitation nodules. Finally, the possibility to generalize the characteristics of Mg-AI to other systems where discontinuous precipitation takes place is also considered.

Three main nucleation mechanisms have been identified for discontinuous precipitation:

In the first mechanism proposed by Tu and Turnbull, a precipitate first nucleates at the grain boundary and then acts to pull it from its initial position; the movement is associated with a reduction of interfacial energy [1-3].

In the second mechanism, the initial displace- ment of the grain boundary is due to chemical forces (similar to the DIGM driving force) as for steady state growth, as proposed by Purdy and Lange [41.

In the third mechanism, the forces responsible for the initial grain boundary motion are capillarity forces, identical to those that act during grain growth or recrystallisation, as proposed by Fournelle and Clark [5].

Direct observation of the initiation of discontin- uous precipitation is difficult, Therefore, Baumann, Michael and Williams have attempted to correlate the morphology of discontinuous precipitation nodules with their nucleation mechanism [6]. They

3035

3036 DULY and BRECHET: DISCONTINUOUS PRECIPITATION IN Mg-A1

have observed that in Cu-Be, nodules may grow either on one side of the grain boundary (the so called "single seam" morphology) or develop alternately on both sides of the boundary. In the latter case, nodules first exhibit the "S" morphology [7], which then evolves towards the "double seam" morphology [8] while the growth proceeds.

Based on these observations, Baumann et aL made the three following assumptions:

(i) Double seam nodules are typical of Tu and Turnbulrs mechanism whereas nodules formed via Fournelle and Clark's mechanism should mainly result in a single seam morphology.

(ii) The proportion of double seam nodules de- creases as T increases. The temperature Tl/2, at which this proportion is 1/2, is related to the melting temperature Tm.

(iii) As a consequence of (i) and (ii), it may be concluded that when T < Tt/2, Tu and Turnbull's mechanism is dominant, whereas when T > T~/:, most discontinuous precipitation nodules initiate via Fournelle and Clark's mechanism.

Recently, Gust, Chuang and Predel have con- firmed for different systems that the fraction of double seam nodules decreases when T increases but have found that Tl/2 is proportional to Ts, the solvus temperature, rather than to Tm [9]. They have pro- posed that Baumann et al.'s assumption (i) may be too simplistic, since double seam nodules might also form via Fournelle et aL's mechanism.

3. MATERIALS AND EXPERIMENTAL PROCEDURES

Four binary Mg-A1 alloys with a solute content ranging from 3.6 to 10at.% A1 were provided by Pechiney as bars whose diameter was approx. 16 mm. The alloys, previously melted using conventional alloying techniques, had been extruded at 250C under a pressure of 250 bars. The alloys were 99.91% pure, and the impurities were mainly Mn (480 ppm), Si (350 ppm) and Fe (30 ppm). For each alloy, two solution annealing heat treatments were carried out. Some specimens were solution treated for 128 h at 420C: after this treatment, their average grain diam- eter was approx. 95 #m. Other samples were annealed at 420C for 8 h, which resulted in an average grain size of approx. 35 tim.

Heat treatments were then carried out at tem- peratures ranging from 140 to 340C. The Vickers hardness was measured after different annealing times. The use of Vickers hardness to investigate discontinuous precipitation is always a subject of concern. In order to feel confident about this tech- nique, we rely on a previous work on the same alloy [10] in which we have characterized the macroscopic kinetics by optical metallography, Vickers hardness and in situ X-ray experiments. The X-ray experiments are difficult to perform but are very precise. They

show that when the whole sample is invaded by discontinuous precipitation, the macroscopic kinetics obey Johnson-Mehl-Avrami's equation and can then be interpreted to give a value of the nucleation rate. In [10], the Vickers measurements were shown to agree with the results of X-ray diffraction as the transformed volume fraction X and the hardness D are then related by

D(t) -D(O) X(t ) = (1)

D(tmax)--O(O)

in which D (0) is the initial hardness value and D (tmax) is the hardness when the precipitation process is completed. The 95% confidence interval for D is generally about 0.7 hV [cf. Fig. l(a)]. From equation (1), it is possible to determine an upper and a lower nucleation rate for which a calculated curve D(t) passes through most of the 95% confidence intervals of the experimentally measured hardness points. It was found that when no continuous precipitation occurs, there is never more than a ratio of 2 between these two limit nucleation rates [Fig. l(b)], and it has been found that the nucleation rate value deter- mined from X-ray experiments always lies within the range given by these two values. In the Mg-A1 system, the macroscopic kinetics of discontinuous precipitation can thus be reliably followed by Vickers hardness.

The statistical analysis of the morphology of dis- continuous precipitation nodules was performed by optical microscopy. Before observation, the samples were etched for one or two seconds with a solution containing 10 ml HF and 90 ml H20, and then rinsed with water and ethanol. N~ and N: being respectively the number of single seam and double seam nodules, the fraction of double seam nodules N2/(N ~ + N2) was determined from a consideration of at least 250 nodules for each sample.

4. NUCLEATION RATE OF DISCONTINUOUS PRECIPITATION

4.1. Results

The dependence of the macroscopic kinetics of discontinuous precipitation on the initial grain size varies with temperature:

(i) at T = 220C, alloys containing between 5.4 and 10at.% A1 are fully or almost fully invaded by discontinuous precipitation. The alloys with the smallest grain size d are systematically softer than the other ones. The effect of d is simply a translation in hardness, and not a modification of the kinetics [Fig. l(a)]. The curve - ln(1 -X ) = g(t) is a straight line [Fig. l(b)] whose slope a represents the nucleation rate per grain, i.e. [10, 11]

a = r~d2l~ (2)

where Is is the nucleation rate per unit area of grain boundary. For alloys with a solute content between

;> e~

>.

100

90

80

70

7 60

0

100

90

80

70

60

DULY and BRECHET:

(a) r = 220C

?

[] d = 35 p_m

d = 95 ktm

1 I I I 1 2 3 4

t (h)

(C) T = 140C

I I I I0 20 30

t (h)

DISCONTINUOUS PRECIPITATION IN Mg-A1

I 40

~ 2

I

3037

(b) r -- 220C

4 I ~ . . / ' " / /

,i 0 0.5 1.0 1.5 2.0

t (h)

(d) T = 140C 1 4

3

l

_=

10 20 30 40

t (h)

Fig. 1. Evolution of the Vickers hardness D of the alloy Mg-10 at.% A1 with time at different annealing temperatures: (a) At 220C, the slope of the curve D =f(t) does not depend on d. The error bars give 95% confidence intervals. They are not shown when they are smaller than the symbol used for the points in the graph. (b) At this temperature, -In(1 -X )= g(t) where X = [D -D(O)]/[D(t~x)- D(0)] can be fitted by a straight line. The plain line shows the best fit straight line whereas the two dashed lines indicate the limits of the domain of good fit (a good fit straight line is expected to cross at least all but one 95% confidence intervals of the experimental points). The ratio between the slopes of the upper and lower dashed lines is 1.95. (c) At 140C, the slope of D =f(t) varies with d. (d) - ln ( l -X )= g(t) cannot be

fitted by a straight line.

5.4 and 10 at.%, the nucleation rate of discontin- uous precipitation per grain does not depend on d (Table 1).

(ii) at T = 140C, discontinuous precipitation only invades about 20% of the alloys which contain 7.7 and 10 at.% A1. In contrast with the previous case,

Table 1. Variation of the nucleation rate of discontinuous precipi- tation with grain size at two different temperatures

nd21s (h t ) 7td21s (h- ~ ) d(#m) C0 = 7.7 at.% Co= 10 at.%

T = 220'C 35 0.18 2.2 95 0.18 2.2

T = 140'~C 35 1.9 10 +3 1.5 10 -2 95 2.8 10 -3 2.1 10 2

there is no systematic influence of d on hardness: the kinetics of discontinuous precipitaiton is influenced by a change in grain size. The error bars on Fig. l(c) clearly demonstrate that the curves cannot be super- imposed by a mere translation. In contrast to the previous temperature, the curves - ln (1 - X )= g(t) are not straight lines [Fig. l(d)]. However, optical metallography has shown that during the first 15 h of the heat treatment, only discontinuous precipitation occurs and that further heating essentially produces continuous precipitation. It has also been shown in a previous work that the contributions to hardness due to discontinuous precipitation and coarse continuous precipitation are roughly equivalent [12]. Thus, we can have a rough estimate of the nucleation rate

3038

%

DULY and BRECHET:

10 -1

10 -2

10 -3

10 -4

10- -

1 - -

_ i

I

I

- i I

_ I

j i 0.18

io

:.l

DISCONTINUOUS PRECIPITATION IN Mg-AI

- - i - - - C0= 9at.% from [12]

~A- - CO= 9at.%

- - -eB C0= 9at.%

. ii . CO= 9at.%

~" ~ 'O- - C 0= 9at.%

/ \ z:---" .... \

y / ' - - , . . . . ~ \ .,Y / ..... ,, \

f ' / /~' I ' - . ~ . I'lb, X ',,., \

. . ., (?) / " "'t) /

I I .. I

'1 | I /I I I x , I 0.20 0.22 0.24 0.26 0.28 0.30

1000 (j- l) RT

Fig. 2. Variation of the nucleation rate of discontinuous precipitation with temperature for different solute contents when d = 95/~m. The symbol (&) for Co = 10 at.% at 140C indicates that 95% confidence interval is more than two orders of magnitude large. The curve giving the variation of the nucleation rate

for the Mg-9 at.% AI alloy studied by Clark [12] is also shown.

of discontinuous precipitation by fitting a Johnson- Mehl expression to the first 15 h. It seems that for both the alloys Mg-7.7 and Mg-10 at.% A1, ~zd2Is tends to increase when d increases (Table 1). How- ever, the nucleation rate values estimated at 140C are much less precise than that obtained at 220, 260 and 300C.

Figure 2 shows the variation of the nucleation rate with temperature for different compositions when d = 95/~m (the curve obtained from the Vickers hardness measurements carried out by Clark [13] on a Mg-9 at.% A1 alloy is also shown for comparison). For a given value of Co, the curve I s vs T has the classical C shape. Note that I s decreases to 0 before the solvus temperature is reached and discontinuous precipitation is replaced by continuous precipitation at high T [14].

4.2. Interpretation Depending on which nucleation mechanism is

dominant, we expect different behaviours of the nucleation rate with the experimental parameters (grain size, initial supersaturation). Conversely, from our experimental observations of these dependences, we can attempt to identify the dominant nucleation mechanism for a given temperature For the nucle- ation mechanism classically proposed, the expected

dependences are as follows:

(i) For Tu and Turnbull's mechanism, we may postulate that the nucleation rate is given by

L,~r = IB P..o,rr (3)

where IB is the heterogeneous nucleation rate of grain boundary precipitates and P..c,rr is the probability that this precipitate induces the first displacement of the boundary. I B is independent of d and is classically given by [15]

IB ocexp[ as(vm)2 / '(0)] ( ~ , , , j (4)

where AGa is the energy of formation of one mole of the precipitate, Vm is the molar volume, tr is the precipitate matrix interface energy, f(O) is a function of the contact angle 0 between the precipitate and the grain boundary. We can assume that P~c,rr does not depend on d, as it is related to a local mechanism of absorption of the precipitate on one side of the grain boundary. For the same reason, AGp or AGo, the molar chemical energy stored in the super- saturated solution, should not enter P.~,rr. The nucleation rate per grain d2Is,rr is thus given by

d2/s'TT OC d2 exp[- L 0"3(Vm) 2 . . . . 7 ]to n. (5) (aG~ A

DULY and BRECHET: DISCONTINUOUS PRECIPITATION IN Mg-AI 3039

(ii) For Purdy and Lange's mechanism, it has been proposed in a previous paper that [10]

exp ' - E 7 [-AGo-] l s , , ocv ~-~JshL -~J P.~,pL (6) I _

where v is the vibration frequency of the grain boundary considered as a membrane, E is the acti- vation energy for the vibration of the membrane, AGo is responsible for the first displacement of the boundary, and Pnuc.PL is the probability that the displacement of the boundary induced by chemi- cal forces will lead to discontinuous precipitation. v was estimated to be proportional to d- l (vibration modes of an elastic membrane) [10]; E is independent of d and only depends on the structure of the grain boundary (more precisely on its surface energy y). Though the details of Purdy and Lange's mechanism are not well understood, it is unlikely that Pnuc,PL is related to d and its dependence on AGo or AGa should be weak. Since AGo ,~ RT, it results that

d2 I~ PL OC d AGo. (7) ' /~1

(iii) For Fournelle and Clark's mechanism, it has also been proposed in [10] that

F E-]TVm :s,,co v exp[- 7 eoc,Fc

3040 DULY and BRECHET: DISCONTINUOUS PRECIPITATION IN Mg-A1

15

~ 1o %

5

- (a )

0 I I I I -400 -300 -200 -100 0

_ AGI 3 ,~-2

15

,~ 10 %

= 5

i I 2 4

In (104 AG0).-~--),

15- (C) /~

( ...~ 10 - -

o I I I 0 0.5 1.0 1.5

(100 AG0~ TM.--~),

Fig. 3. (a) At T=220C, the curve ln(Trd21~)= fI[-(AG#) -2] is not a straight line; (b) the curve ln(nd21s) =f2[ln(AG0)] is not well fitted by a straight line;

(c) the curve ln0td21s)=f3[(AG0) TM] is a straight line.

double seam morphology identified by Frebel and Schenk [8] [Fig. 4(c,d)]. The S and double seam morphologies correspond to two different stages of the same phenomenon [6].

We have measured the evolution of the fraction N2/(N 1 + N2) of double seam nodules with T when C O = 7.7 at.% and C O = 10 at.%. It appears that for

140C ~< T ~< 300C, N2/(N 1 + N2) is a linear, de- creasing function of T [Fig. 4(g)]

N 2 T2--T (lO)

NI + N2 T2- T~"

T2 and T~ are the extrapolated temperatures at which N2 and NI respectively cancel. Table 3 gives the values of /'2, T~, TI/2 = (T2+ 7"1)/2; the melting temperature T m and the solvus temperature T s of the two alloys are also shown for comparison. There is no simple relationship of proportionality between Ta, T 2, TI/2 and T m. But the ratio T~/2/T ~ is equal to 0.63 for both alloys.

Note finally that optical microscopy observations have revealed that in Mg-A1, T 2 is the temperature above which no discontinuous precipitation takes place.

5.2. Interpretation of the evolution of the proportion of single and double seam nodules with temperature

In order to understand the decrease of the fraction of double seam nodules when T increases, it is necessary to consider separately the low temperature domain, in which more than one initiation mechan- ism is active and the high temperature domain, in which only Fournelle and Clark's mechanism operates:

(i) Low temperature domain: following Baumann et al. [6], we may assume that Tu and Turnbull's mechanism should result mainly in the formation of double seam nodules. But with Fournelle and Clark's mechanism we expect a majority of nodules to exhibit a single seam morphology. When T increases, the proportion of nodules that form via Fournelle and Clark's mechanism increases, and as a result, N2/(NI + N2) decreases, in agreement with our exper- imental results.

(ii) In the high temperature domain (T i> 220C) where only Fournelle and Clark's mechanism is effec- tive, the preceding explanation can no longer hold. We have to study within this mechanism itself which parameters favour one of the two morphologies.

The formation of single seam nodules via Fournelle and Clark's mechanism corresponds to the vibration of the boundary in its fundamental eigen- mode (vibration frequency v~, activation energy El and probability of initiation of discontinuous precipitation Pnuc,FCA), whereas the formation of double seam nodules is possible through the exci- tation of a superior (excited) vibration mode for the membrane (vibration frequency Vz, activation energy E 2 > E l and probability of initiation of discontinuous precipitation Pnu~,Fc,2). From equation (8), it follows that

YI Pnuc FC 1 rE2 -- EI~-]- ' Nz -- 1-1 ......... e x p - . (11) NI+N 2 V2Pnuc,FC,2 ~ RT ) J

There comes an apparent paradox: if EE- E~ and Pnu,~C,I/Pnu,FC,2 were independent of T, one would

DULY and BRECHET: DISCONTINUOUS PRECIPITATION IN Mg-A1 3041

N 2

N 2 + N 1

3.7 ~ ~

3.6

C).5

D.4- -

0 .3 - -

0 .2 - -

0.1 - -

0

100

(g)

Co= 10%

C0= 7.7 %

o%

150 200 250 300 350 400

T (C)

Fig. 4. Different morphologies of discontinuous precipitation nodules as observed from optical micro- scopy: (a~l) different stages of growth of double seam nodules; (e, f) examples of single seam nodules;

(g) variation of the fraction of double seam nodules N2/(N L + N2) with temperature.

expect N2/(N1 + N2) to increase when T increases. That is experimentally not the case. Therefore, one needs to assume a T dependence in the parameters of equation (11). This can be justified as follows: E 2 -E l is likely to be proportional to the grain boundary energy ~,, as the higher this energy is, the more difficult it is for the boundary to vibrate.

Table 3. Characteristic temperatures of the morphology of discon- tinuous precipitation nodules in the alloys Mg-7.7at.% AI and

Mg-10 at.% AI

C O (at.%) T I (K) T 2 (K) Ti/2 (K) T s (K) T m (K) 7.7 183 613 398 633 784

10 222 625 424 675 738

7"1 and T 2 are the extrapolated temperatures at which the proportion of single and double seam nodules respectively cancel; TI/2 is defined by Tt/2 = (T I + /'2)/2; T s and T m are respectively the solvus and melting temperatures of the alloy.

STEM annular dark field images have shown that the solute A! tends to segregate at the boundary [16]. (This result has been confirmed by calculation of the segregation energy of Al in Mg via Miedema's model [17].) The absorption of solute by the bound- ary thus reduces y. When Co is fixed, an increase in the temperature leads to an increase in the A1 content in the matrix at equilibrium, therefore reducing the amount of solute likely to segregate in the boundary. This leads to an increase in y, which reduces the proportion of double seam nodules. (Note also that at constant T, the increase in Co leads to an increase in the solute content in the boundary, and thus to a reduction of T and of g 2 -- E l , which tends to favour the formation of double seam nodules, in agreement with the exper- imental results.)

3042 DULY and BRECHET: DISCONTINUOUS PRECIPITATION IN Mg-Al

Therefore, we can understand why, even in the high temperature regime, N2/(N~ + N2) is a decreasing function of T.

5.3. Interpretation of the disappearance of discontinu- ous precipitation at high temperature

The disappearance of discontinuous precipitation at high temperature is experimentally observed to be correlated with the cancellation of N2/(Nt + N2). In order to understand this observation, it is necess- ary to take the variation of Pnuc,FC, l/Pnuc,Vc,2 into account. P..c,FC is the probability that the first dis- placement of the grain boundary allows the for- mation of a discontinuous precipitation nodule, i.e. that the aUotriomorphs that precipitate in the bound- ary are efficient to pin it during its migration. When Co and T are fixed, the smaller the migration speed (i.e. the smaller the vibration frequency) of the boundary, the higher this pinning probability is. It is therefore expected that P..c,FC,2 will cancel whereas P..,FC,] still has a finite value. This is why N2/(N 1 +N:) goes asymptotically to 0 for a finite temperature T2. The coincidence between T2 and the temperature above which discontinuous pre- cipitation is no longer present suggests that P~.c,FC,l has become so small (impossibility of pinning by allotriomorphs) that nucleation of discontinuous pre- cipitation becomes virtually impossible. The dis- appearance of discontinuous precipitation at high temperatures could thus result from its inability to initiate rather than from its inability to propagate, as had been previously proposed [18].

6. EXTENSION OF THE FEATURES ENCOUNTERED IN Mg-AI TO OTHER SYSTEMS WHERE DISCONTINUOUS

PRECIPITATION OCCURS

The variation of the discontinuous precipita- tion nucleation rate with the initial grain size and solute content in Mg-A1 shows that in this system, Fournelle and Clark's mechanism is the only operat- ing system at high temperatures whereas at low temperatures, another mechanism is also active. Ac- cording to Baumann et al., this result should apply in every system that exhibits discontinuous precipitation [6]. The calculations carried out in Section 4.2 are expected to be valid in any such system, and provide a theoretical justification to Baumann et al.'s assump- tion. Table 2 gives for each initiation mechanism the dependence of the nucleation rate on the initial driving energy when T is fixed: as the mobility of the boundary is the same for each mechanism, we just have to compare the activation energies in equations (5), (7) and (9). Tu and Turnbull's mechanism has the highest dependence on T, since it is related to a precipitation event. Then comes Purdy and Lange's mechanism (chemical driving force without precipi- tation) and then Fournelle and Clark's one (capillar- ity forces). The expected variation with T of the

d2Ij/M

ITT 1 I 1 2 3 i ", i "PL \ \ ,

\ "-.

Fig. 5. Variation of l~/M--where M is the grain bound- ary mobility--with temperature for the different initiation mechanisms of discontinuous precipitation. Tu and Turn- bull's, Purdy and Lange's, and Fournelle and Clark's mech-

anisms dominate in zones 1, 2 and 3 respectively.

corresponding three nucleation rates normalized by the mobility is shown in Fig. 5. At high tempera- ture, Fournelle and Clark's mechanism dominates whereas, at low temperatures, Tu and Turnbull's mechanism dominates. Purdy and Lange's mechan- ism may have a significant contribution in an inter- mediate range of temperatures.

It has also been proposed that the decrease in the relative amount of double seam nodules as T increases is a general feature. Our present results in Mg-Al, together with Gust et al.'s investigations on several systems tend to confirm this assumption. At low temperatures, this result can probably be interpreted in all systems as the result of the tran- sition from Tu and Turnhull to Fournelle and Clark's mechanism [6].

However, in order to understand why N2/NI still decreases as Tincreases when only the latter mechan- ism operates, other arguments have to be taken into account. The analysis performed for the Mg-AI system relies on two characteristics: positive solute segregation and necessity of pinning by allotri- omorphs. The necessity of pinning by allotriomorphs is general when nucleation is dominated by Fournelle and Clark's mechanism. Therefore, at high tempera- tures, N2/N t should ultimately decrease towards 0 in all systems. This assumption is supported by Gust et al.'s results on Cu-In, Cu-Sb, Ni-In and Ni-Sn [9]. At the opposite, the solute segregation depends on the system. The four systems studied by Gust et al. are expected to exhibit a negative solute segregation (from Miedema's model), and for all of them, the curve N:/NI vs T always exhibits a more or less well defined plateau (note too that the ratio T~/2/T~ is equal to 0.77 in all these systems, whereas it is only equal to 0.63 in Mg-A1). The analysis carried out in Section 5.2 would even predict the possibility of a non monotonous behaviour due to this counter effect of segregation.

7. CONCLUSION

From the measurement of the nucleation rate of discontinuous precipitation as a function of initial

DULY and BRECHET: DISCONTINUOUS PRECIPITATION IN Mg-A1

grain size, solute content and temperature and from optical microscope observations, we have been able to underline important features of the nucleation of discontinuous precipitation in Mg-AI alloys:

(i) Relative importance of the various nucleation mechanisms: Tu and Turnbull 's, and Fournelle and Clark's mechanisms respectively dominate at low and high temperatures. Purdy and Lange's mechanism may be important at intermediate temperatures.

(ii) Morphological features associated with the nucleation mechanism: with increasing temperature, the relative frequency of double seam nodules is declining, even when Fournelle and Clark's mechan- ism is the dominant one.

(iii) Disappearance of discontinuous precipitation at high temperatures: it coincides with the asymptotic cancelling of the fraction of double seam nodules.

From the existing data in the literature on other systems, it seems that those conclusions may be quite general. However, depending on the nature of solute segregation at the grain boundaries, the decrease in frequency of the double seam morphology may be more or less pronounced.

The method that we have used (determination of the influence of the grain size and initial solute content on the macroscopic kinetics and morpho- logy analysis) allows us to identify the dominant nucleation mechanism for a given concentration and a given temperature. It also gives a simple way to determine the temperature above which dis- continuous precipitation does not occur and would therefore help to draw maps for continuous versus discontinuous precipitation in an initial solute content vs temperature plane.

3043

Acknowledgements--D. Duly wishes to thank Pechiney, Centre de Recherches de Voreppe for providing financial support. The authors also want to thank Dr J. P. Simon and Pr. G. Purdy for enlightening discussion, and M. Ghar- ghouri for careful reading of the paper.

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mater. Submitted. 15. D. Turnbull and J. C. Fisher, J. Chem. Phys. 17, 71

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mater. Submitted. 17. A. R. Miedema, Z. Metallk. 69, 455 (1978). 18. M. Hillert, Metal. Trans. 3, 2729 (1972).