Magnetic and calorimetric study of point defects in FeAl intermetallic compound

Materials Science and Engineering A279 (2000) 282 – 288 www.elsevier.com/locate/msea

Magnetic and calorimetric study of point defects in FeAl intermetallic compound S. Zaroual a,b, O. Sassi a,*, J. Aride a, J. Bernardini c, G. Moya d a

Laboratoire de Physico–Chimie des Mate´riaux, Laboratoire Associe´ a` l’AUPELF·UREF, LAF n°502, Ecole Normale Supe´rieure Takaddoum B.P. 5118 Rabat, Morocco b Laboratoire de Physique des Mate´riaux, Faculte´ des Sciences, A6enue Ibn Batouta, B.P. 1014 Rabat, Morocco c Laboratoire de Me´tallurgie, U.M.R 6815, Faculte´ des Sciences et Techniques de St-Je´roˆme, 13397 Marseille Cedex 20, France d Laboratoire de Physique des Mate´riaux, E.A.2192 (D.S.O), Faculte´ des Sciences et Techniques de St-Je´roˆme, 13397 Marseille Cedex 20, France Received 21 January 1999; received in revised form 3 May 1999

Abstract The behaviour of point defects has been investigated in quenched B2-FeAl intermetallic compounds by using magnetic susceptibility measurements x(T) and differential scanning calorimetry (DSC). During an isochronal annealing, the observed step in magnetic susceptibility at about 410°C reflects the migration of iron antistructure atoms, frozen by the quenching process, to their own sites. Several thermal phenomena have been detected by means of DSC measurements. The principal peak, attributed to the migration and elimination of iron antistructure atoms via vacancy mechanism, depends on the quenching temperature Tq: for Tq =1000°C, the annealing-out temperature range is lower by about 150°C than for Tq = 800°C. The concentration of eliminated vacancies, during this stage, has been determined from fitting the experimental x(T) curves by the Curie –Weiss law: it was found to be 1.76× 10 − 2 for the equiatomic composition and 1.73 ×10 − 2 for the Fe49Al51 compound. The annealing kinetics study allows us to determine the migration enthalpy of 1.95 eV taking into account the formation of vacancy clusters. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Intermetallics; FeAl system; Points defects; Defect concentrations; Defect migration

1. Introduction The intermetallic compound FeAl crystallises, in the B2-structure, in a wide concentration range around the stoichiometric composition (50 at.%) [1]. In the ordered state, for a stoichiometric alloy, the iron and aluminium atoms form interpenetrating primitive cubic lattices. This compound exhibits structural and thermal defects: 1. For the structural defects it has been shown [2,3] that, on the iron rich side of stoichiometry, iron substitutes as antistructure atoms on the aluminium lattice. Whereas, in aluminium-rich compounds, structural vacancies are formed on the iron lattice. In the following, FeAl and VFe represent iron antistructure atoms and vacancies on the iron sublattices, respectively. * Corresponding author. Tel.: + 212-7-752261; fax: + 212-7750047.

2. Besides the structural defects, a large number of thermal defects may be produced by heat treatment. These defects can be retained in the sample by quenching from high temperatures. It was argued that, the predominant thermal defects are FeAl and VFe [4], the aluminium antistructures AlFe and aluminium vacancies VAl also exist, but in a small amount [5–8]. In the literature different methods have been used to determine defect concentrations. So Haberkern [9] has determined by magnetic measurements the iron antistructure atoms concentration [FeAl] at 850°C between 5.17× 10 − 2 and 1.35 × 10 − 2, when the content in iron decreases from 55 to 50 at.% Fe. By differential thermal expansion and for compound containing 49 at.% Fe, Ho and Dodd [10] have found a value of 1.7 ×10 − 2 for the vacancies concentration at 727°C. By field ion-microscopy for Fe50.5Al49.5 quenched from 1000°C, Paris and Lesbats [5,11] have obtained a value of (1.2 9

0921-5093/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 2 1 1 - 7

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C T− u

(1)

0.1)× 10 − 2 for the iron vacancies concentration [VFe] and by a dilatometric technique, they found the total vacancy concentration equals to (1.8590.15) × 10 − 2. For the same composition (50.5 at.% Fe) Sepiol and Vogl [12] have estimated [FeAl]= 1.5 ×10 − 2 at 1065°C by Mo¨ssbauer spectroscopy. For equiatomic compound Fe50Al50 quenched from Tq = 950°C, an activation enthalpy DHa =1.759 0.02 eV, attributed to the vacancy elimination, was obtained by electrical resistivity [13] and DHa =1 9 0.1 eV for Tq = 1000°C using magnetic susceptibility measurements versus temperature [14]. In an earlier study [15] for Tq = 1000°C, we have found DHa =1.22 90.05 eV, during isothermal annealing using x(t) magnetic susceptibility measurements versus time. From the fast Doppler broadening technique, Wolff et al. [16] have determined DHa = 1.2 9 0.2 eV for Fe60Al40. Wu¨rschum et al. [17] have obtained DHa =1.7 90.2 eV in Fe61Al39 by positron lifetime measurements. In the present study, isochronal magnetic susceptibility x(T) and differential scanning calorimetry (DSC) measurements have been carried out to investigate thermal vacancies concentration and defects mobility in a quenched FeAl sample.

2. Materials and experimental techniques

2.1. Samples preparation The FeAl alloys were prepared by melting aluminium of 99.999% purity and iron of 99.995% purity in a high frequency induction furnace under ultra pure argon atmosphere (N60). For magnetic and calorimetric measurements, small cylindrical specimens of 4 mm in diameter and about 9 mm in thickness were cut by spark erosion. To produce non-equilibrium point defects, the sample was first heated at 1050°C for 1 h then annealed for 4 h at 1000 or 800°C, thereafter it was quenched into iced water. These thermal treatments were performed in an inert atmosphere (purified argon) to avoid oxidisation of the sample. The reproducibility of results was found to be quite good after the first heat treatment at 1050°C. The treatment was used: 1. to ensure that equilibrium state was reached before quenching. 2. to reduce the total number of clusters (voids or loops) in quenched samples.

2.2. Defects characterisation by magnetic susceptibility Magnetic susceptibility measurements have revealed a Curie–Weiss law behaviour at high temperatures [18]. So the total magnetic susceptibility versus temperature T can be written as:

x(T)= x 0[1+ dT 2]+

where x 0 is the expression of Pauli paramagnetism, and d is related to the detailed shape of the density of states. The Curie temperature u reflects the interaction of the magnetic moments with their surrounding and depends on the iron antistructure atoms concentration [FeAl]. Eq. (1) can also be written as: x(T)= x 0 + aT 2 +

C T-u

(2)

where a=d·x0 and the measured Curie constant C is correlated with [FeAl]: C=

N[FeAl]m 2eff 3kB

N and kB are the Avogadro number and the Boltzmann constant, respectively. The effective magnetic moment meff, associated with each FeAl has been experimentally determined as about 7.8 mB by Caskey et al. [18] and as about 5.2 mB by Domke and Thomas [19]. In this intermetallic compound, a widely used model assumes triple defects as the dominant defect type. So two thermal iron vacancies VFe are formed for each antistructure atoms FeAl. Then for the stoichiometric compound, the thermal vacancies concentration [VFe] may be calculated from: [VFe]= 2[FeAl] =

6CkB Nm 2eff

(3)

The vacancy mobility may be derived from vacancies elimination kinetics, after quenching from high temperature, during isochronal annealings corresponding to various heat rates. Measurements were carried out under an argon atmosphere, with b= 2, 5, 8 and 10°C/ min, as heating rates, for magnetic and calorimetric experiments.

3. Experimental results

3.1. Migration of thermal FeAl studied by magnetic measurements The temperature dependence of the susceptibility for two heating runs, of the same sample, are presented in Fig. 1. The first one was performed up to 650°C after a quench. Then just after slowly cooling the sample in situ to room temperature, the second heating run was done in the same conditions. At low annealing temperatures a pronounced difference between the two curves x(T) is observed, because the susceptibility is significantly higher after the quench. Above about 500°C both curves are identical. The decrease of x(T) demonstrates that the concentration of the thermal iron antistructure atoms at the beginning of

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Fig. 1. Magnetic susceptibility vs. temperature with b = 2°C/min of Fe50Al50; (a): first heating after a quench from Tq = 1000°C, (b): second heating after slowly cooling; the curves are fitted in the low temperature region by Curie–Weiss law.

the first heating run, after quenching, is larger than that obtained at the end. Since the FeAl atoms is sensitively detected by magnetic susceptibility, the step appearing at 410°C probably reflects the annealing-out of iron antistructure atoms frozen by the quenching process.

3.2. Migration of thermal 6acancies studied by calorimetric measurements Fig. 2 shows the DSC thermograms of samples quenched from 1000 and 800°C. Each thermogram is obtained by the difference between the first and the second heating run. So all detected exothermal effects may be related to the quenched defects elimination. The comparison of the two curves (Fig. 2(a, b)) shows that the temperature range of the principal peak changes with the quenching temperature. We remark that for Tq = 1000°C, the annealing-out behaviour starts at lower temperatures than for Tq =800°C.

Two additional peaks were found: 1. The early exothermic stage, in the range 190–275°C centered around 240°C, was discussed by Ko¨ster et al. [20] as recovery of ferromagnetic domains. Recently Schaefer et al. [21] have observed an internal friction maximum at 187°C. These authors suggested that it may be attributed to the reorientation of (FeAl –VFe) pairs as for the observed maximum at 407°C, but with a higher local mobility of vacancies in disordered surrounding. This later interpretation is in agreement with our results since this phenomenon is linked to the defect behaviour. 2. The second additional peak is endothermic and appears after the principal peak. This thermal effect also observed by Lafi et al. [22] is heating rate-dependent (more pronounced when the heating rate increases to 10 or 15°C/min [23]). Furthermore, this phenomenon occurs in the temperature range where a defect formation begins as detected by magnetic measurements ( 630°C) [14], positron annihilation ( 610°C) [24] and dilatometer experiments ( 700°C) [10]. In the following, we will mainly consider the results corresponding to the principal peak, for Fe50Al50 quenched from Tq = 1000°C. The experiments for other quenching temperatures are currently underway.

3.3. E6aluation of eliminated defects concentrations from magnetic measurements Below 410°C the temperature dependence of magnetic susceptibility is determined by 1/T behaviour of the Curie term. Therefore, it is possible to extract the following parameters x 0, a, C and u from fitting the experimental data of Fig. 1 by Eq. (2). These parameters are listed in Table 1. By considering the second heating, it can be noticed that the value of Curie constant is not equal to zero. This fact can be explained by different reasons: probably the presence of residual FeAl due to the slow vacancy diffusivity, at low temperatures, and/or the low paramagnetism related to the matrix and/or the presence of complex defects as dislocations, loops and disorder in grain boundaries. The Curie constant is connected to the iron antistructure atoms concentration by Eq. (3). If the effective magnetic moment meff is known, the concentration of eliminated antistructure atoms [FeAl] and vacancies [VFe] can be determined by the following formula: [VFe]= 2[FeAl]=

Fig. 2. Thermograms with b = 2°C/min of Fe50Al50 for two quenching temperatures: (a) Tq = 1000°C; and (b) Tq = 800°C.

6kB(C1-C2) Nm 2eff

(4)

where C1 and C2 are the Curie constants corresponding to the first and the second heating run, respectively. Thus, the values obtained with meff = 7.8mB [18] are listed in Table 2.

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Table 1 Coefficients of fitting the x(T) curves of FeAl for 49 and 50 at.% Fe by the Curie–Weiss law at.% Fe

x 0×105 (emu g−1)

a×1012 (emu g−1 K−2)

u(K)

C×103 (emu g−1 K)

49 First heating run Second heating run

1.19 1.19

−4.94 −4.94

−36 −2

1.84 0.24

50 First heating run Second heating run

1.11 1.12

−4.84 −4.80

−38 −2

1.91 0.29

The obtained concentrations [FeAl] and [VFe] are quite similar, taking account of experimental errors, for the two compositions. The vacancy concentrations are comparable to the available experimental data [10,11], but the obtained values of iron antistructure atoms are much smaller than those found by Haberkern [9]. This difference may be due essentially to the value of the effective magnetic moment used in Eq. (4).

3.4. E6aluation of acti6ation enthalpy 3.4.1. Temperature dependence of fraction eliminated defects Y(T) In this section, we will report only the results concerning Fe50Al50. 3.4.1.1. From magnetic measurements. During the first heating run, the magnetic susceptibility can be written from Eq. (2) as follows: x1(T)= x 01 +a1T 2 +

C T −u

If we assume that total quenching defects are eliminated during the first heating, we will have for the second heating run:

F(T)= =

x1(T)− x2(T)=

C(T) T −u

(5)

At temperature T0, where the defects are not yet mobile: x1(T0)-x2(T0)=

C(T0) T0 −u0

(6)

From Eqs. (3), (5) and (6), the fraction F(T) corresponding to free VFe or FeAl in the sample at temperature T is obtained by:

x1(T)-x2(T) T− u × x1(T0)− x2(T0) T0 − u0

(7)

Then the fraction of eliminated defects Y(T) may be written as: Y(T)=1− F(T). In Fig. 3, the temperature dependence of the fraction Y(T) of a quenched sample Fe50Al50 are represented for two extreme values of Curie temperatures u=u1 and u= u2 corresponding, respectively, to the first and second heating runs. At sufficiently high temperatures where FeAl defects are mobile the two curves are perfectly identical. Therefore, both u1 and u2 give the same results. Then, in this study, we have used the value of u= u0 = u1 to determine the fraction of eliminated defects Y(T).

3.4.1.2. From DSC measurements. During an isochronal annealing, the thermal effect corresponding to the elimination of the quenched-in defects may be obtained by the difference between the thermograms of the first and the second heating runs. The area of this thermal effect is connected to the fraction of eliminated defects Y(T) by Eq. (8) [25]: Y(T)=

x2(T)= x 02 +a2T 2 The different values of a and x 0, found during both heating runs, may be considered constant (Table 1), then:

[VFe](T) [FeAl](T) C(T) = = [VFe](T0) [FeAl](T0) C(T0)

A(T) A0

(8)

where A0 and A(T) are, respectively, the area of the total thermogram and the partial thermogram between its beginning and the T temperature.

Table 2 Concentrations of eliminated iron antistructure atoms FeAl and vacancies VFe in FeAl for 49 and 50 at.% Fe, referred to the total number of atoms at.% Fe

(C1−C2)×103(emu K mol−1)

[FeAl]×102

[VFe]×102

49 50

65.79 67.09

0.86 0.88

1.72 1.76

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Fig. 3. Set of isochronal annealing curves for the two extreme values of Curie temperatures u= u1 (+ ) and u=u2 ().

3.4.2. Determination of the acti6ation enthalpy To determine the activation enthalpy DHa related to defect elimination reaction, from both magnetic and DSC measurements using Y(T) curves, we have to vary the heating rate b [25,26]. For a given heating rate, the fraction Y(T) is linked to the activation enthalpy by:

  n

ln

dY dt

=−

Yj

DHa +Aj kBTj

The annealing-out behaviour of quenched samples depends considerably on the quenching temperature, thus for Tq = 1000°C the annealing-out starts at lower temperatures than that of Tq = 800°C (Fig. 2). This is in good agreement with the results of Frantz et al. [14], who investigated FeAl compound by magnetic measurement, assuming that the triple defects dominate at low temperatures (below 850°C), and that the VAl vacancies and double vacancies are responsible for the change in the annealing-out behaviour at higher temperatures. The formation of double vacancies is indicated by a relatively high formation vacancy volume derived from positron annihilation under pressure [16]. Even if we assume that the quantity of double vacancies is important, their concentration remains smaller than that of single vacancies. In this case, we will probably have two annealing-out stages, as that observed in B2-NiAl [27]. In this hypothesis the first peak at 240°C, in the DSC thermograms, can be attributed to double vacancies annealing; in effect the comparison of the area of the DSC peaks is compatible with the smaller concentration of defect in the first peak than in the principal one about 450°C. This assumption is not

(9)

where, Tj is the temperature when Y =Yj and Aj is a constant. In Figs. 4 and 5, the variations of Y(T) (Fig. 4(a, b)) as well as their derivatives as a function of time dY/dt (Fig. 5(a, b)) are presented, for different heating rates b and for both experimental techniques, in Fe50Al50 samples. We observed that the maxima of these different curves are shifted to high temperatures by increasing the heating rate. The slopes of the straight lines, obtained by drawing ln(dY/dt) as a function of 1/T, for Y =0.5 (Fig. 6), allow us to determine the activation enthalpies. So from a least-squares fit the activation enthalpies were derived as 1.199 0.27 and 1.29 0.1 eV for magnetic and calorimetric measurements, respectively.

4. Discussion During the heat treatment before quenching, there is the formation of thermal point defects. After quenching, these defects are trapped in a metastable state. The increase in magnetic susceptibility is due to the formation of the iron antistructure atoms FeAl. The phenomena detected by magnetic and calorimetric measurements occur in the same range of temperature and both techniques lead to the same activation enthalpy. Therefore we conclude that the types of eliminated defect, during these stages, are identical.

Fig. 4. Set of isochronal annealing curves of Fe50Al50 corresponding to Tq =1000°C for different heating rates (": 2°C/min, : 5°C/min,

: 8°C/min, : 10°C/min), determined by: (a) magnetic; and (b) calorimetric measurements.

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ture increases, we assume that this defect dissociates into FeAl antistructure atoms and the VFe vacancies randomly distributed, (VFe − VFe) next and/or thirdnearest neighbour double vacancies can be also considered. Therefore, a different defect type must be frozen-in from different quenching temperatures. Below Tq = 850°C, the triple defect types are trapped, their annealing-out starts approximately at 550°C. Above Tq = 850°C, the vacancies VFe and antistructure atoms FeAl are trapped and their annealing-out starts at about 410°C. The mechanism of this elimination is the combination of the FeAl and VFe and also vacancies clustering as voids and loops as shown by electron microscopy [28,29]. In this case, it seems difficult to identify the measured activation enthalpy DHa to the vacancy migration enthalpy DH m V Fe, because we must take into account additional terms, linked to the formation of these clusters, such as the binding enthalpy of vacancy clusters. An approximate formula joining these two enthalpies is given by [30]: DHa = DH m V Fe −

Fig. 5. Derivatives of set of isochronal annealing curves corresponding to Tq =1000°C for different heating rates (?: 2°C/min, ?: 5°C/min, ?: 8°C/min, ?: 10°C/min), determined by: (a) magnetic; and (b) calorimetric measurements.

inconsistent with the Schaefer’s interpretation [21] for the internal friction maximum at 187°C. So to explain the change of the annealing-out behaviour with the quenching temperature, we can consider as Frantz et al. [14] that the triple defect should be dominant at lower temperature but when the tempera-

p−2 B( 2

(10)

where B( is the average vacancy-clusters binding energy and p is the vacancies number of the critical nucleus. Assuming that B( does not vary much with the cluster size, we can assimilate it to the divacancy binding enthalpy. Theoretically, this enthalpy has been evaluated to be 0.5 eV [31]. With p= 5, in agreement with our previous work [15], we calculate DH m V Fe =1.95 eV. If we suppose, as confirmed by Mo¨ssbauer Spectroscopy [32,33], that at equilibrium the Fe atoms diffusion occurs via single vacancies and nearest-neighbour jumps, we can use this value of DH m V Fe to determine the vacancy formation enthalpy DH Vf Fe by applying a simple relationship as in metals: f DQD = DH m VFe + DH V Fe

(11)

This expression was successfully used in many intermetallic compounds [34–36]. With a self-diffusion enthalpy DQD = 2.76 eV deduced from Fe tracer diffusion measurements [37], then we found DH fV Fe =0.81 eV. This value is in agreement with the one calculated by Fu [38] (DH fV Fe = 0.82 eV). 5. Conclusion

Fig. 6. Determination of activation energy at Y= 0.5 for Tq =1000°C from: (a) magnetic; and (b) calorimetric measurements.

In the present paper, the results of magnetic susceptibility and calorimetric measurements are coupled in order to study the migration kinetic of thermal point defects in B2-FeAl compound. In this compound the magnetic susceptibility is very sensitive to the presence and migration of iron antistructure atoms as well as their surrounding. As the

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migration process of FeAl antistructure atoms is realised via vacancy mechanism, the additional information of vacancy defects can be also deduced. Differential scanning calorimetry applied to the annealing-out of thermal defects, gives information about the whole existent defects. Results are exploitable when the annealing stages are different and/or the concentration of certain defects is dominant as observed in this work where several peaks are detected during isochronal annealing, for quenched B2-FeAl. Two quenching temperatures Tq can be distinguished, where the formed defects have different configurations. At Tq =800°C, we consider that triple defect is the dominant defect and its annealing-out range is located around 600°C. When the temperature increases the configuration of the dominant defect changes and for Tq =1000°C its annealing-out range is located around 450°C. The existence of FeAl thermal antistructure atoms detected by magnetic measurements confirms that the nearest neighbour jumps play an important role in the diffusion process of iron atoms. In addition, the determined iron vacancy migration enthalpy (1.95 eV) is in agreement with the experimental results of diffusion and with the calculated formation enthalpy.

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