Novel Red-Emitting BaBi₂B₄O₁₀:Eu³⁺ Phosphors: Synthesis, Crystal Structure and Luminescence

Abstract

The novel red-emitting BaBi_2−xEu_xB₄O₁₀ (x = 0.05, 0.1, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6) phosphors were obtained by a crystallization from a glass. Distribution of the Eu³⁺ ions over cation sites were refined for x = 0.1, 0.3 and 0.4 from single-crystal X-ray diffraction data. Emission and excitation spectra of the Eu³⁺-doped BaBi₂B₄O₁₀ phosphors were investigated for the first time, where it was shown that characteristic lines are attributed to the intraconfigurational 4f-4f transitions. The optimal concentration for the BaBi_2−xEu_xB₄O₁₀ phosphors is x = 0.4, after which a luminescence intensity decreases. The CIE chromaticity coordinates for the BaBi₂B₄O₁₀:Eu³⁺ (x = 0.4) phosphor (0.65, 0.35) are close to the NTSC standard values (0.67, 0.33) for commercial red phosphor. The obtained results show that the BaBi₂B₄O₁₀:Eu³⁺ phosphors are promising candidates for solid state lighting application.

1. Introduction

Nowadays, white light-emitting diodes (wLED) are an important part of light source devices. The wLED-based devices have many advantages, such as high luminescence efficiency, environmental friendliness, long working lifetime, small size, light weight, durability, etc. [1,2,3] There are several ways to fabricate the wLED: (1) an exciting of single-phase yellow-emitting or mixed green- and red-emitting phosphors by a blue LED chip; (2) the exciting of red-, green- and blue-emitting phosphors by near ultraviolet LED chips; (3) a combination of red, green and blue separate monochromatic LED chips (RGB wLED) [4,5]. The fabrication of the latter ones is associated with many problems, such as high cost, complexity of fabricating, unstable aging of components, different thermal behavior, etc. [6] Generally, a commercial wLED is a combination of yellow-emitting phosphor Y₃Al₅O₁₂:Ce³⁺ (YAG: Ce³⁺) with high photoluminescence quantum yield and good thermal stability with a blue diode chip. However, due to the absence of a red-light component in the emission of YAG: Ce³⁺, this phosphor cannot be used as a source of warm white light with a high-color-rendering index and low correlated color temperature [7]. Thus, it is an actual scientific task to find novel red phosphors to solve the current problems.

Hence, borates activated with rare earth elements are of a great interest, and these are promising materials for the fabrication of various types of the wLED due to wide transparency in the ultraviolet range, relatively easy synthesis, high optical damage threshold and thermal stability, and environmental friendliness in comparison to commercial red-emitting phosphors such as (Sr, Ca)S:Eu²⁺, Y₂O₂S:Eu³⁺ and other.

Complex compounds in the MO–Bi₂O₃–B₂O₃ (M = Ca, Sr, Ba) borate systems are actively studied in order to obtain promising optical matrices and materials. For example, structurally similar MBi₂B₂O₇ (M = Ca, Sr, Ba) [8,9,10,11] borates form a family of prospective red-emitting phosphors. The photoluminescence properties of the M₃Bi₂(BO₃)₄:Eu³⁺ (M = Sr, Ba) compounds were investigated in [12,13], and the crystal structure and photoluminescence of CaBi₂B₄O₁₀:Eu³⁺ phosphors were studied in [14]. Optical, structural, dielectric and photoluminescence properties of MO–Bi₂O₃–B₂O₃ (M = Ca, Sr, Ba) glasses were studied in [15,16,17,18,19,20,21,22,23].

The crystal structure of BaBi₂B₂O₇ contains three crystallographically independent sites for the Ba and Bi atoms. These sites split on the Bi and Ba subpositions. The average distance between centers of photoluminescence in the BaBi_1.60Eu_0.40B₂O₇ sample with optimal concentration is 21.7 Å [11]. The crystal structure of Ba₃Bi₂(BO₃)₄ also contains three disordered independent sites for the Ba and Bi atoms. Initially, the Eu³⁺ ions occupy the M2 site only. The concentration quenching occurs when the Eu³⁺ ions start to distribute over all three cation sites in the Ba₃Bi₂(BO₃)₄:Eu³⁺ phosphor. The critical distance in the Ba₃BiEu(BO₃)₄ sample with optimal concentration is 9.5 Å. In the Ba₃Bi(B₃O₆)₃-Ba₃Eu(B₃O₆)₃ series of phosphors, the concentration quenching does not occur due to the large distance between the Bi(Eu) sites of about 7.2 Å [24].

This paper reports on the synthesis of the novel red-emitting BaBi₂B₄O₁₀:Eu³⁺ phosphors and glasses, its crystal structure refinement from single-crystal X-ray diffraction data, and investigation of its luminescent properties.

2. Materials and Methods

The BaBi_2−xEu_xB₄O₁₀ phosphors (x = 0, 0.05, 0.1, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6) were obtained by high-temperature solid phase synthesis. Barium carbonate BaCO₃ (Neva Reaktiv, 99.90% purity), boric acid H₃BO₃ (Neva Reaktiv, 99.90% purity), bismuth oxide Bi₂O₃ (Neva Reaktiv, 99.90% purity) and europium oxide Eu₂O₃ (Kyrgyz CMC, 99.93% purity) were mixed in stoichiometric proportions. Initially, Eu₂O₃ was heated at 900 °C for 3 h, BaCO₃ and Bi₂O₃—at 600 °C for 10 h. The powders were ground in an agate mortar for 1 h. Then the powders were pressed into pellets using a LabTools hydraulic press at a pressure of 80 kg/cm². The pellets were placed on platinum crucibles and melted in the Nabertherm HTC furnace at 900 °C for 1 h. The melts were poured out onto a cold steel plate. As a result, the BaBi_2−xEu_xB₄O₁₀ glasses were obtained (Figure 1). The polycrystalline samples were obtained by a crystallization of the glasses at 600 °C for 15 h.

Powder diffraction data of the BaBi_2−xEu_xB₄O₁₀ (x = 0–0.6) were collected using a Rigaku MiniFlex II diffractometer (CuKα, 2θ = 10–70°, step 0.02°). The phase composition was determined using PDXL integrated X-ray powder diffraction software and PDF-2 2016 (ICDD) database.

The distribution of the Eu³⁺ ions through the crystallographic sites was studied by means of Rigaku XtaLab Synergy-S diffractometer equipped with high-speed direct-action detector HyPix-6000HE (microfocus monochromatic MoKα radiation (λ = 0.71073 Å), frame widths 1.0° in ω). The optical microscope was used for single crystal selection of the BaBi_2−xEu_xB₄O₁₀ (x = 0.1, 0.3, 0.4) phosphors. Then the crystals were fixed on cryoloops with a Paratone-N oil. The obtained data was analyzed using the CrysAlisPro software (2015).

An absorption correction was introduced using the SCALE3 ABSPACK algorithm. The crystal structures of the BaBi_2−xEu_xB₄O₁₀ (x = 0.1, 0.3, 0.4) phosphors were refined in the P2₁/c space group using JANA2006 program [25]. Crystallographic data and refined parameters are given in

Table 1. Crystal data, data collection and details of refinement of the BaBi_2−xEu_xB₄O₁₀ (x = 0.1, 0.3, 0.4) phosphors.

Formula	BaBi2B4O10 [26]	BaBi1.94Eu0.06B4O10	BaBi1.67Eu0.33B4O10	BaBi1.57Eu0.43B4O10
Crystal system, space group	Monoclinic P21/c
T (K)	293
a (Å)	10.150 (2)	10.1897(4)	10.2051 (6)	10.2360 (6)
b (Å)	6.362 (1)	6.3806 (2)	6.3872 (2)	6.3962 (4)
c (Å)	12.485 (2)	12.4469 (5)	12.4369 (5)	12.3912 (8)
β (°)	102.87 (1)	102.706 (4)	102.597 (6)	102.424 (6)
V (Å3)	786.0 (2)	789.44 (5)	791.15 (7)	792.27 (9)
Z	4
Radiation type	Mo Kα
μ (mm−1)	49.67	48.63	44.65	43.17
Crystal size (mm)	0.14 × 0.08 × 0.06	0.04 × 0.04 × 0.1	0.08 × 0.06 × 0.04	0.06 × 0.04 × 0.02
Data collection
Diffracto- meter	Stoe IPDS II	Rigaku XtaLab Synergy-S
Absorption correction	multi-scan
No. of measured, independent and observed [I > 3σ(I)] reflections	6949/2109/1813	8837/2701/1954	7448/2601/1758	8343/2681/2083
Rint	0.057	0.045	0.047	0.032
(sin θ/λ)max (Å−1)		0.776	0.769	0.777
	Refinement
R (obs), wR (obs), S	0.049, 0.113, 1.14	0.032, 0.033, 1.13	0.034, 0.035, 1.12	0.027, 0.030, 1.22
No. of reflections	2109	2701	2601	2681
No. of parameters	83	150	156	156
∆ρmax, ∆ρmin (e Å−3)	-	2.04/−1.68	2.29/−1.87	2.05/−1.39

, atomic coordinates, equivalent displacement parameters, atomic anisotropic displacement parameters and selected bond lengths are given in Tables S1–S3. Further details of the crystal structure investigations can be obtained from the Cambridge Structural Database on quoting the depository numbers CSD 2222018, 2222019 and 2222020.

The chemical composition (5) was studied using a QUANTA 200 3D electron microprobe equipped with an energy-dispersive spectroscopy system, operated at 16 kV and 780 pA, with a beam size of 1 μ. Analytical results are given in Table S4. The empirical formulae calculated on the basis of 10 O atoms per formula unit are Ba_1.01Bi_1.58Eu_0.40B_4.02O₁₀ (x = 0.4) and Ba_0.98Bi_1.90Eu_0.10B_4.01O₁₀ (x = 0.1).

Raman spectra were measured using Horiba LabRam HR800 spectrometer with a spectral resolution 3 cm⁻¹ at 488 nm excitation. The laser beam was focused on the sample surface with 50× objective; the scattered light was collected four times for 1 min for each spectrum.

Absorption spectra were measured using a PerkinElmer Lambda 1050 spectrophotometer in a 150 mm integrating sphere with spectral resolution of 1 nm. Polycrystalline BaSO₄ powder was used as a reference sample.

The luminescence excitation and emission spectra as well as kinetic curves luminescence quantum yields were measured on a Horiba Fluorolog-3 spectrometer. A Horiba LabRam HR800 spectrometer equipped with confocal microscope was used to correctly compare the efficiency of photoluminescence in glasses and crystalline samples. The emission spectra were obtained using a 50× objective, which allows the excitation light to be focused into a focal region with a diameter of 2 μm. Thus, the emission spectra were measured from the same volume of glass or crystalline samples under other equal experimental conditions.

3. Results and Discussion

3.1. Powder X-ray Diffraction of the BaBi_2−xEu_xB₄O₁₀ (x = 0–0.6)

X-ray phase analysis revealed that the polycrystalline samples of BaBi_2−xEu_xB₄O₁₀ (x = 0–0.3) were homogenous. The sample with x = 0.4 contained in its phase composition BaBi₂B₂O₇ and/or BaBi2-xEuxB₂O₇ as an impurity in a quantity of about 30 wt.% (see Figure 2), which is due to a limitation of the Eu³⁺ → Bi³⁺ isomorphic substitution for these solid solutions. This leads to the area of immiscibility for the 0.3 ≤ x ≤ 0.4 samples. The sample with x = 0.5 contains of about 18 wt.% of Ba(Bi,Eu)₂B₄O₁₀, 36 wt.% of Ba₃(Bi,Eu)B₉O₁₈, 24 wt.% of (Bi,Eu)₄B₂O₉ and 22 wt.% of EuBO₃ (P6₃/mmc), and the sample with x = 0.6 contains 11 wt.% of Ba(Bi,Eu)₂B₄O₁₀, 36 wt.% of Ba₃(Bi,Eu)B₉O₁₈, 31 wt.% (Bi,Eu)₄B₂O₉ and 22 wt.% of EuBO₃ (P6₃/mmc).

Figure 3 shows the unit cell parameters and volume vs. the Eu³⁺ concentration. This dependence can be approximated by a linear function, but a slight bend can be noticed. Perhaps this is due to the fact that, with an increase in the europium content, the Eu³⁺ ions can replace Bi³⁺ in nonequivalent crystallographic sites. It can be also assumed that as the amount of the europium increases, the Eu³⁺ ions can replace the Bi³⁺ ones in different crystallographic sites.

3.2. Crystal Structure of the BaBi_2−xEu_xB₄O₁₀ (x = 0.1, 0.3, 0.4) Phosphors

The BaBi₂B₄O₁₀:Eu³⁺ phosphors crystallize in the BaBi₂B₄O₁₀ structure type, monoclinic system, space group P2₁/c, Z = 4 (Figure 4a) [26]. Refined formulae of the BaBi_1.94Eu_0.06B₄O_10, BaBi_1.67Eu_0.33B₄O₁₀ and BaBi_1.57Eu_0.43B₄O₁₀ crystal structures are close to the BaBi_1.90Eu_0.10B₄O_10, BaBi_1.70Eu_0.30B₄O₁₀ and BaBi_1.60Eu_0.40B₄O₁₀ (5, 15, 20 at % Eu) stoichiometric mixtures. There are one Ba, two Bi, four B and ten O sites in asymmetric unit (Tables S1 and S2). The B(1), B(3) and B(4) atoms are surrounded by four oxygen atoms to form tetrahedra with bond lengths that vary in the range 1.44–1.51, 1.46–1.59, 1.44–1.51 Å (for x = 0.1), 1.44–1.51, 1.45–1.56, 1.45–1.51 Å (x = 0.3) and 1.44–1.50, 1.44–1.62, 1.44–1.50 Å (x = 0.4) (Table S3). The B(2) atom is triangularly coordinated by oxygen atoms and the B–O bonds are in the range 1.36–1.41 Å (for x = 0.1), 1.35–1.40 Å (x = 0.3) and 1.34–1.40 Å (x = 0.4). cm⁻¹.

According to [26], corner-sharing borate polyhedra form the [B₄O₁₀]⁸⁻ chain consisting of triborate group and single BO₃ triangle. The triborate group is formed by three independent tetrahedra B(1)O₄, B(3)O₄ and B(4)O₄. This group can be written as <3□> in accordance with notation of Burns et al. [27]. The full notation of the [B₄O₁₀]⁸⁻ borate polyanion is 4B:∆3□:<3□>∆ (Figure 4b). Such a borate polyanion is unique because it was found only in the BaBi₂B₄O₁₀ structure type.

The Bi(1) and Bi(2) atoms form four short Bi–O bonds in the range 2.14–2.41 Å, and three and two relatively long bonds (2.56–2.87 and 2.59–2.89 Å, respectively). It results in the formation of the BiO₇ and BiO₆ polyhedra with [4+3] and [4+2] coordinations of Bi. Such a coordination of the Bi atoms is asymmetric due to the presence of the 6s² stereoactive lone electron pair. The Bi(1)O₇ and Bi(2)O₆ polyhedra share edges to form the [Bi₂O₁₀] dimers. These dimers are linked through the O(5) atoms to form [Bi₂O₇] chains along the [010] direction [26] (Figure 4c). The Bi–O chains share edges (O3), forming [Bi₂O₅] bismuthate layers in bc plane. The Ba(1) site has an eightfold coordination (Figure 4d) with the Ba–O bond lengths vary in the range 2.75–2.90 Å (x = 0.1), 2.75–2.91 Å (x = 0.3) and 2.74–2.89 Å (x = 0.4). The next four bonds are in the range 3.10–3.20 Å.

Generally, the lone electron pair of the Bi³⁺ ion is stereoactive if the Lewis basicity strength presents in a crystal structure. In the BaBi₂B₄O₁₀ crystal structure, the unique borate anion [B₄O₁₀]⁸⁻ is a structural unit. A knowledge of coordination numbers of cations and anions in a structural unit lets us calculate the Lewis basicity of the unit [27,28,29,30,31]. In the [B₄O₁₀]⁸⁻ structural unit, the average coordination number of the O atoms is 3.9. There are 39 bonds in the crystal structure that involve the O atoms of the structural unit. Within the structural unit, there are 15 bonds in the BO₄ tetrahedra and BO₃ triangle. Therefore, the Lewis basicity of the structural unit is 8/24 = 0.30 vu. The presence of such a strong Lewis base is the determining factor for the stereoactivity of the Bi³⁺ lone electron pair. The bond-valence calculations were performed using empirical parameters taken from Brown and Altermatt (1985) [32] (Table S2).

3.3. A Distribution of the Eu³⁺ Ions over the Crystallographic Sites

The Ba and Bi cations are fully ordered in the BaBi₂B₄O₁₀ crystal structure [26]. In the BaBi_1.90Eu_0.10B₄O₁₀ crystal structure, the Eu³⁺ atoms occupy only the Bi(1) site. Then, the Eu³⁺ atoms occupy 22% of the Bi(1) site and 11% of the Bi(2) site in the BaBi_1.70Eu_0.30B₄O₁₀ crystal structure, and 31% of the Bi(1) site and 11% of the Bi(2) site in the BaBi_1.60Eu_0.40B₄O₁₀ crystal structure, respectively (Figure 5).

The immiscibility of the BaBi_2−xEu_xB₄O₁₀ solid solutions may be caused by structural distortions. Presumably, a main reason for structural distortions is a five-fold coordination of the O(2) atom by the B(1), B(3), Bi(1), Bi(2) and Ba(1) ones. The B(1)–O(2) and B(3)–O(2) bond lengths are 1.49 and 1.56 Å in BaBi₂B₄O₁₀, and 1.50 and 1.62 Å in BaBi_1.60Eu_0.40B₄O₁₀. Usually, the B–O bond lengths in the BO₄ tetrahedron vary in the range 1.462–1.512 Å [33]. Perhaps, the longest B–O bond (1.69 Å) was found in the crystal structure of high boracite [34], where the one O site is surrounded by four B ones. The Bi(1)–O(2) and Bi(2)–O(2) bond lengths are 2.73 and 2.59 Å in BaBi₂B₄O₁₀. The Eu atoms substitute the Bi ones in the Bi(1) and Bi(2) sites. The ionic radius of the Eu³⁺ ion (1.15 Å) is smaller than the Bi³⁺ one (1.24 Å) for the coordination number equals 7 [35]. Therefore, in the BaBi_1.60Eu_0.40B₄O₁₀ crystal structure, the Bi(1)–O(2) and Bi(2)–O(2) bond lengths are shorter (2.66 and 2.60 Å). The Ba(1)–O(2) bond practically does not change (see Table S2). Apparently, these structural distortions are caused by the Eu³⁺ → Bi³⁺ substitution. The bond valence of the B(1)–O(2) bond decreases from 0.60 vu in in BaBi₂B₄O₁₀ to 0.50 vu in BaBi_1.60Eu_0.40B₄O₁₀. Such a decrease is partially compensated by an increase in the valence of the Bi(1)–O(2) bond from 0.18 to 0.21 vu. The bond valence sum for the O(2) site decreases from 1.97 to 1.87 vu. Presumably, this is one of the reasons leading to the immiscibility of the BaBi_2−xEu_xB₄O₁₀ solid solutions.

3.4. Raman Spectroscopy

The Raman spectra of the samples are shown in Figure 6. According to the spectra, the structure of the samples does not change up to when the Eu³⁺ concentration equals 0.30. A further increase in the concentration of the activator ion leads to the area of immiscibility of the BaBi_2−xEu_xB₄O₁₀ solid solutions. The sample with x = 0.4 contained about 70 wt.%, BaBi_2−xEu_xB₄O₁₀ and 30 wt.% BaBi₂B₂O₇ and/or BaBi_2−xEuxB₂O₇ in its phase composition. The samples with x = 0.5 and 0.6 have difficult phase compositions (see Section 3.1). With an increase in the Eu content, the concentration of phases (Ba₃(Bi,Eu)B₉O₁₈ and (Bi,Eu)₄B₂O₉) containing only the BO₃ triangular radicals also increases. Broad Raman bands confirm a disordered model of the crystal structure. The main structural units are the BO₄ tetrahedra and the BO₃ triangles.

Assignment of the Raman bands is presented in

Table 2. Raman bands assignment for the BaBi_2−xEu_xB₄O₁₀ (x = 0–0.6) samples.

Raman Band, cm−1	Assignment
115	Bi-O
135	Bi3+ cations in the form of (BiO6)
165	δ (BO4)
188, 242, 280	γ(BO3)
341	δ (BO4)/γ(BO3)
358	δ (BO3)/γ(BO3)
397, 470	Bi–O–Bi bond vibrations of BiO6 octahedral
534, 569	δ (BO3)/δ(BO4)
582	Stretching vibrations of Bi–O bonds in BiO6 octahedrons
642, 676	δ(BO4)/γ(BO3)
817, 869,	νs (BO4)
940	νs (BO3)
968	νs (BO4)
1060, 1086, 1105	νas (BO4)
1234, 1298	νas (BO3)

ν—stretching vibration, δ—bending vibration, γ—librational vibration, s—symmetrical.

. Due to the combination of one BO₃ and three crystallographic independent BO₄ units consisting the [B₄O₁₀]⁸⁻ chain, the more detailed assignment of the vibrations is difficult. The positions of the Raman bands are assigned in accordance with [36,37].

3.5. Absorption Spectroscopy

The absorption spectra of the BaBi_2−xEu_xB₄O₁₀ (x = 0–0.6) samples (Figure 7a) demonstrate that the blue edge of the optical transparency window is below 400 nm. Narrow peaks correspond to the transitions between electronic states of Eu³⁺ ions. The position of the fundamental absorption edge plotted in Tauc coordinates was used to determine the optical band gap. The obtained values of the optical band gap depending on the concentration of active ions are shown in Figure 7b. The decrease in the band gap may be due to the occurrence of the immiscibility area between the 0.3 ≤ x ≤ 0.4 samples and the formation of defective localized states in the band gap at high concentrations of europium ions.

3.6. Photoluminescence Properties

All narrow bands in the luminescence excitation spectra correspond to the f-f transitions of the Eu³⁺ ions (Figure 8a). The broad band to the left of 350 nm is a charge transfer band which corresponds to the electronic transitions from 2p orbitals of O²⁻ to 4f orbitals of the Eu³⁺ ions [10.1016/j.jlumin.2013.10.002]. It can be seen that the optimal pump wavelength for the BaBi_2−xEu_xB₄O₁₀ (x = 0–0.6) samples is 392 nm, which corresponds to the ⁷F₀-⁵L₆ transition of the Eu³⁺ ions. Therefore, all experiments of the studied samples’ luminescent properties were carried out at 392 nm excitation. Figure 8b shows the luminescence spectra of the BaBi_2−xEu_xB₄O₁₀ (x = 0–0.6) samples depending on the europium ions concentration.

To determine the optimal concentration of active ions, the integrated intensity of the luminescence spectra was compared. The obtained concentration dependence of the integral intensity of Eu³⁺ ions is shown in Figure 9a. Obviously, the optimal concentration of the europium ions in the samples under study is x = 0.4. With a further increase in the concentration, the luminescence intensity decreases due to the concentration quenching and area of the immiscibility of the solid solution. The quantum yield measured for the x = 0.4 sample is 10% (Figure 9b).

All luminescence kinetic curves fit well with a single-exponential function (Figure 10a). One of the parameters sensitive to the environment of the active ions is the lifetime of excited states. The figure shows the dependence of the lifetime of the ⁵D₀ level on the concentration of the Eu³⁺ ions (Figure 10b).

The photoluminescence properties of glass and polycrystalline samples were compared using a Horiba LabRam HR800 spectrometer. The comparison was carried out according to the luminescence band in the region of 700 nm. It can be seen that the band is wider in the amorphous sample than in the crystalline one (Figure 11a). To compare the luminescent properties, the integral intensities were measured. The integrated intensity of amorphous samples is higher than crystalline ones with the corresponding concentration of active ions in the entire concentration range (Figure 11b).

The CIE chromaticity coordinates are given in

Table 3. CIE (CIE 1931) chromaticity coordinates of BaBi_2−xEu_xB₄O₁₀ (x = 0.05–0.6) samples.

C (Eu3+)	x	y
0.05	0.60	0.33
0.1	0.64	0.35
0.2	0.64	0.35
0.25	0.64	0.35
0.3	0.64	0.35
0.4	0.65	0.35
0.5	0.62	0.34
0.6	0.65	0.35

and presented in Figure 12. The CIE chromaticity coordinates for the BaBi_1.60Eu_0.40B₄O₁₀ phosphor at room temperature were (0.65, 0.35). This is close to the NTSC standard values (0.67, 0.33) for commercial red phosphor.

3.7. Energy Migration

The energy transfer between luminescence centers is determined mainly by the distance between the sites occupied by the activator ions in the crystal structure. According to the Dexter’s theory [38], a critical distance of 5 Å or less is necessary for achievement of the exchange interaction. Usually, the emission intensity decreases at high doping concentration and that can be explained as a result of the dipole-dipole interaction between the Eu³⁺ ions, the probability of which increases with decreasing distance between active ions. The distance between the Bi atoms in the chain is approximately 3.6 Å, and between the Bi sites from different [Bi₂O₇] chains within the layer is approximately 3.7 Å (Figure 13). The distance between the Bi sites which belong to different layers is already much greater than ~6.0 Å, which means that in this borate, with a high degree of probability, two-dimensional energy transfer between luminescence centers occurs. According to [39,40], this leads to an increase in the value of concentration quenching relative to the three-dimensional energy transfer between luminescence centers, and a decrease relative to the one-dimensional one.

The emission intensity of these borates can be explained in terms of the area of miscibility of the BaBi_2−xEu_xB₄O₁₀ solid solutions (x = 0–0.35) because the sample with x = 0.4 contains two phases (BaBi_2−xEu_xB₄O₁₀ and BaBi₂B₂O₇ or BaBi_2−xEu_xB₂O₇). Although, the optimal concentration for the BaBi_2−xEu_xB₄O₁₀ phosphors is x = 0.4 because this sample has the highest quantum yield. Although the critical energy transfer distance R_c between the europium ions was not achieved, it seems interesting to compare the energy transfer distance for optimal concentrations. The critical energy transfer distance can be calculated using an equation proposed by [41]:

$$R_c\approx 2{\left[\frac{3V}{4\pi x_{c}N}\right]}^{\frac{1}{3}}$$

where x_c is the critical doping content, N—the number of cation sites in the unit cell that can be occupied by activator ions and V—the volume of unit cell. Using these parameters, R_c was found to be 26.3 Å.

4. Conclusions

The novel red-emitting BaBi_2−xEu_xB₄O₁₀ (x = 0.05, 0.1, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6) phosphors were obtained by a crystallization from the glass. Crystal structures of the novel BaBi_2−xEu_xB₄O₁₀ (x = 0.1, 0.3, 0.4) phosphors were refined. Single-crystal X-ray diffraction showed that the Eu³⁺ → Bi³⁺ isomorphic substitution does not change the monoclinic system of the solid solutions. It is shown that the Eu³⁺ atoms first occupy the Bi(1) and then start to substitute the Bi(2) sites. This leads to the existence of the area of immiscibility for the 0.3 ≤ x ≤ 0.4 samples. An analysis of the distances between the luminescence centers shows that two-dimensional (2D) energy transfer can occur in these phosphors. The highest emission intensity with a quantum yield of 10% was demonstrated by BaBi_1.60Eu_0.40B₄O₁₀. In terms of the highest quantum yield, the optimal concentration for the BaBi_2−xEu_xB₄O₁₀ phosphors is found to be x = 0.4. The CIE chromaticity coordinates for the BaBi₂B₄O₁₀:Eu³⁺ (x = 0.4) phosphor were determined to be (0.65, 0.35) which are close to those for the NTSC standard (0.67, 0.33) for commercial red phosphor.