Effects of vacancies on valence stabilities of europium ions in β-Ca2SiO4: Eu phosphors

Author’s Accepted Manuscript Effects of vacancies on valence stabilities of europium ions in β-Ca2SiO4: Eu phosphors Jun Wen, Yau-Yuen Yeung, Lixin Ning, ChangKui Duan, Yucheng Huang, Jie Zhang, Min Yin www.elsevier.com/locate/jlumin

PII: DOI: Reference:

S0022-2313(16)30339-8 http://dx.doi.org/10.1016/j.jlumin.2016.05.047 LUMIN14018

To appear in: Journal of Luminescence Received date: 15 March 2016 Revised date: 8 May 2016 Accepted date: 26 May 2016 Cite this article as: Jun Wen, Yau-Yuen Yeung, Lixin Ning, Chang-Kui Duan, Yucheng Huang, Jie Zhang and Min Yin, Effects of vacancies on valence stabilities of europium ions in β-Ca2SiO4: Eu phosphors, Journal of Luminescence, http://dx.doi.org/10.1016/j.jlumin.2016.05.047 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Effects of vacancies on valence stabilities of europium ions in β-Ca2SiO4: Eu phosphors Jun Wen a,b,*, Yau-Yuen Yeung a,*, Lixin Ning c, Chang-Kui Duan d, Yucheng Huang c, Jie Zhang b, Min Yin d a

Department of Science and Environmental Studies, Hong Kong Institute of Education, 10 Lo Ping

Road, Tai Po, NT, Hong Kong, P. R. China b

School of Physics and Electronic Engineering, Anqing Normal University, Anqing 246011, P. R. China

c

Center for Nano Science and Technology, Department of Physics, Anhui Normal University, Wuhu

241000, P. R. China d

Department of Physics, University of Science and Technology of China, Hefei 230026, P. R. China

ABSTRACT The formation energies of oxygen and calcium vacancies (VO and VCa) in β-Ca2SiO4 are derived from density functional theory (DFT) calculations performed on constructed supercells, revealing the thermodynamic stabilities of intrinsic defects under Oxygen-poor conditions. On the basis of DFT calculations with HSE06 hybrid functional, defect states produced by vacancies (VO and VCa), dopants Eu (EuCa) and Eu-related defect complexes (EuCa+VO and EuCa+VCa) in the band gap of β-Ca2SiO4 host have been further distinguished. The calculated results indicate that the neutral and single negatively charged VCa (i.e., VCa× and VCa′) and the VO in positive charge states may act as trapping centers for electrons. When approaching to Eu2+ ions, VCa× and VCa′ may capture the electrons of Eu2+ ions and stabilize Eu3+ ions at Ca2+ sites in β-Ca2SiO4, but not the neutral and positively charged VO. This work demonstrates that electronic structure calculations combined with thermodynamic analyses can be utilized to study the interactions between europium ions and their neighboring defects, and further study the tuning mechanisms of the valence stabilities of europium ions in inorganic compounds.

*

Corresponding author. Department of Science and Environmental Studies, Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, NT, Hong Kong, P. R. China. Tel.: +852-29487650; fax: +852-29487676. E-mail address: [email protected] (Y. Y. Yeung), [email protected] (J. Wen)

Keywords: Formation energies; electronic structures; valence stabilities; intrinsic defects; β-Ca2SiO4: Eu

1. Introduction Europium-doped materials have attracted much attention due to their wide applications in long-persisting phosphors and white-light emitting diodes (W-LEDs) [1-9]. In solids, trivalent and bivalent europium ions demonstrate distinct spectroscopic properties, e.g., sharp line and broad band emissions for Eu3+ and Eu2+, respectively, since the luminescence of the former is attributed to intra-configurational 4f6 → 4f6 transitions while that of the latter is ascribed to inter-configurational 4f65d → 4f7 transitions. The coexistence of Eu2+ and Eu3+ in some phosphors has been confirmed by experimentally measured luminescence and luminescence excitation spectra [10-17]. Thus, the tuning of the emitting colors of phosphors could be achieved by co-doping Eu2+ and Eu3+, which may occupy various cation sites with different local environments. Moreover, intrinsic defects (such as vacancies, interstitials, antisite defects and so on) are inevitably generated in phosphors [18-22], owing to the thermal fluctuations during the preparation of the samples as well as the complex crystal structures of some phosphors. When these defects are introduced into the local environments of lanthanide ions, they may result in color changes of the phosphors. Besides, some of these defects may compensate for the charge mismatch between Eu and host cations, stabilizing Eu ions at the sites of phosphors. The distinctions of the energy-level structures of Eu2+ and Eu3+ in phosphors as well as the effects of defects on the spectroscopic properties of Eu-doped phosphors can be confirmed by not only experimental measurements but also density functional theory (DFT) calculations [23-25]. Especially, DFT calculations with hybrid functionals have been proven to be able to correct the deficiencies of conventional DFT calculations in the estimations of the band gap energies of materials and also the descriptions of impurity-induced defect states [26,27]. In the present work, DFT calculations were performed on undoped and Eu-doped β-Ca2SiO4 to investigate energetic properties and electronic structures of intrinsic defects (i.e., oxygen and calcium vacancies) and their influences on the spectroscopic properties of dopant Eu in β-Ca2SiO4. Firstly, the geometric structures of β-Ca2SiO4 supercells containing intrinsic defects and/or dopant Eu in different charge states were obtained from DFT geometry optimization calculations. Based on the calculated total energies of optimized supercells, the

formation energies of intrinsic defects under Oxygen-poor conditions in undoped β-Ca2SiO4 were derived to analyze the relative preferences of intrinsic defects in different charge states. Moreover, the defect states within host band gap as produced by vacancies (VO and VCa), dopants Eu (EuCa) and Eu-related defect complexes (EuCa+VO and EuCa+VCa) were distinguished by the patterns of the density of states (DOS), which were calculated from DFT calculations with Heyd−Scuseria−Ernzerhof screened Coulomb hybrid functional (HSE06 functional). It was found that the neutral and single-negatively charged VCa may act as the trapping centers of electrons and then stabilize Eu3+ ions at Ca2+ sites in β-Ca2SiO4: Eu phosphors. Besides, the 4f energy-level structures of Eu ions in β-Ca2SiO4 are derived from the calculated DOS patterns of the 4f states of Eu2+ and Eu3+, showing reasonably good agreement with both the charge transfer (CT) band of Eu3+−O2- in the experimental spectra and the empirical models. This work demonstrates that hybrid DFT calculations not only accurately predict the host band gap and the impurity-induced defect states located within the band gap, but also present an expedient way to investigate the tuning mechanisms of the valence stabilities of europium ions in inorganic compounds. The rest of this paper is organized as follows. The calculation methods for geometry optimizations, electronic structures and formation energies are described in section 2. In section 3, the results and discussion of the atomic structures, energetic and electronic properties of undoped and Eu-doped β-Ca2SiO4 are presented. The overall conclusions are finally provided in section 4.

2. Calculation methods DFT calculations were carried out on the constructed supercells to obtain the geometric and electronic structures of undoped and Eu-doped β-Ca2SiO4, as implemented in the VASP code [28,29]. The Eu 5s25p64f76s2, O 2s22p4, Si 3s23p2 and Ca 3s23p64s2 electrons were treated as the valence electrons, whose interactions with the respective cores were described by using the projected augmented wave (PAW) method [30]. The Perdew−Burke−Ernzerhof (PBE) [31] exchange-correlation functional from the generalized gradient approximation (GGA) and the HSE06 functional [32,33] were adopted for the geometry optimizations and electronic structure calculations, respectively. The 112-atom 2 × 2 × 1 supercells containing defects were

constructed for the simulation of β-Ca2SiO4: Eu phosphors. The geometric structures of the supercells were then fully relaxed with the convergent criterions of 10−6 eV used for the change in the total energy and of 0.01 eV/Å used for Hellman−Feynman forces on atoms. The cut-off energy of 550 eV was employed for the plane-wave basis set. The 2 × 2 × 2 k-point grids for the sampling of Brillouin zone (BZ) were used for the constructed supercells in PBE calculations, and the sampling of BZ is with only one k-point (Γ point) for HSE06 calculations, in consideration of the large amount of calculations. In addition, the spin polarization and the configuration of broken symmetry were adopted in all the calculations. The oxygen vacancies, calcium vacancies, dopants Eu and defect complexes were taken into account in this work. Krӧger−Vink notations were then adopted to label these defects and defect complexes in different charge states in phosphors. A single charge state of the defect. A single

●

×

indicates the neutral

and ′ signifies a single positive and negative charge,

respectively, and further the number of the symbols

●

and ′ would indicate the number of the

charges of the defects. On the basis of the calculated total energies of defective supercells, the formation energy (ΔEf) of a defect D in the charge state of q can be calculated from the following formula [34],

E f ( Dq )  Etot ( Dq )  Etot (perfect)   ni i  q( VBM  EF )

(1)

i

where Etot(Dq) is the calculated total energy of the β-Ca2SiO4 supercell containing the defect Dq, and Etot(perfect) is the calculated total energy of the perfect β-Ca2SiO4 supercell. ni is the number of the atom of species i which are added to (ni > 0) and/or removed from (ni < 0) the perfect supercell. μi is the atomic chemical potential of the atom of species i. EF is the Fermi energy level of the system with respect to the valence band maximum (VBM) VBM, which is aligned with that of the perfect system. According to eq 1, the derived formation energy is depicted as a function of the EF, which is variable and depends on the level of the electron occupation in the realistic system. The atomic chemical potential μi in the equation above are variable. They have to meet the thermal stability condition of β-Ca2SiO4:

2Ca  Si  4O   -Ca2SiO4

(2)

where the Ca 2SiO4 is the calculated total energy per formula unit for β-Ca2SiO4. The chemical

potential μi (i = Ca, Si and O) can be further constrained by the conditions for the thermodynamic equilibrium of various phases (such as CaO and SiO2) containing the three atomic species. As reported in the previous references [35,36], β-Ca2SiO4: Eu phosphors are usually prepared in an inert-gas atmosphere (e.g., the Ar), which indicates the Oxygen-deficient atmosphere. Hence, O-poor thermodynamic equilibrium conditions were adopted,

Ca  Ca(bulk)

(3)

Si  Si(bulk)

(4)

The μCa and μSi were calculated as the total energies per atom of bulk materials Ca (fcc) and Si (diamond), respectively. Similarly, the μEu was equal to the calculated total energy per atom of bulk material Eu (bcc).

3. Results and discussion 3.1. Geometric and electronic properties of β-Ca2SiO4 host. Calcium silicate has various crystal structures, such as α, α’H, α’L, β and γ phases. Although the stable phase of Ca2SiO4 at room temperature is γ phase, metastable β phase is existent and even demonstrates a significant role as the host material for lanthanide-doped phosphors [35-39]. The β-Ca2SiO4 crystallizes in monoclinic structure (illustrated in Fig. 1a) with space group P21/n (no. 14), and it corresponds to the lattice with a unit cell of 28 atoms (four chemical formulas). The experimental lattice parameters from the previous report are a = 5.502 Å, b = 6.745 Å, c = 9.297 Å and β = 94.590 deg [40]. On the basis of DFT-PBE geometry optimization calculations, the derived parameters are a = 5.574 Å, b = 6.817 Å, c = 9.379 Å and β = 94.694 deg, showing slightly greater than experimental ones. In β-Ca2SiO4, there are two crystallographically different calcium sites, which are coordinated by seven and eight oxygen atoms, respectively (see Fig. 1b). Both types of calcium sites are of C1 symmetry. In Table 1, the optimized distances between Ca and O are listed, with the average ones of 2.526 Å for both Ca1 (experimental value: 2.509 Å) [40] and Ca2 (experimental value: 2.491 Å) [40] sites. The doping Eu ions are supposed to occupy Ca2+ sites in β-Ca2SiO4, due to their

similar charge states and ionic radii (i.e., 1.06, 1.20 and 1.01 Å for seven-coordinated Ca2+, Eu2+ and Eu3+, respectively, and 1.12, 1.25 and 1.07 Å for eight-coordinated Ca2+, Eu2+ and Eu3+, respectively) [41]. The average Eu−O bond lengths in Eu singly doped β-Ca2SiO4 show that the doping of Eu2+ overall enlarges the distances between the cations (Ca and Eu) and coordinated oxygen ions, while the doping of Eu3+ slightly decreases the distances in general. This is consistent with the change of the ionic radii of Eu2+ and Eu3+ with respect to those of Ca2+, indicating the achievements of the double and triple positively charge states of Eu in β-Ca2SiO4. With PBE-optimized geometries, the DOS pattern of undoped β-Ca2SiO4 is thus calculated by using HSE06 hybrid functional which contains 25% Hartree−Fock exchange and 75% PBE exchange. Note that hybrid functional calculations can present a significant improvement on the descriptions of the electronic structures of lanthanide-based phosphors (such as the band gap and positions of defect states within the band gap). The band gap energy (denoted as Egap) of β-Ca2SiO4 calculated from PBE functional is 4.7 eV, while the Egap from HSE06 calculation increases to 6.0 eV, showing a reasonably good agreement with the value (~6.8 eV) obtained from the experimental ultraviolet (UV) excitation spectrum [35,36]. Compared to PBE calculations, the deviation of the Egap of HSE06 calculation from the experimental value is satisfied for further analyses of defect states within the band gap. In Fig. 2, the calculated total and orbital-projected DOS of the 2 × 2 × 1 supercell of undoped β-Ca2SiO4 are illustrated. It is obvious that the top of the host VB and the bottom of the host conduction band (CB) are mainly composed of O 2p and Ca 3d states, respectively, along with the weak hybridization between the two types of states.

Table 1 Calculated Ca−O and Eu−O bond lengths (Å) in undoped and Eu singly doped β-Ca2SiO4. site 1 (CNa = 7) M = Ca1 M = EuCa1× M = EuCa1● M−O1 M−O2 M−O3 M−O4 M−O5 M−O6 M−O7 Average

2.244 2.357 2.428 2.474 2.571 2.672 2.937 2.526

2.314 2.424 2.510 2.532 2.636 2.688 2.978 2.583

2.261 2.368 2.429 2.468 2.555 2.616 2.889 2.512

site 2 (CNa = 8) M = Ca2 M = EuCa2× M = EuCa2● M−O1 M−O2 M−O3 M−O4 M−O5 M−O6 M−O7 M−O8 Average a

2.407 2.414 2.420 2.429 2.479 2.666 2.687 2.704 2.526

2.467 2.502 2.484 2.497 2.530 2.654 2.682 2.687 2.563

2.390 2.389 2.383 2.392 2.439 2.581 2.604 2.567 2.468

CN: Coordination number.

Fig. 1. Schematic representations of (a) the unit cell of β-Ca2SiO4 and (b) the local coordination structures of two calcium sites (Ca1 and Ca2).

120 TDOS Op Ca d

80

DOS (States/eV)

40

Egap=6.0 eV 0

-40

-80

-120 -8

-6

-4

-2

0

2

4

6

8

10

12

14

Energy (eV) Fig. 2. Total and orbital-projected DOS of the 2 × 2 × 1 supercell of undoped β-Ca2SiO4 from HSE06 calculation. The vertical dashed lines stand for Fermi energy levels, similarly hereinafter.

3.2. Energetic and electronic properties of oxygen and calcium vacancies in undoped β-Ca2SiO4. In lanthanide-doped phosphors, the presences of intrinsic defects and dopants are usually crucial for the explanation of the corresponding experimental spectra. Watras et al. [23] demonstrate that the observation of Eu3+ luminescence in europium-doped KCa(PO3)3 phosphors can be due to the presence of calcium vacancies, which not only compensate for the charge mismatch between Eu3+ and Ca2+ ions but also change the locations of the 4f states of Eu3+ ions in the energy band. On the basis of experimental and theoretical analyses of Ji et al. [24] the oxygen vacancies adjacent to the Eu doped in BaMgSiO4 are deemed to play an important role in the color turning of the phosphors. The intrinsic defects can usually form in both undoped and doped hosts of phosphors, due to the thermal fluctuations during the preparation of the samples as well as the complex crystal structures of some phosphors. In

this section, formation energies and electronic structures of neutral and charged intrinsic defects in undoped β-Ca2SiO4 are taken into account for the purpose of a better understanding of their influences on the electronic structures and luminescence of β-Ca2SiO4: Eu phosphors. The calculated formation energies (denoted as ΔEf) of oxygen and calcium vacancies in neutral charge states under O-poor conditions are 0.12 (VO×), 8.42 (VCa1×) and 8.89 eV (VCa2×) according to eqs 2-4. The ΔEf of the VO× would increase to 5.47 eV under O-rich conditions, which indicates that the chemical potential μO is equal to the half of the calculated total energy of isolate O2 molecule. Thus, the more the oxygen contents in the environmental atmosphere, the harder the formation of the oxygen vacancy in β-Ca2SiO4. The neutral vacancies at Ca1 sites have much lower ΔEf than those at Ca2 sites by 0.47 eV. Also, the neutral dopant EuCa× tends to occupy Ca1 site, although the difference of the ΔEf for the EuCa× occupying two Ca sites is only 20 meV. It should be noted that the defects VCa×, EuCa× and NdCa× display similarly consistent variation tendencies of the ΔEf, when they occupy three types of Ca sites in CaAl2O4 crystal [25]. These can be attributed to local coordination structures (i.e., the types and positions of coordinated atoms) around different Ca sites, which determine the interactions between calcium and coordinated atoms. Moreover, the calculated ΔEf as a function of the Fermi level EF for oxygen and calcium vacancies in different charge states in β-Ca2SiO4 are demonstrated in Figs. 3 and 4, respectively. As is well known, the thermodynamic transition energy level (denoted as ε(q/q′)) of a defect corresponds to the EF position where the ΔEf of the defect in the charge state of q is equal to that in the charge state of q′. All the transition energy levels of VO and VCa are calculated within the host band gap of β-Ca2SiO4. Fig. 3 shows that the positively charged VO can act as the trapping centers of electrons from the CB. That is to say, the positively charged VO can trap an electron from the CB and then change its charge state, for example, from +1 to 0. The oxygen vacancy is a deep donor, since the positions of ε(+/0) and ε(2+/+) levels are below the bottom of the CB by more than 1.0 eV. Also, the figure demonstrates that the VO●● is preferred when the EF is below 4.73 eV, while the VO in neutral charge state is more stable when the EF is above 4.91 eV. When the EF is in the narrow range of 4.73 and 4.91 eV, the VO● then becomes much more stable. As for VCa, thermodynamic transition levels ε(0/–) and ε(–/2–) are very close to each other, and the neutral and –2 charge states have the lowest energies when EF locates in the

lower and upper parts of the band gap, respectively. Total and orbital-projected DOS of 2 × 2 × 1 supercells for β-Ca2SiO4 containing oxygen and calcium vacancies are depicted in Figs. 5 and 6, respectively. One can see from Fig. 5a that the neutral VO× introduces a doubly occupied defect state (related to the location of the EF) into the band gap. When the VO× becomes singly positive charge state VO● by trapping a hole from its surroundings (such as the neutral or single-negatively charged VCa), the occupied defect state thus splits into two spin-resolved ones, as shown in Fig. 5b. The spin-up state is occupied while the spin-down one is unoccupied, and they are separated by ~2.8 eV. In Fig. 5c, it can be seen that the defect state produced by VO●● locates below the bottom of the CB by ~1.4 eV. Accordingly, the schematic representations of the position and occupation of defect states introduced by VO× and VO● are illustrated in Fig. 7. As shown in Figs. 6a, 6b and 6c, the defect states introduced by VCa× and VCa′ are very close to the top of the O 2p VB, while there are no defect states within the band gap for the β-Ca2SiO4 supercell containing VCa′′. As a consequence, VCa× and VCa′ may readily capture electrons from the VB and meanwhile leave the holes behind. Our calculations imply that VCa× and VCa′ can act as the trapping centers of electrons when they approach to the dopants, such as EuCa×.

Formation energy (eV)

0.4

0.2

0.0

-0.2

●●

VO VO VO× ●

-0.4 4.6

4.7

4.8

EF   VBM

4.9

5.0

(eV)

Fig. 3. Calculated formation energies (ΔEf) of oxygen vacancies in different charge states as a function of Fermi level position (EF) in the fundamental band gap of β-Ca2SiO4 under O-poor conditions.

9.2 VCa× VCa' VCa''

Formation energy (eV)

8.8

8.4

8.0

7.6 2.2

2.4

2.6

EF   VBM (eV)

2.8

3.0

Fig. 4. Calculated formation energies (ΔEf) of calcium (Ca1) vacancies in different charge states as a function of Fermi level position (EF) in the fundamental band gap of β-Ca2SiO4 under O-poor conditions.

(c) VO••

50

TDOS Op Ca d

0

DOS (States/eV)

-50 (b) VO•

50 0 -50

50

(a) VO×

0 -50 -10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

Energy (eV)

Fig. 5. Total and orbital-projected DOS of the 2 × 2 × 1 supercell of the β-Ca2SiO4 containing (a) VO×, (b) VO● and (c) VO●●.

(c) VCa''

50

TDOS Op Ca d

0

DOS (States/eV)

-50

50

(b) VCa'

0 -50

50

(a) VCa×

0 -50 -10

-8

-6

-4

-2

0

2

4

6

8

10

12

Energy (eV)

Fig. 6. Total and orbital-projected DOS of the 2 × 2 × 1 supercell of the β-Ca2SiO4 containing (a) VCa×, (b) VCa′ and (c) VCa′′.

Fig. 7. Schematic diagrams of defect states produced by (a) VO×, (b) VO● and (c) VO●● within the band gap of β-Ca2SiO4, along with their occupations.

3.3. Electronic properties of dopant Eu and Eu-related defect complexes in β-Ca2SiO4: Eu phosphors The electronic structures of single dopant EuCa in neutral charge state (EuCa×) in β-Ca2SiO4 are firstly calculated, which means that β-Ca2SiO4: Eu2+ phosphors are now taken into account. In Fig. 8a, the calculated total and orbital-projected DOS of 2 × 2 × 1 supercells of the β-Ca2SiO4 containing the single EuCa× are depicted. One can see that the EuCa× hardly changes the locations of VB and CB. In the band gap, the intense defect states which are mainly attributed by the 4f spin-up states of Eu2+ should be occupied, due to their locations below the Fermi level. Besides, the 5d states of Eu2+ emerge in the bottom of the CB. The energy separation between the peak of the DOS of the 4f ground state and the bottom of the 5d excited states of Eu2+ ion is ~3.6 eV (~29000 cm-1), which, to some extent, is related to 4f → 5d transition band with the maximum at 332 nm (30065 cm-1) in the experimental excitation spectra of β-Ca2SiO4: Eu2+ phosphors [35,36]. The coexistence of Eu2+ and Eu3+ in Eu-doped β-Ca2SiO4 phosphors has been confirmed by means of the experimentally measured luminescence and luminescence excitation spectra [35,36]. Thus, it is significant to first distinguish the electronic structures of Eu2+ and Eu3+ separately doped in β-Ca2SiO4. Fig. 8b demonstrates the calculated total and orbital-projected DOS of Eu3+ singly doped β-Ca2SiO4. Through subtracting an electron from the defective supercell containing a single dopant EuCa×,

the triply positive charge state of the europium is thus achieved, which is also verified by the variations of Eu−O bond lengths as shown in section 3.1. It should be noted that the size of the constructed supercell is large enough to neglect the effects of Coulomb interactions between the periodic image charges of defective supercell. The DOS pattern of Fig. 8b shows that the lowest peak of the DOS for the occupied portion of the 4f spin-up states of Eu3+ ion is lower than the Fermi level by ~4.9 eV, and the peak of the unoccupied portion of 4f spin-up states is higher than the Fermi level by ~1.1 eV. Besides, the unoccupied 4f spin-down states locate below the bottom of the host CB and also emerge in the CB. The obvious distinction of the partial DOS of 4f states between Eu2+ and Eu3+ is ascribed to the difference of the number of 4f electrons. The 4f shell of Eu2+ is half-filled, while that of Eu3+ is less than half full, making some of the 4f spin-up states of Eu3+ unoccupied.

•

(b) EuCa

Total Eu f Eu d

50

DOS (States/eV)

0 -50

(a) EuCa×

50 0 -50

-8

-6

-4

-2

0

2

4

6

8

10

12

14

Energy (eV)

Fig. 8. Total and orbital-projected DOS of the 2 × 2 × 1 supercell of the β-Ca2SiO4 containing the dopants (a) EuCa× and (b) EuCa● at Ca2 sites. It is noted that the f and d states of Eu have been amplified 2 and 4 fold, respectively, for a better show of the contributions of states associated with Eu.

The cation and anion vacancies are inevitably generated in β-Ca2SiO4: Eu phosphors, as

mentioned above. Herein, Eu-related defect complexes EuCa×+VO●● and EuCa×+VCa× are constructed for the purpose of investigation on the significant effects of VO●● and VCa×, both of which could act as the trapping centers of electrons. The calculated formation energies of defect complexes reveal that VCa× tends to be close to EuCa×, while VO●● keeps away from EuCa×. Nevertheless, the defect complex EuCa×+VO●● with the shortest distance between EuCa× and VO●● is still taken into account to determine the significant influence of VO●●. The charge state of VO●● in the defect complex can be deduced from the DOS pattern of the defect states below the bottom of the CB (as illustrated in Fig. 9a), which is in reasonably good agreement with the counterpart in Fig. 5c. According to the comparisons of Figs. 8a and 9a, and 8b and 9b, the partial DOS of the Eu 4f and Eu 5d states of β-Ca2SiO4 supercell containing EuCa×+VCa× agree well with those of the supercell containing EuCa●, while those show an excellent agreement between the defective supercells separately containing EuCa×+VO●● and EuCa×. We may conclude that the neutral VCa× in the defect complex EuCa×+VCa× easily traps an electron from the neighboring EuCa× and thus stabilizes the Eu3+ at Ca site in β-Ca2SiO4: Eu phosphors. One neutral VCa× traps at most two electrons from the neutral dopants EuCa×, and meanwhile creates two Eu3+ ions in the phosphors. Similarly, VCa′ may also act as the stabilizer for Eu3+ ions in the phosphors. Otherwise, Fig. 9a reveals that the Eu ion in the defect complex EuCa×+VO●● remains the doubly positive charge state, i.e., Eu2+, due to no transfer of electrons between the neighboring defects. Considering that the VO●● have a greater ability to trap electrons than that of VO× and VO●, it is thus reasonable to assume that there are no transfer of electrons from EuCa× to the neutral and positively charged VO.

(b) EuCa×+VCa×

Total Eu f Eu d

50

DOS (States/eV)

0 -50

••

(a) EuCa×+VO

50 0 -50

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Energy (eV)

Fig. 9. Total and orbital-projected DOS of the 2 × 2 × 1 supercell of the β-Ca2SiO4 containing defect complexes (a) EuCa×+VO●● and (b) EuCa×+VCa×. It is noted that the f and d states of Eu have been amplified 2 and 4 fold, respectively, for a better show of the contributions of states associated with Eu.

Although the detailed experimental excitation and emission spectra of the phosphors cannot be reproduced via DFT calculations [42], the 4f energy-level structures of Eu ions in the phosphors may be derived from previously calculated DOS patterns, for a better understanding of the spectroscopic properties of β-Ca2SiO4: Eu. In Fig. 10, the 4f energy-level diagrams of Eu2+ and Eu3+ in the phosphors are depicted. As shown in the figure, the energy separation between the 4f ground state of Eu2+ and the top of the VB is of ~3.6 eV, which is related to the energy of the CT from the neighboring O2- to the Eu3+ (with the experimental value of 4.13 eV) [35,36]. When the defects VCa are introduced in the vicinity of Eu2+ ions, they would capture the electrons of the Eu2+ and hence stabilize the Eu3+ at Ca2+ sites in β-Ca2SiO4. The 4f ground state of Eu3+ immerges in the VB, and its energy separation with the top of the VB is of ~4.4 eV, as shown in Fig. 9b. Hence, the 4f ground states of Eu2+ and

Eu3+ in β-Ca2SiO4 are separated by ~8.0 eV. This value is in reasonably good agreement with that obtained from Dorenbos models [43-45], i.e., in the range from 5.0 to 8.0 eV, which relates to the distances between the dopant Eu and its ligands.

Fig. 10. Schematic diagrams of the 4f energy-level structures of (a) Eu2+ and (b) Eu3+ ions in β-Ca2SiO4.

4. Conclusions In the present work, the energetic properties and electronic structures of defects/dopants in undoped and Eu-doped β-Ca2SiO4 were investigated by means of DFT calculations performed on the constructed 2 × 2 × 1 supercells containing intrinsic defects (VO and VCa) and/or dopant EuCa. The results of calculated formation energies reveal that neutral defects VCa and EuCa tend to occupy seven-coordinated calcium sites in β-Ca2SiO4, and also clarify that the preferences of intrinsic defects in different charge states changing with the Fermi level. Moreover, the electronic structures of vacancies, dopant EuCa and Eu-related defect complexes (EuCa+VO and EuCa+VCa) were obtained from DFT calculations with HSE06 hybrid functional. It can be found that the neutral and single-negatively charged VCa may trap the electrons of Eu2+ ions, stabilizing Eu3+ ions at Ca2+ sites in β-Ca2SiO4: Eu phosphors, but not the neutral and positively charged VO. The good agreement between the calculation and experiment demonstrates that hybrid DFT calculations can reasonably describe the host band gap (with the calculated and experimental values of 6.0 and 6.8 eV, respectively) and the locations of defect states in the band gap (e.g., Eu 4f states as well as vacancy-induced states) for β-Ca2SiO4: Eu phosphors. Thus, this study may contribute to analyze the stability, transformation and coexistence of the different valence states of europium ions in terms of the chemical compositions and microscopic structure features of solid materials.

Acknowledgments This work was financially supported by Anhui Provincial Natural Science Foundation (Grant No. 1508085QA09), National Natural Science Foundation of China (Grant Nos. 11274299, 11574003 and 11374291) and the Committee on Research and Development and Dean’s Research Grants of the Faculty of Liberal Arts and Social Sciences, HKIEd. Parts of the numerical calculations in this work have been done on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.

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