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Research on Molecular Structure and Electronic Properties of Ln^{3+} (Ce^{3+}, Tb^{3+}, Pr^{3+})/Li^{+} and Eu^{2+} Co-Doped Sr_{2}Si_{5}N_{8} via DFT Calculation

^{1}

^{2}

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## Abstract

**:**

_{2}Si

_{5}N

_{8}:Eu

^{2+}doped with trivalent lanthanides (Ln

^{3+}= Ce

^{3+}, Tb

^{3+}, Pr

^{3+}). Li

^{+}was used as a charge compensator for the charge imbalance caused by the partial replacement of Sr

^{2+}by Ln

^{3+}. The doping of Ln lanthanide atom causes the structure of Sr

_{2}Si

_{5}N

_{8}lattice to shrink due to the smaller atomic radius of Ln

^{3+}and Li

^{+}compared to Sr

^{2+}. The doped structure’s formation energy indicates that the formation energy of Li

^{+}, which is used to compensate for the charge imbalance, is the lowest when the Sr2 site is doped. Thus, a suitable Li

^{+}doping site for double-doped lanthanide ions can be provided. In Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}, the doped Ce

^{3+}can occupy partly the site of Sr

_{1}

^{2+}([SrN

_{8}]), while Eu

^{2+}accounts for Sr

_{1}

^{2+}and Sr

_{2}

^{2+}([SrN

_{10}]). When the Pr

^{3+}ion is selected as the dopant in Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}, Pr

^{3+}and Eu

^{2+}would replace Sr

_{2}

^{2+}simultaneously. In this theoretical model, the replacement of Sr

^{2+}by Tb

^{3+}cannot exist reasonably. For the electronic structure, the energy level of Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}/Li

^{+}doped with Ce

^{3+}and Pr

^{3+}appears at the bottom of the conduction band or in the forbidden band, which reduces the energy bandgap of Sr

_{2}Si

_{5}N

_{8}. We use DFT+U to adjust the lanthanide ion 4f energy level. The adjusted 4f-CBM of Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}is from 2.42 to 2.85 eV. The energy range of 4f-CBM in Pr

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}is 2.75–2.99 eV and its peak is 2.90 eV; the addition of Ce

^{3+}in Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr1}made the 4f energy level of Eu

^{2+}blue shift. The addition of Pr

^{3+}in Eu

_{Sr2}Pr

_{Sr2}Li

_{Sr1}makes part of the Eu

^{2+}4f energy level blue shift. Eu

^{2+}4f energy level in Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr1}is not in the forbidden band, so Eu

^{2+}is not used as the emission center.

## 1. Introduction

_{2}Si

_{5}N

_{8}alkaline earth metal silicon nitride has been extensively studied in recent years [1,2,3]. When Eu

^{2+}is used as the activating ion, the luminous intensity is the highest. Simultaneously, Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}has become the representative of commercial red fluorescent materials because of its outstanding fluorescence performance in all aspects [4]. However, the main problem is that Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}is sensitive to temperature, and Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}luminous intensity is significantly reduced when the temperature is higher. Considering that M

_{2}Si

_{5}N

_{8}is a layered or similar layered structure, its openness is relatively high so that the above problems can be solved through component engineering [5].

^{2+}ion are several vital factors that affect phosphors’ luminescence performance. They determine the luminescence characteristics by indirectly changing the degree of crystal field splitting (CFS) [6], nephelauxetic effect (NE), the highest and lowest 5d energy level splitting [7,8]. For example, from both experiments and calculations Li [9] and Bulloni [10] proved that Ca

^{2+}partially replaced Eu

^{2+}in Sr

_{2}Si

_{5}N

_{8}matrix’s emission peaks, which tended to appear red-shifted in Eu

^{2+}occupied eight coordination sites, though its stability was reduced. Liu used Ba

^{2+}to replace partial Sr

^{2+}in Sr

_{2}Si

_{5}N

_{8}, after the substitution, the emission peak was blue-shifted. As Eu

^{2+}in the ten-coordinate structure is more stable than the eight-coordinate structure, its thermal stability is improved. Chen [11] performed a doping modification based on Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}. In Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}, part of Al

^{3+}is used to replace Si

^{4+}. As the Al-N bond length is longer than that of Si-N, the bond length between Eu

^{2+}and surrounding N

^{3−}is shorter, the crystal field intensity increases, and the emission peak position is red-shifted. Wang [12] used partial AlO

^{+}instead of SiN

^{+}, and the effects of the increase in the crystal field and the increase in electronegativity cancelled each other out, rendering the peak position unchanged, but the thermal stability and strength increased. In Rb

_{3}Ysi

_{2}O

_{7}:Eu

^{2+}system, the weak covalent interaction of Eu

^{2+}and O

^{2−}prevented Eu

^{2+}from showing red emission [13]. The above-mentioned previous studies had found that different activating ions and ligand sites affected the energy level distribution of the activated ions and f orbitals, thereby affecting the luminescence performance.

^{3+}/Er

^{3+}/Lu

^{3+}into Bi

_{2}Mo

_{6}to enhance its photocatalytic performance. Tang [15] introduced Ce

^{3+}and Tb

^{3+}into Na

_{3}SrMg

_{11}(PO

_{4})

_{9}. There are relatively few reports on the lanthanide Eu

^{2+}doped with M

_{2}Si

_{5}N

_{8}as the base material and further doped with another lanthanide. The study found that Tb

^{3+}and Eu

^{2+}co-doped Sr

_{2}Si

_{5}N

_{8}has a 20% increase in emission intensity [16]. Therefore, we want to systematically study the changes in the molecular structure and luminescence properties of Eu

^{2+}and other Ln

^{3+}co-doped systems. Among many lanthanides, the excitation spectrum of Pr

^{3+}4f-5d is relatively simple [8]. In the [Xe] (near nuclear pseudopotential electron) 4f

_{1}5d

_{1}configuration during the excitation, Pr

^{3+}has only one 4f energy level, which can occupy two different electrons. Tb’s advantage is that in 4f

_{7}5d, the 4f

_{7}[

^{8}S

_{7/2}] energy level is relatively stable, and the next higher 4f

_{7}[

^{6}P

_{J}]5d

_{1}energy level is about 3.5–4.0 eV higher. Therefore, it can be observed that 4f

_{8}–4f

_{7}(

^{8}S

_{7/2})5di turns into an isolated state. Ce

^{3+}is widely used as an activating ion in various fluorescent systems: Lu

_{3}Al

_{5}O

_{12}:Ce

^{3+}[17], LaSi

_{6}N

_{11}:Ce

^{3+}[18], Tb

_{3}Al

_{5}O

_{12}:Ce

^{3+}[19], In summary, so we prefer to use any one of Ce

^{3+}, Pr

^{3+}, Tb

^{3+}and Eu

^{2+}doping for the Sr

_{2}Si

_{5}N

_{8}matrix to explore the changes in molecular structure and properties.

^{3+}and Li

^{+}co-doping to replace two Sr

^{2+}, among which Li

^{+}was used as a charge compensator for the charge imbalance caused by the partial replacement of Sr

^{2+}by Ln

^{3+}. Li

^{+}was widely used in phosphor doping such as CaLiAl

_{3}N

_{4}[21], Sr

_{4}LiAl

_{11}N

_{14}[22], Li

_{2}Ca

_{2}Mg

_{2}Si

_{2}N

_{6}[23].

_{2}Si

_{5}N

_{8}(M = Ca, Sr). Shen [25] studied the band structure of Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}through first-principles calculations and combined experiments to reveal the mechanism of luminescence. Density functional theory (DFT) based on first-principles ideas has been successfully applied to the study of microscopic particle systems. In this paper, combined with previous studies, first-principles calculations are used to study the model of Ce

^{3+}, Pr

^{3+}, Tb

^{3+}, respectively, with Li

^{+}co-doped Sr

_{2}Si

_{5}N

_{8}matrix system and Ce

^{3+}/Pr

^{3+}/Tb

^{3+}, respectively, with Eu

^{2+}, Li

^{+}three types of ions co-doped Sr

_{2}Si

_{5}N

_{8}matrix. The optimized structural parameters of the co-doping model for different ion species and sites are presented. We calculate the energy band and density of states of varying doping systems to analyze the electronic structure.

## 2. Results and Discussion

#### 2.1. Structures Distortion of Doped Models

**/**(°) are, respectively, the angle between b and c; a and c; a and b. Polyhedral volume (Å

^{3}) is the coordination polyhedron volume of Ln and N. Distortion index (Å) is the distance a ligand moves after the d/f orbital energy level splits and stabilizes, which reflects distortion effect. Distortion effect: For transition element/rare earth element ions with a high coordination number (>6), high-spin d/f orbitals and low-spin d/f orbitals are unstable in regular polyhedrons, which will cause these d/f orbits to undergo further splitting in energy, in order to stabilize the ion, causing the coordination relationship to deviate from the symmetry of the regular polyhedron. Effective coordination number means that due to the regular coordination polyhedron’s structural distortion, the bond length between the ligand and the central atom changes, resulting in non-integer coordination.

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}cannot converge after optimization. This model is unlikely to exist in the actual doping process, so subsequent calculations are not considered. The ionic radius of Sr

^{2+}(1.18 Å), Eu

^{2+}(1.17 Å), Ce

^{3+}(1.02 Å), Pr

^{3+}(0.99 Å), Tb

^{3+}(0.92 Å), Li

^{+}(0.68 Å) [26] (regardless of the coordination number) decreases from left to right; Eu

^{2+}, Ce

^{3+}/Li

^{+}, Pr

^{3+}/Li

^{+}replace Sr

^{2+}in turn. Due to the cationic ligand’s volume coarctation, the lattice constant and unit cell volume will be slightly smaller. The volume of the doped system is smaller than that of undoped lanthanide ions. Sr

_{2}Si

_{5}N

_{8}volume, unit cell volume and doped ion radius are positively correlated. The average bond length between the lanthanide ion and N becomes shorter, making the bond between the lanthanide ion and the surrounding N stronger. The structure is more compact, the crystal field strength increases, and there will be a redshift tendency. Comparing the system in which the same lanthanide ion replaces eight-coordinate Sr

^{2+}and ten-coordinate Sr

^{2+}, we find that the distortion degree of eight-coordinate Sr

^{2+}is greater than that of ten-coordinate Sr

^{2+}. The formation of an eight-coordinate structure will produce a stronger electron cloud. The nephelauxetic effect (NE) produces a centroid shift, which has a synergistic effect with the above redshift. However, for trivalent lanthanide ions doped with the same coordination number, the different Li

^{+}sites have almost no effect on the structure, which is only used to balance the charge.

_{8}] and [LnN

_{10}], where AE represents the average bond length of [SrN

_{8}] and [SrN

_{10}] ligands in Sr

_{2}Si

_{5}N

_{8}primitive unit cells. It can be seen from the figure that the average bond length decreases with the decrease in the ion radius. Ln

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}has the most extended bond length on average, and Ln

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}is the shortest. Figure 1b is a schematic diagram of Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}[CeN

_{10}] and Eu

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}[EuN

_{10}]. Atoms (10 N) are selected from the 32 N atoms to form a ten-coordinate polyhedron in the figure.

#### 2.1.1. Ln-Li Distance and [SrN] Coordination Polyhedron Parameters of Sr_{2}Si_{5}N_{8}:Ln^{3+}/Li^{+}

^{3+}and Li

^{+}. In the Sr

_{2}Si

_{5}N

_{8}matrix, the selected doping (Sr) site is the same distance as Sr

_{1}-Sr

_{1}and Sr

_{2}-Sr

_{2}, before being replaced by Ln

^{3+}/Li

^{+}, which has a distance of 5.748 Å; the distance is 3.467 Å between Sr

_{1}-Sr

_{2}. When Ln

^{3+}and Li

^{+}are doped to replace Sr

_{1}, in the order of Pr

^{3+}, Ce

^{3+}, Tb

^{3+}, the Ln-Li distances increased by 0.06 Å, 0.066 Å, 0.037 Å, respectively, and the degree of distortion was 1.05%, 1.14% and 0.64%. The overall deviation is not significant. When Ln

^{3+}/Li replaces different sites, the degree of distortion is always above 7.56%. From the perspective of the degree of lattice distortion, it is unlikely to occur in actual situations. When Ln

^{3+}/Li

^{+}is doped to replace Sr

_{2}, the distortion degree of Pr

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}and Ce

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}is about 2.40%. After Ln

_{Sr1}Li

_{Sr}-Sr

_{2}Si

_{5}N

_{81}and Ln

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}are doped to replace the Sr site, the distance between Ln-Li becomes longer, while Ln

_{Sr1}Li

_{Sr2}and Ln

_{Sr2}Li

_{Sr1}have shorter distances than that before doping.

_{10}] tends to appear with two coordination types, one has an effective coordination number greater than 6.707 Å, and the other is less than 6.707 Å (6.707 Å is undoped [SrN

_{10}] effective coordination number). The effective coordination number of [SrN

_{10}] increases, while the effective coordination number of [SrN

_{8}] decreases. When Ln

^{3+}doping replaces the Sr

_{2}site, it is similar to Ln

^{3+}substitution doping of the Sr

_{1}site. [SrN

_{8}] tends to have two effective coordination numbers: the effective coordination number of [SrN

_{8}] increased, and the effective coordination number of [SrN

_{10}] decreased. The above phenomenon showed that after the structure optimization of Ln doping to replace Sr sites, the effective coordination number of [SrN] in other Sr sites is reduced with the same coordination number as doping to replace Sr is reduced. Combining with three factors: [LnN] coordination polyhedron structure, Ln-Li distance and [SrN] coordination polyhedron structure, the Ln

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}doped-model can exist reasonably.

#### 2.1.2. Lattice Constant and [LnN] Ligand Parameters of Sr_{2}Si_{5}N_{8}:Ln^{3+}/Li^{+}/Eu^{2+}

^{3+}/Eu

^{2+}is the coordination polyhedron information of the ion and N. Except for the six ligand structures with three double lanthanide ions substituted for the Sr site, the other structures are not below the theoretical values. Only the following three doping models are Eu

^{2+}and Ce

^{3+}to replace Sr

_{1}, Eu

^{2+}to replace Sr

_{2}, and Ce

^{3+}to replace Sr

_{1}, Eu

^{2+}replaces Sr

_{2}, Pr

^{3+}replaces Sr

_{2}in line with the actual structure. Neither Tb

^{3+}nor Eu

^{2+}co-doped systems are desirable. The unit cell volume and ligand structure of the co-doped system did not change significantly from the single-doped system.

#### 2.1.3. Ln-Li-Eu distance and [SrN] Coordination Polyhedron Parameters of Sr_{2}Si_{5}N_{8}:Ln^{3+}/Li^{+}/Eu^{2+}

_{Sr1}Ce

_{Sr1}Li

_{Sr1}and Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr1}can exist stably after Eu

^{2+}/Ce

^{3+}/Li

^{+}co-doped with Sr

_{2}Si

_{5}N

_{8}, without considering the formation energy conditions. In the Eu

_{Sr2}Pr

_{Sr2}Li

_{Sr1}-model, there are three distance types: Ln-Eu, Ln-Li, and Eu-Li. Compared with the original Sr sites, the distance changes are 5.6%, 8.9%, and 9.7%, respectively. In the Eu

^{2+}/Tb

^{3+}/Li

^{+}-Sr

_{2}Si

_{5}N

_{8}model, the ionic radius of Tb

^{3+}is too small, resulting in excessive structural distortion and difficulty in optimization convergence, so its structure cannot exist stably.

#### 2.2. Formation Energy of Doped Models

^{3+}(Tb

^{3+}, Pr

^{3+})/Li

^{+}co-doped Sr

_{2}Si

_{5}N

_{8}with eight-coordinate (Sr

_{1}) and ten-coordinate (Sr

_{2}). From the definition of formation energy, the lower formation energy value means the target product is easier to form. Among all the values, Ce

^{3+}and Li

^{+}’s formation energy co-doped in eight-coordinate and ten-coordinate systems, respectively, is the lowest. Pr

^{3+}and Li

^{+}co-doped together to replace eight-coordinate Sr has the highest formation energy. For Ce

^{3+}and Tb

^{3+}, Ce

^{3+}(Tb

^{3+}) and Li

^{+}are, respectively, doped at the same Sr site to form lower energy. Pr and Li co-doped to replace ten-coordinate Sr

^{2+}has the lower formation energy, and for co-doped to replace eight-coordinate Sr

^{2+}, the formation energy is the highest. Three kinds of lanthanide ions doping to replace Sr

_{2}are easier to generate in theory. The formation energy of Li

^{+}is lower when it is at the Sr

_{2}site, so the fixed Li

^{+}doping replaces Sr

_{2}

^{2+}. Ce

^{3+}(Tb

^{3+}, Pr

^{3+})/Li

^{+}/Eu

^{2+}co-doped Sr

_{1}and Sr

_{2}of Sr

_{2}Si

_{5}N

_{8}, in which Li

^{+}is fixedly doped instead of Sr

_{1}

^{2+}. Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}and Eu

_{Sr2}Pr

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8′}s formation energy levels are −1.2 eV, −5.2 eV, −5.18 eV. Compared with Eu

_{Sr2}Pr

_{Sr2}Li

_{1}-Sr

_{2}Si

_{5}N

_{8}, Sr

_{2}Si

_{5}N

_{8}:Pr

^{3+}/Li

^{+}has a lower formation energy at around −2.8 eV. The formation energy of Sr

_{2}Si

_{5}N

_{8}:Ce

^{3+}/Li

^{+}/Eu

^{2+}is 1.2 eV lower than Sr

_{2}Si

_{5}N

_{8}:Ce

^{3+}/Li

^{+}, so Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}Ce

_{Sr1}Li-Sr

_{2}Si

_{5}N

_{8}could exist in theory.

#### 2.3. Band Structures and Density of States

^{2+}single-doped Sr

_{2}Si

_{5}N

_{8}and Tb

^{3+}(Ce

^{3+}, Pr

^{3+})/Li

^{+}co-doped Sr

_{2}Si

_{5}N

_{8}systems, as shown in Figure 7, for our subsequent calculations of Eu

^{2+}/Ce

^{3+}(Tb

^{3+}, Pr

^{3+})/Li

^{+}ion co-doping, which provides a basis for comparison. The calculated bandgap of Sr

_{2}Si

_{5}N

_{8}:Eu

_{2}

^{2+}is 3.21 eV, which is slightly smaller than the experimental bandgap because the approximate processing of the DFT exchange-correlation term causes the bandgap to become narrower [27]. In the (a–l) ground-state band structure diagram, their direct bandgaps are Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}: 3.03 eV, Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}: 3.15 eV, Ce

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}:Ce

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}:Sr

_{2}Si

_{5}N

_{8}: 3.09 eV, Pr

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}: 2.97 eV, Pr

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}: 3.27 eV, Pr

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}: 3.27 eV, Pr

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}: 3.30 eV, Tb

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}: 3.30 eV, Tb

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}: 3.27 eV, Tb

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}: 3.24 eV. The high symmetry point G (reciprocal space), has the lowest energy at conduction band minimum (CBM), while some high symmetry points (Z) have the lowest CBM, and the highest valence band maximum (VBM). The lowest point of energy is between Z and G (Figure S1, Supporting Information). Due to the large energy gap between VBM and CBM (0.3 eV), the transition from VBM to CBM is an indirect bandgap transition. The direct bandgaps of (a–k) are 0.51 eV, 0.78 eV, 0.87 eV, 0.57 eV; 0.39 eV, 0.18 eV, 0.18 eV, 0.27 eV, 1.98 eV, 2.07 eV, 2.01 eV (Figure S1, Supporting Information); (a–k)’s indirect bandgaps are 3.03 eV, 3.15 eV, 3.24 eV, 3.09 eV, 2.97 eV, 3.27 eV, 3.27 eV, 3.30 eV, 3.30 eV, 3.27 eV, 3.24 eV. We compare four data from each of the same lanthanide elements. Excluding Pr

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, the bandgap is 3.30 eV, and the other five Ln

_{n}Li

_{n}-Sr

_{2}Si

_{5}N

_{8}are all about 3 eV. Except for Pr

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, (f–h)’s 4f is closed to the CBM, the 4f energy levels of the ground-state lanthanide ions are distributed near the Fermi level (set VBM to 0), which is the premise of the lanthanide ion itself as the luminescence center. (a) Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}and (e) Pr

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}have the smallest band gaps in their respective doping models, indicating that these two doping models have a high peak in the excited state and better luminous performance.

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}are the same as the four PDOS in Sikander Azam’s calculation about Sr

_{2}Si

_{5}N

_{8}:Ce

^{3+}[28]. Figure 7a has strong peaks at 2.04 eV and 2.46 eV, Figure S1b has approximately the same values at 2.07 eV, 2.10 eV, 2.25 eV, and 2.34 eV, while Figure S1c has a higher peak at 2.31 eV. Figure S1d has peaks of similar intensity at 2.25 eV, 2.43 eV, and 2.49 eV. The 4f energy level of Figure S1f–h is between 2.28 and 2.52 eV, and the 4f peak value of Pr

^{3+}in Figure S1e is very high. If Pr

^{3+}is the luminous center, the luminous intensity is much higher than Figure S1f–h. The 4f of Tb

^{3+}in Figure S1j has a higher peak intensity at 1.17 eV, which has a good potential for activating ions.

_{Sr1}Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Pr

_{Sr2}Eu

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}. In Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Eu

^{2+}is the main component in the forbidden band. Ce

^{3+}is close to the bottom of the conduction band. Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}is in the conduction band and has low intensity. Therefore, among the lanthanide ions of this system, only Ce

^{3+}is the luminescence center. For Pr

_{Sr2}Eu

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, the band distribution is relatively dense. The 5d electrons in the excited state may produce multi-level transitions [29].

#### Determination of DFT^{+}U Parameters of Each System

_{eff}increases from 0 to 8 eV, when Eu

^{2+}is equal to 6 eV, the 4f electron orbital of Eu

^{2+}appears at the top of the valence band. When U

_{eff}= 8 eV, the filled state 4f orbital has wholly entered the valence band, and the energy level is about −1 eV (set the top of the valence band as the Fermi level, that is, E

_{f}= 0 eV). When U

_{eff}= 4 eV, Sr

_{2}Si

_{5}N

_{8}:Eu

_{Sr1}

^{2+}and Sr

_{2}Si

_{5}N

_{8}:Eu

_{Sr2}

^{2+}’s 4f–CBM energy difference is 2.22 eV and 2.23 eV, respectively, according to the energy wavelength conversion formula:

^{−34}J·s, k = 1.6 × 10

^{−19}J/eV, C (speed of light) = 3 × 10

^{17}nm/s, λ (wavelength)—nm. The parameters can be obtained in the following formula:

_{eff}value makes 4f-CBM fall in the appropriate energy range, the U

_{eff}introduced by (a–k) are: 5 eV, 5 eV, 5 eV, 6 eV; 4 eV, 6 eV, 6 eV, 6 eV; 2 eV, 2 eV, 2 eV, 2 eV. The energy difference of 4f-CBM in (a–k) with different U

_{eff}is: 2.42 eV, 2.53 eV, 2.62 eV, 2.68 eV, 1.79 eV, 2.28 eV, 2.28 eV, 2.37 eV; 2.69 eV, 2.76 eV, 2.73 eV.

_{eff}to the strongest peak of the 4f energy level and the energy distribution range in Figure 8a–k to make it fall within the appropriate range. The energy ranges of 4f-CBM in Figure 8a–d are 2.42–2.85 eV, 2.80–3.03 eV, 2.65–3.13 eV, 2.67–2.91 eV, respectively. In Figure 8a, Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}is closer to the excitation energy range of Ce

^{3+}doped Sr

_{2}Si

_{5}N

_{8}from 2.85 to 3.25 eV [30] reported in the experiment, but Figure 8a has a global redshift of 0.43 eV. In Figure 7e–h, the energy ranges of 4f-CBM are 2.75–2.99 eV, 2.28–3.06 eV, 2.27–3.08 eV, 2.37–2.97 eV, respectively. In Figure 8e, Pr

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}is closer to the excitation energy range of Pr

^{3+}doped SrAl

_{2}O

_{4}from 2.53 to 2.88 eV [30] reported in the experiment. The energy ranges of 4f-CBM in Figure 8i–k are 2.68–3.04 eV, 2.77–3.07 eV, 2.71–3.07 eV, respectively, which is far from the experimental excitation of Sr

_{2}Si

_{5}N

_{8}:Tb

^{3+}[16]. The U

_{eff}values of Eu

^{2+}and Ce

^{3+}are 4 eV and 6 eV, respectively, and the energy range is mainly 2.27–2.82 eV, and the peak value is 2.27 eV, 2.39 eV, 2.82 eV. In Figure S2b, the Eu

^{2+}4f energy level is not in the forbidden band. When Ce U

_{eff}is 5 eV, the energy range of 4f-CBM is from 2.35 to 2.83 eV. The Eu

^{2+}, Pr

^{3+}U

_{eff}values in Figure S2c are, respectively, 1 eV, 7 eV, and Eu

^{2+}4f energy levels have three strong peaks of 2.19 eV, 2.25 eV, and 2.93 eV. Pr

^{3+}has the highest peak intensity of 2.69 eV in 2.69–2.99 eV.

## 3. Material and Methods

#### 3.1. Theoretical Models

^{3+}= Ce

^{3+}, Pr

^{3+}, Tb

^{3+}) were selected as doping ions to dope Sr

_{2}Si

_{5}N

_{8}and Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}, respectively. As shown in Figure 9a, there are two kinds of Sr doping sites, namely, eight-coordinate Sr

_{1}[SrN

_{8}] (0.5000, 0.8734, 0.9997) and ten-coordinate Sr

_{2}[SrN

_{10}] (0.7500, 0.1158, 0.8683). Since in the doped ions, Ln are all positively trivalent and Sr is bivalent to neutralize the entire system’s charge, every time a positive trivalent lanthanide ion is introduced to replace Sr

^{2+}, a Li

^{+}is introduced to replace Sr

^{2+}to keep the entire system electrically neutral. The chemical formula of Sr

_{2}Si

_{5}N

_{8}doped with Ln

^{3+}/Li

^{+}is Ln

_{Sr1/Sr2}Li

_{Sr1/Sr2}Sr

_{2}Si

_{5}N

_{8}, while the chemical formula of Sr

_{2}Si

_{5}N

_{8}doped with Ln

^{3+}/Li

^{+}/Eu

^{2+}is Ln

_{Sr1/Sr2}Eu

_{Sr1/Sr2}Li

_{Sr1/Sr2}-Sr

_{2}Si

_{5}N

_{8}. Figure 9b has established a 2 × 2 × 1 supercell (60 atoms) with a doping concentration of 12.5% for Ln

^{3+}, Eu

^{2+}, and Li

^{+}. If we continue to expand the unit cell to 3 × 2 × 1 to reduce the doping concentration, the calculation requires more K points than 5 × 8 × 6, and it is complicated for the structure to converge. Notably, 2 × 2 × 1 is the largest supercell structure that can be established under the premise that the structure can converge.

#### 3.2. Computational Methods

^{−4}eV. The convergence tolerance of the relaxation force is 0.01 eV/Å per atom. Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}original unit cell model removed the energy band calculation.

_{eff}values in different host environments.

^{2}3p

^{2}, 2s

^{2}p

^{3}, 4s

^{2}4p

^{6}5s

^{2}, 2s

^{1}, 5s

^{2}5p

^{6}6s

^{2}4f

^{7}, 5s

^{2}5p

^{6}4f

^{1}5d

^{1}6s

^{2}, 5s

^{2}6s

^{2}5p

^{6}5d

^{1}4f

^{2}, and 4f

^{8}5s

^{2}6s

^{2}5p

^{6}5d

^{1}correspond to Si, N, Sr, Li, Eu, Ce, Pr, and Tb in the pseudo-electron composition.

_{i}) and the central atom (M) is different from the bond energy between the nearest ligand (X

_{0}) and the central atom. The energy ratio ${E}_{\left(M-{X}_{i}\right)}$:${E}_{\left(M-{X}_{0}\right)}$ is defined as the contribution of X

_{i}atom to M atom C.N*. If the nearest atom is only affected by the Coulomb force, it is easy to get formula (5)

_{f}(Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}/Ln

^{3+}/Li

^{+}) = E(Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}/Ln

^{3+}/Li

^{+})

^{+}3µ(Sr

^{2+}) − E(Sr

_{2}Si

_{5}N

_{8}) − µ(Eu

^{2+}) − µ(Ln

^{3+}) − µ(Li

^{+})

_{f}(Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}/Ln

^{3+}/Li

^{+}) is the formation energy, E(Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}/Ln

^{3+}/Li

^{+}) is the energy calculated by SCF, µ(Sr

^{2+}), µ(Eu

^{2+}), µ(Li

^{+}) are the chemical potentials of Sr, Eu, Li, and Ln, respectively, and E(Sr

_{2}Si

_{5}N

_{8}) is the energy calculated by the lattice matrix SCF. For the chemical potential of the element, formula (7) can be used

## 4. Conclusions

_{2}Si

_{5}N

_{8}:Ln

^{3+}/Li

^{+}and Sr

_{2}Si

_{5}N

_{8}:Ln

^{3+}/Eu

^{2+}/Li

^{+}were constructed. The calculation of Sr

_{2}Si

_{5}N

_{8}:Ln

^{3+}/Li

^{+}and Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}provides a basic reference for double-doped lanthanide ions. The introduction of Li

^{+}and Ln

^{3+}can achieve the design idea of neutralizing electrons and maintaining the original structure. Three dual-doped models of Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, and Eu

_{Sr2}Pr

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}were screened out. Among the three models mentioned, Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}and Eu

_{Sr2}Pr

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}’s fluorescence performances are expected to exceed that of Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}, which can be regarded as a potential route to increase the quenching temperature of the phosphor. When Ce

^{3+}U

_{eff}in Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}is 5 eV, the energy range of 4f-CBM is 2.42 –2.85 eV. Compared with the experimentally reported excitation range of 2.85–3.25 eV, the redshift is 0.42 eV (75 nm). When Pr

^{3+}U

_{eff}in Pr

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}is 4 eV, the energy range of 4f-CBM is 2.75–2.99 eV, and its peak value is 2.90 eV, which is similar to SrAl

_{2}O

_{4}:Pr

^{3+}430–490nm with peaks around 440 nm. In Sr

_{2}Si

_{5}N

_{8}:Ln

^{3+}/Li

^{+}/Eu

^{2+}, three convergent models of Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, and Eu

_{Sr2}Pr

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}were selected. The addition of Ce

^{3+}in Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}made the 4f energy level of Eu

^{2+}blue shift. Similarly, the addition of Pr

^{3+}in Eu

_{Sr2}Pr

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}makes part of the Eu

^{2+}4f energy level blue shift. The Eu

^{2+}4f energy level in Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}is not in the forbidden band, so Eu

^{2+}is not used as the emission center.

## Supplementary Materials

_{1}LiSr

_{1}-Sr

_{2}Si

_{5}N

_{8}; (b) CeSr

_{1}LiSr

_{2}-Sr

_{2}Si

_{5}N

_{8}; (c) CeSr

_{2}LiSr

_{1}-Sr

_{2}Si

_{5}N

_{8}; (d) CeSr

_{2}LiSr

_{2}-Sr

_{2}Si

_{5}N

_{8}; (e) PrSr

_{1}LiSr

_{1}-Sr

_{2}Si

_{5}N

_{8}; (f) PrSr

_{1}LiSr

_{2}-Sr

_{2}Si

_{5}N

_{8}; (g) PrSr

_{2}LiSr

_{1}-Sr

_{2}Si

_{5}N

_{8}; (h) PrSr

_{2}LiSr

_{2}-Sr

_{2}Si

_{5}N

_{8}; (i) TbSr

_{1}LiSr

_{1}-Sr

_{2}Si

_{5}N

_{8}; (j) TbSr

_{1}LiSr

_{2}-Sr

_{2}Si

_{5}N

_{8}; (k) TbSr

_{1}LiSr

_{2}-Sr

_{2}Si

_{5}N

_{8}; (l) EuSr

_{1}-Sr

_{2}Si

_{5}N

_{8}; (m) EuSr

_{2}-Sr

_{2}Si

_{5}N

_{8}. Figure S2: Densiy of states of doped structures: (a) EuSr

_{1}CeSr

_{1}LiSr

_{2}-Sr

_{2}Si

_{5}N

_{8}; (b) EuSr

_{2}CeSr

_{1}LiSr

_{2}-Sr

_{2}Si

_{5}N

_{8}; (c) PrSr

_{2}EuSr

_{2}LiSr

_{2}-Sr

_{2}Si

_{5}N

_{8}. Table S1: The Key information in the energy band structure of Sr

_{2}Si

_{5}N

_{8}:Ln

^{3+}/Li

^{+}, Eu

^{2+}. Table S2: The Key information in the energy band structure of Sr

_{2}Si

_{5}N

_{8}:Ln

^{3+}/Li

^{+}/Eu

^{2+}.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

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**Figure 1.**(

**a**) Average bond length of [LnN

_{8}] and [LnN

_{10}]. (

**b**) Structure diagram of [CeN

_{8}]. (

**c**) Structure diagram of [EuN

_{10}].

**Figure 2.**The distance change after Ln

^{3+}and Li

^{+}replace Sr

_{1}and Sr

_{2}in doped Sr

_{2}Si

_{5}N

_{8}(

**a**–

**k**) Pr

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Pr

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Pr

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Pr

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Ce

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Ce

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Tb

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Tb

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Tb

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**n**–

**l**) is the Sr-Sr distance before doping.

**Figure 3.**(

**a**–

**c**): Ln-Li, Eu-Li, Eu-Ln’s distance diagram after Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}Pr

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}doped with Sr

_{2}Si

_{5}N

_{8}matrix.

**Figure 4.**[SrN] coordination polyhedron diagram after substitution of Ln

^{3+}/Li

^{+}for Sr

_{1}and Sr

_{2}sites in Sr

_{2}Si

_{5}N

_{8}(

**a**–

**m**) Pr

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Pr

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Pr

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Pr

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Ce

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Ce

_{Sr2}Li

_{Sr2}, Tb

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Tb

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}, Tb

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}.

**Figure 5.**(

**a**–

**c**): [SrN] Coordination Polyhedron Diagram after Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}, Eu

_{Sr2}Pr

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}doped with Sr

_{2}Si

_{5}N

_{8}matrix.

**Figure 7.**Band structures of doped structures: (

**a**) Eu

_{Sr1}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**b**) Eu

_{Sr2}Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**c**) Pr

_{Sr2}Eu

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}.

**Figure 8.**Band structures of doped structures: (

**a**) Ce

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**b**) Ce

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}; (

**c**) Ce

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**d**) Ce

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}; (

**e**) Pr

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**f**) Pr

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}; (

**g**) Pr

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**h**) Pr

_{Sr2}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}; (

**i**) Tb

_{Sr1}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**j**) Tb

_{Sr1}Li

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}; (

**k**) Tb

_{Sr2}Li

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**l**) Eu

_{Sr1}-Sr

_{2}Si

_{5}N

_{8}; (

**m**) Eu

_{Sr2}-Sr

_{2}Si

_{5}N

_{8}.

**Figure 9.**(

**a**) Molecular structure of Sr

_{2}Si

_{5}N

_{8}; (

**b**) 2 × 2 × 1 supercell of Sr

_{2}Si

_{5}N

_{8}: The selected atoms are Sr

_{2}.

**Table 1.**Cell parameters and [LnN] polyheral structures of Sr

_{2}Si

_{5}N

_{8}and Sr

_{2}Si

_{5}N

_{8}doped by Ln (Ce

^{3+}, Pr

^{3+}, Tb

^{3+})/Li

^{+}, Eu

^{2+}.

2 × 2 × 1 | Cell Parameters | Volume (Å^{3)} | [LnN] Polyhedral Volume (Å ^{3}) | [LnN] Distortion Index (Å) | [LnN] Effective Coordination Number | |||
---|---|---|---|---|---|---|---|---|

Supercells | a (Å) | b (Å) | c (Å) | α,β,γ/(°) | ||||

Sr_{2}Si_{5}N_{8}(Sr_{2}) | 11.498 | 6.881 | 9.405 | α = β = γ = 90.0 | 744.074 | 48.866 | 0.062 | 6.707 |

Sr_{2}Si_{5}N_{8}(Sr_{1}) | 11.498 | 6.881 | 9.405 | α = β = γ = 90.0 | 744.074 | 32.657 | 0.075 | 5.448 |

Eu_{Si2}-Sr_{2}Si_{5}N_{8} | 11.498 | 6.876 | 9.403 | α = 89.9, β = γ = 90.0 | 743.131 | 48.545 | 0.072 | 5.771 |

Eu_{Sr1}-Sr_{2}Si_{5}N_{8} | 11.493 | 6.876 | 9.402 | α = 90.1, β = γ = 90.0 | 743.046 | 32.379 | 0.090 | 4.728 |

Ce_{Sr1}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 11.492 | 6.874 | 9.373 | α = 90.4, β = γ = 90.0 | 740.450 | 27.921 | 0.119 | 4.919 |

Ce_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 11.505 | 6.869 | 9.376 | α = 90.1, β = γ = 90 | 741.010 | 27.857 | 0.110 | 4.776 |

Ce_{Sr2}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 11.485 | 6.876 | 9.370 | α = 89.9, β = γ = 90 | 739.910 | 45.191 | 0.092 | 5.550 |

Ce_{Sr2}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 11.504 | 6.863 | 9.380 | α = 89.7, β = γ = 90 | 740.700 | 44.354 | 0.090 | 5.597 |

Pr_{Sr1}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 11.487 | 6.873 | 9.372 | α = 90.4, β = γ = 90 | 739.830 | 27.797 | 0.123 | 4.849 |

Pr_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 11.501 | 6.872 | 9.372 | α = 90.1, β = γ = 90.0 | 740.680 | 27.689 | 0.114 | 4.645 |

Pr_{Sr2}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 11.498 | 6.881 | 9.405 | α = β = γ = 90.0 | 739.340 | 45.213 | 0.101 | 5.420 |

Pr_{Sr2}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 11.502 | 6.863 | 9.380 | α = 89.7, β = γ = 90.0 | 740.450 | 44.345 | 0.093 | 5.337 |

Tb_{Sr1}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 11.470 | 6.863 | 9.360 | α = 90.5, β = γ = 90.0 | 736.970 | 27.321 | 0.154 | 4.676 |

Tb_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 11.493 | 6.859 | 9.370 | α = 90.1, β = γ = 90.0 | 738.970 | 27.300 | 0.147 | 4.496 |

Tb_{Sr2}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 11.479 | 6.850 | 9.376 | α = 89.9, β = γ = 90.0 | 737.230 | 44.902 | 0.150 | 4.724 |

**Table 2.**[SrN] Coordination polyhedron parameters of Sr

_{2}Si

_{5}N

_{8}doped by Ln (Ce

^{3+}, Pr

^{3+}, Tb

^{3+})/Li

^{+}.

2 × 2 × 1 Supercell | [SrN] Average Bond Length (Å) | [SrN] Polyhedral Volume (Å ^{3}) | [SrN] Distortion Index (Å) | [SrN] Effective Coordination Number | [SrN] Coordination Number |
---|---|---|---|---|---|

Ce_{Sr1}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 2.994 | 49.700 | 0.0723 | 7.000 | 10 |

2.942 | 48.317 | 0.0720 | 6.620 | 10 | |

2.886 | 32.405 | 0.0757 | 5.420 | 8 | |

Ce_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 2.925 | 47.655 | 0.063 | 7.070 | 10 |

2.954 | 48.845 | 0.073 | 6.358 | 10 | |

2.907 | 35.144 | 0.086 | 5.052 | 8 | |

Ce_{Sr2}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 2.956 | 49.440 | 0.066 | 6.211 | 10 |

2.963 | 45.359 | 0.088 | 5.889 | 10 | |

2.879 | 32.349 | 0.081 | 5.741 | 8 | |

Ce_{Sr2}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 2.975 | 49.291 | 0.075 | 5.989 | 10 |

2.870 | 34.093 | 0.080 | 5.350 | 8 | |

2.909 | 33.711 | 0.067 | 5.899 | 8 | |

Pr_{Sr1}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 2.940 | 48.289 | 0.072 | 6.646 | 10 |

2.994 | 49.734 | 0.073 | 7.022 | 10 | |

2.884 | 32.335 | 0.076 | 5.434 | 8 | |

Pr_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 2.923 | 47.601 | 0.062 | 7.148 | 10 |

2.956 | 48.950 | 0.072 | 6.378 | 10 | |

2.907 | 35.144 | 0.085 | 5.085 | 8 | |

Pr_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 2.923 | 47.601 | 0.062 | 7.148 | 10 |

2.907 | 35.144 | 0.085 | 5.085 | 8 | |

2.955 | 48.950 | 0.072 | 6.378 | 10 | |

Pr_{Sr2}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 2.970 | 49.192 | 0.073 | 6.087 | 10 |

2.872 | 34.160 | 0.081 | 5.321 | 8 | |

2.908 | 33.695 | 0.068 | 5.886 | 8 | |

Tb_{Sr1}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 2.937 | 48.233 | 0.071 | 6.874 | 10 |

2.999 | 49.821 | 0.075 | 6.968 | 10 | |

2.877 | 32.096 | 0.075 | 5.467 | 8 | |

Tb_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8} | 2.923 | 47.602 | 0.061 | 7.231 | 10 |

2.963 | 49.304 | 0.073 | 6.116 | 10 | |

2.899 | 34.905 | 0.083 | 5.159 | 8 | |

Tb_{Sr2}Li_{Sr1}-Sr_{2}Si_{5}N_{8} | 2.883 | 32.733 | 0.086 | 5.729 | 8 |

2.958 | 49.914 | 0.079 | 5.940 | 10 | |

2.955 | 45.191 | 0.085 | 6.112 | 10 | |

Eu_{Sr1}-Sr_{2}Si_{5}N_{8} | 2.947 | 48.690 | 0.061 | 6.735 | 10 |

2.952 | 48.914 | 0.060 | 6.962 | 10 | |

2.888 | 32.658 | 0.074 | 5.449 | 8 | |

Eu_{Sr2}-Sr_{2}Si_{5}N_{8} | 2.951 | 48.904 | 0.061 | 6.701 | 10 |

2.888 | 32.706 | 0.072 | 5.625 | 8 | |

2.889 | 32.641 | 0.074 | 5.453 | 8 | |

2.942 | 38.657 | 0.085 | 5.536 | 8 |

**Table 3.**Cell parameters and [LnN] polyheral structures of Sr

_{2}Si

_{5}N

_{8}co-doped Eu

^{2+}/Ce

^{3+}/Li

^{+}and Eu

^{2+}/Pr

^{3+}/Li

^{+}.

2 × 2 × 1 | Cell Parameters | Volume (Å ^{3}) | [LnN] Polyhedral Volume (Å ^{3}) | [LnN] Distortion Index (Å) | [LnN] Effective Coordination Number | |||
---|---|---|---|---|---|---|---|---|

Supercells | a (Å) | b (Å) | c (Å) | α,β,γ (°) | ||||

Eu_{Sr1}Ce_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8}(Eu) | 11.490 | 6.874 | 9.375 | α = 90.3, β = γ = 90.0 | 740.470 | 32.042 | 0.0947 | 4.654 |

Eu_{Sr1}Ce_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8}(Ce) | 11.490 | 6.874 | 9.375 | α = 90.3, β = γ = 90.0 | 740.470 | 28.112 | 0.1219 | 4.926 |

Eu_{Sr2}Ce_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8}(Eu) | 11.492 | 6.867 | 9.370 | α = 90.3, β = γ = 90.0 | 739.470 | 48.094 | 0.0613 | 6.455 |

Eu_{Sr2}Ce_{Sr1}Li_{Sr2}-Sr_{2}Si_{5}N_{8}(Ce) | 11.492 | 6.867 | 9.370 | α = 90.3, β = γ = 90.0 | 739.470 | 28.046 | 0.1254 | 5.026 |

Eu_{Sr2}Pr_{Sr2}Li_{Sr2}-Sr_{2}Si_{5}N_{8}(Eu) | 11.480 | 6.8607 | 9.377 | α = 90.3, β = γ = 90.0 | 738.566 | 48.574 | 0.0943 | 5.849 |

Eu_{Sr2}Pr_{Sr2}Li_{Sr2}-Sr_{2}Si_{5}N_{8}(Pr) | 11.480 | 6.8607 | 9.377 | α = 90.3, β = γ = 90.0 | 738.566 | 45.876 | 0.0880 | 4.752 |

**Table 4.**[SrN] Coordination polyhedron parameters of Sr

_{2}Si

_{5}N

_{8}doped by Ln (Ce

^{3+}, Pr

^{3+}, Tb

^{3+})/Li

^{+}/Eu

^{2+}.

2 × 2 × 1 Supercell | [SrN] Average Bond Length (Å) | [SrN] Polyhedral Volume (Å ^{3}) | [SrN] Distortion Index (Å) | [SrN] Effective Coordination Number | [SrN] Coordination Number |
---|---|---|---|---|---|

Eu_{Sr1}Ce_{Sr1}Li_{Sr1} | 2.941 | 48.361 | 0.0666 | 6.884 | 10 |

2.989 | 49.546 | 0.0721 | 7.040 | 10 | |

2.887 | 32.507 | 0.0755 | 5.406 | 8 | |

Eu_{Sr2}Ce_{Sr11}Li_{Sr1} | 2.945 | 48.444 | 0.0718 | 6.590 | 10 |

2.991 | 49.691 | 0.0705 | 7.039 | 10 | |

2.880 | 32.241 | 0.0755 | 5.427 | 8 | |

Eu_{Sr2}Pr_{Sr21}Li_{Sr1} | 2.960 | 49.248 | 0.0646 | 6.260 | 10 |

2.863 | 31.895 | 0.0825 | 5.680 | 8 | |

2.889 | 32.623 | 0.0753 | 5.360 | 8 |

**Table 5.**Energy level difference of Eu 4f-CBM of Sr

_{2}Si

_{5}N

_{8}:Eu

^{2+}with different Ueff parameters.

U_{eff} (eV) | Eu^{2+} 4f—CBM(eV) | |
---|---|---|

Eu_{1}^{2+} | Eu_{2}^{2+} | |

0 | 0.84 | 0.84 |

2 | 1.48 | 1.50 |

4 | 2.22 | 2.23 |

6 | 2.86 | 2.93 |

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**MDPI and ACS Style**

Yin, Z.; Li, M.; Zhang, J.; Shen, Q.
Research on Molecular Structure and Electronic Properties of Ln^{3+} (Ce^{3+}, Tb^{3+}, Pr^{3+})/Li^{+} and Eu^{2+} Co-Doped Sr_{2}Si_{5}N_{8} via DFT Calculation. *Molecules* **2021**, *26*, 1849.
https://doi.org/10.3390/molecules26071849

**AMA Style**

Yin Z, Li M, Zhang J, Shen Q.
Research on Molecular Structure and Electronic Properties of Ln^{3+} (Ce^{3+}, Tb^{3+}, Pr^{3+})/Li^{+} and Eu^{2+} Co-Doped Sr_{2}Si_{5}N_{8} via DFT Calculation. *Molecules*. 2021; 26(7):1849.
https://doi.org/10.3390/molecules26071849

**Chicago/Turabian Style**

Yin, Ziqian, Meijuan Li, Jianwen Zhang, and Qiang Shen.
2021. "Research on Molecular Structure and Electronic Properties of Ln^{3+} (Ce^{3+}, Tb^{3+}, Pr^{3+})/Li^{+} and Eu^{2+} Co-Doped Sr_{2}Si_{5}N_{8} via DFT Calculation" *Molecules* 26, no. 7: 1849.
https://doi.org/10.3390/molecules26071849