Subscriber access provided by UNIV OF NEBRASKA - LINCOLN Communication Nanotwinned Boron Suboxide (B6O): New Ground State of B6O Qi An, Madhav Reddy Kolan, Huafeng Dong, Mingwei Chen, Artem R. Oganov, and William A. Goddard III Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b01204 • Publication Date (Web): 02 Jun 2016 Downloaded from http://pubs.acs.org on June 7, 2016
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1 2 3 4 Nanotwinned Boron Suboxide (B 6O): New Ground State of B 6O 5 6 1 2 3a 2 3 7 Qi An, K. Madhav Reddy, Huafeng Dong, Ming Wei Chen, Artem R. Oganov , William A. 8 1* 9 Goddard III 10 1Materials and Process Simulation Center, 11 12 California Institute of Technology, Pasadena, CA 91125, United States 13 2WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan 14 3a 15 Department of Geosciences and Center for Materials by Design, Institute for Advanced 16 Computational Science, State University of New York, Stony Brook, NY 11794-2100 17 18 3b Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, 3 Nobel St., Moscow 19 20 143026, Russia. 21 3c Moscow Institute of Physics and Technology, 9 Institutskiy Lane, Dolgoprudny city, Moscow 22 23 Region, 141700, Russian Federation 24 3d International Center for Materials Discovery, Northwestern Polytechnical University, 25 26 Xi'an,710072, China 27 *Corresponding author E mail: [email protected] 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 TOC Figure 50 51 52 53 54 55 56 57 58 59 1 60 ACS Paragon Plus Environment Nano Letters Page 2 of 23
1 2 3 4 Abstract: Nanotwinned structures in superhard ceramics rhombohedral boron suboxide (R B6O) 5 6 have been examined using a combination of transmission electron microscopy (TEM) and 7 8 quantum mechanics (QM). QM predicts negative relative energies to R B6O for various twinned 9 10 R B6O (denoted as τ B6O, 2τ B6O, and 4τ B6O), consistent with the recently predicted B6O 11 12 structure with Cmcm space group (τ B6O) which has an energy 1.1 meV / B6O lower than R B6O. 13 14 We report here TEM observations of this τ B6O structure, confirming the QM predictions. QM 15 16 studies under pure shear deformation and indentation conditions are used to determine the 17 18 deformation mechanisms of the new τ B6O phase which are compared to R B6O and 2τ B6O. 19 20 The lowest stress slip system of τ B6O is (010)/<001> which transforms τ B6O to R B6O under 21 22 pure shear deformation. However, under indentation conditions, the lowest stress slip system 23 24 changes to (001)/<110>, leading to icosahedra disintegration and hence amorphous band 25 26 formation. 27 28 29 30 Keywords: Superhard ceramics, Stacking faults energy, DFT, Deformation mechanism. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 2 60 ACS Paragon Plus Environment Page 3 of 23 Nano Letters
1 2 3 4 Crystal twins are ubiquitous in crystalline metals and ceramics, where they form during 5 6 7 growth and deformation processes. They have been studied extensively in metals, where they 8 9 1−5 10 modify significantly the mechanical, thermal and electrical properties. In particular they 11 12 significantly improve the materials strength by blocking dislocation movements.6−8 In some 13 14 15 twinned structures the electrical conductivity of the pure metal is retained with the increased 16 17 9 18 strength, making these planar defects potentially useful for electronic engineering. 19 20 However, for ceramics, the twinned structures are more complex than for simple metals. For 21 22 23 example, we recently used QM and high resolution TEM (HRTEM) to identify a special 24 25 26 asymmetric twin structure in boron carbide (B 4C) that arises from the interplay of stoichiometry, 27 28 atomic positioning, twinning, and structural hierarchy.10 Dislocations in ceramics are often 29 30 31 sessile at normal temperatures because of the rigid structures arising from the covalent or ionic 32 33 34 bonding. Thus, the strengthening mechanism through twinning in metals does not generally 35 36 apply to ceramics. However, recent experiments found that nanoscale twins in c BN and 37 38 11,12 39 diamond dramatically increase the hardness of these strong covalent solids, leading to 40 41 13,14 42 examining the roles of twins in deformation processes of other strong covalent solids. 43 44 Twin boundaries (TBs) are normally coherent grain boundaries with low interfacial energy 45 46 47 compared with normal grain boundaries having random orientations. In general such TBs are 48 49 50 planar defects with positive stacking faults energy (SFE). Even the well known 4H SiC and 51 52 6H SiC stacking structures has positive SFEs of 14.7 and 2.9 mJ/m 2,15 but they are more 53 54 55 favorable at high temperature above 1700 °C because of the entropic effects. 56 57 58 59 3 60 ACS Paragon Plus Environment Nano Letters Page 4 of 23
1 2 3 4 Boron suboxide (B6O) belongs to the family of icosahedral compounds that combine such 5 6 16−18 7 promising properties as high hardness, low density and chemical inertness. Abundant 8 9 10 twinned structures with TB along {100} r plane have been observed in rhombohedral B6O 11 12 16 (R B6O), indicating a unique microstructure for the twinned structure in B6O. We used 13 14 15 subscript “r” to represent the planes and directions in R B6O and the others without “r” represent 16 17 18 the ones in the new predicted twinned B 6O. Thus, understating how the twinned structure in B 6O 19 20 affects the mechanical properties may offer the possibility of designing materials with improved 21 22 23 mechanical properties. 24 25 26 The present studies combined quantum mechanics (QM) calculations with 27 28 spherical aberration corrected scanning transmission electron microscopy (STEM) to 29 30 31 demonstrate the formation of the nanotwinned B 6O that have negative SFE, which is consistent 32 33 19 34 with recent predictions of a new B6O phase more stable than R B6O. The newly predicted B 6O 35 36 phase exhibits 1 × 1 zig zag twinned B 6O, which we denote as τ B6O. We also identify other 37 38 39 twinned phases, denoted as 2τ B6O, and 4τ B6O, and used QM to examine their mechanical 40 41 42 properties, which are compared to R B6O. 43 44 Normal synthesis of B6O leads to a rhombohedral unit cell with eight B12 icosahedral 45 46 16,20 19 47 clusters at the apexes and two O atom chains along the [111] r direction. Recent studies, 48 49 21 50 using evolutionary crystal structure prediction methods, found a new B 6O crystal structure with 51 52 Cmcm space group as shown in Fig. 1(a). This structure was predicted to be 1.1 meV/B6O lower 53 54 19 55 in energy than R B6O. To validate the existence of this new structure in experiments, we 56 57 58 59 4 60 ACS Paragon Plus Environment Page 5 of 23 Nano Letters
1 2 3 22 4 performed STEM measurements on as synthesized B6O (experimental details are in the 5 6 7 supplementary information, SI). Besides the R B6O shown in Fig. S1 of SI, we observed the new 8 9 10 τ B6O structure within some grains, as shown with STEM and HRTEM images in Fig. 1(b), Fig 11 12 S2 and Fig. S3 of SI, providing experimental evidence supporting the theoretical prediction. The 13 14 15 new τ B6O structure belongs to the Cmcm space group. Fig. 1a shows the projection along the 16 17 18 < 100 > direction, which shows the B12 icosahedra and the Oxygen atom (O O) chains. The 19 20 BF STEM image (Fig. 1b) displays this zig zag pattern with the icosahedra alignment alternating 21 22 23 every other plane. This zig zag structure has a mirror symmetry across the 010 planes and 24 25 26 appears to be a uniformly twinned version of R B6O (Fig. S1). The STEM images (Fig. 1b and 27 28 Fig S2) are analogous to the direct projection of structure model (Fig. 1a) along the same 29 30 31 crystallographic direction. 32 33 34 To further validate that this experimentally observed phase is the predicted one, we 35 36 extracted the electron diffraction pattern from STEM measurements and compared it to the 37 38 39 simulated STEM image computed from the QM structure [Fig. 1(c) and (d)]. The basic electron 40 41 42 diffraction vectors from experiments and QM predictions agree very well, confirming that the 43 44 observed phase is the τ B6O phase. However, our experimental pattern shows low intensity spots 45 46 47 half way between two very strong spots that would not be present in the perfect sample. To 48 49 50 explore the origin of these weak spots, we considered models of τ B6O containing ordered 51 52 patterns of either B vacancies or O vacancies, as shown in Fig. S4 of SI. Our calculated 53 54 55 diffraction patterns (Fig. S4 of SI) for both cases lead to low intensity spots half way between 56 57 58 59 5 60 ACS Paragon Plus Environment Nano Letters Page 6 of 23
1 2 3 4 the very strong spots exactly where we observe them experimentally. 5 6 7 The new predicted τ B6O phase is similar to our previously predicted twinned R B6O 8 9 14 10 structure with the τ B6O having 1×1 zig zag structure along the direction perpendicular to the 11 12 twin plane while the n τ B6O twinned structure has an n × n (n > 1) zig zag structure. The most 13 14 15 stable structure in Table 1 is τ B6O. Comparing the energy to R B6O, we can say that the 16 17 2 τ 18 stacking fault energy (SFE) to form R B6O is 1.51 mJ/m . The other n B6O cases all have 19 20 energies between τ B6O to R B6O (Table 1), indicating that it is favorable to put twins into 21 22 23 R B6O. 24 25 26 To gain insight into why the τ B6O phase is more stable than R B6O, we calculated the 27 28 22 natural bond orbital (NBO) charge distributions of the B 12 unit and O atoms in both structures. 29 30 31 The electron counting rules suggest that two electrons must be added to the B 12 unit in R B6O to 32 33 34 satisfy Wade’s rule. In R B6O, the QM calculations find that the O atoms transfer only 0.65 35 36 1.3− electrons to nearby B 12 unit, leading to (B 12 ) , which is short from the value expected from 37 38 39 Wade’s rule. In contrast, for τ B6O each O atom transfers 1.05 electrons to a nearby B 12 unit, 40 41 2.1− 42 leading to (B 12 ) . Thus, the charge transfer in the τ B6O structure nearly exactly matches 43 44 Wade’s rule, suggesting that τ B6O is more stable structure. 45 46 47 To determine the stability of the two phases at finite temperature, we calculated the free 48 49 50 energy as a function of temperature, including the vibrational entropy. We first computed the 51 52 phonon frequencies of these two phases using a finite difference method. 24 These calculations 53 54 55 used the 2 × 2 × 2 supercell for R B6O and the 2 × 2 × 1 supercell for τ B6O. The entropy and the 56 57 58 59 6 60 ACS Paragon Plus Environment Page 7 of 23 Nano Letters
1 2 3 4 Helmholtz free energy were computed from the phonons frequencies for temperature up to 2300 5 6 25 7 K, which is near the melting temperature of B 6O. The entropy difference (S R B6O Sτ B6O ) and 8 9 10 the Helmholtz free energy (A) difference (A R B6O Aτ B6O ) between these two phases are small, as 11 12 displayed in Fig. S5 of the SI. The τ B6O phase has a lower Helmholtz free energy than R B6O 13 14 15 for all temperature up to melting, but the difference decreases gradually to zero at melting. The 16 17 18 entropy of τ B6O is slightly higher than that of R B6O for T < 72 K but lower for higher 19 20 temperatures. 21 22 23 To examine how the negative SFEs affect the mechanical properties, we used QM to predict 24 25 26 the elastic moduli of τ B6O and compare with R B6O and 2,4τ B6O. The predicted elastic moduli 27 28 are listed in Table S1 S3 of SI. For τ B6O this leads to a calculated bulk modulus B = 225.9 GPa 29 30 26 31 and a shear modulus G = 209.2 GPa using Voigt−Reuss−Hill averaging. These values are 32 33 20 34 slightly smaller than the B = 232.0 and G = 210.9 GPa for R B6O. For 2τ B6O and 4τ B6O 35 36 structures, the B = 226.2 GPa, G = 208.5 GPa; and B = 221.8 GPa, G = 206.6 GPa, respectively, 37 38 39 which are similar to those of τ B6O. Thus, all four structures have similar elastic properties, 40 41 42 indicating that the slightly negative SFEs have insignificant influence on the elastic properties of 43 44 B6O. 45 46 47 To examine if the twinned structures influence the mechanical properties of R B6O, we 48 49 27 50 calculated the hardness of τ B6O, R B6O, and twinned R B6O based on the G/B values. The 51 52 computed hardness values are summarized in Table 1. Although the calculated hardness values 53 54 55 for these structures are similar, the twinned structures appear slightly harder than the R B6O, 56 57 58 59 7 60 ACS Paragon Plus Environment Nano Letters Page 8 of 23
1 2 3 4 indicating that twins make B6O stronger. 5 6 7 Amorphous shear band formation is the major failure mechanism for failure of superhard 8 9 28 29−32 10 ceramics B 6O and B 4C . To determine the deformation mechanism leading to brittle failure 11 12 of the new τ B6O phase, we applied pure shear deformation to τ B6O (simulation details in the 13 14 15 SI). We first determined the most plausible slip system by shearing along four possible slip 16 17 18 systems of (100)/<010>, (100)/<001>, (010)/<001>, and (001)/<110>. The (001)/<110> slip 19 20 system corresponds to the slip along the twin boundaries (TBs) in the twinned R B6O. The 21 22 23 stress strain relationships of these slip systems are displayed in Fig. 2. Among these four slip 24 25 26 systems, the (010)/<001> slip system has the lowest shear stress of 39.4 GPa while the other slip 27 28 systems (100)/<010>, (100)/<001>, and (001)/<110> are 43.5, 47.5 and 45.1 GPa, respectively. 29 30 31 Thus, the (010)/<001> is the least stress slip system for τ B6O. For 2τ B6O, QM leads to an ideal 32 33 34 shear stress along (010)/<001> of 37.5 GPa. Thus, the τ B6O is slightly stronger than 2τ B6O, 35 36 consistent with its higher predicted hardness.19 37 38 39 To compare with R B6O, we shear the R B6O along the (011)/ < 21 1 > slip system, which 40 41 42 is the reverse slip system of (010)/<001> for τ B6O. The ideal shear stress of R B6O shearing 43 44 along (011)/ < 21 1 > is 37.9 GPa, which is lower than the shear along (001)/<100> of 43.5 GPa 45 46 20 47 we examined earlier. Thus, the lowest stress slip system for R B6O is actually (011)/ < 21 1 >, 48 49 50 not (001)/<100> that we examined previously. Comparing the ideal shear stress for lowest stress 51 52 slip systems for these three structures, the sequence from high to low strength is τ B6O > R B6O 53 54 55 ~ 2τ B6O. 56 57 58 59 8 60 ACS Paragon Plus Environment Page 9 of 23 Nano Letters
1 2 3 4 In addition, we note that the slip along the TBs [(001)/<110> slip system] has an ideal shear 5 6 7 stress of 45.1 GPa, which is larger than 2τ B6O of 43.3. However, the ideal shear stress along 8 9 10 this slip system for the perfect (non twinned) R B6O is 43.5 GPa, which is similar to 2τ B6O. 11 12 Figure 3 displays the deformation mechanism of τ B6O for shear along the slip system 13 14 15 (010)/<001>. The intact structure is displayed in Fig. 3(a). As the system is sheared to 0.276 16 17 18 strain (corresponding to a maximum stress of 39.4 GPa) the B27 B28 bond between icosahedra 19 20 is stretched from 1.697 to 2.491 Å as shown in Fig. 3(b). But it is not broken as shown from the 21 22 33 23 electron localization function (ELF) (inserted image of Fig. 3(b)). As the system is sheared 24 25 26 continuously to 0.369 strain, the B27 B28 bond breaks, but this releases the shear stress only 27 28 slightly to 35.6 GPa because the icosahedra do not disintegrate. As the critical strain of 0.369 is 29 30 31 exceeded, a new B23 B24 bond forms and the structure transforms to R-B6O with no broken 32 33 34 bonds in the icosahedral clusters. However, the “a” and “c” axes are now along [211] and 35 36 [011] directions of R B6O, respectively. This deformation is similar to the pure shear 37 38 20 14 39 deformation of R B6O and twinned R B6O where the icosahedral clusters do not deconstruct. 40 41 42 To examine the possible reverse transition from R B6O to τ B6O, we performed pure shear 43 44 deformation on the R B6O along the slip system of (011)/ < 21 1 >, which is the reverse slip 45 46 47 from τ B6O to R B6O. The stress strain relationship and structural changes are displayed in Fig. 48 49 50 4(a). We found that the R B6O cannot transform back to τ B6O, instead the icosahedra 51 52 disintegrate, leading to the amorphous band formation, as shown in Fig. 4(b) (d). Indeed 53 54 28 55 previous experimental studies show amorphous band formation in R B6O. However, our 56 57 58 59 9 60 ACS Paragon Plus Environment Nano Letters Page 10 of 23
1 2 3 20 4 previous QM simulations show structure recovery for R B6O shearing along (001)/<100>. Here 5 6 7 we show that shearing along (011)/ < 21 1 > has a lower ideal shear stress, resulting in 8 9 10 icosahedra disintegration that leads to amorphous band formation. Thus, our simulations predict 11 12 that the amorphous band in R B6O is along the (011) plane. This is not consistent with previous 13 14 28 15 experiments which might arise from the complex stress conditions in experiments. 16 17 18 Normally indentation experiments are used to evaluate the strength of brittle materials. To 19 20 13 mimic the stress conditions under indentation, we applied biaxial shear stress on τ B6O along 21 22 23 slip system (010)/<001> which is the lowest stress slip system and the TBs, which is the 24 25 26 (001)/<110> slip system. We also sheared the 2τ B6O and R B6O along the similar slip systems 27 28 for comparison. The shear stress−shear strain relationships for these three structures are 29 30 31 displayed in Fig. 5(a). We see that the ideal shear stress of τ B6O shearing along (001)/<110> is 32 33 34 36.2 GPa, while it is 41.0 GPa shearing along (010)/<001> slip system. Thus, the easiest slip 35 36 system for τ B6O changes from (010)/<001> to (001)/<110> under the simulated indentation 37 38 39 conditions. A similar change for the lowest stress slip system appears for 2τ B6O where the ideal 40 41 42 shear stresses are 36.9 and 40.8 GPa for shearing along (001)/<110> and (010)/<001>, 43 44 respectively. However, for the perfect R B6O, the ideal shear stresses are 39.9 and 37.2 GPa for 45 46 47 shearing along (001)/<100> and (011)/ < 21 1 >, respectively. This indicates that (011)/ < 48 49 50 211 > is still the most plausible slip system in R B6O. Under the biaxial shear stress conditions, 51 52 the sequence from high to low strength is R B6O ~ 2τ B6O > τ B6O, which is reverse compared 53 54 55 to the pure shear deformation. 56 57 58 59 10 60 ACS Paragon Plus Environment Page 11 of 23 Nano Letters
1 2 3 4 The deformation mechanism for τ B6O along (001)/<110> under the biaxial shear stress 5 6 7 conditions is displayed in Fig. 5(b),(c). The icosahedra disintegrate directly under the biaxial 8 9 10 stress conditions at 0.254 strain as the shear stress goes above 36.2 GPa. To examine why the 11 12 most plausible slip system changes from (010)/<001> to (001)/<110> in τ B6O under biaxial 13 14 15 shear conditions, we plotted the structural changes by shearing along (010)/<001> in Fig. 5(d) (f). 16 17 18 We see that the τ B6O also transforms to R B6O at biaxial stress conditions, which is the same as 19 20 for pure shear deformations. The 2τ B6O exhibits a similar deformation mechanism under 21 22 23 indentation conditions: the icosahedra disintegrate when shearing along (001)/<110> with a 24 25 26 lower shear stress of 36.9 GPa, while the structure changes to R B6O when shearing along 27 28 (010)/<001> with a higher minimum shear stress of 40.8 GPa (Fig. S6 of SI). For R B6O, the 29 30 14 31 icosahedra disintegrate for both shear along (001)/<100> and along (011)/<2 1 1> (Fig. S7 of 32 33 34 SI). 35 36 Structural transformations between solids have been widely examined in metals, 34,35 37 38 36,37 20,29 39 semiconductors, and superhard ceramics . Recent studies shows that a possible path for 40 41 42 transforming the zinc blende (ZB) structure to the wurzite phase is a collective glide of Shockley 43 44 36,37 partial dislocations on the (111) plane. We calculate that the shear deformation from R B6O 45 46 47 to τ B6O requires a shear stress over 35 GPa at 0 K. Thus, it is unlikely that τ B6O is formed 48 49 50 from mechanical twinning of R B6O. Instead we expect that τ B6O may be formed during 51 52 nucleation and growth from the melt, as favored by the lower free energy of τ B6O compared to 53 54 55 R B6O. 56 57 58 59 11 60 ACS Paragon Plus Environment Nano Letters Page 12 of 23
1 2 3 4 Summarizing, we confirm with QM and STEM experiments the existence of the new τ B6O 5 6 19 7 phase predicted by Dong et al . The stacking fault energies for nanotwinned R B6O are negative 8 9 10 and the free energy of the τ B6O phase is lower than that of the R B6O, demonstrating that the 11 12 twinned structures are more stable than the R B6O phase. However, the negative SFEs have 13 14 15 trivial influence on the elastic properties of the twinned R B6O. Applying a pure shear 16 17 18 deformation on the new τ B6O structure transforms it to R B6O along the lowest stress slip 19 20 system (010)/<001> but this transformation is irreversible. Imposing biaxial shear stress in a way 21 22 23 similar to the loading conditions for indentation, we find that the new τ B6O phase transforms to 24 25 26 an amorphous phase in which the lowest stress slip system changes from (010)/<001> to 27 28 (001)/<110>. We found that the τ B6O phase is stronger than R B6O under pure shear 29 30 31 deformation, while it is weaker than R B6O for indentation conditions. 32 33 34 ASSOCIATED CONTENT 35 36 Supporting Information 37 38 39 The supporting Information includes details of the experimental and simulation method, the 40 41 42 predicted elastic moduli for τ B6O, 2τ B6O, 4τ B6O, the STEM image for R B6O, the STEM and 43 44 HRTEM images for R B6O and τ B6O, the computed electron diffraction patterns for perfect 45 46 47 τ B6O and vacancy models, the entropy (S) and Helmholtz free energy (A) difference between 48 49 50 R B6O and τ B6O at finite temperature, the transformed structure at 0.345 strain for 2τ B6O 51 52 phase shearing along (010)/<001> slip system, and the structural change for R B6O shear along 53 54 55 (011)/<2 1 1 > under indentation conditions. This material is available free of charge via the 56 57 58 59 12 60 ACS Paragon Plus Environment Page 13 of 23 Nano Letters
1 2 3 4 Internet at http://pubs.acs.org. 5 6 7 Acknowledgements 8 9 10 This work was supported by the Defense Advanced Research Projects Agency 11 12 (W31P4Q 13 1 0010 and W31P4Q1210008, program manager, John Paschkewitz), by the Army 13 14 15 Research Laboratory under Cooperative Agreement Number W911NF 12 2 0022, and by the 16 17 18 National Science Foundation (DMR 1436985, program manager, John Schlueter). 19 20 The TEM experimental work was carried at WPI AIMR, Tohoku University, Japan with 21 22 23 research supported by the ‘World Premier International (WPI) Center Initiative Atoms, 24 25 26 Molecules and Materials,’ MEXT, Japan. We thank Professor Takashi Goto of Institute for 27 28 Materials Research, Tohoku University for providing the B6O sample for experimental 29 30 31 observations. 32 33 34 Additional information 35 36 Notes 37 38 39 The authors declare no competing financial interests. 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 13 60 ACS Paragon Plus Environment Nano Letters Page 14 of 23
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1 2 3 4 (37) Zhang, H.; Wang, J.; Huang, J. Y.; Wang, J. B.; Zhang, Z.; Mao, S. X. Nano Lett. 5 6 2013 , 13 , 6023−6027. 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 17 60 ACS Paragon Plus Environment Nano Letters Page 18 of 23
1 2 3 4 Table 1. The predicted absolute energies (eV/B6O), relative energy, elastic modulus, and 5 hardness of τ B6O, R B6O, and twinned R B6O from VASP. Comparing the total energy of τ B6O 6 with R B6O we can say that the energy to insert stacking faults into τ B6O to form R B6O, is 1.51 7 2 8 mJ/m . 9 10 Structure τ B6O R B6O 2τ B6O 3τ B6O 4τ B6O 11 12 13 Energy (eV/B 6O unit) 50.1366 50.1355 50.1362 50.1361 50.1360 14 15 16 Relative energy 0 1.1 0.4 0.5 0.6 17 (meV/B 6O) 18 Bulk modulus (GPa) 225.9 232.0 226.2 − 221.8 19 20 21 Shear modulus (GPa) 209.2 210.9 208.5 − 206.6 22 23 24 Hardness (GPa) 38.6 37.9 38.3 − 38.6 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 18 60 ACS Paragon Plus Environment Page 19 of 23 Nano Letters
1 2 3 4 Figure 1 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Fig. 1. The Structure of the τ B6O phase from QM prediction and STEM experiments: (a) 42 QM predicted τ B6O phase projected along 〈100 〉 direction. (b) STEM image showing the 43 44 τ B6O phase. (c) An experimental SAED pattern recorded for the region imaged in (b) and 45 indexed to be the τ B6O structure. (d) Simulated SAED pattern from the QM predicted structure 46 projection along the 〈100 〉 direction. In the experimental and simulated SAED 000 47 48 represents the transmitted beam. The identified g vector spots near the transmitted beam are 49 given. The QM structure is predicted at 0 K without thermal fluctuations. 50 51 52 53 54 55 56 57 58 59 19 60 ACS Paragon Plus Environment Nano Letters Page 20 of 23
1 2 3 4 Figure 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Fig. 2. The shear stress shear strain relationship of τ B6O along various slip systems. The 33 34 (010)/<001> is the least stress shear condition, with a maximum shear stress of 39.4 GPa. 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 20 60 ACS Paragon Plus Environment Page 21 of 23 Nano Letters
1 2 3 4 Figure 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Fig. 3. The deformation mechanism for shear along the least shear slip system, (010)/<001> 38 39 (note that each O bonds to three icosahedra, so that is formally O +): (a) The intact structure. (b) 40 41 The structure at 0.276 strain which corresponds to the maximum shear stress of 39.4 GPa. (c) 42 43 The structure at 0.369 strain before phase transition. (d) The structure at 0.392 strain after the 44 45 phase transition where all bonds are reconnected for the sheared phase. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 21 60 ACS Paragon Plus Environment Nano Letters Page 22 of 23
1 2 3 4 Figure 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Fig. 4. The stress strain relationship and the structural changes as the R B6O shear along 38 (011)/<2 > (reverse deformation of τ B6O along (010)/<001>): (a) Stress strain relationship. 39 40 (b) Structure at 0.280 strain corresponding to the maximum shear stress of 37.9 GPa. The B B 41 bond between icosahedra is stretched to 2.40 Å (dashed line). (c) Structure at 0.397 before failure. 42 (d) Failed structure at 0.413 strain. 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 22 60 ACS Paragon Plus Environment Page 23 of 23 Nano Letters
1 2 3 4 Figure 5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fig.5. The stress strain relationships of τ B6O, R B6O, and twinned R B6O shearing along 32 33 various slip systems and the structural changes for τ B6O under indentation conditions. (a) 34 35 Stress strain relationship. (b) τ B6O structure at 0.231 strain shearing along (001)/<110> before 36 37 failure. (c) τ B6O structure at 0.254 strain shearing along (001)/<110> before failure. (d) (f) 38 39 Structural changes of τ B6O shear along (010)/<001> slip system which results in phase 40 41 transition from τ B6O to R B6O. 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 23 60 ACS Paragon Plus Environment