Thermodynamic Stabilities, Electronic Properties, and Optical

Article Cite This: Inorg. Chem. 2018, 57, 6142−6151

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Thermodynamic Stabilities, Electronic Properties, and Optical Transitions of Intrinsic Defects and Lanthanide Ions (Ce3+, Eu2+, and Eu3+) in Li2SrSiO4 Jun Wen,*,† Zhidong Guo,‡ Hai Guo,§ Lixin Ning,*,∥ Chang-Kui Duan,*,⊥ Yucheng Huang,∥ Shengbao Zhan,† and Min Yin⊥

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†

School of Physics and Electronic Engineering and ‡Department of Mathematics, Anqing Normal University, Anqing 246133, China § Department of Physics, Zhejiang Normal University, Jinhua 321004, China ∥ Anhui Province Key Laboratory of Optoelectric Materials Science and Technology, Department of Physics, Anhui Normal University, Wuhu, Anhui 241000, China ⊥ Department of Physics, University of Science and Technology of China, Hefei 230026, China ABSTRACT: Geometric structures, electronic properties, thermodynamic stabilities, and optical transitions of intrinsic defects (vacancies and antisite defects) and lanthanide ions (Ce3+, Eu2+, and Eu3+) in Li2SrSiO4 (LSSO) host are studied by theoretical calculations combined with hybrid density functional theory, the multireference configuration interaction method, and empirical models. Calculations on the defect formation energies and the ab initio simulations of 4f → 5d electronic transitions for Ce3+ ions determine the most possible charge-compensation mechanism and accurately identify excitation bands in experimental spectra for LSSO:Ce3+ phosphors. On the basis of previously reported experimental spectra of Ce3+- and Eu3+-doped LSSO phosphors as well as a series of empirical models developed by Dorenbos, the locations of the 4f ground states and the lowest 5d excited states of Ln3+ and Ln2+ ions in the host (illustrated by the host-referred binding energy scheme, i.e., the HRBE scheme) are obtained, which is useful for the investigation of the electron-transfer and spectroscopic properties in lanthanide-doped LSSO. Moreover, thermodynamic and optical transition energy levels related to intrinsic defects and lanthanide ions (with various charge states) are derived from total energy calculations. The mechanisms of thermoluminescence (TL) and long-lasting luminescence (LLL) in LSSO:Eu2+,Dy3+ phosphors and especially the contributions of oxygen vacancies (VO) and Dy3+ dopants are then interpreted. The aim of this study is thus to deeply understand the mechanisms of charge compensation, TL, and LLL in lanthanide-doped phosphors from theoretical calculations and analyses.

1. INTRODUCTION Inorganic materials activated by Ce3+ or Eu2+ ions have been extensively investigated with experimental1−14 and theoretical15−26 approaches because of their important applications in solid-state lighting based on phosphor-converted light-emitting diodes (pc-LEDs). In phosphors, both Ce3+ and Eu2+ ions usually present prominently intense and wide emissions, which are attributed to electric-dipole-allowed transitions from the 5d to 4f energy levels. The 5d → 4f electronic transitions are relatively easily affected by the local atomic structures around the lanthanide ions. Researchers recently report the tuning of photoluminescence (PL) in Ce3+- and Eu2+-doped phosphors by modulating occupation sites, chemical compositions, and crystal phases.2,4,7,8,12 Under various synthesis conditions, intrinsic defects of different types and concentrations (such as vacancies, antisite defects, and dopants) are inevitably introduced into undoped and dopant-activated hosts. They are sometimes supposed to play an important role in the luminescence procedures of undoped and doped hosts.27−37 On the one hand, the formation of intrinsic defects occasionally © 2018 American Chemical Society

results in an effective transformation from poorly to highly luminescent phases of hosts, a change of the local environments, and conversion of the valence states of the lanthanide ions.27,29,34 Some studies have revealed that the defects/ dopants contribute to the reduction of Eu3+ ions, realizing the tunable coexistence of Eu2+ and Eu3+ ions in the same crystal lattices.27,29 Besides, Zhang et al. show that chemical pressure relaxation via mediation of the oxygen vacancies provides an effective way to significantly improve the PL emission of phosphors containing large size-mismatched dopants.34 On the other hand, defect-induced luminescence has been discovered and studied in a series of hosts without doping lanthanide or other active ions.30,31,35 In the present work, the geometric structures, electronic properties, thermodynamic stabilities, and optical transitions of intrinsic defects (vacancies and antisite defects) and lanthanide dopants (Ce3+, Eu2+, and Eu3+ ions) in the Li2SrSiO4 (LSSO) Received: March 21, 2018 Published: May 9, 2018 6142

DOI: 10.1021/acs.inorgchem.8b00752 Inorg. Chem. 2018, 57, 6142−6151

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Inorganic Chemistry

Etot[perfect] is the counterpart of the perfect supercell. ni denotes the difference in number for the atom of the element i between the supercells of defect-containing and perfect hosts. It should be noted that ni > 0 and ni < 0 when the atoms (of the element i) are added to and removed from the perfect supercell, respectively. μi is the atomic chemical potential of the element i. EF is the location of the Fermi energy level with respect to that of the valence-band maximum (VBM) of the system (εVBM). With PBE0-optimized crystal structures, the Ce3+-center clusters (with the neighboring oxygen and lithium ions) embedded into the LSSO host were constructed and the wave function-based embeddedcluster ab initio calculations (as implemented in the MOLCAS program)51 were sequentially carried out for the purpose of simulating 4f → 5d transitions in LSSO:Ce3+ phosphors. A relativistic effective core potential ([Kr] core) with a (14s10p10d8f3g)/[6s5p6d4f1g] Gaussian valence basis set was used for cerium,52 a [He] core effective core potential with a (5s6p1d)/[2s4p1d] valence basis set was used for oxygen,53 and a [He] core effective core potential with a (5s1p)/ [2s1p] valence basis set was used for lithium.53 The accurate quantumchemical ab initio calculations were used to treat the valence electrons of the atoms in the defect clusters, whose immediate host environments were described by the embedding ab initio model potentials (AIMPs)54 located at the host lattice sites within a sphere with a radius of 10.0 Å. The point charges, which were situated at the lattice sites within a sphere shell with inner and external radii of 10.0 and 50.0 Å, respectively, were used to represent the lattice environments outside the AIMPs. It should be noted that the CASSCF/CASPT2/RASSI−SO methods55−60 adopted in the embedded-cluster ab initio calculations usually present relatively accurate energies and the corresponding oscillator strengths for 4f → 5d transitions of Ce3+ ions in hosts.

host (which has received considerable experimental research38−44) are investigated in detail to understand the mechanisms of charge compensation, thermoluminescence (TL), and long-lasting luminescence (LLL) in the phosphors. The first-principles calculations combined with density functional theory (DFT) under the hybrid Perdew−Burke− Ernzerhof (PBE0) functional and multireference configuration interaction method at the complete-active-space self-consistentfield/complete-active-space second-order perturbation theory/ restricted-active-space state-interaction spin−orbit (CASSCF/ CASPT2/RASSI−SO) level are first performed on the constructed geometric models (supercells and embedded clusters), which accurately simulate local atomic structures around intrinsic defects and/or extrinsic lanthanide dopants. The results from the first-principles calculations above are then analyzed in combination with the point defect thermodynamics and empirical models. Thus, the relationship between the macroscopically spectroscopic properties of lanthanide-doped LSSO phosphors and microstructures around defects/dopants therein is investigated straightaway. Such information is hardly directly determined from the usual experimental measurements. Calculations and analyses of this work may be further extended to other phosphors in order to deeply explore the microcosmic mechanisms of the interaction between lanthanide ions and intrinsic defects and study their influences on the luminescent properties of phosphors. The rest of the study is arranged as follows. Section 2 presents a description of the calculation methods adopted in this work. The results and discussion of the geometric and electronic properties of perfect, defect-contained, and lanthanide-doped LSSO, the 4f → 5d transition of Ce3+ ions, the host-referred binding energy (HRBE) scheme for the 4f ground states and the lowest 5d excited states of lanthanide ions (both bivalent and trivalent ones), the thermodynamic stabilities, and the thermodynamic/optical transition energy levels of defects and dopants in the LSSO host are provided in section 3. Finally, the conclusions are given in section 4.

3. RESULTS AND DISCUSSION 3.1. Geometric Structures of Pure and LanthanideDoped LSSO. The LSSO host crystallizes in the hexagonal structure with the space group P3121 (No. 152), as illustrated in Figure 1a. There are 24 atoms (three chemical formulas) in the unit cell of the lattice. The PBE0-optimized lattice parameters are a = b = 5.019 Å, c = 12.434 Å, α = β = 90°, and γ = 120°, which are in excellent agreement with the experimental measured ones (a = b = 5.023 Å, c = 12.455 Å, α = β = 90°, and γ = 120°).61 The largest deviation of the calculated and experimental values is less than 0.2%, indicating

2. COMPUTATIONAL METHODS The geometric structures and electronic properties of perfect, defectcontaining, and lanthanide-doped (Ce3+-, Eu2+-, and Eu3+-doped) LSSO crystals were obtained from the hybrid DFT calculations (as implemented in the VASP program)45,46 with the revised PBE0 functional, which contains 32% of exact Hartree−Fock (HF) exchange and 68% of PBE exchange as well as 100% of PBE correlation energy.47,48 The Li 2s1, Sr 4s24p65s2, Si 3s23p2, O 2s22p4, Ce 5s25p64f15d16s2, and Eu 5s25p64f76s2 electrons were treated as the valence electrons. Their interactions with ion cores were described by the projected-augmented-wave method.49 The geometric structures of the systems were fully optimized, with a convergence criteria of 10−5 eV used for the change in the total energy and a counterpart of 0.01 eV/Å used for Hellman−Feynman forces on atoms. The cutoff energy of 550 eV was used for the basis set of the plane waves. The one k point (Γ point) for the sampling of the Brillouin zone (BZ) was adopted in the geometry optimization calculations, considering the large amount of hybrid PBE0 calculations. Using PBE0-calculated total energies of the supercells for LSSO hosts without and with defects/dopants, the formation energy (ΔEf) of the defect D (with the charge state q) in the host is derived from50 ΔEf [Dq ] = Etot[Dq ] − Etot[perfect] −

∑ niμi + q(EF + εVBM) i

(1)

Figure 1. Schematic representations of (a) the geometric structure of the 2 × 2 × 1 supercell of the LSSO host and (b) local atomic structures around the Sr atom.

q

where Etot[D ] is the PBE0-calculated total energy of the supercell for the LSSO host containing defect D with the charge state q and 6143


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Inorganic Chemistry the superiority of the hybrid PBE0 functional. In the LSSO host, there are one type of Li site, one type of Sr site, one type of Si site, and two types of crystallographically different O sites (denoted as OI and OII). Both Li and Si atoms are coordinated by four O atoms, while the Sr atom is surrounded by eight O atoms and possesses the point-group symmetry of C2 (see Figure 1b). The ionic radii of Ce3+, Eu2+, and Eu3+ with a coordination number of 8 are 1.143, 1.250, and 1.066 Å, respectively, in comparison with those of 1.260 and 0.920 Å for the eightcoordinated Sr2+ and Li+ ions, respectively.62 In consideration of the relatively large discrepancy of both the valence state and ionic radius between lanthanide and Li ions as well as the low coordination number (of 4) for the Li sites, lanthanide ions (Ce3+, Eu2+, and Eu3+) doped into the LSSO host are supposed to occupy Sr sites rather than Li sites. The formation energy calculations also confirm that the defect configuration CeSr++VLi− is much more energetically stable than the CeLi2++VSr2− with an energy advantage of 1.92 eV. When the LSSO samples doped with trivalent lanthanide ions are synthesized, the defects or dopants would be simultaneously introduced to compensate for the charge mismatch between them (Ce3+ and Eu3+) and the lattice cation (Sr2+). The chargecompensating defects (such as VLi− and LiSr−) tend to approach trivalent lanthanide centers because of their opposite charges, which is also verified by calculated formation energies. Thus, the configurations of defect complexes, with the shortest distance between the Ce3+ (Eu3+) centers and the chargecompensating defects, are taken into account. In Table 1,

Figure 2. Total and orbital-projected DOSs for the LSSO obtained from the DFT−PBE0 method with 32% exact HF exchange. The Fermi energy level is labeled by the vertical dashed line, similarly hereinafter.

along with the hybridization of O 2p states. The band gap of the LSSO host calculated from the revised PBE0 functional is 7.35 eV, a little larger than the energy value (7.12 eV) of the maximum of the band in the vacuum ultraviolet (UV)/UV excitation spectra of Ce3+ emission,41 which corresponds to the host lattice absorption and is actually the optical band gap. According to Dorenbos,63 the band-gap energy of the LSSO host can be estimated to be 1.08 times as much as the energy value above, which just relates to creation of the electron−hole pair in the exciton. It means that the binding energy of the exciton is about 8% of the creation energy of the electron−hole pair. Hence, the electronic band gap of the LSSO host from hybrid DFT calculations (with the revised PBE0 functional) is a little smaller than the experimentally determined one (of 7.69 eV). They demonstrate a significant improvement in comparison with the conventional DFT calculations under local density approximation or generalized gradient approximation. It should be noted that the usual PBE calculations in this work give the LSSO host a band gap (of 4.00 eV) much smaller than the experimental one (by 3.69 eV). The total and orbital-projected DOSs for defect configurations of CeSr++VLi− (i.e., Ce3+ ion), VLi−, EuSr (i.e., Eu2+ ion), and EuSr++VLi− (i.e., Eu3+ ion) in the 2 × 2 × 1 supercell of the LSSO host are calculated from the hybrid DFT with the revised PBE0 functional, as shown in Figures 3a,b and 4a,b, respectively. Figures 3a and 4a,b exhibit the typical characteristics of the DOSs caused by Ce3+, Eu2+, and Eu3+ ions in hosts, respectively, which indicates that lithium vacancies in both the complexes CeSr++VLi− and EuSr++VLi− are actually singly negatively charged (i.e., VLi−), achieving the charge compensation between trivalent lanthanide and divalent strontium ions (i.e., CeSr+ and EuSr+). It can be confirmed by the fact that the defect state (see Figure 3b) relating to the single VLi− with one electron locates in the top section of the VB rather than in the band gap, while that introduced by the single neutral VLi is above the VBM. In Figure 3a, the defect state in the band gap is due to the occupied 4f state of the Ce3+ ion (with one 4f electron), and its energy difference with respect to the VBM is about 1.75 eV. The unoccupied 4f and 5d states of the Ce3+ ion locate at the bottom of the CB. For Eu2+-doped LSSO, the defect states in the band gap (see Figure 4a) are also ascribed to

Table 1. PBE0-Optimized Bond Lengths (Å) between the Sr2+ (Lanthanide) and Coordinated O2− Ionsa bond length

M = Sr2+

M = Ce3+

M = Eu2+

M = Eu3+

M−O1 M−O1 M−O2 M−O2 M−O3 M−O3 M−O4 M−O4 average

2.558 2.558 2.641 2.641 2.644 2.644 2.660 2.660 2.626

2.387 2.595 2.652 2.612 2.403 2.689 2.386 2.765 2.561

2.562 2.561 2.644 2.653 2.648 2.651 2.656 2.661 2.629

2.354 2.569 2.600 2.558 2.319 2.574 2.351 2.854 2.522

a

A vacancy is at the nearest-neighboring Li site around the Ce3+ and Eu3+ ions for charge compensation between them and the Sr2+ ions.

PBE0-optimized bond lengths of the center ions (at Sr sites) and the coordinated O2− ions are listed. One can see that the doping of lanthanide ions would lower the local symmetry of the Sr2+ sites, especially for Ce3+ and Eu3+ ions with VLi− in their local environments. The averaged bond length between Ce3+ and O2− ions is 2.561 Å, a little smaller than that of the counterpart for Sr2+ (Eu2+) ions with a corresponding value of 2.626 (2.629) Å. Besides, the bond lengths for the Eu3+ ion are much smaller than those for the Eu2+ ion, in accordance with the variation trend of the radii of both Eu ions. 3.2. Electronic Structures of Pure, Defect-Containing, and Lanthanide-Doped LSSO. The total and orbitalprojected density of states (DOSs) for the perfect LSSO host (as shown in Figure 2) is derived from hybrid DFT calculations with the revised PBE0 functional. The top of the valence band (VB) is mainly made up of the O 2p states, while the bottom of the conduction band (CB) is constituted by the Sr 3d states 6144


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Figure 3. Total and orbital-projected DOSs for (a) CeSr++VLi− (i.e., Ce3+ ion) and (b) VLi− in the 2 × 2 × 1 supercell of the LSSO host obtained from the DFT−PBE0 method with 32% exact HF exchange. The distance between both defects in the complex CeSr++VLi− is the shortest.

Figure 4. Total and orbital-projected DOSs for (a) EuSr (i.e., Eu2+ ion) and (b) EuSr++VLi− (i.e., Eu3+ ion) in the 2 × 2 × 1 supercell of the LSSO host obtained from the DFT−PBE0 method with 32% exact HF exchange. The distance between both defects in the complex EuSr++VLi− is the shortest.

the LSSO host are derived, as shown in Table 2. Only 4f → 5d transitions of Ce3+ ions at Sr sites in the host are simulated in the present work in consideration of much larger formation energy of Ce3+ ions at Li sites (as described before). Also, the defects VLi− and LiSr− are introduced in the local environments of CeSr+ centers to compensate for the charge mismatch. From Table 2, one can see that the neighboring VLi− around the CeSr+ center would significantly increase its lowest 5d energy level (i.e., 5d1 level) in comparison with the case with a relatively far VLi−, although formation energy calculations show that VLi− tends to be close to the CeSr+ center. The calculated 5d energylevel structure (especially the 5d1−4 levels) for the CeSr+ center accompanied by the nearest antisite defect LiSr− shows a high similarity with those of the CeSr+ center along with a relatively far VLi−. It can be attributed to the fact that the shortest distance between two Sr sites in the host is still relatively far (of 4.897 Å). Besides, the calculated centroids (ΔEced) of the 5d energy levels of the Ce3+ ions in the host slightly change with their local environments and agree well with the experimental value,42 while their crystal-field splittings (ΔEcfs) are much larger than the experimental one.42 By a comparison of the calculated and experimental results, the measured excitation spectra of Ce 3+ -doped LSSO phosphors are mainly ascribed to the 4f → 5d transitions of

the occupied 4f states of the Eu2+ ion (with seven unpaired 4f electrons), showing the much stronger intensity than that of the Ce3+ ion. The energy separation between the occupied 4f states of the Eu2+ ion and the VBM is 3.01 eV, much larger than that for the Ce3+ ion. In the DOS pattern of Eu3+-doped LSSO (as shown in Figure 4b), the spin-up defect states due to the occupied 4f states of the Eu3+ ion (with six unpaired 4f electrons) immerge in the VB, and the energy separation between their first peak (the highest one) and the VBM is about 4.26 eV. As for the unoccupied 4f states of the Eu3+ ion, the spin-up part is situated at 3.75 eV in the band gap, while the spin-down parts immerge in the bottom of the CB. The hybrid DFT calculations could provide relatively accurate locations of the 4f and 5d states of the lanthanide ions (such as Eu2+) in the energy bands of the hosts, in comparison with the conventional DFT calculations.64 For example, PBE calculations in this work predict that the location of the occupied 4f states of the Eu2+ ion approaches the CB minimum (CBM) of the LSSO. 3.3. 4f → 5d Transitions of Ce3+ Ions in LSSO. According to the CASSCF/CASPT2/RASSI−SO calculations performed on the defect clusters (CeSrO8Li5)8− (for the CeSr+ center with a neighboring VLi−) and (CeSrO8Li6)7− (for the CeSr+ center with a relative far VLi− or a LiSr−) embedded into the host, the 4f and 5d crystal-field energy levels of Ce3+ ions in 6145


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Inorganic Chemistry Table 2. Calculated Energies (in cm−1) of the 4f1 and 5d1 Levels for Ce3+ Ions in the LSSO Host by Using the CASSCF/CASPT2/RASSI−SO Methoda centers, clusters CeSr +VLi(1nn)−, (CeSrO8Li5)8−

CeSr++VLi(far)−, (CeSrO8Li6)7−

CeSr++LiSr(1nn)−, (CeSrO8Li6)7−

exptl42

0 615 955 2216 2615 3308 3562 26548 36104 40197 47699 50933 40296 24385

0 383 664 2231 2541 2872 3158 25026 36773 40323 47430 49591 39829 24565

0 521 986 2226 2618 3016 3724 25264 36812 40644 47180 50802 40140 25538

28011 35971 40000 45045 48077 39421 20066

+

4f1 4f2 4f3 4f4 4f5 4f6 4f7 5d1 5d2 5d3 5d4 5d5 ΔEced ΔEcfs

Figure 5. Schematic diagram for the calculated energies and relative oscillator strengths of 4f1 → 5di (i = 1−5) transitions for the CeSr++VLi− complex (with the shortest distances between the two defects) in the LSSO host, along with the experimental excitation spectrum.42

a The “1nn” in the bracket behind the atomic symbol denotes the nearest-neighboring site around the Ce3+ ions, and the “far” in the bracket denotes the relatively far site. It should be noted that the experimental values below are taken from those of the maximum of the peaks of excitation bands.

3.4. Energy-Level Diagram for Ln2+ and Ln3+ Ions in LSSO. Using the experimental spectra of Ce3+- and Eu3+-doped LSSO phosphors,39,41 the HRBE scheme for the 4f ground states (i.e., 4f1) and the 5d1 states of Ln3+ and Ln2+ ions at the Sr sites in the LSSO host is derived from a series of empirical models developed by Dorenbos.65−68 The charge-transfer (CT) model65 gives the positions of the 4f ground states of the lanthanide ions relative to the VBM of the host. The peak energy (of 5.14 eV) of the CT excitation absorption band (with the peak at 241 nm) in the experimental spectra41 of LSSO:Eu3+ phosphor provides the location of the 4f ground state of the Eu2+ ion above the VBM, and the counterpart of the Eu3+ ion is determined from their energy difference [denoted as the Coulomb repulsion energy U(6)]. In the chemical shift model, U(6) is empirically expressed as follows:66

the CeSr+ centers along with the neighboring VLi−. There are two main reasons for the conclusion. First, the deviation of its 5d1 level from the experimental value is about 1500 cm−1 (with an error of ∼5%),42 while the counterparts for the Ce3+ centers along with the relatively far VLi− and LiSr− are ∼3000 and ∼2700 cm−1 (both with errors of ∼10%), respectively. The second reason is that the defect complex CeSr++VLi− with the shortest distance between two defects (denoted as CeSr++VLi(1nn)−) in the LSSO host has the lowest defect formation energy (with the energy advantage of hundreds of millielectronvolts, as listed in section 3.5), implying that they may be more easily generated. The insufficiency of Li sites in the LSSO host is confirmed via the measurement of inductively coupled plasma atomic emission spectroscopy,38 which shows that the molar ratio of Li/total cations is on average 0.48 (less than the value of 0.50 in the ideal stoichiometry of the host). In Figure 5, the schematic diagram for the calculated energies and relative oscillator strengths of the 4f1 → 5di (i = 1−5) transitions for the CeSr++VLi(1nn)− complex in the LSSO host is depicted, showing a reasonably good agreement with the experiment.42 The first three excitation bands in the spectra of Ce3+-doped LSSO phosphors are thus attributed to the 4f → 5d1−3 transitions of the CeSr+ centers with a neighboring VLi−, respectively. Meanwhile, the deviations between ab initio calculated 5d4,5 energy levels and the corresponding experimental values are relatively large (2600−2900 cm−1). It should be noted that the ab initio calculated energies of the 4f → 5d transitions of Ce3+ ions correspond to those of zero-phonon lines (ZPLs), whose positions in the experimental spectra are near long-wavelength edges of the respective broad bands (see bands A−E in Figure 5). In one word, the type of chargecompensating defects in the local environment of the CeSr+ centers and the origins of the excitation bands in the experimental spectra are successfully determined from the theoretical calculations on the defect formation energies and the 4f → 5d transitions of the Ce3+ centers.

U(6) = 5.44 + 2.834e−ΔEC /2.2

(2)

where ΔEC is the shift of the centroid of ab initio calculated 5d levels of the Ce3+ ion in the host (of 5.00 eV) with respect to that in the free-ion case (of 6.32 eV).69 Then, the locations of the 4f ground states for all of the other Ln2+ and Ln3+ ions in the LSSO host are derived from the changing trend of the 4f ground states of the lanthanide ions, which is independent of the hosts.67 With the energy (∼3.31 eV) for the ZPL of the 4f1 → 5d1 transition of the Ce3+ ion (i.e., the energy corresponding to the point of intersection of the experimental excitation and emission spectra of LSSO:Ce3+ phosphors),39 the locations of the lowest 5d1 energy levels of the Ce3+ ion and further the other Ln3+ ions in the host are obtained from the red-shift model.68 In the model, the red-shift D(2+,A) for the Ln2+ ion in the host A can be estimated from the following relationship:68 D(2 + , A) = 0.64D(3 + , A) − 0.233 eV

(3)

where D(2+,A) and D(3+,A) stand for the red shift of the 4f1 → 5d1 transition of the Ln2+ and Ln3+ ions in the host A relative to the free-ion case, respectively. Consequently, the locations of the lowest 5d1 energy levels of the Ln2+ ions in the host are finally presented. It should be noted that both locations of the low-spin (LS) and high-spin (HS) 5d1 levels for trivalent lanthanide ions with more than seven 4f electrons are 6146


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After grinding, the mixtures of the precursor compounds (Li2CO3, SrCO3, SiO2, CeO2, and Eu2O3) are heated at about 1000 K for several hours under a reducing atmosphere. In the present work, intrinsic vacancies at host sites (VO, VLi, VSr, and VSi) and antisite defects (LiSr and SrLi) are thus taken into account to study their thermodynamic stabilities and effects on the electronic and luminescent properties of lanthanide-doped LSSO phosphors. The defect formation energies for various neutral defects are calculated from the PBE0-calculated total energies of the corresponding supercells, as listed in Table 3.

presented, according to the empirical energy differences between the LS and HS 5d1 levels of the Ln3+ ions (from Tb3+ to Lu3+).67 The electronic transitions to the LS 5d states are spin-allowed, while those to the HS 5d states are spinforbidden. Actually, the excitation bands corresponding to the spin-forbidden transitions to the HS 5d states are usually well seen in experimental spectra for heavy lanthanide ions70 because they are situated at lower photon energies than the bands corresponding to the spin-allowed transitions. The locations of the energy levels of the Ln2+ and Ln3+ ions in the energy band of the host from Figure 6 are helpful to

Table 3. Calculated Formation Energies ΔEf (from the PBE0 Total Energies of Various Supercells) of the Neutral Defects and Defect Complexes in the LSSO Host under the Reducing Condition (i.e., the Oxygen-Poor Condition) defects ΔEf (eV)

ΔEf (eV)

VOI

VOII

VLi

0.69

0.62

5.04 defects

LiSr

SrLi

5.42

3.08

VSr

VSi

10.17

14.81

EuSr

EuSr++VLi−

0.34

3.64

defects CeSr++VLi(1nn)− CeSr++VLi(far)− CeSr++LiSr(1nn)− CeLi2++VSr2− ΔEf (eV)

0.42

0.78

0.70

2.34

Considering the reducing condition adopted for preparation of the phosphors, the chemical potentials μ of the Li, Sr, and Si atoms derive from PBE0-calculated energies per atom in the unit cells of the corresponding bulk materials and that of the O atom is calculated from the thermal equilibrium conditions of the host, as follows: 2μLi + μSr + μSi + 4μO = μLi SrSiO (4)

Figure 6. HRBE scheme for the 4f ground states and lowest 5d1 states of the Ln3+ and Ln2+ ions at the Sr sites in the LSSO host. The band gap is set as the experimentally determined value (7.69 eV).

study the electron-transfer and spectroscopic properties and further interpret the luminescent mechanism in lanthanidedoped LSSO phosphors. In experiments, the Eu2+-doped LSSO phosphor shows the intense absorption with the wide band in the range of 370 and 520 nm, and the energy of the ZPL for the 4f1 → 5d1 transition is about 2.38 eV.41 In the derived HRBE scheme, the energy difference between the 5d1 and 4f1 states of the Eu2+ ion in the LSSO host is about 2.65 eV, showing a reasonably good agreement with the experiment. Figure 6 thus provides a relatively accurate prediction for the locations of the 4f1 and 5d1 energy levels of the Ln2+ and Ln3+ ions in the LSSO host. Considering that the 4f energy levels of the lanthanide ions change slightly with respect to the host compounds, the data of the energy levels (with the energy range of more than 5.0 eV) in Dieke (and extending Dieke) energy-level diagrams71,72 can be added to multielectron 4f ground states of trivalent and divalent lanthanide ions in the LSSO host, deriving the locations of the corresponding 4f excited states in the energy band of the host. Moreover, the LSSO:Eu2+,Dy3+ has been recently developed as a novel orange-yellow longlasting phosphor.43 As described above, the positions of the high 4f1 energy levels of the Nd2+, Dy2+, Ho2+, and Tm2+ ions are below and close to the CBM, indicating that the corresponding trivalent lanthanide ions may be predicted to be suitable electron traps for the LLL. 3.5. Defect Formation Energies and Thermodynamic Transition Energy Levels of Intrinsic Defects and Lanthanide Dopants in LSSO. The lanthanide-doped LSSO phosphors are usually synthesized by solid-state reaction.

2

4

where μLi2SrSiO4 is the PBE0-calculated total energy per formula unit of the LSSO host. Among the single defects, the defect formation energies of the neutral VSr and VSi are very large, in agreement with the case (VCa and VSi) of the Ca4F2Si2O7 host.26 This indicates that they hardly exist in the host prepared under the reducing atmosphere. Table 3 also shows that the vacancies at the O sites have relatively low defect formation energies, which are almost the same for the neutral VOI and VOII (of 0.69 and 0.62 eV, respectively) because of similar local environments. The defect formation energies of the neutral VO would increase by 5.67 eV, when the chemical potential of the O atom corresponding to the O-rich condition is considered. This means that the neutral VO is easily created in the host (prepared under the reducing condition) and may contribute to the luminescence in lanthanide-doped LSSO. Besides, the neutral antisite defect SrLi has much smaller formation energy than LiSr. As for lanthanide dopants, they prefer to occupy the Sr sites rather than the Li sites, and the charge-compensating defect (VLi−) tends to approach CeSr+ and EuSr+. From the energy point of view, the CeSr++VLi(1nn)− configuration is the most possible one in LSSO:Ce3+ phosphors, in accordance with the simulated results of the 4f → 5d transitions of the Ce3+ ions in section 3.3. It should be noted that the calculated defect formation energy of EuSr++VLi− (3.64 eV) is in good agreement with that from DFT+U calculations by Kim et al. (3.83 eV).38 From the formation energies of easily generated defects (VO, VLi, SrLi, and LiSr) and lanthanide dopants (CeSr and EuSr) with 6147


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Figure 8. Configuration−coordinate diagram for (a) neutral EuSr (i.e., Eu2+ ion) along with the exchange of an electron with the CBM and (b) EuSr+ (i.e., Eu3+ ion) along with exchange of a hole with the VBM in the LSSO host.

Figure 7. Thermodynamic transition energy levels for the dopants (CeSr and EuSr) and defects (VO, VLi, LiSr, and SrLi) in the LSSO host calculated from the PBE0 hybrid functional.

q′) of a defect D is defined as the position of the Fermi energy level where the defect formation energy of D with the charge state q is equal to that with the charge state q′. In the figure, the label (q/q′) indicates that in the band gap below the horizontal line D with the charge state q will be stable, while D with the charge state q′ will be stable above the line. One can see that VO prefers the positively divalent charge state (VO2+) when the Fermi level is below 3.36 and 3.33 eV for VOI and VOII, respectively, which corresponds to the oxidizing atmosphere in the synthesis.73 It prefers the positively single charge state (VO+) when the Fermi level is in the middle region of the band gap (with widths of 0.45 and 0.57 eV for VOI and VOII, respectively), which approximately relates to the neutral atmosphere. The neutral charge state of VO is the most stable when the Fermi level is in the range of 3.81 and 6.53 eV as well as 3.90 and 6.55 eV for VOI and VOII, respectively, which corresponds to the reducing atmosphere. The ε(0/−) levels of both VLi and LiSr are close to the VBM (0.89 and 0.93 eV, respectively), implying that they would be in the negative single charge state (VLi− and LiSr−) in most regions of the band gap, i.e., under various atmospheres. Besides, the ε(+/0) level of SrLi locates at the 1.03 eV below the CBM, indicating that the SrLi+ is much more stable than the neutral one in the usual experiment. It should be noted that the energy differences of the above ε(q/q′) levels and the CBM/VBM correspond to the energies of the ZPLs for the electronic transitions between the defect levels and CBM/VBM, whose optical transition energy levels are presented in the section below. 3.6. Optical Transition Energy Levels of Intrinsic Defects in LSSO and Mechanisms for TL and LLL in LSSO:Eu2+,Dy3+. On the basis of the differences of the PBE0calculated total energies of the supercells containing the dopant/defect (EuSr and VOI) in different charge states, their optical transition energy levels are derived, as shown in Figures 8−10. The detailed description of the optical transition energy levels can be found in the previous study.74 One can see that the energy for the transformation from Eu2+ to Eu3+ (4.94 eV in Figure 8a) is much larger than that from Eu3+ to Eu2+ (4.10 eV in Figure 8b). Although there are no corresponding

Figure 9. Configuration−coordinate diagram for (a) neutral VOI and (b) VOI+ along with exchange of an electron with the CBM as well as (c) VOI2+ and (d) VOI+ along with exchange of a hole with the VBM of the LSSO host.

Figure 10. Configuration−coordinate diagram for (a) neutral VOI along with exchange of an electron with the VBM and (b) VOI− along with exchange of an electron with the CBM of the LSSO host.

experimental results, the calculated energies related to the transformation between the Eu2+ and Eu3+ ions may be useful for the prediction of the valence stability of Eu ions in phosphors.73 In addition, the energies related to the exchange of the electron (hole) between VOI in different charge states and the CBM (VBM) are calculated, as shown in Figures 9a,b 6148


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contribute to the LLL (as described above), greatly improving the long-persistent properties of the phosphors.

(Figures 9c,d). It should be noted that the differences of optical transition energies between VOI and VOII are slight (∼0.1 eV), so that only the energies for VOI in the LSSO host are given. We may thus conclude that the electronic transitions associated with VO in positive charge states (VO+ and VO2+) are not responsible for the TL of LSSO:Eu2+,Dy3+ because of the much larger excitation energies (of more than 4.0 eV) than the experimentally determined trap depth (of 0.83 eV).43 Cheng et al. attribute the traps exhibited in the TL curve of LSSO:Eu2+,Dy3+ to intrinsic defects in the host.43 They point out that VO2+ (as the electron trap) is responsible for the LLL of the sample. The presented calculations on the thermodynamic stabilities, optical transition levels of intrinsic defects, and energy-level diagram of lanthanide ions in the host demonstrate that neutral VO and VO− may play an important role in the LLL. As shown in Figure 7, neutral VO (with the defect formation energy of less than ∼0.7 eV) is supposed to be stable in phosphors prepared under the reducing condition (corresponding to the Fermi level located in the upper-middle part of the band gap). VO− should be metastable, while VO2− is much more unstable than those with +2, 1+, 0, and 1− charge states, unless the Fermi level of the system is very close to that of the CBM. According to our understanding of the TL mechanism, the electrons can be excited from the VBM to the high defect levels of neutral VO (case 1, see Figure 10a) with the excitation energy of 6.82 eV or from the occupied 4f levels of Eu2+ ions to their empty 5d levels (case 2), after the irradiations adopted in the TL measurements. Because of the fact that the lowest 5d energy levels of the Eu2+ ions in LSSO immerge into the CB, the electrons transited to the 5d levels are easily promoted to the CB, where the electrons may also be trapped by neutral VO (see Figure 10b, with the emission energy of 0.53 eV). In both cases above, VO are always no longer neutral but negatively charged (i.e., VO−). Subsequently, thermal activation during TL measurements would move the electrons away from the metastable VO−, along with the excitation energy of 0.74 eV (see Figure 10b). It is a little smaller than the experimental trap depth of 0.83 eV. When these electrons are excited into the CB and become free, they are very possible to recombine with the holes localized at certain defect levels in the band gap or those located in the VBM, generating TL. As for the LLL procedure in the LSSO:Eu2+,Dy3+ phosphor, the 4f electrons of Eu2+ ions are first promoted to the 5d energy levels under UV excitation. The 5d electrons of the Eu2+ ions then can easily transfer to the CB and further be trapped by neutral VO, which would transform into and maintain the negative charge states for a certain time although the excitation source is removed. With thermal agitation, the electrons of metastable VO− can return to the CB and then transfer to the 5d energy levels of the Eu2+ ions, producing emissions of 5d → 4f. In the experiments, the codoped Dy3+ ions would improve the long-persistent properties of phosphors.43 The codoping of Dy3+ ions would not only provide suitable electron traps (as described in section 3.4) but also introduce many more electrons into the host. More importantly, lithium vacancies would be simultaneously introduced into the host in order to compensate for the charge difference between the Dy3+ and Sr2+ ions. The deficiency of cations would be beneficial to the formation of oxygen vacancies (with positive charge states). Under UV light, the electrons of the VBM may be excited to the positively charged oxygen vacancies (see Figures 9c,d). The oxygen vacancies (VO+ and VO2+) thus become neutral and

4. CONCLUSIONS The geometric structures, electronic properties, thermodynamic stabilities, and thermodynamics/optical transitions of intrinsic defects and lanthanide dopants (Ce3+, Eu2+, and Eu3+ ions) in LSSO are investigated in detail, on the basis of first-principles calculations (at the hybrid DFT−PBE0 and CASSCF/ CASPT2/RASSI−SO levels) and empirical models. The calculations on defect formation energies demonstrate that neutral VO is the most stable defect in the undoped samples prepared under reducing atmospheres. They also imply that Ce3+ ions prefer to occupy Sr sites along with the nearestneighboring VLi− for charge compensation, in good agreement with the ab initio simulations of the 4f → 5d transitions of the Ce3+ ions in LSSO. Then, the first three excitation bands in the experimental spectra of Ce3+-doped LSSO are assigned to the 4f1 → 5d1−3 transitions of the Ce3+ ions, respectively, from the embedded-cluster ab initio calculations. Using the experimental excitation spectra, the energy levels of the 4f1 and 5d1 states of the Ln2+ and Ln3+ ions in the HRBE scheme are derived from the empirical models developed by Dorenbos. One may conclude from the HRBE scheme that Dy3+ ions may provide suitable electron traps, beneficial to the long-persistent properties in LSSO:Eu2+,Dy3+ phosphors. Besides, the derived thermodynamic transition energy levels of various defects (VO, VLi, LiSr, and SrLi) and lanthanide ions (Ce and Eu ions) show their most stable charge states with respect to the Fermi energy level of the system (whose location in the band gap relates to the atmosphere in the preparation). The calculated energy of the ZPLs of electronic transitions between the VO− and CB is about 0.65 eV, and the optical transition energy for the electron from VO− to CB is about 0.74 eV, in accordance with the trap depth (∼0.83 eV) determined from the experimental TL curve. Finally, the procedures of TL and LLL in LSSO:Eu2+,Dy3+ phosphors are presented according to analyses of the point defect thermodynamics and HRBE scheme. The framework of calculations and analyses presented in this work may be extended to other lanthanide-doped phosphors to deeply understand the mechanisms of charge compensation, TL, and LLL.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. ORCID

Jun Wen: 0000-0002-0490-3536 Lixin Ning: 0000-0003-2311-568X Chang-Kui Duan: 0000-0003-1016-4976 Yucheng Huang: 0000-0002-7818-8811 Min Yin: 0000-0001-5478-2456 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding support from the National Natural Science Foundation of China (Grants 11604002, 11574003, and 61635012) and National Key Research and Development Program of China (Grant 2016YFB0701001) is gratefully acknowledged. 6149


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Parts of the numerical calculations have been performed on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.

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Thermodynamic Stabilities, Electronic Properties, and Optical

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