Analysis of the Correlation Between the Energy and Crystallographic Orientation of Grain Boundaries in Fe Based on Atomistic Simulations

doi:10.11900/0412.1961.2023.00172

Acta Metall Sin

2024, Vol. 60

Issue (9): 1289-1298 DOI: 10.11900/0412.1961.2023.00172

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Analysis of the Correlation Between the Energy and Crystallographic Orientation of Grain Boundaries in Fe Based on Atomistic Simulations

HUANG Zengxin¹, JIANG Yihang², LAI Chunming³, WU Qingjie², LIU Dahai²(

), YANG Liang²(

)

^1.Engineering Training Center, Nanchang Hangkong University, Nanchang 330063, China
^2.School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China
^3.School of Mechanical and Electrical Engineering, Hunan Chemical Vocational Technology College, Zhuzhou 412000, China

Cite this article:

HUANG Zengxin, JIANG Yihang, LAI Chunming, WU Qingjie, LIU Dahai, YANG Liang. Analysis of the Correlation Between the Energy and Crystallographic Orientation of Grain Boundaries in Fe Based on Atomistic Simulations. Acta Metall Sin, 2024, 60(9): 1289-1298.

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Abstract

The grain boundary (GB) energy is one of the fundamental structure-dependent properties of GB and plays a crucial role in the GB-related behaviors and properties of polycrystalline materials. An in-depth understanding of GB energy will help to explore the corresponding mechanisms and provide significant guidance for tailoring material properties based on GB engineering. The crystallographic orientation of GB strongly dominates the GB energy. However, a relatively comprehensive understanding of the orientation dependence of the GB energy is still lacking, especially for bcc materials. In this study, the energies of 1568 tilt GBs in bcc Fe, which covers the misorientation angle (θ) of 0°-180° and 40 distinct misorientation axes ( O ), were computed using the cutoff sphere bicrystal molecular dynamics model. The energy dataset was used to statistically analyze the correlation between GB energy (γ) and GB crystallographic orientation, thereby revealing the underlying mechanisms. The results show that the tendencies of γ-θ correlationcan be considerably different in the high-angle range for GBs with distinct O. Statistically, GB energies increase with θ and disorientation angle in the low-angle range and then level off for higher angles. The energies for noncoincident site lattice (non-CSL) GBs are not necessarily higher than those of CSL GBs and follow the same trend in the low-θ range as CSL GBs. The energies of the tilt GBs decrease with the variation of O from the central regions to the edge and then the corners of the stereographic triangle due to the increasing tendency of the symmetry of the boundary structure. Therefore, the lowest energies are observed for GBs with O close to <111>. Relatively low energies are not observed for GBs terminated by low-index or dense planes. The GB energy shows an overall increasing trend with the surface energy of the boundary plane until a plateau in the GB energy is reached. No distinct correlation is observed between the GB energy and coincidence index (Σ) value. However, the cusp in the γ(θ) curve for GBs with a common O is found to be generally located at the GB with a much lower Σ than its neighboring GBs. Additionally, the potential correlations and laws concerning GB energy and its crystallographic orientation for bcc metals are observed to be partially similar or consistent with those of fcc metals.

Key words: grain boundary grain boundary energy crystallographic orientation bcc atomistic simulation

Received: 17 April 2023

ZTFLH:

TG111

Fund: National Natural Science Foundation of China(52065045);Program Foundation for Distinguished Young Scholars of Jiangxi(20192BCBL23002)

Corresponding Authors: LIU Dahai, professor, Tel: 15180185399, E-mail: dhliu@nchu.edu.cn
YANG Liang, Tel: 17770181534, E-mail: L.yang@nchu.edu.cn

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	HUANG Zengxin
	JIANG Yihang
	LAI Chunming
	WU Qingjie
	LIU Dahai
	YANG Liang

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https://www.ams.org.cn/EN/10.11900/0412.1961.2023.00172 OR https://www.ams.org.cn/EN/Y2024/V60/I9/1289

Fig.1 Illustration for constructing a spherical cell containing a grain boundary (GB) with misorientation (Δ g ) and orientation of GB plane ( n ) ( g₀—orientation of initial monocrystal, g_A —orientation for grain A,g_B —orientation for grain B)

Fig.2 Variation of GB energies (γ) with misorientation angle (θ) for GBs with some selected misorientation axes ( O ) in the energy dataset

Fig.3 Computed GB energies plotted against θ for all GBs in the dataset (θ = 5° and 10° are the corresponding misorientation angles of non-coincident site lattice (non-CSL) GBs, other angles marked out by blue triangles stand for CSL GBs) (a), and the energy curves derived from the Read-Shockley model and that obtained by least-squares fitting to the GB energies (i.e., blue open circles) averaged using a constant θ interval of 5° for all GBs in Fig.3a (b)

Fig.4 GB energies plotted against disorientation angle (α) for all GBs in the dataset (The red curve was obtained by least-squares fitting to the discrete GB energies)

Fig.5 Variation of GB energy with O presented in the <hkl> orientation space (a) and standard stereographic triangle (b) (Each data point stands for the average energy of GBs with a common O in the energy dataset. To better exhibit the O -dependency of GB energy, the energies of GBs with six axes located near the three corners of triangle were additionally calculated)

Fig.6 Variation of GB energy with n presented in the standard stereographic triangle (a) and form of deviation angle ( $φ n → (110)$ ) (The red curve was determined by least-squares fitting to the GB energies (open circles) averaged using a deviation angle interval of 0.8°) (b)

Fig.7 Surface energies simulated for free surfaces intentionally selected in bcc Fe (a), variations of the fitted surface energy with the GB plane (b), and GB energy with the corresponding surface energy of GB plane (The magenta circles and curves stand for respectively the average GB energies obtained at a surface energy interval of 8 mJ/m² and the corresponding least-squares fitting) (c) in the dataset

Fig.8 GB energies plotted against coincidence index (Σ) for all GBs in the dataset (a); the GB energies with relatively low Σ (i.e., Σ < 30) marked on the γ-θ curves for selected O of <100> (b), <211> (c), and <541> (d)

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