金属学报, 2026, 62(5): 705-720 DOI: 10.11900/0412.1961.2025.00317

综述

金属材料晶界结构的拓扑性质与表征

朱思瑛,, 易敏, 郭万林,

南京航空航天大学 航空航天结构力学及控制全国重点实验室 南京 210016

Topological Properties and Characteristics of Grain Boundary Structure in Metallic Materials

ZHU Siying,, YI Min, GUO Wanlin,

State Key Lab of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

通讯作者: 朱思瑛,siying.zhu@nuaa.edu.cn,主要从事金属材料晶界结构的力学性能研究;郭万林,wlguo@nuaa.edu.cn,主要从事飞行器结构安全和智能化方面的力学理论与关键技术研究

责任编辑: 梁烨

收稿日期: 2025-10-10   修回日期: 2025-12-24  

基金资助: 国家自然科学基金项目(T2293691)
中央高校基本科研业务费项目(NJ2024001)
江苏省自然科学基金项目(BK20243065)
江苏省自然科学基金项目(BK20243044)
江苏省自然科学基金项目(BK20251410)
机械结构力学及控制国家重点实验室研究基金项目(MCAS-L-0525K01)

Corresponding authors: ZHU Siying, associate professor, Tel: 18202754742, E-mail:siying.zhu@nuaa.edu.cn;GUO Wanlin, professor, Tel: 13222058918, E-mail:wlguo@nuaa.edu.cn

Received: 2025-10-10   Revised: 2025-12-24  

Fund supported: National Natural Science Foundation of China(T2293691)
Fundamental Research Funds for the Central Universities(NJ2024001)
Natural Science Foundation of Jiangsu Province(BK20243065)
Natural Science Foundation of Jiangsu Province(BK20243044)
Natural Science Foundation of Jiangsu Province(BK20251410)
Research Fund of State Key Laboratory of Mechanics and Control for Aerospace Structures(MCAS-L-0525K01)

作者简介 About authors

朱思瑛,女,1994年生,副教授,博士

摘要

金属晶界的拓扑性质对其力学、电学及化学性能具有关键影响,是晶界工程(GBE)研究的核心内容之一。本文系统综述了金属晶界结构拓扑特性在不同尺度上的研究进展,涵盖从原子尺度的拓扑结构到介观尺度的晶界网络拓扑两个方面。首先,总结了晶界原子结构拓扑研究的现状,包括重位点阵(CSL)模型、位移对称完整(DSC)点阵理论、晶界位错网络的拓扑表征以及拓扑缺陷的分析。随后,介绍了介观尺度晶界网络的表征方法,重点阐述了基于离散胞复形(DCC)的拓扑研究框架,并系统分析了晶界网络的拓扑特性。最后,展望了晶界拓扑研究在材料设计中的潜在应用方向。

关键词: 金属材料; 晶界; 拓扑; 微观结构

Abstract

The topological properties of metallic grain boundaries are crucial in determining their mechanical, electrical, and chemical behaviors, making them a major focus of grain boundary engineering. This study systematically reviews recent advancements in understanding the topological characteristics of metallic grain boundary structures at various scales, including atomic-scale topological configurations and mesoscale grain boundary network topology. It begins by summarizing current research on the topology of grain boundary atomic structures, including the coincidence site lattice model, displacement shift complete lattice theory, topological characterisation of grain boundary dislocation networks, and analysis of topological defects. It then introduces characterisation methods for mesoscale grain boundary networks, emphasising a research framework based on discrete cell complexes and systematically examining the topological properties of these networks. Finally, potential applications of grain boundary topology research in materials design are discussed.

Keywords: metallic material; grain boundary; topology; microstructure

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本文引用格式

朱思瑛, 易敏, 郭万林. 金属材料晶界结构的拓扑性质与表征[J]. 金属学报, 2026, 62(5): 705-720 DOI:10.11900/0412.1961.2025.00317

ZHU Siying, YI Min, GUO Wanlin. Topological Properties and Characteristics of Grain Boundary Structure in Metallic Materials[J]. Acta Metallurgica Sinica, 2026, 62(5): 705-720 DOI:10.11900/0412.1961.2025.00317

2016年诺贝尔物理学奖授予Thouless、Haldane和Kosterlitz,以表彰他们在拓扑相变领域的开创性贡献,标志着拓扑概念在凝聚态物理中的核心地位日益凸显。金属材料多具有晶体结构,其原子周期性排列于晶格中。理想晶体具有完美的周期序,但实际金属多为多晶体系,由取向各异而晶体结构相同的晶粒构成。晶界(GB)作为二维面缺陷,在材料科学中至关重要。它不仅是腐蚀、断裂等失效行为的优先发生区域,更是调控材料力学、电化学及催化性能的关键载体。近年来,研究[1,2]表明,晶界及其网络具有拓扑相特征,这一突破性认识引发学术界对“晶界拓扑-材料性能”构效关系的深入探索。尤其在晶界工程(GBE)框架下,通过多尺度拓扑结构设计并优化材料性能已成为前沿方向。当前,有关晶界结构拓扑性质和表征的研究可以大致分为两类:基于晶体几何学的晶界原子尺度的局部结构研究,基于代数拓扑的介观尺度的全局晶界网络结构研究。本文系统地梳理了晶界在原子尺度的拓扑研究及其对理解晶界性能的重要作用;整理了晶界网络的拓扑研究,着重介绍了代数拓扑中离散胞复形方法在解读晶界网络结构信息的创新性和前沿性;最后,进一步总结现有研究的思路,并为金属材料构效关系的研究提供参考。

1 晶界结构及其重要性

金属多晶材料由大量取向各异的晶粒构成,晶界(图1[3])作为晶粒之间的界面,对材料的力学行为、热稳定性、电学特性以及抗腐蚀性能具有决定性的影响[4~10]。研究[11~13]表明,晶界的这些特性与其拓扑结构密切相关。晶界的拓扑结构包括晶界原子排列、晶界位错、晶界取向差等,这些结构共同决定了晶界的能量状态和性质。例如,由重合点阵密度倒数Σ定义的特殊晶界(如Σ3孪晶界)通常表现出较低的界面能和优异的稳定性,而随机大角度晶界则往往成为材料性能的薄弱区域。因此,通过精确调控晶界的拓扑结构,可实现对材料性能的定向优化,这正是现代晶界工程的核心目标。

图1

图1   晶界结构的历史模型[3]

Fig.1   Historical models for grain boundary structure[3]

(a) amorphous cement model, uncrystallized atoms (black dots) fill the interstices between misoriented grains formed by rigid crystal units (rectangles)

(b) ordered boundary model, when rotated 36° around the [100] axis, one in every five atoms (black dots) at the interface is in a coincident position

(c) boundary transition region proposed, this model assumed that atoms (black circles) in the vicinity of the boundary would adopt relaxed positions


从微观尺度看,晶界作为晶体缺陷的聚集区,其原子级拓扑结构(如重位点阵(CSL)/位移对称完整(DSC)几何构型和位错网络)直接主导了原子扩散、位错运动以及相变等过程的发生[2,14,15],这些结构通过低配位原子和晶格应变形成高活性微环境,构成了材料介观和宏观性能的物理基础。在介观尺度上,晶界网络的代数拓扑特性(如Σ3特殊晶界的连通性)构建了低能渗流网络,通过显著提升耐腐蚀性能以抑制晶间的裂纹扩展,并通过增强断裂韧性促进裂纹偏转等效应[16,17]。宏观尺度则体现了晶界拓扑工程的实际价值,如力学性能的位错钉扎强化效应,以及多场耦合环境下跨尺度拓扑机制等[18],这些研究为材料设计提供了新范式(图2[19])。

图2

图2   晶界相图及其在材料设计中的应用[19]

Fig.2   Grain boundary (GB) phase diagrams and their applications for materials design[19] (T—temperature, TM—melting temperature, X—solid solubility of Ga in Al, XMax—maximal solid solubility of Ga in Al, MC—Monte Carlo method, MD—molecular dynamics. P and N—positive and negative transport channels, respectively)


自1986年纳米晶材料首次被报道以来,研究人员[20]致力于通过晶界工程优化材料性能。晶界工程的核心是通过调控晶界特征分布(GBCD)和晶界连通性,从而抑制晶间脆化、疲劳断裂等失效模式。金属材料的性能本质根植于其多尺度微结构的协同演化。从宏观尺度下毫米级别晶粒的几何排布,到介观尺度亚微米级别位错胞的网络,再到纳米尺度溶质原子的偏聚态和原子键等特征,跨越数个数量级的结构共同决定了材料的强度、塑性等性能[21~28]。晶界作为决定材料宏观性能的核心结构单元,不仅是位错滑移、元素扩散和相变等微观过程的关键通道,更是应力集中、腐蚀萌生和裂纹扩展的敏感区域[29~31]。晶界对力学强度、高温稳定性、耐腐蚀性能以及电学性能的调控作用显著[32~37]。这样的调控效果推进了晶界工程这一前沿研究领域的发展,其核心在于通过精准调控晶界的类型、分布、取向以及化学状态,更好地实现对材料性能的剪裁设计[38~43]。借助现有表征技术和计算模拟手段,已发展出了热机械处理、晶界偏析修饰、外场诱导重构等创新方法,成功制备出了兼具超高强度和优异韧性的梯度纳米晶金属、抗辐射损伤的纳米孪晶Cu等突破性材料。大塑性变形(SPD)工艺在晶界工程中具有核心价值,可以通过等通道转角挤压(ECAP)、高压扭转(HPT)等技术引发再结晶过程[44],在材料内部引入高密度位错(位错密度> 1014 m-2),驱动晶界发生原子级拓扑重构:一方面,定向提升低ΣCSL晶界(尤其Σ3孪晶界)比例,构建贯穿性低能渗流网络,从而阻断晶间腐蚀路径;另一方面,优化晶界取向差分布,抑制随机大角度晶界连通性。这种跨尺度调控同步实现了性能的协同强化,高密度晶界通过位错钉扎效应产生Hall-Petch强化,同时Σ3网络促进裂纹偏转。SPD工艺突破了传统性能倒置关系,标志着晶界工程从被动表征迈向主动设计的变革[1,45,46]。通过大塑性变形工艺制造的纳米晶材料因其极高的晶界密度和三叉晶界密度,展现出远超传统多晶材料的强度[47]。当晶界密度因晶粒细化至纳米尺度(晶粒尺寸< 100 nm)而呈指数级增长时,界面主导效应引发材料行为的根本性变革,在传统多晶材料中作为“缺陷通道”的晶界网络,在纳米晶体系中转变为承载质量传输和力学响应的主体相[48]

近年来,晶界研究主要围绕以下几个方向展开。(1) 晶界原子结构和能量特性。借助高分辨率透射电镜(HRTEM)、原子探针断层扫描(APT)等实验手段,研究者能够解析晶界的原子排布特征,并通过CSL模型揭示其周期性结构特征。结合分子动力学(MD)和第一性原理计算,进一步建立晶界结构与能量之间的联系,为预测晶界稳定性和设计低能态晶界提供理论依据[3,11,49]。(2) 晶界动力学行为研究。晶界迁移及其对外界条件的响应是晶界研究的重要议题。近年来,相场法和Monte Carlo方法被广泛用于模拟再结晶和晶粒长大过程;同时,实验与计算相结合的研究揭示了溶质原子偏析对晶界迁移的拖曳效应,并进一步阐明了其在提升材料热稳定性方面的作用[7,50]。(3) 晶界调控和力学性能。晶界作为位错运动的重要障碍,其与位错的交互作用(如位错塞积或透射)直接影响材料的强韧化机制。在此基础上,晶界工程提出通过优化特殊晶界(如低ΣCSL晶界)比例来改善材料的蠕变和疲劳性能。此外,在纳米晶材料中,晶界主导的塑性机制(如晶界滑移)已成为研究前沿[51,52]。(4) 多尺度计算和数据驱动方法。随着计算手段的发展,从原子尺度的密度泛函理论到介观尺度的相场方法,跨尺度模拟逐渐成为理解晶界行为的重要工具。与此同时,机器学习与高通量计算的结合,加速了晶界数据库的构建和性能预测模型的发展,推动了材料设计由经验驱动向理论和数据指导的范式转变[53~58]

拓扑学主要研究空间连续变形下的不变特性,在晶界工程领域,拓扑不仅为理解晶界结构本质提供数学框架,更赋予了研究者从“几何连通性”和“稳定性”角度重构材料的能力。传统几何和能量描述往往关注局域度量信息,如晶粒尺寸分布、晶界曲率、错配角度分布、原子间距等。这些量依赖于坐标尺度、度量空间的定义:数学上定义在具有度量的流形上;改变尺度、旋转、平移或形变都会影响其数值。拓扑描述关注的是结构的连通性及其中的“孔洞”结构,不依赖度量,只与空间的粘连方式相关:数学定义在纯拓扑空间上;拓扑性质在连续形变(不撕裂、不黏合)下不变,从而可以捕捉抽象的结构本质信息。在现有研究成果中,晶界特征的拓扑研究[59~61]以及晶界网络的拓扑特征(包括界面曲率、结点连接度、空间周期性等),深刻影响着应力传递效率、腐蚀路径选择和电热输运特性[62,63]。下文分别对晶界原子结构拓扑以及晶界网络拓扑的研究进展进行简要概述。

2 晶界原子结构拓扑表征

早在20世纪50~70年代,Hirth和Balluffi[64]及Gleiter[65]等的工作就为晶界能和结构模型奠定了理论基础。Hirth和Balluffi[64]重点研究了界面内位错结构和小角度晶界的能量公式,这些早期理论为后续探讨晶界原子级细节提供了指导。Gleiter[65]则从纳米结构的角度揭示了晶界在细晶材料中的特殊行为,为超塑性和纳米强化给出了初步解释。随着HRTEM、APT等技术的发展,研究人员开始在原子尺度对晶界进行直接表征。

Seidman团队[67,68]利用APT技术精确测定了晶界中溶质原子的分布和局部成分,揭示了溶质在晶界处的富集现象及其对晶界能的调控作用。针对晶界中溶质分离现象,近年来,Wagih等[69]利用机器学习和高通量计算方法建立了晶界溶质富集能谱,为系统性设计低能量或特殊功能晶界提供了数据基础。Thomas团队[7,70]借助分子动力学模拟研究了晶界滑移和迁移机制,结合连续介质理论探讨外场驱动下晶界结构的响应,为微观机制与宏观行为的联系提供了定量描述。张泽团队[71]揭示了滑动主导变形是如何在Pt双晶体的一般倾斜晶界下完成的,该研究能够从原子尺度理解一般晶界在多晶材料中的滑动方式。在纳米晶材料设计领域,卢柯团队[8,47,72~74]首创梯度纳米结构金属材料,通过晶界网络的梯度分布实现高强度与高塑性的协同,梯度纳米孪晶Cu的强度能达到粗晶Cu的10倍,同时保持良好的导电性,该研究澄清了30年来关于纳米金属强度反常现象的争议,为晶界工程提供了理论框架。王江伟团队[66,75]进一步揭示了晶界塑性由过剩体积这一微观自由度主导,其触发的瞬态拓扑转变(TTT)过程(图3[66])可作为塑性变形“触发器”,协调晶界迁移、位错发射等传统机制,并通过弛豫或元素偏析恢复极小尺寸晶粒的强化效应。此外,一些团队还关注了晶界内复杂面的相转变,通过调控溶质和微结构实现界面相变,从而改善材料高温稳定性和抗蠕变性能;研究了晶界复合体结构和成分的局部变化对晶体动力学的影响等[76~79]

图3

图3   由过剩体积通过瞬态拓扑转变(TTT)引发晶界塑性变形的示意图、高分辨TEM (HRTEM)像及晶格应变图[66]

Fig.3   Schematics (a, b) and high-resolution TEM (HRTEM) images (c-i) of GB plastic deformation initiated by excess volume through transient topological transition (TTT) (Scale bar: 2 nm)[66]

(a) uniform lattice straining in response to external load in crystalline solid

(b) plastic deformation initiated preferentially at the GB through excess-volume-assisted TTT (The red and blue circles denote atoms with excess volume above and below that of the perfect lattice (black circles), respectively. G1 and G2—grain 1 and grain 2)

(c-e) in situ HRTEM images showing TTT at general high-angle grain boundaries in Au with increasing compressive loading (Insets in Figs.3d and e are lattice strain images)

(c) atomic structure of a 24° [11¯0] asymmetrical tilt GB in Au (Two alternate types of facets are delineated by the white and yellow dashed lines)

(d) TTT of the originally faceted GB into an orthogonal configuration (yellow area) under compressive loading (σ) (TTT mainly occurs at the upper edge of GB)

(e) continuous expansion of the TTT region along the GB with limited thickening into G2

(f-i) TTT at a curved GB in polycrystalline Au

(f, g) atomic structures of the flat and curved segments of the initial 32° [11¯0] tilt GB

(h, i) TTT at the flat and curved GB segments under [112]G1-compression (indicated by the black arrow)


在原子尺度上,晶界本质为晶格失配引发的拓扑缺陷集合[80~83],通过调控设计相邻晶粒的取向差角和旋转轴,可精确设计晶界的失配位错阵列和局域原子配位[84]。当晶粒取向满足特定Σ值时,晶界处形成周期性重合点阵,这类低能界面可显著降低裂纹敏感性,例如,纳米孪晶Cu中存在高密度Σ3晶界,其强度可以达到粗晶Cu的10倍,而不损失其导电性[74]。双晶晶界的几何描述以五自由度宏观参数为核心,自由度包括晶粒间的取向差(3个自由度)和晶界平面取向(2个自由度),共同定义了晶界的几何构型[85~87]。在此基础上,CSL晶格可以定量描述两晶格的周期匹配关系,当两晶格点阵存在公共超晶格时,由其Σ表征[88];DSC晶格为CSL的倒易超晶格,可定义晶界平移对称性[89,90]。DSC矢量直接生成晶界本征缺陷——失配位错(disconnection),通过引入双晶平移对称性,其界面包含一种典型的“位错-台阶”组合缺陷。当取向差增大(Σ > 25)时,局部拓扑特征取代宏观参数主导的描述,此时需要根据晶体几何定义晶界类型[91~95]。向错(又称旋错,disclination)是材料科学和软物质物理中的一种重要的拓扑缺陷,与描述原子面剪切滑移的位错(dislocation)不同,其本质是晶体或有序介质中旋转对称性的破缺。本团队[96]定义了一类离散三叉晶界向错,用于分析Cu-0.4%Mg合金中的向错分布,这是一类在几何拓扑意义上的“瞬时缺陷结构 (instantaneous defect structure)”,对应于电子背散射衍射(EBSD)观测状态下的取向场几何特征,而非演化动力学路径的结果。这种缺陷会引入巨大的长程应力场,对材料的力学、电学及热学性能产生决定性影响[96~99]。向错作为由局部晶体取向场旋转不连续引起的拓扑缺陷,产生较强的长程力学应变场并与位错结构密切耦合,从而通过多条途径影响合金的宏观力学行为。然而,尽管已有研究[100~103]报道了向错或三叉晶界的存在及其与微观力学性能的关联,但该领域缺乏关于向错强度或密度与宏观力学参数之间定量关系的系统性研究。向错效应常与几何必需位错、位错墙、晶界相变、晶界偏析等耦合,单靠静态EBSD观测难以区分哪部分性能变化来自向错的长程应力场、哪部分来自局部结构或者化学成分的改变。因此,因果链条尚未被严格解耦。在塑性加工(如ECAP、HPT)和热激活(再结晶、晶粒粗化)过程中,与时间尺度相比,向错的生成或消散路径不同,现有静态测量不能反映此类演化动力学,而此类动力学对宏观疲劳和蠕变行为至关重要。此外,EBSD的空间分辨率、取向测量误差和后处理也会影响向错强度的反演结果,导致不同研究之间难以直接比较,且HRTEM、三维EBSD及原位表征技术目前尚未实现在大量样本上的常规化应用,因此难以基于二维EBSD实验结果的推断进行校验。

晶界结构在原子尺度的研究长期依赖晶体学与几何学,如图4[3,104],例如基于位错模型、配位多面体、局部应变场以及结构单元等方法对其进行描述。这些方法在理解特定类型晶界的能量、稳定性和迁移机制方面具有重要价值,但其本质仍然是几何或能量驱动的结构表征。它们能够解释局部原子排列的有序性,但难以揭示当外来元素偏聚、形成非晶或准晶型局部单元时,晶界在整体结构层面上发生的根本性转变。

图4

图4   通过蓝色立方晶格绕垂直于纸面的[001]轴旋转获得的共格点阵构型(重合点阵密度倒数Σ ≤ 25)[3]Σ3和Σ9晶界、Σ3晶界在应变驱动下的演化和Σ3 n 相互作用示意图[104]

Fig.4   Σ25 at 16° (a1), Σ13 at 22° (a2), Σ17 at 28° (a3), and Σ5 at 36° (a4) coincident site lattice configurations (reciprocal of coincidence site lattice (CSL) density Σ ≤ 25) obtained by rotations of the blue cubic lattice about a common [001] axis normal to the plane of the paper[3] (Black lines indicate the CSL repeat units); schematics of Σ3 (b1) and Σ9 (b2) boundaries, strain-driven evolution of a Σ3 boundary (b3), and Σ3 n interaction (b4)[104]


最新研究表明,晶界拓扑在材料性能上产生极大影响。例如,具有高连通性晶界网络的镍基超合金在蠕变过程中表现出更强的晶界滑移协调性和更高的蠕变寿命[105];而拓扑约束较强的晶界环结构可有效抑制裂纹萌生,提高疲劳抗力[106]。近年来,基于代数拓扑的分析进一步揭示了晶界网络连通度和孔洞结构在晶粒长大、再结晶以及晶界迁移等过程中的动态调控作用。因此,对晶界拓扑的定量刻画不仅能补充传统几何参数的不足,也为通过晶界工程实现材料性能优化提供了新的途径。随着研究深入,拓扑这一原本源于数学的概念,已在晶界工程和材料科学领域得到广泛认可与应用。研究[107]表明,晶界的原子化学偏析行为并非由宏观几何参数主导,而是由原子基序直接控制,如Fe晶界中B和C的偏析位置与局部原子排列的扭曲八面体或风筝形结构密切相关,这种原子级拓扑特征决定了溶质吸附能以及界面稳定性。近期,Devulapalli团队[2]通过原子分辨TEM表征和原子模拟发现,在Ti-Fe体系中,Fe的偏聚并非简单形成分层或常规的界面结构单元,而是诱导出具有五重对称性的二十面体“笼”(“cage”)结构。这些“cage”作为拓扑意义上的基本单元,能够以孤立体、双cage、簇集乃至类层状的方式组装,形成多个晶界相态(图5[2])。由于五重对称性与晶体周期性不相容,这些拓扑单元无法无限生长成层状或体相结构,而是导致晶界表现出非传统的准晶或玻璃状特征,这一发现使晶界原子尺度拓扑描述得到了广泛关注。而这里所使用的“拓扑”一词,特指晶界的几何形态特征,而非本文最开始的引言中提到的凝聚态物理意义上的量子拓扑序。

图5

图5   纯金属Ti中Σ13 [0001]倾斜晶界处Fe“笼状”结构的三维(3D)原子构型示意图和HAADF-STEM像,及对称Σ13 [0001] {7¯520}倾斜晶界原子结构的HAADF-STEM像[2]

Fig.5   Schematics and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of atomic configuration at tilt GBs in pure Ti[2]

(a) three-dimensional (3D) atomic configuration and HAADF-STEM image of Fe “cages” at the Σ13 [0001] tilt GB (The GB plane is perpendicular to the figure, with basal planes of the adjoining crystals marked as A and B. Fe atoms (red spheres) periodically segregate between successive basal planes, forming icosahedral cage-like units along the [0001] tilt axis. These “cages” are surrounded by Ti (grey and blue spheres) pentagonal rings lying in the basal planes. The rotated Ti pentagons (blue and yellow dotted lines) reproduce the projected 10-atom ring along [0001])

(b1, b2) HAADF-STEM images showing atomic structure of symmetric Σ13 [0001] {7¯520} tilt GBs in pure Ti

(b1) the initial GB without detectable level of segregation (The periodic arrangement of structural units designated as A, B, and C)

(b2) periodic Fe segregation to a GB resulting in the formation of novel structures at the GB core resembling “cages” (The cage centre (red area) is rich in Fe, the shell of the cage (blue area) is rich in Ti, this result is also verified by atomic scale spectroscopy)


3 晶界网络拓扑演化

晶界作为材料微观结构中的关键界面,从几何拓扑的视角出发,晶界网络可被视作包含节点、连通支、孔洞和环结构的复杂网络系统,代数拓扑工具为其结构表征和演化建模提供了新思路。在介观尺度,晶界网络的拓扑连通性决定了跨晶粒的协同响应机制。晶界网络的统计分布、晶界类型及其连通性直接影响材料的整体性能[108~110]。三维晶界曲率[111]和三叉晶界[112]构成介观调控枢纽[97,113],晶界网络连通决定拓扑缺陷的传递效率[98,114] (图6[114]),最终影响宏观塑性[96,99,115,116]。从拓扑结构表征到拓扑相态调控,晶界网络逐步成为连接材料微观构型与宏观性能调控的桥梁,为构建“材料拓扑-性能”关联模型奠定了基础。

图6

图6   {213¯0}[0001]取向下晶界位错网络的拓扑转变[114]

Fig.6   Topological grain boundary dislocation network transformations in {213¯0}[0001] orientation[114]

(a) adding Ti atoms (light blue) to the left half of the ground-state structure and performing high-temperature molecular dynamics simulations trigger a dislocation-pairing transformation in a quasi-2D geometry. The top panels clearly show how the green dislocation lines pair up to form purple ones. The gray atoms are hcp coordinated, while red and dark blue atoms highlight different dislocation core structures

(b) analogously, adding Ti atoms (dark red) to the left half of the metastable structure triggers a dislocation-unpairing transition locally

(c) topological transition of the grain boundary dislocation network upon defect absorption. The view of the grain boundary plane shows a paired-dislocation grain boundary island (nucleus in purple) inside the parent ground state (green dislocation lines)


晶界网络研究的发展始于对多晶材料性能调控的需求,从早期基于几何参数的统计描述逐步深化为多尺度、多参数的系统性探索[108,117~121]。在金属材料研究中,晶界网络(GBN)的结构和演化一直是理解性能优化的重要切入点[122~129]。传统的研究方法主要聚焦于几何和统计学描述,例如晶界角度分布函数、Σ分布、平均晶粒尺寸、连通性指标等。这些方法在常规组织研究中已得到了丰富的成果,能够揭示晶界类型与材料性能之间的统计关联,尤其在再结晶、织构演化和晶粒细化过程中展现了重要作用。在SPD条件下,这类手段也被广泛用于刻画晶界细化过程和大角度晶界比例的变化,为理解SPD驱动的组织优化提供了第一层次的信息。随着实验技术的进步,利用EBSD等技术[112,130,131],研究拓展至五参数联合分布。Rohrer团队[3,110,124]通过系统测量和建模工作,建立了晶界能和晶界特征分布的数据库,为进一步的网络设计提供了实验依据。Langdon团队[45,132]在实验上通过SPD工艺(如ECAP等工艺),对多晶金属的晶界网络进行了有效调控,从而提高了低能晶界的比例,改善了材料的高温抗蠕变和抗疲劳性能。Winning等[133]和Voyiadjis[134]提出晶界迁移及网络动力学模型,为预测整个多晶结构的晶界网络演化提供了理论指导。此外,通过统计网络模型和多尺度模拟方法,例如结合EBSD实验数据与图论算法,一些研究正致力于将原子级别表征结果与宏观网络设计结合,实现针对特定应用的晶界网络优化设计和拓扑结构优化设计[114,135]。多晶材料的性能受到晶界网络介观结构(介于原子与宏观尺度之间)的显著影响,其逐渐成为相关领域的研究重点[136~138]

然而,随着SPD诱导下材料内部晶界网络复杂性的增加(图7[139]),传统指标逐渐显现出局限性。首先,这些方法往往局限于局部统计特征,难以全面反映晶界网络的整体拓扑关联性。其次,晶界网络在SPD作用下呈现出显著的非均质性、层级性和非平衡态特征,单一的几何量度不足以捕捉其全局结构和长期演化规律。此外,不同尺度上的晶界连接模式往往隐藏着关键的物理机制,现有描述手段难以系统地整合这些跨尺度信息。对于SPD过程中GBN的演化规律及其对材料性能的全局性影响,现有工具难以给出系统性的解释。关于晶界如何相互连接的研究较为有限,已有研究尝试基于三叉晶界类型[112,131,140]、孪晶簇[44]、渗透理论[141]等对晶界连通性进行分类,但是拓扑数学工具的应用仍然较少。因此,亟需引入更加系统化和数学化的分析框架,以弥补现有描述方法的不足。

图7

图7   热轧钛合金板材的晶界图、反极图叠加晶界图及取向差角分布[139]

Fig.7   EBSD grain boundary maps (a-c), inverse pole figures overlapped with grain boundary maps (d-f), and corresponding misorientation angle distributions (g-i) of the hot-rolled titanium alloy sheet with different positions[139] (RD—rolling direction, ND—normal direction)

(a, d, g) center (b, e, h) 2/5 of the 1/2 sheet thickness (c, f, i) 4/5 of the 1/2 sheet thickness


代数拓扑,尤其是持久同调(persistent homology)等拓扑数据分析方法,提供了一种超越传统几何统计的手段。该方法能够从全局角度捕捉晶界网络的拓扑特征,刻画其连通性、孔洞和高阶环路等多尺度信息[108,140~146],进而揭示SPD条件下GBN演化的深层规律。这类方法不仅能够补充传统的几何量度,还有望为在晶界工程与性能调控之间建立更严谨的“构效关系”提供理论基础和工具支持。Wanner团队[147]提出了一种新的方法,利用同调理论(homology)分析模拟多晶体的力学响应场拓扑结构,并结合晶体取向数据进行分析。Watanabe团队[148]研究表明,在疲劳实验中循环应力诱导晶粒粗化,形成“菱形”晶界排列,导致晶界滑移主导的疲劳断裂,通过控制晶界连通性和三叉晶界类型(如R0/R1型),可抑制疲劳裂纹萌生,他们由此提出了基于分形维数(fractal dimension)的晶界连通性量化方法,并得到推广运用[149]。Zhu等[1,150]提出,可利用Euler示性数分析晶界网络结构拓扑相变,并结合材料力学性能跃变对其进行模拟预测。

离散胞复形(DCC)提供了一种基于代数拓扑的几何-拓扑统一表述方法[151,152]。这种代数拓扑框架不仅便于算法化处理,还能自然地引入一系列拓扑不变量来刻画GBN的复杂演化,能够完整编码GBN的连通性与局部几何关系。传统的晶界演化模拟,如相场模型和Monte Carlo方法,以体系自由能最小化为核心,能有效描述晶界曲率、表面张力和取向依赖能等热力学驱动力,以及随时间变化的界面迁移和晶粒粗化行为。然而,这类方法主要表征连续的形貌演化,对晶界网络的拓扑重构(如三叉晶界的生成和湮灭、晶界网络的环路断裂或再连接)的敏感性有限。相比之下,基于代数拓扑的DCC框架以顶点、边、面构成的离散复形表示微观结构,不依赖具体能量势函数,关注的是体系的连通性和高阶拓扑不变量演化(如Betti数与同调群)。这种表示方式可直接刻画晶界网络的整体拓扑形态和连接关系,尤其适用于分析非平衡或力驱动过程下的复杂拓扑演化。

DCC将三维晶界网络结构映射到离散胞复形代数拓扑空间上(即四叉节点(quadruple node)、三叉晶界(triple junction)、晶界(grain boundary)、晶粒(grain)),如图8[1,153]所示。用一组多面体(M)描述多晶材料,M中的p-胞在p = 0、1、2、3时分别代表顶点、边界、多边形面和多面体,这是代数拓扑中称为胞复合体的组合结构的几何实现。从拓扑学的角度来看,晶界结构是一个3-复形,具有不同拓扑维度的子结构集合。通过不同维度子结构的划分,可以计算DCC模型中晶界网络四个维度子结构复形之间的边界算子(boundary operators)。在DCC框架中,材料结构被离散为有限个由顶点、边、面和体元组成的胞复形。一个p-胞表示p维单元。采用边界算子p:CpCp-1定义p-胞与其边界(p-1)-胞的对应关系,例如,一条边对应于它的两个端点。由此形成的链复形(Cp,p)的同调群定义为Hp=kerp  /  Im(p+1),其中,Hpp阶同调群,ker(p)为边界算子(p)的核,Im(p+1)p的像,其详细定义可见参考文献[151]。根据获得的边界算子构建离散Laplacian算子(discrete Laplacian,L),从而可以计算拓扑特征不变量Betti数(表征结构在不同维度的偶联程度)和Euler示性数(表征拓扑相与相变的发生)。本团队研究[1,153]表明,对于实验数据(如EBSD数据)和模拟结构,首先根据晶粒的几何邻接关系构建DCC框架;然后根据晶界网络结构信息,计算边界算子。通过计算边界算子矩阵并求解其核与像的维数,得到不同的Betti数:连通区域数(β0)、环结构数(β1)和孔洞数(β2)。上述计算可通过自定义函数代码,或者直接使用GUDHI、Ripser 或Dionysus等开源程序计算。在描述GBN时,使用Betti数(β0β1β2)度量不同维度的拓扑特征:β0表示GBN中孤立晶界结构的数量,可以揭示GBN的连通性;β1刻画了晶界表面环的数量,反映GBN中的闭合循环和复杂连接;β2对应完全由大角度晶界包围的晶粒数量,从而直接关联到再结晶过程中由亚晶粒到新晶粒的形成。Euler示性数(χ= β0 - β1+ β2)则作为全局拓扑不变量,反映GBN整体形态的相变特征。通过这一系列拓扑描述符(如Betti数、Euler示性数等),本团队从晶界网络连通关系和环结构出发,量化了材料在大塑性变形过程中的结构形态重构,上述描述符反映的是结构层面的拓扑不变量,与体系能谱或量子态无关。通过这些描述指标,DCC可以系统描述SPD过程中由连续动态再结晶(CDRX)所引起的介观晶界网络结构拓扑重构,从而为理解和设计晶界工程提供新的量化工具。近年来,本团队还将晶界网络的拓扑研究与有限元(FEM)相结合(图8[1,153]),提供了一种新的方法来预测和解释SPD过程中的微观组织拓扑演化与宏观力学性能变化的关系。

图8

图8   3D晶界网络与离散胞复形的映射关系,不同大塑性变形(SPD)工艺处理的演化范围[1],3D晶界网络的连续动态再结晶(CDRX)演化过程示意图,及Betti数在有限元(FEM)样品中的分布[153]

Fig.8   Mapping relationship between 3D grain boundary network and discrete cell complex structure (a)[1], evolution ranges under different SPDs (SPD—severe plastic deformation, HAGBs—high angle grain boundaries, ARB—accumulative roll bonding, HPT—high-pressure torsion, ECAP—equal-channel angular pressing) (b)[1], schematics of 3D grain boundary network evolution during CDRX (LAGB—low angle grain boundary) (c)[153], and Betti number distributions through finite element method (FEM) sample (d)[153]


4 总结与展望

作为金属多晶材料的关键结构组成,晶界及其连接方式在大塑性变形加工及后续服役过程中均扮演着核心角色。本文系统梳理了从原子尺度到晶界网络尺度的晶界拓扑研究进展,展现了拓扑理论在材料科学领域的应用潜力和未来前景。首先,晶界性能从根本上由其原子结构决定,本文从原子尺度拓扑出发,探讨了晶界结构的形成机制及其与性能之间的构效关系。其次,多晶材料内部多个晶界相互连接形成网络,其拓扑结构对材料宏观性能具有重要影响。在总结现有研究方法与局限性的基础上,重点介绍了基于代数拓扑理论的最新研究进展。晶界的拓扑演化正逐渐成为理解和设计先进材料性能的关键语言。原子尺度上的局域配位和特殊晶界构型塑造了界面的能量、扩散和反应活性;而介观网络中的连通性和环结构则深刻影响着再结晶、裂纹扩展和强韧化机制。随着高分辨率显微技术、高能衍射显微镜(HEDM)和实时EBSD等先进表征手段的不断突破,以及相场模拟、Monte Carlo方法等多尺度模拟技术的深入发展,晶界拓扑的动态演化正逐渐从“难以观测”走向“可视、可预测和可调控”。

在实际分析过程中,几何或能量描述往往高维且冗余,难以直接与性能对应。而拓扑描述可视作对高维几何结构的信息压缩和不变量提取,在结合机器学习建模的情况下,拓扑特征可以提供比几何或者能量特征更稳定、更物理可解释的输入空间。且使用DCC描述介观尺度晶界结构的优势在于其对拓扑结构变化(结点、通道、孔洞等结构)的敏感性和无能量假设的普适性,但其缺乏显式时间演化机制。因此,未来将DCC与能量驱动的模型耦合可能会是一个重要方向。例如,可将DCC提取的瞬时拓扑描述符嵌入相场或Monte Carlo框架,用于实时追踪晶界网络中的拓扑转变,从而在统一框架下兼顾热力学精确性与拓扑敏感性,进而获得更好的模拟分析与预测效果。

展望未来,鉴于晶界拓扑结构的关键作用,晶界工程亟需构建跨尺度的“拓扑-性能”映射框架,并充分利用数字化计算能力,结合高通量模拟与机器学习方法,以推动晶界结构的智能化设计。特殊子结构(如三叉晶界和四重节点)及极端晶界类型对材料失效机制的主导作用将成为新的研究前沿,对这些结构的拓扑分析和理解尤为关键。可以预见,基于拓扑原理的晶界设计正为材料科学开辟全新路径:通过实现原子-网络-宏观的多尺度协同,有望真正达成结构-性能一体化调控,为航空航天高温合金、能源器件和纳米功能材料的可控制造奠定理论基础。这一进展不仅将极大拓展晶界调控策略在材料制备工艺和服役寿命中的应用价值,更标志着材料科学正迈向一个以“拓扑驱动”为核心的新时代。

参考文献

Zhu S Y, Borodin E, Jivkov A P.

Topological characteristics of grain boundary networks during severe plastic deformations of copper alloys

[J]. Acta Mater., 2023, 259: 119290

DOI      URL     [本文引用: 9]

Devulapalli V, Chen E Z, Brink T, et al.

Topological grain boundary segregation transitions

[J]. Science, 2024, 386: 420

DOI      PMID      [本文引用: 6]

Engineering the structure of grain boundaries (GBs) by solute segregation is a promising strategy to tailor the properties of polycrystalline materials. Solute segregation triggering phase transitions at GBs has been suggested theoretically to offer different pathways to design interfaces, but an understanding of their intrinsic atomistic nature is missing. We combined atomic resolution electron microscopy and atomistic simulations to discover that iron segregation to GBs in titanium stabilizes icosahedral units ("cages") that form robust building blocks of distinct GB phases. Owing to their five-fold symmetry, the iron cages cluster and assemble into hierarchical GB phases characterized by a different number and arrangement of the constituent icosahedral units. Our advanced GB structure prediction algorithms and atomistic simulations validate the stability of these observed phases and the high excess of iron at the GB that is accommodated by the phase transitions.

Rohrer G S.

Grain boundary energy anisotropy: A review

[J]. J. Mater. Sci., 2011, 46: 5881

DOI      URL     [本文引用: 8]

Gleiter H.

On the structure of grain boundaries in metals

[J]. Mater. Sci. Eng., 1982, 52: 91

DOI      URL     [本文引用: 1]

Priester L. Grain Boundaries: From Theory to Engineering [M]. New York: Springer, 2012: 1

Randle V. The Measurement of Grain Boundary Geometry [M]. Boca Raton: CRC Press, 2017: 1

Han J, Thomas S L, Srolovitz D J.

Grain-boundary kinetics: A unified approach

[J]. Prog. Mater. Sci., 2018, 98: 386

DOI      URL     [本文引用: 2]

Schuh C A, Lu K.

Stability of nanocrystalline metals: The role of grain-boundary chemistry and structure

[J]. MRS Bull., 2021, 46: 225

DOI      [本文引用: 1]

Palumbo G, Aust K T.

Structure-dependence of intergranular corrosion in high purity nickel

[J]. Acta Metall. Mater., 1990, 38: 2343

DOI      URL    

Liu G H, Wang W G, Rohrer G S, et al.

{111}/{111} near singular boundaries in a dynamically recrystallized Al-Zn-Mg-Cu alloy compressed at elevated temperature

[J]. Acta Metall. Sin., 2024, 60: 1165

[本文引用: 1]

刘光辉, 王卫国, Rohrer G S .

高温压缩变形Al-Zn-Mg-Cu合金动态再结晶后的{111}/{111}近奇异晶界

[J]. 金属学报, 2024, 60: 1165

DOI      [本文引用: 1]

提高{111}/{111}近奇异晶界比例可增强Al-Zn-Mg-Cu合金晶界腐蚀抗力,为了解此类晶界形成机理并探索其调控方法,本工作将470℃、12 h和520℃、6 h双级固溶及冷轧后再结晶的Al-Zn-Mg-Cu合金样品分别在450、480和520℃进行应变速率为0.001 s<sup>-1</sup>、真应变为1.20的压缩变形,压缩后立即水冷。采用电子背散射衍射和基于五参数分析的晶界界面匹配定量表征方法对上述3个样品的显微组织和晶界特征分布进行观察分析。结果表明,高温压缩后的显微组织不均匀,存在间隔分明的细晶组织和粗晶组织,其中细晶组织中的晶界以小角度晶界(LAGB)为主,粗晶组织中的晶界以大角度晶界(HAGB)为主;粗、细晶组织中的{111}/{111}近奇异晶界({111}/{111}-NSB)比例均随压缩温度的升高而增大,其中经520℃压缩的试样,其LAGB中的{111}/{111}-NSB占总晶界的比例为8.77%,HAGB中的{111}/{111}-NSB占总晶界的比例为4.53%。进一步考察各试样的应力-应变曲线以及450℃压缩30%时的显微组织特征可见,应变介于0.05~0.70为稳态流变阶段,主要发生初次动态再结晶(DRX),其主要由粗晶及其HAGB构成。应变介于0.70~1.20为二次硬化阶段,主要发生二次DRX,其中不连续DRX (DDRX)和连续DRX (CDRX)同时进行,且优先发生在某些微区;不论是DDRX因形核和核心长大生成的HAGB,还是CDRX因亚晶合并引入的LAGB,均使对应微区的晶粒细化,导致样品总体流变应力急剧上升。二次DRX阶段,CDRX行为随压缩温度的提高而增强,{111}/{111}-NSB比例也随之增加,特别是LAGB中的{111}/{111}-NSB比例快速增加。

Wang G J, Vitek V.

Relationships between grain boundary structure and energy

[J]. Acta Metall., 1986, 34: 951

DOI      URL     [本文引用: 2]

Bulatov V V, Reed B W, Kumar M.

Grain boundary energy function for fcc metals

[J]. Acta Mater., 2014, 65: 161

DOI      URL    

Ratanaphan S, Olmsted D L, Bulatov V V, et al.

Grain boundary energies in body-centered cubic metals

[J]. Acta Mater., 2015, 88: 346

DOI      URL     [本文引用: 1]

Chen K T, Srolovitz D J, Han J.

Grain-boundary topological phase transitions

[J]. Proc. Natl. Acad. Sci. USA, 2020, 117: 33077

DOI      PMID      [本文引用: 1]

The formation and migration of disconnections (line defects constrained to the grain boundary [GB] plane with both dislocation and step character) control many of the kinetic and dynamical properties of GBs and the polycrystalline materials of which they are central constituents. We demonstrate that GBs undergo a finite-temperature topological phase transition of the Kosterlitz-Thouless (KT) type. This phase transition corresponds to the screening of long-range interactions between (and unbinding of) disconnections. This phase transition leads to abrupt changes in the behavior of GB migration, GB sliding, and roughening. We analyze this KT transition through mean-field theory, renormalization group theory, and kinetic Monte Carlo simulations and examine how this transition affects microstructure-scale phenomena such as grain growth stagnation, abnormal grain growth, and superplasticity.

Wang J W, Chen Y B, Zhu Q, et al.

Grain boundary dominated plasticity in metallic materials

[J]. Acta Metall. Sin., 2022, 58: 726

DOI      [本文引用: 1]

Grain boundaries (GBs) are important planar defects in polycrystalline materials, and they are crucial in plastic deformation and recrystallization of materials. A fundamental understanding of GB deformation kinetics is critical for material design using GB engineering. Although GB dominated structural evolutions have been reported to proceed via different modes, the disconnection-based model has recently become a widely acknowledged approach to unify the GB dominated plasticity. In this paper, recent progresses of GB dominated plasticity in metallic materials based on disconnection-mediated GB migration have been reviewed. Disconnection dynamics, including nucleation, propagation and interactions between different disconnections, were found dominating the shear-coupled GB migration. Lateral motion of different GB disconnections contributes to the overall GB migration, during which dynamic interactions prevail. In the three-dimensional network of GBs, GB-defect interaction and triple junctions can further influence the shear-coupled GB migration by providing extra disconnection sources, which readily change the intrinsic disconnection dynamics. These disconnection-based GB kinetics are generally applicable in the migration of GBs with different structures, as well as other modes of GB dominated deformation. Based on the aforementioned, the effects of GB plasticity on mechanical properties and deformation of metallic materials are further discussed. This review provides a unified understanding of disconnection-based GB plasticity, which not only enriches mechanistic understanding of interface plasticity in metallic materials but also holds important implications for GB engineering toward advanced high-performance metallic materials.

王江伟, 陈映彬, 祝 祺 .

金属材料的晶界塑性变形机制

[J]. 金属学报, 2022, 58: 726

DOI      [本文引用: 1]

晶界是多晶材料中一类重要的面缺陷,在材料的力学和物理化学性能调控中发挥着重要作用。深入理解晶界的塑性变形动力学机制是开展材料晶界工程调控的理论基础。本文从晶界的微观结构和晶界本征缺陷出发,详细总结晶界塑性变形机制的研究进展;在此基础上,围绕晶界阶错形核、扩展、交互作用的动力学机制,深入探讨晶界迁移的原子尺度动力学机制及其在不同因素下的表现形式,阐明不同晶界变形行为之间的关联关系,发展和完善晶界塑性变形理论,为金属材料的晶界工程调控提供理论指导。

Reed B W, Kumar M, Minich R W, et al.

Fracture roughness scaling and its correlation with grain boundary network structure

[J]. Acta Mater., 2008, 56: 3278

DOI      URL     [本文引用: 1]

Gao Y, Liu X, Wang Y Q, et al.

The role of special grain boundaries in enhancing creep performance in the welded joint of a novel Fe-Ni-based superalloy through aging treatment

[J]. Mater. Charact., 2025, 224: 115010

DOI      URL     [本文引用: 1]

Zheng X Y, Chen X, He M L, et al.

Multi-scale simulation of mechanical properties of 6XXX aluminum alloy based on crystal plasticity

[J]. Acta Metall. Sin., 2025, 61: 1758

DOI      [本文引用: 1]

6XXX age-strengthened aluminum alloys are extensively utilized across various fields, including construction, engineering machinery, and transportation, owing to their low density, good electrical conductivity and heat resistance, and excellent overall mechanical properties. Despite such widespread applications, there are no systematic computational frameworks for these alloys that are applicable across diverse processes, including microstructure simulations and performance predictions. Notably, to facilitate the material design and industrial production of 6XXX aged-strengthened aluminum alloys, the following steps are essential: analyzing the precipitation kinetics governing the mechanical properties of 6XXX aged-strengthened aluminum alloys, developing precipitation kinetics models, establishing corresponding strengthening models correlating microstructural features with key mechanical performance metrics, and performing mechanical simulations under standard service conditions to obtain stress-strain response characteristics. Accordingly, this study introduces a full-sequence computational model for 6XXX age-strengthened alloys based on the crystal plasticity theory. The proposed model is applicable to the investigation of several characteristics, including microstructure evolution, mechanical responses, and plastic deformations. Employing “structure-property” relationships as the entry points, the mechanical behaviors of 6XXX age-strengthened aluminum alloys are described through geometrical modeling and intrinsic relationship derivations. During this process, major factors influencing mechanical properties, including grain size and morphology, precipitation data and solid solution phases, and the characteristics of non-precipitation zones at the grain boundaries, are considered. The primary task involves computationally simulating the evolution of the size distribution and volume fraction of precipitated phases as well as variations in solid solution phase contents by sizing precipitated phases according to the grain size using the Kampmann-Wagner Numerical (KWN) method. According to the dislocation-density-based strengthening of materials, an age-strengthening model and a work-hardening model are established based on the interaction mechanism between precipitated phases and dislocations. The model tracks the evolution of yield strength and work-hardening properties with aging time. A method for computing the strength contribution from the precipitation-free zone at the grain boundary and a geometrical modeling strategy are proposed. The hardening model for 6XXX is selected based on the crystal plasticity finite element method, while uniaxial tensile plastic deformation is simulated to obtain stress-strain curves. The proposed multiscale analysis model of 6XXX age-strengthened aluminum alloys constructed based on the relationships among the alloy composition, aging process, microstructures, and mechanical properties of metallic materials provides a systematic framework for designing high-performance 6XXX age-strengthened alloys. It also highlights the key role played by computational mechanics in the development of new high-strength and high-toughness aluminum alloys, offering valuable insights. Furthermore, the analytical workflow of the study is extended to the crystal properties calculation package, which is universally applicable to studies on diverse age-strengthened materials, introducing its features and functions.

郑潇禹, 陈 辛, 何美玲 .

基于晶体塑性的6XXX铝合金力学性能多尺度计算

[J]. 金属学报, 2025, 61: 1758

DOI      [本文引用: 1]

6XXX系时效强化铝合金工程应用价值显著,但尚缺乏系统性的从微结构模拟到性能预测的计算框架。本工作旨在构建完整的多尺度计算流程,根据晶体塑性理论对6XXX铝合金设计了一个基于物理机制从微结构演变到塑性大变形力学响应分析的全序列计算模型。以“结构-性能”关系为切入点,将晶粒尺寸和形貌、析出相和固溶相信息、晶界无析出带特征等对力学性能的主要影响因素考虑在内,通过几何建模、构建本构关系的方式建立模型,对6XXX铝合金的力学行为进行描述。使用Kampmann-Wagner Numerical (KWN)方法模拟析出相的尺寸分布和体积分数演变并追踪固溶相含量;基于位错密度的材料强度学本构理论持续追踪屈服强度和加工硬化等特性随时效时间变化的规律;给出了晶界无析出带的强度贡献计算方法和几何建模策略;基于晶体塑性有限元方法模拟了塑性变形行为并获得应力-应变曲线。本工作分析流程已拓展为了对各类铝合金材料研究具有普遍适用性的晶体性能计算工具包,本文介绍了该工具包的特点与功能。

Hu C Z, Li Y W, Yu Z Y, et al.

Computing grain boundary diagrams of thermodynamic and mechanical properties

[J]. npj Comput. Mater., 2021, 7: 159

DOI      [本文引用: 3]

Marquardt K, Rohrer G S, Morales L, et al.

The most frequent interfaces in olivine aggregates: The GBCD and its importance for grain boundary related processes

[J]. Contrib. Mineral. Petrol., 2015, 170: 40

DOI      URL     [本文引用: 1]

Chookajorn T, Murdoch H A, Schuh C A.

Design of stable nanocrystalline alloys

[J]. Science, 2012, 337: 951

DOI      PMID      [本文引用: 1]

Nanostructured metals are generally unstable; their grains grow rapidly even at low temperatures, rendering them difficult to process and often unsuitable for usage. Alloying has been found to improve stability, but only in a few empirically discovered systems. We have developed a theoretical framework with which stable nanostructured alloys can be designed. A nanostructure stability map based on a thermodynamic model is applied to design stable nanostructured tungsten alloys. We identify a candidate alloy, W-Ti, and demonstrate substantially enhanced stability for the high-temperature, long-duration conditions amenable to powder-route production of bulk nanostructured tungsten. This nanostructured alloy adopts a heterogeneous chemical distribution that is anticipated by the present theoretical framework but unexpected on the basis of conventional bulk thermodynamics.

Garner A, Euesden R, Yao Y C, et al.

Multiscale analysis of grain boundary microstructure in high strength 7xxx Al alloys

[J]. Acta Mater., 2021, 202: 190

DOI      URL    

Wilde G, Divinski S.

Grain boundaries and diffusion phenomena in severely deformed materials

[J]. Mater. Trans., 2019, 60: 1302

DOI     

The present knowledge on grain boundary-related phenomena specific for severely plastically deformed materials is reviewed and critically analyzed in detail. Severe plastic deformation is shown to introduce specific metastable states of the grain boundaries which are characterized by enhanced diffusion rates, high-density of specific structure elements and large (still localized) elastic strains. An intrinsic heterogeneity of the deformation-induced modifications is revealed and examined on different scales. Relations between the existence of deformation-modified grain boundaries, specific microstructure features and resulting properties are highlighted.

Leitner K, Lutz D, Knabl W, et al.

Grain boundary segregation engineering in as-sintered molybdenum for improved ductility

[J]. Scr. Mater., 2018, 156: 60

DOI      URL    

Zhu Y L, Cao Y, Tian W, et al.

New insights into ductility improvement of a nickel-based superalloy through grain boundary engineering

[J]. Mater. Sci. Eng., 2024, A908: 146786

Tikhonova M, Kaibyshev R, Belyakov A.

Microstructure and mechanical properties of austenitic stainless steels after dynamic and post-dynamic recrystallization treatment

[J]. Adv. Eng. Mater., 2018, 20: 1700960

DOI      URL    

Zhuo Z, Xia S, Bai Q, et al.

The effect of grain boundary character distribution on the mechanical properties at different strain rates of a 316L stainless steel

[J]. J. Mater. Sci., 2018, 53: 2844

DOI      URL    

Naydenkin E V, Ratochka I V, Mishin I P, et al.

The effect of interfaces on mechanical and superplastic properties of titanium alloys

[J]. J. Mater. Sci., 2017, 52: 4164

DOI      URL     [本文引用: 1]

Li L L, Zhang P, Zhang Z J, et al.

Strain localization and fatigue cracking behaviors of Cu bicrystal with an inclined twin boundary

[J]. Acta Mater., 2014, 73: 167

DOI      URL     [本文引用: 1]

Jin Y J, Lu H, Yu C, et al.

Study on grain boundary character and strain distribution of intergranular cracking in the CGHAZ of T23 steel

[J]. Mater. Charact., 2013, 84: 216

DOI      URL    

Das A.

Grain boundary engineering: fatigue fracture

[J]. Philos. Mag., 2017, 97: 867

DOI      URL     [本文引用: 1]

Lu K.

Stabilizing nanostructures in metals using grain and twin boundary architectures

[J]. Nat. Rev. Mater., 2016, 1: 16019

DOI      [本文引用: 1]

Van Swygenhoven H.

Grain boundaries and dislocations

[J]. Science, 2002, 296: 66

PMID     

Hirth J P.

The influence of grain boundaries on mechanical properties

[J]. Metall. Trans., 1972, 3: 3047

Palumbo G, Lehockey E M, Lin P.

Applications for grain boundary engineered materials

[J]. JOM, 1998, 50(2): 40

Randle V, Ralph B.

Grain boundary structure and mechanical properties

[J]. Rev. Phys. Appl., 1988, 23: 501

Kheradmand N, Barnoush A, Vehoff H.

Investigation of the role of grain boundary on the mechanical properties of metals

[J]. J. Phys.: Conf. Ser., 2010, 240: 012017

[本文引用: 1]

Randle V, Owen G.

Mechanisms of grain boundary engineering

[J]. Acta Mater., 2006, 54: 1777

DOI      URL     [本文引用: 1]

Randle V.

‘Special’ boundaries and grain boundary plane engineering

[J]. Scr. Mater., 2006, 54: 1011

DOI      URL    

Randle V.

Grain boundary engineering: An overview after 25 years

[J]. Mater. Sci. Technol., 2010, 26: 253

DOI      URL    

Watanabe T.

Grain boundary engineering: Historical perspective and future prospects

[J]. J. Mater. Sci., 2011, 46: 4095

DOI      URL    

Raabe D, Herbig M, Sandlöbes S, et al.

Grain boundary segregation engineering in metallic alloys: A pathway to the design of interfaces

[J]. Curr. Opin. Solid State Mater. Sci., 2014, 18: 253

DOI      URL    

Xu X M, Zhong Y J, Wajrak M, et al.

Grain boundary engineering: An emerging pathway toward efficient electrocatalysis

[J]. InfoMat, 2024, 6: e12608

DOI      [本文引用: 1]

Electrochemical transformation processes involving carbon, hydrogen, oxygen, nitrogen, and small-molecule chemistries represent a promising means to store renewable energy sources in the form of chemical energy. However, their widespread deployment is hindered by a lack of efficient, selective, durable, and affordable electrocatalysts. Recently, grain boundary (GB) engineering as one category of defect engineering, has emerged as a viable and powerful pathway to achieve improved electrocatalytic performances. This review presents a timely and comprehensive overview of recent advances in GB engineering for efficient electrocatalysis. The beneficial effects of introducing GBs into electrocatalysts are discussed, followed by an overview of the synthesis and characterization of GB-enriched electrocatalysts. Importantly, the latest developments in leveraging GB engineering for enhanced electrocatalysis are thoroughly examined, focusing on the electrochemical utilization cycles of carbon, hydrogen, oxygen, and nitrogen. Future research directions are proposed to further advance the understanding and application of GB engineering for improved electrocatalysis.

Tiamiyu A A, Pang E L, Chen X, et al.

Nanotwinning-assisted dynamic recrystallization at high strains and strain rates

[J]. Nat. Mater., 2022, 21: 786

DOI      PMID      [本文引用: 2]

Grain refinement is a widely sought-after feature of many metal production processes and frequently involves a process of recrystallization. Some processing methods use very high strain rates and high strains to refine the grain structure into the nanocrystalline regime. However, grain refinement processes are not clear in these extreme conditions, which are hard to study systematically. Here, we access those extreme conditions of strain and strain rate using single copper microparticle impact events with a laser-induced particle impact tester. Using a combined dictionary-indexing electron backscatter diffraction and scanning transmission electron microscopy approach for postmortem characterization of impact sites, we systematically explore increasing strain levels and observe a recrystallization process that is facilitated by nanotwinning, which we term nanotwinning-assisted dynamic recrystallization. It achieves much finer grain sizes than established modes of recrystallization and therefore provides a pathway to the finest nanocrystalline grain sizes through extreme straining processes.© 2022. The Author(s), under exclusive licence to Springer Nature Limited.

Figueiredo R B, Langdon T G.

Fabricating ultrafine-grained materials through the application of severe plastic deformation: A review of developments in brazil

[J]. J. Mater. Res. Technol., 2012, 1: 55

DOI      URL     [本文引用: 2]

Panzarino J F, Pan Z L, Rupert T J.

Plasticity-induced restructuring of a nanocrystalline grain boundary network

[J]. Acta Mater., 2016, 120: 1

DOI      URL     [本文引用: 1]

Fu H L, Zhou X, Gao Z P, et al.

Effect of grain geometry on the stability of polycrystalline Pt at the nanoscale

[J]. Phys. Rev. Lett., 2025, 134: 056101

[本文引用: 2]

Zhang L, Lu C, Tieu K.

A review on atomistic simulation of grain boundary behaviors in face-centered cubic metals

[J]. Comput. Mater. Sci., 2016, 118: 180

DOI      URL     [本文引用: 1]

Pan X L, Zhou L C, Wang C X, et al.

Microstructure and residual stress modulation of 7075 aluminum alloy for improving fatigue performance by laser shock peening

[J]. Int. J. Mach. Tools Manuf., 2023, 184: 103979

DOI      URL     [本文引用: 1]

Abdeljawad F, Foiles S M, Moore A P, et al.

The role of the interface stiffness tensor on grain boundary dynamics

[J]. Acta Mater., 2018, 158: 440

DOI      URL     [本文引用: 1]

Randle V. The Role of the Coincidence Site Lattice in Grain Boundary Engineering [M]. London: CRC Press, 2024: 1

[本文引用: 1]

Lee D S, Ryoo H S, Hwang S K.

A grain boundary engineering approach to promote special boundaries in Pb-base alloy

[J]. Mater. Sci. Eng., 2003, A354: 106

[本文引用: 1]

Warren P, Raju N, Prasad A, et al.

Grain and grain boundary segmentation using machine learning with real and generated datasets

[J]. Comput. Mater. Sci., 2024, 233: 112739

DOI      URL     [本文引用: 1]

Zhu Q, Samanta A, Li B X, et al.

Predicting phase behavior of grain boundaries with evolutionary search and machine learning

[J]. Nat. Commun., 2018, 9: 467

DOI      PMID     

The study of grain boundary phase transitions is an emerging field until recently dominated by experiments. The major bottleneck in the exploration of this phenomenon with atomistic modeling has been the lack of a robust computational tool that can predict interface structure. Here we develop a computational tool based on evolutionary algorithms that performs efficient grand-canonical grain boundary structure search and we design a clustering analysis that automatically identifies different grain boundary phases. Its application to a model system of symmetric tilt boundaries in Cu uncovers an unexpected rich polymorphism in the grain boundary structures. We find new ground and metastable states by exploring structures with different atomic densities. Our results demonstrate that the grain boundaries within the entire misorientation range have multiple phases and exhibit structural transitions, suggesting that phase behavior of interfaces is likely a general phenomenon.

Huber L, Hadian R, Grabowski B, et al.

A machine learning approach to model solute grain boundary segregation

[J]. npj Comput. Mater., 2018, 4: 64

DOI     

Zhang J N, Koneru A, Sankaranarayanan S K R S, et al.

Graph neural network guided evolutionary search of grain boundaries in 2D materials

[J]. ACS Appl. Mater. Interfaces, 2023, 15: 20520

DOI      URL    

van Beers P R M, Kouznetsova V G, Geers M G D, et al.

A multiscale model of grain boundary structure and energy: From atomistics to a continuum description

[J]. Acta Mater., 2015, 82: 513

DOI      URL    

Song X Y, Deng C.

Atomic energy in grain boundaries studied by machine learning

[J]. Phys. Rev. Mater., 2022, 6: 043601

[本文引用: 1]

Patala S.

Topological analysis of the grain boundary space

[D]. Cambridge: Massachusetts Institute of Technology, 2011

[本文引用: 1]

Wakai F, Shinoda Y, Ishihara S, et al.

Topological transformation of grains in three-dimensional normal grain growth

[J]. J. Mater. Res., 2001, 16: 2136

DOI      URL    

The topological transformation of grains in three-dimensional normal grain growth was analyzed by Brakke's Surface Evolver method that simulated the boundary motion by curvature. The statistics on elemental processes, which change the number of faces f of a grain, were determined from the simulation. The distribution function of the number of faces P(f) in a steady structure could be predicted from the difference in the current of grains arriving at and leaving from state f. For the disappearance of one grain, face-creation switching occurred 3.7 times and face-elimination switching occurred 13.2 times on the average.

Gao N N, Zhao Y, Xia W Q, et al.

Phase-field crystal studies on grain boundary migration, dislocation behaviors, and topological transition under tension of square polycrystals

[J]. Crystals, 2023, 13: 777

DOI      URL     [本文引用: 1]

In this paper, the tensile deformation behaviors of polycrystals after relaxation were studied using the phase-field-crystal (PFC) method. Here, the free energy density map characterized the 2D energy distribution of atomic configuration effectively. The application of the Read–Shockley equation distinguished high-energy grain boundary (HEGB) and low-energy grain boundary (LEGB) in large-angle grain boundary (LAGB), and they demonstrated different migration behaviors at the early and later stages. The behaviors of small-angle grain boundary (SAGB), including its migration and grains’ rotation, were also studied. Two different mechanisms of dislocation emission and absorption were explored, which demonstrates the possibility of dislocation elevating interfacial energy. The simulated results on the topological transition of grain boundaries prompted us to propose the thinking about the applications of the Neumann–Mullins law and Euler formula.

Narang P, Garcia C A C, Felser C.

The topology of electronic band structures

[J]. Nat. Mater., 2021, 20: 293

DOI      PMID      [本文引用: 1]

The study of topology as it relates to physical systems has rapidly accelerated during the past decade. Critical to the realization of new topological phases is an understanding of the materials that exhibit them and precise control of the materials chemistry. The convergence of new theoretical methods using symmetry indicators to identify topological material candidates and the synthesis of high-quality single crystals plays a key role, warranting discussion and context at an accessible level. This Perspective provides a broad introduction to topological phases, their known properties, and material realizations. We focus on recent work in topological Weyl and Dirac semimetals, with a particular emphasis on magnetic Weyl semimetals and emergent fermions in chiral crystals and their extreme responses to excitations, and we highlight areas where the field can continue to make remarkable discoveries. We further examine open questions and directions for the topological materials science community to pursue, including exploration of non-equilibrium properties of Weyl semimetals and cavity-dressed topological materials.

Gupta S, Saxena A.

A topological twist on materials science

[J]. MRS Bull., 2014, 39: 265

DOI      URL     [本文引用: 1]

Hirth J P, Balluffi R W.

On grain boundary dislocations and ledges

[J]. Acta Metall., 1973, 21: 929

DOI      URL     [本文引用: 2]

Gleiter H.

Nanostructured materials: Basic concepts and microstructure

[J]. Acta Mater., 2000, 48: 1

DOI      URL     [本文引用: 2]

Zhu Q, Zhao Q K, Huang Q S, et al.

Grain boundary plasticity initiated by excess volume

[J]. Proc. Natl. Acad. Sci. USA, 2024, 121: e2400161121

DOI      URL     [本文引用: 4]

Grain boundaries (GBs) serve not only as strong barriers to dislocation motion, but also as important carriers to accommodate plastic deformation in crystalline solids. During deformation, the inherent excess volume associated with loose atomic packing in GBs brings about a microscopic degree of freedom that can initiate GB plasticity, which is beyond the classic geometric description of GBs. However, identification of this atomistic process has long remained elusive due to its transient nature. Here, we use Au polycrystals to unveil a general and inherent route to initiating GB plasticity via a transient topological transition process triggered by the excess volume. This route underscores the general impact of a microscopic degree of freedom which is governed by a stress-triaxiality-based criterion. Our findings provide a missing perspective for developing a more comprehensive understanding of the role of GBs in plastic deformation.

Ma K K, Wen H M, Hu T, et al.

Mechanical behavior and strengthening mechanisms in ultrafine grain precipitation-strengthened aluminum alloy

[J]. Acta Mater., 2014, 62: 141

DOI      URL     [本文引用: 1]

Hellman O C, Vandenbroucke J A, Rüsing J, et al.

Analysis of three-dimensional atom-probe data by the proximity histogram

[J]. Microsc. Microanal., 2000, 6: 437

PMID      [本文引用: 1]

The three-dimensional (3D) atom-probe technique produces a reconstruction of the elemental chemical identities and three-dimensional positions of atoms field evaporated from a sharply pointed metal specimen, with a local radius of curvature of less than 50 nm. The number of atoms collected can be on the order of one million, representing an analysis volume of approximately 20 nm x 20 nm x 200 nm (80,000 nm(3)). This large amount of data allows for the identification of microstructural features in a sample, such as grain or heterophase boundaries, if the feature density is large enough. Correlation of the measured atomic positions with these identified features results in an atom-by-atom description of the chemical environment of crystallographic defects. This article outlines a data compilation technique for the generation of composition profiles in the vicinity of interfaces in a geometrically independent way. This approach is applied to quantitative determination of interfacial segregation of silver at a MgO/Cu(Ag) heterophase interface.

Wagih M, Larsen P M, Schuh C A.

Learning grain boundary segregation energy spectra in polycrystals

[J]. Nat. Commun., 2020, 11: 6376

DOI      PMID      [本文引用: 1]

The segregation of solute atoms at grain boundaries (GBs) can profoundly impact the structural properties of metallic alloys, and induce effects that range from strengthening to embrittlement. And, though known to be anisotropic, there is a limited understanding of the variation of solute segregation tendencies across the full, multidimensional GB space, which is critically important in polycrystals where much of that space is represented. Here we develop a machine learning framework that can accurately predict the segregation tendency-quantified by the segregation enthalpy spectrum-of solute atoms at GB sites in polycrystals, based solely on the undecorated (pre-segregation) local atomic environment of such sites. We proceed to use the learning framework to scan across the alloy space, and build an extensive database of segregation energy spectra for more than 250 metal-based binary alloys. The resulting machine learning models and segregation database are key to unlocking the full potential of GB segregation as an alloy design tool, and enable the design of microstructures that maximize the useful impacts of segregation.

Wei C Z, Thomas S L, Han J, et al.

A continuum multi-disconnection-mode model for grain boundary migration

[J]. J. Mech. Phys. Solids, 2019, 133: 103731

DOI      URL     [本文引用: 1]

Wang L H, Zhang Y, Zeng Z, et al.

Tracking the sliding of grain boundaries at the atomic scale

[J]. Science, 2022, 375: 1261

DOI      PMID      [本文引用: 1]

Grain boundaries (GBs) play an important role in the mechanical behavior of polycrystalline materials. Despite decades of investigation, the atomic-scale dynamic processes of GB deformation remain elusive, particularly for the GBs in polycrystals, which are commonly of the asymmetric and general type. We conducted an in situ atomic-resolution study to reveal how sliding-dominant deformation is accomplished at general tilt GBs in platinum bicrystals. We observed either direct atomic-scale sliding along the GB or sliding with atom transfer across the boundary plane. The latter sliding process was mediated by movements of disconnections that enabled the transport of GB atoms, leading to a previously unrecognized mode of coupled GB sliding and atomic plane transfer. These results enable an atomic-scale understanding of how general GBs slide in polycrystalline materials.

Lu K.

Gradient nanostructured materials

[J]. Acta Metall. Sin., 2015, 51: 1

DOI      [本文引用: 1]

In this paper, research progresses on gradient nanostructured materials in recent years is briefly reviewed. It includes classification of gradient nanostructures, properties and processing techniques of the gradient nanostructured materials. Perspectives and challenges on scientific understanding and industrial applications of gradient nanostructured materials are addressed.

卢 柯.

梯度纳米结构材料

[J]. 金属学报, 2015, 51: 1

[本文引用: 1]

Fu H L, Zhou X, Gao Z P, et al.

Pt Schwarz crystals stabilized by minimal-surface grain boundaries and twins at the grain size limit

[J]. Acta Mater., 2024, 276: 120007

DOI      URL    

Lu L, Shen Y F, Chen X H, et al.

Ultrahigh strength and high electrical conductivity in copper

[J]. Science, 2004, 304: 422

PMID      [本文引用: 2]

Methods used to strengthen metals generally also cause a pronounced decrease in electrical conductivity, so that a tradeoff must be made between conductivity and mechanical strength. We synthesized pure copper samples with a high density of nanoscale growth twins. They showed a tensile strength about 10 times higher than that of conventional coarse-grained copper, while retaining an electrical conductivity comparable to that of pure copper. The ultrahigh strength originates from the effective blockage of dislocation motion by numerous coherent twin boundaries that possess an extremely low electrical resistivity, which is not the case for other types of grain boundaries.

Zhu Q, Huang Q S, Guang C, et al.

Metallic nanocrystals with low angle grain boundary for controllable plastic reversibility

[J]. Nat. Commun., 2020, 11: 3100

DOI      PMID      [本文引用: 1]

Advanced nanodevices require reliable nanocomponents where mechanically-induced irreversible structural damage should be largely prevented. However, a practical methodology to improve the plastic reversibility of nanosized metals remains challenging. Here, we propose a grain boundary (GB) engineering protocol to realize controllable plastic reversibility in metallic nanocrystals. Both in situ nanomechanical testing and atomistic simulations demonstrate that custom-designed low-angle GBs with controlled misorientation can endow metallic bicrystals with endurable cyclic deformability via GB migration. Such fully reversible plasticity is predominantly governed by the conservative motion of Shockley partial dislocation pairs, which fundamentally suppress damage accumulation and preserve the structural stability. This reversible deformation is retained in a broad class of face-centred cubic metals with low stacking fault energies when tuning the GB structure, external geometry and loading conditions over a wide range. These findings shed light on practical advances in promoting cyclic deformability of metallic nanomaterials.

Cantwell P R, Tang M, Dillon S J, et al.

Grain boundary complexions

[J]. Acta Mater., 2014, 62: 1

DOI      URL     [本文引用: 1]

Cantwell P R, Frolov T, Rupert T J, et al.

Grain boundary complexion transitions

[J]. Annu. Rev. Mater. Res., 2020, 50: 465

DOI     

Grain boundaries can undergo phase-like transitions, called complexion transitions, in which their structure, composition, and properties change discontinuously as temperature, bulk composition, and other parameters are varied. Grain boundary complexion transitions can lead to rapid changes in themacroscopic properties of polycrystallinemetals and ceramics and are responsible for a variety of materials phenomena as diverse as activated sintering and liquid-metal embrittlement. The property changes caused by grain boundary complexion transitions can be beneficial or detrimental. Grain boundary complexion engineering exploits beneficial complexion transitions to improve the processing, properties, and performance of materials. Here, we review the thermodynamic fundamentals of grain boundary complexion transitions, highlight the strongest experimental and computational evidence for these transitions, clarify a number of important misconceptions, discuss the advantages of grain boundary complexion engineering, and summarize existing research challenges.

Zhang Z B, Yang Z B, Lu S, et al.

Strain localisation and failure at twin-boundary complexions in nickel-based superalloys

[J]. Nat. Commun., 2020, 11: 4890

DOI      PMID     

Twin boundaries (TBs) in Ni-based superalloys are vulnerable sites for failure in demanding environments, and a current lack of mechanistic understanding hampers the reliable lifetime prediction and performance optimisation of these alloys. Here we report the discovery of an unexpected γ″ precipitation mechanism at TBs that takes the responsibility for alloy failure in demanding environments. Using multiscale microstructural and mechanical characterisations (from millimetre down to atomic level) and DFT calculations, we demonstrate that abnormal γ″ precipitation along TBs accounts for the premature dislocation activities and pronounced strain localisation associated with TBs during mechanical loading, which serves as a precursor for crack initiation. We clarify the physical origin of the TBs-related cracking at the atomic level of γ″-strengthened Ni-based superalloys in a hydrogen containing environment, and provide practical methods to mitigate the adverse effect of TBs on the performance of these alloys.

Krause A R, Cantwell P R, Marvel C J, et al.

Review of grain boundary complexion engineering: Know your boundaries

[J]. J. Am. Ceram. Soc., 2019, 102: 778

DOI      [本文引用: 1]

Grain boundary structure-property relationships influence bulk performance and, therefore, are an important criterion in materials design. Materials scientists can generate different grain boundary structures by changes in temperature, pressure, and chemical potential because interfaces attain their own equilibrium states, known as complexions. Complexions undergo first-order transitions by changes in thermodynamic variables, which results in discontinuous changes in properties. Grain boundary complexion engineering is introduced in this paper as a method for controlling complexion transitions to improve material performance. This International Conference on Sintering 2017 lecture describes the tools for grain boundary complexion engineering: complexion equilibrium and time-temperature-transformation (TTT) diagrams. These tools can be implemented in processing design to tailor grain boundary properties, including grain boundary mobility. While impactful, these diagrams are often limited in scope because they are currently empirically derived. This article discusses how measurement techniques can be combined with data analytical methods to build mechanistically derived complexion equilibrium and TTT diagrams.

Grimmer H, Bollmann W, Warrington D H.

Coincidence-site lattices and complete pattern-shift in cubic crystals

[J]. Acta Cryst., 1974, 30A: 197

[本文引用: 1]

Bollmann W. Crystal Defects and Crystalline Interfaces [M]. Berlin: Springer, 2012: 1

Pond R C, Bollmann W.

The symmetry and interfacial structure of bicrystals

[J]. Philos. Trans. Roy. Soc., 1979, 292A: 449

Warrington D H, Bollmann W.

Dislocation networks in high-angle grain boundaries

[J]. Philos. Mag., 1972, 25: 1195

DOI      URL     [本文引用: 1]

Bollmann W.

On the geometry of grain and phase boundaries: I. General theory

[J]. Philos. Mag., 1967, 16: 363

[本文引用: 1]

Randle V, Rohrer G S, Miller H M, et al.

Five-parameter grain boundary distribution of commercially grain boundary engineered nickel and copper

[J]. Acta Mater., 2008, 56: 2363

DOI      URL     [本文引用: 1]

Ratanaphan S, Yoon Y, Rohrer G S.

The five parameter grain boundary character distribution of polycrystalline silicon

[J]. J. Mater. Sci., 2014, 49: 4938

DOI      URL    

An D, Griffiths T A, Konijnenberg P, et al.

Correlating the five parameter grain boundary character distribution and the intergranular corrosion behaviour of a stainless steel using 3D orientation microscopy based on mechanical polishing serial sectioning

[J]. Acta Mater., 2018, 156: 297

DOI      URL     [本文引用: 1]

Brandon D G.

The structure of high-angle grain boundaries

[J]. Acta Metall., 1966, 14: 1479

DOI      URL     [本文引用: 1]

Bollmann W.

The basic concepts of the 0-lattice theory

[J]. Surf. Sci., 1972, 31: 1

DOI      URL     [本文引用: 1]

Bollmann W.

O‐lattice calculation of an F.C.C.-B.C.C. interface

[J]. Phys. Status Solidi, 1974, 21A: 543

[本文引用: 1]

Li M, Xu T.

Topological and atomic scale characterization of grain boundary networks in polycrystalline and nanocrystalline materials

[J]. Prog. Mater. Sci., 2011, 56: 864

DOI      URL     [本文引用: 1]

Jin Z H, Li X Y, Lu K.

Formation of stable schwarz crystals in polycrystalline copper at the grain size limit

[J]. Phys. Rev. Lett., 2021, 127: 136101

DOI      URL    

Xu W, Zhang B, Li X Y, et al.

Suppressing atomic diffusion with the Schwarz crystal structure in supersaturated Al-Mg alloys

[J]. Science, 2021, 373: 683

DOI      PMID     

High atomic diffusivity in metals enables substantial tuneability of their structure and properties by tailoring the diffusional processes, but this causes their customized properties to be unstable at elevated temperatures. Eliminating diffusive interfaces by fabricating single crystals or heavily alloying helps to address this issue but does not inhibit atomic diffusion at high homologous temperatures. We discovered that the Schwarz crystal structure was effective at suppressing atomic diffusion in a supersaturated aluminum-magnesium alloy with extremely fine grains. By forming these stable structures, diffusion-controlled intermetallic precipitation from the nanosized grains and their coarsening were inhibited up to the equilibrium melting temperature, around which the apparent across-boundary diffusivity was reduced by about seven orders of magnitude. Developing advanced engineering alloys using the Schwarz crystal structure may lead to useful properties for high-temperature applications.Copyright © 2021, American Association for the Advancement of Science.

Gu J L, Duan F H, Liu S D, et al.

Phase engineering of nanostructural metallic materials: Classification, structures, and applications

[J]. Chem. Rev., 2024, 124: 1247

DOI      URL    

Meiners T, Frolov T, Rudd R E, et al.

Observations of grain-boundary phase transformations in an elemental metal

[J]. Nature, 2020, 579: 375

DOI      [本文引用: 1]

Zhu S Y, Jivkov A P, Borodin E, et al.

Triple junction disclinations in severely deformed Cu-0.4%Mg alloys

[J]. Acta Mater., 2024, 264: 119600

DOI      URL     [本文引用: 3]

Bollmann W.

Triple lines in polycrystalline aggregates as disclinations

[J]. Philos. Mag., 1984, 49A: 73

[本文引用: 1]

Bollmann W.

Triple-line disclinations representations, continuity and reactions

[J]. Philos. Mag., 1988, 57A: 637

[本文引用: 1]

Liu Y, Leung S, Li F F, et al.

Bulk-disclination correspondence in topological crystalline insulators

[J]. Nature, 2021, 589: 381

DOI      [本文引用: 2]

Wu M S, Zhou K, Nazarov A A.

Crack nucleation at disclinated triple junctions

[J]. Phys. Rev., 2007, 76B: 134105

[本文引用: 1]

Barnett A K, Hussein O, Alghalayini M, et al.

Triple junction segregation dominates the stability of nanocrystalline alloys

[J]. Nano Lett., 2024, 24: 9627

DOI      URL    

Wei C Z, Zhang C L, Han J, et al.

Grain boundary triple junction dynamics: A continuum disconnection model

[J]. SIAM J. Appl. Math., 2020, 80: 1101

DOI      URL    

Annevelink E, Ertekin E, Johnson H T.

Grain boundary structure and migration in graphene via the displacement shift complete lattice

[J]. Acta Mater., 2019, 166: 67

DOI      [本文引用: 1]

We describe grain boundary structure and migration in graphene using the concept of dislocations in the displacement shift complete lattice. The equivalence of displacement shift complete lattice dislocations and grain boundary kinks in graphene is shown both topologically and energetically. Topologically, a grain boundary kink and a displacement shift complete lattice dislocation both translate the coincident site lattice. The energetic equivalence is established through comparison of atomistic and continuum elasticity models of metastable states to show that DSC dislocations are well-described by elasticity theory. The continuum results are fitted to the atomistic results with one adjustable parameter, the DSC dislocation core radius. The atomistic results reveal that low sigma boundaries have large energy barriers to grain boundary motion, which match continuum results obtained for smaller core radii dislocations. The larger energy barriers for low sigma boundaries are consistent with experimental results reporting isolated, low sigma boundaries in grown graphene. The trends in the dislocation Burgers vector and fitted core radii across grain boundaries of different misorientation are expressed in a unified model. The analysis provides a framework for understanding grain boundary motion in graphene and can serve as a basis for engineering the atomic structure of graphene. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd.

Song X Q, Tang L Y, Wang Y X, et al.

Plastic strain-induced evolution of CSL boundaries at elevated temperature for Ni-base superalloy: Experimental and phase-field perspective

[J]. J. Mater. Res. Technol., 2020, 9: 2535

DOI      URL     [本文引用: 3]

Zhou S Y, Hu M H, Li C, et al.

Creep behavior of a Ni-based superalloy with strengthening of γ' and γ'' phases

[J]. Acta Metall. Sin., 2025, 61: 226

[本文引用: 1]

周生玉, 胡明昊, 李 冲 .

一种γ'/γ''相强化镍基高温合金的蠕变行为

[J]. 金属学报, 2025, 61: 226

DOI      [本文引用: 1]

镍基高温合金由于其优异的抗氧化抗腐蚀性能以及良好的组织稳定性,广泛应用于航空航天发动机中涡轮盘等关键热端部件以及超超临界电站的耐热材料。γ'以及γ''相作为镍基高温合金中主要强化相,在合金中发挥重要的强化作用。本工作研究了750 ℃、120 MPa条件下,不同形貌特征的γ'和γ''相强化镍基高温合金的蠕变行为。结果表明,合金中γ'和γ''相尺寸变化会导致蠕变变形行为和蠕变性能的改变。合金析出细小γ'/γ''相时,仅少量位错切入γ'/γ''相,并形成贯穿γ基体和γ'/γ''相的连续层错,合金蠕变性能较差;随着γ'/γ''相尺寸增加,位错易切入γ'相,并在γ'相中形成层错,蠕变性能显著提升;γ'相尺寸继续增大,位错在γ/γ'界面堆积,呈环状包裹γ'相,导致合金蠕变性能降低。晶界附近析出的有害Laves相会弱化晶界;在晶界处析出适量的η/δ相能够提高晶界强度,抑制裂纹扩展,显著提高合金的蠕变寿命;而晶内析出的粗大η/δ相则为裂纹形核提供有利位置,加速合金失效。

Zhang Y, He C Y, Yu Q, et al.

Nacre-like surface nanolaminates enhance fatigue resistance of pure titanium

[J]. Nat. Commun., 2024, 15: 6917

DOI      PMID      [本文引用: 1]

Fatigue failure is invariably the most crucial failure mode for metallic structural components. Most microstructural strategies for enhancing fatigue resistance are effective in suppressing either crack initiation or propagation, but often do not work for both synergistically. Here, we demonstrate that this challenge can be overcome by architecting a gradient structure featuring a surface layer of nacre-like nanolaminates followed by multi-variant twinned structure in pure titanium. The polarized accommodation of highly regulated grain boundaries in the nanolaminated layer to cyclic loading enhances the structural stability against lamellar thickening and microstructure softening, thereby delaying surface roughening and thus crack nucleation. The decohesion of the nanolaminated grains along horizonal high-angle grain boundaries gives rise to an extraordinarily high frequency (≈1.7 × 10 times per mm) of fatigue crack deflection, effectively reducing fatigue crack propagation rate (by 2 orders of magnitude lower than the homogeneous coarse-grained counterpart). These intriguing features of the surface nanolaminates, along with the various toughening mechanisms activated in the subsurface twinned structure, result in a fatigue resistance that significantly exceeds those of the homogeneous and gradient structures with equiaxed grains. Our work on architecting the surface nanolaminates in gradient structure provides a scalable and sustainable strategy for designing more fatigue-resistant alloys.© 2024. The Author(s).

Zhou X Y, Ahmadian A, Gault B, et al.

Atomic motifs govern the decoration of grain boundaries by interstitial solutes

[J]. Nat. Commun., 2023, 14: 3535

DOI      PMID      [本文引用: 1]

Grain boundaries, the two-dimensional defects between differently oriented crystals, tend to preferentially attract solutes for segregation. Solute segregation has a significant effect on the mechanical and transport properties of materials. At the atomic level, however, the interplay of structure and composition of grain boundaries remains elusive, especially with respect to light interstitial solutes like B and C. Here, we use Fe alloyed with B and C to exploit the strong interdependence of interface structure and chemistry via charge-density imaging and atom probe tomography methods. Direct imaging and quantifying of light interstitial solutes at grain boundaries provide insight into decoration tendencies governed by atomic motifs. We find that even a change in the inclination of the grain boundary plane with identical misorientation impacts grain boundary composition and atomic arrangement. Thus, it is the smallest structural hierarchical level, the atomic motifs, that controls the most important chemical properties of the grain boundaries. This insight not only closes a missing link between the structure and chemical composition of such defects but also enables the targeted design and passivation of the chemical state of grain boundaries to free them from their role as entry gates for corrosion, hydrogen embrittlement, or mechanical failure.© 2023. The Author(s).

Schuh C A, Kumar M, King W E.

Analysis of grain boundary networks and their evolution during grain boundary engineering

[J]. Acta Mater., 2003, 51: 687

DOI      URL     [本文引用: 3]

Kumar M, King W E, Schwartz A J.

Modifications to the microstructural topology in f.c.c. materials through thermomechanical processing

[J]. Acta Mater., 2000, 48: 2081

DOI      URL    

Farabi E, Tari V, Hodgson P D, et al.

On the grain boundary network characteristics in a martensitic Ti-6Al-4V alloy

[J]. J. Mater. Sci., 2020, 55: 15299

DOI      [本文引用: 2]

Chen Y B, Han J, Deng H L, et al.

Revealing grain boundary kinetics in three-dimensional space

[J]. Acta Mater., 2024, 268: 119717

DOI      URL     [本文引用: 1]

Priedeman J L, Rosenbrock C W, Johnson O K, et al.

Quantifying and connecting atomic and crystallographic grain boundary structure using local environment representation and dimensionality reduction techniques

[J]. Acta Mater., 2018, 161: 431

DOI      URL     [本文引用: 3]

Palumbo G, Thorpe S J, Aust K T.

On the contribution of triple junctions to the structure and properties of nanocrystalline materials

[J]. Scr. Metall. Mater., 1990, 24: 1347

DOI      URL     [本文引用: 1]

Chen E Z, Heo T W, Wood B C, et al.

Grand canonically optimized grain boundary phases in hexagonal close-packed titanium

[J]. Nat. Commun., 2024, 15: 7049

DOI      PMID      [本文引用: 5]

Grain boundaries (GBs) profoundly influence the properties and performance of materials, emphasizing the importance of understanding the GB structure and phase behavior. As recent computational studies have demonstrated the existence of multiple GB phases associated with varying the atomic density at the interface, we introduce a validated, open-source GRand canonical Interface Predictor (GRIP) tool that automates high-throughput, grand canonical optimization of GB structures. While previous studies of GB phases have almost exclusively focused on cubic systems, we demonstrate the utility of GRIP in an application to hexagonal close-packed titanium. We perform a systematic high-throughput exploration of tilt GBs in titanium and discover previously unreported structures and phase transitions. In low-angle boundaries, we demonstrate a coupling between point defect absorption and the change in the GB dislocation network topology due to GB phase transformations, which has important implications for the accommodation of radiation-induced defects.© 2024. The Author(s).

Yazyev O V, Louie S G.

Topological defects in graphene: Dislocations and grain boundaries

[J]. Phys. Rev., 2010, 81B: 195420

[本文引用: 1]

Korbuly B, Plapp M, Henry H, et al.

Topological defects in two-dimensional orientation-field models for grain growth

[J]. Phys. Rev., 2017, 96E: 052802

[本文引用: 1]

Barr C M, Leff A C, Demott R W, et al.

Unraveling the origin of twin related domains and grain boundary evolution during grain boundary engineering

[J]. Acta Mater., 2018, 144: 281

DOI      URL     [本文引用: 1]

Kinderlehrer D, Liu C.

Evolution of grain boundaries

[J]. Math. Models Methods Appl. Sci., 2001, 11: 713

DOI      URL    

Evolution and trend to equilibrium of a (planar) network of grain boundaries subject to curvature driven growth is established under the assumption that the system is initially close to some equilibrium configuration. Curvature driven growth is the primary mechanism in processing polycrystalline materials to achieve desired texture, ductility, toughness, strength, and other properties. Imposition of the Herring condition at triple junctions ensures that this system is dissipative and that the complementing conditions hold. We introduce a new way to employ the known Solonnikov-type estimates, which are only local in time, to obtain solutions that are global in time with controlled norm. These issues were raised as part of the Mesoscale Interface Mapping Project.

Niño J D, Johnson O K.

Influence of grain boundary energy anisotropy on the evolution of grain boundary network structure during 3D anisotropic grain growth

[J]. Comput. Mater. Sci, 2023, 217: 111879

DOI      URL    

Luo M, Liao X Z, Ringer S P, et al.

Grain boundary network evolution in electron-beam powder bed fusion nickel-based superalloy Inconel 738

[J]. J. Alloys Compd., 2024, 972: 172811

DOI      URL    

Yang X Y, Wang P, Huang M.

Grain boundary evolution during low-strain grain boundary engineering achieved by strain-induced boundary migration in pure copper

[J]. Mater. Sci. Eng., 2022, A833: 142532

[本文引用: 1]

Volovitch P, Traskine V, Barrallier L.

Analysis of grain boundary network topology using grain boundary wetting

[J]. Z. Metallkd., 2004, 95: 215

DOI      URL     [本文引用: 1]

Minich R W, Schuh C A, Kumar M.

Role of topological constraints on the statistical properties of grain boundary networks

[J]. Phys. Rev., 2002, 66B: 052101

Rohrer G S, Miller H M.

Topological characteristics of plane sections of polycrystals

[J]. Acta Mater., 2010, 58: 3805

DOI      URL     [本文引用: 1]

Liu T G, Xia S, Zhou B X, et al.

Three-dimensional geometrical and topological characteristics of grains in conventional and grain boundary engineered 316L stainless steel

[J]. Micron, 2018, 109: 58

DOI      PMID     

The three-dimensional microstructures of a conventional 316L stainless steel and the same material after grain boundary (GB) engineering have been measured by serial sectioning coupled with electron backscatter diffraction mapping. While it is well known that GB engineered materials are differentiated from conventional materials because of the proportion of coincidence site lattice boundaries, the size of their twin-related domains, and their reduced random boundary connectivity, this work provides a quantitative comparison of the geometrical and topological characteristics of grains in 316L stainless steel before and after GB engineering. Specifically, the numbers of grain faces, triple lines, and quadruple unions per grain have been measured and compared. In addition, the distributions of grain sizes, surface areas, and grain boundary areas have been measured and compared. The results show that, in many ways, the three-dimensional geometrical and topological characteristics of the grains in the GB engineered and conventional materials are similar. In both materials, the distributions of the geometrical parameters are well represented by a log-normal distribution. Comparatively, the GB engineered microstructure has grains that, on average, have both fewer faces and higher (specific) surface areas that deviate more from an ideal equiaxed shape, but there are several eccentric or non-compact shaped grains that have a huge number of faces and extremely large surface area in the GB engineered material. All of these characteristics are likely to be a result of the increased number of twins in the GB engineered microstructure. These eccentric grains would have a positive influence on increasing the resistance to intergranular degradation.Copyright © 2018 Elsevier Ltd. All rights reserved.

Li X Y, Jin Z H, Zhou X, et al.

Constrained minimal-interface structures in polycrystalline copper with extremely fine grains

[J]. Science, 2020, 370: 831

DOI      PMID     

Metals usually exist in the form of polycrystalline solids, which are thermodynamically unstable because of the presence of disordered grain boundaries. Grain boundaries tend to be eliminated through coarsening when heated or by transforming into metastable amorphous states when the grains are small enough. Through experiments and molecular dynamics simulations, we discovered a different type of metastable state for extremely fine-grained polycrystalline pure copper. After we reduced grain sizes to a few nanometers with straining, the grain boundaries in the polycrystals evolved into three-dimensional minimal-interface structures constrained by twin boundary networks. This polycrystalline structure that underlies what we call a Schwarz crystal is stable against grain coarsening, even when close to the equilibrium melting point. The polycrystalline samples also exhibit a strength in the vicinity of the theoretical value.Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Rollett A D, Lee S B, Campman R, et al.

Three-dimensional characterization of microstructure by electron back-scatter diffraction

[J]. Annu. Rev. Mater. Res., 2007, 37: 627

DOI      URL    

Christopher W A, Oliver K J.

A decision transformer approach to grain boundary network optimization

[J]. Comput. Mater. Sci., 2025, 253: 113852

DOI      URL    

Irukuvarghula S, Hassanin H, Cayron C, et al.

Evolution of grain boundary network topology in 316L austenitic stainless steel during powder hot isostatic pressing

[J]. Acta Mater., 2017, 133: 269

DOI      URL     [本文引用: 1]

Patala S, Mason J K, Schuh C A.

Improved representations of misorientation information for grain boundary science and engineering

[J]. Prog. Mater. Sci., 2012, 57: 1383

DOI      URL     [本文引用: 1]

Johnson O K, Lund J M, Critchfield T R.

Spectral graph theory for characterization and homogenization of grain boundary networks

[J]. Acta Mater., 2018, 146: 42

DOI      URL     [本文引用: 2]

Valiev R Z, Langdon T G.

Principles of equal-channel angular pressing as a processing tool for grain refinement

[J]. Prog. Mater. Sci., 2006, 51: 881

DOI      URL     [本文引用: 1]

Winning M, Gottstein G, Shvindlerman L S.

On the mechanisms of grain boundary migration

[J]. Acta Mater., 2002, 50: 353

DOI      URL     [本文引用: 1]

Voyiadjis G Z.

Grain boundary migration in metals: Thermodynamics, kinetics, applications

[J]. J. Eng. Mech., 2000, 126: 888

[本文引用: 1]

Jia H R, Duan S Y, Zhang Z, et al.

Homogenization-based topology optimization for self-supporting additive-manufactured lattice-infilled structure

[J]. Mater. Des., 2024, 245: 113264

DOI      URL     [本文引用: 1]

Rohrer G S.

Measuring and interpreting the structure of grain-boundary networks

[J]. J. Am. Ceram. Soc., 2011, 94: 633

DOI      URL     [本文引用: 1]

Barr C M, Thomas S, Hart J L, et al.

Tracking the evolution of intergranular corrosion through twin-related domains in grain boundary networks

[J]. npj Mater. Degrad., 2018, 2: 14

DOI     

Tailoring the grain boundary network is desired to improve grain boundary-dependent phenomena such as intergranular corrosion. An important grain boundary network descriptor in heavily twinned microstructures is the twin-related domain, a cluster of twin-related grains. We indicate the advantages of using twin-related domains and subsequent statistics to provide new insight into how a grain boundary networks respond to intergranular corrosion in a heavily twinned grain boundary engineered 316L stainless steel. The results highlight that intergranular corrosion is typically arrested inside twin-related domains at coherent twins or low-angle grain boundaries. Isolated scenarios exist, however, where intergranular corrosion propagation persists in the grain boundary network through higher-order twin-related boundaries.

Liu T G, Xia S, Li H, et al.

The highly twinned grain boundary network formation during grain boundary engineering

[J]. Mater. Lett., 2014, 133: 97

DOI      URL     [本文引用: 1]

Zhu X J, Fan Q B, Liu X, et al.

Microstructure evolution and mechanical properties of a hot-rolled Ti alloy

[J]. Prog. Nat. Sci.: Mater. Int., 2021, 31: 105

DOI      URL     [本文引用: 3]

Johnson O K, Schuh C A.

The triple junction hull: Tools for grain boundary network design

[J]. J. Mech. Phys. Solids, 2014, 69: 2

DOI      URL     [本文引用: 2]

Frary M, Schuh C A.

Connectivity and percolation behaviour of grain boundary networks in three dimensions

[J]. Philos. Mag., 2005, 85: 1123

DOI      URL     [本文引用: 1]

Liang C G, Yin Y, Wang W X, et al.

A thermodynamically consistent non-isothermal phase-field model for selective laser sintering

[J]. Int. J. Mech. Sci., 2023, 259: 108602

DOI      URL    

Zhang B B, Tang Y G, Mei Q S, et al.

Inhibiting creep in nanograined alloys with stable grain boundary networks

[J]. Science, 2022, 378: 659

DOI      PMID     

Creep, the time-dependent deformation of materials stressed below the yield strength, is responsible for a great number of component failures at high temperatures. Because grain boundaries (GBs) in materials usually facilitate diffusional processes in creep, eliminating GBs is a primary approach to resisting high-temperature creep in metals, such as in single-crystal superalloy turbo blades. We report a different strategy to inhibiting creep by use of stable GB networks. Plastic deformation triggered structural relaxation of high-density GBs in nanograined single-phased nickel-cobalt-chromium alloys, forming networks of stable GBs interlocked with abundant twin boundaries. The stable GB networks effectively inhibit diffusional creep processes at high temperatures. We obtained an unprecedented creep resistance, with creep rates of ~10<sup>-7</sup> per second under gigapascal stress at 700°C (~61% melting point), outperforming that of conventional superalloys.

Bhattacharya A, Shen Y F, Hefferan C M, et al.

Grain boundary velocity and curvature are not correlated in Ni polycrystals

[J]. Science, 2021, 374: 189

DOI      PMID     

[Figure: see text].

Lin B, Jin Y, Hefferan C M, et al.

Observation of annealing twin nucleation at triple lines in nickel during grain growth

[J]. Acta Mater., 2015, 99: 63

DOI      URL    

Liu T G, Xia S, Zhou B X, et al.

Three-dimensional characteristics of the grain boundary networks of conventional and grain boundary engineered 316L stainless steel

[J]. Mater. Charact., 2017, 133: 60

DOI      URL     [本文引用: 1]

Wanner T, Fuller E R, Saylor D M.

Homology metrics for microstructure response fields in polycrystals

[J]. Acta Mater., 2010, 58: 102

DOI      URL     [本文引用: 1]

Kobayashi S, Tsurekawa S, Watanabe T.

A new approach to grain boundary engineering for nanocrystalline materials

[J]. Beilstein J. Nanotechnol., 2016, 7: 1829

DOI      URL     [本文引用: 1]

A new approach to grain boundary engineering (GBE) for high performance nanocrystalline materials, especially those produced by electrodeposition and sputtering, is discussed on the basis of some important findings from recently available results on GBE for nanocrystalline materials. In order to optimize their utility, the beneficial effects of grain boundary microstructures have been seriously considered according to the almost established approach to GBE. This approach has been increasingly recognized for the development of high performance nanocrystalline materials with an extremely high density of grain boundaries and triple junctions. The effectiveness of precisely controlled grain boundary microstructures (quantitatively characterized by the grain boundary character distribution (GBCD) and grain boundary connectivity associated with triple junctions) has been revealed for recent achievements in the enhancement of grain boundary strengthening, hardness, and the control of segregation-induced intergranular brittleness and intergranular fatigue fracture in electrodeposited nickel and nickel alloys with initial submicrometer-grained structure. A new approach to GBE based on fractal analysis of grain boundary connectivity is proposed to produce high performance nanocrystalline or submicrometer-grained materials with desirable mechanical properties such as enhanced fracture resistance. Finally, the potential power of GBE is demonstrated for high performance functional materials like gold thin films through precise control of electrical resistance based on the fractal analysis of the grain boundary microstructure.

Yang D, Bai Q, Hu Y, et al.

Fractal analysis of the effect of grain boundary character on Te-induced brittle cracking in GH3535 alloy

[J]. Acta Metall. Sin., 2023, 59: 248

DOI      [本文引用: 1]

GH3535 alloy has been used as the main structural material of molten salt reactor, which exhibits good high-temperature strength and excellent corrosion resistance to the molten salts. The intergranular cracking of GH3535 was detected after four years of operation of the molten salt reactor experiment, which was attributed to the inward diffusion of fission products Te. Grain boundary engineering (GBE) has been successfully applied to enhance the grain-boundary-related properties of the materials by increasing the frequency of low Σ coincidence site lattice grain boundaries and tailoring the grain boundary network. The in situ three-point bending test was used to assess the cracking properties of Non-GBE and GBE samples following Te infiltration at 700oC for 500 h. Fractal analysis statistics of various types of grain boundaries and cracks following in situ three-point bending tests were used. The result shows that the fractal dimension of cracks is in accord with that of the random grain boundaries (RGBs). The stronger the fracture resistance of materials, the lower the value of the RGB fractal dimension. The GH3535 alloy GBE samples with a bigger average size and more uniformly distributed twin grain clusters will have greater cracking resistance.

杨 杜, 白 琴, 胡 悦 .

GH3535合金中晶界特征对碲致脆性开裂影响的分形分析

[J]. 金属学报, 2023, 59: 248

[本文引用: 1]

Zhu S Y.

In silico grain boundary engineering by analysis on discrete complexes

[D]. Manchester: The University of Manchester, 2023

[本文引用: 1]

Hatcher A. Algebraic Topology [M]. Beijing: Tsinghua University, 2005: 1

[本文引用: 2]

Salnikov V, Cassese D, Lambiotte R.

Simplicial complexes and complex systems

[J]. Eur. J. Phys., 2018, 40: 014001

[本文引用: 1]

Zhu S Y, Gao W J, Yi M, et al.

Integrated discrete cell complexes and finite element analysis for microstructure topology evolution during severe plastic deformation

[J]. Comput. Mater. Contin., 2025, 85: 657

[本文引用: 6]

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