Multiphase-field modelling of concurrent grain growth and coarsening in complex multicomponent systems

doi:10.1016/j.jmst.2019.11.011

Abstract

Abstract:

Phase-field modelling of microstructural evolution in polycrystalline systems with phase-associated grains has largely been confined to continuum-field models. In this study, a multiphase-field approach, with a provision for introducing grain boundary and interphase diffusion, is extended to analyse concurrent grain growth and coarsening in multicomponent polycrystalline microstructures with chemically-distinct grains. The effect of the number of phases and components on the kinetics of evolution is investigated by considering binary and ternary systems of duplex and triplex microstructures, along with a single phase system. It is realised that the mere increase in the number of phases minimises the rate of concurrent grain growth and coarsening. However, the effect of components is substantially dependent on the respective kinetic coefficients. This work unravels that the disparity in the influence of phases and components is primarily due to the corresponding change introduced in the transformation mechanism. While the raise in number of phases convolutes the diffusion paths, the increase in number of component effects the rate of evolution through the interdiffusion, which introduces interdependency in the diffusing chemical-species. Additionally, the role of phase-fractions on the transformation rate of triplex microstructure is studied, and Correspondingly, the interplay of interface- and diffusion-governed evolution is elucidated. A representative evolution of three-dimensional triplex microstructure with equal phase-fraction is comparatively analysed with the evolution of corresponding two-dimensional setup.

Key words: Concurrent grain growth and coarsening, Duplex and triplex microstructure, Microstructural coarsening, Multiphase grain growth, Multiphase-field modelling

P.G. Kubendran Amos, Ramanathan Perumal, Michael Selzer, Britta Nestler. Multiphase-field modelling of concurrent grain growth and coarsening in complex multicomponent systems[J]. J. Mater. Sci. Technol., 2020, 45: 215-229.

Figures/Tables 17

Table 1 List of simulation parameters.

Parameter	Symbol	Value
Grid size	Δx = Δy (= Δz)	1.0
Time-step width	Δt	0.02
Interface-width parameter	?	4 ×Δx
Relaxation parameter	τ	1.0

Fig. 1. Microstructural evolution of single-, two- and three-phase polycrystalline structures indicated as ‘Pure’, ‘C2P2’, and ‘C3P’, respectively. Two duplex microstructures of binary (C2P2) and ternary (C3P2) systems are considered for analysing the effect of number of components.

Table 2 List of material parameters.

Parameter	Symbol	Value
Grain boundary energy	γ_ΘΘΘ∈{α,β,γ}	1.0
Interphase energy	γ_Θδ Θ,δ∈{α,β,γ}	1.0
Bulk diffusivity	D^α = D^β (=D^γ) ≡D	1.0

Table 3 Equilibrium concentration of binary and ternary systems.

Phase	Independent component-i	Independent component-j
(Binary)
Phase-α	0.1	-
Phase-β	0.9	-
(Ternary)
Phase-α	0.05	0.05
Phase-β	0.05	0.9
Phase-γ	0.9	0.05

Fig. 2. Monotonic decrease in the total number of grains during the evolution of single-phase, duplex and triplex microstructures of binary and ternary systems.

Fig. 3. Temporal increase in the average grain size of the polycrystalline systems with chemically-identical and phase-associated grains during the microstructural transformations.

Fig. 4. Change in the average grain size of duplex microstructure with equal and unequal phase-fraction pertaining to binary and ternary systems with time. The binary and ternary duplex microstructures with equal phase-fractions are Correspondingly represented by ‘C2-S2’ and ‘C3-S2’, while ‘C2-S1’ and ‘C3-S1’ respectively denotes the duplex systems with unequal volume-fractions of phases.

Fig. 5. Concurrent grain growth and coarsening of binary and ternary duplex microstructures with unequal phase-fractions.

Fig. 6. Grains of the binary and ternary duplex microstructures are distinguished based on the phases and the increase in its average size during the transformation is plotted with time.

Fig. 7. The disparity in the rate of increase in average grain size of ternary duplex microstructure with equal phase-fraction due to the difference in bulk diffusivity of the phases.

Fig. 8. The marginal difference in the transformation kinetics of binary and ternary duplex systems with an independent component-i of identical diffusivity.

Fig. 9. Microstructural transformation of ternary three-phase polycrystalline systems with equal and unequal phase-fractions. Two setups with varying volume fraction of the major phase-γ is considered to unravel the influence of phase-fraction on evolution kinetics.

Fig. 10. Progressive increase in the average grain size of the ternary triplex microstructures of different phase-fractions with time.

Fig. 11. Temporal change in the grain sizes of the ternary triplex-microstructure with equal and unequal phase-fractions are plotted by distinguishing the grains based on it chemical composition.

Fig. 12. Concurrent grain growth and coarsening of ternary triplex-microstructure with equal volume-fraction of the constituent phases in three-dimension. The volume fraction of the individual during the evolution is monitored and presented as a subplot.

Fig. 13. Change in the average grain size of ternary triplex-microstructure in two- and three-dimension are collectively plotted with time for a comparison.

Fig. 14. The grain-size distribution of the ternary triplex-microstructure in two- and three-dimension are presented by normalising with critical grain-size. Hillert and Weibull fittings are included to unravel the difference in the grain-size distribution.

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