Study on the electronic structure and the optical performance of YB6 by the first-principles calculationsLihua Xiao, Yuchang Su, Hongyang Chen, Min Jiang, Sainan Liu, Zexing Hu, Ruifeng Liu, Ping Peng, YuanlongMu, and Diya Zhu Citation: AIP Advances 1, 022140 (2011); doi: 10.1063/1.3602854 View online: http://dx.doi.org/10.1063/1.3602854 View Table of Contents: http://scitation.aip.org/content/aip/journal/adva/1/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in First-principles study of structural, electronic, vibrational, dielectric and elastic properties of tetragonal Ba2YTaO6 J. Appl. Phys. 116, 144104 (2014); 10.1063/1.4897452 First-principles study of the structural, electronic, and optical properties of Y-doped SrSi2 J. Appl. Phys. 113, 043515 (2013); 10.1063/1.4788715 First-principles study of electronic structure and magnetic properties of Cu-doped CeO2 J. Appl. Phys. 112, 083702 (2012); 10.1063/1.4759359 Electronic structure, vibrational spectrum, and thermal properties of yttrium nitride: A first-principles study J. Appl. Phys. 109, 073720 (2011); 10.1063/1.3561499 Structural stability and electronic properties of SiC nanocones: First-principles calculations and symmetryconsiderations Appl. Phys. Lett. 98, 123102 (2011); 10.1063/1.3567535

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AIP ADVANCES 1, 022140 (2011)

Study on the electronic structure and the opticalperformance of YB6 by the first-principles calculations

Lihua Xiao,1 Yuchang Su,1,a Hongyang Chen,1 Min Jiang,1 Sainan Liu,1

Zexing Hu,1 Ruifeng Liu,1 Ping Peng,2 Yuanlong Mu,1 and Diya Zhu1

1School of Materials Science and Engineering, Central South University, Changsha, Hunan410083, China;2School of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082,China

(Received 10 February 2011; accepted 19 May 2011; published online 13 June 2011)

The electronic structure and the optical performance of YB6 were investigated byfirst-principles calculations within the framework of density functional theory. It wasfound that the calculated results are in agreement with the relevant experimentaldata. Our theoretical studies showed that YB6 is a promising solar radiation shieldingmaterial for windows. Copyright 2011 Author(s). This article is distributed under aCreative Commons Attribution 3.0 Unported License. [doi:10.1063/1.3602854]

Recently lanthanum hexaboride (LaB6), a novel near infrared (NIR) absorbing filter for so-lar radiation, has received tremendous attention. LaB6 was studied thoroughly by theoretical1 andexperimental2–4 methods. It appears that yttrium hexaboride (YB6), belonging to a series of ex-tremely hard, refractory, and stable rare-earth hexaborides,5 is also to be applied as solar radiationshielding material for windows, because it resembles LaB6 in many physical properties, such as theenergy band structure6 and the reflectivity spectra.7, 8 To our knowledge, a lot of researchers haveextensively studied YB6, focusing their attention on its super-conductivity,9–12 thermoelectricity,13

and optical performance.7, 8 However, there have been no detailed theoretical studies concerning theelectronic structure and the optical performance of YB6 up to now, though Kimura et al.7, 8 once mea-sured the reflectivity spectra of YB6 at 300 K and 9 K in a wide range from 1 meV to 40 eV throughsynchrotron radiation (SR), and they obtained the principal optical conductivity spectra and theloss-function spectra through the Kramers–Kronig relation. Thus, we are inspired to study the elec-tronic structure and the optical performance of YB6 resorting to first-principles calculations in thispaper.

The first-principles calculations were performed within the framework of density func-tional theory14, 15 incorporating the plane-wave ultrasoft pseudopotential scheme.16 The exchange-correlation effect was treated with the so-called generalized gradient approximation (GGA) pro-posed by Perdew, Burke, and Ernzerh.17 A plane-wave cutoff energy of 380 eV was adopted. TheMonkhorst–Pack scheme18 was adopted to sample the Brillouin zone. 20×20×20 and 20×20×20 k-point grids were then generated for the electronic structure calculations and the optical performancecalculations of YB6, respectively.

The optical performance of YB6 can be gained by the frequency-dependent dielectric function,

ε (ω) = ε1 (ω) + iε2 (ω) (1)

which arises mainly from the electronic structure. The imaginary part ε2(ω), being the fundamentalfactor of the optical performance of materials, can be obtained through calculating the momentummatrix elements between the occupied and unoccupied electronic states. The other optical constants,such as refractive index, n(ω), extinction coefficient, k(ω), optical conductivity, σ (ω), reflectivity,

aE-mail: ychsu@mail.csu.edu.cn

2158-3226/2011/1(2)/022140/7 C© Author(s) 20111, 022140-1

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022140-2 Xiao et al. AIP Advances 1, 022140 (2011)

TABLE I. Calculated and experimental lattice parameters of YB6

Cal.a Expt.b

a0 (Å) 4.0456 4.1002

aThis work.bReference 20.

FIG. 1. Energy band structure of YB6.

R(ω), absorption coefficient, α(ω), and energy-loss spectrum L(ω) will be deduced from ε1(ω) andε2(ω).19

At ambient pressure, YB6 adopts a CsCl-type with space group Pm3m (No. 221) structure,where yttrium atoms occupy the 1a (0, 0, 0) Wyckoff sites while boron atoms occupy the 6f (0.5,0.5, z) Wyckoff sites with z being an internal parameter. The X-ray diffraction determined structuraldata of YB6 were used as the initial input for geometry optimization. The lattice parameters werecalculated and then fitted to the third order Birch–Murnaghan equation. The calculated equilibriumlattice parameter (a0), together with the corresponding experimental data, is listed in Table I. It canbe seen that the calculated result is in good agreement with the experimental data.

The energy band structure along the high-symmetry direction of the Brillouin zone is presentedin Fig.1. The calculated total density of states (TDOS) and the partial density of states (PDOS) areplotted in Fig. 2.

From Fig. 1, we can infer that YB6 is a conductor. From Fig. 2, it can be seen that the upmostvalence bands (VBs) and the bottommost conduction bands (CBs) of YB6 are mainly composed of B2p states and Y 4d states, respectively. It should be pointed out that our present calculations did nottake into account the scissor operators on both the electronic structure and the optical performance

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022140-3 Xiao et al. AIP Advances 1, 022140 (2011)

FIG. 2. Total and partial DOS of YB6. (a) TDOS, (b) PDOS of Y and (c) PDOS of B.

of YB6. The Y 4p states at about -24 eV are highly localized, as evidenced by a very sharp peak inthe Y-PDOS. The energy bands located around -16 eV and from -12 to -8 eV consist mainly of B 2sand B 2p states. The energy bands located from -8 eV to 0 eV (i.e., the Fermi level) consist mainlyof B 2s and Y 4d states. The energy bands located above 0 eV (i.e., CBs) consist mainly of B 2p andY 4d states. The Y 4d states have a strong hybridization with the B 2p states above the Fermi level.

The complex dielectric function of YB6 is shown in Fig. 3. As well known, the peaks of theimaginary part ε2(ω) of the dielectric function correspond to the electron excitation. In Fig. 3, PeakA at 0.13 eV, Peak B at 3.96 eV, and Peak C at 5.51 eV correspond to the transition from the B 2pVBs to the Y 4d CBs, while peak D at 10.33 eV corresponds to the transition from the B 2p VBs tothe Y 4p CBs. The calculated static dielectric constant ε1(ω) was found to be 261.76.

The calculated refractive index n(ω), extinction coefficient k(ω), absorption spectrum α(ω),reflectivity R(ω), and energy-loss spectrum L(ω) are shown in Fig. 4. In the present calculations, weused Gaussian smearing of 0.5 eV.

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022140-4 Xiao et al. AIP Advances 1, 022140 (2011)

FIG. 3. Dielectric function of YB6

The electron energy-loss function L(ω) describes the energy loss of electrons fast traversing inmaterials. The peaks in the L(ω) spectra, where ε1 reaches the zero point indicating the transitionfrom the metallic performance [ε1(ω)<0] to the dielectric performance [ε1(ω)>0],21 characterizethe plasma resonance with those peak positions corresponding to the relevant plasma frequencies.Combining Fig. 3 with Fig. 4(b), we can conclude that the plasma frequency of YB6 is 1.71 eV, andthe calculated curve is in good agreement with the available loss-function spectra7 indicated by thedotted line. It should be mentioned here that the available loss-function spectra was obtained fromthe Kramers-Kroning transformation of the relevant experimental reflectivity spectrum.

The theoretical transmittance of 50 nm thick YB6 film can be deduced by the followingformula22

T = (1 − R)2 exp(−αd)

1 − R2 exp(−2αd)(2)

which is also plotted in Figs. 4(e) and 5(c).It can be seen from Fig. 5 that there is a partial reflection in the ultraviolet (UV) wavelength

range below 380 nm, and the main reflection of YB6 occurs in the NIR wavelength range between760∼2500 nm. However, the average reflection is 15% in the visible wavelength range between380∼760 nm and there is an obvious minimum reflectivity 7.5% at around 691.0 nm for YB6. Thestrong absorption coefficient occurs in the UV range and the NIR range, whereas the absorption co-efficients are weak in the visible light range and the minimum absorption coefficient is 77192.3 cm-1

at the wavelength of 639.0 nm. Thereby, the curve of theoretical transmittance indicates a hightransmittance in the visible wavelength range between 380∼760 nm and the biggest transmittanceis 55.0% at about 669.2 nm. However, a low transmittance occurs in the UV wavelength range and

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022140-5 Xiao et al. AIP Advances 1, 022140 (2011)

FIG. 4. Optical performance of YB6 (a) refractive index, (b) energy-loss spectrum. The dotted line stands for the availableloss-function spectra,7 (c) reflectivity, (d) absorption spectrum, and (e) theoretical transmittance of 50 nm thick film.

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022140-6 Xiao et al. AIP Advances 1, 022140 (2011)

FIG. 5. Optical Performance of YB6 (a) reflectivity, (b) absorption spectrum, and (c) theoretical transmittance of 50 nmthick film.

especially in the NIR wavelength range. This suggests that YB6 should be a perfect solar radiationshielding material for windows.

In this paper, we have investigated the electronic structure and the optical performance of YB6 bythe first-principles calculations within the framework of the density functional theory. The calculatedresults were found to be in good agreement with the relevant experimental data. Our studies showedthat YB6 is a perfect solar radiation shielding material for windows.

The authors greatly acknowledge Dr. J. Yan for helpful discussions. This research was financiallysupported by Innovation Foundation of the Ministry of Science and Technology of China (Grant No.10C26224302621).

1 Y. C. Su, L. H. Xiao, Y. C. Fu, P. F. Zhang, and P. PENG Sci. China. Ser G-Phys. Mech. Astron. 41, 1 (2011). (in Chinese).2 S. Schelm and G. B. Smith, Appl. Phys. Lett. 82, 24 (2003).3 H. Takeda, H. Kuno, and K. Adachi, J. Am. Ceram. Soc. 91, 9 (2008).

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022140-7 Xiao et al. AIP Advances 1, 022140 (2011)

4 K. Adachi, M. Miratsu, and T. Asahi, J. Mater. Res. 25, 3 (2010).5 S. Otani, M. M. Korsukova, T. Mitsuhashi, and N. Kieda, J. Cryst. Growth. 217, 378 (2000).6 Y. Xu, L. J. Zhang, T. Cui, Y. Li, Y. Xie, W Yu, Y. M. Ma, and G. T. Zou, Phys. Rev. B 76, 214103 (2007).7 S. Kimura, T. Nanba, M. Tomikama, S. Kunii, and T. Kasuya, Phys. Rev. B 46, 12196 (1992).8 S. I. Kimura, T. Nanba, S. Kunii, and T. Kasuya, Phys. Rev. B 50, 1406 (1994).9 B. T. Matthias, T. H. Geballe, K. Andres, E. Corenzwit, G. W. Hull, and J. P. Maita, Science. 159, 530 (1968).

10 R. Kadono, S. Kuroiwa, J. Akimitsu, A. Koda, K. Ohishi, W. Higemoto, and S. Otani, Phys. Rev. B 76, 094501 (2007).11 M. I. Tsindlekht, V. M. Genkin, G. I. Leviev, I. Felner, O. Yuli, I. Asulin, and O. Millo, Phys. Rev. B 78, 024522 (2008).12 M. I. Tsindlekht, V. M. Genkin, G. I. Leviev, and N. Yu. Shitsevalova, J. Phys.: Condens. Matter. 22, 095701 (2010).13 Y. Imai, M. Mukaida, M. Ueda, and A. Watanabe, Intermetallic. 9, 721 (2001).14 P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).15 W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).16 D. Vanderbilt, Phys. Rev. B 41, 7892 (1990).17 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).18 H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976).19 S. Saha, T. P. Sinha, and A. Mookerjee, Phys. Rev. B 62, 8828 (2000).20 R. Lortz, Y. Wang, U. Tutsch, S. Abe, C. Meingast, P. Popovich, W. Knafo, N. Shitsevalova, Yu. B. Paderno, and A. Junod,

Phys. Rev. B 73, 024512 (2006).21 Y. L. Li, W. L. Fan, H. G. Sun, X. F. Cheng, P. Li, and X. Zhao, J. Appl. Phys. 107, 093506 (2010).22 J. H. Chu, Physics of Narrow Gap Semiconductors. Beijing: Science Press. 2005. (in Chinese).

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