1. Molecular Dynamics Simulation Study of Solid-Liquid Interface Properties of HCP Mg Yunfei Bai Supervisor Dr. Jeff Hoyt McMaster University 1

2. Magnesium Other useful properties Abundance High strength to weight ratio 2 little work in HCP Solid-liquid interface Formed by casting Why magnesium?

3. Modeling of Solidification Modeling of solidification by phase-field methods Require the details of solid- liquid interface Such as interface width, interfacial free energy and interface kinetic coefficient, etc. 3 Phase-field simulation of solidification of single crystal, blue (liquid) and red (solid), Morteza Amoorezaei et al. Acta, 2012

4. Solid-liquid Interface Limitation of Laboratory Experiment 1. Two condensed phases 2. Atomic length scale Advantages of Atomistic Simulation 1. Direct study between condensed phases 2. To length scale less than nanometer 4 SolidLiquid nanometer

5. Molecular Dynamics (MD) MD––an atomistic simulation method Particles interact dynamically Determined by Newton’s equations of motion In force fields defined by potential energy LAMMPS code––– A classical MD code Large-Scale Molecular Massively Parallel Simulator Developed by Sandia National Laboratories, US EAM potential energy Embedded-atom method, a multi-body potential EAM potential for Mg metal developed by Y. Sun et al. 2006 Molecular dynamics simulation of the deposition of single copper atom with a kinetic energy of 1eV on a copper surface, Knordlun 2007

6. Solid-liquid Interface by MD 6 Structural details of Solid-liquid interface Interface width Layer separation Anisotropy of interfacial stress Thermodynamic properties Interfacial free energy, excess energy, excess entropy Temperature dependence interfacial free energy Kinetic properties

7. Three low indexes of Orientations 7 most compact, parallel to a parallel to c inclined to both a and c

8. Simulation Procedures 8 Melting Temperature Tm = 911 K Periodic boundary along x, y and z directions. Set up simulation boxesMelt and equilibrateCollect data at equilibrium

9. Interface Structure 9 Coarse-grained density profile Fine-grained density profile Solid liquid Solid liquid Fine-grained Coarse-grained ε Minimize S

10. Interface Width – 10-90 Width 10 In a certain quantity profile (e.g. coarse- grained profile, etc.) Along the interface normal, z direction Z position with 10% of the different amount between the solid and liquid Z position with 90% of the amount. Then the difference between the two z positions is 10-90 width, w10-90 as show in graph. 10-90 width, w10-90, shown in Coarse-grained profile for (0001) orientation in HCP Mg

11. Layer Separation 11 Layer separation A interesting phenomenon that layer distance varying across the interface for a certain orientation and simply defined as In fine-grained profile, the spacing between two adjacent atomic layers along interface normal

12. Layer Separation 12 FIG. The interplane spacing as a function of distance normal to the interface for the FCC (100), (110), and (111) LJ solid-liquid interfaces in LJ reduced unit, Laird et al. 2009 In previous studies of FCC, the distance between adjacent atomic layers in (100) orientation is slightly expanded to that of (111) orientation across the interface, Laird et al. 2009

13. Layer Separation 13 FIG. The interplane spacing as a function of distance normal to the interface for the FCC (100), (110), and (111) LJ solid- liquid interfaces in LJ reduced unit, Laird et al. 2009 Layer separation in HCP Mg

14. Interfacial Stress Stress profile S(z) It is defined as followed, where Pzz is the virial pressure normal to the interface Pxx and Pyy are the transverse pressures Interfacial stress τ 14

15. Anisotropy of Interfacial Stress 15 Negative value of interfacial stress -–– compression Order of anisotropy of interfacial stress different from compact order is the abnormal orientation, which is also the case in anisotropy of layer separation Occupation fraction, defined as ratio of # density per layer over # density per crystal layer

16. Summary of Interface Widths Interface region –– 10-90 widths for various profiles 16 Table. Interfacial widths (Å)

17. Interfacial Free Energy Interfacial free energy, denoted as γ Defined as excess free energy of system over free energy of ideal system solely consisting of bulk solid and liquid γ of HCP Mg has been determined by D.Y.Sun, et al. 2006 With molecular dynamic (MD) method Using the same EAM potential At melting temperature in equilibrium 17

18. Temperature Dependence of γ From the differential form of definition: After derivation from Laird, et al. (2009), the Gibbs-Cahn Integration can be expressed as: where e is the excess energy, defined as: 18

19. Temperature Dependence of γ Frolov and Mishin, 2009 First application of Gibbs-Cahn integration Surface free energy of solid Cu (110) along t-p coexistence curve Solid-liquid interfacial free energy of Cu-Ag along t-c coexistence curve Followed by Laird and Davidchack, 2009, Lennard-Jones (LJ) system along phase coexistence curve (100), (110) and (111) orientations respectively 19 Previous applications of Gibbs-Cahn integration All of them under equilibrium condition

20. Temperature Dependence of γ 20 Estimate of temperature dependece of γ under non-equilibrium condition (undercooling)

21. Temperature Dependence of γ 21 After Gibbs-Cahn integration Estimate of temperature dependece of γ under non-equilibrium condition (undercooling) γ under non-equilibrium condition at selected temperature

22. Conclusions The intrinsic widths around 8 Å with very weak anisotropy The structural widths about 16 Å, almost twice of intrinsic values The interlayer spacing shares the same trend with FCC structures The order of occupation fraction profile corresponds to the sequence of anisotropy of stress profiles γ exhibit linear increasing relationship with increasing temperature till the melting point among three orientations Anisotropy of increasing ratio share the opposite sequence of compact order among three orientations 22 Interface Structure Temperature Dependence of γ (Non-Equilibrium Condition)

23. Acknowledgements Dr. Jeffrey J. Hoyt Dr. Nikolas Provatas My group member: Huajing Song (Wilson) Md Jahidur Rahman Harith Humadi Saidi Payman Thanks to my friends: Shenglong Liang Xiaoxu Zhang Financial Supported by: NSERC MagNET, (NSERC Magnesium Network)

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25. In a simulation, the potential energy of an atom, i, is given by where rij is the distance between atoms i and j, φαβ is a pair-wise potential function, ρα is the contribution to the electron charge density from atom j at the location of atom i, and F is an embedding function that represents the energy required to place atom i of type α into the electron cloud. 25 EAM Potential

26. Fine-grained Density

27. Coarse-grained Density Smoothing to Coarse-grained density profile

28. OP profile and PE profile Order parameter profile PE profile

29. Gibbs-Cahn Integration

30. Thermodynamic Data (Input)