First-principles study on electronic structures of BaMoO4 crystals containing F and F+ color centers

Nuclear Instruments and Methods in Physics Research B 267 (2009) 1093–1096

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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

First-principles study on electronic structures of BaMoO4 crystals containing F and F+ color centers Xiaofeng Guo, Qiren Zhang *, Tingyu Liu, Min Song, Jigang Yin, Haiyan Zhang, Xi’en Wang College of Science, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai 200093, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 31 October 2008 Received in revised form 11 January 2009 Available online 22 January 2009 PACS: 61.72.Ji 61.72.Bb 71.15.M

a b s t r a c t The electronic structures of perfect crystals of barium molybdate (BaMoO4) and of crystals containing F and F+ color centers are studied within the framework of the fully relativistic self-consistent Dirac-Slater theory by using the numerically discrete variational (DV-Xa) method. The calculated results suggest that the donor energy level of the F center as well as F+ center is located within the band gap. The respective optical transition energies are 1.86 eV and 2.105 eV corresponding to the wavelength of the absorption band of 668 nm and 590 nm. It is therefore suggested that these bands are originate from the F and F+ centers in the crystal. Ó 2009 Elsevier B.V. All rights reserved.

Keywords: BaMoO4 crystal Color centers Self-consistent Absorption bands

1. Introduction Scheelite-type tetragonal structures with formula (ABO4) such as barium molybdate (BaMoO4), where molybdenum atoms are arranged in tetrahedral coordination have attracted great attention due to the approved usage as scintillating materials and in electro-optical applications including solid-state lasers and optical fibers [1–4]. Numerous investigations focused on the luminescence properties of BaMoO4, studying e.g. the intrinsic blue and green luminescence at 400–500 nm. At room temperature a decay time of a few nanoseconds was reported due to the radiating transition of the MoO2 4 group [5]. Ryu et al. [6] gave evidence that at room temperature the photoluminescence (PL) emission spectra of BaMoO4 colloidal nanoparticles using an excitation wavelength of 260 nm exhibits a triplet bands structure and can be decomposed by five bands peaked at 340, 440, 465, 500 and 600 nm, respectively, by Gaussian analysis. It is different to the single structured PL spectra of BMO powder and thin film excited by 488 nm reported by Marques et al. [7,8]. After analyzing the shape of the emission bands considering Jahn-Teller splitting of the excited MoO2 4 anion, it is believed [6] that the weak red emission band is probably caused by Frenkel defects due to an oxygen atom shifting to a suitable inter-site position and simultaneous creating an oxygen vacancy. It is well known that the oxygen vacancy existed in the * Corresponding author. Fax: +86 2155270559. E-mail address: [email protected] (Q. Zhang). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.01.013

crystal would electrons to maintain the local electrical neutrality. An oxygen vacancy traps two electrons or one electron would form the F or F+ center, respectively, [9,10]. These vacancies are responsible for the luminescence with green-red emission, while the blue emission is due the slightly distortion on the tetrahedrons in the lattice [11]. The creation of color centers would certainly influence the optical properties of the crystal. Understanding of the color centers can not only reveal the micro-mechanism of the color centers but also enhance the optical properties of the crystal. In this paper, the electronic structures of perfect BaMoO4 crystal and BaMoO4 containing F or F+ center are studied based on the density functional theory (DFT) by computational simulation. The calculated results indicated that the existence of F or F+ center would introduce an electrical state corresponding to 1s of either F or F+ center within the band gap. The transition energy from this 1s state to the bottom of the conduction band of F center and F+ center is 1.86 eV and 2.105 eV corresponding to 668 nm and 590 nm absorption band respectively. Hence the 668 nm and 590 nm absorption band of the crystal is attributed to F and F+ center, respectively. 2. Computational model and method 2.1. Crystal structure The BaMoO4 crystal [12] is scheetelite structured and the unit cell lattice parameters being a = b = 0.5479(9) nm and c = 1.2743(2) nm, as shown in Fig. 1. Its space group is I41/a (n° 88)

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consisting of 8 Ba 7 Mo and 28 O centered at Mo6+. The boundary conditions for the clusters are described by the embedding cluster scheme [20]. The potentials of the crystal ions around the cluster are simulated by Madelung potentials. Pseudo-potentials are used for the cluster ions to avoid false charge transfer from the clusters to the external ‘‘host” [21,22]. The molecular-cluster model with the framework of the fully relativistic self-consistent Dirac-Slater theory, using a numerically discrete variational (DV-Xa) method is adopted to study the electronic structures of BaMoO4 crystal. This method has been shown to be effective and easier to calculate the electronic structures in solids of saving large computational time and keeping high precision [23]. A set of atomic orbits W 5p, W 5d, W 6s, Ba 5s, Ba 5d, Ba 6s, O 2s, O 2p and O 3s reported by Nassif et al. [12] are calculated as basic functions in BaMoO4 crystal. The simulation parameters are listed in Table 2. Considering the relaxation effect produced by the electronic transitions in the crystal, the transition state method is used to calculate the excitation energy. Ionization energy Eion is the minimum energy required to remove an electron from the ground state of the isolated neutral atom

Ba Mo O

z o

x y

Fig. 1. The structure of BaMoO4 crystal.

and symmetry point group is reduced to S4 [13]. Each molybdenum ion Mo6+ is surrounded by four oxygen ions O2 and each barium ion Ba2+ is surrounded by eight oxygen ions O2, the polyhedral of four molybdenum ion Mo6+ surrounding O2 are slightly distorted tetrahedras with the angles of O–Mo–O being 108.3° and 111.8°, respectively [14].

@E Eion ¼ Eðni  1Þ  Eðni Þ ffi  ¼ ei T: @ni ni 1

ð1Þ

2

Similarly, excitation energy is the minimum energy required to bring a system to a specified higher energy level, thus the excitation energy can be expressed as the energy difference between i orbit and j orbit

Ei!j ¼ Eðni  1; nj þ 1Þ  Eðni ; nj Þ ¼ ej T  ei T:

ð2Þ

2.2. Computational method 3. Results and discussion ABINIT code based on density functional theory using the pseudo-potential method [15–17] is employed to calculate the lattice parameters and interatomic distances. The pseudo-potential was generated following the norm-conserving scheme of Troullier and Martins [18,19]. The cell parameters are selected from the experimental reported [12]. The wave functions at each k-point in the first Brillouin zone (BZ) are represented by the numerical coefficients of a finite set of plane-waves, determined by a kinetic energy cutoff. The performed tests for the density of k-point unit cell and also for the energy cutoff have shown that the 4  4  4 points in BZ and a plane-wave basis set with an energy cutoff of 40 Hartree correspond to a quite stable state of the system energy and therefore this choice of parameters is adequate for the calculations. The calculated results are listed in Table 1. It can be seen from Table 1 that the calculated results fitted well with the experimental values, therefore the parameters used in the calculation are believable for further calculations. The electronic structures of the crystal were calculated by using the cluster-embedding calculation method. The as-grown BaMoO4 crystal in laboratory has the scheelite lattice structure. The cluster chosen in the calculation has the chemical formula of [Ba8Mo7O28]2+

The total densities of states (TDOS) and partial densities of states (PDOS) for the perfect BaMoO4 crystal are calculated, as shown in Fig. 2. Comparing TDOS with PDOS, it can be easily observed that the top part of valence band is mainly composed by the O 2p states and the bottom of conduction band is mainly attributed to O 2p states accompanied by some Mo 4d states, while the bottom of the conduction band is mainly composed of Mo 4d states and some O 2p states. However the Ba 6s states distribute mainly on the conduction band and do not overlap with the O 2p states on the top of the valence band. It means that the Mo-O bond presents stronger covalence properties than the Ba 6s bond. The calculated results are in good agreement with the results reported by Nassif et al. [12]. The calculated band gap is about 4.6 eV which is similar to the result reported by Afanasiev [24] and slightly smaller than the band gap of PbWO4 (4.7 eV) [22]. It is well known that [24] the nature of the electropositive ions (Ba2+, Pb2+) seemed to have small impact on the band gap values. Meanwhile the electro-negativity as inferred from the band gap changes in the sequence Mo6+ > W6+ > Nb6+. Therefore for two isostructural solids, the W-containing one Table 2 Calculated properties of perfect BaMoO4 crystal. Property

Table 1 The initial basis sets and the funnel potential well. Ions

Mo0 Ba2+ O2 F F+

Frozen core

1s–4d 1s–4s 1s

Orbits for basis functions

4p, 4d, 5s 5s, 5d, 6s 2s, 2p, 3s 1s, 2s 1s, 2s

Calculated

Experimental [12]

Lattice energy (Ha/formula) 292.8996 Funnel potential well V0 (eV)

R1 (nm)

R2 (nm)

2.5 2.6 3.0 3.0 3.5

0.16 0.25 0.25 0.30 0.32

0.26 0.30 0.30 0.82 0.56

Lattice parameters (Å) a=b c Volume (Å3) Interatomic distance (Å) Ba–O Mo–O

5.5364 12.7153 389.746 4 4 4

5.5479 12.7432 392.225 2.7582 2.7112 1.7623

2.7643 2.7183 1.7653

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800

1000

400

500

O2s

O2p

O2p

O3s

O2s

O2p

O3s

0

0 + F 1s

20 Mo4p

0

Mo4d

Mo4d

DOS

DOS

500 0

300

Mo4d

Mo4d

Mo4p 0

500

Ba6s

Ba5p

500

Ba5p

0 0

4.6 eV

Total

600

+ F 1s

Total

600

Ba6s

2.105eV Mo4d

0

0 -20

-10

0

10

20

-20

-10

0

10

20

Energy/eV

Energy/eV Fig. 2. Total densities of states and partial densities of states for the perfect BaMoO4 crystal.

Fig. 4. Total densities of states and partial densities of states of BaMoO4 crystal containing F+ color enter.

should have higher the band gap value than the Mo-containing counterpart. The TDOS and PDOS of BaMoO4 crystal containing F color center are also calculated using the cluster (Ba8Mo7O27F)2+. The calculated results are shown in Fig. 3. It can be seen from the figure that the top part of the valence band and the bottom of the conduction band are also mainly distributed by the O 2p states and Mo 4d states and the bottom of the conduction band are also distributed by the Mo 4d states and O 2p states. The main difference between the perfect crystal and the F center contained crystal is the energy gap of the F center contained crystal becoming narrower than that of the perfect crystal and there is a new electronic state peak appearing within the energy gap. The F center is defined by an oxygen vacancy trapping two electrons [9]. The oxygen vacancy makes its neighbor ions approach to the vacancy therefore higher the 2p states of the oxygen ions nearest to the central F center resulting in narrows the energy gap of the crystal. The new electronic state peak appeared within the energy gap is just the 1s ground state of the F center. The TDOS and PDOS of BaMoO4.crystal containing F+ color center are also calculated using the cluster (Ba8Mo7O27F+)3+. The calculated results are shown in Fig. 4. Similarly to the results of the crystal containing F center, it can be seen from Fig. 4 that the energy gap is narrower than that of the perfect crystal and there is a new electronic state peak appeared within the energy gap. The

calculation indicated that the state peak appeared within the energy gap is attributed by the 1s state of the F+ center. It can be seen from Figs. 3 and 4 that the position of the 1s state of the F+ center lies lower in energy than the 1s state of the F center. Since the F+ center is an oxygen vacancy trapping one electron, however the F center is an oxygen vacancy trapping two electrons. So the electron in the F+ center is more tightly trapped by the oxygen vacancy than the two electrons in the F center. Therefore the ground state of the F+ center physical reasonable lies lower in energy than that of the F center. The optical absorption transition of F or F+ center corresponding to 1s–2p electronic transition. The calculation of the crystal containing either F or F+ center indicated that the 2p first excited state of F or F+ center emerges in the conduction band. Hence the optical absorption transition of the present cases corresponding to the F or F+ electron transit from the ground state to the bottom of the conduction band. Hence it can be physically predicted that the optical absorption of the F center should peaks in the longer wavelength side of that of the F+ center. The similar results of PbWO4 and PbMoO4 crystals containing F and F+ centers were reported [22,25]. The calculated transition from the 1s state of the F center to the bottom of the conduction band is 1.86 eV corresponding to 668 nm and from the 1s state of the F+ center to the bottom of the conduction band is 2.105 eV corresponding to 590 nm, respectively. So it is concluded that F and F+ color centers in the crystal could be responsible for the absorption bands peaking at 668 nm and 590 nm respectively. It coincides with the conclusion that the oxygen vacancy exhibited in the sheelite structured crystal would cause absorptions in the range of 500–700 nm [26,27].

800 400

O3s

O2p

O2s

0

20

4. Conclusions

F1s

DOS

0

300

Mo4d

Mo4p

The electronic structures of the perfect BaMoO4 and the defect BaMoO4 crystal containing F and F+ color centers have been studied by using the relativistic self-consistent Discrete Variational embedded cluster method with the lattice optimized. The calculated results indicate that the 668 nm and 590 nm absorption bands is originated from the F and F+ color centers contained in the crystal, respectively.

Mo4d

0

500

Ba5p

Ba6s

1.86eV

0

F1s

Total

600

Mo4d

0 -20

-10

0

10

20

Energy/eV Fig. 3. Total densities of states and partial densities of states of BaMoO4 crystal containing F color.

References [1] F.M. Pontes, M.A.M.A. Maureram, A.G. Souzaa, E. Longo, E.R. Leite, R. Magnani, M.A.C. Machado, P.S. Pizani, J.A. Varela, J. Eur. Ceram. Soc. 23 (16) (2003) 3001. [2] J.H. Ryu, J.W. Yoon, C.S. Lim, W.C. Oh, K.B. Shim, J. Alloy Compd. 390 (1–2) (2005) 245.

1096

X. Guo et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1093–1096

[3] X. Wu, J. Du, H. Li, M. Zhang, B. Xi, H. Fan, Y. Zhu, Y. Qian, J. Solid, State Chem. 180 (2007) 3288. [4] Z. Luo, H. Li, H. Shu, K. Wang, J. Xia, Y. Yan, Cryst. Growth Des. 8 (2008) 2275. [5] S.B. Mikhrin, A.N. Mishin, A.S. Potapov, P.A. Rodnyi, A.S. Voloshinovskii, Nucl. Instr. and Meth. A 486 (2002) 295. [6] J.H. Ryu, K.M. Kim, S.W. Mhin, G.S. Park, J.W. Eun, K.B. Shim, C.S. Lim, Appl. Phys. A. Mater. Sci. Process. 92 (2008) 407. [7] A.P.A. Marques, D.M.A. De Melo, E. Longo, C.A. Paskocimas, P.S. Pizani, J. Solid Stat. Chim. 178 (2005) 2346. [8] A.P.A. Marques, D.M.A. de Melo, C.A. Paskocimas, P.S. Pizani, M.R. Joya, E.R. Leite, E. Longo, J. Solid Stat. Chim. 179 (2006) 671. [9] S.G. Fang, Q.R. Zhang, Physics of Color Centers in Crystals, Shanghai Jiaotong University Press, 1989. p. 61. [10] V.M. Longo, E. Orhan, L.S. Cavalcante, S.L. Porto, J.W.M. Espinosa, J.A. Varela, E. Longo, Chem. Phys. 334 (2007) 180. [11] V.M. Longo, A.T. de Figueiredo, A.B. Campos, J.W.M. Espinosa, A.C. Hernandes, C.A. Taft, J.R. Sambrano, J.A. Varela, E. Longo, J. Phys. Chem. A 112 (2008). [12] V. Nassif, R.E. Carbonio, J.A. Alonso, J. Solid Stat. Chim. 146 (1999) 266. [13] J.C. Sczancoski, L.S. Cavalcante, M.R. Joya, J.W.M. Espinosa, P.S. Pizani, J.A. Varela, E. Longo, J. Colloid Interf. Sci. 330 (2009) 227. [14] L.S. Cavalcante, J.C. Sczancoski, R.L. Tranquilin, M.R. Joya, P.S. Pizani, J.A. Varela, E. Longo, J. Phys, Chem. Solids 69 (2008) 2674.

[15] P. Hohenberg, W. Kohn, Phys. Rev. 136 (3B) (1964) 864. [16] W. Kohn, L.J. Sham, Phys. Rev. 140 (4A) (1965) 1133. [17] W. Kohn, M.C. Holthausen, A Chemist’s Guide to Density Functional Theory, second ed., Wiley, VCH, 2001. [18] See for the official developer site. [19] X. Gonze, J.M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.M. Rignanese, L. Sindic, M. Verstraete, G. Zerah, F. Jollet, M. Torrent, A. Roy, M. Mikami, P. Ghosez, J.Y. Raty, J.Y. Raty, Computat. Mater. Sci. 25 (2002) 478. [20] D.E. Ellis, J. Guo, Electronic Density Function Theory of Molecules, Clusters, and Solids [M], Dordrecht, Kluwer Press, 1995. p. 263. [21] Y. Koyama, I. Tanaka, Y.S. Kim, S.R. Nishitani, H. Adachi, Jpn. J. Appl. Phys. 38 (1999) 4804. [22] Z.J. Yi, T.Y. Liu, Q.R. Zhang, Y.Y. Sun, J. Electron Spectrosc. Relat. Phenom. 151 (2) (2006) 140. [23] T. Chen, T.Y. Liu, Q.R. Zhang, F.F. Li, Z.J. Yi, D.S. Tian, X.Y. Zhang, Phys. Stat. Sol. (a) 204 (3) (2007) 776. [24] P. Afanasiev, Mater. Lett. 61 (2007) 4622. [25] J.R. Chen, Q.R. Zhang, T.Y. Liu, Z.X. Shao, C.Y. Pu, Chin. Phys. Lett. 24 (2007) 1163. [26] Q.R. Zhang, T.Y. Liu, J. Chen, Phys. Rev. B 68 (2003) 064108. [27] M. Nikl, K. Nitsch, S. Baccaro, A. Cecilia, M. Montecchi, B. Borgia, I. Dafinei, M. Montecchi, J. Appl. Phys. 82 (11) (1997) 5758.