Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2019 Dec 4;10(1):5533.
doi: 10.1038/s41467-019-13378-w.

Approaching Diamond's Theoretical Elasticity and Strength Limits

Affiliations
Free PMC article

Approaching Diamond's Theoretical Elasticity and Strength Limits

Anmin Nie et al. Nat Commun. .
Free PMC article

Abstract

Diamond is the hardest natural material, but its practical strength is low and its elastic deformability extremely limited. While recent experiments have demonstrated that diamond nanoneedles can sustain exceptionally large elastic tensile strains with high tensile strengths, the size- and orientation-dependence of these properties remains unknown. Here we report maximum achievable tensile strain and strength of diamond nanoneedles with various diameters, oriented in <100>, <110> and <111> -directions, using in situ transmission electron microscopy. We show that reversible elastic deformation depends both on nanoneedle diameter and orientation. <100> -oriented nanoneedles with a diameter of 60 nm exhibit highest elastic tensile strain (13.4%) and tensile strength (125 GPa). These values are comparable with the theoretical elasticity and Griffith strength limits of diamond, respectively. Our experimental data, together with first principles simulations, indicate that maximum achievable elastic strain and strength are primarily determined by surface conditions of the nanoneedles.

Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Characterization of a <100> diamond nanoneedle. a A low-magnitude high-angle annular dark-field scanning TEM (HAADF-STEM) image of a diamond nanoneedle after fabrication. The needle axis is parallel to [100]. b Atomically resolved annular bright-field scanning TEM (ABF-STEM) image of the free surface as marked by the yellow box in a.
Fig. 2
Fig. 2
An example of reversible bending tests and associated lattice expansion determined by electron diffraction. a A TEM image of a <100> diamond nanoneedle with a tip diameter of ~50 nm. b The same nanoneedle during compression. c Finite element methods (FEM) simulation reproducing the shape in b revealing the maximum tensile strain (10.1%) located at the red circle. d The same nanoneedle, after unloading. The nanoneedle returns to its original shape. e-g Selected area electron diffraction (SEAD) patterns taken during the bending test at strain states of a, b, d, respectively. f was taken from the highly curved region (the red circled) in b.
Fig. 3
Fig. 3
A sequence of breaking tests on a single <100> - diamond nanoneedle. Arrows indicate locations of fractures in subsequent breaking tests. a Snapshots (a1–a4) capturing the maximum deformation immediately before the fracture during sequentially breaking the diamond nanoneedle for its high aspect ratio geometry. For more details, see Supplementary Movie 4. b FEM simulations reproducing the critical needle geometry immediately prior to breaking in a and with maximum principle strain distribution in the nanoneedle. c TEM images of the needle after the corresponding breaking tests, revealing that all fracture surfaces consist of {111} facets.
Fig. 4
Fig. 4
Orientation- and size-dependent fracture of diamond nanoneedles. a, b TEM images showing the original shape and the maximum deformation immediately before fracture of a <110> (a) and a <111> (b) nanoneedle. Scalebar is 100 nm. SEAD patterns (insets) indicate orientations in the needles before the tests. c, d FEM simulation reproducing critical geometry of the nanoneedles in a and b, respectively, with maximum principle strain distribution in the nanoneedles. e Relationship between size and fracture strain of the <100>, <110>, and <111> nanoneedles.
Fig. 5
Fig. 5
First principles simulations of diamond under uniaxial tension with and without a free surface. a Theoretical stress-strain relation of uniaxial tension along [100], [110], and [111] directions for a bulk diamond. Experimentally achieved maximum tensile strains are denoted on the curves. b Young’s moduli and the C–C bond length as a function of uniaxial tensile strain along the [100], [110], and [111] directions. Inset b is a perspective section of the diamond crystal. For tension along [111], the bonds parallel to [111] (denoted as the type-I bond) are elongated, while others (type-II bond) are slightly contracted. For tension along [110], type-I bonds are inclined from the (110) plane while type-II bonds are in the (110) plane. For tension along [100], all bonds belong to the type-I category. The bond lengths discussed in the main text belong to type-I bond. c–e Valence charge density at 0.165 e/Bohr3 of a diamond with different surface structures under tension along [100] at strain of 13.4%: c atomically flat surface; d free surface with a 1-atom step; and e free surface with a 2-atom step. The atomic configurations (insets) are constructed based on Fig. 1b. The maximum bond lengths immediately prior to fracture, as denoted in the charge density plots, are plotted as three open circles in the bottom panel of b. Clearly, crystals with larger surface defects tend to break first.

Similar articles

See all similar articles

References

    1. Liu F, Ming P, Li J. Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys. Rev. B. 2007;76:064120. doi: 10.1103/PhysRevB.76.064120. - DOI
    1. Zhu T, Li J. Ultra-strength materials. Prog. Mater. Sci. 2010;55:710–757. doi: 10.1016/j.pmatsci.2010.04.001. - DOI
    1. Griffith AA, Taylor GI. The phenomenon of rupture and flow in solids. Philos. Trans. Roy. Soc. Lond. A. 1921;221:163–198. doi: 10.1098/rsta.1921.0006. - DOI
    1. Frenkel J. Theory of the elastic limits and rigidity of crystalline bodies. Z. Phys. 1926;37:572. doi: 10.1007/BF01397292. - DOI
    1. Orowan E. Fracture and strength of solids. Rep. Prog. Phys. 1949;12:185. doi: 10.1088/0034-4885/12/1/309. - DOI

Publication types

Feedback