Toward Free-Standing Lonsdaleite and Diamond Few Layers: The

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C: Physical Processes in Nanomaterials and Nanostructures

Towards Free Standing Lonsdaleite and Diamond Few Layers: The Nitrogen Effect Prashant Vijay Gaikwad J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b09429 • Publication Date (Web): 10 Dec 2018 Downloaded from http://pubs.acs.org on December 12, 2018

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The Journal of Physical Chemistry

Towards Free Standing Lonsdaleite and Diamond Few Layers: The Nitrogen Effect Prashant Vijay Gaikwad∗ Department of Physics and Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune-411007, India E-mail: [email protected],[email protected]

Abstract Strong, directional, N bonding led surface stabilization is induced to obtain free standing two dimensional layered assemblies of Lonsdaleite and diamond phase carbon by surface termination at 3 coordinated C sites. These assemblies have strong bonding and surface N lone pair induced self protection and achieves respective bulk-like electronic, mechanical and crystallographic properties at as low as 7 atomic layer thickness. Lonsdaleite phase sub-nano thickness free standing as small as 3 layered assembly shows bulk-like thermal stability up to 2900K. Size confinement effect dominates up to four layered assembly and then electronic and crystallographic properties are dominated by bulk stabilization which saturates towards respective bulk-like features from 7 layer assembly. Similarly, free standing hybrid assemblies of Lonsdaleite phase carbon with BeF (C5 NBeF) and BS (C5 NBS) layer are also proposed along with low symmetric Cm-C3 N4 layered assembly. The combination of N and O is shown to stabilize surface of nanodiamond but shows significant variation in structural and electronic properties, which are principally govern by confinement effect because of weak surface stabilization. Our results proposes that, in principle, two dimensional free standing layered ∗

To whom correspondence should be addressed

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assemblies of the sp3 hybridized phases of carbon with surface terminated by only 3 coordinated C sites, can be stabilized and engineered by substitutional doping of N, and in some cases respective bulk-like electronic and crystallographic properties at nano size can be achieved.

Introduction Diamond is of immense interest since many decades due to supreme properties and their applications in the emerging technologies ranging biomedical, energy harvesting, high power electronics and optoelectronics, extreme mechanical strength applications, etc. 1–3 Naturally, diamond and Lonsdaleite phases of carbon forms at high temperature and pressure conditions such as meteoroids impact, while they can be artificially synthesized in the lab using shock conversion of graphite. 4 With technological advent controlled synthesis by various techniques have led to cheap and radially available diamond in various nano-forms for diverse applications in mechanical, optomechanical and nanophotonics components. 5–7 Synthesis of high temperature and pressure Lonsdaleite phase is still challenging. Considerable efforts have been vested for synthesis of confined systems of diamond since last few decades, especially in the form of few layered films. Nanoscale bottom up approach using graphene by chemical junction of layers is a promising technique to synthesis diamond 2D assemblies along with most common hot filament chemical vapor deposition. Thus formed assemblies of confined systems are usually focused on surface stabilization by H, F, Cl and O/ O-radicals termination. 5,8–18 Stabilization of diamond surface using halides, H and O are suffer with various difficulties which limits their scope to achieve bulk-like properties at nano level. For example, stabilization by H generates negative electron affinity (NEA) which reduces band gap. 13,19 The O terminated surface is predicted to be quite reactive and optically active, 20,21 also it is expected to create a lot of defects and facets which could lead to amorphization of surface. 13 Flourination along with mixed phase of C-F and C-OH termination may stabilize defects through surface roughness. 22,23 In addition to that, O or F atoms are 2


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often provided by aggressive acids which limits the efficiency in maintaining desired surface morphology. Contrary to this, recently N terminated diamond surface is reported to yield positive electron affinity as 3.23 eV. 13 Experimentally surface stabilization of diamond films by N is recently realized and shows relatively negligible unwanted spins. 18 However, these experimental studies inherited with substrate interaction which restricts parametrization and underlying science of the free standing layered assemblies and their applications. In the confinement regime, few nanometer sized diamond nanocrystals have opened up scope in the quantum electronic devices based on Coloumb blockade and quantum size effects. 24 There are discrepancies about observation of bulk-like properties in nanodiamonds (ND), some reports ND grains as large as 27 nm to show while other claims as small as 4 nm assemblies not showing confinement effects. 25–30 Experimentally confinement effects in ND are reported to occur within 1 - 4 nm range and also supported by theoretical reports. 24,31 Interestingly, ND are reported to show size independent lower band gap than bulk on account of negative electron affinity. 28,31 The strong sp3 hybridized led crystal structure of diamond and Lonsdaleite phase carbon governs properties such as high mechanical, thermal stability and large band gap. The sp3 hybridized carbon films have drawn considerable efforts due to their magnetic, electronic and elastic properties. 9,32–34 During synthesis, the 2D allotropes of carbon are dominated by energetically most favored sp2 hybridized covalent bonds, which diminishes the band gap and hence limits their applications in semiconducting, optical devices. Not many 2D carbon allotropes are known to possess band gap and very few of them are experimentally synthesized. Recent, theoretically proposed 2D pentagonal carbon (penta-graphene) is reported to show 3.25 eV band gap (by HSE06 functional). 35 However, due to supreme mechanical and thermal properties, already mature field, 2D films of diamond remains optimistic candidates for high band gap next generation applications similar to high power electronics. Doping of lighter B or N can easily vary band gap in 2D films of diamond. 5 N doping in carbon materials is favored on account of inherent higher Pauling electronegativity than carbon

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and comparable ionic radii. Graphene-like 2D allotropes of CN shows strong sp2 hybridized bonding. Carbon nitride in bulk form (α-, β-, Cm-C3 N4 ) also shows highly directional very strong sp3 bonding which leads to immense structural stability. 36,37 Hence the diamond-like 2D assemblies of C and N remains promising candidates for next generation applications. To that endeavor, in the present work N is used to generate free standing few layered assemblies of carbon to engineer bulk-like thermal, mechanical and electronic properties at sub nano-level.

Computational methodology DFT based spin polarized electronic structure calculations 38,39 are performed using accurate plane augmented wave (PAW) method 40 as implemented in Vienna ab-initio simulation package (VASP). 41–44 The Perdew, Burke and Ernzerhof (PBE) exchange-correlation energy functional within GGA 45,46 is employed. The plane wave basis cutoff, total energy and forces on single atom convergence are used of value 400 eV, 10−4 eV and 0.02 (eV/˚ A) respectively. The 20 ˚ A vacuum is maintained along z-direction and 11×11×1 ~k-mesh generated by Monkhorst-Pack scheme is used for unit cell and then scaled appropriately. The stability of layered systems is characterized by comparing respective cohesive energies (Ec ). Ec of a given system is calculated using; Ec = n× EC + m× EN - ECn

Nm ,

where the

term ECn Nm refers to the energy of the CN system with n and m are the numbers of C and N atoms respectively. EC and EN are the respective energies of isolated single C and N ) is calculated by Eatom = atoms. The cohesive energy per atom (Eatom c c

Ec . n+m

To compare

the energetic stability of the systems (with reference to bulk), the total energy per carbon atom of only carbon layer (EC c ) is calculated by per atom energy difference of total energy of CN bilayer and the free standing layered assembly. The dynamical stability of layered assemblies are investigated by performing phonon calculations within the framework of density functional perturbation theory as implemented

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in VASP and using interface of PHONOPY code. 47 A 3×3×1 supercell of three layer (3L) assembly (two CN layers at top and bottom with single C layers in between totaling of 36 C and 18 N atoms) is used. The thermal stability is investigated by performing canonical ensemble ab-initio molecular dynamics calculations at constant temperature using Nos´ e-Hoover thermostat as implemented in VASP. A simulation is performed at single k point using 4×4×1 supercell of smallest assembly of free standing 3L Lonsdaleite phase, containing 96 (64 C and 32 N) atoms, in steps of 1 fs simulated at 2900K for 10 ps. Thus obtained final structure was significantly distorted, however the basic skeleton of the structure remains same. On ionic relaxation, this structure quickly regains ground state initial structure. Mechanical stability is investigated by finite distortion method based on correlating elastic modulus tensor to second order partial derivative of strain energy with respect to strain. 35 The unitcell is subjected to uniaxial and biaxial strain and elastic constants are extracted from fitting quadratic curves of variation in the strain energy with applied strain. Calculated elastic parameters C11 , C66 , Young’s modulus and Poisson’s ratio (v) for penta-graphene are 265, 200, 239 GPa nm and -0.04 respectively which are in good agreement with previously reported results. 35 In present case, elastic constants in bulk units are expressed by dividing layer thickness of free standing layered assemblies. 48

Results and discussion The surface of diamond and Lonsdaleite slabs built along (111) direction have half number of three coordinated surface C atoms. These surface atoms can undergo energetically more favored sp2 hybridization, leading to instability at the surface of sp3 hybridized carbon material. Hence few layered free standing structures of high pressure phases of carbon (sp3 hybridized) at low temperature and pressure gets transforms in to graphitic phases of carbon. Experimentally for layered assemblies, the bottom surface usually stabilized by

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(a)

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Figure 1: (Color online) Free standing four layered (4L) 3×3×1 supercell of Lonsdaleite ((a) and (c)) and diamond phase ((b) and (d)) carbon having surface 3-coordinated C atoms substituted by N atoms at top and bottom layers. The yellow and green balls represent carbon and nitrogen atoms respectively. introducing surface of the substrate on which such assemblies can be grown. In the present case surface stabilization of free standing layered assemblies is achieved by substituting N at 3-coordinated C atom sites. Because of requirement of strong directional bonding, 3coordinated sites at surface is the only possibility for general use. For better visualization of structure, free standing four layered (4L) 3×3×1 supercell assembly of Lonsdaleite and diamond phase carbon terminated with N at top and bottom layers are shown in Fig. 1 (a) and (b). Figure 1 (c) and (d) shows respective side view of Lonsdaleite slab and diamond slab (a-b-c arrangement) respectively. Hence, such 4L assembly will have only two carbon layers sandwiched between top and bottom CN layers. Multilayers formed of free standing 3L assembly slab have shown similar energetic and structural parameters. Strong in-plane bonding and surface lone pair of N establishes self protection and stability of the assemblies, once formed. The details can be found in sup-

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porting information. It is not appropriate to compare the structural energies and electronic structural properties of the calculations performed with and without incorporation of van-der Waals forces. Hence, for consistency purpose, electronic structure and energetics comparison of assemblies are performed without consideration of van-der Waals forces. 50

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Figure 2: Phonon dispersion profile of free standing 3L and 4L assembly of N terminated (a) Lonsdaleite and (b) diamond phase carbon respectively. Figure 2 shows the phonon band structure of free standing 3L and 4L assembly of (a) Lonsdaleite and (b) diamond, respectively. The absence of negative frequencies and remarkable similarities of phonon dispersion curves for respective 3L and 4L layered assemblies establishes dynamical stability and similar dynamical properties irrespective of size of layer as well as type of phase. Calculated bulk electronic and phonon structure of pristine Lonsdaleite and diamond phase are are in agreement with previously reported results. 49 Owing to the high structural strength, as small as 3L assembly of Lonsdaleite phase carbon shows thermal stability upto 2900K, details of which can be found in supporting information.

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and non surface Table 1: Variation in stability (estimated by cohesive energy per atom Eatom c C per C atom Ec ) with increasing number of C layers of N terminated Lonsdaleite and diamond phase free standing layered assemblies. Eg , a and t are the respective band gap, lattice parameter and thickness of layered assembly. Lattice parameter for diamond is defined in √ terms of Lonsdaleite phase ( 2 × a) for comparison of bond lengths.

System

C (CN)L2 (CN)L3 (CN)L4 (CN)L7 (CN)L12 (CN)L16

Lonsdaleite Without VdW forces With VdW forces atom C atom a t EC t Ec Ec Eg a Ec c (eV) (eV) (eV) (˚ A) (˚ A) (eV) (eV) (˚ A) (˚ A) 7.83 7.83 3.28 2.50 6.19 - 4.48 2.40 2.59 6.31 - 2.41 2.61 6.71 7.74 3.92 2.43 4.70 6.89 8.04 2.44 4.74 6.98 7.76 4.00 2.45 6.79 7.19 8.06 2.46 6.84 7.33 7.79 3.89 2.47 13.06 7.58 8.09 2.48 13.13 7.54 7.81 3.53 2.48 23.51 7.80 8.10 2.50 23.62 7.61 7.81 3.43 2.50 31.87 7.88 8.11 2.51 32.01

Diamond Without VdW forces atom Eg a t EC Ec c (eV) (eV) (eV) (˚ A) (˚ A) 7.85 7.85 4.11 2.52 6.19 - 4.45 2.41 2.58 6.71 7.76 3.90 2.45 4.65 6.99 7.78 3.77 2.46 6.73 7.35 7.81 3.83 2.49 12.90 7.56 7.83 3.87 2.49 14.97 7.63 7.84 3.87 2.51 31.46

Mechanical properties of 2D assemblies/structures are investigated by finite distortion method within small applied uniaxial and biaxial strain limit (±5%) at equilibrium. 48 The calculated values of C11 and C66 for free standing 4L Lonsdaleite phase assembly are 1511.8 GPa and 776.8 GPa respectively and establishes mechanical stability by the virtue of Born-Huang criteria. 50 Young’s modulus is calculated by (C211 - C212 )/C11 and is of value 1510.6 GPa, establishing significantly larger elastic parameters than bulk diamond. 51 The calculated Poisson’s ratio (C12 /C11 ) is -0.028 and is in agreement with experimentally realized range. 52 The negative value is due to contraction in layer thickness (along z-direction) on application of in-plane strain (along xy-direction). For comparison purpose, similar calculations are also performed for H terminated 4L free standing Lonsdaleite assembly. The respective calculated values of C11 , C66 , Young’s modulus and v are 1474.6, 775.3, 1470.7 GPa and -0.052. This suggests comparatively lower Young’s modulus of H terminated than N terminated respective free standing 4L assembly. On similar grounds, the mechanical property of 7L free standing diamond layered assembly is also investigated. The calculated values of C11 , C66 , Young’s modulus and v are 1301.8, 675.0, 1300.0 GPa and -0.037 respectively. It suggests slightly 8


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higher values of C11 , Young’s modulus and v than previously reported bulk (diamond) values along (111) direction 51 but the trend suggests achieving bulk-like mechanical properties with increasing thickness of free standing assembly. Interestingly, large variation in mechanical properties are observed with layer thickness and phases, the absence of accurate experimental results for free standing diamond and Lonsdaleite assemblies limits present studies but opens scope for further theoretical investigation. However, present interest of establishing bulk-like mechanical stability remains fulfilled. To understand the crystallographic and electronic structural changes with increasing thickness, the number of C layers is varied to obtain 2L (2.58 ˚ A thickness) to 16L (32 ˚ A is found to increase with thickness) free standing assemblies. As shown in Table 1, the Eatom c is mainly due to increase of C thickness from 6.19 eV to 7.61 eV. This variation in Eatom c layers, since cohesive energy per C layers is larger than CN layer. This can be clearly seen by EC c per atom, which varies slightly from 7.74 to 7.81 eV and is expected to saturate to 7.83 eV per atom as for Lonsdaleite bulk-phase. From 7L till 16L the EC c is barely increased from 7.79 eV till 7.81 eV per atom. This suggests that after 7L the free standing Lonsdaleite phase layered assemblies show bulk-like energetic stability. This is also evident from the lattice parameter which saturates to 2.50 ˚ A. On the application of van-der Waals forces, and EC the respective values of Eatom c per atom are found to increase significantly, however c the trend of variation remains consistent. By structural and stability parameters it is clear that as low as 7L assembly (13.06 ˚ A thickness) the bulk-like energetic stability appears. One the similar grounds, the 4 layer free standing assembly stabilized by H shows NEA lead reduced band gap, while stabilized by F shows direct band gap and results in majorly altered electronic landscape than diamond (refer supporting information). The electronic properties of Lonsdaleite free standing assemblies are studied by probing variation in band structure calculated along hexagonal plane with thickness and are incorporated as shown in Fig. 3. For comparison purpose the band structure of (a) Lonsdaleite bulk-phase and (b) supercell of bulk-phase 4L Lonsdaleite assemblies along the (111) di-

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rection are also incorporated. On N termination, top and deep valance band states are principally contributed by N p states and s states respectively and the hybridized sp3 states of C are pushed to lower energy. These N dominated surface states nearest to Fermi energy maintains the position, while deep level states are pushed to higher energy with increasing the thickness of the structures. The top valance bands near Fermi energy, arising by N states can be even visually distinguish at K and M points by comparing with respective

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Figure 3: Band structure of (a) bulk, (b) 4L supercell of bulk and (c) through (h) N terminated free standing 2L to 16L Lonsdaleite phase assemblies respectively. The respective Fermi energy is shifted to 0 eV for all plots. 10


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Figure 4: (Color online) Site projected l-DOS plots for N terminated Lonsdaleite free standing 2L to 16L assemblies ((b), (c), (d), (f), (g) and (h)) along with (a) bulk Lonsdaleite and (e) single CN layer respectively. The respective Fermi energy is shifted to 0 eV for all plots. tom of the graph around 22 eV. Similar observations are known for N terminated diamond surface grown at (1 0 0) direction. 18 For and above 7L layer assembly the deep level N dominated states and overall valence band width and structure remains constant and with the exception of N derived states, overall band structure landscape shows bulk-like similarities. 11



From the variation of conduction band with size it is clear that, till 4L assembly the minimum of conduction band is at M point while for 7L and beyond it is at K point, similar to bulk Lonsdaleite. The band gap of such assemblies are slightly higher than pristine bulk Lonsdaleite on account of confinement effect at smaller sizes. However, overall electronic structure landscape of such free standing assemblies resembles bulk-like nature even at small as 4L. On comparing Fig. 3 (b) and (e), the similar features can be noticed for bulk and free standing N capped Lonsdaleite assemblies, but the more bulk-like features are visible from 7L layered assembly. Figure 4 depicts the variation in site projected partial density of states (l-DOS) with thickness of free standing assemblies. The graphs supports the respective band structure conclusions. The profile of l-DOS shows discrete nature of states up to 4L suggesting effect of size confinement. It is more eminent by the visual comparison of l-DOS plot of single planar hexagonal-CN structure (Fig. 4 (e)). After 7L the s states of C dominates at Fermi and bulk-like profile starts to appear. Hence by cohesive energy (Table 1), band structure (Fig. 3) and l-DOS profile (Fig. 4) it clear that up to 7L (∼13 ˚ A) thickness the confinement effect dominates while after that the bulk-like electronic properties of layered assemblies starts to appear. It is to be noted that with consideration of van-der Waals forces the variation in the energy and structural landscape remains similar. In the similar manner, diamond N terminated free standing assemblies from 2L to 16L are investigated. Table 1 enlists the variation of stability and structural parameters with thickness of the layered assemblies. Similar trend to Lonsdaleite phase is observed. Figure 5 shows the variation of band structure of N terminated 2L to 16L thickness free standing diamond assemblies. For the comparison purpose, band structure of (a) bulk-phase diamond and (b) 7L supercell of bulk-phase diamond along (111) direction are shown in Fig. 5 (a) and (b) respectively. Similar to Lonsdaleite phase, bands near Fermi energy and deep level valance bands are dominated by p and s states of N. The band decomposed partial charge density plots of bands near to Fermi for 4L Lonsdaleite and diamond phase assemblies can be found in supporting information. Also, these bands can be visually distinguish by

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comparing with respective bulk-phase band structure (Fig. 5 (b)). It can be clearly observed that after 7L assembly not only features but also quantitative nature of bands resembles to bulk as suggested by Fig. 5 (b) and (f). However, it is to be noted that the value of band gap is small but significantly lower than bulk value and with increase in layers the band gap slightly increases, opposite to that of Lonsdaleite phase. At this point it is unclear at which thickness the band gap of free standing assemblies will be exactly respective bulk-like but

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Figure 5: Band structure of (a) bulk phase diamond, (b) 7L bulk phase diamond supercell and (c) through (i) N terminated free standing 2L to 16L assemblies respectively. The respective Fermi energy is shifted to 0 eV for all plots. 13



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Figure 6: (Color online) Site projected l-DOS plots for N terminated free standing diamond 2L to 16L assemblies ((b) through (h)) and (a) bulk diamond. The respective Fermi energy is shifted to 0 eV for all plots. to be not significant. Contradictory to Lonsdaleite phase, even as small as 2L assembly of diamond phase shows conduction band minimum at bulk-like M point and it remains consistent with increasing size. The position and features of bands of 8L, 12L and 16L are very similar. This again suggest that the free standing layered assembly of such diamond 14


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films as low as 4L (6.7˚ A) to 7L (12.9˚ A ) thickness shows bulk-like properties. The l-DOS profile variation of diamond phase free standing layered assemblies up to 16L is depicted by Fig. 6 (b) through (h). For comparison purpose l-DOS of bulk diamond (Fig. 6 (a)) is also incorporated. The graphs supports the band structure conclusions and similar conclusions to Lonsdaleite free standing layered assemblies are observed. From the electronic structure variation of free standing layered assemblies with size it is clear that, there is interplay of dominating two forces, namely confinement effect and bulk stabilization. Despite the differences in the crystallographic structures, the band gap of both the phases are comparable for 2L and 3L layered assemblies due to domination of confinement effect. After 4L, the bulk stabilization starts to dominate and further increase in thickness of the free standing assemblies direct the band gap towards achieving respective bulk-like features. This fact is evident by the opposite trend of variation in band gap of both the assemblies as shown in Table 1. The band gap of bulk Lonsdaleite is 3.28 eV. After 4L of respective free standing layered assembly, the band gap starts to decrease from 4 eV towards bulk value along with similar features with increasing assembly thickness. Whereas, the variation in diamond free standing layered assemblies is opposite. The band gap of diamond layered assemblies increases from 3.77 eV for 4L with thickness towards corresponding bulk value. Moreover, for both the free standing layered assemblies, the conduction band minimum is at M point till 4L but after 7L the clear shift of Lonsdaleite phase to respective bulk-like K point and plateau feature of bands at M point for diamond phase suggests dominance of bulk-stabilization over confinement effect. Also, if the N dominated states are ignored then the striking quantitative electronic structure similarities (reflected by l-DOS and band structures) between both the layered assemblies after 7L with respective bulk structures can be observed. In addition to crystallographic and electronic structure evidence, the bulk-like thermal and mechanical stability of Lonsdaleite layered assembly reflects the effectiveness and authority of N terminated stabilization of free standing assemblies over known other mechanisms to achieve bulk-like properties.

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Further, diamond films can grown along (220), (311) etc. by CVD method. 53 Similar preliminary studies are performed on free standing diamond layered assemblies grown along (220) directions. The (220) direction grown 2L and 4L N terminated assemblies with two N shows up to 2 eV direct band gap. The 4L assembly surface terminated with single N (single three coordinated C atom per unit cell out of two) shows semi-metallic behavior along with spin resolved band gap and hence presents the scope for spintronics applications. The states of surface three co-ordinated C and two coordinated N appears in the forbidden region 8 4 1

0 Energy (eV)

Density of states (arb. unit)

2

0

-1

-10

-8

C-s C-p

(a)

-4 -8 -12 -16

-2 -12

-6 N-s N-p

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(b)

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Γ

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-6 N-s N-p

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Energy (eV) Be-s Be-p

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F-p

K

Γ

(g)

(f)

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(e)

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(j)

-8

-6 C-p

-4

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0

Energy (eV) N-s

(k)

2

4 N-p

6

8

-8 A

Γ

M1

A

M

Γ

(l)

Figure 7: Free standing four layer (4L) CN assembly containing top layer with BS ((a) and (b)), BeF ((e) and (f)), while (i) and (j) are the top and side view of Cm-C16 N14 structure with surface stabilized by doping of 2 C atoms substitutionally and 2 C atom interstitially, respectively. For better visualization purpose 2×2×1 supercell is shown of Cm-C16 N14 structure while 3×3×1 supercells are shown for other two hybrid assemblies. lDOS and band structures are plotted in the graphs (c) and (d) C5 NBS, (g) and (h) C5 NBeF and (k) and (l) Cm-C3 N4 (C16 N14 ) assemblies respectively. The blue, magenta, yellow, green, silver and black balls represent Be, B, C, N, F and S atoms respectively.

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and are responsible for underline properties. Owing to such dangling states, such assemblies shows soft phonons and hence could not full-fill robust dynamical stability criterion hence excluded from present work and will be reported separately. However, such assemblies grown on surface may yield dynamical stability. ), band gap (Eg ), lattice parameters (a and b) Table 2: The cohesive energy per atom (Eatom c and thickness (t) of free standing hybrid layered assemblies. System BS-(CN)L3 BeF-(CN)L3 (Cm-C3 N4 )L4 (C16 N14 )

Eatom c (eV) 6.47 6.52 6.19

Eg a b t (eV) (˚ A) (˚ A) (˚ A) 1.52 2.60 2.60 7.24 1.39 2.50 2.50 7.25 2.40 4.87 4.22 6.72

N termination is also used to stabilize the free standing layered hybrid assemblies. Figure 7 shows the N terminated 4L Lonsdaleite phase CN hybrid assemblies containing top layer of BS (Fig. 7 (a) and (b)) and BeF (Fig. 7 (e) and (f)) respectively. Phonon dispersion curves of the respective structures proposes dynamical stability as incorporated in support, Eg and structural properties of free standing layered ing information. Table 2 lists Eatom c assemblies. As reflected by Table 2, both the assemblies possess comparatively similar energetical stability (reflected by Eatom ). Figure 7 (c) and (g) shows l-DOS and (d) and (h) c shows band structure plots for both the assemblies. As expected, the higher electronegative F terminated C5 NBeF assembly shows more confinement effect and higher stability compared to S terminated C5 NBS assembly. The p states of top layer mostly governs the conduction band in both cases and decreases the forbidden region to 1.5 eV range. However, C5 NBeF is a direct while C5 NBS is a indirect band gap hybrid assembly. After theoretical prediction of β-C3 N4 , harder than diamond, 36,54 large efforts have been invested for its experimental synthesis and other forms of superhard CN. Owing to proposed superiority of N to stabilize the free standing assemblies, we have undertaken structurally more asymmetric and complicated, harder than diamond Cm-C3 N4 37 to stabilized in the

17



form of free standing layered nano-assembly. Figure 7 (i) and (j) shows the 4L Cm-C3 N4 (i.e. C16 N14 ) free standing assembly stabilized by inverting the top surface species i. e. carbon atoms are placed at N sites in order to have tetragonal coordination while N atoms are placed appropriately at the surface so as to accommodate three coordinated sites. This leads to surface reconstructed with two dimers of sp2 hybridized C atoms per unit cell as shown in Fig. 7 (i) and (j). It is to be noted that such reconstruction is at only surface layers and the non-terminal layers of the assembly possesses Cm-C3 N4 structure. Figure 7 (k) and (l) depicts the l-DOS and band structure of free standing C16 N14 layered assembly. It is argued that the sp3 hybridized C atoms and nearby N atoms spatially separates the pz states of sp2 hybridized C atoms and hinders the full electron delocalization leading to 2.40 eV band gap. Lower band gap than respective bulk value 3.74 eV 37 is majorly due to the p-states of C atoms appearing in the forbidden region on account of surface reconstruction as shown Fig.7 (l). The p states of N dominates the Fermi level with small contribution of p states of C. This partially degenerate high DOS valence bands near the Fermi level presents the possibility of Bardeen-Cooper-Schrieffer superconductivity through hole doping. 55 Further, to exploit the possibility of surface stabilization by N and O, a 120 atom (∼9.5 ˚ A diameter) chunk of (111) direction grown nanodiamond (ND) is capped with N and O as shown in Fig. 8 (a). The structure is obtained by removing singly bonded C atoms and obtaining maximum number of 3 coordinated C atoms at the surface. Two and three coordination sites are replaced with O and N atoms respectively. The vibrational frequencies are calculated using VASP by finite difference method at Γ point with ± 0.02 step size. Absence of negative vibrational frequencies suggests the stability of the structure (Fig. 8 (b)). Although the structural skeleton remains similar, the average bond length of ND is shorten to ∼1.5 ˚ A. The states near Fermi energy are principally from p states of O and N and reduces the band gap up to 2 eV. The p states of N bonded with N are the next higher energy states at conduction band after O 2p states and dominantly contributes in valence band. The contraction of bond lengths and larger variation in electronic structure properties

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(a) C54N42O24 10

DOS (arb. units)

2

Arb. unit

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1

0

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200 400 600 800 1000 1200 1400 -1

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-4

Frequency (cm )

C-s C-p

-2 0 Energy (E-Ef) N-s N-p

(b)

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4

6

O-s O-p

(c)

Figure 8: Local ground state (a) geometry, (b) vibrational spectrum and (c) l-DOS profile of 120 atom (111) direction grown nanodiamond. clearly depicts dominance of confinement effect rather than bulk-stabilization. Forbidden region is expected to maintain ∼2 eV band gap on account of quantum confinement effect irrespective of choice of passivator. 28 Variation in the band gap is possible by varying surface N and O atom composition at the expense of structural stability. It is to be noted that, such mixed passivation may not yield higher dynamical stability at elevated temperature due to large variation in the bonding strengths. The use of combination of N and O for surface stabilization of ND is not expected to hold at elevated temperature due to energetically more favored N-O bonding. Hence, although we predict the possibility but experimental realization of N and O caped ND certainly demands further research efforts. Experimentally N terminated (111) phase diamond can be synthesized by homo-epitaxial 19



lateral growth in microwave plasma chemical vapor deposition (MPCVD) under the suitable plasma conditions. Similarly, chemical synthesis methods can be useful for the possible experimental synthesis of free standing nano-regime layered assemblies of diamond, Lonsdaleite and in principle other sp3 bonded phases of carbon. Furthermore, electronic properties of such layered assemblies can be engineered by doping (B, O, N, transition metals etc.) and or defects and such avenues remained to be unexplored for future applications.

Conclusions In conclusion, nano thickness, nitrogen capped highly stable free standing layered assemblies of Lonsdaleite and diamond phase carbon grown along (111) direction are proposed. These non-magnetic assemblies are terminated by N at 3 coordinated surface C sites and owing to high strength bonding along with loan pairs of surface terminating N provides high structural stability and self assembled protection. For few layers (up to 4L) the size confinement and then bulk stabilization effect dominates. The interplay of confinement effect and bulk stabilization governs the electronic properties and there is a shift of paradigm with variation in assembly thickness. Lonsdaleite phase assembly of as small as 3L shows thermal stability up to 2900K, which is comparable to the respective bulk value. The contribution of p and s states of N and C dominates valence band and conduction band respectively. The bulk-like relative contribution of p and s states of C at valence band and conduction band starts to dominate even for as small as 4L layered free standing assembly. Owing to strong bulkstabilization, these layered free standing assemblies shows unusually similar electronic and crystallographic structural and thermo-mechanical properties after 7L (∼13 ˚ A thickness) and maintains 3.5 to 4 eV band gap and 2.5 ˚ A lattice parameter similar to respective bulk values. Bulk-like properties are govern in the respective layered assemblies due to remarkable surface stabilization assisted dominating bulk stabilization over confinement effect. On the similar platform, hybrid multilayered 4L assemblies of surface layer of BeF

20


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(C5 NBeF) and BS (C5 NBS) are proposed to be stable. C5 NBeF shows 1.39 eV direct band gap while the C5 NBS free standing layered hybrid assembly shows 1.52 eV indirect band gap. Owing to high stabilization using N, the free standing 4L assembly of highly asymmetric Cm-C3 N4 , namely C16 N14 , is also proposed to be stable and found to show 2.40 eV direct band gap. Using combination of N and O termination, the surface of ∼9.5 ˚ A diameter nanodiamond is stabilized. O 2p states and p state of N-N bonded N appears within forbidden region and reduces HOMO-LUMO gap along with shortening of bond lengths due to size confinement effect. On the similar footing, 3 coordinated N termination led stabilization is in principle, can be engineered for free standing layered assemblies of sp3 hybridized other phases of carbon. The optoelectronic, thermal and mechanical properties of such nano assemblies can be easily tuned by doping and defects at will and that further remains unexplored.

Supporting Information Available Additional results in support of the findings of this work can be found in supporting information. It consists of stability analysis of multilayered assemblies of Lonsdaleite phase 4L assembly, thermal stability analysis of 4L Lonsdaleite phase assembly, band decomposed partial charge density plots of bands near Fermi of 4L Lonsdaleite and diamond assemblies, electronic structure of H and F passivated 4L Lonsdaleite phase assemblies and phonon dispersion curves of Cm - C16 N14 , C5 NBS and C5 NBeF layered assemblies.

This material is

available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement Author would like to acknowledge DST Nanomission Council, Government of India (DST/NM/NS15/2011(G)), for financial support through a major research project. Prof. Anjali Kshirsagar for constant guidance and Dr. Ranjit Hawaldar, Prof. V. P. Godbole, Prof. S. V. Ghaisas and Prof. Uedono Akira for brainstorming fruitful discussions on diamond and diamond-like 21



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carbon and constant encouragements.

Author information Prashant Vijay Gaikwad: (ORCID 0000-0002-0446-9426) E-mail: [email protected]; [email protected]

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Toward Free-Standing Lonsdaleite and Diamond Few Layers: The

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