- Email: [email protected]
Standard enthalpy of formation of the ζ-phase in the Fe–Zn system at 298 K
Journal of Alloys and Compounds 346 (2002) 211–216
L
www.elsevier.com / locate / jallcom
Standard enthalpy of formation of the z-phase in the Fe–Zn system at 298 K a, a b Y. Feutelais *, B. Legendre , R.R. de Avillez a
´ ´ , F-92290 Chatenay-Malabry, Laboratoire de Chimie Physique Minerale et Bioinorganique ( EA 401), Faculte´ de Pharmacie, Rue J.B. Clement France b Pontificia Universidade Catolica, R. Marques de S. Vicente 225, DCMM, 22453 -900 Rio de Janeiro, RJ, Brazil Received 18 January 2002; received in revised form 10 April 2002; accepted 10 April 2002
Abstract The standard enthalpy of formation D f Hm( 298 ) of the z-phase with composition Fe 0.07 Zn 0.93 was determined using a Tian-Calvet calorimeter (Setaram) by dissolution in an aluminium bath at 801 8C (1074 K). The alloy was prepared by direct melting followed by annealing. The experimental value found was D f Hm( 298 ) 5221786772 J / mol. 2002 Elsevier Science B.V. All rights reserved. Keywords: Transition metal alloys; Enthalpy; Thermodynamic properties; Calorimetry
1. Introduction
2. Experimental procedure
The iron–zinc system is of prime importance for the galvanizing, galvannealing and zinc refining processes. In order to optimise the heat treatment, precise phase equilibria calculations are necessary in the composition range of interest for multicomponent iron–zinc-based alloys. This is accomplished by using the CALPHAD method [1,2], which consists of the determination of the Gibbs function of the whole phase from the available experimental information. This can be achieved only if the boundary systems are well described thermodynamically. Even if the Fe–Zn phase diagram appears to be well established (Fig. 1), measurements of the thermodynamic functions are quite difficult because of the high vapour pressure of zinc. Thus few calorimetric enthalpies of formation are available. This increases the difficulty of obtaining a correct thermodynamic evaluation of this system. The purpose of this work was to measure the enthalpy of formation of the z-phase with composition Fe 0.07 Zn 0.93 in order to obtain an improvement of any quantitative description of the system.
The alloy was prepared from high-purity zinc ($6N) and iron purified by zone melting (.5N). The composition of the prepared alloy was XZn 50.935 in order to be certain of obtaining the z-phase even in the case of the evaporation of Zn. The correct proportion of each element was introduced into a silica tube and sealed under vacuum (4–13 mbar). Because of the high vapour pressure of zinc, the temperature was increased from 450 to 900 8C in steps of 50 8C with a duration of 12 h for each step. The alloy was then annealed for 3 weeks at 450 8C. Identification of the phases was carried out on a PW 1729 (Philips) X-ray diffractometer equipped with a graphite monochromator, Cu Ka radiation, fixed antiscatter and divergence slits and a goniometer adapted to a step motor driven by software developed previously [3]. The 2u angle was scanned from 10 to 808 in a Bragg– Brentano arrangement. A small amount of alloy was crushed into a fine powder and placed on a glass sample holder. The amount of each phase was quantified using a fundamental parameters Rietveld program [4]. The instrument parameters were adjusted with the diffraction lines from LiB 6 powder, used as a standard. Scanning electron microscopy with energy dispersive spectroscopy (EDS, DSM960, Carl Zeiss), equipped with an Oxford detector, was used to observe the morphology of the microstructure and determine the composition of the
*Corresponding author. Tel.: 133-1-4683-5725; fax: 133-1-46835454. E-mail address: [email protected] (Y. Feutelais).
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00664-3
212
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
Fig. 1. Fe–Zn phase diagram according to the description of Ref. [20].
z-phase. The conditions were an accelerated tension of 20 kV, a working distance of 25 mm and an X-ray detector with a Be window. Pure iron and zinc were used as standards and a cobalt sample was used to calibrate the energy spectrum. The results were processed with the program ZAF (Oxford). A high-temperature (T #1273 K) Setaram microcalorimeter of the Tian-Calvet type was used for solution calorimetry. Experimental details are given in a previous study performed on the Al-rich part of the Al–Fe and Al–Cu–Fe systems [5,6]. Aluminium baths were obtained by placing about 3 g pure Al ($6N) in an alumina crucible previously heated to 1273 8C under a dry N 2 flow. These were placed inside silica tubes. The samples were dropped from an air-lock thermoregulated at room temperature (T 0 529863 K) into the liquid aluminium bath maintained at 107461 K. Although some oxidation of the Al bath may occur at such a temperature, this temperature was chosen so as to obtain a sufficiently fast rate for the dissolution of the Fe 0.065 Zn 0.935 alloy in the bath. The samples were guided down into the aluminium bath by stainless steel tubes. This material has the advantage of very low degassing and of absorbing residual traces of oxygen. After degassing in a vacuum of |10 23 mbar, experiments were performed under flowing purified U argon. The sample mass used for each experiment was about 25 mg. The microcalorimeter was calibrated with NIST a-Al 2 O 3 , and confirmed by measuring the enthalpy change of pure Al between 298 and 1074 K.
3. Results and discussion X-ray diffraction showed only two phases, the major compound being the z-phase (C2 /m) with a small amount of pure Zn (P6 3 /mmc). Their lattice parameters agree with the values reported in the literature [7,8]. Three different samples were used to quantify the amount of each phase and the mean weight percent of zinc was found to be 6.3% (s 50.8), and the fitting conditions were better than R wp # 24.323 and gof#1.423 [4]. The composition of the z-phase as determined by EDS was 93 at% Zn and 7 at% Fe. The presence of the zinc phase was, of course, taken into account in the calorimetric investigation by removing it from the measured heat effect for each experiment: • the relative heat of dissolution of Zn in the aluminium bath at T51074 K for dissolution experiments. The partial molar value, D diss H ` 510 466 J / mol, of zinc in aluminium was calculated from the database given in Refs. [9,10]; • the relative enthalpy change of Zn between 298 and 1074 K (DH 1074 298 (Zn)) for the alloy heat content experiments. This value includes the latent heat to melt Zn and was calculated (DH 1074 298 (Zn)530 081.6 J / mol) from the thermodynamic description of pure Zn given in the unary database of Ref. [11]. Thus the standard enthalpy of formation of Fe 0.07 Zn 0.93 at 298 K (D f H ) was obtained indirectly by measuring the
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
heats of dissolution of Fe, Zn and Fe 0.07 Zn 0.93 in the aluminium bath at 1074 K. For 1 mol of Fe 0.07 Zn 0.93 , we have D f Hm (Fe 0.07 Zn 0.93 ) 5 0.07D sol Hm (Fe) 1 0.93D sol Hm (Zn) 2 D sol Hm (Fe 0.07 Zn 0.93 )
(1)
where D sol Hm is the total heat measured for 1 mol of Fe, Zn or Fe 0.07 Zn 0.93 : 1074
D sol Hm 5 DH 298 1 D diss H
`
The first term is the enthalpy change of the compound from 298 to 1074 K, it is the heat content of Fe and 1074 1074 Fe 0.07 Zn 0.93 (DH 298 5 e298 Cp dT ) and for Zn it also includes the latent heat of melting. The second term is the heat of dissolution of the compound in liquid aluminium at 1074 K for infinite dilution. The terms D sol Hm (Fe) and D sol Hm (Zn) are thus the respective total molar enthalpy changes of pure Fe and pure Zn according to the reactions kFel 298 K 1 (Al) ( l, 1074 K) → ((Fe)) (1074 K ) , D sol Hm (Fe) (2) kZnl 298 K 1 (Al) ( l, 1074 K) → ((Zn)) 1074 K , D sol Hm (Zn)
(3)
D sol Hm (Fe 0.07 Zn 0.93 ) is the total molar enthalpy change for the reaction kFe 0.07 Zn 0.93 l 298 K 1 (Al) ( l, 1074 K ) → ((Fe,Zn)) 1074 K , D sol Hm (Fe 0.07 Zn 0.93 ) (4) In Eqs. (1)–(4), kFel, kZnl and kFe 0.07 Zn 0.93 l refer, respectively, to the elements Fe and Zn, and to Fe 0.07 Zn 0.93 in the solid state; (Al) l, 1074 K refers to the liquid aluminium bath at 1074 K; ((Fe)) 1074 K and ((Fe,Zn)) 1074 K refer, respectively, to the element Fe and the alloy dissolved in liquid aluminium at 1074 K. In fact, it is not always possible to measure D diss H ` , since the solution may not be at infinite dilution. Hence, one must use a relationship of the type D diss Hm 5 f(x(alloy)) and extrapolate it for x(alloy)→0, if necessary. x(alloy) denotes the molar fraction of the alloy in the mixture: the aluminium bath plus the total mass of Fe 0.07 Zn 0.93 .
213
1074 K. Due to the high vapour pressure of zinc at this temperature, its rate of vaporisation is higher than its rate of dissolution in the aluminium bath, even if the zinc is wrapped in thin aluminium foil. In this case the results are not consistent and the errors are very important. Thus the total heat effect for the dissolution of Zn in the aluminium bath, D sol Hm (Zn)540 548 J / mol, was obtained from the variation in the enthalpy of Zn between 298 and 1074 1074 K, DH 298 (Zn)530 082 J / mol, and the enthalpy of ` dissolution of Zn in Al at 1074 K, D diss H m 510 466 J / mol [9,10].
3.3. Dissolution of Fe0.07 Zn0.93 in liquid aluminium at 1074 K In order to ascertain the dissolution reaction of the alloy in liquid aluminium, the total thermal effect, D sol Hm (Fe 0.07 Zn 0.93 ), should be compared with the heat 1073 content, DH 298 (Fe 0.07 Zn 0.93 ), of the alloy between 298 and 1074 K. Therefore, three series of measurements of the total heat effect and two series of measurements of the heat content between 298 and 1074 K were undertaken.
3.3.1. Heat content measurements The results are given in Table 1. The average value 1074 obtained from the two runs was DH 298 5123 96762248 J / mol (error for 95% confidence interval). As some evaporation can be expected, this value must be used with caution. It was measured only to check the existence of a difference between the heat content and the heat of dissolution, but it was not used in the final calculation of the enthalpy of formation. 3.3.2. Determination of Dsol Hm ( Fe0.07 Zn0.93 ) The results for the three series are presented in Table 2. The last column is the integral heat of mixing of Al and the ternary alloy at 1074 K. The mean values are D sol Hm (Fe 0.07 Zn 0.93 ) 5 33 8236372 J / mol D diss Hm (Fe 0.07 Zn 0.93 ) 5 2 90 14462279 J / mol
3.1. Dissolution of iron in liquid aluminium at 1074 K This result was given in Refs. [12,13]. The total heat effect of Fe when dropped into the liquid aluminium bath from 298 to 1074 K is D sol Hm (Fe)5 286 63862374 J / mol.
3.2. Dissolution of zinc in liquid aluminium at 1074 K It was not possible to obtain experimentally the variation of the enthalpy of Zn dropped into the aluminium bath at
Table 1 1074 Heat content, DH 1074 298 5e298 C p dT (J / mol), of Fe 0.07 Zn 0.93 between 298 and 1074 K First run
Second run
122 687 126 007 127 982 126 669
121 214 122 552 122 422 122 202
m 1 5 125 836
m 2 5 122 097
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
214
Table 2 Results for the dissolution of Fe 0.07 Zn 0.93 in the Al bath at 1074 K No. of series
x(alloy)
D sol Hm (Fe 0.07 Zn 0.93 ) (J / mol)
D diss Hm (Fe 0.07 Zn 0.93 ) (J / mol)
D mix Hm (Fe 0.07 Zn 0.93 ) (J / mol)
1 3 2 3 1 2 3 1 2 3 1 3 2 3 1 2
0.00316 0.00345 0.00406 0.00680 0.00686 0.00758 0.01002 0.01108 0.01253 0.01292 0.01556 0.01569 0.01673 0.01826 0.01992 0.02158
33 722 34 311 34 660 35 067 33 431 33 405 34 260 33 772 33 731 33 214 33 116 34 483 34 290 33 381 33 766 32 559
290 245 289 656 289 307 288 900 290 536 290 562 289 707 290 195 290 236 290 753 290 851 289 484 289 677 290 586 290 201 291 408
227.67 229.90 236.79 258.91 260.29 269.46 287.28 297.78 2115.47 2113.34 2138.24 2137.92 2154.70 2161.14 2177.59 2201.30
The errors correspond to the 95% confidence interval for the mean. Using the values determined in our previous work [12,13] for Eq. (2), the calculated value for Eq. (3) and the measured value for Eq. (4), the molar standard enthalpy of formation at 298 K of the binary alloy may be calculated using Eq. (1): D f Hm(298) 5 2 21786772 J / mol The indicated error corresponds to the standard deviation associated with Eq. (1), estimating the standard error of D sol Hm (Zn) to be 1% of this value. It should be noted that the mean value of D sol Hm given ` above is valid only in the case where D diss H m can be considered as the average value of the measured D diss Hm . In this case, when plotting D diss Hm versus x(alloy) in the studied composition range, a horizontal straight line, indicating independence between the two variables, should be obtained. Fig. 2 shows the experimental enthalpy of dissolution of the binary alloy in pure aluminium and its linear regression line versus the mole fraction of alloy, D diss Hm 5f(x(alloy)). The independence of the variables was checked by performing an analysis of variance of the linear regression. The analysis of variance led to the conclusion of independence between D diss Hm and f(x(alloy)). This result means that the assumption of using the average value of ` the data to obtain D diss H m 5 290 14462620 J / mol is valid. In a narrow composition range starting from pure aluminium, the integral enthalpy of mixing of the alloy versus composition (D mix Hm 5f(x(alloy))) may be considered linear (Fig. 3). As shown in Table 3, the experimental molar standard enthalpy of formation of the z-phase is lower than the calculated values. In all the proposed assessments [14–18],
the temperature of the peritectic invariant L1d 1 →z of 530 8C proposed in Ref. [19] was accepted. We carried out DSC investigations on the Fe 0.065 Zn 0.935 alloy between 400 and 700 8C. We obtained, in this range of temperature, three invariant phenomena (Fig. 4): L → z 1 (Zn), T 5 418.560.5 8C L 1 d 1 → z, T 5 560.063 8C L 1 G1 → d 1 , T 5 674.561 8C It should be noted that the precision on the temperature of the peritectic invariant related to the decomposition of the z-phase is worse than for the temperatures of the two other invariants.
Fig. 2. Enthalpy of dissolution of the z-phase (x Zn 50.93) in pure Al at 1074 K versus mole fraction of alloy (reference liquid for Al and alloy).
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
Fig. 3. Integral enthalpy of mixing of the z-phase (x Zn 50.93) with pure Al at 1074 K versus mole fraction of alloy (reference liquid for Al and alloy). Table 3 Experimental and calculated molar enthalpy of formation of the z-phase Ref.
D f Hm (Fe 0.07 Zn 0.93 ) (J / mol)
[14] [15] [16] [17] [18] This work
22866.74 28453.27 29008 23265 28739 22178
215
Fig. 5. Enlarged part of the DSC curve around the peritectic phenomenon L1d 1 →j for Fe–Zn alloy of composition x Zn 50.935 (heating rate 1 K / min).
As shown in Fig. 5, there is an important change of baseline before and after the invariant phenomenon. This is interpreted as a modification of the heat capacity of the alloy because of the liquidus line, which becomes flatter in this range of composition. The solution calorimetry in an aluminum bath applied here with success to the most Zn-rich alloy of the Fe–Zn system indicates that the determination of the enthalpy of formation of other solid phases is feasible. This will be done in further work in order to propose a refined thermodynamic evaluation.
Acknowledgements R.R. de Avillez is grateful for partial financial support of this research by the Conselho Nacional de Pesquisa e Desenvolvimento (CNPq Proc. 46.1525 / 00-3, 521025 / 966 and 664106 / 1998-6).
References
Fig. 4. Differential scanning calorimetry curve for Fe–Zn alloy with composition x Zn 50.935 (heating rate 1 K / min).
[1] U.R. Kattner, JOM 49 (1997) 14–19. [2] N. Saunders, A.P. Miodownik, CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide, Pergamon Materials Series, Vol. 1, 1998. [3] B. Fraisse, PhD Thesis, Universite´ des Sciences et Techniques du Languedoc, Montpellier, France, 1995. [4] R.W. Cheary, A.A. Coelho, J. Appl. Crystallogr. 25 (1992) 109–121. [5] N. Saadi, M. Harmelin, B. Legendre, J. Chim. Phys. 90 (1993) 355–366.
216
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
[6] N. Saadi, M. Harmelin, F. Faudot, B. Legendre, J. Non-Cryst. Solids 153 / 154 (1993) 500–503. [7] P.J. Brown, Acta Crystallogr. 15 (1962) 608–612. ¨ Ann. Phys. (Leipzig) 5 (12) (1953) [8] H.E. Swanson, E. Tatgey, 121–144. [9] S. an-Mey, Z. Metallkd. 84 (1993) 451–455. [10] I. Ansara, A.T. Dinsdale, M.H. Rand (Eds.), COST 507 Thermochemical Database for Light Metal Alloys, European Communities, 1998, EUR 18499 EN. [11] A.T. Dinsdale, CALPHAD 15 (1991) 319–427. [12] Y. Li, P. Ochin, A. Quivy, P. Telolahy, B. Legendre, J. Alloys Comp. 298 (2000) 198–202. [13] Y. Li, B. Legendre, J. Alloys Comp. 302 (2000) 187–191. [14] S. Petersen, P.J. Spencer, K. Hack, Thermochim. Acta 129 (1988) 77–87.
¨ ¨¨ [15] M. Hamalainen, R. Luoma, P. Taskinen, Report TKK-V-B55, Helsinki University of Technology, Faculty of Process Engineering and Materials Science, Espoo, Finland, 1990. [16] G. Reumont, P. Perrot, J.M. Fiorani, J. Hertz, J. Phase Equilib. 21 (2000) 371–378. [17] X. Su, N.-Y. Tang, J.M. Toguri, J. Alloys Comp. 325 (2001) 129–136. ´ Nancy I, France, [18] N. David, PhD Thesis, Universite´ Henri Poincare, 2001. [19] J. Schramm, Z. Metallkd. 29 (1937) 222–2224. [20] T.B. Massalski et al. (Ed.), Binary Alloy Phase Diagrams, 2nd Edition, ASM International, Metals Park, OH, 1990, p. 147.
L
www.elsevier.com / locate / jallcom
Standard enthalpy of formation of the z-phase in the Fe–Zn system at 298 K a, a b Y. Feutelais *, B. Legendre , R.R. de Avillez a
´ ´ , F-92290 Chatenay-Malabry, Laboratoire de Chimie Physique Minerale et Bioinorganique ( EA 401), Faculte´ de Pharmacie, Rue J.B. Clement France b Pontificia Universidade Catolica, R. Marques de S. Vicente 225, DCMM, 22453 -900 Rio de Janeiro, RJ, Brazil Received 18 January 2002; received in revised form 10 April 2002; accepted 10 April 2002
Abstract The standard enthalpy of formation D f Hm( 298 ) of the z-phase with composition Fe 0.07 Zn 0.93 was determined using a Tian-Calvet calorimeter (Setaram) by dissolution in an aluminium bath at 801 8C (1074 K). The alloy was prepared by direct melting followed by annealing. The experimental value found was D f Hm( 298 ) 5221786772 J / mol. 2002 Elsevier Science B.V. All rights reserved. Keywords: Transition metal alloys; Enthalpy; Thermodynamic properties; Calorimetry
1. Introduction
2. Experimental procedure
The iron–zinc system is of prime importance for the galvanizing, galvannealing and zinc refining processes. In order to optimise the heat treatment, precise phase equilibria calculations are necessary in the composition range of interest for multicomponent iron–zinc-based alloys. This is accomplished by using the CALPHAD method [1,2], which consists of the determination of the Gibbs function of the whole phase from the available experimental information. This can be achieved only if the boundary systems are well described thermodynamically. Even if the Fe–Zn phase diagram appears to be well established (Fig. 1), measurements of the thermodynamic functions are quite difficult because of the high vapour pressure of zinc. Thus few calorimetric enthalpies of formation are available. This increases the difficulty of obtaining a correct thermodynamic evaluation of this system. The purpose of this work was to measure the enthalpy of formation of the z-phase with composition Fe 0.07 Zn 0.93 in order to obtain an improvement of any quantitative description of the system.
The alloy was prepared from high-purity zinc ($6N) and iron purified by zone melting (.5N). The composition of the prepared alloy was XZn 50.935 in order to be certain of obtaining the z-phase even in the case of the evaporation of Zn. The correct proportion of each element was introduced into a silica tube and sealed under vacuum (4–13 mbar). Because of the high vapour pressure of zinc, the temperature was increased from 450 to 900 8C in steps of 50 8C with a duration of 12 h for each step. The alloy was then annealed for 3 weeks at 450 8C. Identification of the phases was carried out on a PW 1729 (Philips) X-ray diffractometer equipped with a graphite monochromator, Cu Ka radiation, fixed antiscatter and divergence slits and a goniometer adapted to a step motor driven by software developed previously [3]. The 2u angle was scanned from 10 to 808 in a Bragg– Brentano arrangement. A small amount of alloy was crushed into a fine powder and placed on a glass sample holder. The amount of each phase was quantified using a fundamental parameters Rietveld program [4]. The instrument parameters were adjusted with the diffraction lines from LiB 6 powder, used as a standard. Scanning electron microscopy with energy dispersive spectroscopy (EDS, DSM960, Carl Zeiss), equipped with an Oxford detector, was used to observe the morphology of the microstructure and determine the composition of the
*Corresponding author. Tel.: 133-1-4683-5725; fax: 133-1-46835454. E-mail address: [email protected] (Y. Feutelais).
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00664-3
212
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
Fig. 1. Fe–Zn phase diagram according to the description of Ref. [20].
z-phase. The conditions were an accelerated tension of 20 kV, a working distance of 25 mm and an X-ray detector with a Be window. Pure iron and zinc were used as standards and a cobalt sample was used to calibrate the energy spectrum. The results were processed with the program ZAF (Oxford). A high-temperature (T #1273 K) Setaram microcalorimeter of the Tian-Calvet type was used for solution calorimetry. Experimental details are given in a previous study performed on the Al-rich part of the Al–Fe and Al–Cu–Fe systems [5,6]. Aluminium baths were obtained by placing about 3 g pure Al ($6N) in an alumina crucible previously heated to 1273 8C under a dry N 2 flow. These were placed inside silica tubes. The samples were dropped from an air-lock thermoregulated at room temperature (T 0 529863 K) into the liquid aluminium bath maintained at 107461 K. Although some oxidation of the Al bath may occur at such a temperature, this temperature was chosen so as to obtain a sufficiently fast rate for the dissolution of the Fe 0.065 Zn 0.935 alloy in the bath. The samples were guided down into the aluminium bath by stainless steel tubes. This material has the advantage of very low degassing and of absorbing residual traces of oxygen. After degassing in a vacuum of |10 23 mbar, experiments were performed under flowing purified U argon. The sample mass used for each experiment was about 25 mg. The microcalorimeter was calibrated with NIST a-Al 2 O 3 , and confirmed by measuring the enthalpy change of pure Al between 298 and 1074 K.
3. Results and discussion X-ray diffraction showed only two phases, the major compound being the z-phase (C2 /m) with a small amount of pure Zn (P6 3 /mmc). Their lattice parameters agree with the values reported in the literature [7,8]. Three different samples were used to quantify the amount of each phase and the mean weight percent of zinc was found to be 6.3% (s 50.8), and the fitting conditions were better than R wp # 24.323 and gof#1.423 [4]. The composition of the z-phase as determined by EDS was 93 at% Zn and 7 at% Fe. The presence of the zinc phase was, of course, taken into account in the calorimetric investigation by removing it from the measured heat effect for each experiment: • the relative heat of dissolution of Zn in the aluminium bath at T51074 K for dissolution experiments. The partial molar value, D diss H ` 510 466 J / mol, of zinc in aluminium was calculated from the database given in Refs. [9,10]; • the relative enthalpy change of Zn between 298 and 1074 K (DH 1074 298 (Zn)) for the alloy heat content experiments. This value includes the latent heat to melt Zn and was calculated (DH 1074 298 (Zn)530 081.6 J / mol) from the thermodynamic description of pure Zn given in the unary database of Ref. [11]. Thus the standard enthalpy of formation of Fe 0.07 Zn 0.93 at 298 K (D f H ) was obtained indirectly by measuring the
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
heats of dissolution of Fe, Zn and Fe 0.07 Zn 0.93 in the aluminium bath at 1074 K. For 1 mol of Fe 0.07 Zn 0.93 , we have D f Hm (Fe 0.07 Zn 0.93 ) 5 0.07D sol Hm (Fe) 1 0.93D sol Hm (Zn) 2 D sol Hm (Fe 0.07 Zn 0.93 )
(1)
where D sol Hm is the total heat measured for 1 mol of Fe, Zn or Fe 0.07 Zn 0.93 : 1074
D sol Hm 5 DH 298 1 D diss H
`
The first term is the enthalpy change of the compound from 298 to 1074 K, it is the heat content of Fe and 1074 1074 Fe 0.07 Zn 0.93 (DH 298 5 e298 Cp dT ) and for Zn it also includes the latent heat of melting. The second term is the heat of dissolution of the compound in liquid aluminium at 1074 K for infinite dilution. The terms D sol Hm (Fe) and D sol Hm (Zn) are thus the respective total molar enthalpy changes of pure Fe and pure Zn according to the reactions kFel 298 K 1 (Al) ( l, 1074 K) → ((Fe)) (1074 K ) , D sol Hm (Fe) (2) kZnl 298 K 1 (Al) ( l, 1074 K) → ((Zn)) 1074 K , D sol Hm (Zn)
(3)
D sol Hm (Fe 0.07 Zn 0.93 ) is the total molar enthalpy change for the reaction kFe 0.07 Zn 0.93 l 298 K 1 (Al) ( l, 1074 K ) → ((Fe,Zn)) 1074 K , D sol Hm (Fe 0.07 Zn 0.93 ) (4) In Eqs. (1)–(4), kFel, kZnl and kFe 0.07 Zn 0.93 l refer, respectively, to the elements Fe and Zn, and to Fe 0.07 Zn 0.93 in the solid state; (Al) l, 1074 K refers to the liquid aluminium bath at 1074 K; ((Fe)) 1074 K and ((Fe,Zn)) 1074 K refer, respectively, to the element Fe and the alloy dissolved in liquid aluminium at 1074 K. In fact, it is not always possible to measure D diss H ` , since the solution may not be at infinite dilution. Hence, one must use a relationship of the type D diss Hm 5 f(x(alloy)) and extrapolate it for x(alloy)→0, if necessary. x(alloy) denotes the molar fraction of the alloy in the mixture: the aluminium bath plus the total mass of Fe 0.07 Zn 0.93 .
213
1074 K. Due to the high vapour pressure of zinc at this temperature, its rate of vaporisation is higher than its rate of dissolution in the aluminium bath, even if the zinc is wrapped in thin aluminium foil. In this case the results are not consistent and the errors are very important. Thus the total heat effect for the dissolution of Zn in the aluminium bath, D sol Hm (Zn)540 548 J / mol, was obtained from the variation in the enthalpy of Zn between 298 and 1074 1074 K, DH 298 (Zn)530 082 J / mol, and the enthalpy of ` dissolution of Zn in Al at 1074 K, D diss H m 510 466 J / mol [9,10].
3.3. Dissolution of Fe0.07 Zn0.93 in liquid aluminium at 1074 K In order to ascertain the dissolution reaction of the alloy in liquid aluminium, the total thermal effect, D sol Hm (Fe 0.07 Zn 0.93 ), should be compared with the heat 1073 content, DH 298 (Fe 0.07 Zn 0.93 ), of the alloy between 298 and 1074 K. Therefore, three series of measurements of the total heat effect and two series of measurements of the heat content between 298 and 1074 K were undertaken.
3.3.1. Heat content measurements The results are given in Table 1. The average value 1074 obtained from the two runs was DH 298 5123 96762248 J / mol (error for 95% confidence interval). As some evaporation can be expected, this value must be used with caution. It was measured only to check the existence of a difference between the heat content and the heat of dissolution, but it was not used in the final calculation of the enthalpy of formation. 3.3.2. Determination of Dsol Hm ( Fe0.07 Zn0.93 ) The results for the three series are presented in Table 2. The last column is the integral heat of mixing of Al and the ternary alloy at 1074 K. The mean values are D sol Hm (Fe 0.07 Zn 0.93 ) 5 33 8236372 J / mol D diss Hm (Fe 0.07 Zn 0.93 ) 5 2 90 14462279 J / mol
3.1. Dissolution of iron in liquid aluminium at 1074 K This result was given in Refs. [12,13]. The total heat effect of Fe when dropped into the liquid aluminium bath from 298 to 1074 K is D sol Hm (Fe)5 286 63862374 J / mol.
3.2. Dissolution of zinc in liquid aluminium at 1074 K It was not possible to obtain experimentally the variation of the enthalpy of Zn dropped into the aluminium bath at
Table 1 1074 Heat content, DH 1074 298 5e298 C p dT (J / mol), of Fe 0.07 Zn 0.93 between 298 and 1074 K First run
Second run
122 687 126 007 127 982 126 669
121 214 122 552 122 422 122 202
m 1 5 125 836
m 2 5 122 097
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
214
Table 2 Results for the dissolution of Fe 0.07 Zn 0.93 in the Al bath at 1074 K No. of series
x(alloy)
D sol Hm (Fe 0.07 Zn 0.93 ) (J / mol)
D diss Hm (Fe 0.07 Zn 0.93 ) (J / mol)
D mix Hm (Fe 0.07 Zn 0.93 ) (J / mol)
1 3 2 3 1 2 3 1 2 3 1 3 2 3 1 2
0.00316 0.00345 0.00406 0.00680 0.00686 0.00758 0.01002 0.01108 0.01253 0.01292 0.01556 0.01569 0.01673 0.01826 0.01992 0.02158
33 722 34 311 34 660 35 067 33 431 33 405 34 260 33 772 33 731 33 214 33 116 34 483 34 290 33 381 33 766 32 559
290 245 289 656 289 307 288 900 290 536 290 562 289 707 290 195 290 236 290 753 290 851 289 484 289 677 290 586 290 201 291 408
227.67 229.90 236.79 258.91 260.29 269.46 287.28 297.78 2115.47 2113.34 2138.24 2137.92 2154.70 2161.14 2177.59 2201.30
The errors correspond to the 95% confidence interval for the mean. Using the values determined in our previous work [12,13] for Eq. (2), the calculated value for Eq. (3) and the measured value for Eq. (4), the molar standard enthalpy of formation at 298 K of the binary alloy may be calculated using Eq. (1): D f Hm(298) 5 2 21786772 J / mol The indicated error corresponds to the standard deviation associated with Eq. (1), estimating the standard error of D sol Hm (Zn) to be 1% of this value. It should be noted that the mean value of D sol Hm given ` above is valid only in the case where D diss H m can be considered as the average value of the measured D diss Hm . In this case, when plotting D diss Hm versus x(alloy) in the studied composition range, a horizontal straight line, indicating independence between the two variables, should be obtained. Fig. 2 shows the experimental enthalpy of dissolution of the binary alloy in pure aluminium and its linear regression line versus the mole fraction of alloy, D diss Hm 5f(x(alloy)). The independence of the variables was checked by performing an analysis of variance of the linear regression. The analysis of variance led to the conclusion of independence between D diss Hm and f(x(alloy)). This result means that the assumption of using the average value of ` the data to obtain D diss H m 5 290 14462620 J / mol is valid. In a narrow composition range starting from pure aluminium, the integral enthalpy of mixing of the alloy versus composition (D mix Hm 5f(x(alloy))) may be considered linear (Fig. 3). As shown in Table 3, the experimental molar standard enthalpy of formation of the z-phase is lower than the calculated values. In all the proposed assessments [14–18],
the temperature of the peritectic invariant L1d 1 →z of 530 8C proposed in Ref. [19] was accepted. We carried out DSC investigations on the Fe 0.065 Zn 0.935 alloy between 400 and 700 8C. We obtained, in this range of temperature, three invariant phenomena (Fig. 4): L → z 1 (Zn), T 5 418.560.5 8C L 1 d 1 → z, T 5 560.063 8C L 1 G1 → d 1 , T 5 674.561 8C It should be noted that the precision on the temperature of the peritectic invariant related to the decomposition of the z-phase is worse than for the temperatures of the two other invariants.
Fig. 2. Enthalpy of dissolution of the z-phase (x Zn 50.93) in pure Al at 1074 K versus mole fraction of alloy (reference liquid for Al and alloy).
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
Fig. 3. Integral enthalpy of mixing of the z-phase (x Zn 50.93) with pure Al at 1074 K versus mole fraction of alloy (reference liquid for Al and alloy). Table 3 Experimental and calculated molar enthalpy of formation of the z-phase Ref.
D f Hm (Fe 0.07 Zn 0.93 ) (J / mol)
[14] [15] [16] [17] [18] This work
22866.74 28453.27 29008 23265 28739 22178
215
Fig. 5. Enlarged part of the DSC curve around the peritectic phenomenon L1d 1 →j for Fe–Zn alloy of composition x Zn 50.935 (heating rate 1 K / min).
As shown in Fig. 5, there is an important change of baseline before and after the invariant phenomenon. This is interpreted as a modification of the heat capacity of the alloy because of the liquidus line, which becomes flatter in this range of composition. The solution calorimetry in an aluminum bath applied here with success to the most Zn-rich alloy of the Fe–Zn system indicates that the determination of the enthalpy of formation of other solid phases is feasible. This will be done in further work in order to propose a refined thermodynamic evaluation.
Acknowledgements R.R. de Avillez is grateful for partial financial support of this research by the Conselho Nacional de Pesquisa e Desenvolvimento (CNPq Proc. 46.1525 / 00-3, 521025 / 966 and 664106 / 1998-6).
References
Fig. 4. Differential scanning calorimetry curve for Fe–Zn alloy with composition x Zn 50.935 (heating rate 1 K / min).
[1] U.R. Kattner, JOM 49 (1997) 14–19. [2] N. Saunders, A.P. Miodownik, CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide, Pergamon Materials Series, Vol. 1, 1998. [3] B. Fraisse, PhD Thesis, Universite´ des Sciences et Techniques du Languedoc, Montpellier, France, 1995. [4] R.W. Cheary, A.A. Coelho, J. Appl. Crystallogr. 25 (1992) 109–121. [5] N. Saadi, M. Harmelin, B. Legendre, J. Chim. Phys. 90 (1993) 355–366.
216
Y. Feutelais et al. / Journal of Alloys and Compounds 346 (2002) 211–216
[6] N. Saadi, M. Harmelin, F. Faudot, B. Legendre, J. Non-Cryst. Solids 153 / 154 (1993) 500–503. [7] P.J. Brown, Acta Crystallogr. 15 (1962) 608–612. ¨ Ann. Phys. (Leipzig) 5 (12) (1953) [8] H.E. Swanson, E. Tatgey, 121–144. [9] S. an-Mey, Z. Metallkd. 84 (1993) 451–455. [10] I. Ansara, A.T. Dinsdale, M.H. Rand (Eds.), COST 507 Thermochemical Database for Light Metal Alloys, European Communities, 1998, EUR 18499 EN. [11] A.T. Dinsdale, CALPHAD 15 (1991) 319–427. [12] Y. Li, P. Ochin, A. Quivy, P. Telolahy, B. Legendre, J. Alloys Comp. 298 (2000) 198–202. [13] Y. Li, B. Legendre, J. Alloys Comp. 302 (2000) 187–191. [14] S. Petersen, P.J. Spencer, K. Hack, Thermochim. Acta 129 (1988) 77–87.
¨ ¨¨ [15] M. Hamalainen, R. Luoma, P. Taskinen, Report TKK-V-B55, Helsinki University of Technology, Faculty of Process Engineering and Materials Science, Espoo, Finland, 1990. [16] G. Reumont, P. Perrot, J.M. Fiorani, J. Hertz, J. Phase Equilib. 21 (2000) 371–378. [17] X. Su, N.-Y. Tang, J.M. Toguri, J. Alloys Comp. 325 (2001) 129–136. ´ Nancy I, France, [18] N. David, PhD Thesis, Universite´ Henri Poincare, 2001. [19] J. Schramm, Z. Metallkd. 29 (1937) 222–2224. [20] T.B. Massalski et al. (Ed.), Binary Alloy Phase Diagrams, 2nd Edition, ASM International, Metals Park, OH, 1990, p. 147.