非晶一次晶化过程微观组织演化和生长动力学的相场法研究

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

计算物理 ›› 2022, Vol. 39 ›› Issue (4): 403-410.DOI: 10.19596/j.cnki.1001-246x.8461

非晶一次晶化过程微观组织演化和生长动力学的相场法研究

王进¹^,²(), 马文婧¹^,²^,*(), 刘玉周³, 吕美妮¹^,², 张开靖²

1. 广西机器视觉与智能控制重点实验室, 广西梧州 543002
2. 梧州学院电子与信息工程学院, 广西梧州 543002
3. 梧州学院机械与材料工程学院, 广西梧州 543002

收稿日期:2021-10-08 出版日期:2022-07-25 发布日期:2022-11-17
通讯作者: 马文婧
作者简介:
王进(1984-), 男, 讲师, 博士, 研究方向为非晶、纳米晶软磁材料实验及微观组织计算模拟, E-mail: wolfwood_wang@126.com
基金资助:
国家自然科学基金(51765060); 中央引导地方科技发展资金; 广西科技基地和人才专项(桂科AD20238053); 广西高校中青年教师科研基础能力提升项目(2019KY0691); 广西高校中青年教师科研基础能力提升项目(2020KY17010); 梧州学院重大项目(2017A004); 梧州学院重大项目(2017A005)

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

Jin WANG¹^,²(), Wen-jing MA¹^,²^,*(), Yu-zhou LIU³, Mei-ni LÜ¹^,², Kai-jing ZHANG²

1. Guangxi Key Laboratory of Machine Vision and Intelligent Control, Wuzhou, Guangxi 543002, China
2. School of Electronic and Information Engineering, Wuzhou University, Wuzhou, Guangxi 543002, China
3. School of Mechanical and Material Engineering, Wuzhou University, Wuzhou, Guangxi 543002, China

Received:2021-10-08 Online:2022-07-25 Published:2022-11-17
Contact: Wen-jing MA

摘要/Abstract

摘要：

在晶化物理模型中添加扩散系数对晶化过程的影响, 采用相场方法研究初始形核率和初始形核半径对一次晶化过程中微观组织和生长动力学的影响。结果表明: 随着初始形核率的增加, 相同时间内非晶一次晶化的晶粒数量逐渐增加, 晶粒尺寸逐渐减小。晶化分数随着演化时间和初始形核率的增加逐渐增大, 初始形核率越大, 相同演化时间内的晶化分数越高。不同初始形核半径情况下, 非晶一次晶化过程中的晶粒数量和尺寸随着演化时间的增加基本保持不变。晶化分数随着演化时间的增加而增大。不同初始形核率和初始形核半径情况下所对应的生长指数均小于1, 表明初始形核率和初始形核半径对晶化方式无影响, 均为一次晶化。改变初始形核率和初始形核半径可调控一次晶化微观组织结构, 而晶粒尺寸及晶化分数直接关系到合金性能。

关键词: 一次晶化, 相场方法, 生长动力学, 初始形核率, 初始形核半径

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

王进, 马文婧, 刘玉周, 吕美妮, 张开靖. 非晶一次晶化过程微观组织演化和生长动力学的相场法研究[J]. 计算物理, 2022, 39(4): 403-410.

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.

图/表 9

图1 (a)、(b)、(c)一次晶化模拟结果与(d)Fe83.7B14.8Cu1.5合金一次晶化TEM图片[25]

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

图2 不同初始形核率情况下，非晶一次晶化微观组织演化(a)~(d) 0.34%，(e)~(h) 0.98%，(i)~(l) 1.63%；(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.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

图3 不同初始形核率情况晶粒尺寸的分布

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

图4 不同初始形核率, 非晶一次晶化分数随时间的变化

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

表1 不同初始形核率情况非晶一次晶化的体积分数随演化时间变化的指数拟合关系

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

图5 不同初始形核半径情况非晶一次晶化微观组织演化 (a)~(d) 2 nm, (e)~(h) 5 nm, (i)~(l) 10 nm; (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.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

图6 不同初始半径情况下晶粒个数随晶粒尺寸的变化

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

图7 不同初始形核半径情况晶化分数随演化时间的变化

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

表2 不同初始形核半径情况非晶一次晶化的晶化分数随演化时间的指数拟合

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

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非晶一次晶化过程微观组织演化和生长动力学的相场法研究

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

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