Determination of the formation enthalpy of crystalline

J Chim Phys (1993) 90, 355-366 ©Elsevier, Paris

Determination of the formation enthalpy of crystalline and quasicrystalline phases of the Al-Cu-Fe system by solution calorimetry NSaâdi1, MHarmelin1, B Legendre2* 1 CNRS-CECM, 94407 Vitry-sur-Seine Cedex;2Laboratoire de chimie minérale, faculté de pharmacie, Université Paris-Sud, 5, rue JB-Clément, 92296 Châtenay-Malabry, France

‘Correspondence and reprints.

SUMMARY Since its discovery the Al-Cu-Fe quasicrystalline icosahedral (i) phase is considered as a stable equilibrium phase. In order to establish whether the i phase is a ground state of the Al-Cu-Fe system, the determination of the enthalpy of formation of the binary and ternary crystalline phases in the vicinity of the i phase has been undertaken by solution calorimetry. A high-temperature microcalorimeter was used and measurements were performed in an aluminium bath at 976 K. The results of the determination of the enthalpy of formation at 298 K of Alo.67Cuo.33 (9 phase), Alo.7 5 Feo .25 (*· phase), AIq. 7 0Cu 0 . 2 0 Fe0.1 0 phase) and Alo.63 Cuo.25 Feo.i2 (i phase) are reported in the present communication. The values for co and i are of the same order of magnitude. RESUME Dans le cadre de l'étude de la stabilité thermodynamique de la phase icosaédrique dans le système Al-Cu-Fe, nous avons mesuré par calorimétrie de dissolution dans un bain d'aluminium à la température de 976 K l'enthalpie de formation de plusieurs phases binaires et ternaires de ce système. Les mesures ont été effectuées à l'aide d'un microcalorimètre Calvet haute température (SETARAM). L'étalonnage a été réalisé à l'aide d’alumine a du NBS. Les variations d'enthalpie de l'aluminium, du cuivre et du fer ont été mesurées entre 298 et 976 K. On présente dans cette communication les résultats des mesures des enthalpies de dissolution à dilution infinie des phases AlojsFe0,25 (λ), Al0,67Cu0,33 (ϴ), Al0,70Cu0,20Fe0.10 (w) et Al0,63Cuo,25Fe0,12 (Phase icosaédrique) et leurs enthalpies de formation à 298 K.

—356 — 1 - INTRODUCTION For the first three years after the discovery of a quasicrystalline icosahedral (i) phase in a rapidly solidified Al0.86Mn0.14 alloy [1] almost all the quasicrystalline alloys found were in a metastable state. The existence of a stable i phase was reported for the first time by Tsai et a l [2] in rapidly solidified alloys of composition Al0.65Cu0.20Fe0.15· Later, Calvayrac et a l [3] showed that an almost perfect i single-phase could be obtained for compositions close to Alo.63Cuo.25Feo.12 · For this composition, the i phase remained after long annealings such as 4 days at 800°C. A preliminary constitutional Al-Cu-Fe diagram in the Al-rich corner at room temperature was first proposed by Faudot et a l [4] based on experimental results mainly obtained by differential thermal analysis (DTA) and X-ray diffraction (XRD) and literature data [5], It was then modified in order to take into account the existence of an approximant structure (a periodic rhombohedral phase) and of the complexity of the phase diagram in this region [6] [7]. A reaction scheme was recently established by Gayle et a l [8] showing that the i phase can be obtained following a true peritectic reaction at 860°C (L + X + (3i) between the liquid phase L, the intermetallic X phase and a ternary solid solution p. The aim of the present work is to establish on a thermodynamic basis whether the i phase is a ground state of the Al-Cu-Fe system. In the present communication, the results of the determination of the formation enthalpy at 298 K by solution calorimetry are reported for Al0.75 Fe0.25 phase), Al0.67 Cu0.33 (0 phase), Al0.70Cu0.20Fe0.10 phase) and Al0.63Cu0.25Fe0.12 (i phase). The values of the enthalpy of dissolution at infinite dilution in liquid aluminium at 976 K are also given for pure copper and iron. 2 - EXPERIMENTAL PROCEDURE 2.1. Preparation of the alloys Alloys were prepared from high purity metals (Al > 6N, Cu 5N and Fe 5N) by levitation melting under helium except for the icosahedral phase which was obtained by melting in an evacuated Leyboldt device. The alloys were subsequently homogenized by annealing in ultra-high vacuum at temperatures slightly less than the respective solidus of each alloy (Table 1). The structural state of the annealed alloys was measured by X-ray diffraction on powdered samples. For the X composition, we have checked by metallography that the sample was actually a single phase. The existence of a congruent melting point was also observed by differential thermal analysis (DTA) in agreement with the phase diagram proposed by Lee [9] and Lendvai [10], The non-congruent melting of 0 , w and i was also checked by DTA (L + n1 6 [11], L + k w[5] and L + X + p i [8] respectively).

—357 — 2.2. Solution calorimetry Description of the apparatus A high temperature (T < 1273 K) SETARAM microcalorimeter of the TianCalvet-type [12] [13] was used. Aluminium baths (quality "super rafinal" ≥ 6N) were placed in alumina crucibles previously heated to 1000°C. Those were put inside silica tubes (Heraeus, quality Heralux). The aluminium weighed ≈ 5 g. The dropping of the samples from an air-lock thermoregulated (at ± 3 K) at room temperature (T0 = 298 K) down to the liquid aluminium bath maintained at the measurement temperature (T = 976 K) was guided by stainless steel tubes. These had the advantage of not degassing and of absorbing the residual oxygen traces. After degassing the enclosure under a vacuum of = 10'3 mbar, experiments were performed under flowing argon. The sample mass used for each experiment was typically 10 to 15 mg. The microcalorimeter was calibrated with NBS aAl203. This calibration was confirmed by measuring the enthalpy changes of pure Al, Cu and Fe between 298 Kand 976 K(see table 2). Table 1 -

Alloy

Preparation Procedure , heat treatments applied to 0, λ, w and i, and structure of the crystalline phases in the vicinity of the i phase. The composition given for β and ϕ are only indicative. Preparation Heat treatment Structure

ϴ(A10.67Cu0.33) λ(Al0.75Fe0.25) w(Al0.70Cu0 20Fe0 .10) i(A10.63Cu0.25Fe0.12) A10.46Cu0.36Fe0.18) (= B 0(= A10.49Cu0.48Fe0.03)

Levitation melting Levitation melting Levitation melting Leyboldt melting

2 days at 500°C 2 days at 800CC 20h at 650°C 4 days at 750°C

-

-

-

-

tI12 mC102 tP40 Icosahedral cP2 hP5

Description of the experimental procedure [14] [15]

The experiments were performed in two steps : (a) The sample (at To = 298 K) was dropped into the aluminium bath (at T = 976 K). The total heat effect measured for one mole, AS0]ITm(s), is: (1)

—358 — The integral

dT is equal to the enthalpy change of the sample from room

temperature to the temperature of the aluminium bath and will be written as in the following. The term AHdissol corresponds to the heat of dissolution of the sample into liquid aluminium at 976 K. As will be shown below, it can be assumed in the present series of experiments that the addition of samples of = 15 mg to an aluminium bath of = 5 g can be considered as an infinitesimal addition and causes no change in the composition of the aluminium bath. (b)The sample(at To = 298 K) was dropped into empty alumina crucibles (at T= 976K). The enthalpy change, in (1), was thus measured. 3 - RESULTS 3.1. Determination of The experimental enthalpy changes of Al, Cu, Fe, 0, X, w and i between 298 K and 976 K are reported in Table 2 with the standard deviation. For the elements Al, Cu and Fe, a good agreement is observed by comparison with those reported in the literature [16]. 3.2. Determination of AHdissol into liquid aluminium The values of the molar enthalpy of dissolution measured for successive additions of Cu, Fe, 0, X, w and i into liquid aluminium at 976 K versus the molar fraction of the sample [X(s)] are shown in Fig. 1(a) to Fig. 1(f). In all cases, the regression curve of the molar enthalpy of dissolution of the sample (s) into liquid aluminium is nearly horizontal. The corresponding extrapolated values for infinite dilution (AdissolH8 for X(s) = 0) are given in Fig. 1(a) to Fig.l(f) and in Table 3. The horizontal regression curve is proof that no correction is necessary for the measurements carried out with the binary or ternary compounds. The reactions used for dissolution are the following: xt 0 + Al(l, T) →(Al)T ;

yT0 + Al(l, t) →((Cu))T ·

- AsolHm(Al); - AsolHm(Cu);

(2) (3)

—359 — zTo + Al(l, T) →((Fe))T ;

= AsolHm(Fe);

(4)

AS0lHm(AlxCuyFez) is the enthalpy of solution of AlxCuyFez : nTo + Al(l, T)

((Cu,Fe))x;

- AsolHm(AlxCuyFez)

Table 2 -

Phases Al Cu Fe

(5)

in J mol·1 between 298 K(T0) and 976 K(T) for Enthalpy changes Al, Cu, Fe, 0, X, w and i. Literature This work (n) Standard (a) deviation 30114 [16] ±301 30074 (10) 18192 [16] ± 132 18372 (5) ±125 22981 [16] (5) 23196

X

33005 (b) 18677

(6) (5)

± 173 ±182

n.d. n.d.

w i

18671 19229

(7) (5)

±175 ±192

n.d. n.d.

0

(a) mean value over the number (n) of experiments; n.d.: not determined; (b) this value corresponds to the sum of the enthalpy change from 298 Kup to the melting temperature of 0 (863 K) and melting enthalpy. The symbols used in the equations (1) to (5) are the following: ◊ ◊ ◊

x, y and z are the number of moles of Al, Cu and Fe atoms respectively, n is the number of moles of AlxCuyFez , < Al >, , and refer to the elements Al, Cu, Fe and to the binary (y = 0 or z = 0) or ternary phases in the solid state, ◊ (Al)l,t refers to the liquid aluminium bath at the temperature T, ◊ ((Cu))p and ((Fe))T refer to the elements Cu and Fe in solution in liquid ◊

aluminium at T, AQis the heat effect for each experiment.

—360 —

AH dissol (kJ m ol’1)

Fipure 1: Molar enthalpy of dissolution of the various compounds in liquid aluminium at 976 K for successive additions of: (a) Cu, (b) Fe, (c) 0, (d) X, (e) wand (f) i phase. The extrapolated value at infinite dilution, (Xs = 0), is indicated.

AH dissol ( k J m o l -1)

X Cu

XFe

Δ Ηdissol dissol (kJ mol-1)

ΔΗdissol dissol ( kJ mol-1)

— 361 —

X (A l0.67C u 0, 3)

X (A l0.75F e 0.25)

ΔΗ dissol (kJ mol- 1)

— 362 —

ΔΗ

dissol

(kJ m ol·1)

X(A10.70 C u0.20 Fe0.10 )

X(A10.63 C u0.25 Fe0.12 )

—363 — The addition of samples of = 15 mg to an aluminium bath of = 5 g has been shown above to be an infinitesimal amount and causes no change in the composition of the aluminium bath and no variation in AsolHm(s) was detected. Thus, the dissolutions can be considered to be performed at high dilution in the A1 bath and the values of the enthalpies of solution defined above and given in Table 3, can be used without correction for calculating the enthalpies of formation. Table 3 - The total heat effect ASolHm(s), measured for the drop of one mole of sample (s) and the molar enthalpy of dissolution at infinite dilution AdissolH8 in aluminium bath at 976 K (all values in J mol-1) Standard deviation

AdissolH8

10

±301

-

-6594

8

+290

-94842

7

±1345

Phases

AsolHm (s)*m(s)* (n) (a)

Al

30074

Cu Fe ϴ

33923 29088 34335 28746

λ

CO

i

4 4 5 5

±106 ±253 ±573 ±162

(a)

mean value over the number (n) of experiments

(*)

AsolHm(s)

-24893 -21685 ±1200 [17] -117653 -113959

[18]

968 10540 15709 9765

3-3. Determination of AHf The enthalpy of formation of the phases 0, X, w and i, or more generally AlxCuyFez, was obtained indirectly by measuring the heats of dissolution of the pure components, Al, Cu and Fe and of the AlxCuyFez phases in the aluminium

— 364 —

bath at 976 K [Table 3], The enthalpy of formation of one mole of AlxCuyFez at 298 K [Table 4] is obtained following the relationship [15]: AfHm(AlxCuyFeZi cr, T0) = x AsolHm(Al) + y AsolHm(Cu) + zAsolHm(Fe) - AsolHm(A1xCuyFez)

(6)

where : AsolHm(Al) , AsolHm(Cu) and AsolHm(Fe) are the respective enthalpies of solution of pure Al, pure Cu and pure Fe in the aluminium bath. It must be helpful, in the T = A |Hm(Al). present work, to note that for aluminium AHrp

Table 4 - Formation enthalpy (AfHm-) of 0, X, coand i at 298 K. Phases

AfHm(at 298 K, in J mol-1) from literature -13390 ◊ 3350 [20] -13601 [19]

0

this work -15773 ±404

X

-30243 +814

-27900+2000 [20] -27621 [19]

w

- 24086 +976 -22181+586

not determined not determined

i

4 - DISCUSSION The experimental values of the formation enthalpy of the binary phases 0 et l determined in this work are of the same order as the experimental determinations performed by Kubaschewski et a l [19] and those calculated by Kaufman et a l [20] on the basis of Hultgren et a l 's compilation [21], The values obtained for the ternary phases, coand i, seem to be the first determinations made, and no comparison is yet possible with literature data. Nevertheless, as the co phase can be considered to be formed by reaction between AlgFe and Al2Cu following: Al3Fe(k) + 2 Al2Cu(ϴ) →Al7Cu2Fe(w) , and introducing the respective numbers of atoms per mole (let us note that for

—365 — reasons of simplification, the formulae of X, 0 and w are here written as Al3Fe, AigCu and Al7Cu2Fe) and the corresponding heats of formation of the phases X, 0 and w: AfHm(w) - 0.4 AfHm(λ) - 0.6 AfHm(ϴ) →Areact-Hm The exothermic effect Areact-Hm = - 2420 J mol-1 corresponds to the enthalpy decrease in the system when co is formed from 0 and X. The co phase can be thus expected to be stable with respect to 0 and X at 298 K. Regarding the determinations of the molar enthalpy of dissolution of the elements Cu and Fe in liquid aluminium, the value obtained for Fe in this work (- 117653 J mol-1) is in good agree'ement with [18]. For Cu, the previous value reported by Notin and al. [17] is of the same order as that found in this work (see table 3). 5 - CONCLUSION This work is a preliminary step in the determination of the heats of formation of intermetallic crystalline or quasicrystalline phases for which there is a lack of data. For the Al-Cu-Fe system, which is characterized by the existence of a quasicrystalline icosahedral phase, it is not yet possible to draw a conclusion about the respective stabilities of the i phase with respect to the other crystalline phases of the diagram. It would be necessary to obtain equivalent data with other crystalline ternary phases (for instance (3 and [5]) and to know their respective Gibbs free enthalpies. ACKNOWLEDGMENTS The authors gratefully acknowledge Prof. J.W. Cahn (NIST, Gaithersburg) who initiated this study and made useful suggestions. Thanks are also due to Dr C. Colinet (LTPCM, Grenoble) and Dr J.C. Mathieu (CTM, Marseille) for helpful discussions and to Monsieur C. Prévost (CECM, Vitry) who prepared the icosahedral phase. Drs Y. Calvayrac, F. Faudot and A. Quivy are also acknowledged for their kind cooperation. REFERENCES 1 2

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—366 — 3 4 5

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3 9 It 12 13 t4 15 16 17 18 19 29 21

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