An ICME Method for Predicting Phase Dissolution During Solution Treatment in Advanced Super Vacuum Die Cast Magnesium Alloys


An integrated computational materials engineering (ICME) methodology was applied in this study to systematically and quantitatively study the second phase dissolution kinetics during the solution treatment process of a high pressure die cast magnesium sample. The study was conducted on Mg–9 wt% Al, Mg–5 wt% Al, and Mg–11 wt% Al binary alloys after isothermal solution treatments ranging from 380 to 420 °C. The experimental measurements revealed an exponential decrease of the volume fraction of the second β-phase (Mg17Al12) during the solution treatment. A CALPHAD-based computational tool (Thermocalc DICTRA Diffusion Module) was used to simulate the dissolution process. In this study, measurements from as-cast samples were used as input parameters to improve the accuracy of the predicted results. An analytical, physics-based micro-model, based on the Johnson–Mehl–Avrami type equation, was also applied to study the dissolution kinetics. Both the simulation and micro-model quantitatively agree with the experimental results at all solution treatment temperatures. Calibration and verification of a few input parameters help to understand the assumptions made in the modeling, improve the accuracy of the prediction, and can be applicable in different Mg–Al binary alloys. Adopting such an ICME methodology for modeling development and verification in predicting the dissolution kinetics during solution treatment will allow for more rapid optimization of solution treatments procedures to be used in industrial applications.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. 1.

    Pekguleryuz MO, Kainer KU, Arslan Kaya A, Witte F (2013) Fundamentals of magnesium alloy metallurgy. Elsevier, Amsterdam.

    Google Scholar 

  2. 2.

    Berman TD, Deda E, Miao J, Li M, Allison JE (2016) Microsegregation in high pressure die cast AM70. In: Magnesium technology 2016, pp. 47–51

  3. 3.

    Forsmark JH, Boileau J, Houston D, Cooper R (2012) A microstructural and mechanical property study of an AM50 HPDC magnesium alloy. Int J Met 6:15–26

    CAS  Google Scholar 

  4. 4.

    Gjestland H, Westengen H (2007) Advancements in high pressure die casting of magnesium. Adv Eng Mater 9:769–776.

    CAS  Article  Google Scholar 

  5. 5.

    Kim JS, Isac M, Guthrie RIL (2004) Metal-mold heat transfer and solidification of magnesium alloys in belt casting processes. In: Magnesium technology 2004, The Minerals, Metals & Materials Society, pp. 247–255

  6. 6.

    Mirković D, Schmid-Fetzer R (2009) Directional solidification of Mg–Al alloys and microsegregation study of mg alloys AZ31 and AM50: Part I. Methodology. Metall Mater Trans A 40:958–973.

    CAS  Article  Google Scholar 

  7. 7.

    Terbush JR, Saddock ND, Jones JW, Pollock TM (2010) Partitioning of solute to the primary α-Mg phase in creep-resistant Mg–Al–Ca-based cast alloys. Metall Mater Trans A 41:2435–2442.

    CAS  Article  Google Scholar 

  8. 8.

    Zheng X, Luo AA, Zhang C, Dong JIE, Waldo RA (2012) Directional solidification and microsegregation in a magnesium–aluminum–calcium alloy. Metall Mater Trans A 43A:3239–3248.

    CAS  Article  Google Scholar 

  9. 9.

    Khan I, Mostafa AO, Aljarrah M, Essadiqi E, Medraj M (2014) Influence of cooling rate on microsegregation behavior of magnesium alloys. J Mater 2014:1–18

    CAS  Article  Google Scholar 

  10. 10.

    Zhang C, Ma D, Wu K, Cao H, Cao G, Kou S (2007) Microstructure and microsegregation in directionally solidified Mg–4Al alloy. Intermetallics 15:1395–1400.

    CAS  Article  Google Scholar 

  11. 11.

    Paliwal M, Kang DH, Essadiqi E, Jung IH (2014) The evolution of as-cast microstructure of ternary Mg–Al–Zn alloys: an experimental and modeling study. Metall Mater Trans A 45:3596–3608.

    CAS  Article  Google Scholar 

  12. 12.

    Liu S, Yang G, Jie W (2014) Microstructure, microsegregation, and mechanical properties of directional solidified Mg–3.0Nd–1.5Gd alloy. Acta Metall Sin English Lett 27:1134–1143.

    CAS  Article  Google Scholar 

  13. 13.

    Sharifi P, Fan Y, Anaraki HB, Banerjee A, Sadayappan K, Wood JT (2016) Evaluation of cooling rate effects on the mechanical properties of die cast magnesium alloy AM60. Metall Mater Trans A 47A:5159–5168.

    CAS  Article  Google Scholar 

  14. 14.

    Sadayappan K, Kasprzak W, Brown Z, Quimet L, Luo AA (2009) Characterization of magnesium automotive components produced by super-vacuum die casting process. Mater Sci Forum 618–619:381–386.

    Article  Google Scholar 

  15. 15.

    Luo AA, Sachdev AK, Powell BR (2010) Advanced casting technologies for lightweight automotive applications. China Foundry 7:463–469

    CAS  Google Scholar 

  16. 16.

    Li M, Zhang R, Allison J (2010) Modeling casting and heat treatment effects on microstructure in super vacuum die casting (SVDC) AZ91 magnesium alloy. Magnes Technol 623–627

  17. 17.

    Miao J, Li M, Allison JE (2012) Microstructure evolution during heat treatment in a super vacuum die casting Az91 alloy. In: Mg2012 9th international conference magnesium alloy and their application, pp 493–498

  18. 18.

    Wang J, Li M, Ghaffari B, Chen L-Q, Miao J, Allison J (2012) A microstructural evolution model for Mg17Al12 precipitates in AZ91. In: Mg2012 9th international conference on magnesium alloys and their applications, pp 163–170

  19. 19.

    Zuo Q, Liu F, Wang L, Chen CF, Zhang ZH (2014) An analytical model for secondary phase dissolution kinetics. J Mater Sci 49:3066–3079.

    CAS  Article  Google Scholar 

  20. 20.

    Zhang X, Guo M, Zhang J, Zhuang L (2016) Dissolution of precipitates during solution treatment of Al–Mg–Si–Cu alloys. Metall Mater Trans B 47:608–620.

    CAS  Article  Google Scholar 

  21. 21.

    Zhu T, Chen ZW, Gao W (2010) Dissolution of eutectic β-Mg17Al12 phase in magnesium AZ91 cast alloy at temperatures close to eutectic temperature. J Mater Eng Perform 19:860–867.

    CAS  Article  Google Scholar 

  22. 22.

    Vermolen F, Vuik K, van der Zwaag S (1998) A mathematical model for the dissolution kinetics of Mg2Si-phases in Al–Mg–Si alloys during homogenisation under industrial conditions. Mater Sci Eng A 254:13–32.

    Article  Google Scholar 

  23. 23.

    Whelan MJ (1969) On the kinetics of precipitate dissolution. Met Sci J 3:95–97.

    CAS  Article  Google Scholar 

  24. 24.

    Brown LC (1976) Diffusion-controlled dissolution of planar, cylindrical, and spherical precipitates. J Appl Phys 47:449–458.

    Article  Google Scholar 

  25. 25.

    Baty DL, Heckel RW, Engineer M, Divi- ES, Company GE (1970) Solution Kinetics of CuAI2 in an AI–4Cu alloy. Metall Trans 1:1651–1656

    CAS  Article  Google Scholar 

  26. 26.

    Tundal UH, Ryum N (1992) Dissolution of particles in binary alloys: part I. Computer simulations. Metall Trans A 23:433–444.

    Article  Google Scholar 

  27. 27.

    Ferro P (2013) A dissolution kinetics model and its application to duplex stainless steels. Acta Mater 61:3141–3147.

    CAS  Article  Google Scholar 

  28. 28.

    Fukumoto S, Iwasaki Y, Motomura H, Fukuda Y (2012) Dissolution behavior of δ-ferrite in continuously cast slabs of SUS304 during heat treatment. ISIJ Int 52:74–79.

    CAS  Article  Google Scholar 

  29. 29.

    Avrami M (1939) Kinetics of phase change I. General theory. J Chem Phys 7:1103–1112.

    CAS  Article  Google Scholar 

  30. 30.

    Samaras SN, Haidemenopoulos GN (2007) Modelling of microsegregation and homogenization of 6061 extrudable Al-alloy. J Mater Process Technol 193:63–73.

    CAS  Article  Google Scholar 

  31. 31.

    Haidemenopoulos GN, Kamoutsi H, Zervaki AD (2012) Simulation of the transformation of iron intermetallics during homogenization of 6xxx series extrudable aluminum alloys. J Mater Process Technol 212:2255–2260.

    CAS  Article  Google Scholar 

  32. 32.

    Sjölander E, Seifeddine S (2010) Optimisation of solution treatment of cast Al–Si–Cu alloys. Mater Des 31:S44–S49.

    CAS  Article  Google Scholar 

  33. 33.

    Andersson JO, Helander T, Höglund L, Shi P, Sundman B (2002) Thermo-Calc and DICTRA, computational tools for materials science. CALPHAD: Comput Coupling Phase Diagrams Thermochem 26:273–312.

    CAS  Article  Google Scholar 

  34. 34.

    Allison J, Backman D, Christodoulou L (2006) Integrated computational materials engineering: a new paradigm for the global materials profession. JOM 58:25–27.

    Article  Google Scholar 

  35. 35.

    Allison J, Li M, Wolverton C, Su XM (2006) Virtual aluminum castings: an industrial application of ICME. JOM 58:28–35.

    CAS  Article  Google Scholar 

  36. 36.

    Pollock DGB, Tresa M, Allison JE (2008) Integrated computational materials engineering: a transformational discipline for improved competitiveness and national security. National Academies Press, Washington, DC.

    Google Scholar 

  37. 37.

    Ganesan M, Dye D, Lee PD (2005) A technique for characterizing microsegregation in multicomponent alloys and its application to single-crystal superalloy castings. Metall Mater Trans A 36:2191–2204.

    Article  Google Scholar 

  38. 38.

    Miotti Bettanini A, Ding L, Mithieux JD, Parrens C, Idrissi H, Schryvers D, Delannay L, Pardoen T, Jacques PJ (2019) Influence of M23C6 dissolution on the kinetics of ferrite to austenite transformation in Fe-11Cr-006C stainless steel. Mater Des 162:362–374.

    CAS  Article  Google Scholar 

  39. 39.

    Erişir E, Bilir OG, Gezmişoǧlu AE (2017) A study of carbide dissolution in bearing steels using computational thermodynamics and kinetics. In: IOP Conference on series material science engineering. IOP Publishing, p 012021

  40. 40.

    Sadeghi I, Wells MA, Esmaeili S (2017) Modeling homogenization behavior of Al–Si–Cu–Mg aluminum alloy. Mater Des 128:241–249.

    CAS  Article  Google Scholar 

  41. 41.

    Thermo-Calc Software TCMG Mg alloys thermodynamic database version 5

  42. 42.

    Thermo-Calc Software MOBMG Mg alloys mobility database version 1

  43. 43.

    Berman TD, Yao Z, Deda E, Godlewski L, Li M, Allison JE (n.d.) Measuring and modeling microsegregation in high pressure die cast Mg–Al alloys. Metall Mater Trans A (in preparation)

Download references


The authors acknowledge the support of U.S. Department of Energy under Contract DE-EE0006434. We also gratefully acknowledge M. Li, J. Zindel and L. Godlewski of Ford Motor Company who provided the SVDC cast plates.

Author information



Corresponding author

Correspondence to Zhenjie Yao.

Ethics declarations

Data Availability

The experimental data supporting this publication and the MATLAB code for β phase characterization are available in the Materials Commons at

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.



Appendix 1: Relationship Between Volume Fraction and Surface Area

In the multi-particle assumption, each particle now has an initial average radius of \( R_{\beta ,n} \), and n represents the number of particles in the actual samples. In the DICTRA simulation, the initial radius of the secondary phase is \( R_{\beta ,n} \).

In DICTRA simulation setup, the initial volume fraction can be expressed as: \( \frac{{R_{\beta }^{3} }}{{R_{\text{tot}}^{3} }} = \frac{{V_{\beta } }}{{V_{\text{tot}} }} = V_{\beta }^{f} \). For the n particles scenario, the initial volume fraction is: \( \frac{{n \times R_{\beta ,n}^{3} }}{{R_{\text{tot}}^{3} }} = \frac{{V_{\beta ,n} }}{{V_{\text{tot}} }} = V_{\beta ,n}^{f} \). The initial volume fraction should be satisfied that \( V_{\beta }^{f} = V_{\beta ,n}^{f} \), and therefore, \( R_{\beta }^{3} = nR_{\beta ,n}^{3} \Rightarrow R_{\beta } = \sqrt[3]{n}R_{\beta ,n} \)

The surface area of the sphere for n particle scenario is \( A_{n} = 4\pi R_{\beta ,n}^{2} \) for each individual particle. The surface area of the sphere for DICTRA simulation is \( A = 4\pi R_{\beta }^{2} \). Hence, the ratio of the two surface area in these two case is \( \frac{A}{{A_{n} }} = \frac{{R_{\beta }^{2} }}{{n \times R_{\beta ,n}^{2} }} = \frac{{\sqrt[3]{{n^{2} }}R_{\beta ,n}^{2} }}{{n \times R_{\beta ,n}^{2} }} = \sqrt[3]{{\frac{1}{n}}} < 1 \).

Appendix 2: The Volume Fraction Change with Respect to Time

During a diffusion-controlled dissolution process, after time t, the shrinkage scale (solute diffusion length) \( l = a\sqrt {Dt} \), where a is a prefactor constant.

The ratio of the volume fraction of two model can be express as

$$ \frac{{V_{\beta }^{f} \left( t \right)}}{{V_{\beta ,n}^{f} \left( t \right)}} = \frac{{V_{\beta } \left( t \right)}}{{V_{\beta ,n} \left( t \right)}} = \frac{{R_{\beta }^{3} \left( t \right)}}{{n \times R_{\beta ,n}^{3} \left( t \right)}} = \frac{{\left( {R_{\beta } - l} \right)^{3} }}{{n \times \left( {R_{\beta ,n} - l} \right)^{3} }} = \frac{{\left( {\sqrt[3]{n}R_{\beta ,n} - l} \right)^{3} }}{{n \times \left( {R_{\beta ,n} - l} \right)^{3} }} $$
$$ \sqrt[3]{{\frac{{V_{\beta }^{f} \left( t \right)}}{{V_{\beta ,n}^{f} \left( t \right)}}}} = \frac{{\sqrt[3]{n}R_{\beta ,n} - l}}{{\sqrt[3]{n} \times \left( {R_{\beta ,n} - l} \right)}} = \frac{{\sqrt[3]{n}R_{\beta ,n} - \sqrt[3]{n}l + \sqrt[3]{n}l - l}}{{\sqrt[3]{n} \times \left( {R_{\beta ,n} - l} \right)}} = 1 + \frac{{\left( {\sqrt[3]{n} - 1} \right)l}}{{\sqrt[3]{n}\left( {R_{\beta ,n} - l} \right)}} > 1 $$

The volume fraction is now \( V_{\beta }^{f} \left( t \right) = \left( {1 + \frac{{\left( {\sqrt[3]{n} - 1} \right)l}}{{\sqrt[3]{n}\left( {R_{\beta ,n} - l} \right)}}} \right)^{3} V_{\beta ,n}^{f} \left( t \right). \)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yao, Z., Berman, T. & Allison, J. An ICME Method for Predicting Phase Dissolution During Solution Treatment in Advanced Super Vacuum Die Cast Magnesium Alloys. Integr Mater Manuf Innov 9, 301–313 (2020).

Download citation


  • Dissolution kinetics
  • Solution treatment
  • SVDC
  • Magnesium alloys
  • ICME