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Three-Phase Eutectic Microstructures: Influence of solid-solid interfacial energy anisotropy and diffusivities

Three-Phase Eutectic Microstructures: Influence of solid-solid interfacial energy anisotropy and diffusivities


Daniel Wheeler

July 21, 2022

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  1. Three-Phase Eutectic Microstructures: Influence of solid-solid interfacial energy anisotropy and

    diffusivities Sumeet Khanna, Aramanda Shanmukha Kiran, Abhik Choudhury Department of Materials Engineering Indian Institute of Science, Bengaluru
  2. Outline • A brief overview of my group’s activities •

    Complications in three-phase eutectics • Solid-solid interfacial energy anisotropy and its influence • Three-phase eutectics: Anisotropy and diffusivity contrast • Our ongoing work
  3. My group’s activities • Multi-phase multi-component solidification • Multi-component growth

    and coarsening • Multi-physics problems, that include coupling of electric, thermal and mechanical effects • Interfacial instabilities • Multi-scaling • Directional solidification experiments
  4. 4 Modified-Bridgman apparatus Apparatus-1 Apparatus-2

  5. 5 Modified-Bridgman apparatus Schematic Temperature profiles

  6. Experimental Microstructures Nb-Al-Ni; 2 fibrous Ag-Al-Cu; brick structure Ref: Contieri

    et al., Materials Characterization, 2008 Ref: Dennstedt et al., IOP Conf Ser Mater Sci Eng, 2014
  7. Three-phase Eutectic Microstructures • Microstructure ideally classified into 5 distinct

    types Lamellar ABC Ref: D. Lewis, et al., Journal of electronic materials, 2002 Hexagonal (all fibrous) Brick type Fibres in matrix Lamellar BABC Lamellar + fibrous
  8. Parameters affecting Microstructure • Phase fraction, liquidus slopes (thermodynamics) •

    Solidification velocity • Interface energy (relative values) • Interface energy anisotropy(solid/solid and solid/liquid) • Diffusivities (contrast in the solutal diffusivities in multicomponent systems)
  9. Influence of volume fractions

  10. Three-phase pattern formation during solidification (AgAlCu eutectic) Lorenz Ratke, Anne

    Dennstedt, DLR Koln Coupling with databases using Choudhury et al.: Current Opinion in Solid-state and materials science, Vol. 287, 2015.
  11. Other attractors

  12. Statistical characterization of structures (in collaboration with Prof. Surya Kalidindi

    (Acta Materialia110 (2016) 131–141))
  13. Ternary eutectics are more complicated than we thought, as we

    found out upon doing our own experiments
  14. AgCuSb ternary eutectic composition Longitudinal section Transverse section 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =

  15. None
  16. 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 16𝜇𝑚/𝑠 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 32 𝜇𝑚/𝑠

  17. So things are quite complicated indeed !! In this talk

    we are going to try to resolve two aspects pertinent to most metallic and multi- component systems 1) Influence of solid-solid anisotropy 2) The multicomponent nature of the problem and the influence of a diffusivity contrast between the solutes on pattern formation
  18. How can solid-solid interfacial energy anisotropy influence microstructure formation? Let

    us look at a simplified binary first: Experiments and simulations Sn-Zn binary eutectic system
  19. Phase diagram of Sn-Zn system L⇌(Sn)+(Zn) Tm = 198.5 C

    Volume percent: (Sn)=91, (Zn)=9. 21-07-2022 19 S n Zn BC T HCP
  20. 21-07-2022 20 IPF and phase map of Sn-Zn alloy solidified

    at V= 0.58μm/s Inverse pole figure map Phase map
  21. 21-07-2022 21 Microstructures of Sn-Zn eutectic Transverse sections Bright phase

    is tin(Sn) Dark phase is zinc(Zn) V= 0.58 μm/s V= 1 μm/s V= 5. 0μm/s V= 7.5 μm/s V= 10.0 μm/s V= 50 μm/s
  22. 22 T = k1 V + k2 / Jackson-Hunt(1966, AIME)

    predictions 2 min V = k2 /k1 Rods
  23. None
  24. Basal planes of Zn parallel to lamellar interface

  25. Initial transient Steady-state regime

  26. In the presence of solid-solid interfacial energy anisotropy, different interface

    plane orientations for a fixed crystal orientation would have different energies Solid-solid interfacial energy anisotropy
  27. SEM images captured 20mm, 30mm, 40mm, 50mm and 60 mm

    respectively from the bottom Metallurgical and Materials Transactions A volume 51, pages6387– 6405(2020)
  28. Phase-field Model • Phase evolution equation • Diffusion potential evolution

    equation Phas e 𝜙 0 𝜙 1 𝜙 2 Sn 1 0 0 Zn 0 1 0 Liqui d 0 0 1 Ref: A Choudhury, B. Nestler - Physical Review E, 2012 M. Plapp - Physical Review E, 2011
  29. Thermodynamics • Parabolic approximation to free-energies near the eutectic temperature

    Ref: COST 507, Thermochemical database for light metal alloys, 1998
  30. Simulation Setup • Representation of hexagonal symmetry White rectangle =

    Actual simulation domain with reflective boundary conditions Zn = blue Sn = Red Directional solidification setup
  31. Implementation of Anisotropy in 𝛾 Sn-Zn Solid-Solid Interface Energy Anisotropy

    with 2-fold Symmetry 𝜃 R = 0o 𝜃 R = 90o Polar plot of interface energy Equilibrium Rod Shape
  32. Spacing = 1.05𝜆 min ➢ No departure from hexagonal rod

    arrangement 𝜃 R = 0o 𝜃 R = 90o Isotropic Steady state Solid-Liquid Interface
  33. None
  34. None
  35. Spacing = 1.4𝜆 min Equilibrium Solid-Liquid Interface 𝜃 R =

    0o 𝜃 R = 90o ➢ Transformation to lamellar and rectangular arrangement of Zn-phase
  36. Solid-Liquid Interface Temperature 𝜃 R = 0o 𝜃 R =

    90o T I M E Interfaces with higher undercooling get eliminated
  37. Extended Simulations All Zn-rods oriented in only 1 direction with

    respect to the Sn-matrix
  38. You can find more details about this combined study in

    two publications: a) Role of Solid–Solid Interfacial Energy Anisotropy in the Formation of Broken Lamellar Structures in Eutectic Systems Metallurgical and Materials Transactions A volume 51, pages 6327– 6345(2020) b) Crystallographic and Morphological Evidence of Solid–Solid Interfacial Energy Anisotropy in the Sn-Zn Eutectic System Metallurgical and Materials Transactions A volume 51, pages 6387– 6405(2020)
  39. Intermediate conclusions • The solid-solid interfacial energy anisotropy influences solidification

    dynamics although there is no kinetics in the solid!! • In the resultant morphology the orientations of the solid-solid interface correspond to lower energy directions in the gamma-plot
  40. Experimental observations • Turns out there are orientation relationships and

    associated solid-solid interfacial anisotropy even in three-phase eutectics, you can find more information here: • Quasi-isotropic and locked grain growth dynamics in a three-phase eutectic system Samira Mohagheghi, Melis Serefoglu; Acta Materialia 151 (2018) 432e442 • Effects of interphase boundary anisotropy on the three-phase growthdynamics in the β(In) – In2Bi – γ(Sn) ternary-eutectic system; S Mohagheghi, U Hecht, S Bottin-Rousseau, S Akamatsu, G Faivre3, M Şerefoğlu1 IOP Conf. Series: Materials Science and Engineering 529 (2019) 012010
  41. Three-phase eutectics: Influence of solid-solid interfacial energy anisotropy

  42. c A c B c C 0.333 0.333 0.333 0.6

    0.2 0.2 0.2 0.6 0.2 0.2 0.2 0.6 Thermodynamics: Symmetric Phase diagram Parabolic free energies for each phase: Phase composition at T eutectic
  43. Phase-field Model • Phase evolution equation Ref: A Choudhury, B.

    Nestler - Physical Review E, 2012 M. Plapp - Physical Review E, 2011 Gradient energy Driving force • Diffusion potential evolution equation
  44. Simulation Setup • Directional Solidification setup in constrained domain settings

    • Simulations with different spacing Hexagonal configuration Regular Brick Alternating Brick Cross-section of solid-liquid interface Periodic Boundary Neumann Boundary
  45. Isotropic Interfacial Energies Hexagon Regular Brick Alternating Brick

  46. Undercooling-Spacing Plot • Microstructures stable between and

  47. Hexagon Regular Brick Isotropic Interfacial Energies • At lower spacings,

    hexagon transform to lamellae • At larger spacings, hexagon transforms to smaller hexagons • Bricks cannot transform to lamella at smaller spacings
  48. 𝛼βinterface is anisotropic Smaller spacings Larger spacings

  49. 𝜶𝜷, 𝜶𝜹 𝒊𝒏𝒕𝒆𝒓𝒇𝒂𝒄𝒆𝒔 𝒂𝒓𝒆 𝒂𝒏𝒊𝒔𝒐𝒕𝒓𝒐𝒑𝒊𝒄

  50. 𝜶𝜷, 𝜶𝜹 𝒊𝒏𝒕𝒆𝒓𝒇𝒂𝒄𝒆𝒔 𝒂𝒏𝒊𝒔𝒐𝒕𝒓𝒐𝒑𝒊𝒄 𝛼𝛽 𝛼𝛿

  51. 𝛼𝛽, 𝛼𝛿, 𝛽𝛿 𝜶𝜷, 𝜶𝜹, 𝜷𝜹 𝒊𝒏𝒕𝒆𝒓𝒇𝒂𝒄𝒆𝒔 𝒂𝒏𝒊𝒔𝒐𝒕𝒓𝒐𝒑𝒊𝒄

  52. 𝜶𝜷, 𝜶𝜹, 𝜷𝜹 𝒊𝒏𝒕𝒆𝒓𝒇𝒂𝒄𝒆𝒔 𝒂𝒏𝒊𝒔𝒐𝒕𝒓𝒐𝒑𝒊𝒄 𝛼𝛽 𝛼𝛿, 𝛽𝛿

  53. Equal diffusivities: Anisotropic Interfacial Energy Distorted Hexagon Brick Brick Brick

  54. Influence of the solute diffusivity matrix, combined with anisotropic effects

  55. Unequal diffusivities: Isotropic Interfacial Energy • Presence of curved triple

    lines • Reduction in volume fraction • Shape Factor where,
  56. Unequal diffusivities: Isotropic Interfacial Energy • The perimeter/area of the

    phase richer in slower diffusing component increases
  57. Unequal diffusivities: Anisotropic Interfacial Energy Distorted Hexagon Brick Brick Lamella

    𝜆/𝜆𝑚𝑖𝑛 > 1.27 < 0.83 𝜆/𝜆𝑚𝑖𝑛 > 1.27
  58. Unequal diffusivities: Undercooling-Spacing Plot • Similar to equal diffusivities, undercooling

    decreases with increasing number of anisotropic interfaces
  59. Extended Simulations Dl=(1,1) isotropic Dl=(2,1) isotropic

  60. and anisotropic Extended Simulations and anisotropic

  61. Extended Simulations Hexagon, Square Brick Brick Lamella Isotropic

  62. Extended Simulations Perimeter ratio: • Unequal diffusivities leads to a

    higher perimeter ratio
  63. None
  64. Conclusion • Hexagonal microstructures are most probable when everything is

    symmetric---uncommon in experimental situations • Brick microstructures occur most frequently in simulations • Lamellar microstructures occur when all the solid-solid interfaces are anisotropic and the anisotropy functions have the same orientations • Unequal diffusivities lead to curved triple-line projections and the patterns have reduced symmetry • Combination of diffusivities and interfacial energy anisotropy leads to diverse microstructure even when the eutectic solid phases have equal volume fraction
  65. ACKNOWLEDGEMENT • SERC (Supercomputing facility at IISc, Cray XC- 40)

    • Thematic Unit of Excellence-Computational Materials Science (TUE-CMS) • Department of Science and Technology DSTO1679 THANK YOU