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Transformation between Different Hybridized Bonding Structures in Two-Dimensional Diamond-Based Materials Le-sheng Li and Xiang Zhao* Institute for Chemical Physics and Department of Chemistry, Faculty of Science, Xi’an Jiaotong University, Xi’an 710049, China
bS Supporting Information ABSTRACT: Although knowledge about carbon hybrid films comprising both sp2 and sp3 bonding structures is of great importance for innovation applications of diamond-based nanostructures, little is known about the mixed hybridization forms in the same two-dimensional material. In this study, the structural properties of two-dimensional diamond nanoflakes (DNFs) are explored using density functional theory (DFT) simulations. The DFT results indicate that phase transformations between different hybridized bonding structures do occur in two-dimensional DNFs. Moreover, the reconstruction process is proposed to take place on the DNF (100) surface only if the direction in which new CC bonds will be formed is oriented along the crystallographic direction of the principal axis. These outcomes indicate that the stability of DNFs is dependent on both the surface morphology and the principal axis, and mixed hybridization forms of sp2 and sp3 bonding structures can coexist in the same two-dimensional diamondbased material.
’ INTRODUCTION Carbon-based materials in nanoscale have attracted extensive interest in the past decades, especially for diamond-based nanostructures. Due to the high elastic modulus and strength-toweight ratio of diamond-based nanostructures,1 a great number of extensive studies210 have been promoted to investigate various aspects of diamond particles in nanoscale, both theoretically and experimentally. Among those studies, a special interest has been generated on the phase transition between sp3 bonding structures of diamond and sp2 bonding structures of graphene, i.e., the transformation from nanodiamonds (NDs) into graphitic carbon onions as well as the reverse process. The phase transition from NDs into carbon onions and the reverse transformation process from spherical graphitic nanostructures into nanocrystalline diamond have been modeled by means of computer simulations1116 and observed experimentally.1721 More importantly, it has been shown that the stability of the ND was found to be dependent on the surface morphology and the orientation of the dangling bonds on the ND surfaces to a large extent.22 Results of these investigations also clarified that dehydrogenated ND (111) surfaces are structurally unstable,23 with the presence of dangling bonds (DBs) on the (111) surfaces inducing phase transitions from the sp3 into the sp2 bonding structures.22 Meanwhile, a number of elegant studies have also demonstrated the similar phase transition between diamond nanowires (DNWs) and multiple-walled carbon nanotubes.2426 The stability of DNWs has been found to be dependent on both the surface morphology and the principal axis of the nanowire.24 In addition, the so-called bucky-diamonds and bucky-wires have been predicted by theoretical simulations4,7,2426 and confirmed r 2011 American Chemical Society
experimentally2,4,6,2730 as the intermediate in zero-dimensional (0-D) and one-dimensional (1-D) materials during the phase transition process. These findings strongly suggest that hybridization forms of both sp2 bonding structures of graphene and sp3 bonding structures of diamond can coexist in the same diamondbased material of 0-D and 1-D. The outcomes from the studies of lower dimensional diamond-based nanostructures inevitably lead to the question of whether a similar transformation between different hybridized bonding structures occurs in twodimensional (2-D) diamond-based materials or not. With the acknowledgment that hybrid property would facilitate the functionalization process of materials, as well as the very advent of the significant role diamond nanomaterials will play in the nanostructures and nanodevices of the future, it is important and necessary for us to gain a clear understanding of the structural properties of diamond-based materials in 2-D. Recently, carbon hybrid films comprising polycrystalline diamond and graphite nanoflake alternate layers have been fabricated in H2/CH4 gas mixtures using a high-pressure direct current plasma discharge by Lee et al.31,32 The physical and chemical 2-D attributes of the observed hybrid films with both sp2 bonding structures and sp3 bonding structures in Lee’s work may predict novel and, more importantly, innovative applications of diamond-based nanostructures, including electrode materials, functional electronic packaging materials, and catalyst supports.32 Unfortunately, the two-dimensional diamond-based materials Received: June 5, 2011 Revised: October 9, 2011 Published: October 11, 2011 22168
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Figure 1. Corresponding diamond nanowires (DNWs) and diamond nanoflakes (DNFs) generated from octahedral ND C35 as the building block. The initial structure of octahedral ND C35 is illustrated in (a), and the DNWs produced by repeating the initial structure of C35 in [100] and [110] direction as the principal axis are exhibited in (b) and (c), respectively. In addition, four DNFs built by repeating the DNW 35_[100] as well as the DNW 35_[110] are exhibited from (d) to (g), and the surfaces of the four DNFs are demonstrated from (h) to (k).
have not been studied thoroughly by theoretical simulations until now. Therefore, there is still a great deal of work to be done in exploring the phase transition as well as the coexistence of the mixed sp2 and sp3 hybridization forms in the same twodimensional diamond-based materials.
’ COMPUTATIONAL METHODS Presented here is an ab initio study of the structural properties of DNFs, generated by repeating each initial nanodiamond structure in two ordinal directions as the principal axis. All the calculations in this work have been performed with the CASTEP code,33 based on the framework of density functional theory (DFT) under the generalized gradient approximation (GGA), with the exchange-correlation functional of Perdew and Wang,34 to explore the overall stability of the periodic DNFs. In addition, ultrasoft pseudo-potentials were employed in the calculations with the plane-wave cutoff of 240 eV. Furthermore, due to the technique by which investigations in relaxation of the diamond nanowires in one dimension24,25 have been successfully performed, both the ionic positions and supercell volume have been relaxed in our calculation, to make sure that both the symmetry and the lattice parameter are free to alter, resulting in the
expansions or contractions of the entire diamond nanoflakes. In addition, an improved program based on the POAV algorithm35,36 has been developed and employed to measure the extent of hybridization in the present work.
’ RESULTS AND DISCUSSION Four different ND structures selected in our work as the building block are C35 and C84 with octahedral morphology, terminated by eight (111) surfaces, and C29 and C142 with cuboctahedral structures, terminated by eight (111) surfaces and six (100) surfaces. Such a choice of morphologies and sizes succeeds in providing all the surfaces with different indices of crystal face and different sizes of ND particles. The corresponding DNWs and DNFs produced from C35 as the building block are illustrated in Figure 1. As depicted in Figure 1, the initial structure of octahedral ND C35 is illustrated in Figure 1a, and the DNWs produced by repeating C35 in [100] and [110] direction as the principal axis are exhibited in Figure 1b and Figure 1c, respectively. In addition, four DNFs built by repeating the DNW 35_[100] as well as 35_[110] are exhibited from Figure 1d to Figure 1g, and the surfaces of these four DNFs are demonstrated from Figure 1h to 22169
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Figure 2. Structural comparison between the quasi-(100) surface of the DNF (shown in a), and the standard carbon (100) surface (illustrated in b).
Figure 3. Results of density functional theory calculations of the structural geometry optimization of the four DNFs generated from octahedral ND C35 as the building block. The initial structure of the DNF 35_[100]_[100]: quasi-(100), 35_[100]_[110]: (110), 35_[110]_[110]: (100), and 35_[110]_[111]: (111) are shown in the left side from (a) to (d), and the corresponding final geometry optimized structures are depicted in the right side from (a0 ) to (d0 ), respectively. For each DNF produced from octahedral ND C35, the initial (left) and final (right) geometry optimized configurations are shown from the vertical section.
Figure 1k, respectively. It should be accentuated that a parametrized description method is proposed to depict different DNFs
in this present work. The parameters used in the proposed description method are the number of carbon atoms in the 22170
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Figure 4. Illustration of the difference between the neighboring dangling bonds (DBs) above the 2-bonded carbon atoms on the carbon (100) surface (shown in a) and the quasi-(100) surface of the DNF (demonstrated in b). Both configurations of the structures considered are shown from the [110] direction. The green balls are employed to represent the 2-bonded carbon atoms on the surface and the red lines for the DBs above the 2-bonded carbon atoms on the surface.
building block, two principal axes during generating the DNF from the building block in turn, and the index of crystal direction of the DNF surface. Such a parametrized description method succeeds in providing a convenient approach to understand different DNFs thoroughly. As we can see from Figure 1h, the DNF surface is not the same but similar to a carbon (100) surface, so we call such a surface as quasi-(100). According to the proposed description method, the DNF illustrated in Figure 1d is denominated as DNF 35_[100]_[100]: quasi-(100). The reason we call such a DNF surface as quasi-(100) is mainly attributed to the alternating distribution of the 2-coordinated carbon atoms on the DNF surface, which differs from the close distribution manner on the carbon (100) surface. Figure 2 is employed to depict the comparison between a quasi-(100) surface and a carbon (100) surface. It is shown explicitly in Figure 2a that there is a lack of “sawtooth” upon the red, yellow, green, and purple atom pairs on the quasi-(100) surface compared to on the carbon (100) surface as expressed in Figure 2b, resulting in the DNF 35_[100]_[100]: quasi-(100) exhibiting a special crinkle shape from the [100] direction (the serrated edges demonstrated in Figure 1d). On the other hand, the DNF surfaces illustrated from Figure 1i to Figure 1k are indeed (110), (100), and (111) surfaces, respectively. Accordingly, we define these three diamond nanoflakes as DNF 35_[100]_[110]: (110), 35_[110]_[110]: (100), and 35_[110]_[111]: (111). The results of the structural geometry optimization of the four different DNFs built from C35 are illustrated in Figure 3. As for each DNF considered, the initial (left) and final (right) configurations are all exhibited from the vertical section. As indicated in Figure 3, all three DNFs are compressed to some extent after the geometry optimization, except for the DNF 35_[110]_[111]: (111). On the basis of our
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calculation results, the compression ratios of thickness are 2.94%, 6.36%, and 0.21% for the DNF 35_[100]_[100]: quasi-(100), 35_[100]_[110]: (110), and 35_[110]_[110]: (100), respectively. As has been confirmed in the previous studies, graphitization and delamination will take place on the ND (111) surface, and there will be slight structural deformations on the (110) facets as well as reconstructions on the (100) facets of NDs during the geometry optimization process, leading to a transformation from diamond nanoparticles into bucky-diamond with a diamond-like core surrounded by a fullerene-like shell.2,4,5,8,19,20,22 Similar phenomena have also been observed in diamond-based materials in diamond nanowires by Barnard et al.2426 To our surprise, the phenomena that occurred in the DNFs produced from C35 are quite different from what have been observed in the diamondbased materials of 0-D and 1-D. As illustrated in Figure 3a0 , different from the reconstruction process observed on the (100) surface of ND, the DNF 35_[100]_[100]: quasi-(100) exhibits no such process on its quasi-(100) surface. The explanation for such a distinction is proposed to be closely related with the difference between the neighboring dangling bonds (DBs) above the 2-bonded carbon atoms on the carbon (100) surface and the quasi-(100) surface, which is demonstrated in Figure 4. It has been already demonstrated that the distance and interaction between the neighboring DBs above the adjacent 2-bonded carbon atoms on the (100) surface of the ND (depicted in Figure 4a) are the smallest and strongest, respectively; consequently, the adjacent DBs may attract each other intensively, resulting in the formation of new CC bonds between the neighboring 2-bonded carbon atoms on the (100) surface. Ultimately, the reconstruction process does take place on the (100) surface of the ND.22 On the other hand, attributing to the special shape of the surface on the DNF 35_[100]_[100]: quasi-(100), the 2-bonded carbon atoms on the quasi-(100) surface exhibit an alternating distribution form (demonstrated in Figure 4b). Such an alternating distribution form of the 2-bonded carbon atoms directly leads to a dramatic increase as well as to a decrease in the distance and interaction between the neighboring DBs on the DNF surface. Due to the decrease in the interaction between the neighboring DBs above the adjacent 2-coordinated carbon atoms, the intrinsic driving force which will result in the formation of new CC bonds as well as the reconstruction will diminish dramatically and even become negligible. Eventually the reconstruction process will not occur on the quasi-(100) surface of the DNFs. In addition, Figure 3b0 depicts that slight structural deformations do take place on the (110) surface of the DNF 35_[100]_ [110]: (110), just like the phenomenon observed on the ND (110) facet. Such a structural deformation results in the distortion of the crinkle on the (110) surface as well as the increase in the 2pπ2pπ overlap, which make the whole system more stable.22 Figure 3c0 illustrates that unlike the ND cases the reconstruction process is not observed in the DNF 35_[110]_ [110]: (100) with a carbon (100) surface. As we have mentioned above, the intrinsic driving force of the reconstruction on the ND (100) surface depends on the intensive interaction between the neighboring DBs above the adjacent 2-bonded carbon atoms, and what should be emphasized here is that the “isolated” character of the ND plays an indispensable role in such a driving force. The difference between the interaction of the DBs on the (100) surface of the isolated ND and the periodical DNF is illustrated in Figure 5. In Figure 5, the green balls are employed to 22171
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Figure 5. Illustration of the (100) surface of isolated ND and periodical DNF. For each structure considered, the configurations are shown from the [110] direction. The green balls are used to represent the 2-bonded carbon atoms on the (100) surface of the isolated ND (a) and DNF (c) and the red lines for the DBs above the 2-bonded carbon atoms on the surface.
represent the 2-bonded carbon atoms on the (100) surface of isolated ND and red lines for the DBs above these 2-bonded carbon atoms. According to the intrinsic driving force of the reconstruction of the ND (100) surface, there are intensive attractions between the dangling bonds 2 and 3, 4 and 5, and 6 and 7 in the isolated ND case shown in Figure 5a. Unfortunately there is no attraction from the other DBs in the left and the right side for the dangling bond 1 and 8, respectively. As a consequence, the composition of forces parallel to the ND (100) surface upon the 2-bonded carbon atom A and D is rightward and leftward, respectively, which gives rise to the atom A moving rightward as well as D moving leftward. Eventually new CC bonds are formed between the neighboring 2-coordinated carbon atoms (i.e., between A and B as well as C and D) on the ND (100) surface. Finally, the structure in Figure 5a will transform into the one shown in Figure 5b, in company with the occurrence of the reconstruction process, while in the DNF case, although there is also an intensive attraction between the neighboring DBs above the adjacent 2-coordinated carbon atoms on the DNF (100) surface, each of the 2-bonded carbon atoms on the DNF surface is in the periodical potential field, which leads to the structure of the DNF being more like a buck diamond. As demonstrated in Figure 5c, there is also intensive attraction from other DBs in the left and the right side for the dangling bonds 1 and 8 due to the periodical structure of DNF. Hence, the composition of forces parallel to the DNF (100) surface upon each of the 2-coordinated carbon atoms is zero. As a result, all of the 2-bonded carbon atoms on the DNF (100) surface exhibit no displacement along the orientations parallel to the DNF (100) surface, and no reconstruction process is observed.
With regard to the DNF 35_[110]_[111]: (111) depicted in Figure 3d0 , the initial sp3 bonding structures of diamond transform into sp2 bonding structures of graphene after the geometry optimization; consequently, a transformation from DNF into multilayer graphene is finally observed, and the reason for such a transition is suggested to be related with the large number of DBs on the (111) surfaces of the DNF, which is similar to the ND case.22 In addition, the resulting average interplanar distance of the final geometry optimized structure obtained in our work is 4.615 Å, which is very close to the interplanar distance of AA graphite of 4.38 Å measured experimentally in the recent work.37 In addition, the band gap of these DNFs constructed from octahedral ND C35 is obtained as 0.241, 1.112, 0.864, and 0.525 eV for DNF 35_[100]_[100]: quasi-(100), 35_[100]_ [110]: (110), 35_[110]_[110]: (100), and 35_[110]_[111]: (111), respectively. Compared with the value of 4.550 eV for diamond, the band gap of these DNFs has decreased dramatically, where in such a case these DNFs can be considered as semiconductors. Similar to the C35 case, four different DNFs are also produced by repeating the initial ND structures in two ordinal directions as the principal axis, when octahedral ND C84 is considered as the building block, and the results of the structural geometry optimization of the four DNFs built from C84 are quite the same as the C35 cases. Details of the structural geometry optimization of four DNFs built from C84 are presented in the Supporting Information which can be obtained online. The DNWs and DNFs generated from cuboctahedral ND C142 as well as the results of the geometry optimization are exhibited in Figure 6 and Figure 7, respectively. An inspection of Figure 6 reveals that, by repeating the initial structure of ND C142 22172
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Figure 6. Corresponding DNWs and DNFs generated from cuboctahedral ND C142 as the building block. The initial structure of cuboctahedral ND C142 is illustrated in (a), and the DNWs produced by repeating the initial structure of C142 in the [100] and [110] direction as the principal axis are exhibited in (b) and (c), respectively. In addition, four DNFs built by repeating the DNW 142_[100] as well as the DNW 142_[110] are exhibited from (d) to (g), and the surfaces of the four DNFs are demonstrated from (h) to (k).
(shown in Figure 6a) with a principal axis in the [100] and [110] direction, DNW 142_[100] (exhibited in Figure 6b) and 142_ [110] (displayed in Figure 6c) are obtained. For each DNW considered, repetition of the initial structure of the DNW with a principal axis in different directions produced two distinct DNFs. Hence four DNFs are generated and displayed from Figure 6d to Figure 6g. According to the proposed parametrized description method, the four generated DNFs are denominated as DNF 142_[100]_[100]: (100), 142_[100]_[110]: (110), 142_[110]_ [110]: (100), and 142_[110]_[111]: (111), respectively. Additionally, the details of the final geometry-optimized DNF structures shown in Figure 7 indicate that the DNF 142_[100]_[100]: (100), 142_[100]_[110]: (110), and 142_[110]_[110]: (100) are compressed by 3.60%, 1.85%, and 0.38% in thickness after the geometry optimization process, compared with the expansion in thickness by 0.37% for 142_[110]_[111]: (111). Furthermore, it has been depicted in Figure 7a0 that the reconstruction process does take place on the surface of the DNF 142_[100]_[100]: (100), which is not observed in the DNF 35_ [100]_[100]: quasi-(100). It should be stressed here that the surface (shown in Figure 6h) of the DNF 142_[100]_[100]: (100) is indeed a carbon (100) surface, which differs from the one with octahedral ND C 35 as the building block of a
quasi-(100) surface. Hence the neighboring DBs above the adjacent 2-bond carbon atoms on the (100) surface may attract each other intensively just like the situation in the ND case, which gives rise to the formation of new CC bonds between the adjacent 2-bonded carbon atoms on the (100) surface of the DNF 142_[100]_[100]: (100). Ultimately, reconstruction is eventually observed in the DNF 142_[100]_[100]: (100). Such a reconstruction process leads directly to the existence of sp2 bonding structures on the surface of the DNF 142_[100]_ [100]: (100), which means there are both hybridization forms of sp2 and sp3 bonding structures coexisting in the DNF 142_ [100]_[100]: (100). In addition, Figure 7b0 depicts that slight structural deformations do take place in the DNF 142_[100]_ [110]: (110) with a carbon (100) surface, just like the phenomenon observed on the (110) surface of the DNF 35_[100]_[110]: (110), as well as the ND (110) facet. Similar to the DNF 35_[100]_[110]: (110) case, the reconstruction process is still not observed on the (100) surface of the DNF 142_[110]_[110]: (100) as illustrated in Figure 7c0 , and the reasons for the slight deformation in the DNF 142_[100]_[110]: (110) and the absence of reconstruction in the DNF 142_[110]_[110]: (100) are quite the same as the ones in the corresponding DNFs generated from octahedral ND C35 as the building block, which we have 22173
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Figure 7. Results of density functional theory calculations of the structural geometry optimization of the four DNFs generated from cuboctahedral ND C142 as the building block. The initial structures of the DNF 142_[100]_[100]: (100), 142_[100]_[110]: (110), 142_[110]_[110]: (100), and 142_[110]_[111]: (111) are shown in the left side from (a) to (d), and the corresponding final geometry optimized structures are depicted in the right side from (a0 ) to (d0 ), respectively. For each DNF produced from cuboctahedral ND C142, the initial (left) and final (right) geometry-optimized configurations are shown from the vertical section. In addition, the interplanar distance between the delaminated layer and the diamond matrix as well as the average bond length between different layers in the geometry optimized DNF 142_[110]_[111]: (111) are exhibited in (d0 ).
proposed above. Moreover, an inspection of Figure 7d0 reveals that the top surface layer has delaminated from the DNF 142_ [110]_[111]: (111), and part of the initial sp3 bonding structures of diamond transform into sp2 bonding structures of graphene on the bottom surface, leading to the transition from a DNF structure into a special diamond-based nanostructure with a diamond matrix covered with graphite fragments, which are connected to the matrix by 4-coordinated carbon atoms on one side and with a graphene layer on the other side. It should be stressed that the coexistence of sp2 and sp3 hybridized bonding structures exposed in our study strongly accords with the experimental observation32 since the freestanding crystalline diamond/graphite nanoflake hybrid films are indeed deposited in H2/CH4 gas mixtures with a high-pressure direct current plasma discharge. Furthermore, it was indicated from the TEM image in their work that graphite layers of the fabricated carbon hybrid films appeared to be epitaxially related to the diamond (111) planes. Such an indication also agrees with our theoretical results, due to the fact that both graphitization and delamination of the diamond (111) planes explored in our study do transform all or part of the
diamond structure into layered graphitic type materials. It is worthy to point out that the reconstructed structures revealed in the present work are not completely found to be related with the carbon hybrid films fabricated in the previous report by Lee et al.32 In other words, various reconstruction processes illustrated in our work have not been found yet in experiments. Hence, further experimental information on the reconstruction of diamond nanoflakes is expected to achieve a deep understanding of such a process. Moreover, the band gap of these DNFs built from cuboctahedral ND C142 is determined as 1.344, 1.298, and 0.881 eV for DNF 142_[100]_[100]: (100), 142_ [100]_[110]: (110), and 142_[110]_[110]: (100), respectively, indicating that these structures may also be regarded as a semiconductor. More importantly, according to our results, the DNF 142_[110]_[111]: (111) possesses the smallest band gap with the value of 0.070 eV among all DNFs, which may imply that the DNF 142_[110]_[111]: (111) behaves probably as a conductor. Additionally, it can be illustrated from the interplanar distance between the delaminated layer and the matrix, as well as the average bond length between different layers displayed in Figure 7d0 , 22174
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Figure 8. Isosurface of deformation electron density with value of 0.16 electron/Å3 (shown in (a)) and two-dimensional electronic charge density (ECD) profiles (displayed from (b) to (g)) for the geometry-optimized DNF 142_[110]_[111]: (111). The two-dimensional ECD profiles displayed from (b) to (f) are obtained in the cross section between the different layers of the DNF 142_[110]_[111]: (111) represented with the red dashed lines from 1 to 5 in (a), and the ECD profile demonstrated in (g) is obtained in the vertical section (i.e., the paper plane) of (a).
that the variation trend of the corresponding values decreases at first and then increases, and a careful examination of the geometry optimized DNF 142_[110]_[111]: (111) shows that the outer layers possess a more planar configuration than the inner layers do. Furthermore, according to our calculation results, the average values of the hybridization type spx of each carbon atom on different layers of the final geometry-optimized DNF 142_[110]_[111]: (111) are sp2.21, sp2.90, sp3.00, sp2.89, and sp2.27, from the top layer to the bottom layer, respectively.
On the basis of the results, one can easily deduce that there is a transition trend for the DNF 142_[110]_[111]: (111) to transform from the sp3 bonding structure of diamond into the sp2 bonding structure of graphene, through the way of layer by layer, which is consistent with recent observations in diamond nanoparticles both experimentally38 and theoretically.22,3941 The above analyses can be further confirmed from deformation electron density and electronic charge density (ECD) of the DNF 142_[110]_[111]: (111). Figure 8 gives the deformation 22175
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Figure 9. Illustration of the two (100) surfaces in the DNF 142_[100]_[100]: (100) and 142_[110]_[110]: (100) from the [100] direction. The short red arrowheads illustrate the orientation of the interaction between neighboring DBs, along with the long black arrowheads for the orientation in repeating the initial ND.
electron density (shown in Figure 8a) and the two-dimensional ECD profiles (illustrated from Figure 8b to Figure 8g) for the DNF 142_[110]_[111]: (111). The two-dimensional ECD profiles displayed from Figure 8b to Figure 8f are obtained in the cross section between the different layers of the DNF 142_ [110]_[111]: (111) represented with the red dashed lines from 1 to 5 in Figure 8a, and the ECD profile demonstrated in Figure 8g is obtained in the vertical section (i.e., the paper plane) of Figure 8a. Since the deformation electron density is defined as the difference between total density and those of isolated atoms, it can be employed to illustrate the interactions between different layers in the geometry-optimized DNF 142_[110]_[111]: (111) thoroughly. Figure 8a implies that the interaction between different layers in the geometry-optimized DNF 142_[110]_[111]: (111) increases at first and then drops down, which can be also confirmed from the two-dimensional ECD profiles. The interactions between different layers of the geometry-optimized DNF 142_[110]_[111]: (111) based on the deformation electron density as well as the ECD profile are consistent with the information we have already obtained through the interplanar distance between the delaminated layer and the diamond matrix, as well as the average bond length between different layers. Similar to the C142 case, four different DNFs are produced by repeating the initial ND structures in two ordinal directions as the principal axis, when cuboctahedral ND C29 is considered as
the building block, and the results of the structural geometry optimization of the four DNFs built from C29 are quite the same as the C142 cases, except the DNF 29_[110]_[111]: (111) exhibits the same transition from DNF into multilayer graphene as observed in the DNF 35_[110]_[111]: (111). The details of the structural geometry optimization of the four DNFs built from C29 are presented in the Supporting Information which can be obtained online. On the basis of the DFT results and discussion above, it is concluded that the phase transformations between different hybridized bonding structures do take place in the twodimensional DNFs during the geometry optimization process, and both hybridization forms of sp2 and sp3 bonding structures can coexist in the same two-dimensional diamond-based material. In addition, the stability of DNFs is found to be dependent on both the surface morphology and the principal axis just like the DNW cases,24 and the special nanostructure with a diamond matrix covered with graphite fragments is found to be an intermediate during the transition from sp3 into sp2 bonding structures in the two-dimensional diamond-based material. It has been mentioned that the absence of the reconstruction process in the DNFs generated from ND with any morphology along two ordinal [110] directions as the principal axis (i.e., the DNF X_[110]_[110]: (100), where X is a random value) is attributed to the periodical potential field to a great extent. Thus, a critical question comes to the front: why is the reconstruction 22176
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Figure 10. Illustration of the two different reconstructed (100) surfaces of the DNF 142_[100]_[100]: (100) (demonstrated in (a) from the [100] direction) and 29_[100]_[100]: (100) (depicted in (b) from the [100] direction), along with the zoomed in figures (demonstrated in (c) and (d), respectively) of the zones confined in the blue dashed rectangle. The 2-bonded carbon atoms on the surface before reconstruction as well as the corresponding 3-bonded carbon atoms transformed from these 2-bonded carbon atoms after the formation of new CC bonds are represented with red balls in this figure, and the green balls are employed to represent the 4-bonded inner carbon atoms in the second layer.
process observed in the DNF 142_[100]_[100]: (100) during the geometry optimization? Since both the DNFs 142_[100]_ [100]: (100) and X_[110]_[110]: (100) have (100) surfaces, then why is there such a distinction? Does it imply that the proposed reason for the absence of the reconstruction process in the X_[110]_[110]: (100) or the explanation of the reconstruction in the DNF 142_[100]_[100]: (100) is incorrect? Actually, although (100) surfaces do exist in both the DNF X_[110]_ [110]: (100) and 142_[100]_[100]: (100), there is a remarkable structural difference between the two (100) surfaces in the DNF X_[110]_[110]: (100) and 142_[100]_[100]: (100). In this present work, the DNF 142_[100]_[100]: (100) and 142_ [110]_[110]: (100) are taken for example to elucidate the inherent difference between the (100) surfaces in the two DNFs. Two different (100) surfaces in the DNF 142_[100]_[100]: (100) and 142_[110]_[110]: (100) are illustrated in Figure 9. By repeating the initial structure of ND C142 with a principal axis in the [100] and [110] direction, DNW 142_[100] and 142_[110] are obtained, respectively. For each DNW considered, repetition of the initial structure with a principal axis in the [100] and [110] direction, respectively, can produce two DNFs, i.e., the DNF 142_[100]_[100]: (100) and 142_[110]_[110]: (100). For the DNW 142_[100] considered in Figure 9a, the orientation of the interaction between neighboring DBs above the adjacent 2-bonded carbon atoms (i.e., the direction in which new CC bonds will be formed) is along the [110] direction represented with the short red arrowheads, while the orientation
in repeating the initial ND (i.e., the crystallographic direction of the principal axis) is along the [100] direction illustrated with the long black arrowheads. In other words, the direction in which new CC bonds will be formed is not the same as the crystallographic direction of the principal axis. Hence, the composition of forces parallel to the DNW (100) surface upon each of the 2-coordinated carbon atoms is not zero, which results in the reconstruction occurring on the surface of the DNW 142_[100]. Moreover, during the formation process of the DNF 142_ [100]_[100]: (100) by repeating the DNW 142_[100] with a principal axis in the [100] direction, the direction in which new CC bonds will be formed is still not the same as the crystallographic direction of the principal axis. Consequently, no reconstruction will be observed on the surface of the DNF 142_[100]_ [100]: (100) during the geometry optimization process. On the other hand, for the DNW 142_[110] considered in Figure 9b, both the direction in which new CC bonds will be formed (shown with the short red arrowheads in Figure 9b) and the crystallographic direction of the principal axis (displayed with the long black arrowheads in Figure 9b) are along the [110] direction. Hence, the composition of forces parallel to the DNW (100) surface upon each of the 2-coordinated carbon atoms is zero, which gives rise to the occurrence of the reconstruction on the surface of the DNW 142_[110]. In addition, during the formation process of the DNF 142_[110]_[110]: (100) by repeating the DNW 142_[110] with a principal axis in the [110] direction, the direction in which new CC bonds will be formed 22177
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The Journal of Physical Chemistry C is perpendicular to the crystallographic direction of the principal axis. As a consequence, reconstruction will take place on the surface of the DNF 142_[110]_[110]: (100) during the geometry optimization process. According to the results and analyses above, one can safely arrive at the conclusion that the reconstruction process will take place on the DNF (100) surface only if the direction in which new CC bonds will be formed is oriented along the crystallographic direction of the principal axis; otherwise, no reconstruction will be observed. In addition, an inspection of the final geometry-optimized DNF 142_[100]_[100]: (100) as well as 29_[100]_[100]: (100) (details of the DNFs built from cuboctahedral ND C29 as the building blocks are presented in Supporting Information) indicates that there are two different reconstructed (100) surfaces in the two DNFs, which is supposed to derive from two different types of reconstruction process. The two different reconstructed (100) surfaces of the DNF 142_[100]_[100]: (100) and 29_[100]_[100]: (100) are demonstrated in Figure 10. As depicted in Figure 10a as well as Figure 10c, the reconstructed (100) surface of the DNF 142_[100]_[100]: (100) consists of rows of buckled hexagons, which are made up of the 3-bonded carbon atoms (transformed from the 2-bonded carbon atoms on the carbon (100) surface after the reconstruction takes place) on the first layer and the 4-bonded inner carbon atoms on the second layer, and there are interspaces between the rows of buckled hexagons, leading to a ridgelike configuration of the reconstructed (100) surface of the DNF 142_[100]_[100]: (100) from the [110] direction (demonstrated on top of the inset of Figure 10). Moreover, after the reconstruction process, only the period along the direction in which new CC bonds were formed doubled, and hence there is a 2 1 surface after the reconstruction in the DNF 142_[100]_[100]: (100). Accordingly, such a reconstruction process on the (100) surface of the DNF 142_[100]_[100]: (100) is defined as a 2 1 reconstruction. On the other hand, Figure 10b in company with Figure 10d indicate that the reconstructed (100) surface of the DNF 29_ [100]_[100]: (100) is composed of 10-fold rings, which are also made up of the 3-bonded carbon atoms (transformed from the 2-bonded carbon atoms on the carbon (100) surface after the reconstruction takes place) on the first layer and the 4-bonded inner carbon atoms on the second layer. Unlike the DNF 142_ [100]_[100]: (100), the reconstructed (100) surface of the DNF 29_[100]_[100]: (100) exhibits a more planar configuration from the [110] direction (described on the bottom of the inset of Figure 10), due to the fact that no interspaces are found among the 10-fold rings. In addition, both the period along the direction in which new CC bonds were formed and its perpendicular direction doubled after the reconstruction process, and hence there is actually a 2 2 surface after the reconstruction in the DNF 29_[100]_[100]: (100). Consequently, such a reconstruction process on the (100) surface of the DNF 29_[100]_[100]: (100) is denominated as a 2 2 reconstruction.
’ CONCLUSIONS In summary, based on the results of our density functional theory calculations as well as our analyses, the reconstruction process is proposed to take place on the DNF (100) surface only if the direction in which new CC bonds will be formed is oriented along the crystallographic direction of the principal axis; otherwise, no reconstruction will be observed. In addition, similar to the phenomena observed in 0-D and 1-D diamond-based
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materials, the (110) and (111) surfaces of two-dimensional DNFs exhibit the same slight structural deformation and transition from sp3 into sp2 bonding structures. Additionally, two different reconstructed (100) surfaces are observed in the DNFs generated from the cuboctahedral ND as the building block, which is attributed to the proposed two types of reconstruction processes. These results strongly indicate that the stability of DNFs is found to be dependent on both the surface morphology and the principal axis, and phase transformations between different hybridized bonding structures do take place in two-dimensional diamond-based nanostructures. Consequently, we may safely arrive at the conclusion that both hybridization forms of sp2 and sp3 bonding structures can coexist in the same two-dimensional diamond-based materials. Unfortunately, details of two reconstruction types happened on the (100) surface of DNFs which are generated from cuboctahedral ND as the building block still remains to be well understood. Further investigation is required to supply more information and a detailed description of the two reconstruction types, to decipher the puzzles: in which situation will 2 1 and 2 2 reconstruction take place.
’ ASSOCIATED CONTENT
bS
Supporting Information. Details of the DFT results of the DNFs built from octahedral ND C84 as well as cuboctahedral ND C29 as the building block. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Telephone number: +86-29-8266-5671. Fax number: +86-298266-8559. E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was financially supported in part by the National Natural Science Foundation of China (Grant No. 21171138), the National Key Basic Research Program of China (Grant No. 2012CB720904), and the Key Project in the National Science and Technology Pillar Program of China (Grant No. 2010BAK67B12). X.Z. thanks support from the Tengfei Talent Project of Xi’an Jiaotong University. The Ministry of Education (MOE) Key Laboratory for Nonequilibrium Condensed Matter and Quantum Engineering at Xi’an Jiaotong University and the Research Center for Basic Science (XJTU) are gratefully appreciated. ’ REFERENCES (1) Shenderova, O. A.; Zhirnov, V. V.; Brenner, D. W. Crit. Rev. Solid State Mater. Sci. 2002, 27, 227–356. (2) Kuznetsov, V. L.; Chuvilin, A. L.; Butenko, Yu. V.; Mal’kov, I. Y.; Titov, V. M. Chem. Phys. Lett. 1994, 222, 343–348. (3) Winter, N. W.; Ree, F. H. J. Comput.-Aided Mater. Des. 1998, 5, 279–294. (4) Kuznetsov, V. L.; Zilberberg, I. L.; Butenko, Y. V.; Chuvilin, A. L. J. Appl. Phys. 1999, 86, 863–870. (5) Fugaciu, F.; Hermann, H.; Seifert, G. Phys. Rev. B 1999, 60, 10711–10714. (6) Tomita, S.; Sakurai, T.; Ohta, H.; Fujii, M.; Hayashi, S. J. Chem. Phys. 2001, 114, 7477–7482. (7) Barnard, A. S.; Russo, S. P.; Snook, I. K. Phys. Rev. B 2003, 68, 073406. 22178
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