Atomic structure and mechanical response of coincident stacking faults in boron suboxide

ABSTRACT We report the atomic structure of coincident stacking faults (SFs) in superhard boron suboxide (B6O) by combining annular bright field scanning transmission electron microscopy and quantum mechanics (QM) simulations. Different from simple SFs, which only lead to the symmetry breaking, the coincident SF junctions in the complex B6O result in local chemical configuration changes by forming an abnormal three-oxygen-atoms chain linking boron icosahedra, instead of the regular two-oxygen-atoms chain in a perfect B6O crystal. QM studies demonstrate that coincident SFs lead to the decreased shear strength under pure shear and indentation conditions and are responsible to the initial failure and amorphization of B6O. GRAPHICAL ABSTRACT IMPACT STATEMENT Combining ABF-STEM and MD simulations, we demonstrated that the coincident SFs lead to the decrease of shear strength and are responsible for the initial failure and amorphization of B6O.


Introduction
The combination of low density and super-high hardness is often desirable for structural materials and ballistic armor applications where both strength and weight are critical [1,2]. B 6 O belongs to the icosahedral compounds with a rigid covalent bonding and has the promising properties of being ultra-strong ( ∼ 45 GPa in hardness) and lightweight ( ∼ 2.6 g/cm 3 in density) [3][4][5]. Technically, boron suboxide (B 6 O) can be fabricated under ambient pressure without the requirements of extremely high synthesis pressures at high temperatures, unlike other superhard materials such as diamond and cubic boron nitride [2][3][4][5]. B 6 O mainly exist in the form of a stoichiometric compound [2,6], which is different from boron carbide that has a wide solid solution range. The distinct properties arise from the unique atomic structure of B 6 O in which two-oxygen atoms bond to the neighboring boron icosahedra (B 12 ) and do not form direct oxygen-oxygen chemical bonding in a rhombohedral unit cell [7,8]. As a result, the complex atomic configuration in B 6 O has anticipated the high density of planar defects during the crystal growth [9,10].
It has been suggested that planar defects, such as twins, enhance the strength of metals and alloys, identical to that of grain boundaries (GBs) [11,12]. In particular, the interfaces of nanotwins strongly influence the mechanical and thermal properties by blocking dislocation movements [13,14]. Despite the fact that dislocations in covalently bonded superhard materials are usually sessile at room temperature due to high lattice resistance, it has been found that nanotwins can enhance the hardness, toughness and thermal stability of diamond, BN, B 4 C and B 6 O [15][16][17][18]. Similar to twins and GBs, stacking faults also have a planar feature and can lead to strong interactions with dislocations for interface strengthening. For instance, Jain et al. examed an Mg alloy and showed the enhanced strength while maintaining good ductility by introducing a high density of stacking faults, which impeded dislocation slip and promoted dislocation accumulation [19]. Despite the fact that numerous stacking faults (SFs) and coincident SFs have been observed in B 6 O and other superhard ceramics [9,10,[15][16][17][18]20,21], their structure and influence on the mechanical properties of the superhard materials have not been explored partially due to the lack of sufficient spatial resolution to image light elements on atomic scale. In this work we investigate local atomic structure of single-and coincident SFs in B 6 O crystals by means of state-of-the-art aberration-corrected annular bright field STEM (ABF-STEM) and QM simulations. The local structural and chemical variations were characterized by the experimental observations and modeled by QM simulations, which provide atomic insights into the structure and effect of SFs on mechanical properties of B 6 O.  planes, (c,d) Strain map of mean dilatation (δ xy ) and rotation (ω xy ) components of the ABF-STEM atomic structure obtained parallel to SF planes using peak pairs (PP) method. PP strain map and rotations was calculated using (101) and (011) structural reflections, (c) A lattice strain of δ xy within a 1 nm SF region is about ∼ 3-4%. The color ranges from ∼ 5% (black) to +5% (white), (d) Lattice rotation of two SFs represented in color code by black and white, with respect to defect-free crystal (red color). The color varies from −π to +π using same color code. Dotted circle area in the vicinity of SFs from image (b) reveals distortion without rotation from maps (c, d).

Results and discussion
projection clearly shows icosahedral (B 12 ) clusters in the form of atomic rings and in between a linear array of pair of oxygen atomic columns [the experimental details are described in the Supplemental Material]. 1 In addition, the image displays coincidence of two stacking faults, their interfaces are marked with false-coding of green and yellow colors (Figure 1(b)). An inset FFT pattern in Figure 1(b) indicates that the stacking faults growth were predominately along (101) and (011) crystal planes. At proximity of the SFs intersection region, there are visible local structural distortions as represented by white circle (see Figure 1(b)). Figure 1(c,d) shows the twodimensional maps of the mean dilatation elastic strain (δ xy ) and rotation (ω xy ) components derived from the ABF-STEM (Figure 1(a)) by using peak pairs (PP) analysis. The δ xy value marginally increases to ∼ 2-4% in a ∼ 1 nm width of SFs region as compared to that of defectfree B 6 O crystal. The ω xy map ( Figure 1(d)) elucidates the anticlockwise (+π ) and clockwise (−π ) structural orientation of SFs region as compared to defect-free region. By close inspection of Figure 1(c,d), the vicinity region of the SFs intersection does not undergo any structural rotation, as shown by dotted circle (Figure 1(d)). Figure 2(a) is a low-pass filtered ABF-STEM image of Figure S1 illustrates the icosahedral atomic rings of boron (B 12 ) atoms and the positions of oxygen atoms (O-O) in a rhombohedral crystal of B 6 O, which is imaged along the [111] direction. Although atomic columns of boron (B) in individual icosahedra are difficult to illustrate directly due to the short bond length distances along the imaging direction and curved surface of the icosahedron, two-oxygen atoms as the bright spots linking icosahedra are visible vividly. A fault of atomic plane stacking sequence is represented by B 6 O-1SF and the atomic planes with two coincident stacking faults are denoted by B 6 O-2SF as shown in the white box regions. The oxygen atoms in both SFs rotate to an opposite direction as compared to the defect-free B 6 O crystal marked by the red dots (Figure 2(a)). The bond length of O-O atoms at the SFs is nearly identical with respect to the B 6 O crystal of about 3 Å, which is consistent with predicted structure [8,9]. Figure 2(b) is the zoom-in To examine the experimentally observed SF structure (Figure 2(a,b)), we constructed the atomic structure in which two SFs are presented with periodic boundary conditions as shown in the dashed line regions in Figure 2(c). This structure consists of 16 B 12 icosahedra and 16 O···O chains in the supercell structure. The PBE optimized supercell structure has the lattice parameters of a = 23.597 Å, b = 5.015 Å, c = 19.998 Å, α = 90, β = 90, γ = 44.261. On the basis of the QM model, we simulated the ABF-STEM image of the SFs (Figure 2(d)). The excellent consistency between the experimental and simulated ABF-STEM images justifies the reliability of the QM model. It is interesting to notice that the O-O atom chain in the SF region (along the 'a' axis) is separated by the icosahedral B-B bond, leading to an isolated O atom (O16 in Figure 2(c)) among three icosahedra, as shown in the oval in Figure 2 (Table 1).
To understand how the SF structure affects the mechanical properties of B 6 O, we first applied pure shear deformation along (001)[100] slip system and compared with the perfect rhombohedral B 6 O [the computational details are described in the Supplemental Material] (see Note 1). It is worth to notice that the SF structure in simulations is orthorhombic. The slip system is perpendicular to the SF structure and gives rise to a larger shear strain within the SF region. The plot of shear stress vs shear strain is displayed in Figure 3(a). The ideal shear strength of the SF structure is 34.8 GPa at 0.209 strain, which is 3.1 GPa smaller than that of perfect B 6 O (37.9 GPa) shearing along (101)[111] the slip system [20]. The SF structure is also sheared along the interface and much larger shear strength (44.8 GPa) was found, indicating that shear parallel to the interface is not favorable. The details can be found in the Supplemental Material ( Figure S2). Therefore, the present of SFs lower the shear strength and weaken the B 6 O crystal. It is worth noticing that nanotwins can strengthen materials such as metals and c-BN [12,16]. Here in SF-2 structure, the bond distances of O15 with three nearest B atoms increase by at least 7% compared to the normal B-O bond distance. This leads to the weakening of icosahedra around SF-2 structure, lower the critical shear strength for failure. Figure 3(b-d) displays the deformation process of SF structure subjected to shearing along the (001)[100] slip system. The intact structure is displayed in Figure 3(b). As the system is sheared to 0.231 strain (corresponding to a maximum stress of 37.3 GPa) the B23-O15 bond in the SF structure is stretched from 1.596 to 1.840 Å, as shown in Figure 3(c). As the system is sheared continuously to 0.254 strain, the B23-O15 bond breaks with the B23···O15 distance increasing to 3.384 Å. Meanwhile, the icosahedron containing B23 atom is deconstructed, as shown in Figure 3(d). This leads to that the structure fails and the shear stress drops to 27.8 GPa.
It is worth noticing that one icosahedron in the neighboring SF region is disintegrated because of the similar bond broken process of B14-O32, as shown in the oval in Figure 3(d). Thus, the SF structure failure initiates from the weak SF region by breaking the icosahedron-chain B-O bonds. We also examined the failure mechanism of B 6 O-1 SF, as shown in Figure S3. As the shear strain increases to 0.299 which corresponds to the maximum shear stress of 46.9 GPa, the inter-icosahedral B-B bond at SF layer (e.g. B72-B76) is stretched from 1.70 to 2.60 Å, but it is not breaking yet. As the shear strain continuously increases to 0.322, the inter-icosahedral B-B bond is stretched to 3.23 Å and breaks, leading to the decrease of shear stress from 46.9 to 45.90 GPa. As the shear strain further increases to 0.345, the O-B bonds (e.g. O16-B80) break and O16-B76 bond forms. Then the icosahedra rotate without breaking the icosahedra, leading to the shear stress significantly drops. The B 6 O-1 SF increases the strength compare to the perfect B 6 O because the slip system along the SF is different compared to perfect B 6 O [21]. In perfect B 6 O, the most plausible slip system is (101)[111], while the shear along SF plane is along [001] < 100 > rhombohedral slip system. Indentation experiments are used to estimate the hardness of materials. To mimic the stress conditions under indentation experiments [29], we applied biaxial shear strains on the SF structure and compared to that of perfect B 6 O. The shear stress versus shear strain curves of the SF structure and perfect crystals under biaxial shear are displayed in Figure 4(a). The critical shear stress of SF  [20]. Thus, the critical shear stress is significantly decreased as SF structure presents under indentation conditions. The deformation process for SF structure under indentation conditions is displayed in Figure 4(b-f). As the shear strain increases from the intact structure (Figure 4(b)) to 0.144, corresponding to the shear stress of 24.8 GPa, the B23-O15 bond is stretched from 1.596 to 1.639 Å (Figure 4(c)). The bond length increase is less than that of pure shear deformation because of the biaxial shear stress conditions. Then, the B23-O15 bond is broken as it increases to 2.665 Å at 0.166 strain (Figure 4(d)). The corresponding shear stress (the maximum shear stress) is just 24.9 GPa. In comparison with pure shear, the maximum shear stress for the bond breaking of B23-O15 slightly increases and the icosahedral clusters are not deconstructed. As the shear strain increases to 0.187, the shear stress decreases to 24.7 GPa. Correspondingly, the B108 atom is stretched out from the icosahedron near the SF structure (Figure 4(e)) and two icosahedra are deconstructed. As the shear strain continuously increases to 0.209, the shear deformation deconstructs the icosahedra with missing boron atoms in the previous step (Figure 4(f)). In addition, two additional icosahedra in the other SF region are deconstructed, as shown in Figure 4(f). This leads to the failure of SF structure by amorphization, accompanying with a significant drop of shear stress to 15.0 GPa.
The failure mechanism of B 6 O-1 SF under biaxial shear deformation is shown in Figure S4. As the shear strain increases to 0.276 corresponding to the maximum shear stress of 41.5 GPa, the icosahedral B-B bond at both side of SF (e.g. B8-B16) is stretched from 1.79 to 2.14 Å, but it is not breaking yet. As the shear strain continuously increases to 0.299, the B8-B16 bond is stretched to 2.14 Å and breaks, leading to a slight decrease of shear stress from 41.5 to 39.9 GPa. As the shear strain further increases to 0.322, these icosahedra at both sides of SF are disintegrated, leading to a decrease of the shear stress to 32.2 GPa. At 0.369 shear strain, B-O bonds in the SF break, leading to the shear stress drastically decrease to 21.5 GPa and failure.

Conclusions
In this study, we have characterized the atomic structure and mechanical response of single-and coincident SFs using ABF-STEM and QM simulations.

Disclosure statement
No potential conflict of interest was reported by the authors.