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Intrinsic toughening and stable crack propagation in hexagonal boron nitride


If a bulk material can withstand a high load without any irreversible damage (such as plastic deformation), it is usually brittle and can fail catastrophically1,2. This trade-off between strength and fracture toughness also extends into two-dimensional materials space3,4,5. For example, graphene has ultrahigh intrinsic strength (about 130 gigapascals) and elastic modulus (approximately 1.0 terapascal) but is brittle, with low fracture toughness (about 4 megapascals per square-root metre)3,6. Hexagonal boron nitride (h-BN) is a dielectric two-dimensional material7 with high strength (about 100 gigapascals) and elastic modulus (approximately 0.8 terapascals), which are similar to those of graphene8. Its fracture behaviour has long been assumed to be similarly brittle, subject to Griffith’s law9,10,11,12,13,14. Contrary to expectation, here we report high fracture toughness of single-crystal monolayer h-BN, with an effective energy release rate up to one order of magnitude higher than both its Griffith energy release rate and that reported for graphene. We observe stable crack propagation in monolayer h-BN, and obtain the corresponding crack resistance curve. Crack deflection and branching occur repeatedly owing to asymmetric edge elastic properties at the crack tip and edge swapping during crack propagation, which intrinsically toughens the material and enables stable crack propagation. Our in situ experimental observations, supported by theoretical analysis, suggest added practical benefits and potential new technological opportunities for monolayer h-BN, such as adding mechanical protection to two-dimensional devices.

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Fig. 1: In situ tensile test of a monolayer h-BN test specimen without a pre-crack.
Fig. 2: Fracture of pre-cracked monolayer h-BN and stable crack propagation.
Fig. 3: Crack initiation in h-BN and graphene.
Fig. 4: Crack propagation and effective energy release rate.

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Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The LabView codes used in this work are available from the corresponding authors upon reasonable request.


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J.L., Y.Y., H.G. and B.N. gratefully acknowledge financial support by the US Department of Energy, Office of Basic Energy Sciences, under grant number DE-SC0018193. The simulations were performed on resources provided by the Extreme Science and Engineering Discovery Environment through grant MSS090046 and the Center for Computation and Visualization, Brown University.

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Authors and Affiliations



Y.Y. and J.L. designed the experiments and analysed the data. Z.S., B.N., X.L. and H.G. performed simulations and analysed the results. G.L. and X. X. grew h-BN. Q.Z. and L.G. performed TEM analysis. Y.Y., B.Z. and C.W. transferred h-BN and carried out in situ tensile tests. Y.Y. and Z.S., supervised by J.L. and H.G., drafted the manuscript with input, discussion and approval from all co-authors. Y.Y. and Z.S. contributed equally to this work.

Corresponding authors

Correspondence to Huajian Gao or Jun Lou.

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The authors declare no competing interests.

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Peer review information Nature thanks Matthew Begley and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

This file contains supplementary text, supplementary equations s1 – s9, supplementary figure s1 – s14, supplementary tables s1 – s6 and supplementary references.

Supplementary Video 1

In situ tensile test of monolayer h-BN without pre-crack.

Supplementary Video 2

In situ tensile test of monolayer h-BN with pre-crack.

Supplementary Video 3

Quasi-static tensile test of monolayer h-BN channel with pre-crack (~80 nm) coloured by σyy contour.

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Yang, Y., Song, Z., Lu, G. et al. Intrinsic toughening and stable crack propagation in hexagonal boron nitride. Nature 594, 57–61 (2021).

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