In Situ Observation of Fracture along Twin Boundaries in Boron Carbide

The observation of fracture behaviors in perfect and twinned B4C crystals via in situ transmission electron microscopy (TEM) mechanical testing is reported. The crystal structure of the synthesized B4C, composed of B11C icosahedra connected by boron‐deficient C–▫–C chains in a chemical formula of B11C3, is determined by state‐of‐the‐art aberration‐corrected scanning TEM. The in situ TEM observations reveal that cracking is preferentially initiated at the twin boundaries (TBs) in B4C under both indentation and tension loading. The cracks then propagate along the TBs, thus resulting in the fracture of B4C. These results are consistent with the theoretical calculations that show that TBs have a softening effect on B4C with amorphous bands preferentially nucleated at the TBs. These findings elucidate the atomic arrangement and the role of planar defects in the failure of B4C. Furthermore, they can guide the design of advanced superhard materials via planar defect control.


DOI: 10.1002/adma.202204375
and diamond [4] can greatly enhance their hardness and fracture toughness.On the other hand, the introduction of TBs in covalent materials with complex bond types such as boron carbide [5,6] and boron oxide [7] resulted in softening and initiated cracking.Consequently, the need for understanding the TB effects in these covalent materials has been gaining attention.
[13] Although nominally denoted as B 4 C, boron carbide covers a family of compounds with different compositions (i.e., with different B:C ratios), [14][15][16] endowing B 4 C with various mechanical properties. [17,18]B 4 C has a complex crystal structure, generally with 12-atom icosahedra and 3-atom C-B-C chains packed into a rhombohedral lattice.Nevertheless, arguments exist concerning the atomic arrangement and exact atomic site occupation of B 4 C. [19][20][21] Similar debates also exist concerning the atomic arrangement of B 4 C TBs. [22,23] Both symmetric [24] and asymmetric [5] twins have been reported.Theoretical predictions have indicated that the incorporation of nanoscale symmetric twins in B 4 C can effectively enhance the shear strength, [24] while the incorporation of an asymmetric twin in B 4 C may facilitate the disintegration of the icosahedral clusters under applied stress, leading to amorphous band formation and eventually brittle failure. [5,25]Unfortunately, direct experimental evidence revealing the exact role of TBs in the mechanical behaviors of B 4 C has not yet been reported.
In this study, fracture behaviors of B 4 C crystals in the presence and absence of TBs were investigated by in situ mechanical testing in a transmission electron microscope.

Results and Discussion
Prior to the mechanical tests, the crystal structure and atomic arrangement of the as-synthesized B 4 C were investigated.The B 4 C bulk consists of numerous small single-crystal grains with sizes of tens of micrometers (Figure S1, Supporting Information).

Introduction
[3][4] Unfortunately, there is considerable inconsistency in the reported effects of TBs on the mechanical properties of different materials, especially in covalent materials having different bonding types.Tian et al. and Huang et al. have reported that the incorporation of highdensity TBs into strong covalent cubic boron nitride (cBN) [3] Figure 1a shows a typical selected-area electron diffraction (SAED) pattern from an individual grain, whereby the sharp diffraction spots confirmed the rhombohedral structure of B 4 C (taken along the [211] zone axis).The crystal structure of B 4 C was then determined with the state-of-the-art probe-corrected scanning transmission electron microscopy (TEM) (STEM) technique.Figure 1b-d reveals the high-angle annular darkfield (HAADF), low-angle annular dark-field (LAADF), and annular bright-field (ABF) STEM images, respectively.The LAADF and ABF images revealed better contrast of the atoms as compared to the HAADF image due to their improved sensitivity to light elements such as B and C. [26,27] Consequently, the LAADF technique was employed to probe the atomic configuration of B 4 C.The LAADF image (Figure 1d) clearly revealed the featured crystal structure of B 4 C, with periodically packed icosahedra and atomic dumbbells.In contrast to the 3-atom C-B-C chains in previous studies, [27] the B 4 C crystal synthesized in this study showed atomic dumbbells (alternatively, boron-deficient C-▫-C chains) due to the missing B atoms as indicated by the intensity profile (Figure 1f).Furthermore, the composition of the synthesized sample was quantitatively analyzed with energy-dispersive X-ray spectroscopy (EDS) and electron energy loss spectroscopy (EELS).EDS mapping (Figure S2a-c, Supporting Information) of the B 4 C nanopillar revealed uniformly distributed B and C. Both EDS and EELS spectra (Figure S2d,e, Supporting Information) revealed characteristic B and C peaks.The atomic ratio of B:C calculated from the spectra was in the ≈3.57-3.61range, very close to the ratio of B 11 C 3 .[30][31][32] Based on the STEM observation and composition analysis, as well as previous studies, [28,[33][34][35][36][37][38][39] the chemical formula of this boron carbide was determined as B 11 C 3 , consisting of B 11 C icosahedra and boron deficient C-▫-C chains (Figure 1f).
Planar defects such as TBs and stacking faults (SFs) are commonly found in B 4 C crystal grains.Figure 1g   pattern taken from one crystal grain along the [211] zone axis.The two sets of mirror-symmetric diffraction spots indicated a twinned structure of the grain.Furthermore, the corresponding atomic-resolution LAADF image (Figure 1h) clearly revealed crystal twinning with the (011) plane as the TB (mirror plane).The associated twinning angles were 73.3 ± 0.3° (upper crystal) and 73.4 ± 0.3° (lower crystal), indicating a symmetrical twin structure. [23]Based on the LAADF observation and taking into account the interfacial energy, a completely symmetric twin configuration, in which the carbon atoms in the B 11 C icosahedra sit in the TB (Figure 1i) was provided.The atomic arrangement of SF in B 4 C was also investigated with LAADF imaging (Figure S3, Supporting Information).These atomic-resolution structure details of B 4 C provide a solid foundation for understanding its mechanical behavior determined via in situ mechanical tests.
In situ indentation tests were conducted on B 4 C nanosheets, prepared from a B 4 C bulk via focus ion beam (FIB) milling (Figure S4, Supporting Information).A typical TEM image of a single-crystal B 4 C nanosheet before indentation (Figure 2a side view) revealed a smooth and thin edge of the nanosheet.The indentation deformation and cracking in the nanosheet using a flat-topped cylindrical indenter were monitored in situ with TEM (Movies S1 and S2, Supporting Information).Figure 2b,c shows the fractured nanosheet at different locations.Remarkably, semi-elliptical flakes were preferentially peeled off from the nanosheet surface due to indentation.The newly formed crack surface appeared smooth and curved under low magnification TEM observation.A closer examination of the cracked surface revealed a series of {011} steps with an amorphous outer layer containing dangling bonds, as indicated by the atomic-resolution LAADF image (Figure 2d).In situ indentation tests of the B 4 C nanosheets containing TBs were also performed (Figure 2e,f; Movie S3, Supporting Information), where the indenter was pressed perpendicular to the TB in a B 4 C nanosheet.Surprisingly, the fractured semi-elliptical flakes that were observed in the single-crystal B 4 C nanosheets were not present in the twinned B 4 C nanosheets.As the curved crack propagated and encountered the TB, further crack propagation was restricted along the TB (Figure 2f).Atomic-resolution LAADF image (Figure 2g) further confirmed that the newly formed fractured surface was along the TB.In other cases where the indentation was parallel to the TBs (Figure 2h), in situ TEM observation indicated that the crack preferentially occurred near the TB and penetrated into the B 4 C nanosheet along the TB (Figure 2i; Movie S4, Supporting Information).
To investigate the effects of TB and SF on the B 4 C mechanical behavior under tensile loading, in situ tensile tests on B 4 C nanopillars fabricated with FIB milling were also conducted (Figure S5, Supporting Information).Remarkably, the tensile strain of a single crystal B 4 C nanopillar was able to attain a value as high as ≈9.8% before fracture (Figure S6 and Movie S5, Supporting Information).Figure 3a shows a B 4 C nanopillar containing SF before loading.The corresponding SAED pattern from the nanopillar (inset to Figure 3a) indicated an axial orientation nearly perpendicular to the (011) plane.During the tensile test, the gauge length between the two fiducial markers on the nanopillar increased from 607 to 629 nm (Figure 3a,b; Movie S6, Supporting Information).When the tensile strain of the nanopillar reached ≈3.6%, (a value much lower than that of single-crystal nanopillar), a sudden break occurred (Figure 3c).Atomic-resolution LAADF image of the fractured nanopillar (Figure 3d) revealed SFs in the region close to the fractured surface, thus indicating that the SFs may have contributed to the rupture of the nanopillar.A similar fracture behavior was also observed in other B 4 C nanopillar containing SFs (Figure S7, Supporting Information).Figure 3e-h shows the tensile deformation and fracture behavior of a B 4 C nanopillar containing TBs.The TEM image contrast and the corresponding SAED pattern confirmed the existence of TB in the nanopillar (Figure 3e).The nanopillar was stretched up to ≈5.1% before fracture near the TB (Figure 3f,g; Movie S7, Supporting Information).Atomic-resolution LAADF image of the fractured nanopillar further confirmed that the fracture occurred in the vicinity of TB (Figure 3h).In conclusion, cracking was preferentially initiated at the TB in B 4 C under tensile loading, which was further confirmed by other B 4 C nanopillars containing TBs (Figure S8 and Movie S8, Supporting Information).To eliminate the possibility of the size effect on the results, further tensile measurements were conducted on samples with widths ranging between 100 and 300 nm (Figure S9, Supporting Information).The fluctuations in the measured fracture strain of the samples were marginal and size dependence was not observed when the width varied from 100 to 300 nm.Overall, no obvious size dependence was detected and the tensile strain of twinned samples was lower than that of single-crystal ones.
It was thus concluded that fractures in  of B 4 C, DFT calculations were performed to theoretically investigate the strength and failure mechanism in perfect and twinned crystals under biaxial shear deformations.According to the experimental observation, the B 11 C 3 crystal structure was selected for the calculation.Figure 4a shows the calculated stress-strain relationships for the perfect and twinned B 11 C 3 crystals and the results revealed that both crystals underwent linear and nonlinear deformation under shear strain; however, the slope of the linear part for the twin-structured B 11 C 3 was much lower than that for the perfect crystal, and the maximum shear stress of the twinned B 11 C 3 (22 GPa) was also lower than that of the perfect crystal (26 GPa).These results indicated that the strength of the twinned B 11 C 3 is intrinsically lower than that of the perfect B 11 C 3 .To understand the softening effect of TB and the underlying failure mechanism, the structure evolution of the perfect and twinned B 11 C 3 crystals was studied.In a perfect B 11 C 3 crystal, the distance between two C atoms in the C-▫-C chain decreased with an increase in shear strain (Figure 4b).At a shear strain of 0.08, the two C atoms bonded with a length of 1.63 Å. Upon further straining, the B 11 C icosahedra were bent and twisted, and the B atoms on adjacent icosahedra interacted and formed bonds (ε ≈ 0.12), finally leading to the failure of the icosahedra and chains (ε ≈ 0.20).Twinned B 11 C 3 also sequentially went through bonding of the C atoms in the chain (ε ≈ 0.12), distortion of the icosahedra, and bonding of B atoms on adjacent icosahedra (ε ≈ 0.14) before failure (Figure 4c).
Remarkably, these changes were initiated near the TB and propagated outward layer by layer, eventually leading to the failure of the twinned B 11 C 3 structure.The DFT calculations further confirmed the experimental observations that fracture tended to occur at the TBs in the B 4 C crystals.Quantum mechanical simulations conducted in previous studies [24] revealed that the biaxial shear deformation strength of the nanotwinned B 4 C, composed of B 11 C icosahedra and CBC chains, was 12% higher than that of its twin-free counterpart.In contrast, the experimental observation and DFT calculation of this study showed a softening effect from TBs in B 11 C 3 with C-▫-C chains.These results indicated that the chain configuration may play an important role in the mechanical behaviors of the twinned boron carbide.Further experimental confirmation is necessary to elucidate the role of chain configuration in tuning the mechanical response of the twinned boron carbide.To evaluate the mechanical properties of the twinned and twin-free B 11 C 3 structures, uniaxial tensile simulations were also conducted (Figure S10, Supporting Information).The calculated tensile stress-strain relationships revealed comparable tensile strength for the twinned and twin-free B 11 C 3 structures (Figure S10a, Supporting Information).The single-crystal B 11 C 3 exhibited a uniform deformation before failure during uniaxial tension (Figure S10b, Supporting Information) and the twinned B 11 C 3 structure exhibited a two-step failure process (Figure S10c, Supporting Information).One B-B bond broke (marked by red arrows in Figure S10c, Supporting Information) in the icosahedron near the TB as the strain increased to 0.172, then B atoms from adjacent icosahedra near the TB bonded accompanied with a large localized distortion near the TB (marked by red dash box in Figure S10c, Supporting Information) at a strain of 0.195, thus leading to a structure failure of the twinned B 11 C 3 .This large localized lattice distortion near the TB is obviously associated with the twinned structure under tension, which is in accordance with the experimental observations.

Conclusion
The atomic structure of B 4 C and its fracture behaviors were investigated by state-of-the-art aberration-corrected STEM and

Experimental Section
Synthesis and Sintering of the Boron Carbide Powders and Bulk: Boron carbide powders were synthesized from boric acid (H 3 BO 3 , purity 99.9995%, Alfa Aesar) and sucrose (C 12 H 22 O 11 , purity 99%, Alfa Aesar) with a carbothermic reduction method. [40]H 3 BO 3 and C 12 H 22 O 11 (with an atomic ratio of B:C = 1:1) were first dissolved in deionized water at ambient temperature, and the solution was air-dried at 150 °C for 12 h.Then the prepared solids were ground into fine powders with an agate mortar.The powders were loaded into a graphite crucible and heated at 1500 °C for 30 min under a vacuum of 1 × 10 −3 Pa to synthesize boron carbide powders.The synthesized boron carbide powders were filled into a graphite die (15 mm inner diameter) and sintered in vacuum with SPS (50 MPa and 1950 °C for 15 min, Sinter Land SPS-3.20MK-IV).The base pressure was better than 1 × 10 −3 Pa before pressurization and heating.The synthesized boron carbide powders and bulks exhibited similar characteristics in terms of chemical composition, crystal structure, and atomic configuration (Figures S11-S13, Supporting Information).
Microfabrication of the Indentation Samples: The boron carbide nanosheets and the diamond indenter for in situ indentation testing were fabricated with focus ion beam (FIB, Helios G5, Thermo Fisher Scientific).Gallium ion beam currents from 15 nA to 30 pA (working voltage 30 kV) were used from initial engraving to final refinement.First, a sheet (15 µm × 1.5 µm in size, Figure S4a, Supporting Information) was milled from the sintered boron carbide bulk (with an average grain size of ≈50 µm, Figure S1, Supporting Information).The sheet was cut (Figure S4b, Supporting Information) and transferred onto a copper half-grid fixed by Pt welding (Figure S4c, Supporting Information).The boron carbide sheet was further thinned to a final thickness of 100-150 nm (Figure S14a, Supporting Information) followed by argon plasma cleaning.The thinned process was monitored with the scanning electron beam.The diamond indenter was sculpted from a diamond sheet that was cut from a diamond single crystal and fixed onto a tungsten pin by Pt welding (Figure S15a, Supporting Information).
Microfabrication of the Tensile Samples: The boron carbide tensile samples were fabricated from twinned and twin-free boron carbide grains in the sintered bulk with FIB machining.First, a thin lamella was milled from the polished surface of boron carbide bulk (Figure S5a, Supporting Information), cut (Figure S5b, Supporting Information) and transferred onto the TEM half-grid fixed by Pt welding (Figure S5c, Supporting Information).Then the lamella was laterally narrowed with a width of 3 µm (Figure S5d, Supporting Information), and further shaped into a dog-bone specimen with a test width of 100-300 nm and test length of 1-3 µm (Figure S5e, Supporting Information).The presence and orientation of twin in the lamella were ascertained with TEM observation before the final shaping.The corresponding diamond gripper was sculpted from a diamond indenter tip (Figure S15b, Supporting Information).
STEM and In Situ TEM Characterizations: In situ indentation tests were performed using a homemade X-Nano TEM system, [41] with a positioning control of 0.1 nm.The indentation tests were performed by applying displacement-controlled loading with a rate of 7.5 nm s −1 .The in situ tensile experiments were conducted with a displacement loading rate of 0.5 nm s −1 using a Hysitron PicoIndenter PI95 (Hysitron, Inc, USA).All in situ mechanical tests were performed using a JEM-ARM200F microscope (JEOL, Ltd, Japan) at 200 KV.All STEM observations were performed inside an aberration-corrected Themis Z STEM (300 kV, 25-mrad-probe convergence angle).HAADF, LAADF, and ABF images were captured using 60-200, 20-60, and 10-20 mrad inner-out collection angles, respectively.
DFT Calculations: All the details of the DFT calculations are provided in the Supporting Information file.
fracture behaviors in perfect and twinned B 4 C crystals via in situ transmission electron microscopy (TEM) mechanical testing is reported.The crystal structure of the synthesized B 4 C, composed of B 11 C icosahedra connected by boron-deficient C-▫-C chains in a chemical formula of B 11 C 3 , is determined by state-of-the-art aberration-corrected scanning TEM.The in situ TEM observations reveal that cracking is preferentially initiated at the twin boundaries (TBs) in B 4 C under both indentation and tension loading.The cracks then propagate along the TBs, thus resulting in the fracture of B 4 C.These results are consistent with the theoretical calculations that show that TBs have a softening effect on B 4 C with amorphous bands preferentially nucleated at the TBs.These findings elucidate the atomic arrangement and the role of planar defects in the failure of B 4 C. Furthermore, they can guide the design of advanced superhard materials via planar defect control.

Figure 1 .
Figure 1.STEM images and atomic configurations of the single-crystal and twinned B 4 C. a) SAED pattern taken along the [211] zone axis from the rhombohedral B 4 C. b-d) Atomic-scale HAADF, ABF, and LAADF images of B 4 C with single crystal structure, respectively.The images were obtained synchronously.e) Intensity line profile along the direction marked in an arrow in the LAADF image of (d).f) Atomic structure of the single crystal B 4 C. g-i) SAED pattern, atomic-scale LAADF image, and atomic structure of the twinned B 4 C, respectively.

Figure 2 .
Figure 2. In situ TEM indentation testing of the single-crystal and twinned B 4 C nanosheet.a-c) Typical TEM images recording the indentation and fracture of single-crystal B 4 C nanosheet.d) Atomic-scale LAADF image showing unprecedented details of a freshly broken edge of the single-crystal B 4 C nanosheet.e,f) Low-magnification TEM images of a twinned B 4 C nanosheet before and after indentation perpendicular to the TB.g) Atomic-scale LAADF image showing the fracture edge of the twinned B 4 C nanosheet.h,i) Low-magnification TEM images of a twinned B 4 C nanosheet before and after indentation parallel to the TB.
B 4 C crystals tend to occur near the TBs (or SFs) under mechanical loading.To understand the influence of TBs on the mechanical behaviors Adv.Mater.2023, 35, 2204375

Figure 3 .
Figure 3.In situ TEM tensile testing of B 4 C nanopillars within SF or TB.a-c) TEM images of a B 4 C nanopillar containing SF before deformation, with maximum strain, and after fracture, respectively.The inset of (a) shows the corresponding SAED pattern of the B 4 C nanopillar within SF. d) Atomic-scale LAADF image showing the details of the fracture edge of the nanopillar within SF. e-g) TEM images of a B 4 C nanopillar within TB before deformation, with maximum strain, and after fracture, respectively.The inset of (e) shows the corresponding SAED pattern of the B 4 C nanopillar within the TB.h) Atomic-scale LAADF image showing the details of the fracture edge of the nanopillar within the TB.

Figure 4 .
Figure 4. DFT calculations of deformation and failure mechanisms of B 11 C 3 and twinned B 11 C 3 under indentation.a) Shear-stress and shear-strain relationship of B 11 C 3 and twinned B 11 C 3 under biaxial shear deformations.b) Atomic structures of B 11 C 3 at different shear strains of 0.06, 0.08, 0.12, and 0.20, respectively.c) Atomic structures of twinned B 11 C 3 at different shear strains of 0.10, 0.12, 0.14, 0.16, and 0.20, respectively.