Recent Progresses in Modeling of Nucleation During Solidification on the Atomic Scale

doi:10.11900/0412.1961.2017.00425

Acta Metall Sin

2018, Vol. 54

Issue (2): 204-216 DOI: 10.11900/0412.1961.2017.00425

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Recent Progresses in Modeling of Nucleation During Solidification on the Atomic Scale

Jincheng WANG(

), Can GUO, Qi ZHANG, Sai TANG, Junjie LI, Zhijun WANG

State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China

Cite this article:

Jincheng WANG, Can GUO, Qi ZHANG, Sai TANG, Junjie LI, Zhijun WANG. Recent Progresses in Modeling of Nucleation During Solidification on the Atomic Scale. Acta Metall Sin, 2018, 54(2): 204-216.

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Abstract

Nucleation, the starting point of first-order discontinuous phase transformations, has long been an important issue in condensed matter physics and materials science. It plays a key role in determining the microstructures and mechanical properties of crystalline materials. As nucleation occurs at the atomic length scale and the diffusional time scale and is a typical stochastic event, investigating such kind of multiple scale issues will be taken up an enormous challenge. Because of the limitations of present experimental methods, it is still very hard to observe the nucleation process in situ. With the development of computational materials science, a deeper understanding of nucleation process has been obtained with the numerical modeling of nucleation process on the atomic scale. In this paper, some recent developments in modeling and simulation of nucleation process during solidification on the atomic scale are reviewed. Firstly, the development of classical nucleation theory and the step nucleation theory are reviewed. Then the developments in modeling of nucleation process by using the phase field method, Monte-Carlo method, Molecular dynamics method and the phase field crystal model are discussed. After that, some recent progresses in modeling of nucleation process during solidification in our research group by using the phase field crystal model are demonstrated. Finally, the outlooks of the future study on the nucleation during solidification are also presented.

Key words: solidification nucleation numerical simulation research progress

Received: 13 October 2017

Fund: Supported by National Natural Science Foundation of China (Nos.51371151 and 51571165)

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	Jincheng WANG
	Can GUO
	Qi ZHANG
	Sai TANG
	Junjie LI
	Zhijun WANG

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https://www.ams.org.cn/EN/10.11900/0412.1961.2017.00425 OR https://www.ams.org.cn/EN/Y2018/V54/I2/204

Fig.1 The free energy curves and nucleation pathways of classical nucleation (a) and two-step nucleation (b)^[32]

Fig.2 Formation of shish-kebab structure by noise-induced heterogeneous nucleation on tubular, snapshots taken at time t=30 μs (a), t=40 μs (b) and t=50 μs (c) (showing the walls and the solidification front walls) ^[50]

Fig.3 Temporal evolution in homogeneous nucleation process from 10⁹ atom molecular dynamics simulation of solidification of pure metals^[16]

Fig.4 Heterogeneous nucleation on bcc-substrate simulated by the single-mode phase filed crystal (PFC) model with different reduced initial densities ψ₀ (dimensionless)^[76]
(a) ψ₀=-0.3538 (b) ψ₀=-0.3516 (c) ψ₀=-0.3504 (d) ψ₀=-0.3489 (e) ψ₀=-0.3482 (f) ψ₀=-0.3480

Fig.5 Snapshots of atomic configurations during nucleation and subsequent solidification processes for different ψ₀ at dimensionless temperature parameter σ=0.06 (Blue, green and red atoms represent atoms with square, triangle and amorphous configurations, respectively, which are defined by the bond order parameter analysis; the time in Fig.5a~c is dimensionless time)^[84]
(a) ψ₀=-0.09 (b) ψ₀=-0.08 (c) ψ₀=-0.07

Fig.6 Snapshots of the structural transformation pathways during nucleation with different simulation parameters (For each row, four figures from left to right show the temporal evolution of crystal nuclei. And, the blue solid line is the phase boundary, corner mark "tr" and "sq" are the abbreviation of "triangle" and "square", respectively)^[82]
(a) σ=0.05, corresponding to large undercooling, the nucleation is one-step type (b~d) σ=0.06~0.07, temperatures increase slightly, the nucleation is two-step type, and the final crystal is square (e) σ=0.08, temperatures rise to the peritectic line, TS process for metastable triangle crystal in square stabilized region

Fig.7 Crystal nucleation and subsequent growth processes at undercoolings ε =-0.05 (a~c), ε =-0.15 (d~f) and ε =-0.4 (g~i) (The

Δt = 0.5

is the dimensionless time step. Atom color is based on the range of order as determined by

q ? 6

(bond order parameter). In particular, bcc and fcc atoms have long-range order (LRO) and are displayed in orange and red, respectively. Atoms with short-range order (SRO) (

q ? 6 < 0.28

) are blue, and those with medium-range order (MRO) (

q ? 6 > 0.28

) are light blue to green. Regions "free" of atoms are liquid)^[85]

Fig.8 Snapshots in the solidification process with different temperatures, herein, initial composition is c_ini=0.5, σ = 0. In each row, four figures from left to right show the time evolution of atom density field (a) (which is used to distinguish solid and liquid) and concentration field (b)

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