Study of Precipitation Kinetics in Al-3.7 wt% Cu Alloy during Non-Isothermal and Isothermal Ageing

CHINESE JOURNAL OF PHYSICS VOL. 51, NO. 5 October 2013

Study of Precipitation Kinetics in Al-3.7 wt% Cu Alloy during

Non-Isothermal and Isothermal Ageing

Messaoud Fatmi,1, ∗ Brahim Ghebouli,2 Mohamed Amine Ghebouli,1, 3

Tayeb Chihi,1, 4 El-Hadj Ouakdi,5 and Zein Abidin Heiba6, 7

1Research Unit on Emerging Materials (RUEM),University Ferhat Abbas Setif 1, 19000, Algeria

2Laboratory of studies of Surfaces and Interfaces of Solids Materials,University Ferhat Abbas Setif 1, 19000, Algeria

3Microelectronic Laboratory (LMSE), University of Bordj-Bou-Arreridj 34000, Algeria4Laboratory for Elaboration of New Materials and Characterization (LENMC),

University Ferhat Abbas Setif 1, 19000, Algeria5Laboratory of Physics and Mechanics of Metallic Materials (LP3M),

University Ferhat Abbas Setif 1, 19000, Algeria6Department of Physics, Faculty of Sciences, University of Taif, KSA

7Department of Physics, Faculty of Sciences,Ain Shams University of Cairo, Egypt

(Received May 8, 2012; Revised January 1, 2013)

Studies of transformation kinetics during ageing of Al-3.7 wt% Cu were performed by useof X-ray diffraction and Differential Scanning Calorimetry (DSC) methods at different heat-ing rates. Both non-isothermal and isothermal ageing processes were conducted in order todetermine the isothermal transformation kinetics based on the JMA (Johnson-Mehl-Avrami)equation and the Avrami exponent, n, whose mean is ∼ 1.78. The frequency factor calculatedby the isothermal treatment is ∼ 1.65×106 s−1. The activation energy of discontinuous pre-cipitation has been calculated according to the three models proposed by Kissinger, Ozawa,and Boswell.

DOI: 10.6122/CJP.51.1019 PACS numbers: 81.40.Cd, 81.30.Mh, 07.85.Jy

I. INTRODUCTION

Recrystallization is a process of fundamental importance in the thermomechanicalprocessing of metals, since it restores a worked metal to an unworked and formable state.This transformation results from the decomposition of a supersaturated solid solution α0

into a depleted matrix α and new precipitate β [1–4]. The earliest occurrence of DP (dis-continuous precipitation) was reported in 1930 [5]. The processes of precipitation in thealuminum-copper alloys are well known. Starting from supersaturation of the solutes byannealing at about 540 ◦C, the alloys undergo fast cooling to room temperature and a pe-riod of aging by which G-P (Guinier-Preston) zones are incurred. θ′′ (Al2Cu) precipitatesthat nucleate on the most stable G-P zones then follows. The other G-P zones dissolve

∗Electronic address: [email protected]

http://PSROC.phys.ntu.edu.tw/cjp 1019 c⃝ 2013 THE PHYSICAL SOCIETYOF THE REPUBLIC OF CHINA

1020 STUDY OF PRECIPITATION KINETICS IN . . . VOL. 51

in the solid solution, and the copper atoms diffuse to the growing nuclei. When the tem-perature increases, because of aging, the θ′′ dissolves, and θ′ nucleates at defects in thesolid solution. Finally, the equilibrium phase θ (Al2Cu) nucleates at the boundaries of thesolid solution grains, θ′ (Al2Cu) dissolves, and the copper atoms diffuse to the growing θ(Al2Cu) [6–9]. Concerning the previous studies related to discontinuous precipitation inAl-Cu alloys, there are limited publications. Among them, for example, Jing et al. [10]have analyzed the thermodynamics of Guinier-Preston zone formation in aged supersatu-rated Al-Cu alloys by combining interfacial and strain energies in the Gibbs free energy forthe GP zone formation. Many investigations have been devoted to examining the details ofthe precipitation sequence in this alloy system [11–13], using both theoretical models andseveral newly-developed techniques [14]. Through isothermal studies within a temperaturerange of about 210 ◦C from 50–260 ◦C, Wierszy l lowski et al. [28] estimated taht the acti-vation energies of the precipitation processes should fall between ∼ 50 kJ/mol and ∼ 100kJ/mole, while at 377–462 ◦C, the activation energy varies from 226 to 300 kJ/mol.

II. THEORETICAL APPROACH

II-1. Isothermal treatments

From a microstructural standpoint, the first process to accompany a phase trans-formation is nucleation: the formation of very small (often submicroscopic) particles, ornuclei, of the new phase, which are capable of growing. Favorable positions for the forma-tion of these nuclei are imperfection sites, especially grain boundaries. The second stageis growth, in which the nuclei increase in size; during this process, of course, some volumeof the parent phase disappears. The transformation reaches completion if growth of thesenew phase particles is allowed to proceed until the equilibrium fraction is attained.

As would be expected, the time dependence of the transformation rate (which isoften termed the kinetics of a transformation) is an important consideration in the heattreatment of materials. With many kinetic investigations, the fraction of a reaction that hasoccurred is measured as a function of time, while the temperature is maintained constant.Transformation progress is usually ascertained by either microscopic examination or themeasurement of some physical property (such as the electrical conductivity) the magnitudeof which is distinctive of the new phase. Data are plotted as the fraction of transformedmaterial versus the logarithm of time; an S-shaped curve represents the typical kineticbehavior for most solid-state reactions.

The theoretical basis for interpreting the DSC results is provided by the Johnson-Mehl-Avrami (JMA) theory, which describes the evolution of the precipitation fraction, y,with the time, t, during a phase transformation under an isothermal condition [15, 16]:

y(t) = 1 − exp(−ktn), (1)

where k, n are time-independent constants for the particular reaction and Y is the volumefraction crystallised after time t. The above expression is often referred to as the Avramiequation. The temperature dependence is generally expressed by the Arrhenian-type equa-

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VOL. 51 MESSAOUD FATMI, BRAHIM GHEBOULI, ET AL. 1021

tion:

K = K0 exp

(

−Ea

RT

)

, (2)

where k0 is the frequency factor, Ea is the apparent activation energy, R is the ideal gasconstant (8.314 J/mol K), and T is the isothermal temperature in Kelvin. Taking thelogarithm of Eq. (1) and rearranging gives

− ln(1 − y) = (kt)n. (3)

After twice taking the logarithm, one obtains:

ln(− ln(1 − y)) = ln k + n ln(t) (4)

At a given temperature, the values of n and k are obtained from an isothermal DSC curveusing Eq. (4) by least-squares fitting of ln[− ln(1−y)] versus ln(t). The Avrami exponent isdetermined traditionally by an isothermal method [17], and its value depends strictly on theincubation time, which cannot be given exactly. On the other hand, the isothermal heatingis more difficult to perform than non-isothermal annealing by differential scanning calorime-try (DSC). Here, we intend to propose a method of multi-scanning rates for measurementof the Avrami exponent for Al-3.7 wt% Cu alloy.

II-2. Non-isothermal Treatments

In a non-isothermal DSC experiment, the temperature is changed linearly with timeat a known scan rate α(= dT/dt):

T = T0 + αt, (5)

where T0 is the starting temperature, and T is the temperature after time t. As thetemperature constantly changes with time, k is no longer a constant but varies with timein a more complicated form, and Eq. (1) becomes:

y = 1 − exp

{

−k(T − T0)

n

α

}

. (6)

If the rate of transformation is maximal, reflected as a peak of the DSC curve, the maximumis at the DSC curve peak, then T = Tp, and d2y/dt2 = 0.

After deducing Eq. (6), Kissinger [18], Ozawa [19], and Boswell [20] developed a non-isothermal analytical method by using the highest rate of transformation, i.e., the raterelated to the peaks of the DSC data, and found

ln

(

α

Tp2

)

= −Ea

RTp

+ C1, (7)

ln(α) = −Ea

RTp

+ C2, (8)


ln

(

α

Tp

)

= −Ea

RTp

+ C3, (9)

where C1, C2, and C3 are constants, Tp is the temperature at the DSC-curve maximum,α = dT/dt is the heating rate and Ea is the activity energy.

III. EXPERIMENTAL PROCEDURE

These materials were prepared in our laboratory by fusion in a device at a high vacuum(10−5 Torr) using pure materials. After the melting, the ingots have undergone a plasticdeformation by cold rolling before the homogenization treatment in order to accelerate thestructure homogenization kinetics. The homogenization temperature and aging time werechosen from the equilibrium diagrams [21].

The ingots were homogenized in vacuum at 530 ◦C for 5 h and quenched in water toobtain a supersaturated solid solution α0. The samples were prepared into a disk shape of3 mm diameter and 1 mm thickness for the DSC analysis with a NETZSCH 200 PC DSC.To prevent oxidation during analysis, a protective atmosphere of nitrogen was used. X-ray diffraction analysis was performed by a “PAN Analytical X’ Pert PRO” diffractometerusing CuKα radiation, scanned at a speed of 0.9 ◦C/min.

The chemical analysis of the Al-3.7 wt% Cu alloy is presented in Table I.

TABLE I: Chemical composition of Al-3.7 wt% Cu alloy.

Element Al Cu Fe Si Mg

Composition (wt%) 96.20 3.70 0.05 0.03 0.02

IV. RESULTS AND DISCUSSIONS

IV-1. DSC analysis

IV-1-1. Non-isothermal treatments

The non-isothermally treated alloys were also analyzed by DSC at different heatingrates (α = 4, 6, 8, and 10 ◦C/mn) from room temperature to 450 ◦C, as given in Fig. 1.

These curves show an exothermal peak which corresponds to the energy dissipationduring the formation of the θ′ and θ (Al2Cu) phases by discontinuous precipitation [22].In fact, we noticed that the peak moves towards higher temperatures as the heating rateincreases. This can be attributed to two possible effects. The first comes from the decreaseof the precipitated Cu atoms amount due to the higher solid solubility at higher temper-atures and higher heating rates [23, 24], while the second is associated with the diffusivenature of the precipitation reactions.

Determination of the activation energy needed for the θ′ and θ-phases to form wasdone via the Kissinger, Ozawa, and Boswell methods, starting from the change in the


FIG. 1: DSC thermograms of Al-3.7 wt% Cu alloy as a function of the heating rate α.

temperature that corresponds to the maximum of the exothermic peak Tp according to theheating rate α for the first phase θ′ (Fig. 2a) and the second phase θ (Al2Cu) (Fig. 2b).Activation energies derived from the curve slopes are very close, as is shown in the followingTable II: These values for the θ′ and θ-phases formation are in good agreement with workson Al-4.7 wt% Cu alloy, in which the values lie between 60.70 and 303.86 kJ/mol fortemperatures ranging from 200 to 320 ◦C [28].

TABLE II: It presented the values of activation energies for θ′ and θ-phases formation in Al-3.7 wt%Cu alloy.

Method Kissinger Ozawa Boswell

Phases θ′-phase θ-phase θ′-phase θ-phase θ′-phase θ-phase

Ea (KJ/mol) 67.43 ± 3.2 58.19 ± 2.9 79.92 ± 4.8 65.50 ± 3.2 76.67 ± 4.2 73.92 ± 3.8

The transformed fraction Y , which characterizes the running rate of the reaction ata corresponding Tj temperature, is given by the formula, Y =

∆Sj

S=

∆Hj

Hwhere S is the


FIG. 2: Y = f(103/Tp) curves of Al-3.7 wt% Cu alloy using three different methods for the θ′-phase(a) and θ-phase (b).

total surface of the exothermic peak, Sj the partial surface at this temperature, ∆H thetotal enthalpy of the reaction, and ∆Hj the partial enthalpy at this temperature.

On the other hand, investigation of the peaks in Fig. 1 enables us to plot the evo-lution of the transformed fraction Y with temperature for different heating rates (Fig. 3a)and (Fig. 3b) for the formation of the first phase θ′ and the second θ-phase, respectively.


The curves obtained are S-shaped curves or sigmoıdal, showing the transformed fractionaccording to the temperature for various heating rates. It is noticed that the increasedheating rate leads to a shift of the exothermic peaks towards greater temperatures.

FIG. 3: Transformed fraction Y as a function of the temperature at various heating rate of Al-3.7wt% Cu alloy quenched (θ′-phase) (a) and (θ-phase) (b).

To calculate the coefficient n (the Avrami index), a characteristic of the transforma-tion mechanism that controls discontinuous precipitation in Al-3.7 wt% Cu alloy, we usedthe model of Matusita [25–28], which is specifically for non-isothermal precipitation whichconnects the fraction that transformed Y to a constant temperature and the heating rateaccording to the following equation:

ln(− ln(1 − Y )) = −n lnα + ln k. (10)


The plotted curves corresponding to the function ln(− ln(1−Y )) = f(lnα) are presented in(Fig. 4a, b) at three temperatures (245, 250, and 255 ◦C) for the formation of the (θ′-phase),and 285, 290, and 295 ◦C for the formation of the (θ-phase), respectively. Three straightlines are obtained with a slope n = 1.92 for 245 ◦C, n = 1.94 for 250 ◦C, and n = 1.90for 255 ◦C. The mean value for the formation of the (θ′-phase) of the n Avrami coefficientis 1.9, and n = 1.65 for the formation of the (θ-phase), which may correspond to a phasetransformation mechanism driven by diffusion. These values are in agreement with workson Aluminum alloys 2219 and Al-4.7 wt% Cu, in which the values lie between 0.8 and 1.42for temperatures ranging from 124 to 320 ◦C [29, 30].

FIG. 4: ln(ln 1 − y) = f(lnα) curves of Al-3.7 wt% Cu alloy at three different temperatures for theθ′-phase (a) and θ-phase (b).


IV-1-2. Isothermal Treatments

In order to illustrate the reliability of the method with multi-scanning rates, theisothermal DSC was made on the same alloy as used for the non-isothermal heating, thetemperature of with was controlled at 300 ◦C.

The isothermal DSC scan is given in Fig. 5. By means of the Johnson-Mehl-Avramiequation for the isothermal transformation:

ln(− ln(1 − Y )) = ln k + n ln(t− τ), (11)

where Y is the transformed fraction; Y as a function of the isothermal aging time is pre-sented in Fig. 6. This figure shows sigmoidal curves at temperature 300 ◦C for the discon-tinuous precipitation, and n can be obtained by plotting ln(− ln(1 − Y )) versus ln(t − τ).Fig. 7 shows the results for Al-3.7 wt% Cu. Here the incubation time, τ , is adjusted tomake all the points nearly lying in a straight line. From Fig. 7, the Avrami exponentn = 1.8 ± 0.08, which is in good agreement with the value by the non-isothermal methoddescribed in the first section, and the frequency factor is equal to 1.65 × 106 s−1.

FIG. 5: Isothermal DSC curve at temperature 300 ◦C for Al-3.7 wt% Cu alloy quenched.


FIG. 6: Transformed fraction Y as a function of the time at 300 ◦C of quenched Al-3.7 wt% Cualloy.

IV-2. XRD Analysis

For studying the precipitation kinetics in Al-3.7 wt% Cu, the initial samples arehomogenized at 540 ◦C for 10 h and quenched in water. The X-ray diffraction spectrum ofthis quenched alloy, which corresponds to a supersaturated solid solution αo, is shown in(Fig. 8a).

For Al-3.7 wt% Cu alloy aged at 300 ◦C (Fig. 8b–f), the precipitation reactions anddissolution induced changes in the parameter of the mesh matrix. We notice a shift of peaksto larger angles; this means that there is a variation of the lattice parameter of the meshof the aluminum matrix due to the presence of precipitate phases. The first deduction isthat the kinetics of the discontinuous precipitation reaction is fast and the intermetallicsphases θ′ and the θ-phases (CuAl2) correspond to the equilibrium diagram and agree withthe data in the literature [5, 8, 27].

At this temperature (300 ◦C), the last precipitates form quickly and particles ofphase equilibrium θ (Al2Cu) totally incoherent and tetragonal structure (a = 0.607 nm and


FIG. 7: Plots of ln(− ln(1 − Y )) versus ln(t− τ) of Al-3.7 wt% Cu alloy at 300 ◦C.

c = 0.487 nm) take place. According to Martin [31] and Takeda [32], for low temperaturethere is first training of the GP zones rapidly evolving θ′′ phase in the matrix with whichthey are consistent. The growth of these particles increases the elastic strain due to thecoherence and the distortions of the resulting network. When they reach the value of theshear strength of the matrix. On this dislocation the particle phase θ′ can germinate.Becoming more stable, such a particle θ′ grows at the expense of θ′′. When particles θ′

grow, an increasing number of interfacial dislocations (accommodation) are formed, andwhen their density reaches a certain value, the interface of θ′ becomes incoherent.

V. CONCLUSION

In this work, it was possible to observe that the precipitation processes of two phasesθ′ and θ(Al2Cu) present in the precipitation sequence of the Al-3.7 wt% alloy. The valuesof the activation energy of precipitation of θ′ and θ(Al2Cu) using the Kissinger, Ozawa,


FIG. 8: X-rays diffraction spectrum of Al-3.7 wt% Cu alloy, homogenized at 540 ◦C for 10 h quenchedin water (a), aged at 300 ◦C for 2 h (b), 5 h (c), 10 h (d), and 70 h (e).


and Boswell methods are 62.81, 72.71, and 75.30 KJ/mol, respectively, were determined byDSC methods. These values indicate that both processes depend on the diffusion of copperatoms in solid solution. And the n Avrami coefficient that characterizes the transformationmechanism that controls the discontinuous precipitation is determined. This alloy wasstudied with non-isothermal and isothermal kinetics analysis for determining the Avramiexponent, n, which is 1.60 and 1.63, respectively.

References

[1] D. B. Williams and E. P. Buttler, Int. Met. Rev. 26, 153 (1981).doi: 10.1179/095066081790149267

[2] W. Gust, Proc. Conf., Phase Transformations. New York, 11 (1979).[3] Z. Boumerzoug and M. Fatmi, Physica B 405, 4111 (2010). doi: 10.1016/j.physb.2010.06.062[4] M. Fatmi and Z. boumerzoug, Mater. Charact. 60, 768 (2009).

doi: 10.1016/j.matchar.2008.12.015[5] N. Ageew and G. Sachs, Z. Phys. 63, 293 (1930). doi: 10.1007/BF01339604[6] D. Altenpohl, Aluminium und Aluminiumlegirungen, (Springer Verlag, Berlin, 1965) pp 120–

165 (in German).[7] D. A. Porter and K. E. Easterling, Phase Transformations in Metals and Alloys, (Van Nostrand

Reinhold Company, New York, 1981) pp 291–316.[8] J. W. Christian, The Theory of Transformations in Metals and Alloys, 2nd. ed. (Pergamon

Press, London, 1975) p 729–759.[9] L. Lochte, A. Gitt, G. Gottstein, and I. Hurtado, Acta Mater. 48, 2969 (2000).

doi: 10.1016/S1359-6454(00)00073-2[10] Y. Jing, C. Li, Z. Du, F. Wang, and Y. Song, CALPHAD 32, 164 (2008). doi:

10.1016/j.calphad.2007.06.002[11] K. P. Cooper and H. N. Jones, Mater. Sci. 309, 92 (2001). doi: 10.1016/S0921-5093(00)01615-4[12] L. Loechte, A. Gitt, G. Gottstein, and I. Hurtado, Acta Mater. 48, 2969 (2000). doi:

10.1016/S1359-6454(00)00073-2[13] T. B. Wu, Scripta Metall. 17, 1 (1983). doi: 10.1016/0036-9748(83)90379-4[14] A. Wang et al., CALPHAD 33, 768 (2005).[15] M. Avrami, J. Chem. Phys. 7 1103 (1939).10.1063/1.1750380[16] W. A. Johnson and R. F. Mehl, Trans. AIME 135, 416 (1939).[17] M. G. Scott, J. Mater. Sci. 291, 343 (1984). doi: 10.1016/0006-8993(84)91267-8[18] H. E. Kissinger, Anal. Chem. 29,1702 (1957). doi: 10.1021/ac60131a045[19] T. Ozawa, Therm. Anal. 203, 159 (1992).[20] P. G. Boswell, J. Chem. Phys. 18, 353 (1966).[21] B. Massalski, Binary Alloys Phase Diagrams, Ed. ASM, (1990) 1471.[22] A. Hayoune and D. Hamana, J. Alloy. Compd. 474, 118 (2009).

doi: 10.1016/j.jallcom.2008.06.070[23] A. Varschavsky and E. Donoso, Thermochim. Acta 266, 257 (1995).

doi: 10.1016/0040-6031(95)02338-0[24] E. Donoso and A. Varschavsky, J. Therm. Anal. Calorim. 63, 249 (2000).

doi: 10.1023/A:1010113225960[25] K. Matusita and S. Sakka, Bull. Inst. Chem. Res. Kyoto Univ. 59, 159 (1981).[26] S. Mahadevan, A. Giridhar, and A. K. Singh, J. Non-Cryst. Solids 88, 11 (1986). doi:


10.1016/S0022-3093(86)80084-9[27] K. Matusita, T. Komatsu, and R. Yokota, J. Mater. Sci. 19, 291 (1984).

doi: 10.1007/BF00553020[28] N. Rysava, T. Spasov, and L. Tichy, J. Therm. Anal. 32, 1015 (1987). doi: 10.1007/BF01905157[29] I. Wierszy l lowski, S. Wieczorek, A. Stankowiak, and J. Samolczyk, J. Phase Equilib. 26, 5

(2005).[30] J. M. Parazian, Metall. Trans. A 13, 761 (1982).[31] J. W. Martin, Precipitation hardening (Oxford: Pergamon Press, 1968).[32] M. Takeda, S. K. Son, Y. Nagura, U. Schmidt, and T. Endo, Z. Metallkd 96, 870 (2005).

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Study of Precipitation Kinetics in Al-3.7 wt% Cu Alloy during Non-Isothermal and Isothermal Ageing