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Structural transition and migration of incoherent twin boundary in diamond


Grain boundaries (GBs), with their diversity in both structure and structural transitions, play an essential role in tailoring the properties of polycrystalline materials1,2,3,4,5. As a unique GB subset, {112} incoherent twin boundaries (ITBs) are ubiquitous in nanotwinned, face-centred cubic materials6,7,8,9. Although multiple ITB configurations and transitions have been reported7,10, their transition mechanisms and impacts on mechanical properties remain largely unexplored, especially in regard to covalent materials. Here we report atomic observations of six ITB configurations and structural transitions in diamond at room temperature, showing a dislocation-mediated mechanism different from metallic systems11,12. The dominant ITBs are asymmetric and less mobile, contributing strongly to continuous hardening in nanotwinned diamond13. The potential driving forces of ITB activities are discussed. Our findings shed new light on GB behaviour in diamond and covalent materials, pointing to a new strategy for development of high-performance, nanotwinned materials.

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Fig. 1: Coexistent multiple configurations of {112} ITBs in nt-diamond.
Fig. 2: In situ observation of ITB transitions at atomic resolution.
Fig. 3: Configuration-dependent ITB migration.
Fig. 4: Evidence for the stress-driven mechanism of ITB activities.

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The data supporting this study’s findings are available within this article and its Supplementary Information. Additional data are available from the corresponding author on reasonable request.


  1. Sutton, A. P. & Balluffi, R. W. Interfaces in Crystalline Materials (Oxford Univ. Press, 1995).

  2. Chookajorn, T., Murdoch, H. A. & Schuh, C. A. Design of stable nanocrystalline alloys. Science 337, 951–954 (2002).

    Article  ADS  Google Scholar 

  3. Dillon, S. J., Tang, M., Carter, W. C. & Harmer, M. P. Complexion: a new concept for kinetic engineering in materials science. Acta Mater. 55, 6208–6218 (2007).

    Article  ADS  CAS  Google Scholar 

  4. Hu, J., Shi, Y. N., Sauvage, X., Sha, G. & Lu, K. Grain boundary stability governs hardening and softening in extremely fine nanograined metals. Science 355, 1292–1296 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  5. Khalajhedayati, A., Pan, Z. & Rupert, T. J. Manipulating the interfacial structure of nanomaterials to achieve a unique combination of strength and ductility. Nat. Commun. 7, 10802 (2016).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  6. Beyerlein, I. J., Zhang, X. & Misra, A. Growth twins and deformation twins in metals. Annu. Rev. Mater. Res. 44, 329–363 (2014).

    Article  ADS  CAS  Google Scholar 

  7. Guo, Y. et al. Twin thickness and dislocation interactions affect the incoherent-twin boundary phase in face-centered cubic metals. Cell Rep. Phys. Sci. 3, 100736 (2022).

    Article  CAS  Google Scholar 

  8. Yu, K. Y. et al. Removal of stacking-fault tetrahedra by twin boundaries in nanotwinned metals. Nat. Commun. 4, 1377 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  9. Yu, W., Shen, S., Liu, Y. & Han, W. Nonhysteretic superelasticity and strain hardening in a copper bicrystal with a ∑3{112} twin boundary. Acta Mater. 124, 30–36 (2017).

    Article  ADS  CAS  Google Scholar 

  10. Xu, L. et al. Structure and migration of (112) step on (111) twin boundaries in nanocrystalline copper. J. Appl. Phys. 104, 113717 (2008).

    Article  ADS  Google Scholar 

  11. Meiners, T., Frolov, T., Rudd, R. E., Dehm, G. & Liebscher, C. H. Observations of grain-boundary phase transformations in an elemental metal. Nature 579, 375–378 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  12. Langenohl, L. et al. Dual phase patterning during a congruent grain boundary phase transition in elemental copper. Nat. Commun. 13, 3331 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  13. Huang, Q. et al. Nanotwinned diamond with unprecedented hardness and stability. Nature 510, 250–253 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  14. Irifune, T., Kurio, A., Sakamoto, S., Inoue, T. & Sumiya, H. Ultrahard polycrystalline diamond from graphite. Nature 421, 599–600 (2003).

    Article  ADS  CAS  PubMed  Google Scholar 

  15. Lu, K., Lu, L. & Suresh, S. Strengthening materials by engineering coherent internal boundaries at the nanoscale. Science 324, 349–352 (2009).

    Article  ADS  CAS  PubMed  Google Scholar 

  16. Rajeshwari, K. S. et al. Grain boundary diffusion and grain boundary structures of a Ni-Cr-Fe- alloy: evidences for grain boundary phase transitions. Acta Mater. 195, 501–518 (2020).

    Article  ADS  Google Scholar 

  17. Frazier, W. E., Rohrer, G. S. & Rollett, A. D. Abnormal grain growth in the Potts model incorporating grain boundary complexion transitions that increase the mobility of individual boundaries. Acta Mater. 96, 390–398 (2015).

    Article  ADS  CAS  Google Scholar 

  18. Luo, J., Cheng, H., Asl, K. M., Kiely, C. J. & Harmer, M. P. The role of a bilayer interfacial phase on liquid metal embrittlement. Science 333, 1730–1733 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  19. Cantwell, P. R. et al. Grain boundary complexion transitions. Annu. Rev. Mater. Res. 50, 465–492 (2020).

    Article  ADS  CAS  Google Scholar 

  20. Wei, J. et al. Direct imaging of atomistic grain boundary migration. Nat. Mater. 20, 951–955 (2021).

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Wang, Z. et al. Atom-resolved imaging of ordered defect superstructures at individual grain boundaries. Nature 479, 380–383 (2011).

    Article  ADS  CAS  PubMed  Google Scholar 

  22. Wei, J., Feng, B., Tochigi, E., Shibata, N. & Ikuhara, Y. Direct imaging of the disconnection climb mediated point defects absorption by a grain boundary. Nat. Commun. 13, 1455 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  23. Zhu, Q., Samanta, A., Li, B., Rudd, R. E. & Frolov, T. Predicting phase behavior of grain boundaries with evolutionary search and machine learning. Nat. Commun. 9, 467 (2018).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  24. Wang, L. et al. Tracking the sliding of grain boundaries at the atomic scale. Science 375, 1261–1265 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  25. Chu, S. et al. In situ atomic-scale observation of dislocation climb and grain boundary evolution in nanostructured metal. Nat. Commun. 13, 4151 (2022).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  26. Paxton, A. T. & Sutton, A. P. A tight-binding study of grain boundaries in silicon. Acta Metall. 37, 1693–1715 (1989).

    Article  CAS  Google Scholar 

  27. Sawada, H. & Ichinose, H. Structure of {112} Σ3 boundary in silicon and diamond. Scr. Mater. 44, 2327–2330 (2001).

    Article  CAS  Google Scholar 

  28. Sawada, H., Ichinose, H. & Kohyama, M. Gap states due to stretched bonds at the (112) Σ3 boundary in diamond. J. Phys. Condens. Matter 19, 026223 (2007).

    Article  ADS  Google Scholar 

  29. Xiao, J. et al. Strengthening-softening transition in yield strength of nanotwinned Cu. Scr. Mater. 162, 372–376 (2019).

    Article  CAS  Google Scholar 

  30. Liu, Y. et al. In situ nanoindentation studies on detwinning and work hardening in nanotwinned monolithic metals. JOM (1989) 68, 127–135 (2015).

    Article  Google Scholar 

  31. Bufford, D., Liu, Y., Wang, J., Wang, H. & Zhang, X. In situ nanoindentation study on plasticity and work hardening in aluminium with incoherent twin boundaries. Nat. Commun. 5, 4864 (2014).

    Article  ADS  CAS  PubMed  Google Scholar 

  32. Pumphrey, P. H., Malis, T. F. & Gleiter, H. Rigid body translations at grain boundaries. Philos. Mag. 34, 227–233 (1976).

    Article  ADS  CAS  Google Scholar 

  33. Wang, J., Anderoglu, O., Hirth, J. P., Misra, A. & Zhang, X. Dislocation structures of Σ3 {112} twin boundaries in face centered cubic metals. Appl. Phys. Lett. 95, 021908 (2009).

    Article  ADS  Google Scholar 

  34. Yang, S., Zhou, N., Zheng, H., Ong, S. P. & Luo, J. First-order interfacial transformations with a critical point: breaking the symmetry at a symmetric tilt grain boundary. Phys. Rev. Lett. 120, 085702 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  35. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  ADS  CAS  Google Scholar 

  36. Frøseth, A. G., Derlet, P. M. & Van Swygenhoven, H. Dislocations emitted from nanocrystalline grain boundaries: nucleation and splitting distance. Acta Mater. 52, 5863–5870 (2004).

    Article  ADS  Google Scholar 

  37. Wang, J. et al. Detwinning mechanisms for growth twins in face-centered cubic metals. Acta Mater. 58, 2262–2270 (2010).

    Article  ADS  CAS  Google Scholar 

  38. Yue, Y. et al. Hierarchically structured diamond composite with exceptional toughness. Nature 582, 370–374 (2020).

    Article  ADS  CAS  PubMed  Google Scholar 

  39. Wang, J., Misra, A. & Hirth, J. P. Shear response of Σ3 {112} twin boundaries in face-centered-cubic metals. Phys. Rev. B 83, 064106 (2011).

    Article  ADS  Google Scholar 

  40. Rajabzadeh, A., Mompiou, F., Legros, M. & Combe, N. Elementary mechanisms of shear-coupled grain boundary migration. Phys. Rev. Lett. 110, 265507 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  41. Marquis, E. A., Hamilton, J. C., Medlin, D. L. & Léonard, F. Finite-size effects on the structure of grain boundaries. Phys. Rev. Lett. 93, 156101 (2004).

    Article  ADS  CAS  PubMed  Google Scholar 

  42. Koike, J., Parkin, D. M. & Mitchell, T. E. Displacement threshold energy for type IIa diamond. Appl. Phys. Lett. 60, 1450–1452 (1992).

    Article  ADS  CAS  Google Scholar 

  43. Cazaux, J. Correlations between ionization radiation damage and charging effects in transmission electron microscopy. Ultramicroscopy 60, 411–425 (1995).

    Article  CAS  Google Scholar 

  44. Egerton, R. F., Li, P. & Malac, M. Radiation damage in the TEM and SEM. Micron 35, 399–409 (2004).

    Article  CAS  PubMed  Google Scholar 

  45. Regan, B. et al. Plastic deformation of single-crystal diamond nanopillars. Adv. Mater. 32, 1906458 (2020).

    Article  CAS  Google Scholar 

  46. Blumenau, A. T. et al. Dislocations in diamond: dissociation into partials and their glide motion. Phys. Rev. B 68, 014115 (2003).

    Article  ADS  Google Scholar 

  47. Yang, H. et al. Homogeneous and heterogeneous dislocation nucleation in diamond. Diam. Relat. Mater. 88, 110–117 (2018).

    Article  ADS  CAS  Google Scholar 

  48. Hÿtch, M. J., Snoeck, E. & Kilaas, R. Quantitative measurement of displacement and strain fields from HREM micrographs. Ultramicroscopy 74, 131–146 (1998).

    Article  Google Scholar 

  49. Michalewicz, Z. & Fogel, D. B. How to Solve It: Modern Heuristics (Springer, 2004).

  50. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 117, 1–19 (1995).

    Article  ADS  CAS  Google Scholar 

  51. Los, J. H. & Fasolino, A. Intrinsic long-range bond-order potential for carbon: performance in Monte Carlo simulations of graphitization. Phys. Rev. B 68, 024107 (2003).

    Article  ADS  Google Scholar 

  52. Xiao, J. et al. Dislocation behaviors in nanotwinned diamond. Sci. Adv. 4, eaat8195 (2018).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  53. Xiao, J. et al. Intersectional nanotwinned diamond-the hardest polycrystalline diamond by design. NPJ Comput. Mater. 6, 119 (2020).

    Article  ADS  CAS  Google Scholar 

  54. Pan, Y. et al. Extreme mechanical anisotropy in diamond with preferentially oriented nanotwin bundles. Proc. Natl Acad. Sci. USA 118, e2108340118 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).

    Article  ADS  CAS  Google Scholar 

  56. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Article  ADS  Google Scholar 

  57. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    Article  ADS  CAS  Google Scholar 

  58. Perdew, J. P. et al. Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, 6671–6687 (1992).

    Article  ADS  CAS  Google Scholar 

  59. Hirel, P. Atomsk: a tool for manipulating and converting atomic data files. Comput. Phys. Commun. 197, 212–219 (2015).

    Article  ADS  CAS  Google Scholar 

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We are grateful for financial support from the National Natural Science Foundation of China (nos. U20A20238, 52288102, 52090020 and 91963203), the National Key R&D Program of China (nos. 2018YFA0703400 and 2018YFA0305904) and the Natural Science Foundation of Hebei Province of China (no. E2022203109). We thank M. Veron of the Grenoble Institute of Technology for assistance with PED measurements.

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Authors and Affiliations



W.H., B.X. and Y.T. conceived the idea for this project. T.J., Y.G. and D.Y. prepared samples. Y.C., C.L. and S.Z. prepared STEM specimens. X.Z., B.L. and W.H. conducted STEM characterization. K.T., G.G., Z.L., K.L. and Y. Wu constructed the structural models and conducted simulations. B.X., Y. Wang, Z.Z., L.W., Z. Liu, A.N., A.V.S., W.H. and Y.T. analysed the data. W.H., B.X., Y. Wang and Y.T. drafted the manuscript, with contributions from all authors. K.T., X.Z. and Z. Li contributed equally to this work.

Corresponding authors

Correspondence to Wentao Hu, Bo Xu or Yongjun Tian.

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Extended data figures and tables

Extended Data Fig. 1 Microstructural features of nt-diamond.

Crystal orientation distribution of an nt-diamond specimen obtained by precession electron diffraction.

Extended Data Fig. 2 Structure differences among three symmetrical ITB configurations.

a, I. b, II. c, III. The corresponding structural models are shown as insets in the corresponding HAADF-STEM images. Atomic distances along the three lines (orange, red, and green) are measured with the profiles below each image. The difference in measured values reflects the changes in relative spatial positions between atoms (not bond length) on the projected plane, revealing a transition mechanism through the reconstruction of dislocation cores. The resolution difference on both sides of the ITBs (red arrows) originates from the relative displacement between adjacent domains in the \([1\bar{1}0]\) direction caused by ITB transition.

Extended Data Fig. 3 Dislocation characteristics of intrinsic SF, extrinsic SF, and ITB with configuration I.

a, An intrinsic SF bordered by a 30° mixed partial dislocation \((1/6[2\bar{1}\bar{1}])\). b, An intrinsic SF bordered by a 90° pure edge partial dislocation \((1/6[\bar{1}2\bar{1}])\). c, An extrinsic SF bordered by a partial-doublet containing one 30° mixed partial dislocation \((1/6[2\bar{1}\bar{1}])\) and one 90° pure edge partial dislocation \((1/6[\bar{1}2\bar{1}])\). d, An ITB with the configuration I, exhibits a partial triplet containing two 30° mixed partial dislocations (\(1/6[2\bar{1}\bar{1}]\) and \(1/6[\bar{1}\bar{1}2]\)) and one 90° pure edge partial dislocation \((1/6[2\bar{1}\bar{1}])\). e, The Burgers vectors of these partial dislocations. f, The structural models of these SFs and ITB corresponding to a to d, respectively. g,h, EELS line-scan across an ITB performed at an accelerating voltage of 200 kV, confirming the presence of sp2 bonds.

Extended Data Fig. 4 Dislocations, nanocracks, and boundary disordering associated with ITB transitions.

a, HAADF-STEM image of the ITB displayed in Fig. 2d−f, after further STEM scanning. be, A sequence of individual HAADF-STEM images (selected from the cyan box in a) after FFT filtering by choosing {111} diffractions (enclosed red circles in the inset FFT), showing the gradual generation of a dislocation loop. The red symbols mark two cutoff points of this dislocation loop. The Burgers circuits are also drawn in c and e, indicating a vector of \(1/2[0\bar{1}\bar{1}]\) or \(1/2[\bar{1}0\bar{1}]\) that can be identified only by projected on the \((1\bar{1}0)\) plane. fi, Raw HAADF-STEM images corresponding to those displayed in b−e, respectively, overlapped with the corresponding εyy mapping from GPA, revealing a mixed feature of this dislocation loop (the Burgers vector is not lying on the plane where the dislocation loop lies on). j, A HAADF-STEM image shows a VI-variant {112} ITB, which obliquely connects to a {111} twin at its left end. k, HAADF-STEM image of j acquired after 20 sec of STEM scanning. The left half of the ITB displays blurry and disordered features (cyan rectangle), and the rest of the ITB transforms into a mixture with structural units of configurations I, IV, and V. A nano crack can be developed at the ITB/CTB junction (red arrow). CTBs and SFs are labeled in both images with red solid and dash lines, respectively.

Extended Data Fig. 5 ITB transition and associated dislocation behaviours observed at the accelerating voltage of 200 kV.

ac, HAADF-STEM images (each superimposed from five consecutive frames) measured during a continuous STEM observation. The ITB structural transition, nanocracking at the end of ITB, and the junction of SF and CTB were observed. The electron beam was turned off after c for 5 min before d was acquired. d−f, Continuously acquired single STEM frames from a separate continuous observation. In adjacent domains, additional lattice tearing (white arrow) and a dislocation loop (white box) were identified. The inset in f (also the insets in g and h) shows the enlarged inverse fast Fourier filtering (IFFT) image of the selected area, clearly revealing the dislocation loop. g, A single STEM frame aquired after f with a 10 min interval of electron beam shutoff. The dislocation loop was observed to react with the CTB, resulting in dislocation multiplication and a step at the CTB. At the same time, a full dislocation was created at the position of lattice tearing (see the red arrow in f). h, A superimposed image from five consecutive STEM frames obtained with the electron beam turned off for 30 min between g and h. The dislocation loop was annihilated, along with the elimination of the CTB step. Meanwhile, the nanocracks were healed, and the previously created full dislocation evolved into an extrinsic SF (cyan box). i, A superimposed image from five consecutive STEM frames, obtained with the electron beam turned off for 30 min between h and i. Multiple dislocations and CTB steps were generated in addition to the extrinsic SF observed in h. In the panels, solid red lines: CTBs; dashed yellow lines: SFs; white arrow: nanocrack; : dislocation.

Extended Data Fig. 6 Structural features and relative changes of six ITB configurations, viewed along the \([1\bar{1}0]\) (upper) and [111] (lower) zone axes of the left twin domain.

a, I. b, II. c, III. d, IV. e, V. f, VI. The sp2- and dangling-bonded single-atom columns are highlighted in red and green, respectively, and spheres of different sizes represent atoms in adjacent \((1\bar{1}0)\) planes parallel to the page.

Extended Data Fig. 7 RBD across asymmetric ITBs in diamond.

a to c, Profiles of calculated RBD along the boundaries (a, IV; b, V; c, VI). The centre of the boundary is set as the origin of the abscissa. Different coloured profiles in each panel correspond to ITBs with different lengths as indicated in a and c. d, HAADF-STEM image of a short {112} ITB with an asymmetric V unit. e, HAADF-STEM image of a short {112} ITB with an asymmetric VI motif. RBD across the boundary is obvious for these short asymmetric boundaries, as manifested by the dumbbells (paired blue circles) on either side of the ITB that shifted inconsistently from the blue dash lines. fi, HAADF-STEM images of typical hybrid {112} ITBs composed of multiple configurations. Segments of boundaries exhibiting IV, V, and VI units are enclosed with yellow, red, and white boxes, respectively. CTBs and SFs (including CSFs) are labelled with red solid and yellow dash lines, respectively.

Extended Data Fig. 8 Mapping of irradiation-induced strains in an nt-diamond grain using PED.

a, The VBF image of the initial state. b, The orientation map along the y direction. ce, The strain maps at the initial state. f, The VBF image after scanning for 240 seconds within the red-boxed region. g, The orientation map along the y direction, indicating slight orientation variation in the irradiated region (red box). h to j, The strain maps corresponding to VBF image f. k, The VBF image after scanning for 480 seconds within the red-boxed region. l, The orientation map along the y direction. mo, The strain maps corresponding to the VBF image k. The gradient colour scale of the strain maps ranges from −0.5% to +0.5%. The white dots in strain maps mark the reference point for strain calculation. Scale bars, 20 nm.

Extended Data Fig. 9 Contour mappings of in-plane atomic strains during an ITB transition from asymmetric configuration V to symmetric configuration III.

a, Initial ITB with the configuration V. b, Partial transition ITB with configurations III and V, containing a structural unit of IV as an intermediate. c, Final state with configuration III. The strain maps were calculated based on the diffractions from the domain to the right of the ITB. The colour scheme (on the left side of the maps) ranges from −0.05 to +0.05.

Extended Data Fig. 10 Contour mappings of in-plane atomic strains during an ITB transition from mixed IV and VI segments to a hybrid state with multiple configurations f.

a, Initial state of the two-section (V and VI) boundary morphology. b,c, Transition states with a variable wave-like boundary shape, containing multiple configurations. The strain maps are calculated based on the diffractions from the domain to the right of ITB. The colour scheme (on the left side of the maps) ranges from −0.05 to +0.05.

Supplementary information

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Supplementary Video 1

The dynamic processes of {112} ITB transition shown in Fig. 2a–c.

Supplementary Video 2

The dynamic processes of {112} ITB transition shown in Fig. 2d–f.

Supplementary Video 3

Structure evolution during the transitions of configurations V, IV, III, II and I.

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Tong, K., Zhang, X., Li, Z. et al. Structural transition and migration of incoherent twin boundary in diamond. Nature 626, 79–85 (2024).

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