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Strain concentration at the boundaries in fivefold twins of diamond and silicon Rong Yu, Hao Wu, Jiadao Wang, and Jing Zhu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b14564 • Publication Date (Web): 09 Jan 2017 Downloaded from http://pubs.acs.org on January 16, 2017

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ACS Applied Materials & Interfaces

Strain concentration at the boundaries in fivefold twins of diamond and silicon Rong Yu1,*, Hao Wu1, Jia Dao Wang2, Jing Zhu1 1

National Center for Electron Microscopy in Beijing, Key Laboratory of Advanced Materials of Ministry of Education of China and State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China; 2 Department of Mechanical Engineering, Tsinghua University, Beijing 100084,China. *E-mail: [email protected]

Abstract Widely found in metals, semiconductors, oxides, and even organic materials, multiple twinning has important implications in engineering applications of materials. In this work, the intrinsic strain in fivefold twins of diamond and silicon has been studied combining aberration-corrected electron microscopy and first-principles calculations. In contrast to metallic fivefold twins, where the strain distribution is relatively smooth, the semiconductor systems show significant strain concentration at the twin boundaries, which is shear modulus dependent. In silicon with moderate strain concentration, the electronic frontier orbitals are located at the center of the fivefold twins. Accompanying the increased strain concentration in diamond, however, the frontier orbitals are pushed to the surface. The modification of strain state and surface electronic structure by materials elasticity suggest possible routes to tune catalytic, electronic, and mechanical properties of materials.

Keywords: fivefold twins, diamond, silicon, strain concentration, elasticity, brittleness, frontier orbital, twin boundary

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1. Introduction Multiple twinning is a phenomenon widely found in both natural and synthesis matter. The two types of multiple twinning, lamellar and cyclic, have attracted much attention due to their unique structures and properties. Lamellar twinning was shown to give a combination of high strength and toughness in copper and steel 1-2 and highest creep resistance in titanium aluminide alloys 3. Unprecedented hardness has been achieved in diamond with high density lamellar twins 4. The cyclic twinning, as another type of multiple twinning, also occurs in a wide range of materials, including not only inorganic small particles and thin films 5-6, but also proteins and virus 7-8. The fivefold twinning is the most common form for multiple cyclic twinning 7. The fivefold twinning has also attracted attention from the viewpoint of symmetry, which is an important concept in modern science 9. In fact, the fivefold rotational symmetry is geometrically forbidden in periodic crystals, although popular in quasicrystals 10. Due to the geometrical incompatibility, the fivefold twins are intrinsically strained relative to their single-crystalline counterparts. There have been extensive studies on the intrinsic strain in fivefold twins, mostly in metallic systems 11-12. Various models for strain distribution in fivefold twins have been proposed, including the homogeneous- and inhomogeneous-strain models 11, 13. Being a typical example of elastic strain engineering 1, 14, the intrinsic strain in fivefold twins of metals results in different catalytic properties from single-crystalline particles 15-16. Compared with metals, semiconductors have remarkably different bonding characteristic and deformation behaviors. In general, metals are ductile and semiconductors are brittle. Despite many reports about fivefold twinning in semiconductor particles and polycrystals 5, 17-22, it has been unclear how the bonding character modify the intrinsic strain in them. In this work, the atomic structure of the fivefold twins in diamond and silicon have been investigated combining aberration-corrected transmission electron microscopy and first-principles calculations. In contrast to the strain distribution in metallic systems, which has small inhomogeneity, the strain distributions in the fivefold twins of the semiconductors have been shown to depend significantly on the Pugh’s ratio of shear modulus to bulk modulus. For diamond with very high Pugh’s ratio, the strain is highly concentrated at the twin boundaries. Correspondingly, the frontier orbitals are located at the surfaces, in contrast to the case of silicon, where the frontier orbitals are close to the center. The modification of strain state and surface electronic structure by materials elasticity can be employed to tune materials properties for engineering applications. 2. Experimental and calculation details The atomic structural model of diamond fivefold twins was proposed referring cage compounds of carbon and hydrogen atoms 17. In order to confirm directly the atomic structure, sub-Angstrom resolution electron microscopy is required due to the short bonds in diamond, since the largest projected distance of carbon dumbbells is only 0.89 Å. In this


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study, the atomic structure of diamond thin films was analyzed using aberration-corrected transmission electron microscopy with sub-angstrom resolution. The diamond films were deposited onto low-resistivity silicon (p-type) substrates from a hot-filament activated methane hydrogen gas mixture with the pressure of 50 Torr. The filament temperature is 2500 °C and that of substrates is 830 °C. The mixture flows at the rate of 5 L/min, and the growth rate is 0.24 µm/h. A continuous film of diamond was obtained after 15 hours of growth 23. High-resolution transmission electron microscopy (TEM) observations were performed using an FEI Titan 80-300 transmission electron microscope equipped with a spherical aberration (Cs) corrector for the objective lens. SubAngstrom resolution has been demonstrated for imaging not only for perfect lattices, but also for materials defects 24-26. In order to enhance the contrast and the signal-to-noise ratio for the low-Z material, the negative-Cs imaging technique was used 27. The images were taken at a high tension of 300 kV, with the spherical aberration set at around -13 µm. The other residual aberrations measured before and after image recording are two-fold astigmatism A1 < 2 nm, three-fold astigmatism A2 < 15 nm, and coma B2 < 15 nm. Highresolution TEM image simulations were carried out using the multislice method 28 as implemented in the MacTempasX program. Structural relaxations were performed using the projector augmented-wave method 29 within the density functional theory (DFT), as implemented in the VASP code 30-31. For the exchange and correlation functional the local density approximation (LDA) of the PerdewZunger parameterization 32 was used. The energy cutoff was set to 400 eV. Integrations over the Brillouin zone were performed using Monkhorst-Pack grids 33. Large supercells have been adopted in the calculations to ensure that the optimized structures have fivefold symmetry. Because fivefold symmetry is not compatible to periodic lattice, it serves as a good indicator for the supercell size. If a supercell is not large enough, there would be interactions between neighboring fivefold twins and the fivefold symmetry would be broken. For diamond, the supercells have a size of 39.635 Å × 39.635 Å × 2.449 Å, containing 320400 atoms for different surface saturation mechanisms. The closest distance between neighboring models is about 10 Å. The k sampling was 1×1×10 including the Γ point in the Brillouin zone. For silicon, the supercell is 60.646 Å × 60.646 Å × 3.824 Å, and the k sampling is 1×1×6. The structural relaxations were performed until the residual forces were less than 0.01 eV/Å. 3. Results and discussions Figure 1(a) shows an experimental aberration-corrected TEM image of the fivefold twins in the diamond thin film. The electron beam is parallel to the fivefold axis, i.e. the common [110] direction of all the five sections. Since the dumbbell spacing (0.89 Å) of diamond in this orientation is close to the information limit of the microscope (0.8 Å), the image contrast depends sensitively on the sample thickness and orientation, even the residual aberrations of the microscope were kept as small as possible (see the experimental parameters described above). Image simulations showed that the dumbbells cannot be resolved for samples thicker than 6 nm, even at ideal imaging conditions. In the thinnest 3 ACS Paragon Plus Environment


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area (section S3), the dumbbells are clearly resolved. For comparison, a simulated image based on the atomic structure model (Fig. 2c described below) is shown in Fig. 1(b). Around the fivefold axis, there is a good match between the experimental and simulated images, confirming the atomic structure model.

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Fig. 1. (a) Experimental and (b) simulated aberration-corrected TEM images of five-fold twins in diamond.

In the diamond thin film, which is polycrystalline, the fivefold twins are enclosed in other crystalline grains and are subject to the geometrical constraint, since the periodic lattice cannot provide a fivefold environment. Additional strain would be induced by the constraint and lead to different sample tilt for different twin sections. In the image simulation, the best fit between the experimental and simulated images was obtained at sample tilt of 1°, 1.3°, 0°, 0.8° and 0.8° for the five twin sections. In order to analyze the intrinsic strain in the fivefold twins, atomic structure models that are free from the constraint of neighboring crystals were constructed. For symmetry reason, it is necessary for the models to expose (100) surfaces with dangling bonds. Since the intrinsic strain in the fivefold twins is considered in this study, the compensation of the dangling bonds at the surfaces need to be carefully dealt with in order to minimize the surface effect on the strain distribution. Although detailed surface properties of diamond and silicon are not the primary focus in this work, we note that these surfaces have been extensively studied 34-42. An atom on the (100) surface has only two coordinated atoms below it, leaving two dangling bonds. Besides the ideal cleaved surface, three different mechanisms were considered to saturate the dangling bonds, i.e., (2×1) reconstruction, hydrogenation, and oxygenation. For the (2×1) reconstruction mechanism, the size of the supercell was doubled in the fivefold axis direction, forming five (100)-(2×1) reconstructed side surfaces. There are 640 C atoms in the supercell. For fivefold diamond with (2×1) reconstructed clean surface, the relaxed model is given in Fig. 2(a). The side surface is shown in Fig. 2(b). The calculation results indicate that all 4 ACS Paragon Plus Environment

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the dangling bonds are compensated through the surface reconstruction with dimerization. Note that single-, double-, and triple- bonds would form between carbon atoms depending on the number of π bonds. Their bond lengths are 1.54 Å, 1.34 Å, and 1.20 Å, respectively 43 . On the broad surfaces, additional C=C double bonds (1.371 Å in length) are formed parallel to the fivefold axis. At the five corners, however, C−C single bonds (1.553 Å in length) are formed parallel to the fivefold axis, and C=C double bonds (1.363 Å in length) are formed normal to the twin boundaries (also normal to the fivefold axis), replacing the corresponding C≡C triple bonds in the model with ideal (100)-(1×1) surface. Because of the reconstruction that changes the bond angles at the surface, significant rumpling was induced in the sublayers. For the hydrogenated diamond model, two H atoms per surface atom were appended to the bare surface. There are 320 C atoms and 80 H atoms in the supercell. There are only C−C single bonds in the system. The outermost C-C bonds are slightly strengthened, with the bond length changed to 1.51 Å from that inside the bulk (1.53 Å). As shown in Fig. 2(d), the canted (1×1):2H structure was formed on the side faces, consistent with previous studies on single crystalline (100) surface 34-35. In addition to the simple hydrogenation model considered here, more elaborate models have been investigated, considering practical chemical environments like the variation in the chemical potential of hydrogen38. For the oxygenated diamond surface, only one O atom per surface atom is needed to saturate the two dangling bonds. Previous studies on single crystalline (100) surface has revealed the stable configuration with oxygen occupying the bridge site on the surface 36-37. In the current study of diamond fivefold twins with oxygenated surface, there are 320 C atoms and 40 O atoms in the supercell. The side surface is shown in Fig. 2(f). In the relaxed structure, only C−C single bonds can be identified in the system, with the bond length around 1.53 Å. The C−O bond length is 1.479 Å, close to the average length (1.43 Å) of the C−O single bond 43. The C−O−C bond angle is 115.3°, also a typical value in systems containing C−O−C. For example, the bond angle of 112° is found in dimethyl ether CH3-OCH3 44. The results indicate that the O covering is indeed an excellent way to saturate the dangling bonds on the (100) surface of diamond fivefold twins. In the IV-group semiconductors, the spatial extension of the valence electrons in diamond is much smaller than that of the other members. Correspondingly, the covalent bonding in diamond is significantly stronger. It is attractive to see how the angular gap in fivefold twins is accommodated in materials with largely varying bond rigidity. Therefore, the atomic structure of fivefold twins in silicon was also studied for comparison. Due to the large difference in the bond lengths of C-O and Si-O bonds, the surface saturation mechanism by bridging oxygen atoms that works very well for diamond is not expected to work for silicon and is not considered here. Figure 2(g) shows the relaxed model of silicon with hydrogenated surface. Similar to the case of diamond, the canted structure is formed on single crystalline Si (100) (1×1):2H surface 39-40. This feature can also be seen on the side surface of the fivefold twins of Si, as shown in Fig. 2(h).



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Fig. 2. Relaxed fivefold twins with (a) (2×1) reconstructed, (c) hydrogenated, and (e) oxygenated surfaces of diamond, and (g) hydrogenated surface of silicon. The atomic configurations of the corresponding surfaces are shown in (b), (d), (f), (h), respectively.

The bond lengths were calculated for the relaxed structure models of the fivefold twins. As discussed above, the structures with clean and (1×2) reconstructed surfaces have large structural relaxations near the surfaces, giving large changes (>5%) in the bond lengths relative to the bulk. In the following we discuss primarily the intrinsic strain in the systems with small surface relaxations, i.e., the structures with hydrogenated surfaces. For results about the other types of surfaces, see Supporting Information. The distribution of bond length in diamond is plotted in Fig. 3a. The strain is inhomogeneous in both the radial and tangential directions. The bond length increases from the center to the surface. The smallest bond length (1.515 Å) is found close to the fivefold 6 ACS Paragon Plus Environment

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axis. The central five-member ring itself, however, is an exception. This can be attributed to the change in the bond angles (108°) in the five-member ring, which is smaller than that for normal tetrahedral coordination (109.47°). The relatively larger deformation of the tetrahedra weakens the chemical bonds in the five-member ring, giving larger bond length (1.530 Å) relative to the neighboring bonds (1.515 Å). The central part of the three structures with compensated surfaces are almost identical . For the structure with ideal surface, however, the central part has a larger compressive strain, indicating that the structure is subjected to a larger surface tension resulted from the uncompensated dangling bonds. For the other three structures, all the dangling bonds are compensated, giving smaller surface energy and surface tension. 35

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Fig. 3. Bond length distribution in fivefold twins of (a) diamond and (b) silicon with hydrogenated surfaces. The displayed range is ±2% of the bond length in the bulk (1.53 Å for diamond and 2.34 Å for silicon).

The most striking feature in the bond length distribution is the large bond stretching at the twin boundaries. As can be seen in Fig. 3a, the bond lengths at the twin boundaries are significantly larger than those in the remaining areas. This is in contrast to the strain distributions previously predicted in theoretical models 11, 13 and observed in metallic systems 45. Even in the inhomogeneous strain model, where the strain in the radial direction 7 ACS Paragon Plus Environment


depends on the distance from the fivefold symmetry axis, the strain in tangential direction is still angular-independent 11, 13. In order to interpret the large difference in the strain state of metals and semiconductors, we note that the two types of systems have quite different bonding characteristics and deformation behaviors. In contrast to the metallic bonding that is essentially isotropic, the covalent bonding in semiconductors is highly directional, leading to their high shear moduli and hardness 46. For the fivefold twins to fill the angular gap, a homogeneous strain would require the entire system to extend equally in the angular direction and change significantly the bond angles. In the strain concentration state, however, the bond angles away from the boundaries change much less than the homogeneous strain state. In order to see the energetics of the strain concentration process, we constructed a series of models with different degree of strain concentration and calculated their energies. The structure numbers 0 and 10 correspond to the homogeneous strain state and the strain concentration state, respectively. The atomic positions of the other structures are linear interpolations and extrapolations of those of 0 and 10. The result is shown in Fig. 4. Due to the directional covalent bonding and the rigid lattice of diamond, the homogeneous strain led to higher energy at the initial stage. As the strain concentration developed gradually in the fivefold twins, the system gradually lowered its energy, and concentrated the required elastic strain to the twin boundaries, leaving the remaining area in a slightly strained state.

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Fig. 4. Evolution of energy of diamond fivefold twins with the structure changing from the homogeneous (Structure number 0) to the strain concentration state (Structure number 10). Further strain concentration increases the energy again.

The elastic strain concentration at the twin boundaries in the semiconductor systems may have important implications in deformation physics of these materials. The ductility (or its opposite, brittleness) is an important mechanical property of materials. Since the strength of different types of chemical bonds in materials varies significantly, a strength-related property (like the shear modulus G) is not suitable to characterize the brittleness of materials. For example, both NaCl and diamond are brittle but the shear modulus of diamond (535 GPa) is 40 times larger than that of NaCl (13 GPa)47, while copper with intermediate shear modulus (46 GPa) is ductile. To characterize the brittleness of materials, it is desirable to 8 ACS Paragon Plus Environment

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find a property that is not proportional to materials strength. For metals, Pugh 48 proposed to use a dimensionless number as an indicator of materials brittleness, i.e., the ratio of shear modulus to bulk modulus G/B (in Pugh’s original paper B/G was used). A metal is brittle if G/B is above a critical value, otherwise ductile. The reasoning was based on the resistance of metals to the plastic deformation. For a metal with high shear modulus, such as beryllium, the plastic flow (dislocation slip or deformation twinning) is relatively difficult. Thus the stress concentration at a crack will be developed and the fracture is easy to occur. Although only metals were considered in Pugh’s original work 48, the so-called Pugh’s ratio has also been used as an important parameter for characterizing the brittleness and hardness of semiconductors and ceramics in the following years 46, 49-50. For example, diamond has a high Pugh’s ratio (1.21), and is highly brittle. Without plastic deformation involved in the intrinsic strain of fivefold twins, our results show that the strain concentration in a semiconductor may have already been developed at the elastic deformation stage, explaining why the Pugh’s ratio is applicable to semiconductors and ceramics. The idea behind the correlation between the strain concentration and the Pugh’s ratio G/B is similar to above discussion on materials brittleness. For strain concentration to form, a high value of relative rigidity other than absolute rigidity is required. Therefore, the ratio of shear modulus to bulk modulus G/B can serve as a good indicator for the degree of strain concentration. The distribution of bond lengths in the fivefold twins of silicon with hydrogenated surfaces is plotted in Fig. 3(b). The strain concentration at the twin boundaries can also be observed, but is significantly smaller than that in diamond. The Pugh’s ratio of silicon (0.68) is less than diamond, confirming the correlation between the strain concentration and the Pugh’s ratio of shear modulus to bulk modulus.



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Fig. 5. (a) Highest occupied molecular orbitals (HOMO) and (b) lowest unoccupied molecular orbitals (LUMO) in fivefold twins in diamond; (c) HOMO and (d) LUMO for silicon.

Associated with different degree of strain concentration in diamond and silicon, the electronic structure of the two systems show different features. For diamond, the highest occupied molecular orbitals (HOMO, Fig. 5a) and lowest unoccupied molecular orbitals (LUMO, Fig. 5b), both fivefold degenerate, are located around the surface atoms. For silicon, the HOMO (Fig. 5c) and LUMO (Fig. 5d) are located inside the fivefold twins. Note that the LUMO in Fig. 5b doesn’t show fivefold symmetry. This is because the unoccupied molecular orbitals are more extended in space, leading to larger overlap between orbitals in neighboring supercells. Since the LUMO is unoccupied, however, its shape has no effect on the ground state energy of the system and other ground state properties, such as the structure at equilibrium. This is why the atomic structure and the HOMO show fivefold symmetry but the LUMO does not. The difference in the spatial distribution of HOMO and LUMO can be attributed to the different strain concentration. Due to the large strain concentration at the twin boundaries in diamond, the atomic configuration at the rim are changed significantly, leading to the formation of separate bands deep in the energy gap. In fact, the HOMO plotted in Fig. 5a are the gap states. For silicon with less strain concentration at the twin boundaries, the change in atomic configuration at the center is larger, i.e., the formation of the five-member ring other than the six-member rings in bulk silicon. The electronic states associated with the change are therefore located close to the center. Energetically, the HOMO and LUMO 10 ACS Paragon Plus Environment

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states are shallow in the gap, i.e., close to top of the valance band and bottom of conduction band, respectively. The spatial distribution of HOMO and LUMO could have important implications for surface sensitive behaviors. Photocatalysis, for example, involves charge transfer between the reactants and the photocatalysts, leading to the reduction or oxidation of the reactants. A photocatalyst with frontier orbitals (HOMO or LUMO) at the surface would promote the charge transfer, giving higher activity. Therefore, higher catalytic activity could be expected in materials systems with potential of forming large strain concentration and frontier orbitals at the surface. It is interesting to note that reduction of N2 to NH3 has been recently demonstrated using diamond photocatalysis 51.

4. Conclusions In summary, the deformation in the fivefold twins of semiconductors is highly inhomogeneous in both radial and tangential directions. In the radial direction, the bondlength increaces from the center to the surface. In the tangential direction, there is significant strain concentration at the twin boundaries, the magnitude of which depends on the Pugh’s ratio of shear modulus to bulk modulus. A relatively high shear modulus would lead to a high strain concentration, explaining the brittleness of materials with high Pugh’s ratio. Due to the different strain concentration at the twin boundaries, the frontier orbitals of diamond and silicon show distinct spatial distribution. While the HOMO and LUMO in diamond are located at the surface, those of silion are around the center of the fivefold twins.

Supporting Information Fivefold twins of diamond with ideal (100) surfaces, the bond length in fivefold twins of diamond, Fivefold twins of silicon with ideal (100) surfaces, the bond length in fivefold twins of silicon. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments This work was supported by NSFC (51525102, 51371102, 11374174, 51390475). This work used the resources of the National Center for Electron Microscopy in Beijing and Shanghai Supercomputer Center. Reference 1. Yan, F. K.; Tao, N. R.; Archie, F.; Gutierrez-Urrutia, I.; Raabe, D.; Lu, K. Deformation Mechanisms in an Austenitic Single-Phase Duplex Microstructured Steel with Nanotwinned Grains. Acta Mater. 2014, 81, 487-500. 2. Pan, Q.; Lu, L. Dislocation Characterization in Fatigued Cu with Nanoscale Twins. Sci. China Mater. 2015, 58, 915-920. 3. Appel, F.; Wagner, R. Microstructure and Deformation of Two-Phase GammaTitanium Aluminides. Mater. Sci. Eng., R 1998, 22, 187-268. 11 ACS Paragon Plus Environment


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4. Huang, Q.; Yu, D.; Xu, B.; Hu, W.; Ma, Y.; Wang, Y.; Zhao, Z.; Wen, B.; He, J.; Liu, Z.; Tian, Y. Nanotwinned Diamond with Unprecedented Hardness and Stability. Nature 2014, 510, 250-253. 5. Shechtman, D.; Hutchison, J. L.; Robins, L. H.; Farabaugh, E. N.; Feldman, A. Growth Defects in Diamond Films. J. Mater. Res. 1993, 8, 473-479. 6. Wang, Z. W.; Palmer, R. E. Determination of the Ground-State Atomic Structures of Size-Selected Au Nanoclusters by Electron-Beam-Induced Transformation. Phys. Rev. Lett. 2012, 108, 245502. 7. Hofmeister, H. Forty Years Study of Fivefold Twinned Structures in Small Particles and Thin Films. Cryst. Res. Technol. 1998, 33, 3-25. 8. Gryaznov, V. G.; Heydenreich, J.; Kaprelov, A. M.; Nepijko, S. A.; Romanov, A. E.; Urban, J. Pentagonal Symmetry and Disclinations in Small Particles. Cryst. Res. Technol. 1999, 34, 1091-1119. 9. Weyl, H., Symmetry. Princeton University Press: Princeton, 1952. 10. Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W. Metallic Phase with Long-Range Orientational Order and No Translational Symmetry. Phys. Rev. Lett. 1984, 53, 1951-1953. 11. Howie, A.; Marks, L. D. Elastic Strains and the Energy Balance for Multiply Twinned Particles. Philos. Mag. A 1984, 49, 95-109. 12. Marks, L. D. Experimental Studies of Small Particle Structures. Rep. Prog. Phys. 1994, 57, 603-649. 13. Wit, R. d. Partial Disclinations. J. Phys. C: Solid State Phys. 1972, 5, 529. 14. Zhu, T.; Li, J. Ultra-Strength Materials. Prog. Mater. Sci. 2010, 55, 710-757. 15. Wu, J.; Qi, L.; You, H.; Gross, A.; Li, J.; Yang, H. Icosahedral Platinum Alloy Nanocrystals with Enhanced Electrocatalytic Activities. J. Am. Chem. Soc. 2012, 134, 11880-11883. 16. Mavrikakis, M.; Hammer, B.; Norskov, J. K. Effect of Strain on the Reactivity of Metal Surfaces. Phys. Rev. Lett. 1998, 81, 2819-2822. 17. Matsumoto, S.; Matsui, Y. Electron Microscopic Observation of Diamond Particles Grown from the Vapour Phase. J. Mater. Sci. 1983, 18, 1785-1793. 18. Dorignac, D.; Delclos, S.; Phillipp, F. Atomic Structure of a Complex Defect Configuration in Synthetic Diamond: A Fivefold Twin Centre Connected to Two HighOrder Grain Boundaries. Philos. Mag. B 2001, 81, 1879-1891. 19. Narayan, J.; Srivatsa, A. R.; Peters, M.; Yokota, S.; Ravi, K. V. On Epitaxial Growth of Diamond Films on (100) Silicon Substrates. Appl. Phys. Lett. 1988, 53, 1823-1825. 20. Oku, T.; Hiraga, K.; Matsuda, T.; Hirai, T.; Hirabayashi, M. Formation and Structures of Multiply-Twinned Nanoparticles with Fivefold Symmetry in Chemical Vapor Deposited Boron Nitride. Diamond Relat. Mater. 2003, 12, 1918-1926. 21. Yamada, S. Structure of Germanium Nanoparticles Prepared by Evaporation Method. J. Appl. Phys. 2003, 94, 6818-6821. 22. Pei, Y. T.; De Hosson, J. T. M. Five-Fold Branched Si Particles in Laser Clad Alsi Functionally Graded Materials. Acta Mater. 2001, 49, 561-571. 23. Wang, J.; Liu, F.; Chen, H.; Chen, D. The Electron Transfer Behavior of the Hydrogen-Terminated Boron-Doped Diamond Film Electrode. Mater. Chem. Phys. 2009, 115, 590-598. 24. Yu, R.; Hu, L. H.; Cheng, Z. Y.; Li, Y. D.; Ye, H. Q.; Zhu, J. Direct Subangstrom Measurement of Surfaces of Oxide Particles. Phys. Rev. Lett. 2010, 105, 226101. 25. Zhang, W.; Yu, R.; Du, K.; Cheng, Z. Y.; Zhu, J.; Ye, H. Q. Undulating Slip in Laves Phase and Implications for Deformation in Brittle Materials. Phys. Rev. Lett. 2011, 106, 165505. 12 ACS Paragon Plus Environment

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26. He, M.-R.; Yu, R.; Zhu, J. Reversible Wurtzite–Tetragonal Reconstruction in Zno(10-10) Surfaces. Angewandte Chemie International Edition 2012, 51, 7744-7747. 27. Jia, C. L.; Lentzen, M.; Urban, K. Atomic-Resolution Imaging of Oxygen in Perovskite Ceramics. Science 2003, 299, 870-873. 28. Cowley, J. M., Diffraction Physics. 3 ed.; Elsevier: Amsterdam, 1995. 29. Blochl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 1795317979. 30. Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169-11186. 31. Kresse, G.; Furthmuller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15-50. 32. Perdew, J. P.; Zunger, A. Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems. Phys. Rev. B 1981, 23, 5048. 33. Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188-5192. 34. Hong, S.; Chou, M. Y. Theoretical Study of Hydrogen-Covered Diamond (100) Surfaces: A Chemical-Potential Analysis. Phys. Rev. B 1997, 55, 9975-9982. 35. Steckel, J. A.; Kresse, G.; Hafner, J. Structural Characterization of the HydrogenCovered C(100) Surface by Density Functional Theory Calculations. Phys. Rev. B 2002, 66, 155406. 36. Wang, Y. M.; Wong, K. W.; Lee, S. T.; Nishitani-Gamo, M.; Sakaguchi, I.; Loh, K. P.; Ando, T. Recent Studies on Diamond Surfaces. Diamond Relat. Mater. 2000, 9, 15821590. 37. Tamura, H.; Zhou, H.; Sugisako, K.; Yokoi, Y.; Takami, S.; Kubo, M.; Teraishi, K.; Miyamoto, A.; Imamura, A.; N.-Gamo, M.; Ando, T. Periodic Density-Functional Study on Oxidation of Diamond (100) Surfaces. Phys. Rev. B 2000, 61, 11025-11033. 38. Yu, Y.; Gu, C. Z.; Xu, L. F.; Zhang, S. B. \Textit{Ab Initio} Structural Characterization of a Hydrogen-Covered Diamond (001) Surface. Phys. Rev. B 2004, 70, 125423. 39. Ciraci, S.; Butz, R.; Oellig, E. M.; Wagner, H. Chemisorption of Hydrogen on the Si(100) Surface: Monohydride and Dihydride Phases. Phys. Rev. B 1984, 30, 711-720. 40. Northrup, J. E. Structure of Si(100)H: Dependence on the H Chemical Potential. Phys. Rev. B 1991, 44, 1419-1422. 41. Yang, H.; Xu, L.; Gu, C.; Zhang, S. B. First-Principles Study of Oxygenated Diamond (001) Surfaces with and without Hydrogen. Appl. Surf. Sci. 2007, 253, 4260-4266. 42. Andriotis, A. N.; Mpourmpakis, G.; Richter, E.; Menon, M. Surface Conductivity of Hydrogenated Diamond Films. Phys. Rev. Lett. 2008, 100, 106801. 43. Atkins, P.; Paula, J. d., Atkins' Physical Chemistry. 7 ed.; Oxford University Press: Oxford, 2002. 44. McMurry, J.; Simanek, E., Fundamentals of Organic Chemistry. 6 ed.; Thomson: Belmont, 2007. 45. Johnson, C. L.; Snoeck, E.; Ezcurdia, M.; Rodriguez-Gonzalez, B.; Pastoriza-Santos, I.; Liz-Marzan, L. M.; Hytch, M. J. Effects of Elastic Anisotropy on Strain Distributions in Decahedral Gold Nanoparticles. Nat. Mater. 2008, 7, 120-124. 46. Gilman, J. J., Chemistry and Physics of Mechanical Hardness. 1 ed.; John Wiley & Sons: Hoboken, 2009. 47. Newnham, R. E., Properties of Materials - Anisotropy, Symmetry, Structure. 1 ed.; Oxford University Press: Oxford, 2005. 13 ACS Paragon Plus Environment


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48. Pugh, S. F. Relation between the Elastic Moduli and the Plastic Properties of Polycrystalline Pure Metals. Philos. Mag. 1954, 45, 82-843. 49. Chen, X.-Q.; Niu, H.; Li, D.; Li, Y. Modeling Hardness of Polycrystalline Materials and Bulk Metallic Glasses. Intermetallics 2011, 19, 1275-1281. 50. Ching, W.-Y.; Mo, Y.; Aryal, S.; Rulis, P. Intrinsic Mechanical Properties of 20 Max-Phase Compounds. J. Am. Ceram. Soc. 2013, 96, 2292-2297. 51. Zhu, D.; Zhang, L.; Ruther, R. E.; Hamers, R. J. Photo-Illuminated Diamond as a Solid-State Source of Solvated Electrons in Water for Nitrogen reduction. Nat Mater 2013, 12, 836-841.


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