Optical properties and energy transfer in KYF₄:Sm³⁺ and KYF₄:Tb³⁺,Sm³⁺ polycrystalline materials

Abstract

KYF₄ polycrystalline materials singly doped with Sm³⁺ ions and co-doped with Tb³⁺/Sm³⁺ ions were synthesized by the hydrothermal technique. The optical spectra of all samples were measured at room temperature. The features of the ligand field and the optical properties of Sm³⁺ ions in KYF₄ were studied via Judd–Ofelt theory. A three-level model was used to estimate the validity of the Judd–Ofelt analysis for KYF₄:Sm³⁺. The luminescence quenching of KYF₄:Sm³⁺ relates to energy transfer through cross relaxation between Sm³⁺ ions. For KYF₄:Tb³⁺,Sm³⁺, the luminescence of Sm³⁺ ions is enhanced due to the energy transfer process from Tb³⁺ to Sm³⁺. The chromaticity features of the luminescence from KYF₄:Tb³⁺,Sm³⁺ were estimated by the chromaticity coordinates and correlated color temperature (CCT). The dominant interaction mechanism and the energy transfer parameters for the Sm³⁺–Sm³⁺ and Tb³⁺–Sm³⁺ energy transfer processes were analyzed by using the Inokuti–Hirayama model.

---

1. Introduction

In recent years, there has been special attraction in the development of optical devices based on divalent and trivalent lanthanide ions doped into inorganic compounds.^1–3 In comparison to oxide crystals, fluoride crystals have some outstanding advantages such as lower phonon energy, weaker nephelauxetic effect and larger band gap.^4–7 These characteristics can give a high luminescence efficiency for rare earth (RE) ions doped into fluoride crystals.^5,8 Among fluoride crystals, the fabrication technology for polycrystalline materials is much simpler than that for the single crystals.^8–11 For this reason, fluoride polycrystalline materials (e.g. MLnF₄ where Ln = Y, Gd and M = Li, K, Na, Ba) doped with trivalent rare earth ions (RE³⁺) have high potential for applications in lighting, white light emitting diodes (W-LEDs), quantum cutting, and so on.^9–15

The trivalent samarium (Sm³⁺) ion is a rare earth element which has been widely used in many fields such as color displays, undersea communications, solid lasers and high-density memories.^16,17 The luminescence applications of Sm³⁺ ions are mainly related to the strong emission intensity and large stimulated emission cross-section of the red-orange band (⁴G_5/2 → ⁶H_7/2 transition) under excitation with violet or near ultraviolet light.^9,17,18 Beside Sm³⁺, the trivalent terbium (Tb³⁺) ion is also extensively used for practical applications such as scintillators, phosphors, optical windows and lasers.^19–21 It is noted that there are two important excitation levels in the 4f⁸ energy structure of Tb³⁺ ions, which are the ⁵D₃ and ⁵D₄ levels. In materials with low phonon energy, the spectra of Tb³⁺ ions usually express bands originating from both the ⁵D₃ and ⁵D₄ levels.^5,9,10 These bands are often in the range from 370 to 680 nm.^19,22,23 Some emission bands of Tb³⁺ overlap with the excitation bands of Sm³⁺ ions.^9,10,17 Thus, in materials co-doped with Tb³⁺ and Sm³⁺ ions, Tb³⁺ ions usually play a role as sensitizer centers for the emission of Sm³⁺ ions.^9,17,23 For these materials, the luminescence of Sm³⁺ is enhanced significantly through the energy transfer process from Tb³⁺ to Sm³⁺. In addition, the blue and green luminescence of Tb³⁺ as well as the red-orange luminescence of Sm³⁺ may be obtained simultaneously at a suitable excitation wavelength. The intensity ratio between the emission bands of Tb³⁺ and Sm³⁺ ions depends on the ratio of the Sm³⁺/Tb³⁺ concentration.^10,17,23 For a suitable concentration ratio of Tb³⁺ and Sm³⁺, the material can emit white light. For this reason, materials co-doped with Tb³⁺ and Sm³⁺ ions have high potential for W-LED applications. So far, the white emission of the Tb³⁺/Sm³⁺ pair has been obtained in some fluoride crystals such as NaGdF₄,⁹ KGdF₄,¹⁰ and BaGdF₅.²³ In comparison to conventional phosphors, these white light sources are believed to have more advantages such as better color rendering index, higher brightness, lower cost, lower power consumption, longer lifetime span and more environmental benefit.^9,10,23

In this work, we present some new results on the optical properties of the KYF₄:Sm³⁺ polycrystalline material as well as the energy transfer process and white light emission of the KYF₄:Tb³⁺,Sm³⁺ polycrystalline material. Judd–Ofelt (JO) theory^24,25 and the Inokuti–Hirayama (IH) model²⁶ have been used as useful tools for our studies. It is known that the JO intensity parameters (Ω_λ=2,4,6) play the most important role in JO analysis. For the Eu³⁺ ion, these parameters can be calculated by using emission spectra, so it is easy to apply JO theory for polycrystalline materials doped with Eu³⁺. For other RE³⁺ ions, the JO analysis for polycrystalline materials is difficult because their Ω_λ parameters are only estimated through absorption spectra (it is not the diffuse reflection spectrum). To overcome this problem, polycrystalline materials can be compressed into pellets and the absorption spectra are measured by using these pellets. However, a normal hydraulic press only operates at room temperature and uses KBr to bond particles. This technique only creates pellets with low transparency and small density. This creates a large error in absorption intensity, which leads to low reliability in the results of the JO analysis. In our study, the powder products were compressed at a pressure of 100 MPa and temperature of 500 °C in a vacuum using a spark plasma sintering system (LABOX-210). Air bubbles in the pellets are also removed by compressing in a vacuum. At the high temperature, the edge of the particles becomes softer. For these experimental conditions, the obtained samples reach a high tightness. Consequently, they have good transparency (see the inset of Fig. 1) with an almost ideal density of the bulk material. These samples respond well for absorption measurements. The reliability of JO analysis for the KYF₄:Sm³⁺ polycrystalline material is evaluated by a three-level model.^27,29 To the best of our knowledge, this is the first report on the optical properties and energy transfer of Sm³⁺ singly doped as well as Tb³⁺/Sm³⁺ co-doped into KYF₄.

Fig. 1 XRD patterns of the KYF₄ polycrystalline material.

2. Experiment

The KY_1−xF₄:xSm³⁺ and KY_0.99−xTb_0.01F₄:xSm³⁺ (x = 0.1, 0.5, 1.0, 2.0 and 3.0 at%) polycrystalline materials were synthesized by the hydrothermal method as in our previous report.¹⁰ For this technique, the initial chemicals included solutions of KF, Y(NO₃)₃ and RE(NO₃) (RE = Tb³⁺ and Sm³⁺). The mixture and the catalyst PEG were poured into a 60 ml Teflon bottle held in a stainless steel autoclave and were sealed. The mixture was heated to 450 K and kept stable for 48 h, and then cooled down to room temperature. The precipitate product was rinsed with alcohol and distilled water, and then dried in air at 350 K for 24 h. The obtained products were annealed at 300 °C for 48 h. KYF₄ powder products were compressed into pellets with a diameter of 5.0 mm and thickness of 1.0 mm by a using a spark plasma sintering system (LABOX-210). This experiment was carried out in a vacuum at a pressure of 100 MPa and temperature of 500 °C. A visual photograph of a compressed sample is shown in the inset of Fig. 1. X-ray diffraction (XRD) patterns were measured using an X-ray diffractometer SIMEMS D5005, Bruker, Germany, with Cu-Kα1 radiation (λ = 1.54056 Å). Optical absorption measurements in the range from 200 to 2000 nm were performed using a Jascco V770 spectrometer with a spectral resolution of 0.5 nm. The excitation and luminescence spectra were measured using an FLS1000, Edinburgh, UK, with a 450 W Xe lamp. Decay curves of the ⁴G_5/2(Sm³⁺) and ⁵D₄(Tb³⁺) levels were measured using a Varian Cary Eclipse fluorescence spectrophotometer with a 450 watt xenon lamp as the excitation source. The samples were excited by UV/vis pulses having wavelengths of 401 nm (Sm³⁺:⁴G_5/2) or 373 nm (Tb³⁺:⁵D₄) with a duration of 80 μs. The luminescence signals were recorded at wavelengths of 602 and 542 nm for Sm³⁺:⁴G_5/2 and Tb³⁺:⁵D₄, respectively, with a spectral resolution of ±10 μs. All the measurements were carried out at room temperature.

3. Results and discussion

3.1. Structure analysis

Fig. 1 shows the XRD patterns of the prepared samples. These patterns are compared to the standard card for KYF₄ (JCPDS No. 027-0466). It can be seen that the diffraction peaks of the KYF₄ polycrystalline material coincide with those of the hexagonal phase of the standard card. There are no diffraction peaks belonging to other phases. This result indicates that the KYF₄:RE³⁺ polycrystalline material was crystallized in a hexagonal single phase. The average size (D) of the particles in the obtained samples can be estimated by the expression: D = Kλ/β cos θ, where K is a constant that has a value of 0.89, λ is the wavelength of the X-rays, θ is the diffraction angle of an observed peak, and β is the full-width at half-maximum at θ diffraction angle.^10,23 From the XRD patterns of the KYF₄ polycrystalline material, the value of D was estimated to be approximately 26 nm.

3.2. Optical properties of the KYF₄:Sm³⁺ polycrystalline material

3.2.1. Optical absorption spectra and Judd–Ofelt parameters. The absorption spectra of some KYF₄:Sm³⁺ samples are presented in Fig. 2. It can be seen that the absorption bands were recorded in the regions of UV-vis (390–520 nm) and NIR (1000–1650 nm). The origin of these bands is given in Carnall's publication.³⁰ In the NIR region, the Sm³⁺ absorption spectra consist of five bands at wavelengths of 1071, 1228, 1374, 1478 and 1536 nm. These bands correspond to the transitions from the ⁶H_5/2 ground level to the ⁶F_9/2, ⁶F_7/2, ⁶F_5/2, ⁶F_3/2 and ⁶H_15/2 levels, respectively.³⁰ The transitions in the NIR region are allowed by the spin selection rule (ΔS = 0), so they express strong intensities. The ⁶H_5/2 → ⁶F_3/2 transition is a hypersensitive (HS) transition because it obeys the selection rule of ΔS = 0, ΔJ = 1 and ΔL = 1 (the HS transition: ΔS = 0, |ΔJ| ≤ 2 and |ΔL| ≤ 2). It is noted that the energy levels in the UV-vis region of Sm³⁺ are very close to each other,³⁰ so there is always an overlap of the transitions from the ⁶H_5/2 ground level to the ^2S+1L_J levels. For KYF₄:Sm³⁺, the absorption spectra in the UV-vis region show a narrow band at 401 nm (⁶H_5/2 → ⁶P_3/2,⁴F_7/2 transition) and some broad bands centered at around 416, 439, 466, 475 and 489 nm. They are assigned to the ⁶H_5/2 → ⁶P_5/2 + ⁴M_19/2, ⁶H_5/2 → ⁴M_17/2 + ⁴G_9/2, ⁶H_5/2 → ⁴I_13/2,⁶H_5/2 → ⁴I_11/2 and ⁶H_5/2 → ⁴I_9/2 transitions, respectively.³⁰ The absorption transitions in the UV-vis region indicate a weak intensity (except the ⁶H_5/2 → ⁶P_3/2 transition) because they are forbidden by the spin selection rule. The energies of the absorption transitions for Sm³⁺ in KYF₄ (ν_c) are indicated in Table 1 (see column 3) in comparison with those of free Sm³⁺ ions (ν_aqo). It can be seen that there is a shift of some transitions toward high energy when the Sm³⁺ ions were doped into the KYF₄ polycrystalline material. This shift relates to the extension effect of the electron cloud (nephelauxetic effect).^5,31 The influence of the nephelauxetic effect is characterized by the bonding parameter (δ). The calculation expressions for the bonding parameter were presented in our previous reports.^5,8 The values of δ can provide information about the nature of the RE³⁺–ligand bond (ionic or covalent bond) in any host. For the KYF₄:Sm³⁺ polycrystalline material, the bonding parameters were found to be −0.745, −0.723, −0.708, −0.672, −0.551 and −0.624 for Sm³⁺ concentrations of 0.1, 0.5, 1.0, 1.5, 2.0 and 3.0 at%, respectively. The δ parameter gets a negative value for all samples, indicating an ionic feature for the Sm³⁺–F⁻ bond in KYF₄:Sm³⁺. This bonding nature is the same as that of the Sm³⁺–F⁻ bond in some crystals such as K₂GdF₅:Sm³⁺⁸ and K₂YF₅:Sm³⁺.³²

Table 1 Energies (ν_aqo, ν_c) and oscillator strengths (f_exp, f_cal) for some transitions in the Sm³⁺-doped KYF₄ polycrystalline material (KYF₄:0.5Sm³⁺ sample)

^6H5/2 →	ν aqo (cm^−1)	ν c (cm^−1)	f exp (×10^−6)	f cal (×10^−6)
^6H15/2	6508	6493	0.24	0.02
^6F3/2	6630	6766	0.67	0.71
^6F5/2	7100	7294	1.77	1.58
^6F7/2	8000	8130	2.64	3.25
^6F9/2	9200	9319	3.19	2.38
^4I9/2	20 526	20 534	0.26	0.45
^4I11/2	21 100	21 097	0.53	0.16
^4I13/2	21 600	21 505	0.92	0.38
^4M17/2, ^4G9/2	22 706	22 831	—	—
^6P5/2, ^4M19/2	24 050	24 154	—	—
^4F7/2, ^6P3/2	24 950	24 937	3.46	3.22
	δ = −0.723		RMS = 0.55 × 10^−7

---

Fig. 2 Absorption spectra of the KY_1−xF₄:xSm³⁺ samples: (a) x = 0.5 at%, (b) x = 1.5 at% and (c) x = 3.0 at%.

It is known that Judd–Ofelt theory is a useful tool for studying the spectroscopy of RE³⁺ ions doped into any matrix. This theory allows us to not only calculate the optical parameters of the RE³⁺ ions but also estimate the features of the ligand field. The set of Ω_λ (λ = 2, 4, 6) intensity parameters, which are the key of JO theory, can be calculated by using the absorption spectrum. For an electric dipole absorption transition in a RE³⁺ ion, the oscillator strength (f_cal) is calculated by the following formula:^18,32

where Ω_λ are the Judd–Ofelt parameters, n is the refractive index of the material, J is the total angular momentum of the ground level, and ‖U^λ‖² are the squared doubly reduced matrix elements of the unit tensor operator of rank λ = 2, 4, 6. The values of ‖U^λ‖² are considered independent from the host and can be found in Carnall's report.³⁰

From the absorption spectra of the RE³⁺ ions, the experimental oscillator strength (f_exp) is estimated by the expression:^18,28

where α is the molar extinction coefficient at energy ν (cm⁻¹).

Using the absorption spectra of the RE³⁺ ion doped material, the experimental oscillator strength of all transitions can be calculated from eqn (2). The Ω_2,4,6 parameters were evaluated by solving the equation system f_cal = f_exp through the method of least squares. It is noted that the magnitude of Ω_λ relates to the kind of RE³⁺ ions and host matrix, but they do not depend on any particular transition.²⁷ In order to minimize the error, we only use the strong absorption bands for calculating the Ω_λ parameters. For the bands having an overlap of transitions, the matrix elements are the sum of the elements for each individual transition. For the KYF₄:Sm³⁺ polycrystalline material, the experimental oscillator strengths of some absorption bands are presented in column 4 of Table 1. The intensity parameters for Sm³⁺-doped KYF₄ were calculated and are indicated in Table 2. The obtained results are compared with those of the Sm³⁺ ion in some fluoride crystals.^8,32–34 It is reported that the Ω₂ parameter strongly depends on the characteristics of the local environment around RE³⁺ ions such as the ligand asymmetry and covalency of the RE³⁺–ligand bond. A larger value of the Ω₂ parameter indicates a higher degree of ligand asymmetry as well as the higher covalency in the RE³⁺–ligand bond. The data in Table 2 show that the Ω₂ magnitude in KYF₄:Sm³⁺ is higher than that in some other fluoride crystals (see Table 2). This result shows that the ligand asymmetry and covalent of the RE³⁺–ligand bond in the KYF₄:Sm³⁺ polycrystalline material are higher than those in K₂GdF₅:Sm³⁺,⁸ K₂YF₅:Sm³⁺,³² BaY₂F₈:Sm³⁺,³³ and LiYF₄:Sm^3+ 34 crystals. Using the Ω_λ intensity parameters, the oscillator strength of the absorption transitions was recalculated through eqn (1). The calculated results for the KYF₄:0.5Sm³⁺ sample are presented in column 5 of Table 1. The root mean square (RMS) deviation for this sample was found to be 0.55 × 10⁻⁷. The small value of the RMS deviation shows that there is good agreement between the experimental and calculated results for the KYF₄:Sm³⁺ polycrystalline material.

Table 2 The Ω_λ (×10⁻²⁰ cm²) intensity parameters for Sm³⁺ in some fluoride crystals

Materials	Ω 2	Ω 4	Ω 6	Ref.
KYF4:0.1%Sm^3+	0.85 ± 0.12	2.85 ± 0.25	3.03 ± 0.34	Present
KYF4:0.5%Sm^3+	0.84 ± 0.15	3.00 ± 0.31	2.68 ± 0.36	Present
KYF4:1.0%Sm^3+	0.92 ± 0.12	2.81 ± 0.32	3.01 ± 0.25	Present
KYF4:1.5%Sm^3+	0.95 ± 0.14	2.98 ± 0.33	3.12 ± 0.28	Present
KYF4:2.0%Sm^3+	1.02 ± 0.16	3.01 ± 0.29	2.78 ± 0.32	Present
KYF4:3.0%Sm^3+	0.94 ± 0.13	3.02 ± 0.36	2.98 ± 0.35	Present
K2YF5:1.0%Sm^3+	0.38	3.55	2.18	32
K2GdF5:1.0%Sm^3+	0.50	2.96	2.05	8
BaY2F8:1.0%Sm^3+	0.37	2.03	1.12	33
LiYF4:1.0%Sm^3+	0.55	2.44	1.72	34

---

3.2.2. Excitation and emission spectra and radiative parameters. The excitation spectra of the Sm³⁺-doped KYF₄ polycrystalline material were measured in the range from 350 nm to 500 nm by monitoring at the emission wavelength of 602 nm (⁴G_5/2 → ⁶H_7/2 transition). As shown in Fig. 3 (curve a), the excitation spectrum exhibits some bands which are generated by the ⁶H_5/2 → ^2S+1L_J intra-transitions 4f⁵ configuration of the Sm³⁺ ions. Among the excitation transitions, the ⁶H_5/2 → ⁴F_7/2 + ⁶P_3/2 transition centered at 401 nm has the strongest intensity, so it is usually used for luminescence excitation of Sm³⁺ ions. It can be seen that the excitation bands are in the UV-vis region, which is the activity region of popular sources such as Xe lamps and UV or blue LEDs. This shows an advantage in the application of phosphors doped with Sm³⁺ ions.

Fig. 3 Excitation spectra of Sm³⁺ (a) and (b) Tb³⁺ in the KYF₄ polycrystalline material.

Fig. 4 presents the luminescence spectra of the KYF₄:Sm³⁺ samples under excitation at 401 nm. The luminescence spectra consist of four emission bands at wavelengths of 563, 602, 649 and 711 nm. These bands are attributed to the transitions from the ⁴G_5/2 excited level to the ⁵H_5/2, ⁵H_7/2, ⁵H_9/2 and ⁵H_11/2 ground levels, respectively.³⁰ The ⁴G_5/2 → ⁵H_9/2 and ⁴G_5/2 → ⁵H_11/2 transitions are induced electric dipole transitions, i.e. their intensity may change strongly between various hosts. The ⁴G_5/2 → ⁵H_5/2 and ⁴G_5/2 → ⁵H_7/2 bands include both electric dipole and magnetic dipole transitions. However, the main mechanism of the ⁴G_5/2 → ⁵H_7/2 transition is electric dipole, whereas ⁴G_5/2 → ⁵H_5/2 has a dominant magnetic dipole mechanism.^8,16 It can be seen that the ⁴G_5/2 → ⁵H_7/2 transition has the strongest intensity of all. The red-orange characteristic luminescence of Sm³⁺-doped phosphors under UV excitation is mainly due to this emission band. In fact, the ⁴G_5/2 → ⁵H_7/2 transition may be used for laser action because its branching ratio is usually higher than 50%.^8,18 For the KYF₄:Sm³⁺ compressed samples, the experimental branching ratio of the ⁴G_5/2 → ⁵H_7/2 transition is highest among the emission bands and has values larger than 50% for all samples (see column 2 of Table 3). For this reason, some radiative parameters (e.g. stimulated emission cross-sections (σ_λp, 10⁻²² cm²), gain bandwidth (σ_λp × Δλ_eff, 10⁻²⁸ cm³) and optical gain (σ_λp × τ_cal, 10⁻²⁵ cm² s⁻¹)) would be calculated for the ⁴G_5/2 → ⁵H_7/2 transition. The calculation expressions for these parameters were expressed in our previous studies.^16,32 The obtained results are presented in Table 3 in comparison with the radiative parameters of some other fluoride crystals.^8,32,34 It can be seen that the β_exp value for the ⁴G_5/2 → ⁵H_7/2 transition of the KYF₄:Sm³⁺ samples is slightly lower than that of K₂YF₅:Sm³⁺ and K₂GdF₅:Sm³⁺ but higher than that of LiYF₄:Sm³⁺. The stimulated emission cross-section of the ⁴G_5/2 → ⁵H_7/2 transition in KYF₄:Sm³⁺ is equivalent to that in K₂YF₅:Sm³⁺ and K₂GdF₅:Sm³⁺.

Fig. 4 Emission spectra of the KYF₄:Sm³⁺ samples.

Table 3 The radiative parameters of the ⁴G_5/2 → ⁵H_7/2 transition of Sm³⁺ ions doped in various hosts

Materials	β exp (%)	σ λp	σ λp × Δλeff	σ λp × τcal	Ref.
KYF4:0.1%Sm^3+	52.3	5.71	7.04	25.0	Present
KYF4:0.5%Sm^3+	54.6	5.51	6.79	24.9	Present
KYF4:1.0%Sm^3+	53.9	5.42	6.97	23.8	Present
KYF4:1.5%Sm^3+	54.6	5.98	7.31	25.2	Present
KYF4:2.0%Sm^3+	53.2	5.49	6.93	23.7	Present
KYF4:3.0%Sm^3+	54.5	5.72	7.18	24.3	Present
K2YF5:1.0%Sm^3+	56.5	6.40	—	—	32
K2GdF5:1.0%Sm^3+	58.2	5.98	—	—	8
LiYF4:1.0%Sm^3+	45.8	10.39	—	—	34

---

3.2.3. Evaluating the reliability of JO analysis for the KYF₄:Sm³⁺ polycrystalline material. As shown in Fig. 4, beside the luminescence bands originating from the ⁴G_5/2 level, the emission spectra of KYF₄:Sm³⁺ also recorded a weak luminescence band in the range from 490 to 545 nm. This band is attributed to the ⁴F_3/2 → ⁶H_5/2 transition in Sm³⁺ ions.³⁰ The appearance of the ⁴F_3/2 → ⁶H_5/2 luminescence band can be explained as follows. Upon excitation at a 401 nm wavelength, the Sm³⁺ ions are excited to the ⁶P_3/2 level. Because of the small energy gap between levels from ⁴F_3/2 to ⁶P_3/2, the ions quickly relax to the ⁴F_3/2 level by a multi-phonon process. It is noted that the energy distance from the ⁴G_5/2 level to ⁴F_3/2 is about a few hundred cm⁻¹, which is approximately the energy of two typical phonons in fluoride crystals.^5,7,8 Thus, the relaxation rate of ions becomes slower than the previous one. Then, from the ⁴F_3/2 level, the Sm³⁺ ions can relax to the lower levels in two ways. In the first way, they relax to the ground state by emitting photons and yield the ⁴F_3/2 → ⁶H_J (J = 5/2, 7/2,…) weak emission bands. However, it is difficult to obtain the ⁴F_3/2 → ⁶H_7/2,9/2 bands because they are overlapped with the ⁴G_5/2 → ⁶H_7/2,9/2 bands. In the second one, the Sm³⁺ ions drop to the ⁴G_5/2 level through multi-phonon relaxation. In addition, it is known that there is a resonance between the (⁴F_3/2 → ⁴G_5/2) and (⁶H_5/2 → ⁶H_7/2) energy gaps. Thus, the Sm³⁺ ions can also relax to the ⁴G_5/2 level through the (⁴F_3/2 → ⁴G_5/2) → (⁶H_5/2 → ⁶H_7/2) cross-relaxation channel. On the other hand, because of the small energy gap from the ⁴G_5/2 level to ⁴F_3/2, the electrons in the ⁴G_5/2 level can also be transferred to the ⁴F_3/2 level by the thermal population process.^27,29 This process contributes to the luminescence bands originating from the ⁴F_3/2 level. In this case, a three-level model including the ⁶H_5/2 (level 0), ⁴G_5/2 (level 1) and ⁴F_3/2 (level 2) levels can be used to describe the thermalization of the ⁴F_3/2 level. This model is given by the following relation:^27,29Here A_T(⁴F_3/2) and A_T(⁴G_5/2) are the total emission probabilities from the ⁴F_3/2 and ⁴G_5/2 levels, respectively. These parameters, which were calculated using JO theory, have values of 146 and 235 s⁻¹, respectively. I(⁴F_3/2) and I(⁴G_5/2) are the intensities of the ⁴F_3/2 → ⁶H_5/2 and ⁴G_5/2 → ⁶H_15/2 transitions, respectively. k is the Boltzmann constant; kT = 201.6 cm⁻¹ at room temperature. hν₁ = 17 998 cm⁻¹ and hν₂ = 18 405 cm⁻¹ are the highest Stark energy of the ⁴G_5/2 → ⁶H_5/2 band and the lowest Stark energy level of the ⁴F_3/2 → ⁶H_5/2 band, respectively. These quantities are found from the emission spectra of Sm³⁺ ions. g₁ = 6 and g₂ = 4 are the degeneracies (2J + 1) of the ⁴G_5/2 and ⁴F_3/2 levels, respectively. ΔE = 407 cm⁻¹ is the energy distance from the highest Stark energy of the ⁴G_5/2 → ⁶H_5/2 band to the lowest Stark energy level of the ⁴F_3/2 → ⁶H_5/2 band. Using these parameters, the I(⁴F_3/2)/I(⁴G_5/2) ratio was evaluated to be 0.056. From the experimental luminescence spectrum, the I(⁴F_3/2)/I(⁴G_5/2) ratio was found to be approximately 0.063. It can be seen that the experimental and JO calculated results are in good agreement. The deviation of about 11.1% is within the allowed error area (∼15%) of JO theory. This result indicates that JO theory can be used well for studying the KYF₄:Sm³⁺ polycrystalline samples which were prepared as our study.

3.3. Energy transfer in KYF₄:Sm³⁺

3.3.1. Concentration quenching phenomenon. As shown in Fig. 4, the luminescence intensity of KYF₄:Sm³⁺ increases with an increase in the concentration of the Sm³⁺ ions and reaches a maximum value at 1.5 at%, and then decreases. The decrease of the luminescence intensity after a certain concentration is called the concentration quenching phenomenon. It is known that the increase of the Sm³⁺ concentration leads to the increase of the number of emission centers. The luminescence intensity of Sm³⁺ ions increases linearly with concentration if there is not energy transfer. In fact, the energy transfer process between Sm³⁺ always exists in KYF₄:Sm³⁺ (for higher concentrations than 0.5 mol%) and it competes with the radiative process. This means that a part of the excitation energy is released by emitting phonons and the remaining energy is lost due to nonradiative energy transfer. For the dipole–dipole interaction, the energy transfer rate depends on the average distance between ions R as R⁻⁶.^16,26 The decrease of the ion–ion distance with increasing concentration will cause a strong increase of the energy transfer rate. This will slow down the increase of the luminescence intensity, so the luminescence intensity can only reach a maximum intensity at a certain concentration (e.g. 1.5 mol% for KYF₄:Sm³⁺). After this concentration, the nonradiative process becomes dominant, so the luminescence intensity will decrease rapidly. In KYF₄:Sm³⁺, if the Sm³⁺ concentration increases beyond 1.5 mol%, the energy transfer rate continues to increase and gradually reaches a saturation value, whereas the luminescence of Sm³⁺ can be quenched completely.

It is noted that the energy transfer between Sm³⁺ ions usually relates to the cross relaxation (CR) mechanism.^8,16 Some CR channels leading to luminescence quenching of the Sm³⁺ ions in KYF₄ are illustrated in Fig. 5a. After being excited to the ⁶P_3/2 level, Sm³⁺ ions quickly turn back to the ⁴G_5/2 level by multi-phonon decay, and then they continue to relax to ⁶H_J (J = 5/2, 7/2, 9/2 and 11/2) by emitting the characteristic radiation. However, increasing the Sm³⁺ concentration causes a decrease in the ion–ion average distance. This leads to an increase in the interaction between Sm³⁺ ions. When the interaction is strong enough, the excitation energy can be transferred from an excited ion (at the ⁴G_5/2 level) to a neighbor ion at the ground level (⁶H_5/2). Then, both ions enter the ⁷F_J (J = 5/2–11/2) energy levels (see Fig. 5a). Finally, the Sm³⁺ ions relax to the ground level through multi-phonon decay. Thus, the luminescence of the ⁴G_5/2 level ions would be quenched.

Fig. 5 (a) The CR channels between Sm³⁺ ions; and (b) the emission process of Tb³⁺ ions and the energy transfer from Tb³⁺ ions to Sm³⁺.

3.3.2. Decay curve analysis. The decay curves of the ⁴G_5/2 level in the KYF₄:Sm³⁺ samples were observed at an emission wavelength of 602 nm under excitation at 401 nm. The results are exhibited in Fig. 6. At a low concentration of the Sm³⁺ dopant (0.1 mol%), the decay curve, which is mono-exponential, is fitted to a single exponential, I(t) = I₀ exp(−t/τ). When the energy transfer process becomes significant at high concentration, the decay curves are not mono-exponential. The experimental lifetime is determined by the formula:^8,16

Fig. 6 Decay curves of some KYF₄:xSm³⁺ samples: (a) x = 0.1 at%, (b) x = 0.5 at%, (c) x = 1.5 at% and (d) x = 3.0 at%.

For the KYF₄:Sm³⁺ samples, the experimental lifetime (τ_exp) of the ⁴G_5/2 level was found to be 4.34, 3.72, 3.12, 2.54, 2.19 and 1.85 ms for Sm³⁺ concentrations of 0.1, 0.5, 1.0, 1.5, 2.0 and 3.0 at%, respectively. The experimental lifetime decreases with the increase of the Sm³⁺ concentration. The quenching of the lifetime is also assigned to the CR process between Sm³⁺ ions.⁸ Using JO theory, the calculated lifetime (τ_cal) was estimated to be 4.38, 4.44, 4.38, 4.21, 4.31 and 4.28 ms for Sm³⁺ concentrations of 0.1, 0.5, 1.0, 1.5, 2.0 and 3.0 at%, respectively. It can be seen that the experimental lifetime is always smaller than the calculated lifetime because the nonradiative processes have been ignored in JO analysis. The quantum efficiency of a material is defined as the ratio of the experimental lifetime to the calculated lifetime: η = τ_exp/τ_cal.^16,32 The energy transfer rate (W_ET) was estimated by using the following formula:^27,32

For KYF₄:Sm³⁺, the calculated results for η and W_ET are presented in Table 4. It can be seen that the quantum efficiency and energy transfer rate decrease with an increase of the concentration of Sm³⁺ ions.

Table 4 Energy transfer parameters between Sm³⁺ ions in the KYF₄:Sm³⁺ material

C (Sm^3+)	η (%)	W ET (s^−1)	Q	C DA (cm^6 s^−1)	R 0 (Å)
0.1	—	—	—	—	—
0.5	83.78	43.59	0.136	4.06 × 10^−41	7.49
1.0	71.23	92.21	0.315	5.45 × 10^−41	7.86
1.5	60.33	156.17	0.512	6.40 × 10^−41	8.08
2.0	50.81	224.60	0.695	6.63 × 10^−41	8.13
3.0	43.22	306.89	1.017	6.32 × 10^−41	8.06

---

As shown in Fig. 6, the decay curve is a single exponential at low concentration (0.1 at%) because the energy transfer process is negligible at this concentration. However, the decay curves are no longer single exponentials because of the appearance of the energy transfer process between the ions at higher concentrations.^16,19 Information about the interaction mechanism and energy transfer parameters can be found by analyzing the decay curves through the Inokuti–Hirayama (IH) model.²⁶ According to the IH model, when only taking into account energy transfer via CR, the decay curves are given by the equation:^27,35

where t is the time after excitation; I and I₀ are the luminescence intensities at time t and t₀ = 0, respectively; τ₀ is the intrinsic lifetime of the donor; Q is the energy transfer parameter; and S is a parameter depending on the kind of interaction between ions. S can take values of 6, 8 or 10 for interactions of dipole–dipole (DD), dipole–quadrupole (DQ) or quadrupole–quadrupole (QQ), respectively.

For the KYF₄:xSm³⁺ (x = 0.5–3.0 at%) samples, the decay curves of the ⁴G_5/2 level were fitted to eqn (6), in which the τ₀ value is the lifetime of the KYF₄:0.1%Sm³⁺ sample (4.34 ms). The results are indicated in Fig. 6, where the red lines are the fitting lines for samples with S = 6 and the blue dashed lines are the fitting lines for the KYF₄:3.0%Sm³⁺ sample with S = 8 and 10. It can be seen that the decay curves of all samples are fitted the best with S = 6. This result indicates that the DD interaction mechanism plays a dominant role in the energy transfer process between Sm³⁺ ions. The main interaction mechanism depends on the local environment around the RE³⁺ ions. For Sm³⁺ ions, the DD interaction mechanism was also recorded in some materials such as the LiYF₄:Sm³⁺ crystal,³⁵ zinc potassium fluorophosphates glass,³⁶ telluroborate¹⁶ glasses and lead fluoroborate,³⁷ whereas a DQ dominant interaction mechanism was found in the K₂GdF₅:Sm³⁺ single crystal.⁸ The Q energy transfer parameter was also found by fitting the decay curves and is shown in Table 4. From the Q values, the microinteraction parameter (C_DA) and the critical distance (R₀) for the Sm³⁺–Sm³⁺ energy transfer process were calculated by using the formulas in our previous reports.^8,16 The obtained results are indicated in Table 4.

Yamaga reported that the reason for the quenching of the luminescence and lifetime of the Sm³⁺:⁴G_5/2 level is the nonradiative energy transfer process between ions in each Sm³⁺–Sm³⁺ pair.³⁵ In KYF₄:Sm³⁺, the Sm³⁺ ions substitute for Y³⁺ ions and a Sm³⁺ ion at the origin (a Y³⁺ site) has high potential to form a pair with a neighbor Sm³⁺ ion at the first, second or third shortest distances in the crystal lattice.³⁵ The probability of pair formation depends on the separation distance between the ions. Because the radius of the Sm³⁺ ion is larger than that of the Y³⁺ ion, the increase of the Sm³⁺ concentration in KYF₄ causes a decrease in the separation distance between the Sm³⁺ ions, having a large pair formation probability.³⁵ This behavior increases the probability of Sm³⁺–Sm³⁺ pair formation, leading to the enhancement of the nonradiative energy transfer between the Sm³⁺ ions. This result is expressed by the increase of the W_ET, Q and C_DA parameters (see Table 4). Additionally, for high concentrations of Sm³⁺ ions, the crystal field of an ion (e.g. ion A) is perturbed by other ions, in which each ion generates an axial distortion or strain toward ion A.³⁵ This modifies the energy levels and creates an electric dipole moment into the f–f forbidden transitions of the Sm³⁺ ion, leading to line-broadening and shortening of the lifetime of the Sm³⁺ excitation level.

3.4. Energy transfer in the KYF₄:Tb³⁺,Sm³⁺ polycrystalline material

Energy transfer from a donor ion to an acceptor ion often leads to the fluorescence quenching of materials if these ions have the same feature (e.g. Sm³⁺–Sm³⁺ or Dy³⁺–Dy³⁺ ions).^16,35 However, the energy transfer process between ions with different features (e.g. Tb³⁺ and Sm³⁺) can yield an enhancement of the luminescence of the acceptor center.^1,3,17 In this section, the luminescence enhancement of the Sm³⁺ ions in KYF₄:Tb³⁺,Sm³⁺ through the energy transfer process from Tb³⁺ to Sm³⁺ ions will be discussed in detail.

Curve b in Fig. 3 shows the excitation spectrum of Tb³⁺ ion singly doped KYF₄. This spectrum was recorded by monitoring at an emission wavelength of 543 nm corresponding to the ⁵D₄ → ⁷F₅ transition. There are three excitation bands which are observed in the range from 360 to 500 nm. These bands are assigned to the ⁷F₆ → ⁵G₆ (373 nm), ⁷F₆ → ⁵D₃ (377 nm) and ⁷F₆ → ⁵D₄ (484 nm) intra-transitions 4f⁸ configuration of the Tb³⁺ ions.²² It can be seen that the excitation band centered at 373 nm was observed in the excitation spectra of both Tb³⁺ and Sm³⁺ ions. Thus, the luminescence of both the Tb³⁺ and Sm³⁺ ions can be obtained simultaneously with this excitation wavelength. Fig. 7 exhibits the emission spectra of the KYF₄:Tb³⁺ and KYF₄:Tb³⁺,Sm³⁺ samples under excitation at 373 nm. For KYF₄:Tb³⁺, the emission includes some bands centered at 413, 434, 455, 467, 484, 542, 581 and 621 nm. These are characteristic emission bands of Tb³⁺ ions. They are attributed to the ⁵D₃ → ⁷F₅, ⁵D₃ → ⁷F₄, ⁵D₃ → ⁷F₃, ⁵D₃ → ⁷F₂, ⁵D₄ → ⁷F₆, ⁵D₄ → ⁷F₅, ⁵D₄ → ⁷F₄ and ⁵D₄ → ⁷F₃ transitions, respectively.²² For the KYF₄:Tb³⁺,Sm³⁺ samples, beside the Tb³⁺ emission bands, the luminescence spectra also show some characteristic emission bands of Sm³⁺ ions at 563 nm (⁴G_5/2 → ⁶H_5/2), 602 nm (⁴G_5/2 → ⁶H_5/2) and 449 nm (⁴G_5/2 → ⁶H_5/2).

Fig. 7 Emission spectra of the KYF₄:1%Tb³⁺,xSm³⁺ samples (x = 0, 1.0, 2.0 and 3.0 at%) upon excitation at 373 nm.

In order to estimate the application potential of the KYF₄:Tb³⁺,Sm³⁺ polycrystalline material for light-emitting diodes, the Commission Internationale de L’Eclairage (CIE) chromaticity coordinates were calculated by using the emission under excitation at 373 nm. The obtained results are indicated in Table 5 and Fig. 8. The correlated color temperature (CCT) is often used to interpret the luminescence properties of a light source.³⁸ The CCT is the temperature of a black body whose color tone most closely resembles that of a light source.¹ This parameter is estimated by using the following formula:^27,38

CCT = –449n³ + 3525n² − 6823n + 5520.33 (7)

where n = (x − x_e)/(y − y_e) and (x_e = 0.332, y_e = 0.186).

Table 5 The color coordinates (x, y) and correlated color temperature of KYF₄:Tb³⁺,Sm³⁺

C (Sm^3+) (at%)	x	y	CCT (K)
0	0.247	0.422	8455
0.5	0.271	0.408	7670
1.0	0.328	0.372	5669
2.0	0.371	0.356	4135
3.0	0.352	0.361	4785

---

Fig. 8 CIE chromaticity coordinate diagram of KYF₄:1.0%Tb³⁺,xSm³⁺ under excitation at 373 nm.

The calculated data for the chromaticity coordinates show that the luminescence of the samples doped with 1.0 and 3 at% Sm³⁺ ions is near the white light region. For Sm³⁺ concentrations of 0 and 0.5 at%, the CCTs are higher than 6000 K, i.e. the color feature of these samples is in the cool light region, whereas the CCT value of the KYF₄:1.0%Tb³⁺,1.0%Sm³⁺ and KYF₄:1.0%Tb³⁺,3.0%Sm³⁺ samples is in the neutral white light region with the vision of humans.

As shown in the emission spectra of KYF₄:Tb³⁺,Sm³⁺ (see Fig. 6), the emission intensity of Tb³⁺ decreases strongly with an increase in the Sm³⁺ concentration. This shows the existence of energy transfer from Tb³⁺ ions to Sm³⁺. The emission spectra also show that the emission intensity of Sm³⁺ ions increases firstly and reaches a maximum intensity at a concentration in the range from 1.0 to 2.0 at%, and then decreases. The decrease of the Sm³⁺ luminescence intensity after this concentration results from concentration quenching, which is due to the cross relaxation between Sm³⁺ ions. The CR channels have been shown in Fig. 5a. The energy transfer from Tb³⁺ ions to Sm³⁺ can be illustrated as the energy diagram in Fig. 5b. After being excited to the ⁵G₆ level, the Tb³⁺ ions relax non-radiatively to the ⁵D₃ level. From this level, the Tb³⁺ ions can return to the ground state through two ways. In the first way, the Tb³⁺ ions relax to ⁷F_J=0–6 by emitting luminescence in the range from 413 to 467 nm. In the second one, the Tb³⁺ ions relax to the ⁵D₄ level through emitting multi-phonon or infrared radiation or [⁵D₃ → ⁵D₄] → [⁷F₆ → ⁷F₀] cross relaxation (see Fig. 5b). However, until now, infrared radiation yielded from the ⁵D₃ → ⁵D₄ transition has not been observed in any material yet. The Tb³⁺ ions then continue to relax to the ⁷F_J=0–6 level and generate emission bands in the region of 484–621 nm. Nevertheless, the ⁵D₃ and ⁵D₄ levels in Tb³⁺ ions are very close to the ⁴G_11/2 and ⁴G_7/2 levels of Sm³⁺ ions, respectively. Thus, a part of the excited energy can be transferred from the Tb³⁺ ions to Sm³⁺ (see Fig. 5b). This process leads to the luminescence enhancement of Sm³⁺ and the luminescence quenching of Tb³⁺ ions.

Energy transfer also causes lifetime quenching of the Tb³⁺ excited levels (e.g. the ⁵D₄ level). This is confirmed through the decay curves of the Tb³⁺:⁵D₄ level, which are shown in the inset of Fig. 6. In order to the get these curves, the emission wavelength was fixed at 542 nm (⁵D₄ → ⁷F₅ transition) under excitation at 373 nm. For the KYF₄:1.0%Tb³⁺ sample, the decay curve is a single exponential with a lifetime of 4.67 ms. This experimental lifetime is typical for the Tb³⁺:⁵D₄ level in some fluoride crystals such as KGdF4:Tb³⁺,¹⁰ K₂YF₅:Tb³⁺,⁵ and K₂GdF₅:Tb³⁺.³⁹ For the KYF₄:Tb³⁺,Sm³⁺ samples, the decay curves become non-exponential and the luminescence intensity decreases faster than that of the KYF₄:Tb³⁺ sample. The lifetimes were found to be 3.82, 3.28, 2.45 and 1.97 ms for Sm³⁺ concentrations of 0.5, 1.0, 2.0 and 3.0 at%, respectively. The energy transfer efficiency (η_ET) from Tb³⁺ to Sm³⁺ is calculated by the following formula:^23,40

where τ(Tb) and τ(Tb,Sm) are the lifetimes of the Tb³⁺:⁵D₄ level in the KYF₄:Tb³⁺ and KYF₄:Tb³⁺,Sm³⁺ samples, respectively. The values of η_ET were estimated to be 18.2, 29.8, 47.5 and 58.9% for Sm³⁺ concentrations of 0.5, 1.0, 2.0 and 3.0 at%, respectively. It is known that the interaction between ions depends on their average distance: the shorter the distance, the stronger the interaction. The increase of the Sm³⁺ concentration in KYF₄:Tb³⁺,Sm³⁺ results in the decrease of the Tb³⁺–Sm³⁺ average distance. The reduction of the ion–ion separation distance creates an increase in the interaction between them, leading to an increase in the Tb³⁺–Sm³⁺ ion formation.³⁵ This is the main reason for the increase of the rate and efficiency of the energy transfer process from Tb³⁺ ions to Sm³⁺. The critical distance (R_c) of the energy process is the Tb³⁺–Sm³⁺ average distance, at which the radiative probability of the Tb³⁺ ion equals the energy transfer rate from the Tb³⁺ ion to Sm³⁺. In other words, the energy transfer efficiency is 50% at this distance. For the crystals, the R_c value can be estimated by Blasse's formula:^41,42where V is the volume of a unit cell of the crystal matrix; N is the number of host cations in a unit cell; and C_x is the total concentration of Tb³⁺ and Sm³⁺ ions when η_ET = 0.5. For KYF₄:Tb³⁺,Sm³⁺, the V and N parameters, which are found from the JCPDS No. 027-0466 standard card, are 1709.73 ų and 18, respectively. From the dependence of η_ET on the Sm³⁺ concentration, the value of C_x was found to be approximately 3.2 at%. Thus, the critical distance for KYF₄:1%Tb³⁺,Sm³⁺ is estimated to be 17.83 Å. In general, energy transfer from a donor to an acceptor may occur through exchange interaction or electric multipolar interaction.^10,42 However, the exchange interaction only appears at ion–ion distances which are less than 5 Å.^17,23,41 For KYF₄:1.0%Tb³⁺,Sm³⁺, the Tb³⁺–Sm³⁺ critical distance of 17.83 Å is too large for the exchange interaction to take place, i.e. the Tb³⁺–Sm³⁺ interaction happens via the multipolar interaction. Using the IH model as in our previous reports,^17,39 the decay curves of the Tb³⁺:⁵D₄ level were fitted the best with S = 6 (see the inset of Fig. 6). This result implies that the energy transfer from Tb³⁺ ions to Sm³⁺ takes place via a main mechanism of the DD interaction. This interaction seems to be typical for the Tb³⁺–Sm³⁺ pair because it is found in many crystals such as K₂YF₅:Tb³⁺,Sm³⁺,³⁹ K₂GdF₅:Tb³⁺,Sm³⁺,³⁹ BaGdF₅:Tb³⁺,Sm³⁺,²³ NaGdF₄:Tb³⁺,Sm³⁺,⁹ KGdF₄:Tb³⁺,Sm³⁺,¹⁷ Ba₃La(PO₄):Tb³⁺,Sm³⁺,⁴³ Y₃Al₂Ga₃O₁₂:Tb³⁺,Sm³⁺,⁴⁴ and Na₃Bi(PO₄)₂⁴⁵ as well as some glasses as telluroborate¹⁷ and zinc phosphate barium titanate.⁴⁶

4. Conclusion

A three-level model has shown that Judd–Ofelt analysis can be applied well for the KYF₄:Sm³⁺ polycrystalline material. The large values of the experimental branching ratio and stimulated emission cross-sections for the ⁴G_5/2 → ⁵H_7/2 transition indicate high application potential for KYF₄:Sm³⁺ in the optical amplifier area. For the KYF₄:Sm³⁺ material, the luminescence quenching relates to cross relaxation between Sm³⁺. The DD interaction is the dominant mechanism in this process. In KYF₄Tb³⁺,Sm³⁺, the Tb³⁺ ion plays role as a sensitizer center for the luminescence of Sm³⁺ ions under excitation at 373 nm. For this excitation condition, the color tone of KYF₄:1%Tb³⁺,xSm³⁺ is near white at 2.0 and 3.0 at% Sm³⁺ concentrations. The energy transfer from Tb³⁺ ions to Sm³⁺ in KYF₄:1%Tb³⁺,xSm³⁺ takes place through the DD interaction mechanism with a critical distance of 17.83 Å. The energy transfer efficiency (η_ET) from Tb³⁺ to Sm³⁺ increases from 18.2 to 58.9% when the Sm³⁺ concentration increases from 0.5 to 3.0 at%.

Conflicts of interest

There are no conflicts to declare.

References

1. S. Ye, F. Xiao, Y. X. Pan, Y. Y. Ma and Q. Y. Zhang, Phosphors in phosphor-converted white light-emitting diodes: recent advances in materials, techniques and properties, Mater. Sci. Eng., R, 2010, 71, 1–34.
2. N. T. Hien, Y. Y. Yu, K. C. Park, N. X. Ca, T. T. K. Chi, B. T. T. Hien, L. D. Thanh, P. V. Do, P. M. Tan and P. T. T. Ha, Influence of Eu doping on the structural and optical properties of Zn_1−xEu_xSe quantum dots, J. Phys. Chem. Solids, 2021, 148, 109729.
3. G. B. Santos, B. G. Hernandez, I. R. Martin, L. G. Lemus and J. Sanchiz, Visible and NIR emitting Yb(III) and Er(III) complexes sensitized by β-diketonates and phenanthroline derivatives, RSC Adv., 2020, 10, 27815–27823.
4. H. Boubekri, M. Diaf, K. Labbaci, L. Guerbous, T. Duvaut and J. P. Jouart, Synthesis and optical properties of Tb³⁺ doped CdF2 single crystals, J. Alloys Compd., 2013, 575, 339–343.
5. V. P. Tuyen, V. X. Quang, N. M. Khaidukov, L. D. Thanh, N. X. Ca, N. V. Hao, N. V. Nghia and P. V. Do, K₂YF₅:Tb³⁺ single crystal: an in-depth study of spectroscopic properties, energy transfer and quantum cutting, Opt. Mater., 2020, 106, 109939.
6. P. Rawat, S. K. Saroj, J. Kaur and R. Nagarajan, Luminescent properties of K₂SbF₅:Ln (Ln = Eu³⁺, Tb³⁺, Er³⁺) obtained by a facile room temperature mechanochemical synthesis, J. Lumin., 2019, 210, 392–396.
7. M. A. Gusowski, A. Gągor, M. T. Gusowska and W. R. Romanowski, Crystal structure and vibrational properties of new luminescent hosts K₃YF₆ and K₃GdF₆, J. Solid State Chem., 2006, 179, 3145–3150.
8. P. V. Do, V. P. Tuyen, V. X. Quang, N. M. Khaidukov, N. T. Thanh, B. Sengthong and B. T. Huy, Energy transfer phenomena and Judd-Ofelt analysis on Sm³⁺ ions in K₂GdF₅ crystal, J. Lumin., 2016, 179, 93–99.
9. H. Guan, G. Liu, J. Wang, X. Dong and W. Yu, Multicolor tunable luminescence and paramagnetic properties of NaGdF₄:Tb³⁺/Sm³⁺ multifunctional nanomaterials, Dalton Trans., 2014, 43, 10801–10808.
10. P. V. Do, V. X. Quang, L. D. Thanh, V. P. Tuyen, N. X. Ca, V. X. Hoa and H. V. Tuyen, Energy transfer and white light emission of KGdF₄ polycrystalline co-doped with Tb³⁺/Sm³⁺ ions, Opt. Mater., 2019, 92, 174–180.
11. M. Karbowiak, A. Mech, L. Kepinski, W. Mielcarek and S. Hubert, Effect of crystallite size on structural and luminescent properties of nanostructured Eu³⁺:KGdF₄ synthesised by co-precipitation method, J. Alloys Compd., 2005, 400, 67–75.
12. P. M. Tan, N. X. Ca, N. T. Hien, H. T. Van, P. V. Do, L. D. Thanh, V. H. Yen, V. P. Tuyen and P. T. Tho, New insights on the energy transfer mechanisms of Eu-doped CdS quantum dots, Phys. Chem. Chem. Phys., 2020, 22, 6266.
13. S. Zheng, W. Chen, D. Tan, J. Zhou, Q. Guo, W. Jiang, C. Xu, X. Liu and J. Qiu, Lanthanide-doped NaGdF₄ core-shell nanoparticles for non-contact self-referencing temperature sensors, Nanoscale, 2014, 6, 5675–5679.
14. N. T. Hien, N. X. Ca, N. T. Kien, N. T. Luyen, P. V. Do, L. D. Thanh, H. T. Van, S. Bharti, Y. Wang, N. T. M. Thuy and P. M. Tan, Structural, optical properties, energy transfer mechanism and quantum cutting of Tb³⁺ doped ZnS quantum dots, J. Phys. Chem. Solids, 2020, 147, 109638.
15. R. T. Wegh, H. Donker, K. D. Oskam and A. Meijerink, Visible quantum cutting in LiGdF₄:Eu³⁺ through downconversion, Science, 1999, 283, 663–669.
16. P. V. Do, V. P. Tuyen, V. X. Quang, L. X. Hung, L. D. Thanh, T. Ngoc, N. V. Tam and B. T. Huy, Investigation of spectroscopy and the dual energy transfer mechanisms of Sm³⁺-doped telluroborate glasses, Opt. Mater., 2016, 55, 62–67.
17. V. Uma, M. Vijayakumar, K. Marimuthu and G. Muralidharan, Luminescence and energy transfer studies on Sm³⁺/Tb³⁺ co-doped telluroborate glasses for WLED applications, J. Mol. Struct., 2018, 1151, 266–276.
18. K. S. Rudramamba, D. V. K. Reddy, T. S. Rao, S. K. Taherunnisa, N. Veeraiah and M. R. Reddy, Optical properties of Sm³⁺ doped strontium bismuth borosilicate glasses for laser applications, Opt. Mater., 2019, 89, 68–79.
19. V. X. Quang, P. V. Do, N. X. Ca, L. D. Thanh, V. P. Tuyen, P. M. Tan, V. X. Hoa and N. T. Hien, Role of modifier ion radius in luminescence enhancement from ₅D⁴ level of Tb³⁺ ion doped alkali-alumino-telluroborate glasses, J. Lumin., 2020, 221, 117039.
20. S. N. C. Santos, K. T. Paula, J. M. P. Almeida, A. C. Hernandes and C. R. Mendonça, Effect of Tb³⁺/Yb³⁺ in the nonlinear refractive spectrum of CaLiBO glasses, J. Non-Cryst. Solids, 2019, 524, 119637.
21. T. O. Sales, R. J. Amjad, C. Jacinto and M. R. Dousti, Concentration dependent luminescence and cross-relaxation energy transfers in Tb³⁺ doped fluoroborate glasses, J. Lumin., 2019, 205, 282–286.
22. W. T. Carnall, P. R. Fields and K. Rajnak, Electronic energy levels in the trivalent lanthanide aquo ions. III. Tb³⁺, J. Chem. Phys., 1968, 49, 4447–4449.
23. H. Guan, Y. Sheng, Y. Song, K. Zheng, C. Xu, X. Xie, Y. Dai and H. Zou, White lightemitting, tunable color luminescence, energy transfer and paramagnetic properties of terbium and samarium doped BaGdF₅ multifunctional nanomaterials, RSC Adv., 2016, 6, 73160–73169.
24. B. R. Judd, Phys. Optical Absorption intensities of rare earth ions, Phys. Rev., 1962, 127, 750–761.
25. G. S. Ofelt, Intensities of crystal spectra of rare earth ions, J. Chem. Phys., 1962, 37, 511–520.
26. M. Inokuti and F. Hirayama, Influence of energy transfer by the exchange mechanism on donor luminescence, J. Chem. Phys., 1965, 43, 1978–1989.
27. V. P. Tuyen, V. X. Quang, P. V. Do, L. D. Thanh, N. X. Ca, V. X. Hoa, L. V. Tuat, L. A. Thi and M. Nogami, An in-depth study of the Judd-Ofelt analysis, spectroscopic properties and energy transfer of Dy³⁺ in alumino-lithium-telluroborateglasses, J. Lumin., 2019, 210, 435–443.
28. M. G. Brika, T. Ishii, A. M. Tkachuk, S. E. Ivanova and I. K. Razumova, Calculations of the transitions intensities in the optical spectra of Dy³⁺:LiYF₄, J. Alloys Compd., 2004, 374, 63–68.
29. M. D. Shinn, W. A. Sibley, M. G. Drexhage and R. N. Brown, Optical transitions of Er³⁺ ions in fluorozirconate glass, Phys. Rev. B: Condens. Matter Mater. Phys., 1983, 27, 6635.
30. W. T. Carnall, P. R. Fields and K. Rajnak, Electronic energy levels of trivalent lanthanide aquo ions. I. Prz³⁺, Nd³⁺, Pm³⁺, Sm³⁺, Dy³⁺, Ho³⁺, Er³⁺, and Tm³⁺, J. Chem. Phys., 1968, 49, 4424.
31. K. Binnemans, Interpretation of europium(III) spectra, Coord. Chem. Rev., 2015, 295, 1–45.
32. P. V. Do, V. P. Tuyen, V. X. Quang, N. T. Thanh, V. T. T. Ha, N. M. Khaidukov, Y. I. Lee and B. T. Huy, Judd–Ofelt analysis of spectroscopic properties of Sm³⁺ ions in K₂YF₅ crystal, J. Alloys Compd., 2012, 520, 262–265.
33. D. P. Thomas, Spectroscopic properties and Judd-Ofelt analysis of BaY₂F₈:Sm³⁺, J. Opt. Soc. Am. B, 2014, 31, 1777–1789.
34. G. Q. Wang, Y. F. Lin, X. H. Gong, Y. J. Chen, J. H. Huang, Z. D. Luo and Y. D. Huang, Polarized spectral properties of Sm³⁺:LiYF₄ crystal, J. Lumin., 2014, 147, 23–26.
35. M. Yamaga, H. Uno, S. I. Tsuda, J. P. R. Wells and T. P. J. Han, Resonant energy transfer and cross relaxation between Sm³⁺ ions in LiYF₄ crystals, J. Lumin., 2012, 132, 1608–1617.
36. S. Thomas, R. George, S. Nayab Rasool, M. Rathaiah, V. Venkatramu, C. Joseph and N. V. Unnikrishnan, Optical properties of Sm³⁺ ions in zinc potassium fluorophosphate glasses, Opt. Mater., 2013, 36, 242–250.
37. S. Arunkumar and K. Marimuthu, Concentration effect of Sm³⁺ ions in B₂O₃–PbO–PbF₂–Bi₂O₃–ZnO glasses – structural and luminescence investigations, J. Alloys Compd., 2013, 565, 104–114.
38. C. S. McCamy, Correlated color temperature as an explicit function of chromaticity coordinates, Color Res. Appl., 1992, 17, 142–144.
39. P. V. Do, V. P. Tuyen, V. X. Quang, L. D. Thanh, N. M. Khaidukov, V. N. Makhov and N. T. Thanh, Sensitization of luminescence from Sm³⁺ ions in fluoride hosts K₂YF₅ and K₂GdF₅ by doping with Tb³⁺ ions, J. Lumin., 2019, 209, 340–345.
40. S. Marchesi, C. Bisio and F. Carniato, Novel light-emitting clays with structural Tb³⁺ and Eu³⁺ for chromate anion detection, RSC Adv., 2020, 10, 29765–29771.
41. C. K. Chang and T. M. Chen, Sr₃B₂O₆:Ce³⁺,Eu²⁺: a potential single-phased white-emitting borate phosphor for ultraviolet light-emitting diodes, Appl. Phys. Lett., 2007, 91, 081902.
42. Z. Xia and R. S. Liu, Unable blue-green color emission and energy transfer of Ca₂Al₃O₆F:Ce³⁺,Tb³⁺ phosphors for near-UV white LEDs, J. Phys. Chem. C, 2012, 116, 15604–15609.
43. W. Zhou, M. Gu, Y. Ou, C. Zhang, X. Zhang, L. Zhou and H. Liang, Concentration-driven selectivity of energy transfer channels and color tunability in Ba₃La(PO₄)₃:Tb³⁺,Sm³⁺ for warm white LEDs, Inorg. Chem., 2017, 56, 7433–7442.
44. Z. Li, B. Zhong, Y. Cao, S. Zhang, Y. Lv, Z. Mu, Z. Hu and Y. Hu, Energy transfer and luminescence properties of Y₃Al₂Ga₃O₁₂:Tb³⁺,Sm³⁺ as a multi-colour emitting phosphors, J. Mater. Sci.: Mater. Electron., 2019, 30, 10491–10498.
45. Z. Zhu, G. Fu, Y. Yang and Y. Yang, Energy transfer, tunable luminescence, and thermal stability of Tb³⁺–Sm³⁺-codoped Na₃Bi(PO₄)₂ phosphors, J. Mater. Sci., 2016, 51, 6944–6954.
46. K. Jha, A. K. Vishwakarma, M. Jayasimhadri and D. Haranath, Multicolor and white light emitting Tb³⁺/Sm³⁺ co-doped zinc phosphate barium titanate glasses via energy transfer for optoelectronic device applications, J. Alloys Compd., 2017, 719, 116–124.

---