Three-Dimensional Atomic Structure of Grain Boundaries Resolved by Atomic-Resolution Electron Tomography

Abstract

•3D atomic structure and crystallography of general grain boundaries are resolved•High-angle GB loses translational periodicity due to undulated curvature•3D structure of a decahedron structural unit is experimentally determined•Kinks and jogs are atomically resolved in a dislocation-type GB Grain boundaries (GBs) are one of the most widely existing interfaces in polycrystalline materials. Scientists have devoted great efforts in understanding the structures and behaviors of GBs for more than a century. However, due to the complexity of GBs and the limitations of widely used two-dimensional imaging techniques, the structure of general GBs still remains largely unknown. To this end, by using atomic-resolution electron tomography, we present quantitative study of the three-dimensional atomic structure and crystallography of general GBs in nanometals. Our findings will have significant impact on the fundamental understanding of GB behaviors and properties of polycrystals in general, and this research also shows the importance of developing methods to include the non-planar nature of GBs in order to statistically evaluate their behaviors in modeling studies. The application of atomic-resolution electron tomography could be extended to film and bulk materials with proper sample-preparation techniques. Grain boundaries (GBs) determine the properties of polycrystals, and tailoring the GB structure offers a promising method for the discovery and engineering of new materials. However, GB structures are far from well understood because of their structural complexity and limitations of conventional projection imaging methods. Here, we decipher three-dimensional atomic structure and crystallography of GBs in nanometals using atomic-resolution electron tomography. Unlike conventional descriptions, whereby they are either straight or curved planar planes with one-dimensional translational symmetry, we show that the high-angle GBs completely lose translational symmetry due to undulated curvature related to configurations of structural units. Moreover, we directly visualize kinks and jogs at the single-atom scale in dislocation-type GBs and investigate their mobilities. Our findings bring new insights to the conventional wisdom of GBs and show the importance of developing methods to include the non-planar nature of GBs to statistically evaluate the behavior of GBs in modeling studies. Grain boundaries (GBs) determine the properties of polycrystals, and tailoring the GB structure offers a promising method for the discovery and engineering of new materials. However, GB structures are far from well understood because of their structural complexity and limitations of conventional projection imaging methods. Here, we decipher three-dimensional atomic structure and crystallography of GBs in nanometals using atomic-resolution electron tomography. Unlike conventional descriptions, whereby they are either straight or curved planar planes with one-dimensional translational symmetry, we show that the high-angle GBs completely lose translational symmetry due to undulated curvature related to configurations of structural units. Moreover, we directly visualize kinks and jogs at the single-atom scale in dislocation-type GBs and investigate their mobilities. Our findings bring new insights to the conventional wisdom of GBs and show the importance of developing methods to include the non-planar nature of GBs to statistically evaluate the behavior of GBs in modeling studies. Grain boundaries (GBs) are one of the most important crystalline defects and most widely existing interfaces in crystalline materials.1Sutton A.P. Balluffi R.W. Interfaces in Crystalline Materials. 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Mater. 2012; 11: 930Crossref PubMed Scopus (251) Google Scholar applied discrete approaches in characterizing the 3D atomic lattices of a ∼3-nm free-standing Ag nanoparticle and an Au nanorod, respectively, based on a number of atomically resolved discrete high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images. Nevertheless, the special requirement of images taken along certain low-index zone axes relies on prior knowledge of orientation of the crystal sample. Meanwhile, it is notable that these methods are only applicable to single-crystalline nanoparticles or nanorods rather than general polycrystalline materials, as it is almost impossible to obtain atomic-resolution images of two crystals at both sides of a general GB along a series of low-index zone axes at the same time. Recently, Miao and coworkers41Scott M.C. Chen C.C. Mecklenburg M. Zhu C. Xu R. Ercius P. Dahmen U. Regan B.C. Miao J. 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Nathanson M. et al.Observing crystal nucleation in four dimensions using atomic electron tomography.Nature. 2019; 570: 500-503Crossref PubMed Scopus (129) Google Scholar have made a significant breakthrough in using atomic-resolution electron tomography to determine the 3D atomic structure of nanocrystals, although the atomic-resolution electron tomography technique has so far only been applied to systems such as individual nanoparticles or needles. Here, for the first time, 3D atomic structures of general GBs are deciphered with electron tomography at sub-ångström resolution. We determine the 3D atomic structure of both GBs composed of SUs and dislocation arrays in nanoporous metal. The SU-type GBs are non-planar at atomic scale and lose translational periodicity in all directions. Based on the GB atomic coordinates, the statistical distribution of GB coordination numbers (CNs), SUs, and curvature are correlatively analyzed. The undulated GB curvature is found to be closely related to distribution of different types of SUs. Moreover, by thoroughly deciphering the 3D atomic configuration of kinks and jogs on dislocations, we provide direct experimental evidence for the dislocation kink-and-jog model45Hirth J.P. Lothe J. Theory of Dislocations.Second Edition. Wiley, 1982Google Scholar proposed over half a century ago. Nanoporous gold (NPG) is used as a model material in this work. The NPG sample is specially designed for electron tomography experiments by directly dealloying a perforated alloy foil with a large thickness gradient from regions of interest to the substrate at the outer rim (for details see Experimental Procedures). The atomic-resolution electron tomography was performed on the basis of a tilt series of aberration-corrected HAADF-STEM images along a single axis (see schematic illustration in Figure 1A). Details of the tomographic reconstruction are described in Experimental Procedures. Figure 1B shows the 3D microstructure of the NPG specimen obtained by electron tomography with nanometer resolution and a 3D reconstructed single-crystalline NPG ligament with atomic resolution. Detailed analysis of 3D power spectra (Figure 1C) from the tomographic reconstruction shows that the resolution of the tomography reaches 0.53 Å (see details in Figure S1). In a more specific case, we mapped the tilting path and reconstruction results of a ligament on a stereographic projection (Figure 1D). The reconstruction was based on a tilting series obtained along an axis denoted by the magenta line, and representative images of the reconstructed NPG ligament viewed from different zone axes were atomically resolved, including both low-index zone axes such as <110> and <001> and high-index zone axes such as <112> and <013> (Figure S2). Agreeing well with the result of 3D reconstructed power spectrum, a series of atomically resolved reconstructed projections (not experimentally acquired) (Figure S3) demonstrate that sub-ångström resolution is achieved in different directions. Using atomic-resolution electron tomography, 3D atomic structures of bicrystals and polycrystals containing different GBs were resolved. For example, Figure 2A shows the 3D reconstruction of an NPG ligament containing a random GB. An atomically resolved cross-section of the GB (Figure 2B) shows that the two crystals have different crystallographic orientations. Moreover, a polycrystalline ligament composed of four crystals was reconstructed (Figures 2C, 2D, and S4). By tilting the reconstructed polycrystals in 3D real space, the orientation relationships of all the crystals were successfully determined. According to the orientation map (inset in Figure 2C), the three GBs can be identified as general GBs. 3D crystallography and atomic structures of GBs were systematically investigated based on atomic-resolution electron tomography results. Figure 3A shows the 3D reconstruction of a high-angle GB (see experimental tilt series and reconstructed projections in Figures S5 and S6 and Video S1, and see also a detailed evaluation of the quality of the reconstruction in Figures S7–S11 and Table S1). By normalizing atomic coordinates of the two crystals, the crystallographic parameters of the GB, i.e., the rotation axis and angle (Figure 3B) of the GB, were determined as [0, 0.73, 0.69] and 27.0°, and the transformation matrix between the two crystals is [0.89−0.310.330.310.950.05−0.330.050.94](for details see Experimental Procedures and Figure S12).46Altmann S.L. Rotations, Quaternions, and Double Groups. Clarendon Press; Oxford University Press, 1986Google Scholar The GB plane is near (57-7) of the top half-crystal in Figure 3A. Moreover, the 3D atomic structure of the GB was analyzed based on the 3D reconstruction (Videos S2, S3, and S4; Figures S7–S10). The result (Figure S13) shows that the GB can be described by a combination of D- and E-type SUs47Rittner J.D. Seidman D.N. <110> symmetric tilt grain-boundary structures in fcc metals with low stacking-fault energies.Phys. Rev. B. 1996; 54: 6999-7015Crossref Scopus (308) Google Scholar and pentagons (hereafter termed P-type SUs). In particular, the 3D atomic structure of P-type SUs was experimentally identified for the first time. The reconstructed result (Figure 3C) shows that P-type SU has a decahedron configuration, which was theoretically proposed decades ago48Ashby M.F. Spaepen F. Williams S. The structure of grain boundaries described as a packing of polyhedra.Acta Metall. Mater. 1978; 26: 1647-1663Crossref Scopus (188) Google Scholar,49Vitek V. Sutton A.P. Smith D.A. Pond R.C. Grain-Boundary Structure and Kinetics. American Society for Metals, 1980Google Scholar but has never been directly resolved. Next, a characteristic angle between two vectors (from one atom to its two random nearest-neighbor atoms) was employed to describe the GB structure (Figure 3D). Characteristic angle for perfect crystals shows two sharp peaks at ∼60° and ∼90°, which agree well with a face-centered cubic (fcc) structure. In contrast, for the GB region, the peak at 90° is significantly weakened and an evident broadening can be observed at ∼60° (for details see Supplemental Experimental Procedures). Moreover, the statistical distribution and map of CNs of all GB atoms (Figures 3E and 3F) were determined by identifying the nearest neighbors of each GB atom. This indicates that the average CN of GB atoms is evidently reduced to ∼9.5 from 12 of the perfect fcc structure. These characteristics imply that the GB structure deviates from fcc crystals. Besides, it is worth noting that a valley-shaped region (Figure 3F) mainly composed of P-type SUs (Figure S13) is identified with lower CN, which confirms that P-type SU is less coordinated than E-type SU. Contour and curvature maps (Figures 3G and 3H) and 3D geometry of the GB (Figure S14) show that the GB is non-planar and has inhomogeneous curvatures. As a result, the distribution of the GB SUs is found not to obey translational periodicity. Remarkably, the distribution of P- and E-type SUs is found to be highly related to local curvatures of the GB, as P-type SUs mainly locate in regions with positive curvature while E-type SUs are in regions with negative curvature. https://www.cell.com/cms/asset/5bc165cf-ab4f-4a67-90e3-54be168aa740/mmc2.mp4Loading ... Download .mp4 (5.98 MB) Help with .mp4 files Video S1. 3D Visualization of the GB, Related to Figure 3 https://www.cell.com/cms/asset/0c09e0ee-6053-460c-88f3-6b146383d2c8/mmc3.mp4Loading ... Download .mp4 (3.22 MB) Help with .mp4 files Video S2. Multiple Cross-Sections Parallel to the xz Plane of a Structural-Unit-Type GB, Related to Figure 3 https://www.cell.com/cms/asset/c604ce2d-bfc9-487b-b71b-c2765a4059a8/mmc4.mp4Loading ... Download .mp4 (1.35 MB) Help with .mp4 files Video S3. Multiple Cross-Sections Parallel to the yz Plane of a Structural-Unit-Type GB, Related to Figure 3 https://www.cell.com/cms/asset/72cf629e-c722-49b1-bf1a-aa5ff8f1801f/mmc5.mp4Loading ... Download .mp4 (1.43 MB) Help with .mp4 files Video S4. Multiple Cross-Sections Parallel to the xy Plane of a Structural-Unit-Type GB, Related to Figure 3 Furthermore, 3D atomic structure of a dislocation-type GB (Figures 4A, 4B , and S15) was determined based on the 3D reconstruction (Video S5 and Figure S16). The GB comprises three dislocations, all with Burgers vectors of 1/2[1-10], resulting in a misorientation of approximately 8°. We directly observed core defects including both jogs (Figure 4C) and kinks (Figure 4D) in the GB dislocations. Interestingly, versatile configurations were observed: single kinks or jogs, kink or jog pairs, and kink-jog complexes. Using MD simulations, we investigated the mobilities of kinks and jogs and their influence on the deformation behavior of GBs (for details see Experimental Procedures and Figure S17). Figure 4E shows stress-strain curves for a perfect dislocation-type GB and that composed of dislocation arrays with kinks and jogs, respectively. The curve of GB with kinks shows characteristics similar to those of the perfect GB; in contrast, the GB with jogs shows much higher shear resistance and yield strength compared with the others. Detailed trajectory analyses show that the GB with kinks and perfect GB show smooth migration during shear deformation (Figure S18), while for the GB with jogs, a strong pinning effect is introduced to dislocations by existing jogs (jogs 1 and 2 in Figure 4F) and the newly generated ones (jog 3 in Figure 4F) during deformation. https://www.cell.com/cms/asset/820b06b8-5554-4bb5-b1ea-cdb910adc3fa/mmc6.mp4Loading ... Download .mp4 (3.02 MB) Help with .mp4 files Video S5. Multiple Cross-Sections of a Dislocation-Type GB, Related to Figure 4 GB curvature and its local atomic configuration are two crucial factors defining GB mobility.50Upmanyu M. Smith R. Srolovitz D.J. Atomistic simulation of curvature driven grain boundary migration.Interf. Sci. 1998; 6: 41-58Crossref Google Scholar In this work, we uncovered that P-type SUs are prone to aggregate in regions with positive curvatures while E-type SUs aggregate with negative curvatures in a high-angle GB (Figures 3G and 3H). P-type SUs have been theoretically proposed in close-packed metals (including fcc-structured metals) decades ago by Ashby et al.48Ashby M.F. Spaepen F. Williams S. The structure of grain boundaries described as a packing of polyhedra.Acta Metall. Mater. 1978; 26: 1647-1663Crossref Scopus (188) Google Scholar and Vitek et al.49Vitek V. Sutton A.P. Smith D.A. Pond R.C. Grain-Boundary Structure and Kinetics. American Society for Metals, 1980Google Scholar In particular, as one of the eight polyhedral models proposed by Ashby et al., pentagonal bipyramids or decahedrons have been demonstrated to exist in a variety of GBs with different misorientations by theoretical calculations, although they have not yet been experimentally observed. This pentagonal bipyramid model is exactly consistent with our experimental observations of P-type SUs. In addition, it should be noted that when curved GBs are imaged by conventional high-resolution TEM, the constituent SUs will be overlapped along the projection direction due to the non-planar nature of the GBs. As a result, the atomic arrangements at the GBs in 2D projection, which are easily misinterpreted, can scarcely reveal the real structure of the SUs. We believe this to be the main reason why P-type SUs have not been effectively resolved by conventional experiments. Moreover, compared with E-type SUs, P-type SUs are found to have lower averaged CN (Figure 3F and Supplemental Experimental Procedures). Owing to the distinct atomic configurations and coordination environments, the free energy and, thereby, the mobilities51Sutton A.P. Vitek V. On the structure of tilt grain-boundaries in cubic metals .1. Symmetrical tilt boundaries.Philos. Trans. R. Soc. A. 1983; 309: 1-68Google Scholar,52Cahn J.W. Mishin Y. Suzuki A. Coupling grain boundary motion to shear deformation.Acta Mater. 2006; 54: 4953-4975Crossref Scopus (609) Google Scholar of these two types of SUs could vary under stress field. Therefore, the roughening of GB with 3D undulated curvature observed in this work could be induced by the different mobilities of P- and E-type SUs, in response to the overall curvature-induced driving force that draws GBs toward their center of curvature.50Upmanyu M. Smith R. Srolovitz D.J. Atomistic simulation of curvature driven grain boundary migration.Interf. Sci. 1998; 6: 41-58Crossref Google Scholar This SU-dependent GB roughening behavior may have significant influence on the mechanical and other physical properties of GBs in nanometals. Two types of defects exist in dislocation cores: segments lying in a glide plane, i.e., kinks, and segments normal to a glide plane, i.e., jogs. It is generally accepted that the mobility of kinks and jogs controls the mobility of dislocations.45Hirth J.P. Lothe J. Theory of Dislocations.Second Edition. Wiley, 1982Google Scholar,53Kacher J. Cui B. Robertson I.M. In situ and tomographic characterization of damage and dislocation processes in irradiated metallic alloys by transmission electron microscopy.J. Mater. Res. 2015; 30: 1202-1213Crossref Scopus (8) Google Scholar, 54Tanaka M. Higashida K. Kaneko K. Hata S. Mitsuhara M. Crack tip dislocations revealed by electron tomography in silicon single crystal.Scripta Mater. 2008; 59: 901-904Crossref Scopus (71) Google Scholar, 55Barnard J.S. Sharp J. Tong J.R. Midgley P.A. Weak-beam dark-field electron tomography of dislocations in GaN.J. Phys. Conf. Ser. 2006; 26: 247-250Crossref Scopus (15) Google Scholar Also, interactions between kinks and jogs will influence the glide process of dislocations. In our simulations, during shear deformation of the GB with jogs, kinks will also initiate from the existing jogs to facilitate GB dislocation migration. It is noteworthy that in the MD simulation, kinks always coexist with jogs, while in the 3D reconstructed dislocation-type GB (Figure 4A), jogs existing separately from kinks (e.g., dislocation 2 in Figure 4) were also experimentally observed. This could be induced by a more complex local stress state and/or geometry of GBs in the NPG investigated in this work. Moreover, as the frictional drag of jogs on a dislocation is much stronger than that of kinks (Figure 4E), mobilities of the GB dislocations should be distinct from each other due to different configurations of kinks and jogs on each dislocation. Consequently, it will lead to inhomogeneous mobility of dislocation-type GBs, which may be further investigated by combining time-resolved atomic-resolution electron tomography and high-throughput MD simulations. GB behaviors depend on both their crystallographic misorientations56Gottstein G. Molodov D.A. Shvindlerman L.S. Srolovitz D.J. Winning M. Grain boundary migration: misorientation dependence.Curr. Opin. Solid State Mater. Sci. 2001; 5: 9-14Crossref Scopus (60) Google Scholar and local atomic structures.57Zhu Q. Cao G. Wang J. Deng C. Li J. Zhang Z. Mao S.X. In situ atomistic observation of disconnection-mediated grain boundary migration.Nat. Commun. 2019; 10: 156Crossref PubMed Scopus (73) Google Scholar There are existing methods to acquire a 3D orientation map at a variety of length scales, such as X-ray tomography,58Ludwig W. Schmidt S. Lauridsen E.M. Poulsen H.F. X-ray diffraction contrast tomography: a novel technique for three-dimensional grain mapping of polycrystals. I. Direct beam case.J. Appl.Crystallogr. 2008; 41: 302-309Crossref Scopus (178) Google Scholar EBSD tomography,19Inkson B.J. Mulvihill M. Möbus G. 3D determination of grain shape in a FeAl-based nanocomposite by 3D FIB tomography.Scripta Mater. 2001; 45: 753-758Crossref Scopus (136) Google Scholar dark-field imaging,59Liu H.H. Schmidt S. Poulsen H.F. Godfrey A. Liu Z.Q. Sharon J.A. Huang X. Three-dimensional orientation mapping in the transmission electron microscope.Science. 2011; 332: 833-834Crossref PubMed Scopus (97) Google Scholar and precession electron diffraction.60Eggeman A.S. Krakow R. Midgley P.A. Scanning precession electron tomography for three-dimensional nanoscale orientation imaging and crystallographic analysis.Nat. Commun. 2015; 6: 7267Crossref PubMed Scopus (52) Google Scholar However, the orientation information revealed by these methods is limited to resolutions from micrometer-to-nanometer scales. Moreover, atomic structural information is barely obtainable by these methods. In this work, the crystallographic orientation information (including transformation matrix) and local 3D atomic structures of GBs are simultaneously obtained for the first time through atomically tomographic reconstruction. Therefore, it provides a comprehensive tool enabling simultaneous 3D orientation and atomic structural analysis for GB or interface study in the future. In conclusion, by using electron tomography with sub-ångström resolution, we directly deciphered the 3D atomic structure of general GBs in nanometals for the first time. We anticipate that the novel insights revealed by the atomic-resolution electron tomography will significantly advance our understanding of the structure of general GBs and thus open the door to the study of fundamental issues of interfaces such as interface motion, segregation, phase transition, diffusion, and defect interactions in a variety of materials with 3D atomic resolution.