A periodic density functional theory study on the

A periodic density functional theory study on the effects of halides encapsulated in SiC nanotubes S.-P. Huang, W.-D. Cheng, J.-M. Hu, Z. Xie, H. Hu, and H. Zhang Citation: The Journal of Chemical Physics 129, 174108 (2008); doi: 10.1063/1.3006425 View online: http://dx.doi.org/10.1063/1.3006425 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/129/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hydrogen intercalation of single and multiple layer graphene synthesized on Si-terminated SiC(0001) surface J. Appl. Phys. 116, 083502 (2014); 10.1063/1.4893750 A density functional theory study of epitaxial graphene on the ( 3 × 3 )-reconstructed C-face of SiC Appl. Phys. Lett. 102, 093101 (2013); 10.1063/1.4794176 Size- and surface-dependent electronic structures of crystalline SiC nanotubes J. Appl. Phys. 109, 084318 (2011); 10.1063/1.3567114 Adsorption of transition-metal atoms on boron nitride nanotube: A density-functional study J. Chem. Phys. 125, 044711 (2006); 10.1063/1.2218841 Density-functional theory calculations of X H 3 -decorated SiC nanotubes ( X = { C , Si } ) : Structures, energetics, and electronic structures J. Appl. Phys. 97, 104311 (2005); 10.1063/1.1891281

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THE JOURNAL OF CHEMICAL PHYSICS 129, 174108 共2008兲

A periodic density functional theory study on the effects of halides encapsulated in SiC nanotubes S.-P. Huang, W.-D. Cheng,a兲 J.-M. Hu, Z. Xie, H. Hu, and H. Zhang State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, The Chinese Academy of Sciences, Fuzhou 350002, People’s Republic of China

共Received 21 August 2008; accepted 29 September 2008; published online 6 November 2008兲 In this paper we present results of density functional theory calculations on the configurations, band structures, and optical properties of halides MCl 共M = K , Ag兲 intercalated single-wall SiC nanotubes. The results show that the M–Cl distances perpendicular to the tube axis are slightly smaller than the ones parallel to the tube axis, which could be due to the axial strain of MCl. The electronic and optical properties of the resulting MCl@SiCNT composite are modified with respect to both the bulk halide and the empty nanotube. It is shown that AgCl affects the structures and properties of SiC nanotubes more significantly than KCl, and that the interaction between the nanotube and the encapsulated halide is stronger for narrower SiC nanotube. The AgCl encapsulation into SiCNTs results in band gap narrowing of AgCl@SiCNTs. © 2008 American Institute of Physics. 关DOI: 10.1063/1.3006425兴 I. INTRODUCTION 1

Since the discovery of carbon nanotubes 共CNTs兲 in 1991, filling the inner single-wall carbon nanotube 共SWCNT兲 cavity with various compounds has attracted considerable interests. Metals,2–6 nonmetals,7 halides,8–10 oxides,11,12 carbides,13 nitrides,14 and endohedral 15–17 fullerenes have been encapsulated into CNTs. Actually, one of the main interests of filling SWCNTs is to enforce the filling materials to adopt a one-dimensional morphology. Another possible application would be to use SWCNTs as containers for nanosized catalysts with delayed action. In addition, introducing foreign materials into SWCNT cavity may significantly modify the physical and chemical properties of SWCNT. For example, the potassium encapsulation into SWCNTs causes band gap narrowing,2 and the electronic properties of double-walled carbon nanotubes 共DWCNTs兲 filled with ferrocene molecules are greatly modified due to the charge transfer between ferrocene molecules and DWCNTs.18 The properties of the filled CNTs are now being studied extensively. Vavro et al. reported measurements of electrical resistivity, thermopower, and thermal conductivity of highly C60-filled SWCNTs, from 1.5 to 300 K.19 The magnetic and hysteretic properties of Fe-filled CNTs have been examined by Prados et al.,20 and catalytic properties of metalnanocluster-filled CNTs and their possible applications in electrochemical energy storage have been studied by Che et al.21 Garcia-Vidal et al. analyzed the optical properties of arrays of CNTs filled with silver from a theoretical point of view.22 The effect of KI encapsulation in narrow 共HiPCO兲 SWCNTs has been studied via Raman spectroscopy and optical absorption.23 Besides filling CNTs, there was work done about filling BN nanotubes. The filling of BN nanotubes with a兲

Author to whom correspondence should be addressed. Electronic mail: [email protected].

0021-9606/2008/129共17兲/174108/6/$23.00

one-dimensional crystals, including carbides, nitrides, oxides, fullerenes, and potassium halide, have already been demonstrated.24–30 However, no theoretical or experimental work has been reported about the structure and properties of filling SiC nanotubes 共SiCNTs兲 until now. What modifications will occur in the SiCNTs after encapsulation of materials? The properties of SiCNTs are different from those of the covalently bonded, homopolar CNTs. Previous studies31,32 have shown that SiCNTs are always semiconducting while CNTs have been found to be either metallic or semiconducting depending on their helicity. SiCNTs are expected to have advantages over CNTs because they may possess high reactivity of exterior surface, facilitating sidewall decoration and stability at high temperature. Halides form the most comprehensive series of currently characterized filling materials for singe-walled carbon and BN nanotubes. Accordingly, it is possible that the halides filled SiCNTs will be synthesized. In this work, we will employ periodic density functional theory to investigate the effects of KCl and AgCl encapsulated in SiCNTs. We will look into whether the halide encapsulation into SiCNT controls the gap width of semiconducting SiCNTs, and how is the influence of the space structural changes on optical properties for halides@SiCNT composites. II. THEORETICAL METHOD AND COMPUTATIONAL DETAILS

Based on the van der Waals interaction between the filling and nanotube,23,33 the optimum and threshold diameters34 of SiCNTs are calculated in order to accommodate 2 ⫻ 2 KCl and 2 ⫻ 2 AgCl. Here, 2 ⫻ 2 means a 2 ⫻ 2 bulk unit cell cluster in the nanotube cavity. The optimum and threshold diameters of SiCNTs to accommodate 2 ⫻ 2 KCl are 12.26 and 11.06 Å, respectively, and those of SiCNTs to accommodate 2 ⫻ 2 AgCl are 11.74 and 10.54 Å, respectively. Thus,

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we select the 共7,7兲 and 共8,8兲 SiCNTs to accommodate 2 ⫻ 2 KCl. The 共8,8兲 SiCNT with diameter of 13.383 Å can accommodate 2 ⫻ 2 KCl more easily than 共7,7兲 SiCNT with diameter of 11.847 Å. It is reported that the filling is not sensitive to the type of nanotubes, either armchair or zigzag tubules can be chosen.23 So 2 ⫻ 2 AgCl can be encapsulated in both 共7,7兲 SiCNT and 共12,0兲 SiCNT. However, the smallest unit cell of 2 ⫻ 2 AgCl@共7 , 7兲SiCNT contains so many atoms that it is beyond the capability of our present computations by first principles. Therefore, the 2 ⫻ 2 KCl@共7 , 7兲SiCNT, 2 ⫻ 2 KCl@共8 , 8兲SiCNT, and 2 ⫻ 2 AgCl@共12, 0兲SiCNT have been built by the optimizations of first-principles method 共ab initio method兲. The ab initio calculations of halides@SiCNTs use the total-energy code CASTEP,35,36 which employs pseudopotentials to describe electron-ion interactions and represents electronic wave functions using a plane-wave basis set. The coordinates of all atoms in the halides@SiCNTs in our calculations were optimized without any symmetry constraint using Broyden–Fletcher–Goldfarb–Shanno37 scheme, ultrasoft pseudopotentials,38,39 and the Perdew–Burke– Ernzerhof generalized gradient approximation,40 though all calculations published so far do not include nanotube relaxation. The length of c axis of the SiC nanotube was fixed in the optimization. Because the calculations of optical properties by using ultrasoft pseudopotentials are less accurate than those by using norm-conserving pseudopotential41 in CASTEP calculations, we use norm-conserving pseudopotentials in total energy, band structure, density of states, and optical property calculations. We have used approximately 10 Å vacuum in the lateral directions to avoid artificial tube-tube interaction. This should be a sufficient distance since the basis functions do not overlap. The selected unit is periodic in the direction of the tube axis 共z axis兲. Considering the balance of the computational cost and precision, we choose a cutoff energy of 470 eV and a 1 ⫻ 1 ⫻ 4 Monkhorst–Pack k-point set for 2 ⫻ 2 AgCl@共12, 0兲SiCNT, a 1 ⫻ 1 ⫻ 3 Monkhorst– Pack k-point set for 2 ⫻ 2 KCl@共7 , 7兲SiCNT, and 2 ⫻ 2 KCl@共8 , 8兲SiCNT. The imaginary part ␧2共␻兲 of dielectric function ␧共␻兲 can be thought of as detailing the real transitions between occupied and unoccupied electronic states, and it is given by the following equation: ␧ij2 共␻兲 =

picv共k兲pivc共k兲 8 ␲ 2ប 2e 2 ␦关Ecv共k兲 − ប␻兴, 共f − f 兲兺兺 c v m2Veff k cv E2vc 共1兲

where Ecv共k兲 = Ec共k兲 − Ev共k兲. Here, f c and f v represent the Fermi distribution functions of the conduction and valence band. The term picv共k兲 denotes the momentum matrix element of transition from the energy level c of the conduction band to the level v of the valence band at the kth point in the BZ, and Veff is the effective unit cell volume. The effective unit cell volume is given by Veff = ␲共D / 2 + d / 2兲2T, where D is the diameter of the nanotube, and d is the thickness of the SiCNT cylinder which is set to the interlayer distance of h-SiC 共4.5 Å兲.

FIG. 1. 共Color online兲 The optimized units of 共a兲 2 ⫻ 2 KCl@共7 , 7兲 SiCNT, 共b兲 2 ⫻ 2 KCl@共8 , 8兲 SiCNT, and 共c兲 2 ⫻ 2 AgCl@共12, 0兲 SiCNT.

The real part ␧1共␻兲 of the dielectric function ␧共␻兲 follows from the Kramer–Kronig relationship. All the other optical constants may be derived from ␧1共␻兲 and ␧2共␻兲.42,43 For example, the loss function L共␻兲 can be calculated using the following expressions:

冋册

L共␻兲 = Im

−1 . ␧共␻兲

共2兲

The loss function L共␻兲 is an important optical parameter describing the energy loss of a fast electron traversing in the material. The peaks represent the characteristic associated with the plasma oscillation and the corresponding frequencies are the so-called plasma frequencies.44 It is noted here that the orbital plots given below are calculated by the DMOL3 module based on the optimized geometrical structures from CASTEP code. For the calculations using DMOL3, we have used generalized gradient approximation functional in the manner suggested by Perdew–Burke– Ernzerhof, and double numerical plus d-functions basis set. III. RESULTS AND DISCUSSION A. Structure

The optimized cells of 2 ⫻ 2 KCl@共7 , 7兲SiCNT, 2 ⫻ 2 KCl@共8 , 8兲SiCNT, and 2 ⫻ 2 AgCl@共12, 0兲SiCNT are illustrated in Fig. 1. The calculated results show that the bond angle of K–Cl–K or Cl–K–Cl is about 176.1° along the tube axis in 共7,7兲 SiCNT, and about 177.3° along the tube axis in 共8,8兲 SiCNT. The bond angle of Ag–Cl–Ag or Cl–Ag–Cl is about 165.3° along the tube axis. The Ag atoms move inward while the Cl atoms exhibit a small expansion in 2 ⫻ 2 AgCl@共12, 0兲SiCNT. It shows that the bond angles of Cl–K–Cl only have a small change after KCl encapsulated into SiCNTs, and that the bond angles of Cl–Ag–Cl have a large change after AgCl encapsulated into SiCNTs 共Cl– M – Cl= 180° in free bulks兲. It can also be seen from Fig. 1 that the encapsulation influences more remarkably on the geometry of AgCl than that of KCl. Table I shows the values of a, b, and R, where, a is the average M–Cl 共M = K , Ag兲 distance perpendicular to the tube axis, b is the average M–Cl distance parallel to the tube axis, and R


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TABLE I. Values of a, b, and R. a is the average M–Cl 共M = K , Ag兲 distance perpendicular to the tube axis, and b is the average M–Cl distance parallel to the tube axis. The extent of the distortions of halides in SiCNTs is given by the ratio R = a / b, and R is unity for the cubic bulk crystal.

2 ⫻ 2 KCl@共7,7兲SiCNT 2 ⫻ 2 KCl@共8,8兲SiCNT 2 ⫻ 2 AgCl@共12,0兲SiCNT

a共Å兲

b共Å兲

R=a/b

3.078 3.080 2.692

3.119 3.120 2.722

0.9869 0.9872 0.9890

= a / b describes the extent of the distortions of halides in SiCNTs. The R values for the three nanocomposites are slightly smaller than unity, which is unity for the cubic bulk halides crystal. This indicates that both KCl and AgCl are stretched along the tube axis. The difference between the average M–Cl bond lengths parallel and perpendicular to the tube axis could be due to the axial strain of MCl. The extent of the distortions of halides in SiCNTs is smaller than that of potassium halides in BN nanotubes30 and that of 2 ⫻ 2 KI in 共10,10兲CNT.45,46 Accordingly, it is possible that the SiCNTs are used as a good container in one-dimensional crystal growth. The average lengths 共Å兲 of C–Si bonds, the charges 共e兲 of C and Si atoms, and the diameters D 共Å兲 of SiCNTs and MCl@SiCNTs are tabulated in Table II. The halide encapsulations only cause small changes in the geometrical structures of the SiCNTs. For instance, the average lengths of C–Si bonds have a little bit of increase for 2 ⫻ 2 KCl@共7 , 7兲SiCNT and 2 ⫻ 2 AgCl@共12, 0兲SiCNT, but have a little bit of decrease for 2 ⫻ 2 KCl@共8 , 8兲SiCNT. There is a slight decrease in the absolute values of the charges of C and Si atoms after the filling of halides, which indicates that the chemical bonding strength between C and Si atoms decrease a little. The changes in the absolute values of the charges of Si are larger than those of C atoms, which indicate that there are charge transfer interactions between the SiCNTs and the encapsulated halides. B. Electronic structure

The band gaps of SiCNTs and MCl@SiCNTs are given in Table II. The calculated gaps of unfilled 共8,8兲 and 共12,0兲

FIG. 2. 共Color online兲 The band structure of 共a兲共12,0兲 SiCNT and 共b兲 2 ⫻ 2 AgCl@共12, 0兲 SiCNT and density of states of 共c兲共12,0兲 SiCNT and 共d兲 2 ⫻ 2 AgCl@共12, 0兲 SiCNT.

SiCNTs are 2.26 and 1.84 eV, respectively, which are close to the results 共2.32 and 1.89 eV, respectively兲 of Wu and Guo using the full-potential projector augmented wave method.47 However, they are smaller than the calculated gaps of Baumeier et al.,48 who employed self-interactioncorrected pseudopotentials. From Table II, we can see that after filling KCl the gaps of SiCNTs keep nearly constant, however, the gap of 共12, 0兲SiCNT decreases after filling AgCl. The influence of the filling of AgCl on the properties of SiCNT can be demonstrated by the band structure and density of states in Fig. 2, and explained by the highest occupied orbital and the lowest unoccupied orbital at G point using DMOL3 code in Fig. 3. It is found from Fig. 2 that the filling has little influence on the density of states of C and Si atoms. The highest occupied band below Fermi level originates from the p states of C and Si atoms, and the lowest unoccupied band of the SiCNT filling AgCl is contribution from the Ag-5s states. This can also be seen from the orbital plots given in Fig. 3. So it is mainly the interaction between the Ag-5s states and the unoccupied C- or Si-p states that leads to the energy decrease

TABLE II. The average lengths 共Å兲 of C–Si bonds, the charges 共e兲 of C and Si atoms, the diameters D 共Å兲, gaps 共eV兲, and zero frequency dielectric constants of SiCNTs and MCl@ SiCNTs. ␧z共0兲 and ␧x共0兲 are zero frequency dielectric constants with electric fields parallel and perpendicular to the tube axis, respectively. dC–Si

Charge of Si

Charge of C

D

Gap

␧x共0兲

␧z共0兲

共7,7兲

1.7907

1.43–1.44

−1.44to−1.43

11.847

3.5674

5.4086

KCl@共7,7兲共8,8兲

1.7910 1.7881

1.32–1.37 1.43–1.45

−1.42to−1.40 −1.45to−1.43

11.857 13.383

3.7995 3.3779 6.91b

5.5047 5.0370 10.19b

KCl@共8,8兲共12,0兲

1.7865 1.7895

1.38–1.42 1.43–1.45

−1.44to−1.43 −1.45to−1.43

13.409 11.648

AgCl@共12,0兲

1.7911

1.39–1.41

−1.42to−1.41

11.757

2.256 3.63a 2.244 2.261 2.32b 3.65a 2.260 1.841 1.89b 1.594

3.4956 3.5039 6.76b 3.8462

5.1531 5.7146 10.58b 6.1291

a

Reference 41. Reference 47.

b


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FIG. 3. 共Color online兲共a兲 Top view of the highest occupied orbital, 共b兲 top view of the lowest unoccupied orbital, and 共c兲 the side view of the lowest unoccupied orbital at G point of 2 ⫻ 2 AgCl@共12, 0兲 SiCNT.

of the lowest unoccupied band 共i.e., energy gap decreases between the occupied and unoccupied bands兲 of SiCNT after filling AgCl. The fillings of KCl do not contribute to the states close to the band edges 共the band structure and density of states not shown here兲, so their gaps remain nearly unchanged. Accordingly, the AgCl of encapsulation will result in the band gap narrowing of semiconducting SiCNTs, and it is expected that SiCNTs could act effectively as chemically and electrically inert protecting layers and enhance the stability of KCl crystals in harsh chemical, thermal, and electrical/optical environments. C. Optical properties

Table II also gives ␧z共0兲 and ␧x共0兲 of SiCNTs and MCl@SiCNTs, which are the zero frequency dielectric constants with electric fields parallel and perpendicular to the tube axis, respectively. Our calculated zero frequency dielectric constants of unfilled SiCNTs deviate significantly from those of Wu and Guo,47 while the trends 关␧z共0兲 ⬎ ␧x共0兲兴 are the same as theirs. The deviation is due to the different method used and the effective unit cell volume defined differently. The effective unit cell volume of Wu and Guo was given by ⍀ = ␲关共D / 2 + d / 2兲2 − 共D / 2 − d / 2兲2兴T = ␲DdT, which subtracted the cavity volume. But the effective unit cell volume of ours is defined including the cavity volume. The interlayer spaceings d of SiCNTs were reported ranging from 3.5 to 4.5 Å.49 We set the thickness d of the SiCNT cylinder to 4.5 Å, while they set it to be 3.51 Å. As shown in Table II, the filling of halides results in changes in the zero frequency dielectric constants. The zero

frequency dielectric constants increase after filling halides in SiCNTs, and the filling of AgCl affects the optical properties of SiCNTs more significantly than the filling of KCl. The photonics effect of the filling of halides on the SiCNTs is also depicted from the spectra in Figs. 4 and 5. Figure 4 gives the dispersion of dielectric function of the 共12,0兲 SiCNT and 2 ⫻ 2 AgCl@共12, 0兲SiCNT for different light polarizations. Figure 5 shows the dispersion of dielectric function of the 共7,7兲 SiCNT, 共8,8兲 SiCNT, 2 ⫻ 2 KCl@共7 , 7兲SiCNT, and 2 ⫻ 2 KCl@共8 , 8兲SiCNT for different light polarizations. For all studied species, there are quantum confinement effects along the perpendicular direction while the effects do not exit along the parallel direction. The onset of the absorption of ␧2储共␻兲 occurs always at lower energies than the onset of ␧2⬜共␻兲 and it is usually sharper for ␧2储共␻兲 than for ␧2⬜共␻兲. The filling of halides leads to redshift of the peaks of ␧共␻兲, which is in accord with the electronic results. That is, the interactions between the encapsulated halides and SiC nanotubes result in the decrease of band gap and redshift of dielectric function peaks. At low energy region 共0 – 5 eV兲, the filling of halides almost does not affect the value of the imaginary parts of dielectric function. The filling leads to more changes on the value and shift of dielectric function for light polarization perpendicular to the tube axis than for light polarization parallel to the tube axis. This indicates that the filling enhances the quantum confinement. From Fig. 5, it can be found that for a given halide KCl, the filling affects more significantly on the optical spectra of 共7,7兲 SiCNT than on those of 共8,8兲 SiCNT, because the interaction between the nanotube and the encapsulated KCl is stronger for narrower 共7,7兲 SiCNT. IV. CONCLUSION

We studied modifications of geometries, electronic structures, and optical properties occurring in halides encapsulated single-walled SiCNTs by ab initio calculations. The results show that the geometrical structures of encapsulated MCl crystals have a large change with respect to free bulk crystals, while those of SiCNTs keep almost constant in the MCl@SiCNTs composite. The band structure near the Fermi level alters largely upon the AgCl intercalation, while the one

FIG. 4. 共Color online兲 The dielectric function for the direction 共a兲 perpendicular and 共b兲 parallel to the 共12,0兲 SiCNT and 2 ⫻ 2 AgCl@共12, 0兲 SiCNT.


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FIG. 5. 共Color online兲 The dielectric function for the direction 共a兲 perpendicular and 共b兲 parallel to the 共7,7兲 SiCNT and 2 ⫻ 2 KCl@共7 , 7兲 SiCNT and the dielectric function for the direction 共c兲 perpendicular and 共d兲 parallel to the 共8,8兲 SiCNT and 2 ⫻ 2 KCl@共8 , 8兲 SiCNT.

near the Fermi level remains almost unchanged after the KCl filling. It is shown that AgCl affects the structures and properties of SiC nanotubes more significantly than KCl and that the interaction between the nanotube and the encapsulated halide is stronger for narrower SiC nanotube. These findings tell us that the AgCl of encapsulation will result in the band gap narrowing of semiconducting SiCNTs and that SiCNTs would act effectively as chemically and electrically inert protecting layers and enhance the stability of KCl crystals in harsh chemical, thermal, and electrical/optical environments.

ACKNOWLEDGMENTS

This investigation was based on work supported by the National Natural Science Foundation of China under Project No. 20773131, the National Basic Research Program of China 共No. 2007CB815307兲 and the Funds of Chinese Academy of Sciences 共KJCX2-YW-H01兲, and Fujian Key Laboratory of Nanomaterials 共No. 2006L2005兲.

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