Thermodynamic Analysis of Contamination by Alloying Elements in

Jun 10, 2010 - In previous studies on the physical chemistry of pyrometallurgical processing of aluminum scrap, only a limited number of thermodynamic...
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Environ. Sci. Technol. 2010, 44, 5594–5600

Thermodynamic Analysis of Contamination by Alloying Elements in Aluminum Recycling K E N I C H I N A K A J I M A , * ,† O S A M U T A K E D A , ‡ TAKAHIRO MIKI,‡ KAZUYO MATSUBAE,§ SHINICHIRO NAKAMURA,| AND TETSUYA NAGASAKA§ Research Center for Material Cycles and Waste Management, National Institute for Environmental Studies, Tsukuba 305-8506, Japan, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan, Graduate School of Environmental Studies, Tohoku University, Sendai 980-8579, and Graduate School of Economics, Waseda University, Tokyo 169-8050, Japan

Received December 21, 2009. Revised manuscript received April 15, 2010. Accepted May 14, 2010.

In previous studies on the physical chemistry of pyrometallurgical processing of aluminum scrap, only a limited number of thermodynamic parameters, such as the Gibbs free energy change of impurity reactions and the variation of activity of an impurity in molten aluminum, were taken into account. In contrast, in this study we thermodynamically evaluated the quantitative removal limit of impurities during the remelting of aluminum scrap; all relevant parameters, such as the total pressure, the activity coefficient of the target impurity, the temperature, the oxygen partial pressure, and the activity coefficient of oxidation product, were considered. For 45 elements that usually occur in aluminum products, the distribution ratios among the metal, slag, and gas phases in the aluminum remelting process were obtained. Our results show that, except for elements such as Mg and Zn, most of the impurities occurred as troublesome tramp elements that are difficult to remove, and our results also indicate that the extent to which the process parameters such as oxygen partial pressure, temperature, and flux composition can be changed in aluminum production is quite limited compared to that for iron and copper production, owing to aluminum’s relatively low melting point and strong affinity for oxygen. Therefore, the control of impurities in the disassembly process and the quality of scrap play important roles in suppressing contamination in aluminum recycling.

1. Introduction Although aluminum is recycled in large quantities, contamination by alloying elements is a problem in the recycling of end-of-life aluminum products. Figure 1 shows the usespecific demand for aluminum materials in Japan. Most aluminum is used in the form of alloys rather than as pure metal. Cu, Fe, Mn, Mg, Si, and Zn are commonly added to aluminum to impart required properties. Nearly pure * Corresponding author. † National Institute for Environmental Studies. ‡ Graduate School of Engineering, Tohoku University. § Graduate School of Environmental Studies, Tohoku University. | Waseda University. 5594

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aluminum, classified as “1000 series” according to the Japanese Industrial Standards (JIS), is primarily used for producing foil materials, and its proportion of the total aluminum production is small. Figure 2 shows the chemical composition of various aluminum alloys specified by the standards of the American Society for Testing and Materials (ASTM). (Note that JIS and ASTM use essentially the same code numbers for industrial aluminum products.) The ASTM 6000 series alloys are typical industrial aluminum alloys. The chemical and mechanical properties that are necessary for the uses to which the products are put can be achieved by alloying mainly Mg, Si, and Cu into aluminum. The ASTM 1000 series alloys contain aluminum at purities exceeding 99.9% and are produced mostly from virgin aluminum, which in turn is produced by electrolytic smelting. In contrast, most casting and die-casting products contain substantial amounts of alloying elements. For instance, the total concentration of alloying elements in Al-Si-Cu-Mg-Ni alloy for casting is approximately 27%. According to the International Aluminum Institute (IAI) (3), the ratio of the amount of secondary aluminum to that of virgin aluminum was a mere 17% in 1960, and this value had increased to 33% by 2006. By 2040, this ratio is targeted by IAI to be increased to 40%. The electrolytic smelting of primary aluminum, produced mostly from bauxite, requires extremely large amounts of energy, 256 GJ/t (4). In contrast, the recycling of aluminum, that is, the production of secondary aluminum by remelting, requires only 5-10% of the energy required for producing primary aluminum (3, 5). This low energy requirement is the main reason for the promotion of aluminum recycling. Aluminum has a high ionization tendency and thermodynamic reactivity (the standard electrode potential of aluminum in an aqueous solution at 25 °C is -1.676 V vs normal hydrogen electrode) (6). Accordingly, when the oxidation method, which is the typical refining technique, is employed for the removal of impurities from aluminum scrap, aluminum tends to be preferentially oxidized and lost to slag or dross. In the recycling of aluminum beverage cans (can-to-can recycling), the scrap quality is carefully controlled so as to meet industrial standards. For example, both the end tab (JIS H4000, 5182) and the body (JIS H4000, 3004) of used aluminum cans must be exclusively recycled into aluminum beverage can bodies. These standards have been imposed owing to the severe limitations associated with impurity removal. Because of these limitations, most used aluminum undergoes cascade recycling. Because cast and die-cast aluminum products can tolerate high impurity concentrations, these products effectively act as a final sink for relatively low grade aluminum scrap. There have been technological studies on the removal of impurities by flux addition in the remelting process and by pretreatment processes. Gao et al. (7) proposed a method for removing Fe from molten aluminum by Na2B4O7 slagging. For recycling of used beverage cans, Rabah (8) proposed methods for removing inorganic pigments such as Sn and for recovering Mg and Al salts from slag by means of solvent extraction, sandblasting, and firing. In addition, some technological studies have been done on the removal of Zn by vacuum distillation, elimination of impurities by fractional crystallization, and suppression of inclusions by means of internal filters (9). However, the thermodynamic basis for the limitations on impurity removal during the aluminum remelting process has not been extensively investigated. With the goal of minimizing recycling losses and contamination and maximizing efficient use of resources, Castro 10.1021/es9038769

 2010 American Chemical Society

Published on Web 06/10/2010

FIGURE 1. Demand for aluminum materials in Japan (2003 fiscal year). Data are estimated from an article by Hatayama (1) and statistics by Japan Aluminum Association (2).

FIGURE 2. Composition of aluminum alloys from the ASTM standards (upper limit). et al. (10) introduced the concept of the THERMA (thermodynamic evaluation of materials combinations) model as a tool for evaluating the materials combinations present in product systems. However, the model was limited with regard to the quantitative evaluation of the removability of alloying elements in metallurgical processes. In particular, these investigators demonstrated only the variation of the activity coefficients of Fe in molten aluminum and Cu in molten iron with temperature and concentration together with the oxidation tendency exhibited by the Ellingham diagram while this diagram shows the standard free energy of the formation of a pure oxide from pure metal. Although the activity coefficient is an important parameter for pyrometallurgical processes, it is not the only index for predicting the reaction direction. In this study, our aim was to develop quantitative criteria for evaluating the possibility of removing impurities during the aluminum recycling process by considering all the

relevant thermodynamic parameters. For 45 elements that are likely to occur in aluminum products, we investigated the equilibrium distribution ratios among metal, slag, and gas phases in the aluminum remelting process. For six elements, Cu, Si, Fe, Mn, Mg, and Zn, that are typical alloying elements for aluminum products, we investigated in great detail the mutual effects of oxygen partial pressure and temperature on the distribution behavior. A number of thermodynamic studies of many multicomponent alloys have been done by means of the CALPHAD (calculation of phase diagrams) approach, and the interaction parameters of solutes in molten aluminum as a function of alloy composition and temperature are available in the literature (11). This information was exploited for the analysis in this study.

2. Materials and Methods 2.1. Thermodynamic Analysis. Verhoef et al. (12) and Reuter et al. (13) suggested the importance of describing the complex VOL. 44, NO. 14, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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web of metals and their intricate connections, and these investigators proposed a “metal wheel,” based on mineralogy and metallurgy, to describe metal linkages in natural resource processing. However, this tool is insufficient for answering questions about which impurity elements can be removed in a metallurgical process and to what extent an impurity can be removed. In particular, with regard to the remelting process, neither the recoverability nor the recyclability of elements that do not occur in natural resources (ores) has been sufficiently evaluated. In a previous study, the present authors used a chemical thermodynamics approach to evaluate the recyclability of steel, Cu, Pb, and Zn products from secondary resources and the limitations on impurity removal in pyrometallurgical processes (14), and they proposed an alternative metal wheel (Element Radar Chart) that explicitly shows the connection of minor elements to commodity metals and the extent to which certain metals can economically be recovered by using existing processes. On the basis of the results of the current study, information for aluminum was added to the Element Radar Chart. This information will be extremely useful for aluminum recycling because, as we will see, the control of alloying elements is much more difficult in aluminum processing than in steel and copper. In this study, the same analytical approach was applied to evaluate the recyclability or removability of various elements during the aluminum remelting process. In particular, the refining capabilities of oxidization and evaporation, which are suitable for removing impurities from the main metal product during remelting, were thermodynamically evaluated. Oxidization is the typical method for removing impurities in metallurgical processes. The direction of a chemical reaction can be effectively evaluated in terms of the change in the Gibbs free energy. The driving force of a reaction can be determined from the value of the free energy change. Furthermore, if an element is distributed by reaction with ambient oxygen among different phases such as molten metal and oxide slag, the distribution can be quantified by calculating the equilibrium constant from a change in the Gibbs free energy, and subsequently converting the equilibrium constant into the concentration of the element in each phase. The parameters controlling the distribution of elements among the metal, slag, and gas phases can be obtained as follows. For the evaporation of an impurity element M from a solvent metal, M ) M(g)

(1)

the equilibrium constant, K, is given by K)

pM pM o ) ) pM aM γMxM

(2)

o , pM, aM, γM, and xM are the partial pressure of the where pM pure element M (Pa); the partial pressure of M in the alloy (Pa); the activity of M in the Raoultian standard state (pure liquid substance), which is defined by aM ) pM/poM; the activity coefficient of M; and the mole fraction of M in the solvent metal, respectively. Rearrangement of eq 2 gives

o pM ) pM γMxM

(3)

The distribution ratio of M between the metal and gas phases is defined by L′′ )

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pM ) pAl

o pM γMxM

pAl

(4)

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where pAl is the partial pressure of aluminum vapor (Pa). A greater gas-metal distribution ratio L′′ corresponds to easier removal of M by evaporation. For the oxidation of M, mM +

n O ) MmOn 2 2

(5)

the equilibrium constant, K’, is given by eq 6:

(

K′ ) exp -

)

aMmOn γMmOnxMmOn ∆Go ) m n/2 ) n/2 RT aMpO2 (γMxM)mpO 2

(6)

where pO2 is the oxygen partial pressure (Pa), and ∆Go, R, and T are the Gibbs free energy change(J · mol-1), the gas constant (J · K-1 · mol-1), and the absolute temperature (K), respectively. Note that aMmOn, γMmOn and xMmOn are the activity in the Raoultian standard state (pure solid oxide); the activity coefficient; and the mole fraction of oxide MmOn distributed into slag phase by the oxidation, respectively. Rearrangement of eq 6 gives the distribution ratio of M between slag and metal, L’: L′ )

xM xMmOn

)

γMmOn m m-1 n/2 K′γM xM pO2

(7)

Smaller metal-slag distribution ratio L’ results in easier removal of M into the slag phase by oxidation. In the real situation of aluminum remelting, halide flux such as chrolide mixture is often used for the surface coverage of the metal bath and to remove hydrogen and inclusions. Removal of impurities by the reaction with chloride flux can be evaluated in the same manner. However, the use of chlorination in aluminum remelting is impractical because aluminum itself is easily chlorinated, and thus aluminum loss cannot be ignored (15). It should be emphasized that oxygen partial pressure is determined by eq 8 even in the use of chloride flux whenever the equilibrium condition is assumed. 2Al(l) + 3/2O2(g))Al2O3(s)

(8)

The maximum partial pressure of oxygen is evaluated as pO2 ) 10-39 Pa at 1073K in the equilibrium of pure liquid aluminum and pure solid Al2O3. 2.2. Thermodynamic Data. Figure 3 shows a schematic diagram of the current system for aluminum production and recycling, including the target process analyzed in this study. Aluminum (the primary material), oxygen, minor elements, and gangue minerals are not shown. “Electrolysis” includes the Hall-He´roult and trinal electrolytic processes, and “Fabrication, Machinery” includes casting and die-casting. In remelting, primary and scrap aluminum are used as the principal materials for the production of aluminum alloys, which are used for products such as plates and rods and for die-casting and casting. During remelting, the alloy composition is adjusted to a target value by the addition of Cu, Mn, and other pure metals. The aluminum alloy scrap contains various kinds of impurities along with the alloy components. Therefore, the control of impurities and scrap composition is important. The activity coefficient γ for element M in an Al-M binary alloy is obtained from eq 9: 2 2 RTln γM ) 0ΩAl-MxAl + 1ΩAl-MxAl (4xAl - 3) + 2

2 ΩAl-MxAl (2xAl - 1)(6xAl - 5) 2 + 3ΩAl-MxAl (2xAl - 1)2(8xAl - 7)

(9)

For the 45 elements in molten aluminum, the thermodynamically assessed Redlich-Kister parameters ΩAl-M (11)

FIGURE 3. Substance flow associated with aluminum production and recycling processes.

FIGURE 4. Distribution of elements among gas, slag, and metal phases for simulated aluminum remelting. were taken from the references in the Supporting Information (SI). The standard Gibbs free energies for oxide formation and the vapor pressures of pure elements were taken from thermodynamic tables (16, 17).

3. Results and Discussion The activity coefficient of MmOn depends on the slag composition, but the coefficient was fixed at unity in the present analysis as a baseline. The initial mole fraction of elements in the solvent metal was fixed at 0.01 as a first approximation. The boundary between the metal and gas phases was assumed to satisfy the conditions log (pM/pAl) ) 1 and log (pM) ) 2 (pM > 102Pa), owing to the limitation of industrial vacuum equipment (18). Figure 4 shows the distribution ratio of the elements among the various phases during the remelting process. The smaller gray circles denote typical additive elements. The figure indicates that Mg, Ca, and Be can be removed by oxidization (transferred to slag) and that Zn, Cd, and Hg can be removed by evaporation. The removal of the other 39 elements, including Cu, Si, Fe, and Mn, is difficult; they remain in the metal phase. These results support the

observation that most impurities contained in aluminum alloy scrap are not removed to any appreciable extent under actual operational conditions. The concentration range of alloying elements varied widely depending on the alloy categories (Figure 2). We investigated how the distribution ratios of typical additive elements (Cu, Si, Fe, Mn, Mg, and Zn) were changed by varying xM and, thus, γM in eqs 4 and 7; the xM values were chosen on the basis of the maximum and minimum concentrations of M specified in ASTM standards. The resulting ranges are shown in Figure 4 by horizontal bars for these six common elements. We found that Cu, Fe, Si, and Mn remained in the metal, whereas Mg could be removed by means of oxide formation irrespective of its concentration. Zn could be removed by evaporation when its concentration was high, although its removal was difficult at low concentrations. Mashahadi et al. (20) experimentally tested the recyclability of aluminum turnings by melting them at 1023 K under the presence of salt flux (NaCl-KCl-KF). After the melting treatment, weight loss of the metal and the chemical composition were measured. It was demonstrated that Cu, Ni, and Si exhibited no essential change in the concentrations, whereas Mg contents became half or less after the remelting. Their findings support the results of the present work. As described in the Materials and Methods section, the removability of an impurity from remelted metal by evaporation or oxidation is thermodynamically governed by at least five parameters; total pressure, activity coefficient (composition of the metal bath containing the target impurity), temperature, oxygen partial pressure, and activity coefficient of the oxidation product (slag composition). Even when an impurity has a small activity coefficient in the metal, removal of the impurity will be possible if a sufficiently low activity coefficient of oxidation product is achieved by selecting an adequate slag composition. This condition is actually met in the dephosphorization of molten steel. The opposite example is Cu in molten Fe. Cu is a typical tramp element and must be removed from remelted steel scrap (19). The activity coefficient of Cu in molten Fe exhibits a large positive deviation from ideality; for example, γCu in molten Fe at 1873 K equals 7.37 at infinite dilution (21). Therefore, a relatively strong repulsive force acts between Cu and Fe atoms in VOL. 44, NO. 14, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 5. Temperature and pO2 dependence of the distribution of elements between metal and slag during aluminum remelting process. molten Fe-Cu alloy. In spite of this physicochemical situation, removing Cu from molten Fe is difficult. This is due to the fact that there is no effective slag component that can sufficiently lower the activity coefficient of Cu2O in the slag, together with high Gibbs free energy value of Cu oxidation reaction. Castro et al. (10) explained the difficulty of Cu removal based on γCu in molten Fe. However, their values of γCu were unreasonably low (0.13-0.15 at 1873 K), and discussing the removability of an impurity without a sufficient number of parameters is not advisible. The abovementioned process parameters should also be taken into account simultaneously. We will now discuss the limitations on impurity removal from an aluminum bath in detail for the above-mentioned six elements by considering the effects of several thermodynamic parameters on the distribution ratio. Figure 5(a) shows the effect of temperature on the distribution ratios of the six common elements between the slag and metal phases. Although the distribution ratios were slightly better at higher temperatures, the improvement was not large enough to permit removal of any of the elements except Mg. Figure 5(b) shows the effect of oxygen partial pressure on the distribution ratio. No significant change was observed for any of the elements except Mg, which indicates that Mg can be removed or immobilized in the metal phase by controlling the oxygen partial pressure. At 1073 K, aluminum was oxidized at an oxygen partial pressure above the critical equilibrium value, 4 × 10-39 Pa. Accordingly, higher oxygen partial pressures than this critical value will result in substantial oxidative loss of aluminum. The oxygen partial pressure should therefore be carefully controlled. The activity coefficient of oxides in slag was assumed to be unity in the present study. If the activity coefficient of oxides was lowered to 0.1 by appropriate selection of the slag composition, the distribution ratio of elements between the metal and slag would be improved by 1 order of magnitude. One of the most important parameters for the design of slag composition is basicity. For example, basic slag components like CaO should be added to the slag to lower the activity coefficient of acidic oxidation products such as SiO2. However, it should be noted that the remelting temperature of aluminum alloys is relatively low, and therefore the composition of molten slag formation will be limited because of the high melting point of oxides. For example, Al2O3-CaO-SiO2 slag has a wide homogeneous molten region at steel-making temperature (1873 K), but no molten phase appears in the slag at a temperature lower than the ternary eutectic point (1443 K). Even if a chloride or fluoride flux which can be in molten state in the aluminum 5598

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remelting process is used, solubility of oxide in the molten halide system is generally very low except for some limiting cases. Therefore, controlling the activity of oxides in slag at a sufficiently low level will be difficult. These results indicate that the extent to which the process parameters such as oxygen partial pressure, temperature, and flux composition can be changed in aluminum production is quite limited compared to that for iron and copper production, owing to the aluminum’s relatively low melting point and strong oxygen affinity. However, the removal of impurities may result in the formation of a solid aluminate instead of a pure oxide in some cases. For instance, MgAl2O4 may form instead of MgO during the removal of Mg from an aluminum alloy. In such a case, the activity of MgO will decrease from 1 to 0.015 at 1073 K (22), and Mg removal will be thermodynamically enhanced. In this regard, it is important to note that, in the decision tree model and the THEMA model/matrix for the evaluation of materials combinations involved in the recycling of aluminum scrap proposed by Castro et al. (10), Mg and Zn are classified as metals that should be separated from aluminum scrap before the scrap is supplied to a remelting process. Our analysis, however, has demonstrated that, so far as the thermodynamics are concerned, Mg and Zn belong to exceptional elements which can be separated from aluminum scrap in the remelting process. Our analysis can thus provide thermodynamic criteria for their highly innovative decision model. In our previous study (14), “Element Radar Chart” was used to graphically represent the distribution tendencies of the elements in the remelting of steel, Cu, Pb, and Zn. Incorporating the above results for aluminum, as shown in Figure 4, into this chart is useful for comparison of the relative ease of removal of impurities among the base metals (Figure 6). In the element radar chart, radian direction indicates element distribution tendency for oxidation, and circular arc direction indicates that for volatilization, which is same as Figure 4. Comparison with Fe shows that the removal of impurities is far more difficult for aluminum than for Fe. In the case of Fe/steel recycling, Cu and Sn (19) occur as tramp elements that are difficult to remove. For aluminum, most of impurities, except for some elements such as Mg and Zn, occur as tramp elements that are difficult to remove. In contrast, the smelting of Cu and Pb includes an effective impurity removal process (electrolytic smelting) as a postprocess, which acts as an excellent refiner for a number of impurities. This is not the case for aluminum remelting. Therefore, the control of impurities in the disassembling

FIGURE 6. Element radar chart for the metallurgical process of base metals, where the initial mole fraction of impurities in solvent metal, oxygen partial pressure and total pressure are 1 mol %, the equilibrium pO2 between pure solvent metal and its pure oxide (e.g., eq 8), and 102 Pa, respectively. The temperature is set at that of conventional melting process of each solvent metal. Other conditions are referred to Figure 4 and previous work (4). process and the management of scrap quality play important roles in suppressing the contamination in aluminum recycling. Castro et al. (10), Verhoef et al. (12) and Reuter and Vefhoef (13) have proposed “Metal Wheel”, where the linkage among several metals in the extraction and production of primary metals is classified in the pie chart. This unique diagram is able to visually show the complex web of metals and intricate connections in the metal production and recycling, whereas the metal wheel cannot show difficulty of impurities removal in metal remelting process depending on the process parameters. As contrasted with metal wheel, the element radar chart overcomes such insufficiency and can further show distribution tendencies and the removability of impurities in each metallurgical process. The thermodynamic criteria on the removability of alloying elements from remelted aluminum scrap by oxidation and evaporation have been quantitatively shown in this paper. On the other hand, the real situation of the aluminum remelting process is further affected by other factors such as temperature distribution in the furnace, kinetic problem, fluidity of metal bath, nonuniformity of gas phase, reaction with refractory, metal suspension in the dross, and so forth. Xiao and Reuter (23) experimentally discussed the melting behavior of aluminum turning scrap under the presence of salt flux and demonstrated that scrap distribution, contaminant, type, and size of the scrap had significant effect on the melting behavior. Due to complex situation in the actual remelting process, distribution behavior of alloying element in a practical operation may be different from the ideal case. However, it is expected that the results of the present work can be used as a measure of removal limit of metal contaminants. Finally, some possibilities for sustainable use of aluminum products may be suggested. On the basis of chemical thermodynamics, this study quantitatively demonstrated the limit of removal of impurity elements during the aluminum remelting process. It also suggests that the immobilization of alloying elements in the metallic phase occurs easily. Thus, quality management of scrap should be promoted to avoid the contamination of impurities. One possible way is scrap sorting based on the composition of aluminum products.

This also enables the saving of the amount of alloying elements. Needless to say, a new technology for removing and recovering alloying elements from aluminum scrap should be developed for the sustainable supply of high quality aluminum products. In the present technological status, aluminum recycling is done with cascade way and sometimes it is not be achieved without dilution by virgin aluminum (24). As it is seen in Figure 2 for example, 3000 series of aluminum products contain relatively high Mn, so that its scrap should be diluted for other use. The removability of elements during remelting process should also be taken into account for alloy design. Evaluation of those environmental effects by an econometric model (25) is a future subject of our study.

Acknowledgments This research was partially supported by Nippon Steel Corporation and JSPS (KAKENHI 22360218). The authors thank the members of Research Group of the Development of “Material Vision 2100” of the Iron and Steel Institute of Japan for valuable comments and encouragement.

Supporting Information Available Calculation of the activity coefficient (γ) and references of interaction parameters, three tables, and 39 additional references. This material is available free of charge via the Internet at http://pubs.acs.org.

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(7) Gao, J. W.; Shu, D.; Wang, J.; Sun, B. D. Effects of Na2Ba4O7 on the elimination of iron from aluminum melt. Scr Mater. 2007, 57, 197–200. (8) Rabah, M. A. Preparation of aluminum-magnesium alloys and some valuable salts from used beverage cans. Waste Manage. 2003, 23, 173–182. (9) Ohzono, T. Environmentally harmonious technology and national project, “Environmentally friendly technologies and national projects” (in Japanese). J. Jpn Inst. Light Met. 2003, 53, 130–137. (10) Castro, M. B. G.; Remmerswaal, J. A. M.; Reuter, M. A.; Boin, U. J. M. A thermodynamic approach to the compatibility of materials combinations for recycling. Resour., Conserv. Recycl. 2004, 43, 1–19. (11) Hillert, M. Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis, 2nd ed.; Cambridge University Press: Cambridge, UK, 2008. (12) Verhoef, E. V.; Dijkema, G. P. J.; Reuter, M. A. Process, knowledge, system dynamics, and metal ecology. J. Ind. Ecol. 2004, 8, 23–43. (13) Reuter, M. A.; Verhoef, E. V. A dynamic model for the assessment of the replacement of lead solders. J. Electron. Mater. 2004, 33, 1567–1580. (14) Nakajima, K.; Takeda, O.; Miki, T.; Nagasaka, T. Evaluation method of metal resource recyclability based on the thermodynamic analysis. Mater. Trans. 2009, 50, 453–460. (15) Kellog, H. H. Thermodynamic relationships in chlorine metallurgy. J. Metals 1950, 188, 862–872. (16) Chase, M. W.; Jr., Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed.; American Chemical Society and American Institute of Physics for National Bureau of Standards: Washington, DC, 1985.

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