Mechanical and Electronic Properties of Carbon Nitride Methanediide

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Mechanical and Electronic Properties of Carbon Nitride Methanediide Under High Pressure Sorajit Arrerut, Kenichi Takarabe, and Udomsilp Pinsook J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06594 • Publication Date (Web): 19 Jul 2017 Downloaded from http://pubs.acs.org on July 22, 2017

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The Journal of Physical Chemistry

Mechanical and Electronic Properties of Carbon Nitride Methanediide under High Pressure Sorajit Arrerut,† Kenichi Takarabe,‡ and Udomsilp Pinsook∗,† †Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand ‡Okayama University of Science, 1-1 Ridai, Okayama 700-0005, Japan E-mail: [email protected]

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Abstract We used ab initio calculation to study the mechanical and electronic properties of carbon nitride methanediide (C2 N2 (CH2 )) under high pressure. We found that the C-N and C-C bonds contract about 2% in the pressure range of 30 GPa. The bulk modulus at 0 GPa is approximately 45% of that of diamond. Its Vickers hardness is 34.9 GPa at 0 GPa. Major Raman peaks are at 1269, 1405, 3110, 3203 cm−1 corresponding to the vibration modes C-H. The calculated energy gap is 4.261 and 6.071 ev at 0 GPa, using the GGA and sX-LDA functionals, respectively. It is a wide band gap semiconductor. The GGA band gap reduces at the rate of 7.5 meV/GPa in the pressure range of 50 GPa. The mechanism of gap reduction is discussed.

Introduction In 2011, the carbon nitride methanediide, C2 N2 (CH2 ), compound was synthesized under high pressure and high temperature for the first time by Sougawa et.al. 1 They claimed that this compound could be an initial substrate for C3 N4 , a candidate of superhard materials. There have been a number of theoretical studies of this C2 N2 (CH2 ) compound using the first principle calculations. 2–4 The studies were conducted in terms of its elastic property and the contraction of the C-N single bond. The band structure calculation showed that it has a wide band gap of about 6.0 eV. Thus it can also be classified into a wide band gap semiconductor. A wide band gap semiconductor typically has a band gap larger than about 1.1 eV as of Si. It has a number interesting optical and electrical properties. For the optical property, a semiconductor with a band gap of more than 3.1 eV emits light in the range of UV 5 which has many applications, such as solar UV measurement, missile plume detection, used in bactericidal agent or vitamin syntheses. 5,6 Furthermore, wide band gap devices can operate at high temperature, whereas the maximum junction temperature limit for most Si devices is at 150 ◦ C. Diamond is a unique example of the wide band gap materials with the gap of 5.5 eV. 7 It 2


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is also the natural hardest material. This is because each C atom in diamond forms an sp3 hybridization bonding with other C atoms, resulting in a very short interatomic distance, low bond contraction and very low compressibility. The main challenge at the present time is to search for materials which have hardness close to, or even higher than that of diamond. In 1989, Liu and Cohen proposed a structure of β-C3 N4 which is similar to that of β-Si3 N4 . They found theoretically that the bulk modulus of β-C3 N4 is 427 ± 15 GPa 8 which is close to 442 GPa of diamond. After Lin and Cohen proposed this phase of C3 N4 , there were many theoretical studies 9–13 of other phases of C3 N4 and also experimental searches for this compound. 14–20 As mentioned earlier, C3 N4 and C2 N2 (CH2 ) are closely related. 1 Thus, we would like to examine the possibility that C2 N2 (CH2 ) could be a very hard material. In this paper, we focused on the mechanical and the electronic properties of the C2 N2 (CH2 ) compound. We calculated the bond contraction, the bulk modulus, the hardness, and the band structure under high pressure by using the density functional theory (DFT). We examined the band gap and the mechanism of the band gap reduction under high pressure. In addition, we reported the Raman spectrum at 0 GPa. The calculation results are compared with available experimental data.

Calculation methods We used the CASTEP code 21 which is based on the DFT with the self-consistent field (SCF) method. 22,23 We used the norm-conserving pseudopotential and the plane wave basis. For the LDA functional, we chose a functional proposed by Ceperley, Alder, Perdew and Zunger (CA-PZ). 24,25 For the GGA functional, we chose a functional proposed by Perdew, Burke and Ernzerhof (PBE). 26 We also used a non-local functional which incorporates a screening exponent into the exact exchange term, hence called screened exchange (sX). This method improves the part of the long-range correlation effect of the system. Hence, the other part of the correlation effect is short-range and can be fixed by local density approximation (LDA).

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The explicit method is the so-called sX-LDA method. 27 In this work, the k-point is set at 4×4×4 and the energy cut-off is set at 770 eV. The condition for the convergence of the SCF calculation is set to the total energy change of less than 5 × 10−7 eV/atom. The convergence condition for calculating the geometry optimization is set to the total energy change of less than 5 × 10−6 eV/atom and the atomic maximun force change of less than 0.01 eV/Å. During the optimization, the simulation cell is fully relaxed. For phonon calculations, the k-point is set to a finer mesh of 8 × 8 × 8.

Results and discussion From the experimental data, the C2 N2 (CH2 ) compound has an orthorhombic Cmc21 structure. 1 The unit cell is shown in FIG. 1a. It consists of two types of C atoms, denoted by C1 and Cb , as shown in FIG. 1b. Each C atom locates at the center of a tetrahedral. For the C1 tetrahedral, each of three corners is occupied by an N atom, and the fourth corner is occupied by a Cb atom. For the Cb tetrahedral, each of two opposite corners is occupied by an H atom, and each of other two opposite corners is occupied by another C1 atoms. Thus, the linkage between C1 and Cb forms an extensive three dimensional network structure. This exhibits also the strong characteristic of an sp3 hybridization bonding. The three N atoms which connect with C1 , denoted as N1 , N2 , and N3 , are at symmetry points at 0 GPa. Therefore, they are equivalent by symmetry. The lattice parameters and bulk modulus were calculated by using the LDA, the GGA and the sX-LDA functionals, and compared with the previous works as listed in Table 1. The results showed that the sX-LDA calculation gives the most accurate lattice constant. The errors are 4.7%, 1.6% and 0.5% for the lattice parameters a, b, and c, respectively. The LDA and GGA phonon calculation showed that this structure is dynamically stable in the pressure range between 0 and 50 GPa. The bulk modulus is calculated by fitting the E-V curve with the third-order Birch-Murnaghan equation of states. The bulk modulus is 254,

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(a)

(b)

Figure 1: (1a) Structure of C2 N2 (CH2 ) with Cmc21 space group and (1b) A section of C2 N2 (CH2 ) which shows the link between C1 and Cb . 229 and 301 GPa, from the LDA, GGA and sX-LDA calculations, respectively, compared with 258 GPa from the experiment. 1 It is worth mentioning here that the bulk modulus of the C2 N2 (CH2 ) compound is approximately 45% of that of diamond. Table 1: The lattice parameter and the bulk modus at 0 GPa, compared with theoretical 4 and experimental 1,2 works. a b c bulk modulus

Exp 1,2 7.625 4.490 4.047 258±3.4

LDA 8.029 4.584 4.090 254

GGA 8.148 4.660 4.141 229

sX-LDA 7.980 4.561 4.067 301

LDA 4 8.0168 4.5662 4.0667 263

GGA 4 8.1259 4.6381 4.1178 239

Next, we examined the contraction of the C-N and the C-C single bonds in the C2 N2 (CH2 ) compound. The changes in the interatomic distances under high pressure relative to those at 0 GPa were calculated, and also compared with those of β-C3 N4 and diamond. The results were showed in FIG. 2. The contraction of the C-N single bond under pressure is about 2% at 30 GPa, which is similar to that of β-C3 N4 (FIG.2a). The contraction of the C-C single bond is about 2% as well. However, the C-C single bond in diamond contract only 1% (FIG. 2b). It is obvious that C2 N2 (CH2 ) has higher compressibility than diamond. Furthermore, the C1 -Cb -C1 angle changes noticeably under pressure, i.e. approximately 3% at 30 GPa, where as the C-C-C angle in diamond and β-C3 N4 are barely change. We also found that the N1 -C1 -N2 and N2 -C1 -Cb angles change slightly (6 0.5%) under high pressure. These angle 5



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changes are slightly sensitive to the xc functionals.

(a)

(b)

Figure 2: The contraction ration l/l0 of (2a) the average C-N bond length in C2 N2 (CH2 ) compared with that of β-C3 N4 (2b) the C-C bond length in C2 N2 (CH2 ) , compared with that of diamond. The empirical formula for Vickers hardness calculation was first proposed by Chen, 28 and Xing-Qiu et.al. 28 have recently improved the accuracy of Chen’s model by a slight modification as HV = 2 k 2 G

0.585

− 3.

The parameter k = G/B is the Pugh′ s modulus ratio, B is bulk modulus and G is shear modulus, which are evaluated by using the Voigt-Reuss-Hill (VRH) approximation. 29 The Table.2 shows the calculated Vickers hardness of some well-known hard and superhard materials, derived from the modified Chen’s model. 30 From the GGA calculation, we found that the hardness of the C2 N2 (CH)2 compound is 34.9 GPa. As C2 N2 (CH)2 consists of the C, N and H atoms, it is possible that the Van der Waals force is active. Thus, the GGA with Grimme model was used to optimize structure and calculate the elastic constants. The calculated hardness is 34.5 GPa with the Van der Waals interaction. This is similar to the GGA hardness without the Van der Waals interaction. At this stage, we examine the electronic property of C2 N2 (CH2 ). We found that its band gap at 0 GPa are 4.146 eV, 4.261 eV and 6.071 eV from the LDA, the GGA and the sX-LDA calculations, respectively. It is a direct band gap. Under high pressure, the LDA and the 6


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Table 2: The calculated hardness values of some well-known materials using modified Chen’s model. 28 Materials Diamond 28 BC2 N 28 γ−B28 28 B6 O 28 C2 N2 (CH)2

Method

GGA 4 GGA GGA+Grimme

G (GPa) 535.5 446.0 236.0 204.0 210 209.7 213.8

B (GPa) 442.3 403.0 224.0 228.0 256 245.8 255.2

k 1.211 1.107 1.054 0.895 0.820 0.853 0.838

HV (GPa) 95.7 76.9 50 38 37.7 34.9 34.5

sX-LDA band gap decrease as pressure increases. However, the GGA band gap increases a little to the highest at 5 GPa before decreases after 5 GPa onwards. The band gap differences under pressure are shown in FIG. 3. We also examined the partial density of states (PDOS) in FIG.4. We found that the C-N band width is the widest and extend into deep energy, i.e. -25 eV below Fermi level. The C-C band width, as shown in FIG.4a, is also wide but does not extend as deep into lower energy as the C-N band in FIG.4b. Both C-C and C-N band contribute significantly to the valence band maximum (VBM) at 0 GPa. The C-H band width is relatively narrow and contributes a little to the VBM,as shown in FIG.4c. Under high pressure, these bondings contract only a little as discussed earlier. In terms of the energy bands, they response to pressure by shifting their energy up, but at different rates. We found that the C-N band shifts up with a larger rate than that of the C-C band. This is because C-C-C angle is found to be relaxing a little under high pressure. Consequently, the shifting rate of the VBM is dominated by the shifting rate of the C-N band, whereas the smaller shifting rate of the C-C band manifest itself in the smaller shifting rate of the conduction band minimum (CBM). The C-H band also dominates the CBM and also have a dE 31 small shifting rate. The shifting rate is defined as ap = . We have reported the shifting dp rate of the VBM and the CBM in Table 3. According to the different shifting rates in the VBM and the CBM, the band gap tends to shrink under pressure. We estimated the average reduction of the band gap at the rate of 7.5 meV/GPa in the GGA scheme. Finally, we calculated the first-order differential Raman cross section 32 to identify the 7



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Figure 3: The band gap difference at various pressure. The band gap at 0 GPa is set as a reference. Table 3: The incremental rate of the VBM and the CBM. aVBM p aCBM p

LDA (meV/GPa) 50.2 36.6

GGA (meV/GPa) 49.8 42.3

Raman spectra. The calculation also gives the eigenvectors, so that we can analyze the vibration of each atom in each vibration mode. The GGA Raman peaks at 0 GPa is shown in FIG.5. The LDA result also has a similar trend. We also gave some numerical values and the corresponding modes in Table.4. The major peaks appear at 1269, 1405, 3110, and 3203 cm−1 corresponding to distinctive vibration modes of the C-H bonds. The star marks in the FIG.5 refer to some available experimental data 33 of the same bond with a similar mode of vibration, but in a different compound. The numerical values are also shown in Table.4. Of course, this comparison is not exact, but they are a reasonable guide. We hope that our result would urge experimentalists to perform exact measurement.

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total Cs Cp Cb s Cb p

total Cs Cp Ns Np

B

10

B

10

5

5

0

0 -25

-20

-15

-10

-5

0

5

10

-25

-15

-10

E

(a)

(b)

total Cb s Cb p Hs

total Cs Cp Ns Np

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-5

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Cb s Cb p Hs

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5

5

0

0 -25

-20

-15

-10

-5

0

5

10

-25

-20

-15

-10

E

E

(c)

(d)

Figure 4: The partial density of state (PDOS) of C2 N2 (CH2 ) at 0 GPa. (4a) C1 -N (4b) C1 -Cb (4c) Cb -H (4d) all PDOS. Table 4: The Raman peaks from our calculation, compared with some available data 33–35 Lable 1 2 3 4

Wavenumber (cm−1 ) 1269 1405 3110 3203

Ref ⋆ ⋆ ⋆ ⋆

Bond C-H2 C-H2 C-H2 C-H2

Mode Twist Wag s-stretch a-stretch

Wavenumber (cm−1 ) 1278 33 1338 33 3008 33 3087 33

Conclusions In conclusion, we have studied the mechanical and electronic properties of (C2 N2 (CH2 )) under high pressure. We found that the C-N and C-C bonds are very strong as they contract only about 2% in the pressure range of 30 GPa. As a result, the bulk modulus at 0 GPa is quite large, i.e. approximately 45% of that of diamond. Its Vickers hardness is 34.9 GPa 9



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intensity 0.025

0.0050 1

2 3 4

0.020 0.0025

0.015 0.0000 500

0.010

1000

1500 -1

wavelength (cm )

0.005

1

2

0.000 1000

2000

3000 -1

wavelength (cm )

Figure 5: Raman spectrum of the relaxed structure at 0 GPa using GGA. The inset shows peaks between 0-1700 cm−1 at 0 GPa. The calculated energy gap is 4.261 and 6.071 ev at 0 GPa, using the GGA and sX-LDA functionals, respectively. It is also a wide band gap semiconductor. The GGA band gap reduces at the rate of 7.5 meV/GPa in the pressure range of 50 GPa. We also calculated the first-order differential Raman cross section. We found that major Raman peaks are at 1269, 1405, 3110, 3203 cm−1 corresponding to the vibration modes C-H bond. The Raman spectrum should be a good guide to expermental measurement in the future.

Acknowledgement We gratefully acknowledge the computing facilities from Chulalongkorn University Centenary Academic Development Project (CU56-FW10), and the Ratchadaphiseksomphot Endowment Fund of Chulalongkorn University (RES560530180-AM), and financial support from the Special Task Force for Activating Research (GSTAR 56-003-23-002), and 90th Year 10


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Chulalongkorn Scholarship from Graduate School, Chulalongkorn University.

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(31) Wei, S. H.; Zunger, A. Predicted band-gap pressure coefficients of all diamond and zinc-blende semiconductors: Chemical trends. Phys. Rev. B 1999, 60, 5404–5411. (32) Porezag, D.; Pederson, M. R. Infrared intensities and Raman-scattering activities within density-functional theory. Phys. Rev. B 1996, 54, 7830. (33) Shimanouchi, T.; Pederson, M. R. Tables of Molecular Vibrational Frequencies. Nat. Stand. Ref. Data. Ser., Nat. Bur. Stand (U.S.) 1972, 39 . (34) Yap, Y. K.; Kida, S.; Aoyama, T.; Mori, Y.; Sasaki, T. Influence of negative dc bias voltage on structural transformation of carbon nitride at 600 C. Appl. Phys. Lett. 1998, 73, 915. (35) Ferrari, A.; Rodil, S.; Robertson, J. Resonant Raman spectra of amorphous carbon nitrides: the G peak dispersion. Diam. Relat. Mater. 2003, 12, 905–910.

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1 0

B

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45


5

0 -2 5

-2 0

-1 5

-1 0

E

-5


0

5

1 0


to ta l C s C p N s N p

1 0

C b s C b p H s

B

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Page 24 of 25

5

0 -2 5

-2 0

-1 5

-1 0

E

-5


0

5

1 0

Page 25 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45


in te n s ity 0 .0 2 5

0 .0 0 5 0 1

2 3 4

0 .0 2 0 0 .0 0 2 5

0 .0 1 5

0 .0 1 0

0 .0 0 0 0 5 0 0

1 0 0 0 w a v e le n g th ( c m

0 .0 0 5

1

1 5 0 0 -1

)

2

0 .0 0 0 1 0 0 0

2 0 0 0

3 0 0 0


w a v e le n g th ( c m

-1

)

Mechanical and Electronic Properties of Carbon Nitride Methanediide

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