b' and b precipitation in an al±mg alloy studied by dsc and tem

7/29/2019 b' AND b PRECIPITATION IN AN Al±Mg ALLOY STUDIED BY DSC AND TEM

http://slidepdf.com/reader/full/b-and-b-precipitation-in-an-almg-alloy-studied-by-dsc-and-tem 1/17

b' AND b PRECIPITATION IN AN Al±Mg ALLOY STUDIED

BY DSC AND TEM

M. J. STARINK{{ and A.-M. ZAHRA

Centre de Thermodynamique et de Microcalorime Â trie du CNRS, 13331 Marseille Cedex 3, France

(Received 29 November 1996; accepted 6 February 1998)

Abstract ÐPrecipitation in Al±16 at.%Mg is investigated by dierential scanning calorimetry (DSC) andtransmission electron microscopy (TEM). The shape of the b' formation DSC eect is interpreted with anovel theory and the curves obtained on the basis of this new theory ®t well to the experimental curves.The s parameter derived from these ®ts, which is akin to the Avrami parameter n appearing in the John-

son±Mehl±Avrami±Kolmogorov model, is larger than 2.5, indicating that b' precipitation is an autocataly-tic process. TEM showed the abundant presence of defects (mostly dislocation loops) but no evidence of nucleation of b' precipitates on these defects. The enthalpies of formation of the b and b' phases are de-rived as 15.7 and 11.5 kJ per mol Mg, respectively. # 1998 Acta Metallurgica Inc.

1. INTRODUCTION

In the introduction of a recent publication by the

present authors, work on the precipitation in Al±

Mg alloys has been reviewed [1]. It was concluded

that although dierent symbols for the zones and

phases have been used, these publications (see, i.e.

Refs [2±8]) are consistent with the following precipi-

tation sequence (symbols as used in Ref. [2]):

sssa 3 GP zones 3 bHH 3 bH 3 b

where sssa is the supersaturated solid solution, GP

zone (also indicated as d0) stands for Guinier±

Preston zone, b0 (other indications: ordered GP

zone [9] or d') is an L12 ordered phase (composition

Al3Mg) [8], b' is a semi-coherent hexagonal inter-

mediate phase (approximate composition Al3Mg2)

with lattice parameters a = 1.002 nm and

c = 1.636 nm [5, 10], it is the main hardening

precipitate [11], and b is the equilibrium phase (ap-

proximate composition Al3Mg2) having a complex

f.c.c. structure with a = 2.824 nm [5, 10].

When solid solutions with up to 18 at.%Mg are

aged at temperatures in excess of about 1008C, no

L12 ordered phases or GP zones form. In solid-

quenched and liquid-quenched Al±Mg aged

between about 100 and 2508C the b' phase forms

®rst and the b phase only appears in the later stages

of ageing when the Mg depletion of the matrix is

nearly complete [5, 12].

Although precipitation in binary Al±Mg alloys

has been studied by many researchers, several ques-

tions relating to the nucleation of b', the kinetics of

b' formation and its transformation to b persist.

Several explanations have appeared in the literature

concerning the nucleation mechanisms of b'.

Bouchear et al . [7] concluded from a transmission

electron microscopy (TEM) study on precipitation

in Al±8.8 at.%Mg and Al±9.9 at.%Mg alloys that

b' nucleates on dislocation loops, which are abun-

dantly present in Al±Mg alloys. This interpretationis in agreement with early work by Embury and

Nicholson [13]. However, this view is at odds with

a TEM study on precipitation in an Al±8.3 wt%Mg

alloy from which Itoh et al . [14] concluded that dis-

location loops played no role in the nucleation of

b', and this latter interpretation is in agreement

with early TEM work by Eikum and Thomas [15].

Instead, Itoh et al . observed nucleation on tetrahe-

dron shaped voids. Little is known about the over-

all kinetics of b'/b formation. The present authors

have recently shown that it does not correspond

to Johnson±Mehl±Avrami±Kolmogorov (JMAK)

kinetics [16].

To shed light on these issues an extended rangeof isothermal and non-isothermal ageing exper-

iments were performed on an Al±Mg alloy, and

specimens were investigated using dierential scan-

ning calorimetry (DSC) and TEM. The experiments

were devised to illuminate two main topics. Pre-age-

ing around the stability limit of b0 followed by

DSC was performed in order to establish whether

b0 or defect structures in¯uence the kinetics of b'

formation, and experiments at a large range of

heating rates were performed to investigate whether

the heating rate in¯uences the transition from b' to

b. Further the DSC heat eects due to b' formation

were analysed with a new method for analysingnucleation and growth reactions occurring during

experiments at constant heating rates, which was

Acta mater. Vol. 46, No. 10, pp. 3381±3397, 1998# 1998 Acta Metallurgica Inc.

Published by Elsevier Science Ltd. All rights reservedPrinted in Great Britain

1359-6454/98 $19.00 + 0.00PII: S1359-6454(98)00053-6

{Currently at Dept. of Engineering Materials,

University of Southampton, Southampton SO17 1BJ,U.K.{To whom all correspondence should be addressed.

3381



recently developed by the present authors [17, 18]. It

will be shown that DSC curves can be ®tted per-

fectly with this new theory and parameters obtained

from the ®ts are interpreted in terms of the operat-ing reaction mechanisms. To study the precipitate

morphologies and defect structures, and for phase

identi®cation TEM was used.

2. EXPERIMENTAL

2.1. Alloy

A high purity alloy with nominal composition

Al±16 Mg was produced by conventional casting

and subsequent rolling at Centre de Recherches de

Voreppe (Aluminium Pechiney). Chemical analysis

of the alloys shows a Mg content of 14.5 wt% (15.8

at.%). Typical total impurity content is about 0.03

wt% (mainly Si). The grain size is large: about

0.2 mm.

2.2. Dierential scanning calorimetry

For DSC experiments, disks of 6 mm diameter

and 1 mm height (average mass about 70 mg) were

machined from homogenized ingots. The alloys

were solution treated (typically 2 h at 4408C) and

subsequently quenched in ice±water (IWQ). Alloys

were aged at 208C for up to 3 years and at selected

temperatures between 80 and 1508C for up to 8

days. Arti®cial ageing treatments were concluded by

cooling in air. Generally samples were stored inliquid nitrogen, and were kept at room temperature

for no longer than 15 min.

DSC experiments were performed at heating rates

between 1.23 and 808C using a Perkin±Elmer 1020

series DSC7. The system and its performance have

been described elsewhere [19]. The heat ¯ow is cali-

brated by measuring the heat of fusion of In. The

temperature is calibrated by taking the deviation

DT from the uncalibrated temperature equal to

DT DT 0 pT tF 1

(T in 8C) where F is the heating rate, p is a (small)

constant, t is a parameter depending on the time

constant of the DSC in combination with the

sample used [19] and DT 0 is DT extrapolated to

F = 0 DT 0 and p are determined by measuring the

onset of melting of In and Zn at various heating

rates and subsequently extrapolating to zero heating

rate, whilst t is determined from the variation of

the onset of (incipient) eutectic melting with heating

rate in the Al±16 at.%Mg alloy. In our Al±16

at.%Mg samples (incipient) eutectic melting occurs,

and hence this reaction can serve as a check for the

calibration. For F108C/min the eutectic tempera-

ture was constant within 20.18C and averaged

449.78C. This corresponds well with the values of

550218C quoted in the literature [20,21]. Forhigher F the measured eutectic temperature

increased to 550.58C, which is ascribed to small

inaccuracies in the method of calibration for T .

Temperatures at these heating rates were further

corrected by taking the eutectic melting point

(449.78C) as an internal reference and adding a(small) heating rate dependent term to equation (1).

Generally three experiments per heating rate were

performed, characteristic temperatures were repro-

ducible within about 20.78C. The procedures for

baseline correction are described elsewhere [17].

DSC curves presented re¯ect the heat ¯ow due to

reactions.

2.3. TEM

For TEM experiments, samples were heat treated

according to the above described procedures.

Additionally, some specimens were heated in the

DSC at 2.5 or 208C/min to selected temperature

and subsequently rapidly cooled. For specimens

heated at 2.58C/min, cooling was achieved inside the

DSC (cooling rateH1008C/min), whilst for samples

heated at 208C/min to 1508C, specimens were taken

out of the DSC and quenched in water. All specimens

were ground to about 100 mm and electropolished in

a 3:1 mixture of methanol and HNO3 at À208C. The

foils were examined in a Philips EM 400 T micro-

scope operated at 100 kV and a JEOL JEM 2000

microscope operated at 200 kV.

3. THEORY AND ANALYSIS METHODS

3.1. Nucleation and growth reactions at constant

heating rate

Recently [17], the present authors developed a

new method for analysing nucleation and growth

reactions occurring during experiments at constant

heating rates. As this method will also be used in

the present paper a brief description of it will be

given here.

The transformation is described using the so-

called ` extended volume'' concept (see also

Refs [22±27]). In the ``extended volume'' the indi-

vidual nuclei grow without any limitation of space.

In applying this concept ®rst the volume, V p, of the

region transformed at time t which nucleated at anearlier time z will be calculated. For diusion con-

trolled precipitation reactions, the transformed

volume will be de®ned as the volume of an imagin-

ary fully depleted area around a precipitate (with

the rest of the matrix undepleted) needed to give a

precipitate size equal to the real case with a diu-

sion zone. In general the following holds:

V p A1Gt À zm 2

where G is the average growth rate, A1 is a constant

which is related to the initial supersaturation, the

dimensionality of the growth and the mode of

transformation, whilst m is a constant related to thedimensionality of the growth and the mode of

transformation, i.e. diusion controlled growth or

STARINK and ZAHRA: b' AND b PRECIPITATION3382



growth in which each part of the interface has a

constant velocity (so-called linear growth). An over-

view of the values of m that occur for dierent

types of reactions has been given by Christian [25].The contribution of the particles which nucleated

during the time interval (z,z + dz) to the volume

transformed in the ``extended volume'' at time t,

V ext(t), is obtained by using equation (2):

dV ext A1I zV 0Gt À zm dz 3

where I (z) is the nucleation rate per unit volume.

Integrating and introducing aext=V ext/V 0, where V 0is the volume of the sample, yields

aext

t

0

A1I zGt À zm dzX 4

Generally, the growth rate is ruled by diusion andcan hence be approximated by an Arrhenius type

temperature dependency

GT G0 expÀE G

kBT

X 5

Further it is assumed that also the nucleation rate,

I (T ), can be approximated by an Arrhenius type

temperature dependency, i.e.

I T I 0 expÀE N

kBT

6

where kB is Boltzmann's constant, and E G and E N

are the activation energies for growth and nuclea-tion, respectively. The latter equation implies that

nucleation depends only on the mobility of atoms.

Especially when the driving force for the formation

of nuclei (i.e. the change in the Gibbs free energy

due to the transformation of a region) is small,

equation (6) may become invalid. However, nuclea-

tion during heating is considered (i.e. the exper-

iment starts at low temperature), and thus the

driving force for formation of nuclei will generally

be large and the current approximation will be

valid. From equations (4)±(6) follows (see

Refs [28, 29]:

aext FkB

E Gkc exp

ÀE eff

kBT

!T

F

2

2 3s

7

where

E eff mE G E N

m 18

s m 1 9

and kc is a constant. It should be noted that

equation (7) is an approximation which is only

accurate if E NIE G (see Ref. [28]). Also for the case

where nuclei are present before the start of the

transformation and no further nucleation occurs,equation (7) is a valid approximation [28, 29]. In

this case s = m and E e =E G. Note that provided

the assumptions concerning the type of temperature

dependence of the nucleation and growth processes

(both Arrhenius type) hold, the parameter s in non-

isothermal studies is equal to the so-called Avramiparameter n in isothermal studies.

Impingement is taken account of by using (see

Ref. [17])

da

daext

1 À ali 10

where li will be termed the impingement factor (see

also Ref. [30]). The general solution of equation (10)

for li61 is

a 1 Àaext

Zi

1

ÀZi

11

where Zi=1/(liÀ1). For li=1 the solution is

a 1 À expÀaextX 12

Alternatively an expression equivalent to

equation (12) is obtained from equation (11) for the

limit of Zi 4I, and hence equation (11) incorpor-

ates equation (12).

In many systems of technological importance,

metastable equilibrium states are of greater import-

ance than stable ones. In this paper, for reactions

involving the formation of equilibrium phases

ceq(T ) will denote the equilibrium concentration,

and for reactions where a metastable phase forms

ceq(T ) will denote the metastable equilibrium con-centration for that phase. It is assumed that the

variation of ceq(T ) as a result of the increase in tem-

perature is relatively slow as compared to variations

in the local concentrations of alloying atoms due to

diusion of atoms. This means that local concen-

trations of solute atoms in the matrix,

c(x, y,z,t,ceq(T )), can be obtained, in good approxi-

mation, from the concentrations as obtained in the

hypothetical case where ceq is constant:

c0 À cxY yY zY tY ceqT c0 À cxY yY zY tY ceq 0

c0 À ceqT

c0

13

where c0 is the initial concentration of alloying

atoms in the matrix. The amount of atoms trans-

formed in the course of the reaction is proportional

to the volume average of the left-hand side of the

equation. The volume average of the term

[c0Àc(x, y,z,t,ceq=0)] is proportional to a for the

case where ceq is constant. This latter case led to

equations (7) and (11). Hence, it follows that

x dx

dt

d

dta

c0 À ceqT

c0

!A2 14

where A2 is a constant, x is the amount of atoms in-

corporated in the growing nuclei divided by themaximum amount of atoms that can be incorpor-

ated according to the equilibrium phase diagram.

STARINK and ZAHRA: b' AND b PRECIPITATION 3383



As dx/dt is proportional to the heat eect caused

by a reaction, the combination of equations (7),

(11) and (14) can be used to ®t heat eects due to

precipitation reactions.

3.2. Determination of activation energies

From equation (7) it follows that for tempera-

ture, T f , at constant aext the following equation

holds:

lnF

T 2f

ÀE eff

kBT f

C 1 15

where C 1 is a constant which depends on the reac-

tion stage. This equation is similar to the one used

in the so-called Kissinger method but the latter is

usually obtained via a dierent set of assumptions

(see Ref. [31]). The Kissinger method allows the de-

termination of an average activation energy, E A,

but does not specify activation energies for nuclea-

tion or for growth.

In a previous paper [31] it was shown that the

Kissinger analysis is more accurate than the so-

called Ozawa method which is derived on the basisof a dierent approximation. It was also found that

the following expression is even more accurate than

the Kissinger method:

lnF

T 1X8f

ÀAE A

kBT f

C 2 16

with

A 1X0070 À 1X2 Â 10À5 E AE A in kJamol 17

C 2 is a constant which depends on the reaction

stage and on the kinetic model. Hence, to obtain

the activation energy with this new method the

slope of a plot of 1n(T f 1.8

/F) vs 1/kBT f should becalculated, whilst A can be evaluated using this

slope as a ®rst approximation for E A.

4. RESULTS AND DISCUSSION

4.1. DSC experiments and identi®cation of eects

In Fig. 1 DSC curves of Al±16 at.%Mg aged for

about a week at temperatures between 80 and

1508C are presented. Up to seven heat eects,

marked A±G, can be distinguished in these curves.

Generally the same eects appear in DSC curves

obtained for other heat treatments and at other

heating rates (see Fig. 2). To assist in the identi®-

cation of the eects, DSC samples have been heatedin the DSC to selected temperatures and sub-

sequently studied by TEM. Several micrographs

obtained from these experiments are presented in

Figs 3±5. The identi®cation of the DSC eects are

discussed below in reverse order.

Eect G is observed only for the present rather

concentrated alloy; alloys with Mg content lower

than 14 at.% do not show this eect [1]. Its

measured onset temperature 449.78C agrees well

with the reported eutectic temperature for Al-rich

Al±Mg alloys (5508C, see Ref. [21]). The eect is

very sharp (full width half peak is about 2.78C at a

heating rate of 208C/min), ruling out a diusion

controlled dissolution reaction. An additional ex-

periment showed that slow cooling at a rate of 28C/

min from 4608C, which will cause the formation of

the equilibrium b phase, causes a sharp increase in

the magnitude of eect F during a subsequent DSC

run. From these observations it is clear that the

eect is due to the incipient eutectic melting reac-

tion

bs Als 3 liqX

As the b phase which precipitates in the grains

during a DSC run is thought to dissolve during

eect F (see below), the b phase involved in incipi-

ent melting is thought to be mainly situated on thegrain boundaries. TEM has indeed revealed the pre-

sence of grain boundary precipitates. As the rela-

Fig. 1. DSC curves for Al±16 at.%Mg aged at 80, 100, 120 and 150 8C for about one week. Heatingrate is 208C/min.




tively large grain size causes the amount of grain

boundary area to vary from sample to sample, the

magnitude of eect G varies from sample to

sample, even when prior heat treatments are identi-

cal. The eutectic melting will not be studied further

in this work.

In the Al±16 Mg sample aged for 6 days at 1508C,

b' phase formation is nearly complete (see Ref. [16]).

Figure 1 shows that irrespective of previous heat

treatments and irrespective of b' phase formation,

the heat ¯ow of all samples from about 3308C until

the end of eect F at 4408C is identical. The peak

temperature of eect F corresponds roughly with

the solubility limit of b (see Ref. [21]) and hence the

eect between 330 and 4408C is ascribed to dissol-

ution of the b phase (see also Ref. [32]). The for-

mation of the b' phase as a result of ageing for 6

days at 1508C eliminates eect C whilst eect D

takes its place. Hence it is clear that these eects are

due to b' phase formation and dissolution, respect-

Fig. 2. DSC curves for Al±16 at.%Mg aged for 2 years at 208C obtained at heating rates of 1.2, 2.5, 5,10, 20, 40 and 808C/min.

Fig. 3. TEM micrograph (two-beam conditions) of defects in an Al±16 Mg sample heated at 20 8C/minto 1508C.




ively. The above indicates that eect E, which ismore pronounced at lower heating rates (see Fig. 2),

is due to the evolution of a state with b' phase to a

state with b phase. TEM in conjunction withselected area diraction (SAD) indeed con®rms that

before eect E all or nearly all precipitates are b'

Fig. 4. Dark ®eld micrograph (a) and corresponding SAD pattern (b) of an Al±16 Mg sample heated at2.58C/min to 2408C. B = [110].




phase (Fig. 4), whilst just after eect E SAD shows

that all b' phase has disappeared (Fig. 5). Note alsothe dierence in shape of the b' and b phase precipi-

tates that can be observed from these ®gures.

Isothermal calorimetry in combination with TEM

has shown that in the Al±16 at.%Mg alloy the sol-vus of the L12 ordered b0 phase is situated at about

908C [1]. This and other DSC work [6] shows that

Fig. 5. Bright ®eld micrograph (a) and corresponding SAD pattern (b) of an Al±16 Mg sample heatedat 2.58C/min to 2868C. B = [110].




dissolution of the b0 phase occurs during eect B.

TEM in conjunction with SAD on a DSC sample

heated to a temperature approximately midway

between eects B and C reveals that no precipitates

or L12 ordered phase are present and only defect

structures are observed (Fig. 3). Hence, b0 dissol-

ution during eect B is complete. A more detailedinvestigation of eect B for various Al±Mg alloys,

in combination with TEM experiments, led to the

conclusion that eect B in fact contains two subef-

fects, B1 and B2, due to dissolution of GP zones

and b0, respectively [1].

Before eect B a very small exothermic is

observed (Fig. 1). This eect, eect A, is ascribed to

the formation of GP zones or b0 phase. The identi-

®cation of the eects is summarized in Table 1.

4.2. TEM study of b' nucleation

To further investigate the eect of pre-ageing on

b' precipitation, TEM experiments were performed

on samples pre-aged and subsequently heated in the

DSC. A sample aged at 958C for 6 days and sub-

sequently heated in the DSC to 1508C (i.e. well

before eect C) shows the presence of a few scat-

tered b' precipitates (Fig. 6). On the other hand, a

sample aged at 858C for 7 days and subsequently

heated in the DSC to 1508C does not show any b'

but does show a very high density of defects (see

Fig. 7). These defects are nearly exclusively loops.

(For detailed studies on defect structures in

quenched and aged Al±Mg alloys, see e.g.

Refs [33, 34].) After heating to 2208C subsequent to

pre-ageing the defect structure still mainly consist

of loops, which have now grown to sizes ranging

from 30 to 200 nm (Fig. 8). The density and size of

these loops vary with distance to the grain bound-

ary (Fig. 8(a)). The latter is due to a diusion zone

of vacancies resulting from migration of vacancies

to grain boundaries.

Table 1. Identi®cation of the DSC eects

Eect Endo/exo Approx. range (8C) Identi®cation

A exothermic GP zone/b0 formationB1 endothermic 40±100 GP zone dissolutionB2 endothermic 80±140 b0 dissolutionC exothermic 180±290 b' formationD endothermic 200±300 b' dissolutionE exothermic 280±330 b'->bF endothermic 330±430 b dissolutionG endothermic 449.7±455 b melting

Fig. 6. Bright ®eld TEM micrograph of an Al±16 Mg sample aged for 6 days at 95 8C and subsequentlyheated in the DSC at 208C/min to 1508C. Note the presence of (relatively small) b' precipitates.




As noted in Section 1, some controversy exists in

the literature on whether b' precipitates nucleate on

defects. Figure 6 shows the very ®rst stages of for-

mation of these precipitates during ageing at 958C,

whilst Fig. 8 shows a similar stage after heating at

208C/min to 2208C subsequent to pre-ageing at

Fig. 7. Bright ®eld TEM micrographs (two-beam conditions) of Al±16 at.%Mg aged for 7 days at 85 8Cand subsequently heated at 208C/min to 1508C. A high density of small (40±150 nm diameter) loops are

observed. (a) The density of the loops varies with distance to a subgrain boundary (b).




Fig. 8(a,b).




858C. Hence these two ®gures show the very ®rst

stages of b' formation at a broad range of tempera-

tures, in the presence of a high density of defects.

Examination of these micrographs (and others)

shows that apparently there is no correlation

between the positions of the defects and the precipi-

tates, and careful TEM investigation of several

samples con®rms this observation, which appears to

contradict earlier observations by Bouchear et al . [7]

and by Embury and Nicholson [13]. Two possible

interpretations are envisaged: (i) b' precipitates do

not nucleate on defects, or (ii) b' precipitates nucle-

ate on or in the vicinity of vacancy type defects,

which then dissolve as a result of the nucleation

process, thus leaving no trace of the in¯uence of

those defects on nucleation. Analysis of the shape

of DSC eects (see next section) suggest that the

latter is the case.

4.3. Heating rate dependence of precipitation and dis-

solution

In Fig. 2 the DSC curves for Al±16 at.%Mg

aged for 2 years at 208C and heated at various rates

are presented. To study the main precipitation

eect, eect C, several methods of analysis were

used. First the activation energies were obtainedusing the isoconversion method given by

equation (16). The apparent activation energy

decreases with increasing amount of heat evolved

(see Fig. 9) and extrapolating to DH -> yields

E e =78 kJ/mol (0.81 eV).

To further study eect C this eect was ®tted

using the analysis method described in Section 3.1.

For E e the above value was used. From a study of

the available data on the equilibrium solubility of

Mg in the Al-rich phase of binary Al±Mg it was

found that this data can be well represented by

ceqT 0X016 8X88expÀ0X25 eV

kBT X 18

(For a review of the data see, e.g. Ref. [21].) In

Figs 10 and 11 two examples of such a ®t using the

expressions obtained in Section 3.1 are presented.

These ®gures show a very good correspondence

between experiment and theoretical expressions,

and also for experiments at other heating rates ®ts

of a similar good quality were obtained. Taken

together with an analysis of precipitation in Al±Si

alloys, which also showed a very good correspon-

dence between theory and experiment (see Ref. [17]),

this shows that the analysis method in Section 3.1 is

sound.

Figure 10 shows that for F = 408C/min no dis-tinct eect E can be observed, i.e. the formation of

b is complete at the end of the exothermic eect.

Fig. 8. Bright ®eld TEM micrographs (two-beam conditions) of Al±16 at.%Mg aged for 7 days at 85 8Cand subsequently heated at 208C/min to 2208C. Note the presence of b' precipitates (light, needle androd shaped) in (a), (b) and (c), and (contrast due to) defect loops, the size and density of which varywith distance to the grain boundary (see (a)). Note further that the b' precipitates do not seem to be re-

lated to defects.




Fig. 9. Apparent activation energies for b' formation obtained using equation (16).

Fig. 10. Eect C (broad, grey curve) and ®t (thin black curve) based on equations (7), (11) and (14) forAl±16 at.%Mg aged for 2 years at 208C. Heating rate 408C/min.

Fig. 11. Experimental DSC curve for Al±16 at.%Mg aged for 2 years at 208C (thick, grey curve) and®t based on equations (7), (11) and (14) (thin, black curve). The end temperature and the heat eect of

b' formation are derived from the ®t. Heating rate 58C/min.




For lower heating rates eect E appears to continue

beyond the end temperature of the exothermic

eect, i.e. the formation of b is only partially com-

plete at the end of the exothermic eect. The above

described ®ts and their extrapolations will be used

to obtain the heat due to b' formation, DQb', and

the end temperature of b' phase formation, T end(b').

This procedure is outlined in Fig. 11. Also the total

exothermic heat evolved during the main precipi-

tation eect up to T end(exo), DQend, was obtained.

This data is analysed in the following manner.

As at the end of a precipitation eect the average

concentration of alloying elements should equal the

equilibrium or metastable equilibrium composition,

the following relation generally holds (see also

Ref. [35]):

DQ DH c0 À ceqT end 19

where DH is the enthalpy of formation of the phase

concerned. In Fig. 12 the data obtained for DQend

and DQb' are plotted as a function of their end tem-

peratures. In the same ®gure also the total heats

evolved during isothermal calorimetry (see Ref. [16])are indicated. The lines presented in this ®gure are

obtained by taking ceq as in equation (18) and

adjusting DH b' and DH b to ®t the upper and the

lower range of the data. This results in DH b'=11.5

kJ per mol Mg and DH b=15.7 kJ per mol Mg.

Figure 12 shows that within experimental error the

evolved heats measured with DSC and with isother-

mal calorimetry are contained between the two lim-

iting cases for b' phase and for b phase formation.

From the position of the measured heats relative to

the two curves we can deduce:

(i) DQb' from the DSC experiments corresponds to

b' formation;(ii) DQend for the DSC experiment at 408C/min cor-

responds to b formation;

(iii) DQend for the DSC experiments at F208C/

min corresponds to a mixture of b formation

and b' formation;

(iv) the DQ values for the isothermal experiments

at T 1708C correspond to b' formation;

(v) the DQ values for the isothermal experiments at

T >2108C correspond to b formation;

(vi) at intermediate isothermal ageing temperatures

DQ values indicate a gradual shift from b' for-

mation to b formation.

The good correspondence between the data shows

that the presented interpretation of the heat eects

and their end temperatures is essentially sound.

In the above interpretation of the integrated heat

of eect C it has been assumed that the solvi of b'

and b are identical. This evidently is an oversimpli-

®cation, as in general the metastable solvus of b'

should be situated at higher concentrations as com-

pared to the one for b. The good correspondence

obtained with this simpli®cation may indicate that

there is indeed little dierence between the two

solvi. However, by assuming several hypothetical b'

solvi it can be shown that a b' solvus with ceqwhich is 1.1±1.2 times the one for b still yields

reasonable results in an interpretation based on

equation (19). It should be stressed that these var-

ious hypothetical solvi do not aect conclusion (i)±

(vi) above.

In Table 2 the values of the transformation expo-

nent s as obtained from the above described ®tting

procedure are presented. It is observed that s

decreases with increasing heating rate from about 6

to 3.2 at 808C/min. (Note that a variation in s can

generally be detected by comparing the initial parts

of DSC precipitation peaks: a large slope indicates

a high s.) At this point it is important to note thatthe high values of s cannot directly be explained by

the theory as presented in Section 3.1, as this theory

Fig. 12. Exothermic heats of formation of b' and b as measured by DSC: eect C up to T end(exo) (q),extrapolated up to T end(b') (w). Also indicated are the exothermic heats obtained from isothermalcalorimetry experiments (Q). The lines are obtained from theoretical expressions for the heats of for-

mation and solubilities (see text).




would yield a maximum value of 2.5 for s. Values

for s larger than 2.5 indicate an autocatalytic pro-

cess, i.e. a process in which the presence of precipi-

tates enhances the nucleation of new precipitates.

This ®nding is in agreement with precipitation stu-

dies using isothermal calorimetry [36] in which it

was found that at temperatures above 2008C b' for-

mation is an autocatalytic process. Several mechan-

isms responsible for the autocatalytic nature of b'

formation may be considered. Firstly, it may be

envisaged that mis®t stresses around newly formed

b' precipitates can create dislocations which can act

as nucleation sites for new precipitates. A similar

process has been identi®ed to be responsible for the

autocatalytic formation of AlN precipitates during

internal nitriding of recrystallized Fe±2 at.%Al [37],

resulting in n values which are comparable to the s

values given in Table 2. However, the present TEM

and DSC experiments fail to conclusively show that

dislocations created around precipitates play a rolein autocatalytic b' formation. Instead of dislo-

cations (i.e. plastic deformation), the elastic defor-

mation around newly formed mis®tting b'

precipitates may cause favourable conditions for the

formation of other precipitates.

Whereas TEM experiments fail to give conclusive

evidence for the mechanisms mentioned above, they

do show (Fig. 7) that just before the start of b' for-

mation a high density of defects is present, but the

®rst b' precipitates do not appear to be spatially

linked to the defects (Fig. 8). The fact that defect

structures are observed up to relatively high tem-

peratures (2208C in Fig. 8) indicates that they are

stabilized by the presence of regions enriched in Mg

(i.e. solute clusters). This suggests a third possible

mechanism for autocatalytic precipitation: emission

of vacancies on formation of precipitates.

Speci®cally, this means that ®rst the formation of a

precipitate occurs in a region which is enriched in

solute (possibly a cluster). This then leads to the

dissolution of the vacancy type defect which was

stabilized by the cluster, and the released vacancies

can subsequently accelerate further precipitation by

enhancing the diusion of Mg atoms. This would

imply that vacancies have to diuse away from the

solute depleted region around a newly formed pre-

cipitate in order to assist in the formation of another precipitate in a solute rich region. This

mechanism can explain why s decreases with

increasing heating rate: at high heating rate less

time is available for diusion of vacancies, and

hence less possibility for an autocatalytic process to

be eective. As the processes considered in the pre-

vious paragraph are basically instantaneous, they

cannot account for the decrease of s with increasing

heating rate, and hence it is concluded that the lat-

ter process is the most likely explanation of the

observed autocatalytic nature of b' formation.

A further means of investigating the connection

between vacancies and the autocatalytic formation

of b' precipitates is through variation of the

vacancy concentration. The latter generally

increases with increasing solution treatment tem-

perature and increasing cooling rate, and on the

basis of this two additional experiments were

devised. Firstly DSC experiments have been per-

formed on the Al±16 Mg alloy cooled at dierent

rates. Also in these DSC experiments eect C can

be ®tted very well with the model outlined inSection 3 (®gures not presented), and results show

that s increases with cooling rate, i.e. s increases

with vacancy concentration. In a second experiment

Al±16 Mg samples were either water quenched or

slowly cooled by introduction into a furnace at

1508C. Subsequently both samples were studied by

isothermal calorimetry (see Ref. [36]), and the

curves were analysed to obtain the Avrami par-

ameter n. This analysis yielded n = 5 for the

quenched sample and n = 3 for the slowly cooled

sample. Both experiments show that vacancies

enhance the autocatalytic formation of b' precipi-

tates, and are hence further indications that the

mechanism for autocatalytic formation of b' pre-

cipitates outlined above is correct. A further vali-

dation of the in¯uence of vacancies can be obtained

from the work of van Rooyen et al . [6], in which

precipitation in liquid-quenched (LQ) and solid-

quenched (SQ) Al±Mg alloys is compared. From a

study of the activation energy for the dissolution of

b0 phase (eect B) they concluded that SQ alloys

contained a higher concentration of vacancies than

LQ alloys. Their DSC experiments (see, e.g. Figure

5 in Ref. [6]) show that, for the two types of

samples, the SQ samples have a much higher value

for s, again indicating that vacancies enhance auto-

catalytic formation of b' precipitates.The results presented thus far have shown that s

is dependent on heating rate. Consequently descrip-

Table 2. Analysis of b'/b phase precipitation DSC eect for IWQ Al±16 Mg samples ( T pis the peak temperature, T (DQ = À 2 J/g) is the temperature at which DQ equals À2 J/g)

F (8C/min) T (DQ = À 2 J/g) (8C) T p (8C) s Zi

1.25 198 211 5.4 0.302.5 212 224 6.3 0.285 227 241 5.7 0.29

10 244 261 5.0 0.2920 265 285 4.5 0.1640 292 319 3.3 0.2780 327 353 3.2 0.14




tions of the reaction rate by an equation of the type

da

dt gT f a 20

with f (a) a function depending only on the fraction

transformed, and g(T ) a function of temperature,

cannot be valid for the present transformation. If,

notwithstanding this, an activation energy analysis

is performed on the Al±16 Mg alloys, the decrease

of s with increasing heating rate will cause E e to

decrease with the amount transformed. (This can be

proven, for instance, by generating theoretical

curves of reactions using s values which decrease

with heating rate, and analysing them with the

methods presented in Section 3.2.) The observed

decrease of E A with fraction transformed as pre-

sented in Fig. 9 is consistent with this. From TEM

experiments it was further noted that when isother-

mally aged samples with a similar fraction trans-

formed were compared, the length of the b'

precipitates increases strongly with ageingtemperature [36]. This shows that for this trans-

formation process it is not possible to de®ne a state

variable, i.e. a single variable which de®nes the

state of the transformation for all types of isother-

mal or non-isothermal ageing, and that

equation (20) as well as a standard Arrhenius analy-

sis are not valid. Hence derived activation energies

cannot be interpreted on the basis of underlying

processes, and comparison with activation energies

obtained by other researchers can be in¯uenced by

the choice of the transformation stage. It is never-

theless noted that E A values for an IWQ Al±12.5

at.%Mg alloy obtained by Nozato and Ishihara [4]

(77.5 kJ/mol) and for liquid-quenched Al±10.5

at.%Mg and Al±16.7 at.%Mg by van Mourik et

al . [12] (about 90 kJ/mol{) are broadly in line with

our results. Dierences in E e may well be due to

dierences in vacancy concentration, the latter

being higher for IWQ alloys than for liquid-

quenched alloys.

4.4. In¯uence of pre-ageing on b' phase formation

In Fig. 1 DSC curves of Al±16 Mg samples aged

for about a week between 80 and 1508C were pre-

sented. In order to study b' formation in more

detail, several more IWQ samples were pre-aged

between 20 and 1008C for about a week and sub-

sequently analysed in the DSC apparatus. All

samples which were aged at room temperature for

up to 3 years and those aged up to 808C for up to

1 week yielded nearly identical DSC curves forT >1508C. This indicates that neither GP zone nor

b0 formation in¯uences b' precipitation. Several par-

ameters obtained from the analysis of the DSC

curves are presented in Table 3. The total heat evol-

ution during eects C±F, DQC±F, as presented in

this table, is calculated by integrating the curves

from 180 to 4488C. The obtained DQC±F is the total

heat due to b' phase and b phase formation and b'

phase and b phase dissolution, and in the case

neither b' phase nor b phase is present at the start

of the DSC experiment, DQC±F should equal zero.

The values given in Table 3 show that for ageing

temperatures between 20 and 908C, DQC±F is indeed

nearly constant and close to zero. The small nega-

tive values are ascribed to minor inaccuracies in the

determination of the baseline, or a possible small

variation of the calibration constant of the DSC ap-

paratus with temperature. On increasing the ageing

temperature beyond 908C, DQC±F increases signi®-

cantly, indicating that b' phase forms during these

ageing treatments. This interpretation is corrobo-

rated by the TEM micrographs in Figs 6 and 7

which show that at 1508C (i.e. well before the start

of the b' phase precipitation eect in the DSC run),

the DSC sample pre-aged at 958C contains small (b'

phase) precipitates whilst the one pre-aged at 858C

does not.Also for eect C in the DSC curves of pre-aged

Al ±16 at.%Mg ®ts were obtained using

equations (7), (11) and (14). Fits were of the same,

very good quality as those presented in Figs 10 and

11. The s and Zi values obtained from these ®ts are

presented in Table 3. This data show that when the

ageing temperature is increased from 80 to 1008C, s

decreases from about 4.5 to 1.5. Values of s larger

than 2.5 are again interpreted as being due to an

autocatalytic nucleation process, and the decrease

with increasing ageing temperature can be explained

as follows. For the case of site saturation, i.e. when

a relatively large number of nuclei is created duringpre-ageing, s should equal 1.5 (see Section 3.1).

Hence, when during a pre-ageing treatment some b'

Table 3. Analysis of b' phase precipitation DSC eect for Al±16 Mg samples quenched and sub-sequently naturally or arti®cially aged for about 1 week (T (DQ = À 2 J/g) is the temperature at

which DQ equals À2 J/g)

T a (8C) t (days) T (DQ = À 2 J/g) (8C) T p (8C) s Zi DQC±F (J/g)

20 7 265 282 4.3 0.18 0.380 7 263 280 4.5 0.33 À1.585 7 251 270 3.7 0.39 À0.790 8 223 252 2.8 0.39 À1.395 6 211 252 1.9 0.61 0.1

100 6 204 246 1.5 1.21 7.2

{This value is obtained from a reanalysis of van Mourik

et al .'s lattice parameter data, which shows that the acti-vation energy quoted in their original paper (H70 kJ/mol)is inaccurate.




nuclei are formed, s will start to decrease, and when

the amount of nuclei created during pre-ageing is

suciently large to make further nucleation during

the DSC run negligible, s reaches the value of 1.5.It can be seen from the discussion in the previous

paragraph that a state with important amounts of

b' nuclei is encountered in the sample aged at

1008C for 1 week. Indeed Table 3 shows that for

that sample s has decreased to 1.5. Apparently,

after this pre-ageing treatment the amount of nuclei

formed is so large that further nucleation during

the DSC run is negligible. Further investigation of

Table 3 shows that the decrease in s in fact starts at

a pre-ageing temperature of about 858C. As a re-

duction of vacancy concentration caused s to

decrease, one may take this as evidence for vacancy

annihilation. However, for the same pre-ageing

treatment, the start temperature of the b' formation

eect (taken as T at DQ = À 2 J/g) begins to

decrease, which cannot be explained by vacancy an-

nihilation. Instead it is thought that already after

one week at 858C some very small nuclei have

formed and that TEM failed to detect these nuclei.

5. CONCLUSIONS

The precipitation of the b and b' phases in Al±16

at.%Mg is investigated by DSC and TEM. The

results may be summarized as follows:

.DSC curves show up to seven eects, and the

eects occurring above 1508C have been identi®edwith the aid of TEM. There is no direct transform-

ation from b0 to b'.

.A novel theory for the analysis and ®tting of

nucleation and growth reactions was applied to

analyse the shape of the b' formation eect, which

is the ®rst eect to occur above 1508C. One of the

parameters in this theory is the transformation

exponent s, which is akin to the Avrami parameter

n appearing in the Johnson±Mehl±Avrami±

Kolmogorov model.

.The curves obtained on the basis of the new the-

ory ®t well to the experimentally obtained curves,

and s parameters larger than 2.5 obtained from

these ®ts show that b' precipitation is an autocataly-

tic process.

.s depends on vacancy concentration, and, on the

basis of this, a model for the autocatalytic for-

mation of b' precipitates is presented.

.Pre-ageing experiments show that when b' nuclei

have formed during the pre-ageing, s decreases to

1.5. This is in agreement with the novel theory pre-

sented for nucleation and growth reactions.

.TEM showed the abundant presence of vacancy

type defects (mostly dislocation loops) but no evi-

dence of nucleation of b' precipitates on defects.

.The integrated heat of the b and b' phase for-

mation eect is analysed and compared with iso-thermal calorimetry data. Both sets of data

correspond well with a model for integrated heats

of precipitation eects. The formation enthalpies of

b and b' phase are derived to be 15.7 and 11.5 kJ

per mol Mg, respectively.

Acknowledgements ÐThis work is ®nanced in part by theEC Human Capital and Mobility project. C. Zahra isthanked for performing DSC experiments. The authorsare grateful to Dr A. Charaõ È of CP2 M, Universite Â d'Aix-Marseille III, and S. Nitsche of CRMC2 du CNRS,Marseille for making available TEM facilities.

REFERENCES

1. Starink, M. J. and Zahra, A-M., Phil. Mag. A, 1997,76, 701.

2. Osamura, K. and Ogura, T., Metall. Trans., 1984,15A, 835.

3. Dauger, A., Boudili, E. K. and Roth, M., Scr. metall.,

1976, 10, 1119.4. Nozato, R. and Ishihara, S., Trans. Japan. Inst., 1980,

21, 580.5. Bernole, M., Thesis, University of Rouen, Rouen,

France, 1974.6. van Rooyen, M., Sinte Maartensdijk, J. A. and

Mittemeijer, E. J., Metall. Trans., 1988, 19A, 2433.7. Bouchear, M., Hamana, D. and Laoui, T., Phil. Mag.

A, 1996, 73, 1733.8. Sato, T., Kojima, Y. and Takahashi, T., Metall.

Trans., 1982, 13A, 1373.9. Dauger, A., Fumeron, M., Guillot, J. P. and Roth,

M., J. Appl. Cryst., 1979, 12, 429.10. Bernole, M., Raynal, J. and Graf, R., J. Microscopie,

1969, 8, 831.11. Nebti, S., Hamana, D. and Cizeron, G., Acta metall.

mater, 1995, 43, 3583.12. van Mourik, P., Maaswinkel, N. M., de Keijser, Th.

H. and Mittemeijer, E. J., J. Mater. Sci., 1989, 24,3779.

13. Embury, J. D. and Nicholson, R. B., Acta metall.,1963, 11, 347.

14. Itoh, G., Cottereau, B. and Kanno, M., Mater. Trans.JIM , 1990, 31, 1041.

15. Eikum,A. and Thomas, G., Acta metall., 1964, 12, 537.16. Starink, M. J. and Zahra, A-M., Mater. Sci. Forum,

1996, 217, 795.17. Starink, M. J. and Zahra, A-M., Thermochim. Acta,

1997, 292, 159.18. Starink, M. J. and Zahra, A-M., Phil. Mag. A, 1998,

77, 187.19. Zahra, C. Y. and Zahra, A-M., Thermochim. Acta,

1996, 276, 161.

20. Chartrand, P. and Pelton, A. D., J. Phase Equilibria,1994, 15, 591.

21. Murray, J. L., Bull. Alloy Phase Diagr., 1982, 3, 60.22. Avrami, M., J. chem. Phys., 1939, 7, 1103.23. Avrami, M., J. chem. Phys., 1940, 8, 212.24. Avrami, M., J. chem. Phys., 1941, 9, 177.25. Christian, J. W., in The Theory of Transformation in

Metals and Alloys, 2nd edn, Part 1. Pergamon Press,Oxford, 1975.

26. Cumbrera, F. L. and Sanchez-Bajo, F., Thermochim.Acta, 1995, 266, 315.

27. Sessa, V., Fanfoni, M. and Tomellini, M., Phys. Rev.B, 1996, 54, 836.

28. Woldt, E., J. Phys. Chem. Solids, 1992, 53, 521.29. Kru È ger, P., J. Phys. Chem. Solids, 1993, 54, 1549.30. Lee, Eon-Sik and Kim, Young G., Acta metall.

mater., 1990, 38, 1669.

31. Starink, M. J., Thermochim. Acta, 1996, 288, 97.32. Abis, S., Ledda, F. and Evangelista, E., Mater. Lett.,

1987, 5, 369.




33. Smallman, R. E. and Eikum, A., in Proc. ``LatticeDefects in Quenched Materials'', Argonne, Illinois,U.S.A., June 1964, ed. R. M. J. Cotterill, M. Doyama,J. J. Jackson and M. Meshii. Academic Press,

London, 1965, p. 591.34. Swart, V. P. and Kritzinger, S., Acta metall., 1973, 21,

605.

35. Starink, M. J. and Gregson, P. J., Scripta metall.mater., 1995, 33, 893.

36. Starink, M. J. and Zahra, A-M., J. Mater. Sci ., inpress.

37. Somers, M. A. J., Ph.D thesis, Chap. II, DelftUniversity of Technology, Delft, The Netherlands,1989.


b' and b precipitation in an al±mg alloy studied by dsc and tem

Documents