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Intermetallic compound layer growth between solid iron and molten aluminium


Materials Science and Engineering A249 (1998) 167 – 175

Intermetallic compound layer growth between solid iron and molten aluminium
K. Bouche a, F. Barbier a,*, A. Coulet b ?<

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CEA-CEREM/SCECF, BP 6, 92265, Fontenay-Aux-Roses Cedex, France b CNRS-CTM, 26 rue du 141eme RIA, 13003, Marseille, France ` Received 6 October 1997; received in revised form 2 February 1998

Abstract The interaction between solid iron and liquid aluminium is studied by immersion tests. At ?rst, the intermetallic layers formed at the solid–liquid interface and their growth mechanisms are characterized. The Fe2Al5 and FeAl3 phases are identi?ed in the temperature range from 700 to 900°C, and their growth is found to be mainly controlled by a diffusion regime. Then, a theoretical approach of the phase growth based on the solutions of the diffusion equations is presented. Theory and experiment agree rather well. ? 1998 Elsevier Science S.A. All rights reserved.
Keywords: Solid – liquid interaction; Intermetallic compounds; Iron; Liquid aluminium

1. Introduction The formation and growth of intermetallic compound layers during dissimilar metal contact at high temperatures is a common phenomenon. Such behaviour in the solid state is often observed in diffusion bonding and in ?ber-matrix reactions in composites [1,2]. This occurs also when a liquid metal is used as terminal component, for example in the case of hot-dip coating, liquid metal corrosion, composites prepared by liquid in?ltration, soldering and brazing [3 – 6]. It is established that the growth of the intermediate phases can be governed by chemical reactions at the interfaces (linear kinetics) and by interdiffusion of the reacting species through the different phases (parabolic kinetics). Description of the growth kinetics in multiphase binary couples can be found in many papers [7 – 11]. In near equilibrium conditions, the interfacial phases formed at a given temperature during contact are closely related to the phase diagram of the system. However, according to experimental observations, some equilibrium phases seem to be missing, this indicates that various effects have to be considered in growth mechanisms such as nucleation conditions at the beginning of the
* Corresponding author. Tel: +33 1 46548669; fax: +33 1 42537231; e-mail: barbier@cyborg.cea.fr 0921-5093/98/$19.00 ? 1998 Elsevier Science S.A. All rights reserved. PII S0921-5093(98)00573-5

process, chemical reactions, low diffusivity in the missing phases.... It is clear that the types of intermetallic layers formed and their thicknesses play an important part in obtaining materials with optimum performances. Thus, it is essential to understand the phase formation at the interfaces, the interface morphology and the growth mechanisms to provide guidelines for the prediction and control of interface reactions. The purpose of this work is to examine the interaction between solid iron and liquid aluminium. The Fe–Al system has been selected because of its technological applications. Previous studies were mainly concerned with steels and effort was often directed towards adherence. Eggeler et al. [12,13] studied the reactions between low alloyed steels and pure as well as iron-saturated aluminium melts. They detected two intermetallic layers (the Fe2Al5 phase adhering to the steel substrate by an irregular interface and the FeAl3 phase adhering to the solidi?ed aluminium) with a growth showing negative deviations from the parabolic relationship after long reaction times. Their results showed kinetic discrepancies with those reported by Eremenko et al. [14]. More recently, Dybkov [15] studied the interaction of stainless steel with liquid aluminium by using the rotating disc method. The time dependence of the total thickness of both layers was described in terms of paralinear kinetics. With regard to earlier works

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dealing with the reaction between pure iron and pure liquid aluminium, Gebhardt and Obrowski [16] detected the Fe2Al5 phase layer but they were unable to formulate unambiguously the growth kinetics whereas Heumann and Dittrich [17] identi?ed the Fe2Al5 phase as the major constituent of the layer and found a parabolic time dependence. In another investigation, Denner and Jones [18] reported that the thickness of the layer also obeyed a parabolic time relationship but the activation energy deduced from their work was higher than that obtained in previous studies. Reasons for this discrepancy were given in terms of simultaneous growth and spalling of the intermetallic layer for long dipping times. A tongue-like interface was also observed between the iron and the Fe2Al5 phase as in the case of studies with low alloyed steels [12,13] but the FeAl3 phase was not detected. Therefore, the literature shows that the determination of the types of intermetallic layers and the knowledge of the growth kinetics are still incomplete and contradictory in the Fe – Al system. In the work presented hereafter, experiments were carried out with pure iron in contact with static and unsaturated molten aluminium, so that dissolution of iron could take place simultaneously with the interlayer growth. The intermetallic layers formed at the solid– liquid interface at various temperatures and for different dipping times were identi?ed. Their microstructures, their growths and probable growth mechanisms were determined. Attention was drawn to the interface phase morphology. The experimental data were then used and discussed taking into account the theoretical aspects of the reactive diffusion.

700, 800 and 900°C), the sample was lowered for preheating above the surface of the melt during 20 min and then dipped into the static molten Al for a ?xed time (t=30 s–45 min). The solid–liquid interaction was interrupted by switching off the heating system and cooling the crucible together with the melt and the sample under ?owing gas (helium gas pre-cooled with liquid nitrogen).

2.2. Characterization
The Fe–Al couples were sectioned normal to the long axis of the solid sample (i.e. normal to the solid– liquid interface) and then mechanically polished (mirror ?nished). The bimetallic samples were examined by both optical and scanning electron microscopy. Composition of the phases and concentration pro?les were obtained by electron microprobe. Identi?cation of the phases was also veri?ed by X-ray diffraction. Here, the samples were sectioned parallel to the solid–liquid interface. Then, the aluminium part was polished step by step to remove successively the various phases until the iron was reached. At different stages of the metal removal, X-ray diffraction patterns were made.

3. Results and discussion

3.1. Phase layer characterization
For all experiments carried out in the temperature range from 700 to 900°C, two phase layers were observed whatever the time of contact between solid Fe

2. Experimental procedure

2.1. Immersion tests
The interaction between iron and liquid aluminium was studied by immersion tests performed in isothermal conditions. Armco iron (99.78%) was used for this work, the surfaces of specimens (35×5 × 3 mm3) were electrolytically polished. Aluminium (99.997%) was cleaned of its oxide ?lm in 5% NaOH solution for 1 min before melting. The tests were carried out in the device presented in Fig. 1. A small quantity of aluminium (10 g) was melted in a 15 mm internal diameter alumina crucible under vacuum (10 ? 5 mbar). A tungsten wire surrounded by tantalum thermal shields was used for the heating of the crucible in order to achieve a good temperature homogeneity. The temperature was measured (9 1°C) using a thermocouple put in contact with the crucible. The iron sample was attached to a specimen holder ?xed at the top of the vacuum chamber, its longer axis parallel to the crucible axis. When the aluminium reached the required temperature (T=

Fig. 1. Schematic view of the device used for immersion tests.

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Fig. 2. Intermetallic compounds observed between solid iron and liquid aluminium at T =800°C: (a) and (b), optical micrographs, respectively for t= 30 s and t =30 min; (c) scanning electron micrograph showing Fe2Al5 and FeAl3 formed after an immersion time equal to 15 min.

and molten Al. Fig. 2 shows a typical interfacial microstructure formed at 800°C. The electron microprobe analysis indicated that the phases were clearly identi?ed to Fe2Al5 (layer adjacent to iron) and FeAl3 (layer adjacent to aluminium). This was con?rmed by the X-ray diffraction patterns which were consistently indexed assuming an orthorhombic structure for Fe2Al5 (a = 0.7675 nm, b= 0.6403 nm, c= 0.4203 nm) and a monoclinic structure for FeAl3 (a = 1.5489 nm, b= 0.8083 nm, c =1.2476 nm) [19]. The identi?ed phases coincide with the Al-rich phases of the Fe – Al binary phase diagram (Fig. 3). Moreover, the analyses showed that the values of the concentrations at the various phase boundaries corresponded to the equilibrium compositions dictated by the Fe – Al binary phase diagram. The Fe2Al5 layer is larger than the FeAl3 one. It can

also be observed that the interface between Fe and Fe2Al5 appears highly irregular with peaks orientated towards the iron. This tongue-like morphology varies with time. Concerning the Fe2Al5/FeAl3 interface, irregularities observed for short contact times (30 s) decrease with a longer interaction. The boundary between FeAl3 and the liquid phase is also made of irregularities orientated towards the aluminium. They were found to increase with time, forming thin platelets for longer times (t\ 30 min at 800°C). Thin needles and platelets of FeAl3 were found to be uniformly dispersed in the solidi?ed aluminium matrix. These elements are formed by eutectic reaction during the solidi?cation of the melt containing some amount of dissolved iron. The platelets attached to the outer part of the FeAl3 layer and orientated towards the

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Fig. 3. Fe – Al phase diagram (from [20]).

aluminium, mainly observed for long immersion times, were also formed during the cooling. The Fe enrichment was larger in the melt adjacent to the solid–liquid interface and thereby, the excess solute could precipitate in FeAl3 crystals during solidi?cation. In fact, only a part of the FeAl3 layer is due to interdiffusion and thus the thick FeAl3 crystals due to solidi?cation will be ignored for the study of the FeAl3 layer growth.

3.2. Phase layer growth
Growth properties were studied by measuring the thickness of each layer. However, owing to the interface morphology of the Fe2Al5 phase, various measurements were made. Fig. 4 shows schematically the phase layers with the de?nition of the features used in this investigation. The thickness loss of solid (Xloss) which represents the solid–liquid interface displacement was also measured. It is de?ned by the difference between the initial

solid thickness and ?nal solid thickness (including the intermetallic layers). A positive value for Xloss means that the solid–liquid interface moves towards the solid substrate, indicating that dissolution mainly takes place. On the contrary, when Xloss is negative, the interface moves towards the liquid, which corresponds to a solid expansion and a predominance of phase growth over dissolution. The temperature dependence of the Fe2Al5 layer thickness is plotted in Fig. 5 for two immersion times. As shown, the amplitude of the layer grows with temperature but this variation as a function of temperature is lowered for longer reaction times. Fig. 6 presents the thickness loss of solid iron as a function of temperature. Depending on immersion times, different behaviours are observed. For short times, negative values are obtained at all temperatures. On the contrary, in the case of longer times, the loss of thickness shows a negative value at 700°C (solid expansion) and attains positive values at higher temperatures (solid dissolution). This observation indicates that more than one mechanism are involved during the solid–liquid interaction.
Table 1 Kinetic constants associated to phase growth and interface displacement Phase growth K p i (m s?1/2) Interface displacement K p i/j (m s?1/2) Fe/Fe2Al5 5.3 · 10?6 Fe2Al5/FeAl3 3.0 · 10?6 FeAl3/Al 2.9 · 10?6

Fig. 4. Schematic representation of the phases with their characteristics. Xmax (Fe2Al5) and Xmax (FeAl3): maximum thickness of Fe2Al5 and FeAl3; Xmin (Fe2Al5) and Xmin (FeAl3): minimum thickness of Fe2Al5 and FeAl3; Xmean (Fe2Al5) and Xmean (FeAl3): mean thickness of Fe2Al5 and FeAl3.

Fe2Al5 2.3 · 10?6

FeAl3 0.1 · 10?6

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thicknesses are large enough, the phases grow via a diffusion regime and their dissolution can be observed. However, the transient period being very short, the present experimental thickness measurements can only exhibit the parabolic stage of the process. The parabolic kinetic constants, associated to the growth of the phase i(K p) and to the displacement of i the interface i/j between phases i and j (K p ), can be i/j calculated. In order to take account of the nonparabolic transient period, K p is de?ned by the relation: i X p = Xi ? X 0 = K p
t ? t0 i i i where: X p is the thickness of the part of the layer grown i during the parabolic stage, Xi is the average layer thickness measured experimentally, X 0 is the layer i thickness at the end of the transient period, t0 is the time at the end of the transient period, t is the total time. Obviously, the position of the three interfaces (Fe/ Fe2Al5, Fe2Al5/FeAl3, FeAl3/Al) can be obtained from the thickness loss of the solid and from the average thickness of each phase: xFeAl3/Al = ? Xloss xFe2Al3/FeAl3 = ? XFeAl3 xFe/Fe2Al5 = ? Xloss ? XFeAl3 ? XFe2Al5 in which xi/j describes the position of the i/j interface. Finally, K p is de?ned by: i/j x p = xi/j ? x 0 = K p
t ? t0 i/j i/j i/j where x 0 is the position of the i/j interface at the end i/j of the transient period. Therefore, K p and K p can be deduced. They were j i/j determined assuming that the time t0, end of the tran-

Fig. 5. Temperature dependence of the Fe2Al5 layer thickness: (a) t= 30 s; (b) t =15 min.

The average thickness of each layer formed at T= 800°C is plotted as a function of the square root of time in Fig. 7. The curve shows that the time and the thickness are related according to a parabolic law, suggesting that the layer growth is governed by diffusion. However, the initial conditions (x = 0 at t= 0) are not satis?ed, which indicates the existence of an initial short transient period of faster kinetics before the parabolic growth. This assumption is also con?rmed by the study of thickness loss at the same temperature (Fig. 8). This ?gure shows that dissolution governed by a parabolic law takes place after expansion of the solid for 0B tB30 s. These results are in agreement with those presented in Fig. 5. In fact, this indicates that the Fe2Al5 and FeAl3 phase formation proceeds via an interface reaction control at the beginning of the process, their growth taking place without signi?cant dissolution in the liquid. At the end of this period when their

Fig. 6. Thickness loss of the solid versus temperature for two immersion times.

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Fig. 8. Variation of the thickness loss with t 1/2 at T =800°C.

For example, sinusoidal curvatures have been observed at solid–liquid interfaces in the Mo–Ni system [21]. In that case, they were explained by stress effects due to the atomic size mismatch between nickel and molybdenum. Such effects could also produce the instability observed in the Fe–Al system (atomic radius equal to 0.126 nm for Fe and 0.143 nm for Al). Another effect could be anisotropic diffusion (high vacancy concentration in the c-axis of the Fe2Al5 phase) as reported by Heumann et al. [17]. From a microstructural viewpoint, Fig. 9 shows that the Fe2Al5 phase has a polycrystalline structure in the part close to FeAl3, while only a long grain seems to be present in the upper part adjacent to the iron. MoreFig. 7. Variation of the layer average thickness with t 1/2 at T = 800°C: (a) Fe2Al5; (b) FeAl3.

sient period, coincides with the shortest experimental time. The values of the kinetic constants (Table 1) show that the rate of displacement of the solid – liquid interface (FeAl3/Al) has the same order of magnitude than the growth rate of Fe2Al5. Moreover, the parabolic constant associated to Fe2Al5 is higher than that related to FeAl3.

3.3. Interface phase morphology
As shown in Fig. 2, the interface between iron and Fe2Al5 is not planar, it is irregularly formed with peaks and valleys. The interface morphology having a major effect on the mechanical properties of the couple, it is interesting to examine the shape of the Fe2Al5 phase. The origin of the wavy Fe/Fe2Al5 boundary already observed by several authors [12,13,17,18] is not clear.

Fig. 9. Microstructure of the interface zone (T =800°C, t =15 min) after etching: Fe is etched with 5% Nital and Fe2Al5 is etched with 10% NaOH.

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layer formation, spreads continuously during the growth of the layer. Finally, the change in interface morphology can be described through this study but unfortunately the origin of the tongue-like shape cannot be explained.

3.4. Theoretical approach of the phase growth
The analysis given in the previous sections shows that the growth of both intermediate phases is mainly controlled by interdiffusion after a short transient period. A theoretical treatment based on the resolution of Fick’s laws can be applied [22,23]. In the present case, the interface displacement kinetics can be obtained by solving the time dependent diffusion equations in each phase, assuming a unidirectional diffusion ?ow, planar interfaces, local equilibrium conditions, concentration independent interdiffusion coef?cients and constant partial molar volumes. The resolution procedure is described in details in a previous work [24] for the growth of (n) intermediate phases and is associated to a parametric study in [25]. Therefore, only the main points of this treatment are presented hereafter before being applied to the Fe–Al system. The concentration of species throughout the multiphase binary system is expressed by the concentration of one of the two diffusing species as a function of the time t and of the distance x from the initial interface location. The concentration in each of the (n+2) phases, solution of Fick’s second law for semi-in?nite terminal phases, can be written [26]: Ci (x,t)=ai + bi erf

Fig. 10. Average width of Fe2Al5 tongue elements at 800°C for various immersion times: z represents the distance from the Fe2Al5/ FeAl3 interface to iron.

over, no relationship is observed between the grains of the iron substrate and the Fe2Al5 phase. In fact, this phase seems to cut the iron grains either transgranularly or intergranularly. The morphology of the Fe2Al5 phase is found to change with time as shown in Fig. 10. Each curve presents the average shape of the tongue elements obtained by a plot of the average width of the tongues at increasing distances z from the Fe2Al5/FeAl3 interface (z = 0) to the Fe substrate. It can be observed that the tongue pro?le is narrow for short times while it broadens out for longer times. This observation may suggest that the Fe/Fe2Al5 interface tends to ?atten during immersion and thus could become planar. This possibility was examined by measuring the amount of Fe2Al5 parallel to the solid – liquid interface as a function of z for Xmin B zB Xmax. In order to eliminate the effect of volume expansion during the phase growth, a non-dimensional variable de?ned by L = z/Xmean was used instead of the z value, as seen in Fig. 11. The curves (% Fe2Al5 versus L) presented in this ?gure for different immersion times are not identical, indicating a change in morphology. Moreover, Table 2 shows that the ratio Xmax/Xmean tends to two for the longest dissolution times. Now, taking into account that for a ?at tendency interface, the amount of Fe2Al5 must tend to a stepped pro?le (one for LB 1, 0 for L \1) and that the ratio Xmax/Xmean must tend to one, it becomes obvious that the interface cannot tend to a planar shape. The experimental data collected at 800°C show that the amount of Fe2Al5 deviates from a stepped pro?le for longer dissolution times. Thus, the pertubation of the Fe/ Fe2Al5 interface, appearing from the beginning of the



x

2
Dit



(1)

Fig. 11. Amount of Fe2Al5 (%) parallel to the solid – liquid interface versus L=z/Xmean for various immersion times at 800°C.

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Table 2 Experimental values of ratios (Xmax/Xmean)Fe2 Al5 for various times at T=800°C Time Xmean (mm) Xmax (mm) (Xmax/Xmean) 30 s 137 188 1.37 50 s 151 205 1.36 5 min 172 265 1.54 10 min 182 285 1.56 15 min 200 335 1.67 30 min 240 408 1.70 45 min 260 490 1.88

where erf is the error function, Di is the interdiffusion coef?cient in the ith phase, ai and bi are constants determined by initial and boundary conditions. The local equilibrium conditions mean that the concentration at each of the (n + 1) interfaces remains unchanged during the growth process, thus the interface position xi ? 1/i obeys the parabolic rate law and is given by: xi ? 1/i =2ki ? 1/i
Dn + 1t (2)

where ki ? 1/i is the kinetic coef?cient of the i? 1/i interface and where we have introduced the interdiffusion coef?cient Dn + 1 in the terminal phase which has the highest diffusivity. Diffusivity in each phase appears through the dimensionless ratio is related to the experimental parabolic constant K p? 1/i by: i K p? 1/i =2ki ? 1/i
Dn + 1. i Taking account of the initial and boundary conditions at each interface, the ai and bi constants associated with the ith phase can be expressed and the concentration within each phase is determined. At each interface i?1/i, the ?ux balance is given by: DCi ? 1/i dxi ? 1/i = Ji ? 1 ?Ji dt (3)

where DCi ? 1/i is the miscibility gap at the interface and where Ji ? 1 and Ji are the interdiffusion ?uxes (Fick’s ?rst law) in the (i?1)th and ith phases. Calculating the partial derivatives of the set of (n + 2) Eq. (1) and substituting them in the (n +1) Eq. (3), leads to a non linear system of (n +1) coupled equations with (n+ 1) unknown kinetic coef?cients, where the concentrations at each interface are given by the phase diagram for a ?xed temperature and where the interdiffusion coef?cients are assumed to be known. The numerical solution of this system can be obtained by means of an iterative method [24,25]. The kinetic coef?cients being determined, the position of each interface, the rate of its displacement and the thickness of each phase can be deduced. In the present case, two intermediate phases [(1) for Fe2Al5 and (2) for FeAl3] formed at 800°C between the two terminal phases [(0) for pure solid iron and (3) for pure liquid aluminium ]. As aforementioned, the unknown kinetic coef?cients k0/1, k1/2 and k2/3 can be obtained by solving the system of three equations,

assuming that the concentrations at the interfaces and the relative values of the interdiffusion coef?cients D3/ D0, D2/D1 and D3/D2 are known. Moreover, the interdiffusion coef?cient in an initial phase (DAl) must be speci?ed in order to correlate the experimental measurements with the calculation results. The concentration values at the interfaces are equal to the equilibrium values taken from the Fe–Al diagram at T=800°C. The main dif?culty is to ?nd reliable values for interdiffusion coef?cients in each phase. Some data can be collected in the literature [27–30] in the temperature range from 700 to 1000°C. The values reported at T=800°C are: DAl/DFe $ 10 ? 6, 10 ? 2 B DFeAl3/DFe2Al5 B 10 ? 1, 103 B DAl/DFeAl3 B 5 · 106 and 10 ? 9 m2 s ? 1 B DAl B 5 · 10 ? 7 m2 s ? 1. For this range of values, numerical solutions of the system of three equations have been obtained. It was found that kFe2Al5 is always larger than kFeAl3(kFe2Al5/ kFeAl3 $ 10). This indicates a faster growth for Fe2Al5 and is in agreement with the experimental kinetic constants reported in Table 1. Moreover, the calculation shows that the rate of displacement of the solid–liquid interface (FeAl3/Al) is very similar to the growth rate of Fe2Al5. This is also consistent with the experimental values (Table 1). Pursuing further the examination of theoretical results, it is also possible to ?nd a whole set of Di so that ki or ki/j (Table 3) are very close to experimental behaviours characterized by K p or K p i i/j (Table 1). This appropriate set of Di and relative ratios is: DAl = 1.35 · 10 ? 8 m2 s ? 1, DFeAl3 = 5 · 10 ? 2, DFe2Al5 DAl = 10 ? 6, DFe

DAl = 1.25 · 103. DFeAl3

Although this set is in the range of appropriate experimental values, it leads to the following interdiffuTable 3 Calculated kinetic constants associated to phase growth and interface displacement Phase growth 2ki
DAl (m s?1/2) Fe2Al5 FeAl3 Interface displacement 2ki/j
DAl (m s?1/2) Fe/Fe2Al5 Fe2Al5/FeAl3 FeAl3/Al 2.90 · 10?6

2.30 · 10?6 0.12 · 10?6 5.33 · 10?6 3.02 · 10?6

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sion coef?cients in the intermediate phases: DFeAl3 = 9.2 · 10 ? 10 m2 s ? 1 and DFe2Al5 =1.84 · 10 ? 8 m2 s ? 1. These coef?cients are at least two orders of magnitude higher than the values reported in literature. This difference can be due to the experimental conditions, one of the most critical i-point being the knowledge of the compacity of the intermediate layers. It seems that the concept of the homogeneous solid layer is a simpli?ed model and that grain-boundaries or inhomogeneities observed in the growing layers could increase their diffusivity. Only the Al-rich phases of the Fe – Al phase diagram were detected from the experimental observations. In fact, the kinetic coef?cients associated to the growth of the Fe-rich phases (FeAl and FeAl2) and calculated via the numerical approach are very low compared to those obtained for the Fe2Al5 and FeAl3 phases. Therefore, these phases with higher diffusivity grow much faster than FeAl and FeAl2 which cannot be observed.

References
[1] A.J. Hickel, R.W. Heckel, Met. Trans. A 6A (1975) 431. [2] R.B. Bhagat, Composites 9 (5) (1988) 393. [3] A.J. Stavros, in: J.R. Davis (Ed.), Metals Handbook, Corrosion, vol. 13, 9th edn., ASM, International, Materials Park, OH, 1987, p. 432. [4] C. Bagnell, W.F. Brehm, in: J.R. Davis (Ed.), Metals Handbook, Corrosion, vol. 13, 9th edn. ASM, International, Materials Park, OH, 1987 p. 91 [5] G.L. Bailey, H.C. Watkins, J. Inst. Metals 80 (1951) 57. [6] T. Ishida, J. Mater. Sci. 21 (1986) 1171. [7] G.V. Kidson, J. Nucl. Mater. 3 (1) (1961) 21. [8] C. Wagner, Acta Met. 17 (1969) 99. [9] F.M. D’Heurle, Mater. Sci. Forum 1 (1994) 155. [10] V.I. Dybkov, J. Mater. Sci. 21 (1986) 3078. [11] F.J.J. Van Loo, Prog. Solid State Chem. 20 (1990) 47. [12] G. Eggeler, W. Auer, H. Kaesche, Z. Metallkunde 77 (4) (1986) 239. [13] G. Eggeler, H. Vogel, J. Friedrich, H. Kaesche, Pract. Met. 22 (1985) 163. [14] V.N. Yeremenko, Ya.V. Natanzon, V.I. Dybkov, J. Mater. Sci. 16 (1981) 1748. [15] V.I. Dybkov, J. Mater. Sci. 25 (1990) 3615. [16] E. Gebhardt, W. Obrowski, Z. Metallkunde 4 (1953) 154. [17] T. Heumann, S. Dittrich, Z. Metallkunde 50 (10) (1959) 617. [18] S.G. Denner, R.D. Jones, Metals Technol. 3 (1977) 167. [19] W.B. Pearson, in: P. Villars, L.D. Calvert (Eds.), Handbook of crystallographic data for intermetallic phases, ASM, Metals Park, OH, 1985. [20] U.R. Kattner, in: T.B. Massalski (Ed.), Binary alloy phase diagrams, ASM International, Materials Park, OH, 1990, p. 147. [21] C.A. Handwerker, J.W. Cahn, J.R. Manning, Mater. Sci. Eng. A 126 (1990) 173. [22] W. Jost, Diffusion in Solids, Liquids, Gases, Academic Press, New York, 1952. [23] J. Philibert, Diffusion et transport dans les solides, Editions de Physique, les Ulis, France, 1985. [24] K. Bouche, Etude thermocinetique de la dissolution de metaux ? ? ? solides (fer et nickel) dans l’aluminium liquide, Thesis, University of Provence, Marseille, France, 1995. [25] A. Coulet, K. Bouche, F. Marinelli, F. Barbier, J. Appl. Phys., ? 82 (1997) 6001. [26] H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd edn., Oxford University Press, Oxford, 1959, p. 50. [27] L.N. Larikov, V.V. Geichenko, V.M. Fal’chenko, Diffusion processes in ordered alloys, Naukova Dumka Pub, Kiev, 1975, National Bur. Stand. New Delhi, 1981. [28] H. Bakker, Landolt-Bornstein, New Series, III/26, Springer Ver¨ lag, Berlin, 1990, p. 221. [29] R. Drewett, Corrosion Sci. 9 (1969) 823. [30] R.K. Bamsla, L.L. Seigle, Met. Trans. A 20A (1989) 2561.

4. Conclusions The intermetallic layers formed between solid iron and liquid aluminium have been characterized. Two phases, Fe2Al5 and FeAl3, have been identi?ed in the temperature range from 700 to 900°C. It is shown that their growth is controlled by interdiffusion after a non-parabolic initial transient period. The interface between iron and Fe2Al5 has been found to be highly irregular. This perturbation is ampli?ed for increasing reaction times. A theoretical approach of the phase growth based on the solutions of diffusion equations has been presented and a rather good description of the experimental data has been obtained through this numerical method. In particular, the absence of FeAl and FeAl2 phases can be attributed to their very low growth rates. The calculated values for the growth rate of the two intermediate phases, Fe2Al5 and FeAl3, are consistent with the experimental observations.

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