Calorimetric Measurements of Liquid Al-Zn Alloys ADAM DE ˛ BSKI, WŁADYSŁAW GA ˛ SIOR, and KATARZYNA SZMIT The integral molar enthalpies of mixing were determined by the drop calorimetric method for binary AL-Zn liquid solutions and compared with the Miedema model as well as the earlier experimental data. The measurements were conducted at two temperatures: 957 K and 1001 K (684 C and 728 C), in the entire concentration range. Based on the experimental calorimetric data of this study as well as those available in the literature and the results of the activity studies, the interaction parameters of the Redlich-Kister equation for the liquid Al-Zn phase were worked out with the use of the least square method. The partial and integral Gibbs energies, entropies and enthalpies were calculated and presented in tables and figures. Additionally, the concentration-concentration partial structure factors for the ideal and real Al-Zn solutions were calculated and graphically presented. DOI: 10.1007/s11661-016-3643-z  The Minerals, Metals & Materials Society and ASM International 2016

I.

INTRODUCTION

THE Zn-containing aluminum alloys have a good castability and a low casting shrinkage. Furthermore, the addition of zinc increases the mechanical properties as well as improves the weldability and the corrosion resistance. Therefore, these alloys are used in the automotive industry, among others, on panels or fans. The Al-Zn alloys are interesting extensively for the aerospace industry because of their abilities to withstand high pressure and stress during flights at high altitude and considerable speeds.[1–4] At present, the Al-Znbased alloys are of great interest because of their good damping properties as well as a considerably lower density as compared to the conventional cast iron. The Al-Zn system has been investigated extensively by many researchers. The solidus and liquidus curves were studied by References 5 through 17 with the use of the thermal analysis. The activity of Al in the Al-Zn liquid alloys was measured with the use of the EMF method by Batalin and Beloborodova[18] at 960 K (687 C), Predel and Schallner[19] at 1000 K and 1100 K (727 C and 827 C), and Sebkova and Beranek[20] at 973 K and 1073 K (700 C and 800 C). Their results agree fairly well with each other. The activity of Zn in the Al-Zn liquid alloys was determined by means of the isopiestic method by Bolsaitis and Sullivan[21] at 1076 K (803 C), with the use of the dew point method by Lutz and Voigt[22] at 950 K and 1050 K (677 C and 777 C) and Yazawa and Lee[23] at 1073 K (800 C), with the use of the EMF method by Eremenko[24] at 960 K (687 C) and 1120 K ADAM DE ˛ BSKI, Assistant Professor, and WŁADYSŁAW GA ˛ SIOR, Professor, are with the Institute of Metallurgy and Materials Science, Polish Academy of Sciences, 30-059 Krako´w, 25, Reymonta Street, Poland. Contact e-mail: [email protected] KATARZYNA SZMIT, Student, is with AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krako´w, Poland. Manuscript submitted May 7, 2015. Article published online July 20, 2016 METALLURGICAL AND MATERIALS TRANSACTIONS A

(847 C), and with the use of the X-ray method by Schneider and Stoll[25] at 923 K and 1073 K (650 C and 800 C). The mixing enthalpy of the liquid Al-Zn alloys was performed calorimetrically by Wittig and Keil[26] at 953 K and 973 K (680 C and 700 C). Connell and Downie[27] determined the enthalpies of formation of the fcc alloys at 599 K, 637 K, and 648 K (326 C, 364 C, and 375 C). In 1987, Shaarbaf et al.[28] used differential scanning calorimetry (DSC) to measure the enthalpy change associated with the dissociation of a 29.5 at.pct Zn alloy into Al (fcc) and Zn (hcp) phases. Their results agree with the research of Wittig and Scho¨ffl[29] and the data of Lyashenko,[30] but there is a significant discrepancy between them as well as the results of several EMF studies[31–36] of solid alloys. In 2014, Balanovic´ et al.,[37] on the basis of the Olsen calorimetric method, determined the thermodynamic properties (activities, activity coefficients, partial, and integral excess Gibbs energy and mixing energies) at 1000 K (727 C). Murray[38] developed a thermodynamic description for the Al-Zn system. However, the calculated phase diagram of Al-Zn was not in good agreement with the experimental data available in the literature. Subsequently, in 1986, Mey and Effenberg[39] presented a thermodynamic evaluation of the system using the computer program written by Lukas.[40] Later, a thermodynamic calculation of the Al-Zn system was carried out by Mey[41] (Figure 1), Chen and Chang,[42] and Mathon et al.[43] These three optimizations provide very similar phase diagrams.

II.

EXPERIMENTAL

A. The Miedema Model The Miedema model[44,45] is one of the semiempiric models allowing for the estimation of the integral molar enthalpy of mixing in binary systems. According to this VOLUME 47A, OCTOBER 2016—4933

protective atmosphere of high-purity argon (Air Products 99.9999 wt pct). In the calorimetric study, alumina crucibles with a protective alumina tube were used. At the beginning of the whole series, the calorimeter was calibrated by way of using pieces of Al or Zn. Before each experimental run and before the pieces of the sample of Al or Zn were dropped into the calorimeter, the apparatus was evacuated with a turbo molecular pump several times and then flushed with high-purity argon (Air Products 99.9999 wt pct). For the determination of the heats effects, the Calisto software was used.

III. Fig. 1—Phase diagram of the Al-Zn system.[41]

model, the integral molar mixing enthalpy of Al-Zn liquid alloys can be calculated by way of applying Eq. [1].   Dmix H¼ XAl XZn csAl DH0Zn; Al þ csZn DH0Al; Zn ; ½1 where XAl and XZn are the molar fractions of aluminum and zinc, respectively. csAl , csZn , DH0Al;Zn and DH0Zn;Al are determined with the use of the following equations: 2

csAl

XAl V3Al

=

2

2

;

csZn ¼ 1  csAl ;   1 2 3 2VAl  PðDU Þ þQ Dnws RðlÞ h 1  1 i ; ¼ 3 Zn 3 nAl þ n ws ws 2 3

DH0Al;Zn

DH0Zn;Al

½2

XAl V3Al + XZn V3Zn



½3

 2

   1 2 2 2V3Zn  PðDU Þ2 þQ Dn3ws RðlÞ h 1  1 i ; ¼ 3 3 þ nZn nAl ws ws

½4

½5

P, Q, R(l), are the empiric constants determined by Zn Miedema et al.;[45] nAl ws and nws are the densities of the electrons at the Wigner–Seitz cell boundary. More details can be found in our previous work.[46] B. Calorimetric Study In the determination of the integral enthalpy of mixing of liquid Al-Zn alloys, 99.999 wt pct Al and 99.999 wt pct Zn Alfa Aesar were used. Calorimetric measurements were performed with the use of the Setaram MHTC 96 Line evo calorimeter. All the calorimetric measurements were carried out in the 4934—VOLUME 47A, OCTOBER 2016

RESULTS AND DISCUSSION

In the case of the Al-Zn system, the measured enthalpy is the integrated heat flow at a constant pressure, and it follows the following equations:     ½6 HDISSX ¼ DHSignal  K  HTXD !TM  nX ; P Dmix H ¼

HDISSX ; nAl þ nZn

½7

where DHSignal is the heat effect of each drop of metal (Al or Zn) which equalled the added drop enthalpy, K is the calorimeter constant, TD and TM are the drop temperature and the calorimeter temperature of the respective measurement in Kelvin, respectively. HTXD !TM is the enthalpy of the pure metals (Al or Zn) obtained from Pandat 2014 (Pan_SGTE database based on the original SGTE v4.4 database), nAl and nZn are the numbers of moles of aluminum and zinc, respectively. HDISS-X is the enthalpy of dissolution of pure aluminum or zinc. The enthalpy of the pure metals, the numbers of moles, the mole fraction of pure zinc, the drop enthalpy, and the integral molar enthalpy of mixing of liquid Al-Zn alloys obtained in four separate series are given in Table I. All the experimental results, compared to the literature data[26,41,47–49] and those obtained from the Miedema model,[45,46] are also shown in Figure 2. The experimental results obtained in this study of the integral molar enthalpy of mixing, together with those for the Zn activity measured in References 19, 21 through 25, 37 were applied for the description of the excess Gibbs energy of the Al-Zn liquid solution by means of the Redlich–Kister equation given below: Dmix GE ¼ XAl  XZn  ð10785:2  4:43208TÞ ðJ=molÞ: ½8 The parameters in Eq. [8] were calculated with the use of two-stage optimization. After the first one, the experimental data with the deviation over 1 kJ/mol higher than those calculated with the use of the obtained interaction parameters were rejected, and they were not taken into consideration in the second stage. The parameters in Eq. [8] were calculated with the use of the least square method, and the counted standard deviation equals 312 J/mol. METALLURGICAL AND MATERIALS TRANSACTIONS A

METALLURGICAL AND MATERIALS TRANSACTIONS A

VOLUME 47A, OCTOBER 2016—4935

Number of Moles ni (mol) Mole Fraction XZn

Heat Effect DHSignal K (kJ)

Integral Enthalpies of Mixing of Liquid Al-Zn Alloys Drop Enthalpy HDISSX (kJ)

Integral Enthalpy DmixH (kJ/mol)

HAl =29.5904 Series 1: starting amount: nAl = 0.0460463 mol, K = 0.000003779 kJ/lVs, TD=298 K (25 C), TM = 957 K (684 C), DmixH error ±0.279 kJ/mol. nZn HZn ¼26.41421 0.002277 0.0471 0.08463 0.024 0.507 0.003243 0.1070 0.11513 0.029 1.046 0.011135 0.2656 0.37860 0.084 2.208 0.016325 0.4173 0.51237 0.081 2.779 0.013495 0.5023 0.40441 0.048 2.892 0.017242 0.5805 0.50242 0.047 2.866 HAl =29.5904 Series 2: starting amount: nZn = 0.072470174 mol, K = 0.000003729 kJ/lVs, TD=298 K (25 C), TM = 957 K (684 C), DmixH error ±0.071 kJ/mol. HZn ¼26.41421 nAl 0.007787 0.9076 0.29865 0.068 0.807 0.00795 0.8294 0.29132 0.056 1.342 0.008039 0.7629 0.28759 0.049 1.728 0.007994 0.7065 0.28448 0.048 2.041 0.007809 0.6590 0.27025 0.039 2.239 0.007724 0.6179 0.26409 0.035 2.384 0.008131 0.5798 0.27743 0.037 2.514 0.008031 0.5465 0.26694 0.029 2.578 0.008287 0.5160 0.27894 0.033 2.659 0.007954 0.4897 0.25858 0.023 2.671 0.007794 0.4664 0.26137 0.030 2.730 0.008157 0.4443 0.26757 0.026 2.751 HAl =30.9556 Series 3: starting amount: nAl= 0.029694 mol, K= 0.000003649 kJ/lVs, TD=298 K (25 C), TM = 1001 K (728 C), DmixH error ± 0.673 kJ/mol. HZn ¼27.79491 nZn 0.001704 0.0543 0.07674 0.029 0.936 0.001903 0.1083 0.06727 0.014 1.314 0.002911 0.1800 0.10126 0.020 1.771 0.00336 0.2496 0.11228 0.019 2.098 0.003449 0.3098 0.11723 0.021 2.426 0.00347 0.3613 0.11659 0.020 2.678 0.004243 0.4147 0.13706 0.019 2.831 HAl =30.9556 Series 4: starting amount: nAl = 0.033226423 mol, K = 0.000003564 kJ/lVs, TD=298 K (25 C), TM = 1001 K (728 C), DmixH error ±0.789 kJ/mol HZn ¼27.79491 nZn 0.00206 0.0584 0.0805 0.023 0.658 0.001606 0.0994 0.0593 0.015 1.025 0.002059 0.1470 0.0751 0.018 1.429 0.002253 0.1936 0.0779 0.015 1.723 0.001987 0.2307 0.0657 0.010 1.886 0.001961 0.2641 0.0660 0.012 2.059 0.002048 0.2961 0.0683 0.011 2.210 0.001696 0.3205 0.0560 0.009 2.315 0.002241 0.3502 0.0724 0.010 2.412 0.001762 0.3719 0.0553 0.006 2.450 0.002441 0.3996 0.0787 0.011 2.539

Enthalpy of the Pure Metals HTi D !TM (kJ)

Table I.

2.733 2.634 2.675 2.706 0.016 0.001 0.009 0.011 0.0734 0.0666 0.0796 0.1061

Integral Enthalpy DmixH (kJ/mol) Drop Enthalpy HDISSX (kJ) Heat Effect DHSignal K (kJ)

Standard states: pure liquid metals.

Mole Fraction XZn

0.4210 0.4440 0.4667 0.4944 0.00205 0.002375 0.002533 0.003415

Enthalpy of the Pure Metals HTi D !TM (kJ)

Number of Moles ni (mol)

continued Table I.

4936—VOLUME 47A, OCTOBER 2016

As can be seen in Figure 2, the results of the integral molar enthalpy of mixing of liquid Al-Zn alloys are in good agreement with the data evaluated by References 41, 47 through 49 and the experimental data measured at 953 K (680 C) by Witting and Keil;[26] however, those calculated by means of the Miedema model (integral enthalpy of mixing)[45,46] differ significantly from the ones determined in this study. They are characterized by a positive deviation from the ideal solutions; however, their values are about five times lower than most of the values shown in Figure 2. This is not surprising as the great differences between the Miedema data and the experimental ones obtained by the authors of this work have been observed many times for intermetallic phases and solutions.[50,51] We may say that for many binary systems values of the mixing and formation enthalpy for liquid solutions as well as intermetallic phases obtained with the use of the Miedema model, it differed less or more significantly with the experimental ones. The analysis of Eqs. [1] through [5] shows that, for the given system, the values of the interfacial enthalpy similar to the surface molar fractions given by Eqs. [2] through [5] are determined only by the molar volume in 2/3 power. Because the molar volumes of Al and Zn are very similar, the values of the interfacial enthalpies (Eqs. [4] and [5]) are almost the same. As a result, the mixing enthalpy change is almost symmetric, which is in good accordance with the experimental data. However, the values of DmixH calculated from Eq. [1] are about five times lower than most of the values shown in Figure 2. The only reason of such divergence are the values of the empiric parameters in Eq. [1] determined on the basis of the experimental data, as the difference of the electronegativity (DF) and the electron density on the Wigner–Seitz boundary cell (nws) is precisely determined for the given system. One can point at the following reasons for the significant deviations observed between the experimental and the calculated data. First, the number of empiric parameters in Eq. [1] should be higher. Second, the parameters should be different for the alloys with a positive and negative deviation from the ideal liquid and solid solutions, and third, the electron density difference is a function of the alloy composition. It is very hard to explain the great deviation between the experimental results of Reference 26 at 950 K and 973 K (677 C and 700 C) (about 50 pct). It is also difficult to account for the fact that, at a higher temperature, the mixing enthalpy is higher than that at a lower one, as it would mean that the Al-Zn liquid solutions are characterized by a higher tendency for segregation at higher temperatures than at lower ones. This observation is inconsistent with the generally accepted fact that, with the temperature increase, the thermodynamic properties of real solutions tend to reach the ideal ones, as well as with the other data shown in Figure 2. The values of DmixH from the dew point study[22] are inconsistent with all the others as they are of the opposite sign. This inconsistency is the most probably caused by the high experimental error of the dew point method which additionally can be the temperature function. As a result, the temperature METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 2—Enthalpy of mixing of liquid Al-Zn alloys obtained in this work compared with literature data.[22,26,41,45–49]

Fig.3—The concentration-concentration partial structure factor Scc(0)[52] for real and ideal Al-Zn liquid solutions and their difference.[53]

Table II.

coefficient values measured for the Gibbs energy is too high. In such case, the change of mixing enthalpy as the extrapolated Gibbs energy change to zero takes values much lower in comparison to calorimetric ones even of opposite sign (negative). The concentration-concentration partial structure factor Scc(0)[52] at 1000 K (727 C) for the real solutions, presented in Figure 3, show higher values in comparison with that for the ideal solution, and its maximal value equals 0.42 for the concentration equalling 0.5 mole fraction of zinc. It means that liquid Al-Zn solutions are characterized by a tendency for segregation. In Figure 3, the difference between Scc(0) of the ideal solution and that of the real solution is also shown. This function was proposed by Sommer[53] for the identification of the kind of associates existing in the liquid solutions of a negative deviation from the ideal behavior, especially in such a case when Scc(0) has no minimum. For the solutions characterized by positive values of the excess Gibbs energy, the minimal negative value of Scc(0) informs of a solution composition of the highest

Integral Quantities for the Al-Zn Liquid Phase at 1000 K (727 °C)

XZn

DmixG (kJ/mol)

DmixH (kJ/mol)

DmixS [J/(mol K)]

DmixGE (kJ/mol)

DmixSE [J/(mol K)]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 2.131 3.144 3.744 4.07 4.174 4.07 3.744 3.144 2.131 0

0 0.971 1.726 2.265 2.588 2.696 2.588 2.265 1.726 0.971 0

0 3.101 4.869 6.009 6.659 6.871 6.659 6.009 4.869 3.101 0

0 0.572 1.017 1.334 1.525 1.588 1.525 1.334 1.017 0.572 0

0 0.399 0.709 0.931 1.064 1.108 1.064 0.931 0.709 0.399 0

METALLURGICAL AND MATERIALS TRANSACTIONS A

VOLUME 47A, OCTOBER 2016—4937

Table III.

Partial Quantities for Aluminum in the Al-Zn Liquid Phase at 1000 K (727 °C)

XAl

DGAl (kJ/mol)

DHAl (kJ/mol)

DSAl [J/(mol K)]

DGEAl (kJ/mol)

DSEAl [J/(mol K)]

aAl

cAl

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0 0.812 1.601 2.393 3.23 4.174 5.331 6.896 9.314 13.997 ¥

0 0.108 0.431 0.971 1.726 2.696 3.883 5.285 6.903 8.736 10.785

0 0.92 2.032 3.364 4.956 6.871 9.213 12.181 16.217 22.733 ¥

0 0.064 0.254 0.572 1.017 1.588 2.287 3.113 4.066 5.146 6.353

0 0.044 0.177 0.399 0.709 1.108 1.596 2.172 2.837 3.59 4.432

1 0.9069 0.8248 0.7498 0.678 0.6053 0.5267 0.4363 0.3262 0.1857 0

1 1.0077 1.031 1.0712 1.1301 1.2105 1.3167 1.4542 1.6308 1.8571 2.1472

Table IV. Partial Quantities for Zinc in the Al-Zn Liquid Phase at 1000 K (727 °C) XZn

DGZn (kJ/mol)

DHZn (kJ/mol)

DSZn[J/(mol K)]

DGEZn (kJ/mol)

DSEZn [J/(mol K)]

aZn

cZn

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

¥ 13.997 9.314 6.896 5.331 4.174 3.23 2.393 1.601 0.812 0

10.785 8.736 6.903 5.285 3.883 2.696 1.726 0.971 0.431 0.108 0

¥ 22.733 16.217 12.181 9.213 6.871 4.956 3.364 2.032 0.92 0

6.353 5.146 4.066 3.113 2.287 1.588 1.017 0.572 0.254 0.064 0

4.432 3.59 2.837 2.172 1.596 1.108 0.709 0.399 0.177 0.044 0

0 0.1857 0.3262 0.4363 0.5267 0.6053 0.678 0.7498 0.8248 0.9069 1

2.1472 1.8571 1.6308 1.4542 1.3167 1.2105 1.1301 1.0712 1.031 1.0077 1

Fig. 4—Molar and partial excess Gibbs energies of Al-Zn solutions at T=1000 K (727 C) calculated using Eq. [8] and those from experimental studies.[19,37,41]

tendency for segregation. For the Al-Zn solutions, the structure functions discussed in this passage show extremes in the same solution composition; however, one can notice that such an excellent correlation is not always observed and that this is the effect of the parabolic shape of the Redlich–Kister equation [8]. The thermodynamic integral and partial thermodynamic functions of liquid Al-Zn alloys calculated at 1000 K (727 C) with the use of Eq. [8] are presented in Tables II, III, and IV, and some of them are also shown 4938—VOLUME 47A, OCTOBER 2016

Fig. 5—Molar and partial excess entropies in Al-Zn system calculated applying Eq. [8].

in Figures 4, 5 and 8, together with the experimental data of several authors. The excess Gibbs energy values of zinc, experimental and calculated with the use of Eq. [8], very well correlates with the data of Predel[19] for the liquid solutions of the concentration of Zn lower that 0.5 mole fraction, whereas those measured by Balanovic´ et al.[37] are higher than the ones from this study, in the entire concentration range. The partial and integral excess entropies from this work and two other ones[47,48] are shown in Figures 5. Differences smaller than 0.5 J/(mol K) are observed METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 6—Molar entropy times the absolute temperature in Al-Zn system at T=1000 K (727 C) calculated using Eq. [8] and obtained by Refs. [41], [47], [48].

Fig. 8—Excess Gibbs energy of Al-Zn solutions at 1000 K (727 C).

mixing enthalpy (this work) applied in the optimization which are a little more endothermic to that measured by Wittig and Keil.[26] Second, the new aluminum activity values measured by Reference 37 in 2014, and third two step elaboration which eliminated data with the highest deviations (over 1 kJ/mol) from these calculated based on the interaction parameters obtained when all Al activity experimental values were taken into the data optimization (first optimization).

IV.

Fig. 7—Activities of aluminum and zinc in the liquid phase at T=1000 K (727 C) calculated using Eq. [8] on the background of experimental data.[19,37]

between the integral excess entropies. The data of this work are higher than those from References 47, 48 and similar to Reference 44. They are symmetrical and those evaluated by Hultgren et al.[47] are asymmetrical with the maximum for XZn = 0.6. The entropy part of the mixing Gibbs energy by the same authors are presented in Figure 6. The Zn and Al activities and the integral excess Gibbs energy on the background of the earlier data at 1000 K (727 C) are shown in Figures 7 and 8, respectively. Although the Zn and Al activities show small deviations from the data of the cited authors[37,45,46], the excess Gibbs energy of Balanovic´ et al.[37] is higher than those from this study, as well as References 45 and 46 by about 1 to 1.4 kJ/mol. The lowest values of DmixGE are those calculated with the use of Eq. [8], which was evaluated in this study. The observed differences between the values calculated with the use of the elaborated in this work Eq. [8] and those form earlier one are the most probably caused by three reasons. First, the new experimental data of the METALLURGICAL AND MATERIALS TRANSACTIONS A

CONCLUSIONS

Measurements of the integral molar mixing enthalpy of Al-Zn liquid solutions by means of drop calorimetry at 957 K and 1001 K (684 C and 728 C) are almost identical, which points to the lack of a temperature dependence of this thermodynamic function. This conclusion is in contradiction with the data of Wittig et al., which suggests a strong temperature dependence of the mentioned mixing function. The observed maximal value of the mixing enthalpy equals DmixH = 2.892 kJ/mol, for the mole fraction of zinc XZn = 0.5023, which is much higher than that calculated by the Miedema model, with the maximal value DmixH = 0.637 kJ/mol, for the mole fraction of zinc XZn = 0.5. The obtained results of the integral molar enthalpy of mixing of liquid Al-Zn alloys show a very good agreement with the previous data of Hultgren et al. as well as with the Landolt–Bo¨rnstein database. The mixing excess entropy, similarly to the mixing enthalpy, shows positive deviations from the ideal solution, which means that Al-Zn liquid solutions tend to reach the ideal ones with a temperature increase. This trend is in agreement with the generally accepted opinion. Except for the data of the molar excess Gibbs energy of Hultgren et al., which are asymmetrical, other critical evaluations show a symmetrical shape of this function.

ACKNOWLEDGMENTS The authors wish to express their gratitude to the Ministry of Science and High Education of Poland VOLUME 47A, OCTOBER 2016—4939

and the European Union for the financial support of Project POIG.02.01.00-12-175/09 (Adaptation of the research potential of IMMS PAS to the requirements of the global standards for a comprehensive research in the field of materials science) which enabled the realization of presented investigations with the use of Setaram MHTC Line 96 evo calorimeter, which was bought within the frames of cited project.

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METALLURGICAL AND MATERIALS TRANSACTIONS A