CALPHAD-Based Modeling and Experimental Validation of Microstructural Evolution and Microsegregation in Magnesium Alloys During Solidification

  • Chuan Zhang
  • Jiashi Miao
  • Shuanglin Chen
  • Fan Zhang
  • Alan A. LuoEmail author


The microstructural evolution and microsegregation of a series of magnesium alloys (Mg-Al, Mg-Al-Ca and Mg-Al-Sn) at various cooling rates were investigated using a CALPHAD-based solidification model called PanSolidification. Experimental validations were carried out in a wide range of cooling rate (0.12 ~ 55 K/s) using both directional solidification and die casting techniques. The back-diffusion effect in solidified solid was included in the solidification model. Good agreements have been achieved between the simulated and measured solidification microstructure parameters (phase fraction and secondary dendrite arm spacing) and microsegregation within the α(Mg) phase. This modeling approach demonstrated the reliability of the CALPHAD-based models for the prediction of solidification microstructure of magnesium alloys and their applicability for the optimization of magnesium castings.


back diffusion in solidification CALPHAD (CALculation of PHAse Diagram) microstructure simulation solidification modeling 



This investigation is a part of research sponsored by the U.S. Department of Energy under Project DE-EE0006450. This paper was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.


  1. 1.
    A.A. Luo, Magnesium Casting Technology for Structural Applications, J. Mag. Alloys, 2013, 1(1), p 2-22CrossRefGoogle Scholar
  2. 2.
    F. Pan, M. Yang, and X. Chen, A Review on Casting Magnesium Alloys: Modification of Commercial Alloys and Development of New Alloys, J. Mater. Sci. Technol., 2016, 32, p 1211-1221CrossRefGoogle Scholar
  3. 3.
    W.J. Joost and P.E. Krajewski, Towards Magnesium Alloys for High-Volume Automotive Applications, Scripta Mater., 2017, 128, p 107-112CrossRefGoogle Scholar
  4. 4.
    M. Esmaily, J.E. Svensson, S. Fajardo, N. Birbilis, G.S. Frankel, S. Virtanen, R. Arrabal, S. Thomas, and L.G. Johansson, Fundamentals and Advances in Magnesium Alloy Corrosion, Prog. Mater Sci., 2017, 89, p 92-193CrossRefGoogle Scholar
  5. 5.
    F. Grosselle, F. Bonollo, G. Timelli, A. Tiziani, and E.D. Corte, Correlation Between Microstructure and Mechanical Properties of Al-Si Cast Alloys, Metall. Ital., 2009, 1, p 25-32CrossRefGoogle Scholar
  6. 6.
    National Research Council, Committee on Integrated Computational Materials Engineering. Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security, ed., National Academic Press, 2008Google Scholar
  7. 7.
    A.A. Luo, Material Design and Development: From Classical Thermodynamics to CALPHAD and ICME Approaches, Calphad, 2015, 50, p 6-22CrossRefGoogle Scholar
  8. 8.
    M.C. Flemings, Solidification Processing, McGraw-Hill, New York, 1974CrossRefGoogle Scholar
  9. 9.
    W. Kurz and D.J. Fisher, Fundamentals of Solidification, Trans Tech Publications, Switzerland, 1985Google Scholar
  10. 10.
    K.-O. Yu, Modeling for Casting and Solidification Processing, CRC Press, Boca Raton, 2001CrossRefGoogle Scholar
  11. 11.
    Y.A. Chang, S.L. Chen, F. Zhang, X.Y. Yan, F.Y. Xie, R. Schmid-Fetzer, and W.A. Oates, Phase Diagram Calculation: Past, Present and Future, Prog. Mater Sci., 2004, 49, p 313-345CrossRefGoogle Scholar
  12. 12.
    M. Hillert, Phase Transformations, Materials Park, ASM, 1968, p 181Google Scholar
  13. 13.
    L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams, Academic Press, Cambridge, 1970Google Scholar
  14. 14.
    Y.A. Chang, Phase Diagram Calculations in Teaching, Research, and Industry, Metall. Trans. B, 2006, 37B, p 7-39CrossRefGoogle Scholar
  15. 15.
    E. Scheil, Remarks on the Crystal Layer Formation, Z. Metallkd., 1942, 34, p 70-72Google Scholar
  16. 16.
    G.H. Gulliver, The Quantitative Effect of Rapid Cooling Upon the Constitution of Binary Alloys, J. Inst. Met., 1913, 9, p 120-157Google Scholar
  17. 17.
    J. Guo and M. Samonds, Modeling of Casting and Solidification Processing, Casting Design and Performanceed, ASM International, Russell Township, 2009, p 37-60Google Scholar
  18. 18.
    U.R. Kattner, The CALPHAD Method and Its Role in Material and Process Development, Technol. Met. Mater. Min., 2016, 13(1), p 3-15CrossRefGoogle Scholar
  19. 19.
    V.G. Smith, W.A. Tiller, and J.W. Rutter, A Mathematical Analysis of Solute Redistribution During Solidification, Can. J. Phys., 1955, 33(12), p 723-745ADSCrossRefGoogle Scholar
  20. 20.
    H.D. Brody and M.C. Flemings, Solute Redistribution During Dendrite Solidification, Trans. Met. Soc. AIME, 1966, 236, p 143-150Google Scholar
  21. 21.
    T.W. Clyne and W. Kurz, Solute Redistribution During Solidification with Rapid Solid State Diffusion, Metall. Trans. A, 1981, 12, p 965-971CrossRefGoogle Scholar
  22. 22.
    A. Roósz, Z. Gácsi, and E.G. Fuchs, Solute Redistribution During Solidification and Homogenization of Binary Solid Solution, Acta Metall., 1984, 32(10), p 1745-1754CrossRefGoogle Scholar
  23. 23.
    I. Ohnaka, Mathematical Analysis of Solute Redistribution During Solidification with Diffusion in Solid Phase, Trans. Iron Steel Inst. Jpn., 1986, 26(12), p 1045-1051CrossRefGoogle Scholar
  24. 24.
    J.A. Sarreal and G.J. ABbaschian, The Effect of Solidification Rate on Microsegregation, Metall. Trans. A, 1986, 17(11), p 2063-2073CrossRefGoogle Scholar
  25. 25.
    S. Kobayashi, Solute Redistribution During Solidification with Diffusion in Solid Phase: A Theoretical Analysis, J. Cryst. Growth, 1988, 88(1), p 87-96ADSCrossRefGoogle Scholar
  26. 26.
    S. Ganesan and D.R. Poirier, Solute Redistribution in Dendritic Solidification with Diffusion in the Solid, J. Cryst. Growth, 1989, 97(3-4), p 851-859ADSCrossRefGoogle Scholar
  27. 27.
    C.Y. Wang and C. Beckermann, A Unified Solute Diffusion Model for Columnar and Equiaxed Dendritic Alloy Solidification, Mater. Sci. Eng. A, 1993, 171(1-2), p 199-211CrossRefGoogle Scholar
  28. 28.
    C.Y. Wang and C. Beckermann, A Multiphase Solute Diffusion Model for Dendritic Alloy Solidification, Met. Trans. A, 1993, 24, p 2787-2802CrossRefGoogle Scholar
  29. 29.
    L. Nastac and D.M. Stefanescu, An Analytical Model for Solute Redistribution During Solidification of Planar, Columnar and Equiaxed Morphology, Metall. Trans., 1993, 24, p 2017-2118CrossRefGoogle Scholar
  30. 30.
    M. Hillert, L. Hoglund, and M. Schalin, Role of Back-Diffusion Studied by Computer Simulation, Metall. Mater. Trans. A, 1999, 30(6), p 1635-1641CrossRefGoogle Scholar
  31. 31.
    V.R. Voller, A Model of Microsegregation During Binary Alloy Solidification, Int. J. Heat Mass Transf., 2000, 43, p 2047-2052CrossRefzbMATHGoogle Scholar
  32. 32.
    M. Wu, J. Li, A. Ludwig, and A. Kharicha, Modeling Diffusion-Governed Solidification of Ternary Alloys—Part 1: Coupling Solidification Kinetics with Thermodynamics, Comput. Mater. Sci., 2013, 79, p 830-840CrossRefGoogle Scholar
  33. 33.
    T. Kraft, M. Rettenmayr, and H.E. Exner, An Extended Numerical Procedure for Predicting Microstructure and Microsegregation of Multicomponent Alloys, Modell. Simul. Mater. Sci. Eng., 1996, 4(2), p 161-177ADSCrossRefGoogle Scholar
  34. 34.
    T. Kraft, A. Roósz, and M. Rettenmayr, Undercooling Effects in Microsegregation Modelling, Scripta Mater., 1996, 35, p 77-82CrossRefGoogle Scholar
  35. 35.
    T. Kraft and Y.A. Chang, Predicting Microstructure and Microsegregation in Multicomponent Alloys, JOM, 1997, 49(12), p 20-28ADSCrossRefGoogle Scholar
  36. 36.
    F.Y. Xie, T. Kraft, Y. Zuo, C.H. Moon, and Y.A. Chang, Microstructure and Microsegregation in Al-rich Al-Cu-Mg Alloys, Acta Mater., 1999, 47(2), p 489-500CrossRefGoogle Scholar
  37. 37.
    X. Yan, Thermodynamic and Solidification Modeling Coupled with Experimental Investigation of the Multicomponent Aluminum Alloys, University of Wisconsin-Madison, Madison, 2001Google Scholar
  38. 38.
    W. Cao, S.-L. Chen, F. Zhang, K. Wu, Y. Yang, Y.A. Chang, R. Schmid-Fetzer, and W.A. Oates, PANDAT Software with PanEngine, PanOptimizer and PanPrecipitation for Multi-component Phase Diagram Calculation and Materials Property Simulation, Calphad, 2009, 33(2), p 328-342CrossRefGoogle Scholar
  39. 39.
    Pandat™, Thermodynamic Calculations and Kinetic Simulations, CompuTherm LLCGoogle Scholar
  40. 40.
    J.H. Perepezko and M. Uttormark, Undercooling and nucleation during solidification, ISIJ Int., 1995, 35(6), p 580-588CrossRefGoogle Scholar
  41. 41.
    K. Eckler, D.M. Herlach, and M.J. Aziz, Search for a Solute-Drag Effect in Dendritic Solidification, Acta Metall. Mater., 1994, 42(3), p 975-979CrossRefGoogle Scholar
  42. 42.
    W.J. Boettinger and S.R. Coriell, Microstructure Formation in Rapidly Solidified Alloys, Science and Technology of the Undercooled Melted, P.R. Sahm, H. Jones, and C.M. Adam, Ed., Martinus Nijhoff Publisher, Leiden, 1986, p 81-108CrossRefGoogle Scholar
  43. 43.
    M.J. Aziz and T. Kaplan, Continuous Growth Model for Interface Motion During Alloy Solidification, Acta Metall., 1988, 36(8), p 2335-2347CrossRefGoogle Scholar
  44. 44.
    M. Carrard, M. Gremaud, M. Zimmermann, and W. Kurz, About the Banded Structure in Rapidly Solidified Dendritic and Eutectic Alloys, Acta Metall. Mater., 1992, 40(5), p 983-996CrossRefGoogle Scholar
  45. 45.
    T.F. Bower, H.D. Brody, and M.C. Flemings, Measurements of Solute Redistribution in Dendritic Solidification, Trans. Metall. Soc. AIME, 1966, 236, p 624-634Google Scholar
  46. 46.
    R. Trivedi and K. Somboonsuk, Constrained Dendritic Growth and Spacing, Mater. Sci. Eng. A, 1984, 65(1), p 65-74ADSCrossRefGoogle Scholar
  47. 47.
    K. Somboonsuk, J.T. Mason, and R. Trivedi, Interdendritic Spacing: Part I. Experimental Studies, Metall Trans A, 1984, 15, p 967-975CrossRefGoogle Scholar
  48. 48.
    A. Roósz, E. Halder, and H.E. Exner, Numerical Calculation of Microsegregation in Coarsened Dendritic Microstructures, Mater. Sci. Technol., 1986, 2(11), p 1149-1155CrossRefGoogle Scholar
  49. 49.
    A. Roósz and H.E. Exner, Numerical Modelling of Dendritic Solidification in Aluminium-rich Al-Cu-Mg Alloys, Acta Metall. Mater., 1990, 38(2), p 375-380CrossRefGoogle Scholar
  50. 50.
    M.C. Flemings, D.R. Poirier, R.V. Barone, and H.D. Brody, Microsegregation in Iron Base Alloys, J. Iron Steel Inst., 1970, 208, p 371-381Google Scholar
  51. 51.
    M.N. Gungor, A Statistically Significant Experimental Technique for Investigating Microsegregation in Cast Alloys, Metall. Trans. A, 1989, 20(11), p 2529-2533CrossRefGoogle Scholar
  52. 52.
    M. Paliwal and I.-H. Jung, The Evolution of the Growth Morphology in Mg-Al Alloys Depending on the Cooling rate During Solidification, Acta Mater., 2013, 61(13), p 4848-4860CrossRefGoogle Scholar
  53. 53.
    M. Paliwal, Microstructural Development in Mg Alloys During Solidification: An Experimental and Modeling Study, McGill University, Montreal, 2013Google Scholar
  54. 54.
    M. Paliwal and I.-H. Jung, Solid/Liquid Interfacial Energy of Mg-Al Alloys, Metall. Mater. Trans. A, 2013, 44, p 1636-1640CrossRefGoogle Scholar
  55. 55.
    C. Zhang, D. Ma, K.-S. Wu, H.-B. Cao, G.-P. Cao, S. Kou, Y.A. Chang, and X.-Y. Yan, Microstructure and Microsegregation in Directionally Solidified Mg-4Al Alloy, Intermetallics, 2007, 15(10), p 1395-1400CrossRefGoogle Scholar
  56. 56.
    X.W. Zheng, A.A. Luo, C. Zhang, J. Dong, and R.A. Waldo, Directional Solidification and Microsegregation in a Magnesium-Aluminum-Calcium Alloy, Metall. Mater. Trans. A, 2012, 43(9), p 3239-3248CrossRefGoogle Scholar
  57. 57.
    G. Neumann and C. Tuijn, Self-diffusion and Impurity Diffusion in Pure Metals: Handbook of Experimental Data, Elsevier, Amsterdam, 2009Google Scholar
  58. 58.
    D. Mirković and R. Schmid-Fetzer, Directional Solidification of Mg-Al Alloys and Microsegregation Study of Mg Alloys AZ31 and AM50: part I. Methodology, Metall. Mater. Trans. A, 2009, 40, p 958-973CrossRefGoogle Scholar
  59. 59.
    J. Lacaze, P. Benigni, and A. Howe, Some Issues Concerning Experiments and Models for Alloy Microsegregation, Adv. Eng. Mater., 2003, 5(1-2), p 37-46CrossRefGoogle Scholar
  60. 60.
    M. Ganesan, D. Dye, and P.D. Lee, A Technique for Characterizing Microsegregation in Multicomponent Alloys and Its Application to Single-Crystal Superalloy Castings, Metall. Mater. Trans. A, 2005, 36(8), p 2191-2204CrossRefGoogle Scholar
  61. 61.
    D. Mirković and R. Schmid-Fetzer, Directional Solidification of Mg-Al Alloys and Microsegregation Study of Mg Alloys AZ31 and AM50: part II: Comparison between AZ31 and AM50, Metall. Mater. Trans. A, 2009, 40, p 974-981CrossRefGoogle Scholar

Copyright information

© ASM International 2019

Authors and Affiliations

  • Chuan Zhang
    • 1
  • Jiashi Miao
    • 2
  • Shuanglin Chen
    • 1
  • Fan Zhang
    • 1
  • Alan A. Luo
    • 2
    Email author
  1. 1.CompuThermMiddletonUSA
  2. 2.The Ohio State UniversityColumbusUSA

Personalised recommendations