Phase-field modeling of multiphase single-component system microstructure formation

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Abstract

The present study employs a phase-field description to consider the crystallisation process of one-component systems with microstructure formation. A closed physical and mathematical model of thermodynamically consistent relaxation equations for phase fields and heat conduction equations describing the interaction of different phases and crystallites of one phase with each other is obtained. The model incorporates latent heat of phase transition and is derived from the principle of entropy increase and enthalpy conservation law. A method of introducing phase-field fluctuations is proposed, with the aim of simulating homogeneous nucleation in the melt. The investigation of edge angle formation at the contact of three phases is undertaken on the basis of the obtained model. The crystallite size distribution obtained from the model is then compared with the theoretical Hillert distribution. The study goes on to examine the dependence of crystallite shape and size distribution on thermal gradient, and the influence of thermodynamic conditions on the process of polymorphic δ–γ transformation.

About the authors

S. A. Korobeynikov

Udmurt Federal Research Center, Ural Branch of the Russian Academy of Sciences; Udmurt State University

Author for correspondence.
Email: sa.korobeynikov@yandex.ru
Russian Federation, Izhevsk, 426067; Izhevsk, 426034

V. G. Lebedev

Udmurt Federal Research Center, Ural Branch of the Russian Academy of Sciences

Email: sa.korobeynikov@yandex.ru
Russian Federation, Izhevsk, 426067

V. I. Lad'yanov

Udmurt Federal Research Center, Ural Branch of the Russian Academy of Sciences

Email: sa.korobeynikov@yandex.ru
Russian Federation, Izhevsk, 426067

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Supplementary files

Supplementary Files
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2. Fig. 1. Two-dimensional Perlin noise at some point in time and its localization for different values ​​of the parameter A.

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3. Fig. 2. Profiles of interphase boundaries (gray lines) for different ratios of surface energies with the found contact angles and calculated values ​​(in brackets) according to the system of equations (16).

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4. Fig. 3. Nucleation and normal growth of the δ-phase in the melt for different moments of dimensionless time (τ = 0.6, 1.2, 4.0) in a square region of 125 × 125 (12.5 × 12.5 μm). The color indicates the temperature field, the black solid lines are grain boundaries (φi = 0.5), and the hatching is the solid phase.

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5. Fig. 4. Spatial distribution of δ-phase grains during abnormal growth at different moments of dimensionless time τ = 12.0, 36.0, 60.0 in a square region of size 125 × 125 (12.5 × 12.5 μm). Black lines are crystallite boundaries (φi = 0.5).

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6. Fig. 5. Distribution of grain radii normalized to the mean value for different moments of dimensionless time τ in comparison with the Hillert distribution [20].

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7. Fig. 6. The process of nucleation, crystallization and polymorphic transformation involving two types of solid phases δ and γ in the melt in a rectangular region of 200 × 75 (20.0 × 7.5 μm). Three moments of dimensionless time τ = 2, 25, 60 are shown. The upper fragments in pairs are phase fields with crystallite boundaries (φ{i,j} = 0.5), the lower ones are the temperature field with crystallite boundaries. In the fragments for phase fields: white fill is the liquid phase L, blue is the δ-phase, green is the γ-phase.

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