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Validation of an effective oxidation pressure model for liquid binary alloys
Materials Science and Engineering A 495 (2008) 27–31
Validation of an effective oxidation pressure model for liquid binary alloys E. Ricci a,∗ , D. Giuranno a , E. Arato a,b , P. Costa b a
CNR-IENI, Department of Genoa, Via De Marini, 6-16149 Genova, Italy b DICAT, University of Genoa, Via Opera Pia, 15-16145 Genova, Italy
Received 4 April 2007; received in revised form 15 September 2007; accepted 12 October 2007
Abstract Dynamic surface-tension measurements using the sessile drop method and acquisition times of a few seconds make it possible to study the evolution of the surface of molten metals and alloys and so reliably validate the predictive models of the interactions between pure liquid metals and an oxidizing atmosphere, in both an inert gas carrier and in a vacuum. The presence of active oxidation contributes to maintaining surface cleanness and then strongly affects the shape of the boundary separating oxidation and de-oxidation regimes. Recently the general physical–mathematical analysis we developed for pure liquid metals has been extended to liquid binary alloys and their oxides. In this work we present the experimental results of tests on some binary alloys chosen as test systems to try to obtain a preliminary validation of the extended model. The theoretical results obtained, indicating that the behaviour of the alloy towards oxidation tends to be similar to that of the less oxidizable component, have thus been confirmed experimentally. © 2008 Elsevier B.V. All rights reserved. Keywords: Metal oxidation; Binary alloys; Interface saturation; Transport phenomena; Dynamic surface-tension measurements
1. Introduction The evaluation of gas-atmosphere mass exchanges under stationary conditions allows the evaluation of the effective oxygen pressure at which the oxidation of a liquid metal becomes evident. This effective oxygen pressure can be considered as a property of the system and can be many orders of magnitude greater than the actual equilibrium pressure [1]. The estimates of the degree of contamination of the surface and the mechanism of the gas mass-transfer at the liquid metal–gas interface are obtained from different theoretical models [2,3]. The application of these models is even more useful when dealing with measurements of the surface properties of metals of particular technological interest such as silicon [4], tin [5,6] and aluminium [7], which are often the main components of more complex metal systems. Knowledge of the
∗
Corresponding author. Tel.: +39 0106475720; fax: +39 0106475700. E-mail address: [email protected] (E. Ricci).
0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.10.115
surface conditions of multi-component alloys is essential for developing a suitable casting model. Nowadays, the numerical modelling of casting and solidification of metallic alloys is of increasing importance in industrial processing [8] for the optimisation of production technology or designing new and improved casting techniques [9–12] in order to deliver high-quality products or new production routes. In both cases, the processes are primarily governed by alloy solidification behaviour and consequently, essentially related to thermodynamics, kinetics and capillarity [13]. Recently, thermodynamic and transport theories able to offer a reasonable prediction of the interactions of a liquid binary alloy with oxygen in different diffusive regimes have been formulated [14]. These theories have been developed to explain the mechanisms that keep a molten alloy oxygen-free despite the thermodynamic driving forces of the pure metals involved [15]. For the liquid binary alloys, the theoretical results obtained by the model proposed [14] indicate that the behaviour of the alloy towards oxidation tends to be similar to that of the element for which the volatile oxide prevents the surface oxidation even if it is present in low percentages.
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E. Ricci et al. / Materials Science and Engineering A 495 (2008) 27–31
In this work we present a validation of the general physical–mathematical analysis applied to liquid binary In–Sn and Cu–Sn alloys and their oxides. 2. Theoretical background The effective oxygen pressure [15] can be considered as a property of each metal. This property can be defined by making reference to a liquid metal phase formed by a metal (B) and traces of oxygen (A), in contact with a gas phase. The liquid metal has a known composition (xB ∼ = 1; xA xB ) and is maintained at constant temperature T and total pressure P. The gas phase is characterised by the oxygen partial pressure PAG and the presence of an inert gas. The saturation condition of the metal (xA = xAs , PAG = PAs ) corresponds to the appearance of the most stable oxide (D) as a new phase on the metal surface. Then, by also considering the presence of the most volatile oxide (C) at the saturation condition (PCG = PCs ), and the evaporation of the metal (PBG = PBs ), the three-phase equilibrium (liquid metal, atmosphere, condensed oxide) is fully determined. This equilibrium condition is univocal at given T and P, because the thermodynamic system being considered is bi-variant. However, experimental findings do not support this thermodynamic condition: as a matter of fact, stable clean surfaces can be systematically observed under oxygen partial pressures much greater than PAs . Therefore, a better understanding of these phenomena can be obtained only by using a reference condition somewhat different from equilibrium. This alternative and more realistic reference condition is the steady state of the liquid phase in relationship to the oxygen: the liquid phase is still considered in equilibrium with the gas–liquid interface, but it undergoes exchanges of oxygen and oxide with the atmosphere, under the steady condition that the net exchange of atomic oxygen has to be null. Therefore, on the basis of the evaluation of the order of magnitude of the various terms contributing to the effective oxygen pressure, it can be assumed that a stationary pure liquid has an effective oxygen pressure roughly corresponding to the pressure of its most volatile oxide at saturation, PCs (i.e. PAeff ≈ a PCs , where a is the stoichiometric coefficient of oxygen in the formation reaction of the oxide C). However, for some very poorly oxidizable metals, such as copper and nickel, the saturation oxygen pressure PAs is greater than the saturation oxide pressure PCs , so that the effective oxygen pressure coincides with the former (i.e. PAeff ≈ PAs ). In the case of a liquid phase formed by a binary alloy [14] of metals B and B (xB ∼ = 1 − xB ; xA 1), there are two thermodynamic equilibrium reference conditions, one for each component metal. The first is the condition previously described, which considers only metal B as saturated by oxygen A and the equilibrium between the oxidizing atmosphere and the condensed phases, metal B and oxide D (xB ∼ = 1, PAs , PBs , PCs , PAs ). The second condition, mirroring the first, and referring to the second metal, B , considers B saturated by A and the equilibrium between the oxidizing atmosphere and the condensed phases, metal B and oxide D (xB ∼ = 1, PA s , PB s , PC s , xA s ). However, as there are two volatile alloy oxides, C and C , the oxygen content of the gas phase consistent with the steady state of the interface depends on
the volatility of both. Any further step depends on hypothesising about the phases: for instance the liquid phase could be considered as an ideal solution and the oxide phase as the sum of two immiscible oxides. However, the real metal–atmosphere system can show various deviations from ideality, either due to the interactions between the liquid and the surface (for instance segregation phenomena of one of the metals [16]), or the interactions of the gas phase and the surface (for instance oxide condensation inside the gas phase [17]). Simple deviations of the liquid from the ideal state can be taken into account by replacing the molar fractions of the liquid metal with its activities, but in most cases these deviations should not modify the order of magnitude of the effective pressures. On the other hand, the interactions of the oxide phases are very poorly understood: for instance, the behaviour of two immiscible oxide phases might also depend on the fraction of evaporation surface at the disposal of each oxide. This aspect could be especially relevant in Knudsen regime, while it should be only of secondary importance in Fick regime, where the diffusive forces can be assumed to be independent of the surface microstructure. The situation might be further complicated by the presence of mixed oxides. If the ideality of the liquid phase and the immiscibility of the two stable oxides of metals B and B is assumed, the maximum effective pressure of the binary alloy is reached where the curves describing the effective pressure PAeff of the two metals cross each other and is the sum of the effective pressures of the two pure metals. The resulting curve has two branches: the branch corresponding to the first metal, B, starts at a divergence point (X = xB = 0) and then decreases monotonically towards the single metal B value (PAeff /PCs = 1); the branch of the second metal, B , starts from the single metal B value (PAeff /PCs = fC ) and then increases towards divergence. The combination of the two curves shows a maximum at their intersection [14]. The ratio between the effective pressure of the alloy and the effective pressure of the pure metal B can be expressed in terms of the composition xB and the two thermodynamic parameters fA = (PA s /PAs ) and fC = (a PC s /a PCs )(where a and a are the stoichiometric coefficients of oxygen in the formation reactions of the oxide C and C, respectively). The first of these (fA ) can be considered as an oxidizability ratio of the metals from a purely thermodynamic point of view, while the second is the volatility ratio of the oxides. It is worth noting that in the approach presented here the order of the metals B and B will always be chosen in such a way that fC > 1, that is by assuming metal B as the “more oxidizable” of the two, due to the counter-effect of the most volatile oxide of B (i.e. C ), which prevents the oxidation of the liquid alloy surface. The model has also been extended to ideal binary alloys showing an ideal oxide solution [14]. 3. Experimental procedure Experimentally, the surface tension is utilised as the sensitive parameter for the interaction of the oxygen and metal. Two experimental methods can be adopted to obtain different kinds of information: (1) the isothermal procedure, starting with a “clean surface”[15] (i.e. oxide removal conditions), where the imposed
E. Ricci et al. / Materials Science and Engineering A 495 (2008) 27–31
oxygen partial pressure of the feed gas is increased at constant temperature until a significant decrease in the surface tension is obtained and (2) the isobaric procedure, where the imposed temperature is changed under the constant oxygen partial pressure of the feed gas until the tensioactive effect is obtained, as revealed by the change of the sign of the temperature coefficient. The existence of the effective oxygen pressure, which is well above the saturation equilibrium curve, has been demonstrated for pure metals using the first procedure, as reported in Refs. [18–26]. In order to obtain the actual experimental curve, and thus indicate the oxygen tensioactive effect on the liquid metal more quickly, the second experimental procedure has been utilised in this work. The advantage of the isobaric procedure over the isothermal one is that the variations in temperature can be set automatically. As saturation conditions strongly depend on temperature, a temperature modulation corresponds to a modulation in the saturation level and is then equivalent to a modulation in the oxygen concentration in the liquid phase. The large-drop technique [27] is a suitable method for performing systematic dynamic surface-tension measurements on liquid metals and alloys, as the evolution of the drop can be successfully observed as a function of the surrounding atmosphere. The experimental apparatus used for the dynamic surface tension determinations as well as the procedures adopted have been described in Refs. [7,15,23]. In order to validate the extended theoretical analysis recently developed [14], two binary systems have been chosen for testing: In–Sn and Cu–Sn. The alloys (In–20 at.% Sn; In–50 at.% Sn In–90 at.% Sn, Cu–80 at.% Sn; Cu–50 at.% Sn) were prepared from high purity (Marz-grade) Cu, In and Sn. The pure metals were enclosed in a quartz tube under high vacuum conditions (Ptot = 10−4 Pa), and then melted in a high-frequency generator furnace under pure Argon. The composition of each alloy was checked with EDS analysis. Each alloy sample of about 2.5 g was mechanically cleaned by scratching, then chemically rinsed with a solvent in an ultrasonic bath. During the test, the sample was placed in an ad hoc-designed sapphire crucible to maintain the axial symmetry of the liquid metal drop [15]. The dynamic surface-tension measurements were performed by following the procedure described in Refs. [15,23]. In particular, the temperature was measured and regulated by two “S”-type thermocouples placed close to the sample, with an accuracy of ±3 K; the oxygen partial pressure was measured with three solid-state oxygen sensors: two of them were placed outside the furnace to measure the oxygen content of the feed and exhausted gases, the third was placed inside the test chamber close to the sample. The three oxygen sensors were all maintained at constant T = 973 K.
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Fig. 1. Surface tension (䊉) and temperature (—) vs. time of the In–50 at.% Sn alloy under Knudsen regime and isobaric conditions (PO2 = 1.06 × 10−4 Pa).
4. Results and discussion Following the theoretical description [14] briefly reported in Section 2, let us now consider Indium as metal B and tin as metal B. Indium and tin are two very similar metals in many respects and their liquids behave substantially as ideal solutions [28]. Moreover, no oxide condensation has been detected in the gas phase and the stable oxides involved are solid in the temperature range of interest. All these considerations suggest that it is possible to refer to them as immiscible oxides with an ideal liquid phase. On the other hand, indium and tin are rather different in their interactions with oxygen. The most volatile tin oxide is SnO, while the most volatile indium oxide is In2 O. From a thermodynamic point of view, indium should be more oxidizable than tin: the saturation pressure of indium is two or three orders of magnitude lower and the thermodynamic ratio fA is of the order of 10−3 . On the contrary, the volatility of the oxides favour indium, so that indium maintains the cleanness of its surface under greater oxygen partial pressures: the saturation pressure of the most volatile oxide of indium is two or three orders of magnitude greater than that of tin and the volatility ratio fC is of the order of 102 –103 . In Table 1 the thermodynamic values of In and Sn oxides are presented at T = 600 K [1,29]. The experimental tests were performed under isobaric conditions, varying the temperature at a rate = 5 K/min. The test performed on the In–50 at.% Sn alloy under the Knudsen regime (Ptot = 10−3 Pa) is shown in Fig. 1. The oxygen partial pressure was constant at PO2 = 10−4 Pa. The temperature was increased and decreased between 540 and 843 K. The temperature modulation made it possible to observe some significant inversions
Table 1 Thermodynamic values of tin [1] and indium [29] oxides calculated at T = 600 K Volatile oxides
◦
Gf (J/mol) Vapour pressure (Pa)
SnO(G) [1]
In2 O(G) [29]
InO(G) [29]
−1.222 × 105
−7.383 × 104
1.348 × 105 9.40 × 10−29
1.33 × 10−18
1.37 × 10−10
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E. Ricci et al. / Materials Science and Engineering A 495 (2008) 27–31
Fig. 2. The effective oxygen pressure of the indium–tin alloys at constant temperature (T = 600 K). Bold line: calculated effective oxygen pressure; broken line: best fitting of the experimental points; experimental points: () pure indium [30]; (♦) In–Sn alloys; () pure tin [23].
in the behaviour of the surface tension [7,15,22]. The meaning of the ‘inversions’ is clearly explained in [15,23]: if a negative temperature coefficient is considered as a characteristic of a pure metal-system, the oxygen tension-active effect over the liquid becomes evident between the two “inversion points”, where the slope of the surface tension versus temperature is positive showing the presence of an oxygen adsorption. The position of the second “inversion point” is approximately symmetrical to that of the first one, as a sign of the reversible oxygen dissolution in the metal drop. The portion of the curve between the two “inversions” reflects the surface adsorption due to the segregation of the oxygen dissolved into the liquid bulk (a consequence of the variation of the temperature) more than the effect of the externally imposed oxygen partial pressure. The experimental conditions of the inversion points (coordinates) are linked to tension-active effect, but not necessarily to the formation of stable oxides on the surface and this effect is identified by the sign inversion of the temperature coefficient of the surface tension. All the coordinates of the experimental points that characterised the inversion of the surface tension against the temperature measured during the dynamic surface tension tests are then reported as singular points in the effective oxygen pressure diagram and compared with the calculated curve. Making reference to a constant temperature of 600 K, and fA = 1.68 × 10−3 and fC = 1.03 × 103 [14], the effective oxygen pressure curve calculated as a function of the alloy composition and the experimental findings [22,30] of the two pure metals and their alloys In–20 at.% Sn, In–50 at.% Sn and In–90 at.% Sn are reported in Fig. 2. As often happens with this type of measurement [10,17], the differences between the experimental data and theoretical predictions are of some orders of magnitude (about 6 in this case). When compared to the thermodynamic predictions, where the differences were of some tens of orders of magnitude (about 35 in this case) the result is encouraging. Moreover, the differences could be further reduced if the effect
Fig. 3. Surface tension (䊉) and temperature (—) vs. time of the Cu–80 at% Sn alloy under Fick regime and isobaric conditions (PO2 = 6 × 10−3 Pa).
of the liquid mass-transfer is considered [15,22,25,26]. However, the important point here is that the experimental findings do not contradict a substantial invariance in the oxidizability of the indium–tin alloys with a tin content ranging from 0 to 80%. Other experimental tests were performed on a Cu–Sn alloy: in the Cu–Sn system tin is considered as metal B and copper as metal B. In fact, from a thermodynamic point of view, tin should be more oxidizable than copper: the saturation pressure of tin is about nine orders of magnitude lower than that of copper. With regard to the volatility, only the most volatile oxide of tin, i.e. SnO, have to be taken into account. In this case, the volatility of the oxides favour tin, so that it maintains the cleanness of its surface under a greater oxygen partial pressures. The dynamic surface-tension measurements of the Cu–Sn alloys (Cu–80 at.% Sn; Cu–50 at.% Sn) were performed following the same procedure adopted for the In–Sn ones, but in the temperature range 1130–930 K. In Fig. 3 the test performed on
Fig. 4. The effective oxygen pressure of the copper–tin alloys. Black line: calculated effective oxygen pressure at T = 1050 K; grey line: calculated effective oxygen pressure at T = 980 K; experimental points: () Cu–80 at.% Sn alloy; (䊉) Cu–50 at.% Sn alloy.
E. Ricci et al. / Materials Science and Engineering A 495 (2008) 27–31
the Cu–80 at.% Sn alloy under the Fick regime (Ptot = 105 Pa) and PO2 = 6 × 10−3 Pa is presented. The Cu–Sn data are reported in Fig. 4 where the effective oxygen pressures calculated at T = 1050 K for the Cu–50 at.% Sn alloy and T = 980 K for the Cu–80 at.% Sn alloys are shown. A quite satisfactory agreement was found between the experimental data and the theoretical predictions. In particular, the analysis of binary alloys formed with a poorly oxidizable metal such as Cu, revealed some peculiarities: the effective oxygen pressure coincided with the saturation oxygen pressure and some anomalous experimental dependencies of surface tension on temperature variations were highlighted. In addition, the deviation from the ideality of the liquid alloy behaviour would have to be taken into account in the theroretical description. A closer analysis of the surface phenomena of these alloys is obviously necessary. 5. Conclusions The phenomena of oxygen transport at a molten metal– atmosphere interface, and particularly the mechanisms whereby a molten metal or alloy surface is kept clean even in the presence of atmospheric oxygen impurities, play a very important role in many technological processes. From the results obtained with our models, it is possible to straightforwardly and qualitatively explain the mechanisms that keep a molten metallic system oxygen-free, despite the thermodynamic driving force, as due to an oxygen flux in the opposite direction to the oxygen adsorption/reaction. The experimental results for some binary alloys, presented here, and the results already obtained for the single metals Sn, Al, In and Si using dynamic surface-tension measurements demonstrate that experimental oxidation–de-oxidation transitions occur at values very close to those predicted by the models and, therefore, higher than the thermodynamic ones, due to the non-negligible contribution of the linked oxygen in the form of oxides. When this consideration was extended from pure liquid metals to liquid binary alloys, the theoretical results obtained indicated that the behaviour of the alloy towards oxidation tended to be similar to that of the less oxidizable component: in many instances the existence of a volatile oxide prevented surface oxidation even if the corresponding metal was only present in very low percentages. The experimental results performed on the two binary systems chosen for testing seem to confirm the predictions.
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Acknowledgments The authors wish to thank Tiziana Lanata and Michela Bernardi for their experimental work. This work was partially supported by the European Space Agency (ESA-ESTEC) within the framework of the ThermoLab-MAP Project no. AO-99-022. References [1] O. Knacke, O. Kubashewski, K. Hesselmann, Thermochemical Properties of Inorganic Substances, 2nd edition, Springer Verlag, D¨usseldorf, 1991. [2] C. Wagner, J. Appl. Phys. 29 (1958) 1295. [3] M. Ratto, E. Ricci, E. Arato, J. Cryst. Growth 217 (2000) 233. [4] T. Azami, S. Nakamura, T. Hibiya, J. Cryst. Growth 223 (2001) 116. [5] E. Ricci, P. Castello, A. Passerone, P. Costa, Mater. Sci. Eng. A 178 (1994) 99. [6] M. Ratto, L. Fiori, E. Ricci, E. Arato, J. Cryst. Growth 249 (2003) 445. [7] D. Giuranno, E. Ricci, E. Arato, P. Costa, Acta Mater. 54 (2006) 2625. [8] R. Aune, L. Battezzati, R. Brooks, I. Egry, H. Fecht, J. Garandet, K. Mills, A. Passerone, P. Quested, E. Ricci, S. Schneider, S. Seetharaman, R. Wunderlich, Microgravity Sci. Technol. XVI (2005) 7. [9] C. Garcia-Cordovila, E. Louis, A. Pamies, J. Mater. Sci. 21 (1986) 2787. [10] H. John, H. Hausner, J. Mater. Sci. Lett. 5 (1986) 549. [11] C. Garcia-Cordovila, E. Louis, J. Narciso, Acta Mater. 47 (1999) 4461. [12] D.J. Jarvis, D. Voss, IMPRESS web-site: www.spaceflight.esa.int/impress. [13] Thermolab-MAP Project no. AO-99-022, Final Report phase II, ESAESTEC, Noordwijk, November 2006. [14] E. Arato, E. Ricci, P. Costa, Surf. Sci. 602 (1) (2008) 349. [15] E. Ricci, E. Arato, A. Passerone, P. Costa, Adv. Colloid Interface Sci. 117 (1–3) (2005) 15. [16] R. Novakovic, E. Ricci, F. Gnecco, D. Giuranno, G. Borzone, Surf. Sci. 599 (2005) 230. [17] M. Ratto, E. Ricci, E. Arato, P. Costa, Met. Trans. B 32B (2001) 903. [18] P. Castello, E. Ricci, A. Passerone, P. Costa, J. Mater. Sci. 29 (1994) 6104. [19] E. Ricci, A. Passerone, P. Castello, P. Costa, J. Mater. Sci. 29 (1994) 1833. [20] E. Ricci, L. Nanni, E. Arato, P. Costa, J. Mater. Sci. 33 (1998) 305. [21] E. Ricci, L. Nanni, A. Passerone, Phil. Trans. R. Soc. Lond. A 356 (1998) 857. [22] E. Arato, E. Ricci, P. Costa, J. Mater. Sci. 40 (9–10) (2005) 2133. [23] L. Fiori, E. Ricci, E. Arato, Acta Mater. 51 (2003) 2873. [24] E. Arato, E. Ricci, L. Fiori, P. Costa, J. Cryst. Growth 282 (3–4) (2005) 525. [25] L. Fiori, E. Ricci, E. Arato, P. Costa, J Mater. Sci. 40 (9–10) (2005) 2155. [26] E. Arato, E. Ricci, D. Giuranno, P. Costa, J. Cryst. Growth 293 (1) (2006) 186. [27] Y.V. Naidich, in: D.A. Cadenhead, J.F. Danielli (Eds.), Progress in Surface and Membrane Science, vol. 14, Academic Press, 1981, p. 353. [28] M. Komiyama, H. Tsukamoto, Y. Ogino, J. Solid State Chem. 64 (1986) 134. [29] Y. Austin Chang, K.-C. Hsieh, Phase Diagrams of Ternary Copper–Oxygen–Metal Systems, ASM International Metals Park, OH, 1989. [30] D. Giuranno, PhD Thesis on Chemical Engineering, University of Genoa, April 2005.
Validation of an effective oxidation pressure model for liquid binary alloys E. Ricci a,∗ , D. Giuranno a , E. Arato a,b , P. Costa b a
CNR-IENI, Department of Genoa, Via De Marini, 6-16149 Genova, Italy b DICAT, University of Genoa, Via Opera Pia, 15-16145 Genova, Italy
Received 4 April 2007; received in revised form 15 September 2007; accepted 12 October 2007
Abstract Dynamic surface-tension measurements using the sessile drop method and acquisition times of a few seconds make it possible to study the evolution of the surface of molten metals and alloys and so reliably validate the predictive models of the interactions between pure liquid metals and an oxidizing atmosphere, in both an inert gas carrier and in a vacuum. The presence of active oxidation contributes to maintaining surface cleanness and then strongly affects the shape of the boundary separating oxidation and de-oxidation regimes. Recently the general physical–mathematical analysis we developed for pure liquid metals has been extended to liquid binary alloys and their oxides. In this work we present the experimental results of tests on some binary alloys chosen as test systems to try to obtain a preliminary validation of the extended model. The theoretical results obtained, indicating that the behaviour of the alloy towards oxidation tends to be similar to that of the less oxidizable component, have thus been confirmed experimentally. © 2008 Elsevier B.V. All rights reserved. Keywords: Metal oxidation; Binary alloys; Interface saturation; Transport phenomena; Dynamic surface-tension measurements
1. Introduction The evaluation of gas-atmosphere mass exchanges under stationary conditions allows the evaluation of the effective oxygen pressure at which the oxidation of a liquid metal becomes evident. This effective oxygen pressure can be considered as a property of the system and can be many orders of magnitude greater than the actual equilibrium pressure [1]. The estimates of the degree of contamination of the surface and the mechanism of the gas mass-transfer at the liquid metal–gas interface are obtained from different theoretical models [2,3]. The application of these models is even more useful when dealing with measurements of the surface properties of metals of particular technological interest such as silicon [4], tin [5,6] and aluminium [7], which are often the main components of more complex metal systems. Knowledge of the
∗
Corresponding author. Tel.: +39 0106475720; fax: +39 0106475700. E-mail address: [email protected] (E. Ricci).
0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.10.115
surface conditions of multi-component alloys is essential for developing a suitable casting model. Nowadays, the numerical modelling of casting and solidification of metallic alloys is of increasing importance in industrial processing [8] for the optimisation of production technology or designing new and improved casting techniques [9–12] in order to deliver high-quality products or new production routes. In both cases, the processes are primarily governed by alloy solidification behaviour and consequently, essentially related to thermodynamics, kinetics and capillarity [13]. Recently, thermodynamic and transport theories able to offer a reasonable prediction of the interactions of a liquid binary alloy with oxygen in different diffusive regimes have been formulated [14]. These theories have been developed to explain the mechanisms that keep a molten alloy oxygen-free despite the thermodynamic driving forces of the pure metals involved [15]. For the liquid binary alloys, the theoretical results obtained by the model proposed [14] indicate that the behaviour of the alloy towards oxidation tends to be similar to that of the element for which the volatile oxide prevents the surface oxidation even if it is present in low percentages.
28
E. Ricci et al. / Materials Science and Engineering A 495 (2008) 27–31
In this work we present a validation of the general physical–mathematical analysis applied to liquid binary In–Sn and Cu–Sn alloys and their oxides. 2. Theoretical background The effective oxygen pressure [15] can be considered as a property of each metal. This property can be defined by making reference to a liquid metal phase formed by a metal (B) and traces of oxygen (A), in contact with a gas phase. The liquid metal has a known composition (xB ∼ = 1; xA xB ) and is maintained at constant temperature T and total pressure P. The gas phase is characterised by the oxygen partial pressure PAG and the presence of an inert gas. The saturation condition of the metal (xA = xAs , PAG = PAs ) corresponds to the appearance of the most stable oxide (D) as a new phase on the metal surface. Then, by also considering the presence of the most volatile oxide (C) at the saturation condition (PCG = PCs ), and the evaporation of the metal (PBG = PBs ), the three-phase equilibrium (liquid metal, atmosphere, condensed oxide) is fully determined. This equilibrium condition is univocal at given T and P, because the thermodynamic system being considered is bi-variant. However, experimental findings do not support this thermodynamic condition: as a matter of fact, stable clean surfaces can be systematically observed under oxygen partial pressures much greater than PAs . Therefore, a better understanding of these phenomena can be obtained only by using a reference condition somewhat different from equilibrium. This alternative and more realistic reference condition is the steady state of the liquid phase in relationship to the oxygen: the liquid phase is still considered in equilibrium with the gas–liquid interface, but it undergoes exchanges of oxygen and oxide with the atmosphere, under the steady condition that the net exchange of atomic oxygen has to be null. Therefore, on the basis of the evaluation of the order of magnitude of the various terms contributing to the effective oxygen pressure, it can be assumed that a stationary pure liquid has an effective oxygen pressure roughly corresponding to the pressure of its most volatile oxide at saturation, PCs (i.e. PAeff ≈ a PCs , where a is the stoichiometric coefficient of oxygen in the formation reaction of the oxide C). However, for some very poorly oxidizable metals, such as copper and nickel, the saturation oxygen pressure PAs is greater than the saturation oxide pressure PCs , so that the effective oxygen pressure coincides with the former (i.e. PAeff ≈ PAs ). In the case of a liquid phase formed by a binary alloy [14] of metals B and B (xB ∼ = 1 − xB ; xA 1), there are two thermodynamic equilibrium reference conditions, one for each component metal. The first is the condition previously described, which considers only metal B as saturated by oxygen A and the equilibrium between the oxidizing atmosphere and the condensed phases, metal B and oxide D (xB ∼ = 1, PAs , PBs , PCs , PAs ). The second condition, mirroring the first, and referring to the second metal, B , considers B saturated by A and the equilibrium between the oxidizing atmosphere and the condensed phases, metal B and oxide D (xB ∼ = 1, PA s , PB s , PC s , xA s ). However, as there are two volatile alloy oxides, C and C , the oxygen content of the gas phase consistent with the steady state of the interface depends on
the volatility of both. Any further step depends on hypothesising about the phases: for instance the liquid phase could be considered as an ideal solution and the oxide phase as the sum of two immiscible oxides. However, the real metal–atmosphere system can show various deviations from ideality, either due to the interactions between the liquid and the surface (for instance segregation phenomena of one of the metals [16]), or the interactions of the gas phase and the surface (for instance oxide condensation inside the gas phase [17]). Simple deviations of the liquid from the ideal state can be taken into account by replacing the molar fractions of the liquid metal with its activities, but in most cases these deviations should not modify the order of magnitude of the effective pressures. On the other hand, the interactions of the oxide phases are very poorly understood: for instance, the behaviour of two immiscible oxide phases might also depend on the fraction of evaporation surface at the disposal of each oxide. This aspect could be especially relevant in Knudsen regime, while it should be only of secondary importance in Fick regime, where the diffusive forces can be assumed to be independent of the surface microstructure. The situation might be further complicated by the presence of mixed oxides. If the ideality of the liquid phase and the immiscibility of the two stable oxides of metals B and B is assumed, the maximum effective pressure of the binary alloy is reached where the curves describing the effective pressure PAeff of the two metals cross each other and is the sum of the effective pressures of the two pure metals. The resulting curve has two branches: the branch corresponding to the first metal, B, starts at a divergence point (X = xB = 0) and then decreases monotonically towards the single metal B value (PAeff /PCs = 1); the branch of the second metal, B , starts from the single metal B value (PAeff /PCs = fC ) and then increases towards divergence. The combination of the two curves shows a maximum at their intersection [14]. The ratio between the effective pressure of the alloy and the effective pressure of the pure metal B can be expressed in terms of the composition xB and the two thermodynamic parameters fA = (PA s /PAs ) and fC = (a PC s /a PCs )(where a and a are the stoichiometric coefficients of oxygen in the formation reactions of the oxide C and C, respectively). The first of these (fA ) can be considered as an oxidizability ratio of the metals from a purely thermodynamic point of view, while the second is the volatility ratio of the oxides. It is worth noting that in the approach presented here the order of the metals B and B will always be chosen in such a way that fC > 1, that is by assuming metal B as the “more oxidizable” of the two, due to the counter-effect of the most volatile oxide of B (i.e. C ), which prevents the oxidation of the liquid alloy surface. The model has also been extended to ideal binary alloys showing an ideal oxide solution [14]. 3. Experimental procedure Experimentally, the surface tension is utilised as the sensitive parameter for the interaction of the oxygen and metal. Two experimental methods can be adopted to obtain different kinds of information: (1) the isothermal procedure, starting with a “clean surface”[15] (i.e. oxide removal conditions), where the imposed
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oxygen partial pressure of the feed gas is increased at constant temperature until a significant decrease in the surface tension is obtained and (2) the isobaric procedure, where the imposed temperature is changed under the constant oxygen partial pressure of the feed gas until the tensioactive effect is obtained, as revealed by the change of the sign of the temperature coefficient. The existence of the effective oxygen pressure, which is well above the saturation equilibrium curve, has been demonstrated for pure metals using the first procedure, as reported in Refs. [18–26]. In order to obtain the actual experimental curve, and thus indicate the oxygen tensioactive effect on the liquid metal more quickly, the second experimental procedure has been utilised in this work. The advantage of the isobaric procedure over the isothermal one is that the variations in temperature can be set automatically. As saturation conditions strongly depend on temperature, a temperature modulation corresponds to a modulation in the saturation level and is then equivalent to a modulation in the oxygen concentration in the liquid phase. The large-drop technique [27] is a suitable method for performing systematic dynamic surface-tension measurements on liquid metals and alloys, as the evolution of the drop can be successfully observed as a function of the surrounding atmosphere. The experimental apparatus used for the dynamic surface tension determinations as well as the procedures adopted have been described in Refs. [7,15,23]. In order to validate the extended theoretical analysis recently developed [14], two binary systems have been chosen for testing: In–Sn and Cu–Sn. The alloys (In–20 at.% Sn; In–50 at.% Sn In–90 at.% Sn, Cu–80 at.% Sn; Cu–50 at.% Sn) were prepared from high purity (Marz-grade) Cu, In and Sn. The pure metals were enclosed in a quartz tube under high vacuum conditions (Ptot = 10−4 Pa), and then melted in a high-frequency generator furnace under pure Argon. The composition of each alloy was checked with EDS analysis. Each alloy sample of about 2.5 g was mechanically cleaned by scratching, then chemically rinsed with a solvent in an ultrasonic bath. During the test, the sample was placed in an ad hoc-designed sapphire crucible to maintain the axial symmetry of the liquid metal drop [15]. The dynamic surface-tension measurements were performed by following the procedure described in Refs. [15,23]. In particular, the temperature was measured and regulated by two “S”-type thermocouples placed close to the sample, with an accuracy of ±3 K; the oxygen partial pressure was measured with three solid-state oxygen sensors: two of them were placed outside the furnace to measure the oxygen content of the feed and exhausted gases, the third was placed inside the test chamber close to the sample. The three oxygen sensors were all maintained at constant T = 973 K.
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Fig. 1. Surface tension (䊉) and temperature (—) vs. time of the In–50 at.% Sn alloy under Knudsen regime and isobaric conditions (PO2 = 1.06 × 10−4 Pa).
4. Results and discussion Following the theoretical description [14] briefly reported in Section 2, let us now consider Indium as metal B and tin as metal B. Indium and tin are two very similar metals in many respects and their liquids behave substantially as ideal solutions [28]. Moreover, no oxide condensation has been detected in the gas phase and the stable oxides involved are solid in the temperature range of interest. All these considerations suggest that it is possible to refer to them as immiscible oxides with an ideal liquid phase. On the other hand, indium and tin are rather different in their interactions with oxygen. The most volatile tin oxide is SnO, while the most volatile indium oxide is In2 O. From a thermodynamic point of view, indium should be more oxidizable than tin: the saturation pressure of indium is two or three orders of magnitude lower and the thermodynamic ratio fA is of the order of 10−3 . On the contrary, the volatility of the oxides favour indium, so that indium maintains the cleanness of its surface under greater oxygen partial pressures: the saturation pressure of the most volatile oxide of indium is two or three orders of magnitude greater than that of tin and the volatility ratio fC is of the order of 102 –103 . In Table 1 the thermodynamic values of In and Sn oxides are presented at T = 600 K [1,29]. The experimental tests were performed under isobaric conditions, varying the temperature at a rate = 5 K/min. The test performed on the In–50 at.% Sn alloy under the Knudsen regime (Ptot = 10−3 Pa) is shown in Fig. 1. The oxygen partial pressure was constant at PO2 = 10−4 Pa. The temperature was increased and decreased between 540 and 843 K. The temperature modulation made it possible to observe some significant inversions
Table 1 Thermodynamic values of tin [1] and indium [29] oxides calculated at T = 600 K Volatile oxides
◦
Gf (J/mol) Vapour pressure (Pa)
SnO(G) [1]
In2 O(G) [29]
InO(G) [29]
−1.222 × 105
−7.383 × 104
1.348 × 105 9.40 × 10−29
1.33 × 10−18
1.37 × 10−10
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E. Ricci et al. / Materials Science and Engineering A 495 (2008) 27–31
Fig. 2. The effective oxygen pressure of the indium–tin alloys at constant temperature (T = 600 K). Bold line: calculated effective oxygen pressure; broken line: best fitting of the experimental points; experimental points: () pure indium [30]; (♦) In–Sn alloys; () pure tin [23].
in the behaviour of the surface tension [7,15,22]. The meaning of the ‘inversions’ is clearly explained in [15,23]: if a negative temperature coefficient is considered as a characteristic of a pure metal-system, the oxygen tension-active effect over the liquid becomes evident between the two “inversion points”, where the slope of the surface tension versus temperature is positive showing the presence of an oxygen adsorption. The position of the second “inversion point” is approximately symmetrical to that of the first one, as a sign of the reversible oxygen dissolution in the metal drop. The portion of the curve between the two “inversions” reflects the surface adsorption due to the segregation of the oxygen dissolved into the liquid bulk (a consequence of the variation of the temperature) more than the effect of the externally imposed oxygen partial pressure. The experimental conditions of the inversion points (coordinates) are linked to tension-active effect, but not necessarily to the formation of stable oxides on the surface and this effect is identified by the sign inversion of the temperature coefficient of the surface tension. All the coordinates of the experimental points that characterised the inversion of the surface tension against the temperature measured during the dynamic surface tension tests are then reported as singular points in the effective oxygen pressure diagram and compared with the calculated curve. Making reference to a constant temperature of 600 K, and fA = 1.68 × 10−3 and fC = 1.03 × 103 [14], the effective oxygen pressure curve calculated as a function of the alloy composition and the experimental findings [22,30] of the two pure metals and their alloys In–20 at.% Sn, In–50 at.% Sn and In–90 at.% Sn are reported in Fig. 2. As often happens with this type of measurement [10,17], the differences between the experimental data and theoretical predictions are of some orders of magnitude (about 6 in this case). When compared to the thermodynamic predictions, where the differences were of some tens of orders of magnitude (about 35 in this case) the result is encouraging. Moreover, the differences could be further reduced if the effect
Fig. 3. Surface tension (䊉) and temperature (—) vs. time of the Cu–80 at% Sn alloy under Fick regime and isobaric conditions (PO2 = 6 × 10−3 Pa).
of the liquid mass-transfer is considered [15,22,25,26]. However, the important point here is that the experimental findings do not contradict a substantial invariance in the oxidizability of the indium–tin alloys with a tin content ranging from 0 to 80%. Other experimental tests were performed on a Cu–Sn alloy: in the Cu–Sn system tin is considered as metal B and copper as metal B. In fact, from a thermodynamic point of view, tin should be more oxidizable than copper: the saturation pressure of tin is about nine orders of magnitude lower than that of copper. With regard to the volatility, only the most volatile oxide of tin, i.e. SnO, have to be taken into account. In this case, the volatility of the oxides favour tin, so that it maintains the cleanness of its surface under a greater oxygen partial pressures. The dynamic surface-tension measurements of the Cu–Sn alloys (Cu–80 at.% Sn; Cu–50 at.% Sn) were performed following the same procedure adopted for the In–Sn ones, but in the temperature range 1130–930 K. In Fig. 3 the test performed on
Fig. 4. The effective oxygen pressure of the copper–tin alloys. Black line: calculated effective oxygen pressure at T = 1050 K; grey line: calculated effective oxygen pressure at T = 980 K; experimental points: () Cu–80 at.% Sn alloy; (䊉) Cu–50 at.% Sn alloy.
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the Cu–80 at.% Sn alloy under the Fick regime (Ptot = 105 Pa) and PO2 = 6 × 10−3 Pa is presented. The Cu–Sn data are reported in Fig. 4 where the effective oxygen pressures calculated at T = 1050 K for the Cu–50 at.% Sn alloy and T = 980 K for the Cu–80 at.% Sn alloys are shown. A quite satisfactory agreement was found between the experimental data and the theoretical predictions. In particular, the analysis of binary alloys formed with a poorly oxidizable metal such as Cu, revealed some peculiarities: the effective oxygen pressure coincided with the saturation oxygen pressure and some anomalous experimental dependencies of surface tension on temperature variations were highlighted. In addition, the deviation from the ideality of the liquid alloy behaviour would have to be taken into account in the theroretical description. A closer analysis of the surface phenomena of these alloys is obviously necessary. 5. Conclusions The phenomena of oxygen transport at a molten metal– atmosphere interface, and particularly the mechanisms whereby a molten metal or alloy surface is kept clean even in the presence of atmospheric oxygen impurities, play a very important role in many technological processes. From the results obtained with our models, it is possible to straightforwardly and qualitatively explain the mechanisms that keep a molten metallic system oxygen-free, despite the thermodynamic driving force, as due to an oxygen flux in the opposite direction to the oxygen adsorption/reaction. The experimental results for some binary alloys, presented here, and the results already obtained for the single metals Sn, Al, In and Si using dynamic surface-tension measurements demonstrate that experimental oxidation–de-oxidation transitions occur at values very close to those predicted by the models and, therefore, higher than the thermodynamic ones, due to the non-negligible contribution of the linked oxygen in the form of oxides. When this consideration was extended from pure liquid metals to liquid binary alloys, the theoretical results obtained indicated that the behaviour of the alloy towards oxidation tended to be similar to that of the less oxidizable component: in many instances the existence of a volatile oxide prevented surface oxidation even if the corresponding metal was only present in very low percentages. The experimental results performed on the two binary systems chosen for testing seem to confirm the predictions.
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Acknowledgments The authors wish to thank Tiziana Lanata and Michela Bernardi for their experimental work. This work was partially supported by the European Space Agency (ESA-ESTEC) within the framework of the ThermoLab-MAP Project no. AO-99-022. References [1] O. Knacke, O. Kubashewski, K. Hesselmann, Thermochemical Properties of Inorganic Substances, 2nd edition, Springer Verlag, D¨usseldorf, 1991. [2] C. Wagner, J. Appl. Phys. 29 (1958) 1295. [3] M. Ratto, E. Ricci, E. Arato, J. Cryst. Growth 217 (2000) 233. [4] T. Azami, S. Nakamura, T. Hibiya, J. Cryst. Growth 223 (2001) 116. [5] E. Ricci, P. Castello, A. Passerone, P. Costa, Mater. Sci. Eng. A 178 (1994) 99. [6] M. Ratto, L. Fiori, E. Ricci, E. Arato, J. Cryst. Growth 249 (2003) 445. [7] D. Giuranno, E. Ricci, E. Arato, P. Costa, Acta Mater. 54 (2006) 2625. [8] R. Aune, L. Battezzati, R. Brooks, I. Egry, H. Fecht, J. Garandet, K. Mills, A. Passerone, P. Quested, E. Ricci, S. Schneider, S. Seetharaman, R. Wunderlich, Microgravity Sci. Technol. XVI (2005) 7. [9] C. Garcia-Cordovila, E. Louis, A. Pamies, J. Mater. Sci. 21 (1986) 2787. [10] H. John, H. Hausner, J. Mater. Sci. Lett. 5 (1986) 549. [11] C. Garcia-Cordovila, E. Louis, J. Narciso, Acta Mater. 47 (1999) 4461. [12] D.J. Jarvis, D. Voss, IMPRESS web-site: www.spaceflight.esa.int/impress. [13] Thermolab-MAP Project no. AO-99-022, Final Report phase II, ESAESTEC, Noordwijk, November 2006. [14] E. Arato, E. Ricci, P. Costa, Surf. Sci. 602 (1) (2008) 349. [15] E. Ricci, E. Arato, A. Passerone, P. Costa, Adv. Colloid Interface Sci. 117 (1–3) (2005) 15. [16] R. Novakovic, E. Ricci, F. Gnecco, D. Giuranno, G. Borzone, Surf. Sci. 599 (2005) 230. [17] M. Ratto, E. Ricci, E. Arato, P. Costa, Met. Trans. B 32B (2001) 903. [18] P. Castello, E. Ricci, A. Passerone, P. Costa, J. Mater. Sci. 29 (1994) 6104. [19] E. Ricci, A. Passerone, P. Castello, P. Costa, J. Mater. Sci. 29 (1994) 1833. [20] E. Ricci, L. Nanni, E. Arato, P. Costa, J. Mater. Sci. 33 (1998) 305. [21] E. Ricci, L. Nanni, A. Passerone, Phil. Trans. R. Soc. Lond. A 356 (1998) 857. [22] E. Arato, E. Ricci, P. Costa, J. Mater. Sci. 40 (9–10) (2005) 2133. [23] L. Fiori, E. Ricci, E. Arato, Acta Mater. 51 (2003) 2873. [24] E. Arato, E. Ricci, L. Fiori, P. Costa, J. Cryst. Growth 282 (3–4) (2005) 525. [25] L. Fiori, E. Ricci, E. Arato, P. Costa, J Mater. Sci. 40 (9–10) (2005) 2155. [26] E. Arato, E. Ricci, D. Giuranno, P. Costa, J. Cryst. Growth 293 (1) (2006) 186. [27] Y.V. Naidich, in: D.A. Cadenhead, J.F. Danielli (Eds.), Progress in Surface and Membrane Science, vol. 14, Academic Press, 1981, p. 353. [28] M. Komiyama, H. Tsukamoto, Y. Ogino, J. Solid State Chem. 64 (1986) 134. [29] Y. Austin Chang, K.-C. Hsieh, Phase Diagrams of Ternary Copper–Oxygen–Metal Systems, ASM International Metals Park, OH, 1989. [30] D. Giuranno, PhD Thesis on Chemical Engineering, University of Genoa, April 2005.