Chemical bond parameters, bond energy and the local crystal sites of Eu³⁺ in Ca₅(BO₃)₃F:1% Eu³⁺ phosphor

Abstract

The local crystal sites occupied by Eu³⁺ in Ca₅(BO₃)₃F:1% Eu³⁺ phosphor were investigated experimentally and theoretically. Ca₅(BO₃)₃F:1% Eu³⁺ was synthesized by high-temperature solid-state method in air. The crystal structure and optical properties of the phosphor were studied by X-ray powder diffraction and photoluminescence, respectively. Two different O²⁻ → Eu³⁺ CT broad bands with the peaks at 266 and 283 nm in Ca₅(BO₃)₃F:1% Eu³⁺ were detected, indicating the Eu³⁺ sites occupied Ca2 and Ca1, respectively. The different sharp f–f emission spectra under the excitation of 283 and 266 nm proved that there are two different local lattice environments around Eu³⁺ existing in Ca₅(BO₃)₃F:1% Eu³⁺. Environmental factor h_e, the standard deviation of environmental factor (EFSD) and the bond energy were used to illustrate and explain the site occupancy mechanism of Eu³⁺ into the host lattice. By comparing the intensity ratios of ⁵D₀ → ⁷F₂ transition to the ⁵D₀ → ⁷F₁ transition, I(⁵D₀/⁷F₂)/I(⁵D₀/⁷F₁) of Eu³⁺ at Ca2 (7.381) was found to be 2.5 times stronger than that of Eu³⁺ at Ca1 site (2.933). was calculated to analyze the I(⁵D₀/⁷F₂)/I(⁵D₀/⁷F₁) value. On the basis of the bond valence model, a bond-energy method was used to study the occupancy of the Eu ion, which indicated that the preferential sites of Eu ion occupancy in the Ca₅(BO₃)₃F are the Ca2 and Ca1 sites. All three theoretical calculation results are consistent with each other.

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1. Introduction

White LEDs have the advantages of high brightness, low energy consumption, long life, small size, no radiation, no pollution, etc. It is considered the new generation of green light sources. The two commonly used methods for implementing white LEDs are: blu-ray chip and YAG:Ce³⁺ yellow phosphor combination, and near-ultraviolet LED chip combined with the trichromatic phosphor. However, the former lacks the red portion, resulting in a lower color rendering index (less than 80) and a higher color temperature (greater than 40), while the latter is less commercially available and lacks suitable red light materials.^1–6 Therefore, finding a suitable red luminescent material and improving the color rendering index has become an important issue in the development of trichromatic white LEDs. In the rare earth family, Eu³⁺ ions are widely used in various fields of luminescent materials because they have good luminescence properties and can emit red fluorescence with good monochromaticity.^7–9 The luminescence of Eu³⁺ derived from the 4f⁶ transition consists of sharp peaks of the Eu³⁺-doped inorganic compound in the red region.^10–12

Rare earth ion-doped borate luminescent materials have high UV transparency, nonlinear characteristics, good stability and optical properties, and they are expected to become a promising fluorescent material, attracting more and more research worldwide.^13–15 Among the nonlinear optical crystal materials that have been found, ultraviolet and deep ultraviolet nonlinear optical crystals that have excellent performance are almost all borate compounds. Ca₅(BO₃)₃F was first reported by Lei et al. in 1989. The crystal was also a new type of nonlinear optical crystal. The powder doubling effect was measured to be 2–3 KDP, and the transmission range was 190–3600 nm.^16,17 There are many published papers focusing on energy transfer and color-tunability of rare earth (e.g., Bi³⁺, Ce³⁺, Tb³⁺)-doped Ca₅(BO₃)₃F.^18,19 There are three kinds of octahedrons surrounding the Ca ions that could be substituted by Eu³⁺. They have different covalence, average bond lengths, central ion coordination numbers, and charges of ligands in chemical bonds. These result in Eu³⁺ ions with different photoluminescence properties. For the above reasons, Ca₅(BO₃)₃F compound with Ca²⁺ and B³⁺ cationic sites can be selected as a host lattice, and Eu³⁺ ions are used as a good activator. However, studies on the effects of Eu³⁺ on the CT properties and the local crystal sites occupied by Eu³⁺ in Ca₅(BO₃)₃F:1% Eu³⁺ phosphor are rarely reported.

The environmental factor (h_e) was used to investigate the sites of Eu³⁺ based on the relationship between the CT bands of Eu³⁺ and the crystal structure of the host lattice. h_e can be calculated using the complex crystal chemical bond theory. The smaller the h_e, the larger the charge transfer energy from O²⁻ to Eu³⁺. Through the literature, we know that the PL intensity ratio between the ⁵D₀ → ⁷F₂ and ⁵D₀ → ⁷F₁ transition of Eu³⁺ increases as the crystal distortion increases. The degree of distortion was calculated by the environmental factor standard deviation (EFSD) . This can provide information on the Eu ion sites. At the same time, the bond energy theory can be used to discuss the site occupancy of dopants into the host. In previous papers, this method has been proven; for example, the site preferential occupancy for Eu in Sr₂V₂O₇, Sr₉Gd(VO₄)₇ and Sr₂V₂O₇/Sr₉Gd(VO₄)₇, CaAl₂Si₂O₈ phosphors,²⁰ as well as Bi²⁺ in β-Ca₂P₂O₇ crystals,²¹ have been solved though the bond energy method. Furthermore, this method was also used in study of bond energy and preferential occupancy of Eu³⁺ doped in the Ca₁₀M(PO₄)₇ (M = Li, Na, K) systems.²²

In our work, Eu³⁺ doped Ca₅(BO₃)₃F was prepared by a high-temperature solid-state method. We firstly used the chemical bond parameters and analyzed the sites of Eu ion systematically based on the refined crystal structure parameters. Then, the site occupancy of Eu³⁺ was investigated by analyzing the luminescent properties and environmental factor h_e and the standard deviation of environmental factor (EFSD) of Ca₅(BO₃)₃F:1% Eu³⁺ when Eu³⁺ replaced the different Ca²⁺ sites in the matrix. Finally, the bond energy method was applied to illustrate and explain the site occupation of Eu³⁺ into the host lattice.

2. Experimental

2.1 Synthesis of material

Ca₅(BO₃)₃F:1% Eu³⁺ phosphor was prepared by high-temperature solid-state reaction in air. The desired CaF₂ (A.R., Macklin), H₃BO₃ (A.R., Sinopharm), CaCO₃ (99.99%, Aladdin), and Eu₂O₃ (99.99%, Aladdin) were weighed according to the stoichiometric ratio of Ca₅(BO₃)₃F:1% Eu³⁺, and the raw materials were placed in an agate mortar and ground for half an hour. The uniformly mixed raw materials were transferred to an alumina crucible, heated in a crucible calciner to 1150 °C, and then kept for 4 h. After the sample was cooled to room temperature, it was ground into a powder to obtain the desired sample.

2.2 Material characterization

In this experiment, we used a Bruker D8 Advance X-ray diffractometer to analyze the crystal structure of the prepared phosphor with Cu Kα (λ = 1.54056 Å) radiation and acceleration voltage of 30 kV. The scanning range was 5 to 80 degrees. The sample was detected by FLS980 fluorescence spectrometer to obtain the excitation spectrum and emission spectrum. The excitation source was a 450 W Xe lamp with a slit width of 2 nm and a measured spectral range of 200 nm to 750 nm, with a resolution of 0.2 nm. The sample was tested at room temperature. The Rietveld structure refinement was performed using the General Structure Analysis System (GSAS)²³ software in order to determine the change of crystal structure.

3. Results and discussion

3.1 Phase characterization and crystal analysis

Fig. 1 is an XRD pattern of Ca₅(BO₃)₃F:1% Eu³⁺ sample. Comparing the sample diffraction pattern with the standard card, it was found that the diffraction peak data were basically consistent with the Ca₅(BO₃)₃F (ICSD-65763) card data, with a C1m1 space group and a monoclinic crystal system. There is an impurity phase, namely, Ca₃B₂O₆. Fortunately, a very small amount of Ca₃B₂O₆ has no effect on our system. Therefore, the substitution of Eu³⁺ for Ca²⁺ into Ca₅(BO₃)₃F did not change the structure of the crystal.

Fig. 1 Observed, calculated and difference X-ray diffraction patterns of an Eu³⁺ (1%)-doped Ca₅(BO₃)₃F phosphor (the inset gives [20–40] 2θ range).

Fig. 2 shows the crystal structure of Ca₅(BO₃)₃F. There are three Ca ion coordination environments in this structure, namely, Ca1, Ca2 and Ca3. The anionic structural group of the Ca₅(BO₃)₃F crystal is a planar BO₃ group. Both Ca and the surrounding anions form a CaO₄X₂ (X = F or O) octa-coordination, in which Ca(1) forms a CaO₅F octahedron with five O atoms and one F atom, and Ca(2) forms a distorted octahedral structure with six O atoms. Ca(3) is coordinated with two F atoms and four O atoms. These polyhedrons are connected to the BO₃ group by sharing O atoms to form a three-dimensional space structure.

Fig. 2 Crystal structure of Ca₅(BO₃)₃F and the coordination environment of Ca1, Ca2, and Ca3.

The crystal structure of Ca₅(BO₃)₃F (ICSD-65763) was used as the starting model for structure refinement. The Rietveld method refers to the point-by-point comparison of the calculated and measured values of the diffraction intensity of a crystal using a computer program, and the least squares method is used to adjust the parameters of the structural atoms and of the peak shape, so that the calculated peak shape is consistent with the measured peak shape. In the structural refinement of this paper, based on the XRD peak of the existing Ca₅(BO₃)₃F:1% Eu³⁺ crystal and Ca₅(BO₃)₃F standard card as the background, the set function is type 4, and about 30 terms were refined. Fig. 1 shows the observed, calculated and difference results for the Rietveld refinement of Ca₅(BO₃)₃F:1% Eu³⁺ phosphor. The peak intensities and positions exhibited few differences between the experimental and calculated patterns. Crystallographic and refinement parameters are summarized in Table 1. The results show that almost all diffraction peaks can be directed to Ca₅(BO₃)₃F with a monoclinic unit cell (C1m1). The cell parameters a, b, c, and β, etc., are close to those of Ca₅(BO₃)₃F (ICSD-65763). The atomic coordinates and isotropic displacement parameters of Ca₅(BO₃)₃F:1% Eu³⁺ phosphor are listed in Table 2. The above results show that the crystal structure data of Ca₅(BO₃)₃F:1% Eu³⁺ simulated by refinement can be well matched with its experimental data.

Table 1 Final crystallographic and refinement of parameter of Ca₅(BO₃)₃F:1% Eu³⁺; E is the error between the original and refined value

Formula	Ca5(BO3)3F	E
Space-group	C1m1
a/Å	8.132	0.003
b/Å	16.054	0.003
c/Å	3.542	0.003
α = γ	90°	0
β	100.946°	0
Rwp	5.30%
Rp	9.35%
χ^2	6.806

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Table 2 Atomic coordinates and isotropic displacement parameters (U_iso/Ų) for Ca₅(BO₃)₃F:1% Eu³⁺; E is the error between the original and refined value

Name	x	y	z	Eposition	Mult	Occ	Uiso	EUiso
Ca1	0.6501	0.1177	0.7786	0.013	4	1	0.0231	0.001
Ca2	0.0278	0.1796	0.4421	0.02	4	1	0.0145	0.002
Ca3	0.2583	0	0.0769	0.04	2	1	0.0283	0.02
F1	0.4691	0	−0.3287	0.03	2	1	0.0737	0.01
O1	0.8282	0.0743	0.3639	0.01	4	1	0.0603	0.002
O2	−0.001	0.3279	0.2448	0.018	4	1	0.0504	0.001
O3	0.0722	0	0.5116	0.024	2	1	0.0066	0.002
O4	0.829	0.2254	0.8459	0.049	4	1	0.0307	0.02
O5	0.2071	0.143	0.0125	0.02	4	1	0.0134	0.001
B1	0.8626	0.307	0.0036	0.014	4	1	0.0594	0.011
B2	0.9239	0	0.3499	0.006	2	1	−0.0113	0.003

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3.2 Photoluminescence properties

Fig. 3(b) is an excitation spectrum of the Ca₅(BO₃)₃F:1% Eu³⁺ sample at a monitoring wavelength of 633 nm, which is composed of a broad excitation band of 225–350 nm, derived from the charge transfer transition of O²⁻ to Eu³⁺, where the strongest absorption peak is at 266 nm. The emission spectrum at an excitation wavelength of 266 nm is shown in Fig. 3(d), consisting of emission peaks at around 576, 592, 612, 652 and 708 nm, corresponding to ⁵D₀ → ⁷F₀, ⁵D₀ → ⁷F₁, ⁵D₀ → ⁷F₂, ⁵D₀ → ⁷F₃, and ⁵D₀ → ⁷F₄ transitions of Eu³⁺ ions, respectively.^24,25 We can clearly see that the charge transfer transition peaks of samples O to Eu have a significant shift when the monitoring wavelengths are 576, 612, 619 and 633 nm, as shown in Fig. 3(a) and (b). The two broadband peaks (O²⁻ → Eu³⁺) are located at 266 and 283 nm, respectively, which means that the Eu³⁺ ions exhibit two lattice environments in the Ca₅(BO₃)₃F matrix. However, the excitation and emission spectra of Eu-doped Ca₃B₂O₆ are completely different with our luminescence properties of Eu-doped Ca₅(BO₃)₃F. The former shows an emission band peaking at 422 nm and excitation peaks at 362, 380 and 394 nm (λ_em = 616 nm). These prove that the different luminescence of Eu is due to Eu occupying the different sites in the Ca₅(BO₃)₃F.²⁶

Fig. 3 (a) and (b) Excitation spectra under different monitoring wavelengths of Ca₅(BO₃)₃F:1% Eu³⁺; (c) and (d) emission spectra of Ca₅(BO₃)₃F:1% Eu³⁺ under 266 and 283 nm excitation.

When the Eu³⁺ ion deviates from the center of the inversion, due to the opposite parity configuration in the 4f configuration, the parity selection in the crystal is relaxed and the ⁵D₀ → ⁷F₂ electric dipole transition will occur. If the Eu³⁺ ion is located in the non-inversion center, its emission spectrum will be dominated by the ⁵D₀ → ⁷F₂ electric dipole transition, and the emission spectrum will be around 610 nm. For the electronic transition of Eu³⁺ ion, the ⁵D₀ → ⁷F₀ transition originally belongs to the forbidden transition. However, when it is in the ten symmetry positions of C_s, C₁, C₂, C₃, C₄, C₆, C_2V, C_3V, C_4V and C_6V, ⁵D₀ → ⁷F₀ transition emission will occur, and the emission spectrum peak will be around 580 nm. A ⁵D₀ → ⁷F₀ transition peak appears in each site.²⁷ Therefore, based on the number of the peaks, the number of occupied sites of the Eu³⁺ ion crystals can be judged. Fig. 3(c) and (d) show the emission spectra of Ca₅(BO₃)₃F:1% Eu³⁺ upon excitation at 266 nm and 283 nm, respectively. Their peaks locate at 576 nm, which is due to ⁵D₀ → ⁷F₀ transition of Eu³⁺ ions. Each ⁵D₀ → ⁷F₀ transition peak corresponds to a lattice. Two ⁵D₀ → ⁷F₀ peaks, A₁ and A₂, were found in Fig. 3(c) and (d), which indicate that Eu³⁺ doping in Ca₅(BO₃)₃F has two sites.^28–30 The data are shown in Table 3 for the luminescent levels of Ca₅(BO₃)₃F:1% Eu³⁺ upon 266 and 283 nm excitation.

Table 3 The data for the luminescent levels of Ca₅(BO₃)₃F:1% Eu³⁺ upon 266 and 283 nm excitation

Energy level transition	The location of the peak (nm) (λex = 266 nm)	Intensity	The location of the peak (nm) (λex = 283 nm)	Intensity
^5D0 → ^7F0	576		576
	583		581
^5D0 → ^7F1	592	233 668.172	592	149 367.984
^5D0 → ^7F2	612	685 254.813	618	1 102 500
^5D0 → ^7F3	652		651
^5D0 → ^7F4	708		708
		2.933		7.381

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Since CT energy is susceptible to the central ionic environment, it can be quantitatively expressed by using environmental factors (h_e). h_e consists of four chemical bond parameters: the bond volume polarization , the covalency , the coordination number (C. N.) and the presented charge of the ligand . Its calculation formula is as follows:³¹

where represents the covalent value of μ type bond, is the charge exhibited by the nearest anion and stands for the polarizability of the μ-type chemical bond volume.

The four chemical bond parameters, with any change, will cause a shift in the CT bands. As h_e increases, the CT energy decreases, which means that the CT bands will produce a red shift. In Table 4, we can see that the h_e values of Ca1, Ca2, and Ca3 are 0.6397, 0.7439, and 0.3514, respectively. Therefore, it can be known that Eu will occupy the Ca1 and Ca2 sites, and at the same time, the O–Eu1 CT band at the Ca1 site corresponds to the peak at 266 nm and the O–Eu2 CT band at Ca2 corresponds to the position at 283 nm.

Table 4 The chemical bond parameters, environmental factor h_e, the experimental O² → Eu³⁺ charge transfer band, the environmental factor of any individual bond and their standard deviation of the Ca–O environmental factors

Central ion	Bond type	Distance (Å)				C.N.	he			O–Eu charge transfer peak
Ca1/Eu	Ca1–O1	2.3556	0.1160	0.4491	1.3333	1	0.6397	0.3043	0.1607	266 nm
	Ca1–O1	2.3960	0.1151	0.4819	1.3333	1		0.3140
	Ca1–O2	2.2283	0.1191	0.3569	1.3333	1		0.2748
	Ca1–O2	2.4020	0.1150	0.4870	1.3333	1		0.3155
	Ca1–O4	2.2428	0.1187	0.3666	1.3333	1		0.2781
	Ca1–F	2.3810	0.0258	0.2053	1.3333	1		0.0970
Ca2/Eu	Ca2–O1	2.3237	0.1167	0.4244	1.3333	1	0.7439	0.2967	0.0184	283 nm
	Ca2–O2	2.4795	0.1135	0.5557	1.3333	1		0.3348
	Ca2–O4	2.4653	0.1137	0.5426	1.3333	1		0.3312
	Ca2–O4	2.5136	0.1129	0.5882	1.3333	1		0.3436
	Ca2–O5	2.3311	0.1165	0.4300	1.3333	1		0.2984
	Ca2–O5	2.3726	0.1156	0.4627	1.3333	1		0.3083
Ca3/Eu	Ca3–O3	2.2691	0.1050	0.3493	1.0000	1	0.3514	0.1915	0.0520
	Ca3–O3	2.3551	0.1031	0.4080	1.0000	1		0.2051
	Ca3–O5	2.3363	0.1056	0.2512	0.6667	1		0.1086
	Ca3–O5	2.3371	0.1056	0.2515	1.0000	1		0.1630
	Ca3–F	2.4366	0.0257	0.2289	1.0000	1		0.0767
	Ca3–F	2.4497	0.0257	0.2347	1.0000	1		0.0777

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Obviously, the intensity of f–f transitions is affected by the crystal environment because of the different symmetry of the doping ions occupying the host sites. When the Eu³⁺ is doped into Ca₅(BO₃)₃F, the Eu ions occupy the Ca²⁺ sites, wherefore, the f–f transition relative intensity is mainly affected by the Ca²⁺ symmetry. The different ⁵D₀ → ⁷F_J transition intensities of Eu³⁺ depend on the local symmetry of the Eu³⁺ ion crystal field. The ⁵D₀ → ⁷F₂ transition is sensitive, while the ⁵D₀ → ⁷F₁ transition is stable to the crystal field environment. For example, when the Eu³⁺ ion is in a site with a strict inversion center, it will be dominated by the allowable ⁵D₀ → ⁷F₁ magnetic dipole transition, and the emission spectrum is around 590 nm, which is orange light. When the Eu³⁺ ion is in the site away from the inversion center, the parity selection in the crystal is relaxed, and a ⁵D₀ → ⁷F₂ electric dipole transition will occur; the emission spectrum is around 610 nm, emitting red light. If the intensity of the ⁵D₀ → ⁷F₂ transition is much higher than the intensity of ⁵D₀ → ⁷F₁, the Eu³⁺ ion mainly occupies the non-inversion symmetry of the lattice. It is known that the PL intensity ratio between ⁵D₀ → ⁷F₂ and ⁵D₀ → ⁷F₁ transition of Eu³⁺ increases as the crystal distortion increases. The degree of distortion can be calculated by using the standard deviation of environmental factor (EFSD),^22,32 which can be calculated as below:

whereand

The related chemical parameters of the covalency , the present charge of the ligand in the binary crystals, and the polarizability of the chemical bond volume are shown in Table 4. On the basis of the eqn (2)–(4), their standard deviation for the six Ca–O environmental factors of Ca1O₅F, Ca2O₄F₂, and Ca3O₆ polyhedrons in Ca₅(BO₃)₃F:1% Eu can be calculated to be 0.1607, 0.0184 and 0.052, respectively. Generally, the I(⁵D₀/⁷F₂)/I(⁵D₀/⁷F₁) value of Eu³⁺ increases with increasing . The value of Ca1O₅F in Ca₅(BO₃)₃F:1% Eu is larger than that of Ca2O₄F₂. By comparison, the intensity ratio of ⁵D₀ → ⁷F₂ transition to the ⁵D₀ → ⁷F₁ transition of Eu³⁺ at Ca2 (7.381) is 2.5 times stronger than that of Eu³⁺ at Ca1 site (2.933). Therefore, the I(⁵D₀ → ⁷F₂)/I(⁵D₀ → ⁷F₁) of Eu³⁺ in the Ca1O₅F site is stronger than that in the Ca2O₄F₂ site. Ca1 and Ca2 correspond to excitations at 283 nm and 266 nm, respectively. However, this is contrary to the conclusion drawn in Table 4. In ideal state, the order of is in Fig. 4. When Eu³⁺ is doped into Ca₅(BO₃)₃F, part of the Ca²⁺ ions must be occupied by Eu³⁺, so the local environment of Eu³⁺ must be changed in order to keep the conservation of charge in Fig. 4(a) and (b). At this time, one F of the sub-stationary [(Eu1)O₅F]* and [(Eu3)O₄F₂]* will be replaced by an O to maintain their own stability; [(Eu2)O₆]* will receive an F, and it will eventually become a 7-coordinated environment in Fig. 4(c). In summary, we can conclude that the Ca2 distortion degree should be greater than that of Ca1. Therefore, Ca1 and Ca2 correspond to excitations at 266 nm and 283 nm, respectively, consistent with the results obtained in Table 4.

Fig. 4 The coordination environment mechanism of Ca1 (or Eu1), Ca2 (or Eu2), and Ca3 (or Eu3) in Ca₅(BO₃)₃F:1% Eu.

3.3 Chemical bond energy calculation

From the point of view of matched valence, the bond energy of Eu³⁺ into the Ca₅(BO₃)₃F phosphor can be estimated by the following equation,^20,33where V_M presents the dopant valence and V_N stands for the valence state of N. When the pure Ca₅(BO₃)₃F phosphor does not have any dopant, the value of V_N/V_M is 1. This indicates that the valence state has no effect on the bond energy. If V_N/V_M is not equal to 1, it implies that the valence state effectively affects the crystal bond energy. Consequently, the effect of different valence states of the dopant on the Ca²⁺ site bond energy can be quantitatively described through eqn (5). The J and d₀ values are given in the report of Li;³⁴ d_M–O represents the bond length between atoms M and O. Required d₀ and J value tables are in Table 5. When Eu enters Ca₅(BO₃)₃F, the bond energy difference is calculated by the following equation:

Table 5 Required d₀ and J values

Ions	d0 (Å)	J (kcal mol^−1)
Ca^2+–O^2−	1.967	126.60
Ca^2+–F^−	1.842	187.03
B^3+–O^2−	1.371	126.30
Eu^3+–F^−	2.056	163.35
Eu^3+–O^2−	2.074	109.40

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Here, is the bond energy difference when the Eu ion locates at the site of Ca²⁺. As previously reported, we can know that the dopants preferentially occupy a site where the bond energy difference is small , that is, a site having a smaller absolute value of .²⁰

According to the detailed crystallographic data from a pure Ca₅(BO₃)₃F phosphor (longer Ca–O bonds of 1.967 Å; shorter B–O bonds of 1.371 Å; longer Ca–F bonds of 1.842 Å), all calculated E_M–O and ΔE_M–O values of Eu³⁺ on both Ca²⁺ and B³⁺ sites are shown in Table 6. The corresponding occupancies of Eu³⁺ are summarized, according to the calculated values. Dopants preferentially occupy the sites where the bond energy difference is smaller; that is, Eu³⁺ ions preferentially occupy Ca²⁺ sites if ; they preferentially occupy B³⁺ sites if , otherwise.

Table 6 The bond parameters of the central atom and values of bond energy when Eu³⁺ locates at Ca and B sites in Ca₅(BO₃)₃F. All of the bond energy units are kcal mol⁻¹

Central atom	Coordination atom	Count	d (Å)	EM–O
Ca1	O2	1×	2.2283	62.4781	48.0633	11.0351
	O4	1×	2.2428	60.0770	46.2162
	O1	1×	2.3556	44.2901	34.0716
	O1	1×	2.3960	39.7088	30.5473
	O2	1×	2.4020	39.0701	30.0559
	F1	1×	2.3810	41.3517	31.8111
Ca2	O1	1×	2.3237	48.2781	48.0632	1.7744
	O2	1×	2.4795	31.6867	46.2162
	O4	1×	2.4653	32.9264	34.0716
	O4	1×	2.5136	28.8969	30.5473
	O5	1×	2.3311	47.3221	30.0559
	O5	1×	2.3726	42.3012	31.8111
Ca3	O3	1×	2.2691	55.9549	37.1394	14.2389
	O3	1×	2.3551	44.3500	24.3760
	O5	1×	2.3363	46.6617	25.3297
	O5	1×	2.3371	46.5609	22.2299
	F1	1×	2.4366	35.5821	36.4041
	F1	1×	2.4497	34.3444	32.5416
B1	O4	1×	1.4296	107.8004	734.209	551.7228
	O5	1×	1.5032	88.35499	707.712
	O2	1×	1.3091	149.2999	687.725
B2	O1	1×	1.4297	107.7712	624.1322	636.8898
	O1	1×	1.4304	107.5676	622.9525
	O3	1×	1.2329	183.4429	1062.3664

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There are three Ca²⁺ sites and two B³⁺ sites in the structure of Ca₅(BO₃)₃F. On the basis of the bond energy method, the values of and have been listed in Table 6. The order of difference of bond energy that Ca²⁺and B³⁺ ions are replaced by Eu³⁺ is , which means that Eu³⁺ preferentially replaces Ca2 and Ca1. According to our calculation, Eu³⁺ preferentially occupies Ca2 and Ca1 sites, which is consistent with the environmental factor, the analysis and PL spectrum.

4. Conclusions

The photoluminescence of Ca₅(BO₃)₃F:1% Eu³⁺ shows that the excitation spectrum consists of some broadband from the O²⁻ → Eu³⁺ charge transfer (CT) band and some sharp emission peaks derived from the f–f transition of Eu³⁺. Two different O²⁻ → Eu³⁺ CT broad bands with the peaks at 266 and 283 nm in Ca₅(BO₃)₃F:1% Eu³⁺ can be assigned to the Eu³⁺ sites occupying Ca1 and Ca2, respectively. Two ⁵D₀ → ⁷F₀ peaks, A₁ and A₂, were found, which implies that Eu³⁺ doped in Ca₅(BO₃)₃F has two sites. According to the dielectric theory of the crystal, the important chemical bonds such as the polarizability, the covalency and the environmental factor were quantitatively calculated. When Eu³⁺ ions occupy the Ca1, Ca2 and Ca3 sites of Ca₅(BO₃)₃F, their environmental factors are 0.6397, 0.7439 and 0.3514, respectively. The intensity ratio of ⁵D₀ → ⁷F₂ transition to the 5D₀ → 7F₁ transition of Eu³⁺ at Ca2 (7.381) is 2.5 times stronger than that of Eu³⁺ at Ca1 site (2.933). The calculated ideal showed that the I(⁵D₀/⁷F₂)/I(⁵D₀/⁷F₁) value at Eu1 is larger than that at Eu2 site. The local nonequivalence substitution distortion model was proposed to explain the result. The smaller deviation value of the bond energy method of and showed that the preferential sites of Eu³⁺ ion occupancy in Ca₅(BO₃)₃F are Ca2 and Ca1. All of results are consistent with each other. The three theoretical methods provide us a new strategy to study the occupancy of Eu³⁺ in Eu³⁺-doped inorganic compounds.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is financially supported by the National Natural Science Foundations of China (Grant no. 21301053 and 21571165) and Hubei Natural Science Foundations from Science and Technology Department of Hubei Province (2018CFB517).

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