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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

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  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

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  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

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  4. 4
    Modified-Bridgman
    apparatus
    Apparatus-1 Apparatus-2

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  5. 5
    Modified-Bridgman
    apparatus
    Schematic Temperature
    profiles

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  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

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  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

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  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)

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  9. Influence of volume fractions

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  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.

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  11. Other attractors

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  12. Statistical characterization of structures
    (in collaboration with
    Prof. Surya Kalidindi (Acta Materialia110 (2016) 131–141))

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  13. Ternary eutectics are more
    complicated than we thought, as
    we found out upon doing our own
    experiments

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  14. AgCuSb ternary eutectic composition
    Longitudinal section Transverse section
    𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 0.5𝜇𝑚/𝑠

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  15. View Slide

  16. 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 16𝜇𝑚/𝑠 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 32 𝜇𝑚/𝑠

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  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

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  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

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  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

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  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

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  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

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  22. 22
    T = k1
    V + k2
    /
    Jackson-Hunt(1966, AIME)
    predictions
    2
    min
    V = k2
    /k1
    Rods

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  23. View Slide

  24. Basal planes of Zn parallel to lamellar
    interface

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  25. Initial transient Steady-state regime

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  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

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  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)

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  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

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  29. Thermodynamics
    ● Parabolic approximation to free-energies near the eutectic temperature
    Ref: COST 507, Thermochemical database for light metal alloys, 1998

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  30. Simulation Setup
    ● Representation of hexagonal symmetry
    White rectangle = Actual simulation
    domain with reflective boundary
    conditions
    Zn = blue Sn = Red
    Directional solidification setup

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  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

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  32. Spacing = 1.05𝜆
    min
    ➢ No departure from hexagonal rod arrangement
    𝜃
    R
    = 0o 𝜃
    R
    = 90o
    Isotropic
    Steady state Solid-Liquid Interface

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  33. View Slide

  34. View Slide

  35. Spacing = 1.4𝜆
    min
    Equilibrium Solid-Liquid Interface
    𝜃
    R
    = 0o 𝜃
    R
    = 90o
    ➢ Transformation to lamellar and rectangular arrangement of Zn-phase

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  36. Solid-Liquid Interface Temperature
    𝜃
    R
    = 0o 𝜃
    R
    = 90o
    T
    I
    M
    E
    Interfaces with higher
    undercooling get eliminated

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  37. Extended Simulations
    All Zn-rods oriented in only 1 direction with respect to the Sn-matrix

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  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)

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  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

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  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

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  41. Three-phase eutectics:
    Influence of solid-solid
    interfacial energy anisotropy

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  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

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  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

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  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

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  45. Isotropic Interfacial Energies
    Hexagon Regular Brick Alternating Brick

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  46. Undercooling-Spacing Plot
    ● Microstructures stable between and

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  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

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  48. 𝛼βinterface is anisotropic
    Smaller
    spacings
    Larger spacings

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  49. 𝜶𝜷, 𝜶𝜹 𝒊𝒏𝒕𝒆𝒓𝒇𝒂𝒄𝒆𝒔 𝒂𝒓𝒆 𝒂𝒏𝒊𝒔𝒐𝒕𝒓𝒐𝒑𝒊𝒄

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  50. 𝜶𝜷, 𝜶𝜹 𝒊𝒏𝒕𝒆𝒓𝒇𝒂𝒄𝒆𝒔 𝒂𝒏𝒊𝒔𝒐𝒕𝒓𝒐𝒑𝒊𝒄
    𝛼𝛽
    𝛼𝛿

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

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

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

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

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  55. Unequal diffusivities: Isotropic Interfacial Energy
    ● Presence of curved triple lines
    ● Reduction in volume fraction
    ● Shape Factor where,

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  56. Unequal diffusivities: Isotropic Interfacial Energy
    ● The perimeter/area of the phase richer in slower diffusing component
    increases

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  57. Unequal diffusivities: Anisotropic Interfacial Energy
    Distorted Hexagon Brick Brick
    Lamella
    𝜆/𝜆𝑚𝑖𝑛 > 1.27
    < 0.83
    𝜆/𝜆𝑚𝑖𝑛 > 1.27

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  58. Unequal diffusivities: Undercooling-Spacing Plot
    ● Similar to equal diffusivities, undercooling decreases with increasing number
    of anisotropic interfaces

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  59. Extended Simulations
    Dl=(1,1) isotropic Dl=(2,1) isotropic

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  60. and anisotropic
    Extended Simulations
    and anisotropic

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  61. Extended Simulations
    Hexagon, Square Brick Brick Lamella
    Isotropic

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  62. Extended Simulations
    Perimeter ratio:
    ● Unequal diffusivities leads to a higher perimeter ratio

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  63. View Slide

  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

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  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

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