Phase transformation kinetics during the heating of an Al ... - CiteSeerX

High Temperatures ^ High Pressures, 2002, volume 34, pages 535 ^ 548

DOI:10.1068/htjr045

Phase transformation kinetics during the heating of an Al ^ 8 at% Li alloy Nasser Afify, Abdel-Fattah Gaber, Mostafa Saad Mostafa, Saud Bin Anooz ô

Physics Department, Faculty of Science, Assiut University, Assiut 71516, Egypt; fax: +20 88 342708; email: [email protected]; [email protected] Received 13 June 2001, in revised form 14 January 2002

Abstract. The kinetics of the reactions (dissolution and precipitation) in Al ^ 8 at% Li alloy were investigated by differential scanning calorimetry (DSC). Analysis of nonisothermal DSC scans at different heating rates was carried out to evaluate the overall activation energies associated with the transformation processes during continuous heating of the quenched alloys. An average activation energy associated with dissolution of Guinier ^ Preston zones was found to be 73:42 5:41 kJ molÿ1 , which implies that the dissolution process is controlled by the migration of lithium atoms through the aluminium matrix. The average activation energy of d0 phase precipitation was 62:65 4:43 kJ molÿ1. The activation energies of dissolution of the d0 phase and dissolution of the d phase or lithium in the matrix were 132:47 4:03 and 398:40 3:98 kJ molÿ1 , respectively. The reaction order of all processes indicates that they occur three-dimensionally throughout the aluminium matrix. d and d0 phases have been detected in naturally (1800 min) aged specimens by x-ray diffraction.

1 Introduction The properties of heat-treatable automotive alloys depend on their microstructure, which is controlled by alloy chemistry and processing. However, the material is characterised by measuring different properties of the product, while the microstructural state is rarely monitored. Monitoring microstructural changes by a microscopic technique can be a time-consuming exercise. It would be useful to develop a more rapid means of relating microstructure to the properties of alloys. The differential scanning calorimetry (DSC) is one way of achieving this goal in a commercial environment. Modern DSC instruments are economical, fast, sensitive, and yield reproducible results. They are used for quality control, and in the process of material development. Appropriate procedures have been described by Gupta et al (1998). DSC has been used to study the kinetics of precipitation and dissolution of metastable and stable phases in aluminium alloys (Antonion et al 1988; Gupta et al 1998; Van Rooyen and Mittemeijer 1989; Staring 1996; Starink and Zahra 1998a, 1998b). Gaber (1999) measured the total heat effect in Al ^ 16 at% and 18 at% Mg alloys and estimated the activation energies associated with the precipitation and dissolution of the precipitates. Jena et al (1989) estimated the activation energies for precipitation and dissolution of Guinier ^Preston zones and the s 0 ^ (Al2 CuMg) precipitates in the Al ^ 1.53 wt% Cu ^ 0.79 wt% Mg alloy from the peak temperature corresponding to exothermal and endothermal reactions. 2 Experimental techniques 2.1 Sample preparation and homogenisation Al ^ 3 wt% Li ( 10:8 at% Li) standard alloy supplied by Air Bus Company, Bremen, Germany was used to prepare specimens of Al ^ 8 at% Li by dilution with 99.99% pure aluminium. The preparation technique consisted of melting the required weights of ô Permanent address: Hadhramout University of Science and Technology, Mukalla 50511, Yemen; email: s [email protected].

536

N Afify, A-F Gaber, M S Mostafa, S Bin Anooz

Al ^3 wt% Li and pure aluminium under argon in Forschungszentrum Ju«lich, Germany. The quartz tube containing the melt was homogenised by frequent shaking, and then cooled in the furnace to room temperature. The prepared ingot was cylindrical, 20 mm in diameter. 2.2 Chemical analysis of the ingots Chemical analysis of the prepared ingot was performed by atomic absorption spectrometry (BUCK Scientific, model 210 VGP). The actual content of lithium in the alloy was 7.892 at%. Trace elements included 0.05% Fe, 0.03% Si, 0.02% Zn, and < 0:01% Ti by weight. 2.3 Differential scanning calorimetry (DSC) Disc-shaped DSC samples (5 mm diameter and 0:5 mm thick) were machined and solution heat treated for 30 min at 803 K in a standard convection furnace. An annealed pure aluminium disc of very similar weight was used as a reference. Nonisothermal thermograms were obtained for the as-quenched specimens (quenching medium temperature 273 K) with a Schimadzu DSC thermal analyser TA-50 at heating rates ranging from 2.5 to 50 K minÿ1. DSC scans were started at room temperature and completed at 773 K, under a nitrogen atmosphere at a flow rate of 35 ml minÿ1. The output was in milliwatts and the net heat flow to the reference material (pure aluminium) relative to the sample was recorded as a function of temperature. The calorimetric sensitivity was 8 10ÿ5 J sÿ1 cmÿ1 and the temperature measurement precision was 0:1 K. This means that the peak temperatures of the reaction processes were determined with an accuracy of 0:1 K by using the microprocessor of the thermal analyser. 2.4 x-Ray diffraction (XRD) Al ^ 8 at% Li specimens measuring 12 17 mm2 were prepared for XRD; the specimens were naturally aged for 1800 min and artificially aged at 425 and 500 K for 30 min. The XRD investigations of the specimens were carried out with a Philips type 1710 chart diffractometer. The radiation source was CuKa with a graphite monochromator with l 0:154178 nm, operating at 40 kV and 30 mA. The scanning speed was 0:068 sÿ1. The scattering angle 2y was measured between 58 and 908 at steps of 0:028. All XRD investigations were performed at room temperature. The characteristic XRD CuKa (l 0:154056 nm) was extracted from the spectra by stripping CuKa from it by using the ratio Ka =Ka 0:52. 1

2

2

1

3 Results and discussion 3.1 Differential scanning calorimetry (DSC) Figure 1 shows a nonisothermal DSC thermogram of supersaturated Al ^ 8 at% Li. The experiments were carried out on as-quenched alloys from room temperature to 773 K at heating rates ranging from 2.5 to 50 K minÿ1. Five main processes can be identified from the DSC thermogram. (I) Trough Iöthis endothermal process takes place at temperatures ranging from 410 to 435 K depending on the scanning rates. We suggest that this process is due to the dissolution of the performed Guinier ^ Preston zones (figure 1). From the DSC scans one can notice that this process becomes less pronounced at lower heating rates. (II) Peak IIöthis exothermal process can be attributed to the formation of d0 (Al3 Li) phase and occurs at temperatures ranging from 435 to 525 K, depending on the scanning rates. (III) Trough IIIöthis endothermal process can be attributed to the dissolution of the formed d0 (Al3 Li) phase which appears at temperatures ranging from 530 to 550 K, depending on the scanning rates, as can be observed in figure 1.

Phase transformation kinetics during heating of Al ^ 8 at% Li alloy

IV V

50.0 Exo

537

I II III

40.0

b=K minÿ1

30.0 25.0 20.0 15.0

Endo

10.0 7.5 5.0 2.5

200

400

600

800

T=K

Figure 1. DSC thermograms of Al ^ 8 at% Li at different heating rates, b.

(IV) Peak IVöthis exothermal process occurs at temperatures ranging from 555 to 675 K, depending on the scanning rates. It suggests the formation of d (AlLi) phase, and becomes less pronounced at lower heating rates (figure 1). This exothermal process is too broad, so there is an uncertainty in identifying its peak. Therefore the precipitation kinetics cannot be analysed. (V) Trough Vöat a temperature of 695 K, an endothermal reaction takes place, (figure 1). This reaction is believed to be due to the dissolution of lithium or d phase in the matrix. The observed dependence of exothermal and endothermal peak temperatures in reactions I, II, and III on the scanning rates indicates that these processes are thermally activated, whereas the trough V temperature exhibits practically no shift towards higher temperature with increasing heating rate. This behaviour indicates that this reaction is dominated by its temperature-dependent thermodynamic equilibrium. 3.2 Transformation kinetics Studies of transformation kinetics (precipitation and dissolution of the precipitates) are always connected with the concept of activation energy. The studies of precipitation processes are associated with nucleation and growth processes, which dominate in supersaturated alloys. In general, separate activation energies must be identified with individual nucleation and growth steps in a transformation, although they have usually been combined into an activation energy representative of the overall precipitation process (Afify 1992; Gaber et al 1999). In the present work, the nonisothermal method was used, with the sample heated at a fixed rate b, and the heat evolved recorded as a function of temperature or time. The theoretical basis for interpreting DSC data is provided by the formal theory of transformation kinetics, as the volume fraction, w, precipitated or dissolved in time, t, by the Johnson ^ Mehl ^ Avrami equation (Afify 1992; Gaber et al 1999; Vazuez et al 2000; Yinnon and Uhlmann 1983): n

or

w 1 ÿ exp ÿkt ,

(1)

1 1=n ÿln 1 ÿ w , t k

(2)

538


where n (the time exponent) is the reaction order which depends on the mechanism of nucleation growth and the dimensionality of the crystal (specimen) (Afify 1992; Yinnon and Uhlmann 1983). k is defined as the effective overall reaction rate constant, which is usually assumed to have an Arrhenian temperature dependence: E k k0 exp ÿ , (3) RT where E is the effective activation energy describing the overall transformation process, k0 is the pre-exponential constant, and R is the universal gas constant. In addition, in nonisothermal precipitation, it is assumed that there is a constant heating rate, b, in DSC experiments. The relation between the sample temperature, T, and the heating rate, b, can be written in the form T T0 bt ,

(4)

where T0 is the initial temperature. Differentiating equation (1) results in the following expression: t (5) w_ 1 ÿ w nk n t n ÿ 1 1 k_ , k where w_ dw=dt and k_ dk=dt. The derivative of k with respect to time is obtained

from equations (3) and (4): dk dT bE k_ k . dT dt RT 2

(6)

Thus equation (5) becomes w_ 1 ÿ w nk n t n ÿ 1 1 at ,

(7)

2

where a bE=RT . Any operation on equation (7), such as differentiation or integration of dw=dt, can be expressed as (Afify 1992; Yinnon and Uhlmann 1983) w_ gwkT .

(8)

Thus, if the dependence of w_ on temperature can be separated from its dependence on w, a number of ways exist in which g(w) and k(T ) can be formulated, since both w and T are functions of time. 3.2.1 Method of Ozawa. The method proposed by Ozawa (1971) is used, in addition to determining the activation energy associated with individual processes, to deduce the reaction order of each transformation process (n). From equations (3) and (8), we can write: E _w gwk0 exp ÿ . (9) RT By rearranging equation (9) and integrating we obtain w t dw E dt Gw . k0 exp ÿ RT 0 gw 0

(10)

The integration is carried out from the beginning of the reaction until some volume fraction w is transformed. The fraction G(w) is independent of the heating rate and used to obtain the transformed fraction w. The time integral in equation (10) is transformed into a temperature integral, yielding k0 T E Gw dT . (11) exp ÿ b T RT 0


539

If T0 5 T and E=RT 4 1, the solution of equation (11) is (Abramowitz and Stegun 1972; Afify 1992; Doyle 1965; Gradshteyn and Ryzhik 1980): k RT 2 E 1=n (12) Gw ÿ ln1 ÿ w 0 exp ÿ Eb RT or in logarithmic form ln 1 ÿ w nE k0 R ÿ1 ln ÿ . ÿn ln b=K min ÿ n ln 2n RT nE T=K

(13)

Differentiation of equation (13) at constant temperature gives dfln ÿln 1 ÿ wg ÿn . dln b=K minÿ1

(14)

On this basis, plotting ln [ ÿ ln (1 ÿ w)] versus ln (b=K minÿ1 ) obtained at the same temperature from a number of precipitation exotherms taken at different heating rates should yield the value of n. Equation (13) can be rewritten in the form: 1 E ln b=K minÿ1 ÿ ln ÿln 1 ÿ w ÿ ln T 2 =K2 const . (15) n RT Using the approximation of Mahadevan et al (1986) we find that the variation of ln (T 2 =K2 ) with ln (b=K minÿ1 ) is much slower than that of [1=(T=K)] with ln (b=K minÿ1 ). Thus, assuming that the transformed fraction w at the peak temperature is constant, the relation ln (b=K minÿ1 ) versus [1=(Tp =K)] yields the overall activation energy E of the process under consideration. The fraction w, defined above, is obtained from the ratio of partial area of the process at the given T (calculated by computer program) to the total area of the process. Figure 2 shows a plot of w as a function temperature for process II. 1.0 b=K minÿ1 ! 2:5

5.0

15

20

40

50

0.8

b=K minÿ1 50

0.6

40 w

30 25 0.4

20 15 10 7.5

0.2

5.0 2.5

0.0 400

420

440

460

480 T=K

500

520

540

560

Figure 2. The precipitate volume fraction w plotted against T for process II (precipitation of d0 phase) in Al ^ 8 at% Li alloy.

540


The reaction order (time exponent), n, for process II [formation of d0 (Al3 Li)] in Al ^ 8 at% Li sample can be obtained by using equation (14). This is based on plotting ln [ ÿ ln (1 ÿ w)] versus [1=(T=K)]. w, the fraction of d0 precipitated at temperature T, lies in the range from the onset of the precipitation and the peak temperature for the specific heating rate b. Using the plot of w against T (figure 2) for different heating rates, we obtain a family of straight lines (figure 3) for Al ^ 8 at% Li. By intersecting the set of the straight lines at a fixed temperature, say T 500 K, we obtain a plot of ln [ ÿ ln (1 ÿ w)] versus ln (b=K minÿ1 ) shown in figure 4. The slope of the straight line thus obtained yields the reaction order n. The reaction order n for process II is found to be 2:61 0:09.

2 15

5.0

2.5

b=K minÿ1 50

50

ln [ ÿ ln (1 ÿ w )]

1

40 30 25

0

20 15 10

ÿ1

7.5 5.0 2.5

ÿ2

ÿ3 1.8

1.9

2

2.1

2.2 103 K=T

2.3

2.4

2.5

2.6

Figure 3. ln [ ÿ ln (1 ÿ w )] plotted against 103 K=T for process II (precipitation of d0 phase) in Al ^ 8 at% Li alloy. 7 T 500 K

6

ln [ ÿ ln (1 ÿ w )]

5 4 3 2 1 0 ÿ1 ÿ2

0

1

2 3 ln ( b=K minÿ1 )

4

5

Figure 4. ln [ ÿ ln (1 ÿ w )] plotted against ln ( b=K minÿ1 ) at T 500 K for process II (precipitation of d0 phase) in Al ^ 8 at% Li alloy.


541

Similar calculation for process I yields the value of n 0:77 0:13. Processes I, II, III suggest the dissolution of GP zones, the precipitation of d0 (Al3 Li), and the dissolution of d0, respectively. Process V is believed to be due to dissolution of lithium or the d phase in aluminium matrix. By using the Ozawa method, plotting ln (b=K minÿ1 ) against [1=(Tp =K)] [equation (15)] we obtain figure 5, which yields the overall activation energy of the processes I, II, III, and V as E 80:90 0:34 (a), 69 0:27 (b), 139 0:73 (c), and 407 0:33 (d) kJ molÿ1, respectively.

ln ( b=K minÿ1 )

4

3

2

1

(c) (d)

0 1.2

1.5

1.8

(b)

2.1

(a)

2.4

103 K=T

Figure 5. ln ( b=K minÿ1 ) plotted against 103 K=T for (a) process I (dissolution of GP zones), (b) process II (precipitation of d0 phase), (c) process III (dissolution of d0 phase), and (d) process V (dissolution of lithium or d phase in the matrix) in Al ^ 8 at% Li alloy.

3.2.2 Method of Takhor. If T0 5 T and E=RT 5 1, equation (7) becomes w_ 1 ÿ w nk n t n ÿ 1 .

(16)

The method of Takhor (1972) is based on differentiating equation (16) twice. It will be recalled that equation (16) does not take proper account of the change of k with time (and temperature), and Takhor's method makes the same inappropriate assumption of ignoring the time dependence of k in the second differentiation. Assuming that k 6 k(t) and the maximum rate of precipitation occurs at the peak of the exotherm (x___ 0) at time tp and temperature Tp (Afify 1992; Yinnon and Uhlmann 1983), the differentiation of equation (16) with respect to time yields w___ nk n t n ÿ 2 n ÿ 1 ÿ nk n t n 0 .

(17)

Then

nE n . n ÿ 1 nk0 tp exp ÿ RTp

Equation (4) is then invoked to convert the time tp to temperature Tp, yielding b 1 n E ln k0 =minÿ1 ÿ minÿ1 ln . ln Tp ÿ T0 n nÿ1 RTp

(18)

(19)

By using Takhor's method, equation (19), the effective activation energy can be determined from the relation between ln [b=(Tp ÿ T0 )] and 1=Tp as shown in figure 6. The activation energies deduced from the slopes of the straight lines for processes I, II, III, and V are 68:80 0:34 (a), 58:70 0:26 (b), 129:90 0:72 (c), and 398:20 0:36 (d) kJ molÿ1 , respectively.

542


ÿ2:5

ÿ3:5

ln

b Tp ÿ T0

minÿ1

ÿ1:5

ÿ4:5

(c)

ÿ5:5 0.75

(b)

(a)

(d) 1.25

1.75

2.25

2.75

103 K=T

Figure 6. lnf[ b=(Tp ÿ T0 )]=minÿ1 g plotted against 103 K=T for (a) process I, (b) process II, (c) process III, and (d) process V in Al ^ 8 at% Li alloy.

3.2.3 Method of Kissinger. For transformation studies performed at a constant heating rate, a method for determining E can be derived by integrating equation (9) by separation of variables and assuming E=RTp 4 1 (Kissinger 1956). At a constant fraction transformed, w, this leads to: b E ÿ1 ÿ1 ln K min ÿ C . (20) Tp2 RTp Here C is a constant which depends on the reaction stage and on the kinetic model. According to equation (20), plots of ln (b=Tp2 ) versus 1=Tp should result in straight lines; the slope of these straight lines yields E=R. For the evaluation of the activation energy from the variation of Tp with b we can use equation (20). Plots in figure 7 show the ln (b=Tp2 ) versus 1=Tp relationships. The values of E for processes I, II, III, and V deduced from this relation equal to 73:80 0:34 (a), 61:70 0:28 (b), 131:30 0:73 (c), and 391:50 0:37 (d) kJ molÿ1, respectively. ÿ7:5

ÿ9:5

ÿ10:5

ln

b Tp2

Kÿ1 minÿ1

ÿ8:5

ÿ11:5

ÿ12:5

(d) 1

1.5

(c) 2

(b)

(a) 2.5

3

103 K=Tp

Figure 7. ln [( b=Tp2 )=Kÿ1 minÿ1 ] plotted against 103 K=T for (a) process I, (b) process II, (c) process III, and (d) process V in Al ^ 8 at% Li alloy.


543

3.2.4 Method of Piloyan ^ Borchardt. In the Piloyan et al (1983) ^ Borchardt (1960) method, the term bt was neglected in comparison to unity on the assumption that E=RT 5 1. This assumption can cause an unacceptable error in most studies because for most precipitation and dissolution reactions E=RT is greater than unity (typically E=RT 5 25). Therefore the unity was neglected in comparison to 25 (Afify 1992). In our study we calculated the term E=RT and we found a good agreement with Afify's suggestion. A better approach seems reasonable, if T0 in equation (4) is much smaller than T. The term at E=RT, and equation (7) becomes w_ 1 ÿ wnk n t n ÿ 1

E . RT

(21)

Combining equation (21) with the concept of Borchardt (1960) that, at least for w < 0:5, the reaction rate w_ at a particular temperature T is proportional to the heat flow difference between the sample and the reference (Dq), leads for DSC to w_ CDq ,

(22)

where C is a constant. In proceeding further, the following operations are performed: (a) Substituting for t from equation (2) into equation (21) gives w_

nkE Fw , RT

(23)

where the function F(w) is defined as n ÿ 1=n

Fw 1 ÿ wÿ ln1 ÿ w

.

(b) Combining equations (22) and (23) gives E E CDq nk0 Fw exp ÿ . RT RT (c) Taking the logarithm and rearranging equation (25) gives TDq nk0 E E mW minÿ1 ln K mW ln K ÿ ln ; C Fw R RT

(24)

(25)

(26)

ln [(TDq)=F(w)] is a linear function of (1=T ). The slope of this relation yields the effective activation energy of precipitation, E. The relation between ln [(TDq)=F(w)] and (1=T ) for process II at various heating rates is shown in figure 8. The average activation energy obtained is 61:20 1:76 (b) kJ molÿ1 . Similarly the activation energies for processes I, III, and V, 70:20 0:34 (a), 129:70 1:91 (c), and 391:50 2:10 (d) kJ molÿ1, are obtained by the same method. Effective activation energies, and the reaction orders (time exponents) of the processes which are obtained by nonisothermal DSC by the different methods considered above are summarised in table 1. Our results on activation energies associated with the individual processes can be compared with other reports. The activation energy associated with the precipitation of d0 (Al3 Li) phase is lower than 84:2 kJ molÿ1 reported by Luo et al (1993) for d0 formation in Al ^ Li (8090) alloy. This discrepancy can be attributed to the additional elements such as copper and magnesium in Al ^ Li (8090). On the other hand, the value of 62:65 4:43 kJ molÿ1 is also lower than the energy of 82:43 kJ molÿ1 determined for GP zones and d0 precipitation in Al ^ Li (8090) alloy determined by Gaber and Afify (1997). For the dissolution of d0 precipitates, an activation energy of 132:47 4:03 kJ molÿ1 has been determined. This value is in fair agreement with the energy of 128:5 3:5 kJ molÿ1 obtained by Luo et al ( ..... ) for Al ^ Li (8090). Furthermore, our value is in excellent agreement with the energy of 131:5 kJ molÿ1 deduced by Balmuth (1984) for an Al ^ 3 wt% Li (10.8 at%) binary alloy.

544


From the above statement, it is clear that our results are more consistent with those for Al ^ Li binary alloys rather than for the multi-element Al ^ Li base alloys. In Al ^ Li and Al ^ Li ^ Mg systems, the only strengthening metastable phase present appears to be d0. Since d0 nucleates homogeneously quite easily (Sanders and Starke 1989), the decomposition of the supersaturated solid solution can occur without the need for introducing heterogeneous nucleation sites such as dislocations. The kinetics of each process can be characterised by assuming the presence of diffusion-controlled continuous transformation processes in precipitation or dissolution of the precipitates. Therefore, the transformation mechanisms as well as the nucleation conditions can be discussed by comparing the reaction order results obtained in this 8.3 8.1 b=K minÿ1 50 30

20

40 30

7.7

25 40

7.5

20 15

ln

TDq F(w)

K mW

7.9

10

7.3

7.5

10 7.1

6.9 6.7

1.9

50 7 1.95

2

2.05

2.1

2.15

2.2

103 K=T

Figure 8. lnf[TDq=F (w )]=K mWg plotted against 103 K=T for process II (precipitation of d0 phase) in Al ^ 8 at% Li alloy. Table 1. Overall activation energies associated with the transformation processes and the time exponents of the early stages of precipitation. Process

Activation energy E=kJ molÿ1 Ozawa

Dissolution of 80:90 0:34 GP zone Precipitation 69:00 0:27 of d0 Dissolution 139:00 0:73 of d0 Dissolution of 407:00 0:33 lithium or d phase in the matrix

Takhor

Kissinger

Piloyan ± Borchardt

average

Time exponent, n

68:80 0:34

73:80 0:34 70:20 0:83 73:43 5:41 0:73 0:13

58:70 0:26

61:70 0:28 61:20 1:76 62:65 4:43 2:61 0:09

129:90 0:72 131:30 0:73 129:70 1:91 132:40 4:03 398:20 0:36 396:90 0:37 391:50 2:10 398:40 3:98


545

study with those deduced from different mechanisms of transformation (table 2). I in this table stands for the nucleation rate, which is expressed by: I

1 dNv , 1 ÿ w dt

where Nv is the number of nucleation particles per unit volume of the crystal (Christian 1975; Raghavan 1987). According to the determined activation energies of the transformation processes and the reaction orders (tables 1 and 2, respectively), the transformation and nucleation growth of the precipitates as well as their dissolution can be summarised as follows: (i) Dissolution of GP zones (process I ). The average activation energy obtained for this process is 73:42 5:41 kJ molÿ1. Using the value of 140 kJ molÿ1 for the diffusion of lithium atoms in aluminium (Mondolfo 1976) and the value of 67:74 kJ molÿ1 for the formation energy of a vacancy in aluminium (Furukawa et al 1976), the migration energy of lithium atoms in aluminium can be calculated as 72:26 kJ molÿ1. This value is consistent with the obtained activation energy associated with the dissolution of GP zones. This suggests that the dissolution mechanism of GP zones is controlled by migration of lithium atoms in the aluminium matrix. (ii) Precipitation of d0 (Al3 Li) phase (process II ). For this process, an average activation energy of 62:65 4:43 kJ molÿ1 has been determined (table 1). This energy is in excellent agreement with the value of 62:5 1:9 kJ molÿ1 obtained from the resistivity measurements in Al ^ Li (8090) alloy (Luo et al 1993). The obtained value is close to the migration energy of lithium in aluminium (72:26 kJ molÿ1 ) which suggests, also, that the precipitation mechanism of d0 phase is associated with migration of lithium atoms to the nucleation sites of the precipitates. The reaction order n 2:61 0:09 implies that the nucleation and growth of d0 precipitates take place in the three dimensions simultaneously, with increasing nucleation rate of new tiny precipitates. (iii) Dissolution of d0 precipitates (process III ). The average activation energy associated with the dissolution of d0 precipitates is determined as 132:47 4:03 kJ molÿ1. This energy is close (within the experimental error) to that of diffusion of lithium in aluminium, which suggests that the dissolution of the d0 phase is controlled by a diffusion mechanism. This mechanism is accomplished three-dimensionally in the bulk of the matrix. (iv) Dissolution of lithium or the d phase in the matrix (process V). It is seen from the DSC scans at different heating rates that the reaction peak exhibits a slight shift with increasing heating rate. This indicates that the reaction is not thermally activated, but, rather, is to some extent temperature-dependent. Thus, it should be associated with a high activation energy. The obtained activation energy for this process is 398:40 3:98 kJ molÿ1. This value is three times that obtained for dissolution of the d0 phase. Table 2. Time exponent for diffusion-controlled growth. Description of the transformation Particles of all shapes growing in all three dimensions (1) increasing I (2) constant I (3) decreasing I (4) zero I Rod-like particles growing radially, zero I Disc-like particle thickening, zero I

n >2.5 2.5 1.5 ± 2.5 1.5 1.0 0.5

546


3.3 x-Ray diffraction In order to obtain confirmation that the precipitates of d0 (Al3 Li) and d (AlLi) phase are formed by ageing, an x-ray diffraction (XRD) study has been carried out. The characteristic XRD spectra were obtained with a powder diffractometer with CuKa radiation (l 1:5418 A). The Ka radiation was stripped from the spectra by using the ratio Ka =Ka 0:52 to obtain CuKa radiation (l 1:54056 A). Transmission x-ray powder diffraction data were collected in the range 58 4 2y 4 908. Figure 9a shows the characteristic XRD for naturally aged (1800 min) Al ^ 8 at% Li solid solution. Figure 9b shows the same spectrum with a suitable amplification. With the aid of the data reported in table 3 which show the angular position and the relative intensity associated with a, d0, and d phases, the peaks in the spectrum can be identified (Perez-Landazabal et al 2000). Taking into consideration that the parameter of d0 (ad 4:03 A), the d0 phase reflection could be made to coincide with a-Al or occur at slightly higher angle (aAl 4:05 A). From the data listed in table 3 for an Al ^ Li binary alloy (Al ^ 8.1 at% Li ^ 0.03 at% Zr), it is found that the most intense d0 diffraction peaks coincide with the most intense a peaks that occur in (1 1 1) and (2 0 0) planes (Perez-Landazabal et al 2000). In addition, d0 phase appears at Bragg angle adjacent to a-Al peaks from (2 2 0), (3 1 1), and (2 2 2) planes. An additional d0 peak is observed at the Bragg angle of 2y 73:938 from (3 1 0) reflection plane. In a specimen naturally aged for 1800 min, minor d phase particles, compared with d0 phase, have been also detected at 2y ' 258 from (1 1 1) reflection planes, and at 2y 47:38 and 78:58 from (3 1 1) and (5 1 1) reflection planes, respectively. 2

2

1

1

0

3000 2500

Counts

2000 1500 1000 500 35

45 2y=8

Al (111) d0

120 80 40

(b)

5

15

25

65

35

45 2y=8

75

d0

d0 d (311) d0 (2 10 ) d (3 31)

d0 (1 0 0) d (111)

Counts

160

0

Al (2 0 0)

200

55

55

65

85

Al (3 11)

25

d0

75

d0

Al (2 2 2)

15

Al (2 2 0)

5

d0 (2 2 1) d0 (3 1 0) d (511)

0

(a)

d0

85

Figure 9. The x-ray spectrum of an Al ^ 8 at% Li specimen naturally aged for 1800 min. (a) Fullscale spectrum, and (b) suitably amplified spectrum.


547

Table 3. Angular position and relative intensity associated with the a, d0, and d phases. 2y=8

I=I0 21.90 24.17 31.20 38.48 40.00 44.70 47.30 50.31 55.51 57.85 63.62 65.09 69.59 72.65 73.93 77.85 78.20 82.40 86.30 86.60

d0

a (h k l )

d

I=I0

(h k l )

28

(1 0 0) (1 1 0) (1 1 1)

100

(1 1 1)

25 100

52

(2 0 0)

52

(2 0 0)

8 6

(2 1 0) (2 1 1)

23 3

(2 2 0) (2 2 1)

2

(3 1 0)

18 4

(3 1 1) (2 2 2)

1

(3 2 0)

25

21 5

(2 2 0)

(3 1 1) (2 2 2)

I=I0

(h k l )

75

(1 1 1)

100

(2 2 0)

27

(3 1 1)

12 8

(4 0 0) (3 3 1)

17

(4 2 2)

5

(5 1 1)

3

(4 4 0)

4 Conclusions (1) The DSC results indicate that the precipitation sequence in supersaturated Al ^ Li alloys is as follows: supersaturated a phase ! Guinier ^ Preston (GP) zones ! d0 (Al3 Li) phase precipitates ! d (AlLi) phase precipitates. The characteristic temperature at which the processes occur depends on the heating rate, ie the processes are thermally activated. (2) The overall activation energy associated with the dissolution of GP zones (73:42 5:41 kJ molÿ1 ) is close to the migration energy of lithium atoms in aluminium (72:26 kJ molÿ1 ); this indicates that the dissolution mechanism is characterised by migration of lithium atoms in the aluminium matrix. (3) The time exponent and the average effective activation energy associated with the precipitation process of d0 (Al3 Li) process (n 2:61 0:09 and E 62:65 4:43 kJ molÿ1 ) suggest that the precipitation mechanism of d0 phase proceeds through migration of lithium atoms to the nucleation sites of the precipitates. The nucleation and growth of d0 precipitates take place in three dimensions during the increasing nucleation rate of new tiny precipitates. (4) The average activation energy of dissolution of metastable d0 (Al3 Li) phase is 132:47 4:03 kJ molÿ1 . This energy is close to that of diffusion of lithium in aluminium, which suggests that dissolution of the d0 phase is controlled by a diffusion mechanism. (5) No valid estimate can be made with regard to the precipitation mechanism of the d (AlLi) phase on the basis of the kinetics of thermal analysis, owing to the high uncertainty in identifying the peak temperature of the very broad effect associated with the process. (6) For the dissolution of the d phase or lithium in aluminium the activation energy is 398:40 3:98 kJ molÿ1 . The reaction peak of this process exhibits a slight shift with increasing heating rate. This indicates that the reaction is not thermally activated, but rather, to some extent, temperature dependent. (7) With the use of XRD, d0 phase has been detected in specimens naturally aged for 1800 min.

548


Acknowledgements. We gratefully acknowledge the technical assistance of Dr M A Hussein, Physics Department, during the course of this work. The Deutsche Gessellschaft fu«r Technishche Zusammenarbeit (GTZ) and the Deutsche Akademische Austauschdienst (DAAD), Germany are acknowledged for partly supporting this work by a grant-in-aid (projects No. PN 87.2061.7-01.100 and PN 87.2061.7-02.300-9314). References Abramowitz M, Stegun I E, 1972 Handbook of Mathematical Functions (New York: Dover) Afify N, 1992 J. Non-Cryst. Solids 142 247 ^ 259 Antonion C, Marino F, Riontino G, 1988 Mater. Chem. Phys. 20 13 ^ 35 Balmuth E S, 1984 Scr. Metall. 18 301 ^ 304 Borchardt H J, 1960 J. Inorg. Nucl. Chem. 12 252 Christian J W, 1975 The Theory of Transformations in Metals and Alloys: An Advanced Textbook in Physical Metallurgy (Oxford: Pergamon Press) pp 525 ^ 548 Doyle C D, 1965 Nature 207 290 ^ 291 Furukawa K, Takamura J, Kuwana N, Tahara R, Abe M, 1976 J. Phys. Soc. Jpn. 41 1584 ^ 1592 Gaber A, 1999 Aluminium Trans. 1 93 ^ 102 Gaber A, Afify N, 1997 Appl. Phys. A 65 57 ^ 62 Gaber A, Afify N, Gadalla A, Mossad A, 1999 High Temp. ^ High Press. 31 613 ^ 625 Gradshteyn I S, Ryzhik I M, 1980 Tables of Integrals, Series, and Products (New York: Academic Press) Gupta A K, Jena A K, Lloyd D J, 1998, in Proceedings of the 6th International Al-alloys Conference Eds T Sato, S Kumai, T Kobayashi, Y Murakomi (5 ^ 10 July, Toyohashi, Japan) volume II, pp 663 ^ 669 [available from the Department of Materials Science, Faculty of Engineering, University of Virginia, Charlottesville, VA 22903, USA] Jena A K, Gupta A K, Chaturvedi M C, 1989 Acta Metall. Mater. 37 885 ^ 895 Kissinger H E, 1956 J. Res. Natl. Bur. Stand. 57 217 ^ 221 Luo A, Lloyd D J, Gupta A K, Youdelis W V, 1993 Acta Metall. Mater. 41 769 ^ 776 Mahadevan S, Giridhar A, Singh K, 1986 J. Non-Cryst. Solids 88 11 ^ 34 Mondolfo L F, 1976 Aluminium Alloys: Structure and Properties (London: Butterworths) pp 311 ^ 323 Ozawa T, 1971 Polymer 12 150 ^ 158 Perez-Landazabal J I, No M L, Madariaga G, Recarte V, San Juan J, 2000 Acta Mater. 48 1283 ^ 1296 Piloyan G O, Rybachikov I D, Novikov O S, 1983 Nature 212 1229 Raghavan V, 1987 Solid State Phase Transformations (New Delhi: Prentice Hall of India) pp 82 ^ 93 Sanders T H Jr, Starke E A Jr, 1989, in Proceedings of the 5th International Al ^ Li Conference (27 ^ 31 March, Virginia, USA) pp 4 ^ 35 [available from the Department of Materials Science, Faculty of Engineering, University of Virginia, Charlottesville, VA 22903, USA] Starink M J, 1996 Thermochim. Acta 288 97 ^ 104 Starink M J, Zahra A M, 1998a Phil. Mag. A 77 187 ^ 199 Starink M J, Zahra A M, 1998b Acta Mater. 46 3381 ^ 3397 Takhor R L, 1972 Advances in Nucleation and Crystallization of Glasses (Columbus, OH: American Ceramic Society) p. 166 Van Rooyen M, Mittemeijer E J, 1989 Metall. Trans. A 20 1207 ^ 1214 Vazuez J, Lopez-Alemany P L, Villares P, Jimenez-Garay R, 2000 J. Phys. Chem. Solids 61 493 ^ 500 Yinnon H, Uhlmann D R, 1983 J. Non-Cryst. Solids 54 253 ^ 275

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