Morphological Evolution and Growth Kinetics in Primary Crystallization of Amorphous: Phase Field Method

doi:10.19596/j.cnki.1001-246x.8461

Abstract

Abstract:

Influence of diffusion coefficient on crystallization process is considered in a crystallization physical model. A phase field method is employed to study influence of random nucleation rates and nucleation radii on microstructure and growth kinetics in primary crystallization process. It shows that the number of grain crystal of primary crystallization increases with the increase of initial nucleation rate, and the crystal size of primary crystallization decreases with the increase of initial nucleation rate. The crystallization fraction increases with evolution time and initial nucleation rate. The greater the initial nucleation rate, the higher the crystallization fraction. With different initial nucleation radii, the quantity and size of grains in the primary crystallization process remains basically unchanged with the increase of evolutionary time. The crystallization fraction increases with the increase of evolutionary time. The growth index corresponding to different initial nucleation rates and initial nucleation radii is less than 1, which means random nucleation rate and random nucleation radius have no significant effect on the crystallization mode. The crystallization modes are primary crystallization. Control of random nucleation rate and initial nucleation radius changes effectively microstructure of the primary crystallization. The grain size and crystallization fraction affect properties of the alloy directly.

Key words: primary crystallization, phase field method, growth kinetics, initial nucleation rate, initial nucleation radius

Jin WANG, Wen-jing MA, Yu-zhou LIU, Mei-ni LÜ, Kai-jing ZHANG. Morphological Evolution and Growth Kinetics in Primary Crystallization of Amorphous: Phase Field Method[J]. Chinese Journal of Computational Physics, 2022, 39(4): 403-410.

Figures/Tables 9

Fig.1 (a), (b), (c) Primary crystallization simulation results and (d) TEM image of crystallized Fe83.7B14.8Cu1.5 alloy[25]

Fig.2 Morphological evolution of primary crystallization of amorphous under different initial nucleation rates (a)~(d) 0.34%, (e)~(h) 0.98%, (i)~(l)1.63% at time steps (a), (e), (i) t = 0;(b), (f), (j) t = 0.4 × 104; (c), (g), (k) t = 0.6 × 104; (d), (h), (t) t = 1.0 × 104

Fig.3 Number of crystals vs grain size under different initial nucleation rates

Fig.4 Crystallization fraction of primary crystallization as functions of simulation time

Table 1 Exponential fittings of crystallization fraction evolution of primary crystallization with different initial nucleation rates

random nucleation rate/%	k	n
0.34	0.028 78	0.764 01
0.98	0.322 24	0.536 81
1.63	1.516 23	0.385 78

Fig.5 Morphological evolution of primary crystallization of amorphous under different initial nucleation radii (a)~(d) 2 nm, (e)~(h) 5 nm, (i)~(l)10 nm; at time steps (a), (e), (i) t = 0; (b), (f), (j) t = 0.4 × 104; (c), (g), (k) t = 0.6 × 104; (d), (h), (l) t = 1.0 × 104

Fig.6 Number of crystals vs grain size under different initial nucleation radii

Fig.7 Crystallization fraction of primary crystallization as functions of simulation time

Table 2 Exponential fittings of volume fraction evolution of primary crystallization of amorphous under different initial nucleation radii

initial nucleation radii/nm	k	n
2	1.516 23	0.385 78
5	1.902 32	0.362 77
10	2.476 83	0.335 65

References 25

1	BRUNA P , PINEDA E , CRESPO D . Phase-field modelling of microstructural evolution in primary crystallization[J]. Journal of Alloys and Compounds, 2009, 483 (1): 645- 649.
2	CHRISTIAN J M. The Theory of transformations in metals and alloys (Part Ⅰ+Ⅱ)[M]. Newnes, 2002.
3	KELTON K F , GREER A L , THOMPSON C V . Transient nucleation in condensed systems[J]. The Journal of Chemical Physics, 1983, 79 (12): 6261- 6276. DOI
4	MALINOV S , SHA W . Modeling thermodynamics, kinetics, and phase transformation morphology while heat treating titanium alloys[J]. The Journal of the Minerals, 2005, 57 (9): 42- 45.
5	MALINOV S , SHA W . Application of artificial networks for modelling correlations in titanium alloys[J]. Materials Science and Engineering: A, 2004, 365 (1): 202- 211.
6	WANG Y Z , MA N , CHEN Q , et al. Predicting phase equilibrium transformation and microstructure evolution in titanium alloys[J]. The Journal of the Minerals, 2005, 57 (9): 32- 39.
7	SAUMDERS N . Phase diagram calculations for high-temperature structural materials[J]. Philosophical Transactions of the Royal Society of London.Series A: Physical and Engineering Sciences, 1995, 351 (1697): 543- 561.
8	HOU Z Y , NIU Y , XIAO Q X , et al. Simulation of mechanical behavior and deformation mechanism of Al nanowires along different crystal orientations[J]. Chinese Journal of Computational Physics, 2022, 39 (3): 341- 351.
9	ZHANG H Y , YIN X C . Molecular dynamics study on growth mechanism of pure metals solid-liquid interface during solidification[J]. Chinese Journal of Computational Physics, 2019, 36 (1): 80- 88.
10	LIANG H , LI M S . Molecular dynamics study of mechanical properties of single crystal aluminum with voids and vacancies[J]. Chinese Journal of Computational Physics, 2019, 36 (2): 211- 218.
11	WANG J F , JIA S G , CHEN S H , et al. Effect of deformation on recrystallization behavior of Cu-Ni-Si alloy[J]. Journal of Henan University of Science and Technology, 2012, 33 (1): 5.
12	FENG Q H , ZHAO Y C , WANG S , et al. Pore-scale oil-water two-phase flow simulation based on phase field method[J]. Chinese Journal of Computational Physics, 2020, 37 (4): 439- 447.
13	陈伟鹏, 赵宇宏, 张冰, 等. 金属凝固过程枝晶生长相场法模拟研究进展[J]. 材料导报, 2018, 32 (S2): 535- 539.
14	席文, 陈铮, 胡石. 形变诱发纳米晶局域固态非晶化的研究进展[J]. 材料导报, 2018, 32 (01): 116- 121.
15	何日, 王明涛, 金剑锋, 等. 外应力对AZ31镁合金晶粒长大和织构影响的相场模拟[J]. 中国有色金属学报, 2018, 28 (06): 1083- 1091.
16	刘启海, 杨功能, 刘志远, 等. 非晶碳氢膜晶化凝聚的蒙特卡罗模拟[J]. 计算物理, 1992, 9 (S1): 569.
17	高英俊, 罗志荣, 胡项英, 等. 相场方法模拟AZ31镁合金的静态再结晶过程[J]. 金属学报, 2010, 46 (10): 1161- 1172.
18	罗志荣, 高英俊, 邓芊芊, 等. 定向退火条件下柱状晶形成及连续扩展的相场模拟[J]. 中国有色金属学报, 2014, 24 (07): 1778- 1784.
19	LUO Z R , GAO Y J , MAO H , et al. Phase field modeling of columnar grain growth: Effect of second-phase particles[J]. Chinese Journal of Computational Physics, 2016, 33 (3): 367- 373.
20	李文韬. 金属凝固及晶粒熟化相场法模拟研究进展[J]. 热加工工艺, 2020, 49 (07): 1- 5.
21	BRUNA P , CRESPO D , CINCA R , et al. On the validity of Avrami formalism in primary crystallization[J]. Journal of Applied Physics, 2006, 100, 054907.
22	MAO M , ALTOUNIAN Z , RYAN D H . The glass transition in Zr₆₇(Ni_1-xCu_x) metallic glasses[J]. Journal of Non-Crystalline Solids, 1996, (205-207): 476- 479.
23	DUINE P A , SIETSMA J , BEUKEL A V D . Atomic transport in amorphous Pd₄₀Ni₄₀P₂₀ near the glass-transition temperature: Au diffusivity and viscosity[J]. Physical Review B, 1993, 48 (10): 6957- 6965.
24	BRUNA P , PINEDA E , CRESPO D . Phase-field modeling of glass crystallization: Change of the transport properties and crystallization kinetic[J]. Journal of Non-Crystalline Solids, 2007, (353): 1002- 1004.
25	CHEN Y M , OHKUBO T , OHTA M , et al. Three-dimensional atom probe study of Fe-B-based nanocrystalline soft magnetic materials[J]. Acta Materialia, 2009, 57 (19): 4463- 4472.

[1]	FENG Qihong, ZHAO Yunchang, WANG Sen, ZHANG Yigen, SUN Yeheng, SHI Shubin. Pore-scale Oil-Water Two-phase Flow Simulation Based on Phase Field Method [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(4): 439-447.
[2]	LUO Zhirong, GAO Yingjun, MAO Hong, LU Chengjian, HUANG Shiye. Phase Field Modeling of Columnar Grain Growth:Effect of Second-Phase Particles [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(3): 367-373.