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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 1

Research Unit on Emerging Materials (RUEM), University Ferhat Abbas Setif 1, 19000, Algeria 2 Laboratory of studies of Surfaces and Interfaces of Solids Materials, University Ferhat Abbas Setif 1, 19000, Algeria 3 Microelectronic Laboratory (LMSE), University of Bordj-Bou-Arreridj 34000, Algeria 4 Laboratory for Elaboration of New Materials and Characterization (LENMC), University Ferhat Abbas Setif 1, 19000, Algeria 5 Laboratory of Physics and Mechanics of Metallic Materials (LP3M), University Ferhat Abbas Setif 1, 19000, Algeria 6 Department of Physics, Faculty of Sciences, University of Taif, KSA 7 Department 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 use of X-ray diffraction and Differential Scanning Calorimetry (DSC) methods at different heating rates. Both non-isothermal and isothermal ageing processes were conducted in order to determine 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 calculated by the isothermal treatment is ∼ 1.65 × 106 s−1 . The activation energy of discontinuous precipitation 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 thermomechanical processing 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 (discontinuous precipitation) was reported in 1930 [5]. The processes of precipitation in the aluminum-copper alloys are well known. Starting from supersaturation of the solutes by annealing at about 540 ◦ C, the alloys undergo fast cooling to room temperature and a period of aging by which G-P (Guinier-Preston) zones are incurred. θ′′ (Al2 Cu) precipitates that 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

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c 2013 THE PHYSICAL SOCIETY ⃝ OF THE REPUBLIC OF CHINA

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STUDY OF PRECIPITATION KINETICS IN . . .

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in the solid solution, and the copper atoms diffuse to the growing nuclei. When the temperature increases, because of aging, the θ′′ dissolves, and θ′ nucleates at defects in the solid solution. Finally, the equilibrium phase θ (Al2 Cu) nucleates at the boundaries of the solid solution grains, θ′ (Al2 Cu) dissolves, and the copper atoms diffuse to the growing θ (Al2 Cu) [6–9]. Concerning the previous studies related to discontinuous precipitation in Al-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 supersaturated Al-Cu alloys by combining interfacial and strain energies in the Gibbs free energy for the GP zone formation. Many investigations have been devoted to examining the details of the precipitation sequence in this alloy system [11–13], using both theoretical models and several newly-developed techniques [14]. Through isothermal studies within a temperature range of about 210 ◦ C from 50–260 ◦ C, Wierszyllowski et al. [28] estimated taht the activation energies of the precipitation processes should fall between ∼ 50 kJ/mol and ∼ 100 kJ/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 transformation is nucleation: the formation of very small (often submicroscopic) particles, or nuclei, of the new phase, which are capable of growing. Favorable positions for the formation of these nuclei are imperfection sites, especially grain boundaries. The second stage is growth, in which the nuclei increase in size; during this process, of course, some volume of the parent phase disappears. The transformation reaches completion if growth of these new phase particles is allowed to proceed until the equilibrium fraction is attained. As would be expected, the time dependence of the transformation rate (which is often termed the kinetics of a transformation) is an important consideration in the heat treatment of materials. With many kinetic investigations, the fraction of a reaction that has occurred is measured as a function of time, while the temperature is maintained constant. Transformation progress is usually ascertained by either microscopic examination or the measurement of some physical property (such as the electrical conductivity) the magnitude of which is distinctive of the new phase. Data are plotted as the fraction of transformed material versus the logarithm of time; an S-shaped curve represents the typical kinetic behavior for most solid-state reactions. The theoretical basis for interpreting the DSC results is provided by the JohnsonMehl-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 volume fraction crystallised after time t. The above expression is often referred to as the Avrami equation. The temperature dependence is generally expressed by the Arrhenian-type equa-

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tion:

MESSAOUD FATMI, BRAHIM GHEBOULI, ET AL.

( ) Ea K = K0 exp − , RT

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(2)

where k0 is the frequency factor, Ea is the apparent activation energy, R is the ideal gas constant (8.314 J/mol K), and T is the isothermal temperature in Kelvin. Taking the logarithm 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 curve using Eq. (4) by least-squares fitting of ln[− ln(1 − y)] versus ln(t). The Avrami exponent is determined traditionally by an isothermal method [17], and its value depends strictly on the incubation time, which cannot be given exactly. On the other hand, the isothermal heating is more difficult to perform than non-isothermal annealing by differential scanning calorimetry (DSC). Here, we intend to propose a method of multi-scanning rates for measurement of 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 time at 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 the temperature constantly changes with time, k is no longer a constant but varies with time in a more complicated form, and Eq. (1) becomes: } { k(T − T0 )n y = 1 − exp − . (6) α If the rate of transformation is maximal, reflected as a peak of the DSC curve, the maximum is at the DSC curve peak, then T = Tp , and d2 y/dt2 = 0. After deducing Eq. (6), Kissinger [18], Ozawa [19], and Boswell [20] developed a nonisothermal analytical method by using the highest rate of transformation, i.e., the rate related to the peaks of the DSC data, and found ( ) α Ea ln =− + C1 , (7) 2 RTp Tp ln(α) = −

Ea + C2 , RTp

(8)

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( ln

α Tp

) =−

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Ea + C3 , RTp

(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 plastic deformation by cold rolling before the homogenization treatment in order to accelerate the structure homogenization kinetics. The homogenization temperature and aging time were chosen from the equilibrium diagrams [21]. The ingots were homogenized in vacuum at 530 ◦ C for 5 h and quenched in water to obtain a supersaturated solid solution α0 . The samples were prepared into a disk shape of 3 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. Xray diffraction analysis was performed by a “PAN Analytical X’ Pert PRO” diffractometer using 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 heating rates (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 dissipation during the formation of the θ′ and θ (Al2 Cu) phases by discontinuous precipitation [22]. In fact, we noticed that the peak moves towards higher temperatures as the heating rate increases. This can be attributed to two possible effects. The first comes from the decrease of the precipitated Cu atoms amount due to the higher solid solubility at higher temperatures and higher heating rates [23, 24], while the second is associated with the diffusive nature of the precipitation reactions. Determination of the activation energy needed for the θ′ and θ-phases to form was done via the Kissinger, Ozawa, and Boswell methods, starting from the change in the

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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 the heating rate α for the first phase θ′ (Fig. 2a) and the second phase θ (Al2 Cu) (Fig. 2b). Activation energies derived from the curve slopes are very close, as is shown in the following Table II: These values for the θ′ and θ-phases formation are in good agreement with works on Al-4.7 wt% Cu alloy, in which the values lie between 60.70 and 303.86 kJ/mol for temperatures 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 at ∆S ∆H a corresponding Tj temperature, is given by the formula, Y = S j = H j where S is the

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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 the total 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 evolution 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.

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The curves obtained are S-shaped curves or sigmo¨ıdal, showing the transformed fraction according to the temperature for various heating rates. It is noticed that the increased heating 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-3.7 wt% Cu alloy quenched (θ′ -phase) (a) and (θ-phase) (b).

To calculate the coefficient n (the Avrami index), a characteristic of the transformation mechanism that controls discontinuous precipitation in Al-3.7 wt% Cu alloy, we used the model of Matusita [25–28], which is specifically for non-isothermal precipitation which connects the fraction that transformed Y to a constant temperature and the heating rate according to the following equation: ln(− ln(1 − Y )) = −n ln α + ln k.

(10)

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The plotted curves corresponding to the function ln(− ln(1 − Y )) = f (ln α) 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 straight lines are obtained with a slope n = 1.92 for 245 ◦ C, n = 1.94 for 250 ◦ C, and n = 1.90 for 255 ◦ C. The mean value for the formation of the (θ′ -phase) of the n Avrami coefficient is 1.9, and n = 1.65 for the formation of the (θ-phase), which may correspond to a phase transformation mechanism driven by diffusion. These values are in agreement with works on Aluminum alloys 2219 and Al-4.7 wt% Cu, in which the values lie between 0.8 and 1.42 for temperatures ranging from 124 to 320 ◦ C [29, 30].

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

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IV-1-2. Isothermal Treatments In order to illustrate the reliability of the method with multi-scanning rates, the isothermal DSC was made on the same alloy as used for the non-isothermal heating, the temperature of with was controlled at 300 ◦ C. The isothermal DSC scan is given in Fig. 5. By means of the Johnson-Mehl-Avrami equation 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 presented in Fig. 6. This figure shows sigmoidal curves at temperature 300 ◦ C for the discontinuous 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 to make all the points nearly lying in a straight line. From Fig. 7, the Avrami exponent n = 1.8 ± 0.08, which is in good agreement with the value by the non-isothermal method described 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.

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

IV-2. XRD Analysis For studying the precipitation kinetics in Al-3.7 wt% Cu, the initial samples are homogenized at 540 ◦ C for 10 h and quenched in water. The X-ray diffraction spectrum of this 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 and dissolution induced changes in the parameter of the mesh matrix. We notice a shift of peaks to larger angles; this means that there is a variation of the lattice parameter of the mesh of the aluminum matrix due to the presence of precipitate phases. The first deduction is that the kinetics of the discontinuous precipitation reaction is fast and the intermetallics phases θ′ and the θ-phases (CuAl2 ) correspond to the equilibrium diagram and agree with the data in the literature [5, 8, 27]. At this temperature (300 ◦ C), the last precipitates form quickly and particles of phase equilibrium θ (Al2 Cu) totally incoherent and tetragonal structure (a = 0.607 nm and

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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 temperature there is first training of the GP zones rapidly evolving θ′′ phase in the matrix with which they are consistent. The growth of these particles increases the elastic strain due to the coherence and the distortions of the resulting network. When they reach the value of the shear 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, and when 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 phases and θ(Al2 Cu) present in the precipitation sequence of the Al-3.7 wt% alloy. The values of the activation energy of precipitation of θ′ and θ(Al2 Cu) using the Kissinger, Ozawa, θ′

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

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and Boswell methods are 62.81, 72.71, and 75.30 KJ/mol, respectively, were determined by DSC methods. These values indicate that both processes depend on the diffusion of copper atoms in solid solution. And the n Avrami coefficient that characterizes the transformation mechanism that controls the discontinuous precipitation is determined. This alloy was studied with non-isothermal and isothermal kinetics analysis for determining the Avrami exponent, n, which is 1.60 and 1.63, respectively.

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