The Development and Application of a Thermodynamic Database for ...

Magnesium: Phase Diagrams and Solidification

Research Summary

The Development and Application of a Thermodynamic Database for Magnesium Alloys ShunLi Shang, Hui Zhang, Swetha Ganeshan, and Zi-Kui Liu

The available thermodynamic databases for magnesium alloys are discussed in this paper. Of particular interest are the features of a magnesium database developed by the authors with 19 elements: Mg-Al-Ca-Ce-Cu-Fe-KLa-Li-Mn-Na-Nd-Pr-Si-Sn-Sr-Y-Zn-Zr. Using this database, two applications are presented. One is the phase evolution in AZ61 magnesium alloy including the variations of phase fractions, alloying compositions, and partition coefficients of alloying elements as a function of temperature (or solid fraction). The other is to understand sodium-induced high-temperature embrittlement in the Al-Mg alloy, which is ascribed to the formation of a liquid phase due to the presence of sodium traces. INTRODUCTION The reduction of vehicle weight through material innovations is of growing importance to improve vehicle fuel economy and reduce emissions. This initiative is an especially high priority in light of rising oil prices and also global climate change due to greenhouse gases. With a density that is two-thirds aluminum and one-quarter steel, magnesium alloys hold great promise as future vehicle structural materials. To accelerate the understanding and design of magnesium alloys, computational thermodynamics based on CALPHAD (calculation of phase diagram)1 is emerging as akey technology. This technology can predict phase equilibrium, phase stability, and phase transformation, and in turn, link the properties of multi-phase materials to those of the individual phases. A thermodynamic database, as a prerequisite of thermodynamic calculations, is therefore critically needed. This work will discuss current progVol. 60 No. 12 • JOM

How would you… …describe the overall significance of this paper? A thermodynamic database, as a prerequisite of computational thermodynamics, is critically needed to accelerate the understanding and design of materials. In this work, the progress and applications of thermodynamic databases for magnesium alloys is discussed, and in particular the works done in the authors’ group. …describe this work to a materials science and engineering professional with no experience in your technical specialty? To accelerate the pace of understanding and design of materials, computational thermodynamics based on the idea of CALPHAD (calculation of phase diagrams) is emerging as a key technology because of its ability to predict phase equilibrium, phase stability, and phase transformation. This work presents the current progress of thermodynamic databases for magnesium alloys and presents two applications of one such database: the phase evolution in the AZ61 magnesium alloy and the understanding of sodium-induced high-temperature embrittlement in the Al-Mg alloy. …describe this work to a layperson? With a density that is two-thirds aluminum and one-quarter steel, magnesium alloys hold great promise as future vehicle structural materials in order to improve vehicle fuel economy and reduce emissions. To accelerate the pace of understanding and design of magnesium alloys based on computational thermodynamics, the thermodynamic database is a prerequisite. This work discusses the current progress of thermodynamic databases for magnesium alloys and current applications using one such thermodynamic database.

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ress of thermodynamic databases for magnesium alloys. See the sidebar for details on the thermodynamic database. APPLICATIONS Based on the Gibbs energy for each phase in the thermodynamic database described in the sidebar, all kinds of thermodynamic properties can be predicted at the conditions of interest. Two applications are discussed here. The first application is the phase evolution in AZ61 (Mg-6Al-1Zn in wt.%) alloy. Figure 1 shows the calculated (Mg + 1Zn)-Al phase diagram by Thermo-Calc software,3,12 and the phase evolution of AZ61 alloy as a function of temperature is clearly shown. Quantitatively, the relations between mole fractions and temperature for liquid, solid (hexagonal close-packed [hcp]), and G-Al12Mg17 phases are given in Figure 2, calculated according to the equilibrium solidification model via lever rule and the Scheil model,13 respectively. In the equilibrium model, the diffusion of alloying elements is complete in both liquid and solid phases, whereas in the Scheil model the same is assumed to be complete only in the liquid phase with no diffusion in the solid phase. Therefore, it is believed that the realized solidification is between the equilibrium calculation and Scheil simulation. Figure 2 shows that with decreasing temperature the solid (hcp) fraction increases whereas the liquid phase decreases at lower temperatures (580 K by equilibrium calculation and 702 K by Scheil model) and the G phase appears (see also Figure 1). Figure 3 shows the distributions of alloying elements aluminum and zinc in the solid (hcp), liquid, and G phases in AZ61 alloy as a function of temperature predicted 45

by equilibrium calculation and Scheil model. Based on Figure 3, the partition coefficients of alloying elements also can be calculated and used to predict and understand the formation of solidification defects (e.g., freckle and center segregation).14,15 Partition coefficient

k is defined as the ratio of solid/liquid concentrations at the solidification front (i.e., k = csolid/cliquid). Figure 4 shows the partition coefficients of aluminum and zinc in the AZ61 alloy as a function of solid (hcp) fraction calculated by equilibrium and Scheil models. The

partition coefficients of aluminum and zinc are predicted around 0.1 and 0.35, respectively, indicating the trends to form solidification defects due to inhomogeneous alloying compositions during solidification (k far from unity 1). The thermodynamic database for

Figure 2. The predicted fractions of solid (hcp), liquid, and G phases in AZ61 alloy by equilibrium and Scheil models. Figure 1. A calculated phase diagram of Mg (+ 1 wt.% Zn)-Al system.

Figure 4. The predicted partition coefficients of aluminum and zinc as a function of solid (hcp) fraction in AZ61 alloy by equilibrium and Scheil models.

Figure 3. The predicted distributions of aluminum and zinc in solid (hcp), liquid, and G phases in AZ61 alloy by equilibrium and Scheil models.

Figure 5. A calculated phase diagram of Al (+ 5 wt.% Mg)Na system.9,16

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manufacturing process.9,16 Although sodium is present only in a very small amount in Al-Mg alloys, it causes HTE due to the formation of an intergranular sodium-rich liquid phase, weakening

magnesium alloys is also used to understand the sodium-induced high-temperature embrittlement (HTE) in an AlMg alloy, where sodium is an undesirable impurity introduced in the normal

THERMODYNAMIC DATABASE The thermodynamic database consists of descriptions of Gibbs energy (represented by a multi-parameter expression) for each phase in a specified multi-component system, such as magnesium alloys studied herein. Therefore the key to develop a thermodynamic database is to determine (optimize) the parameters in Gibbs energy expressions based on the available thermochemical data (e.g., enthalpy, entropy, heat capacity, activity, etc.) and phase equilibrium data (liquidus, solidus, phase boundary, etc). For example, the mole Gibbs energy for solution phase & (liquid, face-centered cubic [fcc], body-centered cubic [bcc], or hexagonal close-packed [hcp], etc.) is usually written as1

G m   x i o G i i

RT x i ln x i  xs G m

(A)

i

where ºGi is the molar Gibbs energy of a pure element (component) i, usually taken from the SGTE database2 in order to share the research works between different groups, xi is the concentration of element i; R is the gas constant; T is temperature; XS G m represents the excess Gibbs energy expressed by

xs

G m   i

 x i x jL ij  x i x jx k I i, j,k , where Li,j and

Table A. Elements Included in the Available Thermodynamic Databases for Mg Alloys

TC3 Pan4 SF5 Du6 Liu7 PSU*

Elements

Mg Al Ca Mg Ag Al Ca Mg Al Ca Mg Al Mg Al Mg Al Ca

Ce Cu Fe Gd La Mn Nd Sc Ce Cu Fe Gd Li Mn Nd Sc Ce Cu Gd Li Mn Nd Sc Fe Mn Ce Ce Cu Fe K La Li Mn Na Nd Pr

Si Sr Y Zn Zr Si Sn Sr Y Zn Zr Si Sr Y Zn Zr Si Y Zn Si Sn Sr Y Zn Zr

* The present magnesium database.

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ACKNOWLEDGEMENTS This work is funded by the National Science Foundation through Grant Nos. DMR-0510180 and DMR-0205232.

j i

Ii,j,k are the binary and ternary interaction parameters, respectively, between components i, j, and k, and may depend on temperature. Note that the interactions between four components and more are usually ignored and only the binary and ternary interaction parameters need to be determined. After thermodynamic optimization, the obtained Gibbs energy parameters have the ability to reproduce self-consistent results of thermochemical and phase equilibrium data. The thermodynamic databases available for magnesium alloys together with the elements included are listed in Table A, two of which (TC and PAN) are commercial databases from the Thermo-Calc3 and CompuTherm4 companies, respectively. Besides the commercial ones, magnesium alloy databases developed by groups of Schmid-Fetzer,5 Du,6 and Liu7 are listed in Table A. In addition, a 19-element magnesium database (PSU) has been developed in the authors’ group based on available publications and the critical thermodynamic modelings of binary and ternary systems.8–10 In comparison with other magnesium databases, special concerns have been considered in this database. First, it is suitable for both magnesium- and aluminum-based alloys. Second, the predicted firstprinciples energetics have been used in the optimizations of compounds and solid solutions when the energetic data are inaccurate or absent in the literature. For instance, the thermodynamic modeling of the Al-Mg system used the data of first-principles enthalpies of formation for E-Al30Mg23, G-Al12Mg17 and three laves phases and the enthalpies of mixing of fcc and hcp solution phases predicted by first-principles special quasirandom structures.10,11 Third, more attention has been paid to rare earth elements in this database due to their growing importance to improve the room-temperature formability of magnesium alloys. Finally, the alkali elements sodium and potassium, together with iron are involved in order to analyze the influence of impurities in Al-Mg alloys.

Source

significantly the strength of grain boundaries. To understand the mechanism of sodium-induced HTE, in the Al + 5 wt.% magnesium commercial alloy, for example, the (Al + 5Mg)-Na phase diagram is calculated and shown in Figure 5. The HTE is closely related to the formation of the liquid-2 phase (most likely at the grain boundaries),9,16 and therefore the hot-rolling safe zone is located in the single-phase fcc region as shown in Figure 5. High-temperature embrittlement can be suppressed by avoiding the formation of liquid-2 phase, and the phase boundary between fcc and “fcc + liquid-2” separates the hot-rolling safe zone and the sensitive zone, respectively.


References 1. N. Saunders and A.P. Miodownik, CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide (Oxford: Pergamon, 1998). 2. A.T. Dinstale, CALPHAD, 15 (1991), pp. 317–425. 3. Thermo-Calc Software, Stockholm, Sweden; www. thermocalc.com. 4. CompuTherm LLC, Madison, Wisconsin; www.computherm.com. 5. R. Schmid-Fetzer et al., Adv. Eng. Mater., 7 (2005), pp. 1142–1149. 6. Y. Du et al., Z. MetaIlkd., 96 (2005), pp. 1351–1362. 7. X.J. Liu et al., Rare Met., 25 (2006), pp. 441–447. 8. K. Ozturk, “Investigation in Mg-Al-Ca-Sr System by Computational Thermodynamics Approach Coupled with First-principles Engergetics and Experiments” (Ph.D. thesis, Pennsylvania State University, 2003). 9. S.J. Zhang, “Thermodynamic Investigation of the Effect of Alkali Metal Impurities on the Processing of Al and Mg Alloys” (Ph.D. thesis, Pennsylvania State University, 2006). 10. Y. Zhong, “Investigation in Mg-Al-Ca-Sr-Zn System by Computational Thermodynamics Approach Coupled with First-principles Energetics and Experiments” (Ph.D. thesis, Pennsylvania State University, 2005). 11. Y. Zhong, M. Yang, and Z.K. Liu, CALPHAD, 29 (2005), pp. 303–311. 12. J.O. Andersson et al., CALPHAD, 26 (2002), pp. 273–312. 13. E. Scheil, Z. MetaIlkd., 34 (1942), pp. 70–72. 14. M. Ganesan, D. Dye, and P.D. Lee, Metall. Mater. Trans. A, 36A (2005), pp. 2191–2204. 15. W.Q. Jie, R.J. Zhang, and Z. He, Mater. Sci. Eng. A, 413 (2005), pp. 497–503. 16. S. Zhang, Q. Han, and Z.K. Liu, Philos. Mag., 87 (2007), pp. 147–157. ShunLi Shang is a research associate, Hui Zhang and Swetha Ganeshan are Ph.D. candidates, and Zi-Kui Liu is a professor in the Department of Materials Science and Engineering at Pennsylvania State University, University Park, PA 16802. Dr. Shang can be reached at [email protected].

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