Crystal Field Asymmetry and Radiative Properties of Eu³⁺ Ions in LiNaSO₄ Phosphor: A Judd–Ofelt Approach

ABSTRACT

Eu³⁺‐activated LiNaSO₄ phosphors were synthesized via a sol–gel technique and investigated to understand their structural, morphological, and luminescent properties. X‐ray diffraction and Rietveld refinement confirmed the formation of a single‐phase trigonal LiNaSO₄ structure with high crystallinity and successful incorporation of Eu³⁺ ions without disturbing the host framework, whereas FTIR spectra verified the presence of characteristic sulfate vibrational modes, and SEM analysis revealed agglomerated polycrystalline grains with well‐defined boundaries. Photoluminescence measurements under 395‐nm excitation showed intense red emission dominated by the hypersensitive ⁵D₀ → ⁷F₂ transition at 614 nm, indicating that Eu³⁺ ions occupy noncentrosymmetric lattice sites. The emission intensity increased with dopant concentration up to 0.8 mol% and then decreased due to concentration quenching governed by multipolar interactions. CIE chromaticity analysis demonstrated deep red emission with high color purity and reduced correlated color temperature, supporting suitability for warm white LED applications. Judd–Ofelt analysis yielded an asymmetry ratio of 2.07 and an intensity parameter Ω ₂ = 1.43 × 10⁻²⁰ cm², confirming strong crystal field asymmetry and enhanced Eu–O covalency, which contribute to the observed intense red luminescence. These results establish LiNaSO₄:Eu³⁺ as a promising red‐emitting phosphor for solid‐state lighting and display technologies.

LiNaSO₄:Eu³⁺ phosphors were synthesized with high phase purity. Eu³⁺ ions are stably incorporated without disturbing the host lattice. Strong red emission is obtained under near‐UV excitation. Judd–Ofelt analysis confirms efficient radiative transitions of Eu³⁺ ions.

1. Introduction

Rare‐earth–activated inorganic phosphors have become indispensable in advanced lighting, display technologies, and photonic devices because of their sharp emission lines, high color purity, and strong chemical stability [1, 2]. Among various rare‐earth ions, trivalent europium (Eu³⁺) is widely known as an efficient red‐emitting activator, exhibiting characteristic luminescence arising from intra‐4f electronic transitions. These transitions are partially shielded by outer 5s²5p⁶ orbitals, leading to narrow emission bands that are weakly affected by lattice vibrations but strongly influenced by the local symmetry and bonding environment of the host. Owing to this sensitivity, Eu³⁺‐doped materials serve as excellent systems for investigating the relationship between crystal structure and optical properties, while also being technologically important for red components in solid‐state lighting [3, 4, 5, 6, 7].

The host lattice plays a crucial role in controlling the luminescence behavior of rare‐earth ions. Sulfate‐based compounds have emerged as promising hosts due to their structural stability, chemical durability, and comparatively lower phonon energies than many oxide systems, which help minimize nonradiative losses [8, 9]. LiNaSO₄, built from SO₄ tetrahedral units linked with alkali metal ions, provides a stable framework with multiple cationic sites that can accommodate Eu³⁺ ions. The local coordination and asymmetry around the dopant significantly influence the relative intensities of magnetic dipole (⁵D₀ → ⁷F₁) and electric dipole (⁵D₀ → ⁷F₂) transitions, thereby affecting emission strength and color purity [10, 11, 12, 13, 14]. To obtain quantitative insight into these effects, Judd–Ofelt (J‐O) theory is widely applied to rare‐earth‐doped systems [15, 16]. The J–O intensity parameters (Ω₂, Ω₄, and Ω₆) provide valuable information regarding local symmetry, covalency, and rigidity of the host environment and allow evaluation of radiative transition probabilities, branching ratios, and lifetimes [17, 18, 19, 20, 21].

Recent studies have reported Eu³⁺‐activated phosphors with comprehensive spectroscopic investigations, including J‐O analysis, high color purity, thermal stability, and codoping strategies for enhanced luminescence performance. In particular, Dy³⁺/Eu³⁺ codoped LiNaSO₄ and related sulfate hosts have demonstrated energy transfer behavior and improved optical properties [22]. However, systematic investigations on single Eu³⁺‐activated LiNaSO₄ phosphors synthesized via the sol–gel route remain limited. The present work focuses on the structural refinement, local symmetry analysis, concentration‐dependent photoluminescence, colorimetric characteristics, and J‐O analysis of a single‐doped LiNaSO₄ ³⁺ system prepared by a sol–gel method, thereby providing a detailed understanding of the intrinsic luminescence behavior of Eu³⁺ ions in the LiNaSO₄ host without the influence of codopant‐assisted energy transfer.

In the present work, Eu³⁺‐activated LiNaSO₄ phosphors are synthesized using a sol–gel technique to ensure good compositional homogeneity and controlled particle formation. The structural and phase purity of the prepared samples is examined using X‐ray diffraction (XRD), whereas Fourier transform infrared (FTIR) spectroscopy is employed to confirm the presence of sulfate groups and bonding characteristics. Surface morphology and particle features are analyzed through scanning electron microscopy (SEM). The photoluminescence (PL) properties are systematically studied, and J‐O analysis is carried out to correlate the spectroscopic parameters with the local environment of Eu³⁺ ions in the LiNaSO₄ host, thereby assessing the material's potential as an efficient red‐emitting phosphor.

2. Experimental

2.1. Materials and Synthesis

Eu³⁺ doped LiNaSO₄ phosphors were synthesized via the sol–gel method using high‐purity analytical reagents without further purification. Lithium nitrate (Li [NO₃], 99.9 mol%), sodium nitrate (Na [NO₃], 99.9 mol%), ammonium sulfate ([NH₄]₂SO₄, 99 mol%), and europium nitrate pentahydrate (Eu [NO₃]₃·5H₂O, 99.9 mol%) were used as starting materials. Citric acid (C₆H₈O₇) served as a chelating agent, whereas ethylene glycol (C₂H₆O₂) acted as a polymerization medium to promote gel formation.

Stoichiometric quantities of the precursors were weighed according to the general chemical formula Li_1−xNaSO₄:x mol % Eu³⁺. The nitrates of Li⁺, Na⁺, and Eu³⁺ were first dissolved separately in a small amount of deionized water to form clear solutions. These were then mixed together under constant stirring at 70°C. Ammonium sulfate was added dropwise to maintain a cation‐to‐phosphate ratio of 1:1. Citric acid was introduced in a 1:1 M ratio with total metal ions, followed by the addition of ethylene glycol in a 1:4 (citric acid: EG) ratio to facilitate polyesterification. The pH of the resulting sol was adjusted to ~7 using dilute ammonia to ensure complete chelation and homogeneous distribution of metal ions. The transparent sol was continuously stirred and heated at 80°C until it transformed into a viscous gel. The gel was then dried at 120°C for 12 h in a hot‐air oven to remove residual water and organics, resulting in a fluffy xerogel. After calcination, the samples were slowly cooled to room temperature, reground, and stored in airtight containers for further characterization.

2.2. Characterization Techniques

The crystalline phase and structural features of the synthesized phosphors were examined using X‐ray diffraction measurements carried out on a Rigaku Miniflex 600 diffractometer employing Cu Kα radiation (λ = 1.5406 Å), operated at 40 kV and 15 mA. Diffraction patterns were collected over a 2θ range of 10°–80° with a step size of 0.02°. Phase identification was performed by comparing the experimental patterns with standard ICSD reference data, and precise lattice parameters were obtained through Rietveld refinement using the FullProf Suite. The surface morphology and particle size distribution of the calcined samples were investigated using a Carl Zeiss EVO‐18. Vibrational characteristics and functional group analysis of both gel‐derived and calcined samples were studied using Fourier‐transform infrared spectroscopy with a Shimadzu IRTracer‐100 in the wavenumber range of 400–4000 cm⁻¹ employing the KBr pellet method. Photoluminescence excitation and emission measurements were carried out at room temperature using a Shimadzu RF‐6000 equipped with a 150‐W xenon lamp. To ensure reliable comparison, all luminescence spectra were recorded under identical experimental conditions. The colorimetric properties, including chromaticity coordinates and color purity, were derived from the emission spectra using the CIE 1931 framework to evaluate the suitability of the phosphors for white light‐emitting diode and plant growth lighting applications.

3. Result and Discussion

3.1. XRD Analysis and Phase Purity

The phase purity and crystal structure of the synthesized LiNaSO₄:x mol% Eu³⁺ (x = 0.2–1.0) phosphors were examined using X‐ray diffraction (XRD), and the corresponding patterns are shown in Figure 1a. All diffraction peaks of the Eu³⁺‐doped samples are well indexed to the standard LiNaSO₄ phase (ICSD No. 01‐071‐2172), confirming the formation of a single‐phase structure. No secondary or impurity peaks are observed in any of the patterns, indicating the successful incorporation of Eu³⁺ ions into the host lattice without altering its crystallographic symmetry. The sharp and well‐defined diffraction peaks reflect the high crystallinity of the synthesized phosphors. Furthermore, the absence of peak broadening or splitting suggests that Eu³⁺ doping does not introduce significant lattice strain or amorphous phases. No noticeable peak shift is observed with increasing Eu³⁺ concentration, indicating that the crystal structure remains stable upon doping. Considering the crystal structure of LiNaSO₄, Eu³⁺ ions are more likely to substitute at the Na⁺ site rather than the Li⁺ site. According to Shannon's ionic radii, Eu³⁺ in sixfold coordination possesses an ionic radius of approximately 0.947 Å, which is closer to that of Na⁺ (1.02 Å, CN = 6) than Li⁺ (0.59 Å, CN = 4). Furthermore, the Li⁺ ions occupy tetrahedral sites, whereas Na⁺ ions are located in octahedral coordination environments that can more readily accommodate the larger Eu³⁺ ion. Therefore, Eu³⁺ substitution at the Na⁺ site is energetically more favorable. The absence of significant peak shifts or structural distortion in the XRD patterns, together with the satisfactory Rietveld refinement parameters, suggests that Eu³⁺ ions are incorporated into the host lattice without altering the overall crystal symmetry. Because of the low dopant concentration and the similar scattering factors of the involved ions, the present Rietveld refinement does not permit unambiguous determination of site occupancy; however, the structural considerations strongly support preferential occupation of Na⁺ sites by Eu³⁺ ions. The consistent diffraction patterns across all compositions demonstrate that the LiNaSO₄ structure is stable upon codoping. The structural integrity of the host lattice is maintained even at the highest Eu³⁺ concentration (1.0 mol%), suggesting that the dopant levels remain within the solid solubility limit. The results conclusively establish that the synthesized LiNaSO₄: Eu³⁺ phosphors possess a pure crystalline phase identical to that of the reference compound, making them structurally suitable for luminescent and energy‐transfer investigations.

FIGURE 1.

X‐ray diffraction–based microstructural analysis of the synthesized LiNaSO₄ phosphor: (a) experimental XRD pattern confirming single‐phase formation; (b) crystallite size distribution obtained from the Debye–Scherrer method; (c) size–strain plot (SSP) used to evaluate crystallite size and lattice strain; (d) Williamson–Hall (W‐H) plot under the uniform deformation model; (e) Halder–Wagner (H‐W) plot for refined size–strain separation; and (f) Rietveld refinement of the XRD pattern showing the observed, calculated, and difference profiles.

An initial estimate of the crystallite size was obtained from the broadening of prominent diffraction peaks using the Debye–Scherrer approach. The calculated crystallite sizes fall within the range of approximately ~38 nm, with an average value close to 37 nm, confirming the nanocrystalline nature of the LiNaSO₄ phosphor. The corresponding crystallite size distribution derived from individual reflections is shown in Figure 1b. The histogram exhibits a relatively narrow distribution centered around the mean value, indicating uniform crystallite growth during synthesis. In this representation, the frequency axis corresponds to the number of diffraction peaks contributing to each size interval rather than a physical unit, which is commonly adopted for Scherrer‐based size distribution analysis. The Debye–Scherrer relation employed for this estimation is given below:

$$D=\frac{\mathit{k\lambda }}{\mathit{\text{βcosθ}}}$$ (1)

Further confirmation of the size–strain behavior was obtained using the Williamson–Hall (W‐H) method under the uniform deformation assumption. The corresponding W‐H plot, presented in Figure 1d, shows a near‐linear relationship between the relevant broadening parameters. The crystallite size extracted from the intercept is found to be in the range of 42 nm, whereas the lattice strain derived from the slope is approximately 6.5 × 10⁻⁴. The relatively small slope of the W–H plot indicates that crystallite size effects play a dominant role in peak broadening, whereas strain contributions remain comparatively low. The W‐H relation applied in this analysis is given by

$$\left(\beta \cos \theta \right)=\left(\frac{\mathit{k\lambda }}{D}\right)+4\epsilon \sin \theta$$ (2)

To achieve a more reliable interpretation of peak broadening by separating size‐related and strain‐related contributions, the size–strain plot (SSP) method was applied, and the resulting plot is shown in Figure 1c. The SSP plot exhibits a good linear trend, indicating that the adopted size–strain model is appropriate for the present system. From the linear fitting parameters, the average crystallite size obtained using this method is approximately 44 nm, whereas the corresponding lattice microstrain is on the order of 5.4 × 10⁻⁴. The small magnitude of strain suggests that the crystal lattice experiences only minor distortion, which is consistent with the high crystallinity observed in the XRD pattern. The governing relation used in the SSP analysis is expressed as

$${\left(\mathit{\text{βcosθ}}\right)}^2=\left(\frac{\mathit{k\lambda }}{D}\right)\left(d^2\mathit{\text{βcosθ}}\right)+{\left(\frac{\epsilon }{2}\right)}^2$$ (3)

To improve the accuracy of the microstructural parameters, the Halder–Wagner (H‐W) approach was employed, as illustrated in Figure 1e. This method is particularly effective for systems where diffraction peak broadening follows a mixed Gaussian–Lorentzian profile. The H‐W plot shows excellent linearity, and the residuals are randomly distributed around zero, confirming the suitability of the model. The crystallite size calculated from this method is approximately 46 nm, and the corresponding lattice strain is around 4.3 × 10⁻⁴. The close agreement between the crystallite sizes obtained from the Scherrer, SSP, W‐H, and H‐W analyses demonstrates the internal consistency of the results and reinforces the reliability of the extracted microstructural parameters. The H‐W relation used for this refined analysis is given by

$${\left(\frac{\beta }{\tan \theta }\right)}^2=\frac{\mathit{k\lambda }}{D}\left(\frac{\beta }{\tan \theta \sin \theta }\right)+16{\epsilon }^2$$ (4)

The structural parameters of the synthesized LiNaSO₄ phosphor were refined using the Rietveld method to confirm phase purity and crystal structure. The background was modeled with a polynomial function, and peak shapes were fitted using a pseudo‐Voigt profile to account for both Gaussian and Lorentzian components of peak broadening [23, 24, 25]. The refinement process included adjustments of the scale factor, zero shift, lattice constants, and atomic positional parameters until convergence was achieved with stable and physically meaningful values. Figure 1f presents the Rietveld refinement profile, illustrating excellent agreement between the observed (Y _obs ) and calculated (Y _calc ) diffraction patterns. The difference curve (Y _obs − Y _calc ) shows minimal deviation throughout the 2θ range, and all Bragg reflection positions coincide precisely with the observed peak maxima. The refinement yielded reliability factors of R _P  = 6.89, R _WP  = 8.43, and R _exp  = 6.89, with a goodness‐of‐fit parameter (χ ²) of 1.43, indicating a satisfactory refinement quality. The close correspondence between R _WP and R _exp values, along with a χ ² value near unity, confirms the high accuracy of the structural model. It is observed reflections were indexed to a single‐phase LiNaSO₄ structure with no evidence of secondary or impurity phases, demonstrating that the synthesis process produced a phase‐pure compound. The sharp and well‐defined peaks further confirm the high crystallinity of the phosphor.

LiNaSO₄ adopts a trigonal crystal structure belonging to the P31c space group (Figure 2). The Na⁺ ions occupy octahedral coordination environments, each surrounded by six O²⁻ ions, with Na–O bond lengths varying between 2.39 and 2.78 Å. In contrast, Li⁺ ions are tetrahedrally coordinated by four oxygen atoms, forming LiO₄ tetrahedra. These tetrahedra are interconnected through corner‐sharing with two other LiO₄ units as well as with four SO₄ tetrahedra. The Li–O bond distances fall in the range of 1.94–2.09 Å. Sulfur exists in three crystallographically distinct S⁶⁺ positions, each forming SO₄ tetrahedral units. In the first sulfur environment, the SO₄ tetrahedra are linked by corners to six equivalent LiO₄ tetrahedra. This site exhibits three shorter S–O bonds of 1.49 Å and one slightly longer bond of 1.52 Å. The second sulfur site also forms SO₄ tetrahedra, but these share corners with only three equivalent LiO₄ units. Here, one S–O bond measures 1.49 Å, whereas the remaining three are slightly longer at 1.50 Å. In the third sulfur environment, all four S–O bonds are equivalent, each having a bond length of 1.49 Å, and the tetrahedra again connects to three LiO₄ tetrahedra.

FIGURE 2.

Crystal structure of LiNaSO₄ phosphor.

There are six distinct oxygen positions within the structure, each exhibiting different coordination. The first oxygen site is four‐coordinated, bonded to two Na⁺ ions, one Li⁺ ion, and one S⁶⁺ ion. The second oxygen position shows threefold coordination with one Na⁺, one Li⁺, and one S⁶⁺. Oxygen at the third site adopts a distorted trigonal pyramidal arrangement, linking three Li⁺ ions and one sulfur atom. The fourth oxygen site is coordinated to three Na⁺ ions and one S⁶⁺ ion in a distorted geometry. The fifth oxygen position is also four‐coordinated, bonded to three Na⁺ ions and one sulfur atom. Finally, the sixth oxygen site displays threefold coordination, connected to one Na⁺, one Li⁺, and one S⁶⁺ ion.

3.2. SEM Analysis

The surface morphology of the synthesized LiNaSO₄ phosphor was examined by scanning electron microscopy, revealing densely agglomerated particles forming irregular clusters, which is typical of high‐temperature processed phosphor materials (Figure 3). At higher magnification, the agglomerates consist of polycrystalline grains with irregular, block‐like shapes, and well‐defined boundaries, indicating good crystallization. The particles are nonuniform in size and appear strongly interconnected, with smooth surfaces accompanied by fine adhered crystallites resulting from grain growth and partial sintering during calcination [26, 27, 28]. The average particle size lies in the micrometer range, which is beneficial for reducing surface defect density while maintaining adequate packing. The observed surface roughness and interparticle connectivity can promote internal light scattering, a factor that may contribute to improved luminescence performance in LiNaSO₄‐based phosphor systems.

FIGURE 3.

SEM analysis of LiNaSO₄ phosphor.

3.3. FTIR Analysis

The functional groups and local bonding environment in the LiNaSO₄ phosphor were examined using Fourier transform infrared (FTIR) spectroscopy (Figure 4). The spectrum exhibits the characteristic vibrational features of sulfate (SO₄ ²⁻) tetrahedra, confirming the formation of the LiNaSO₄ framework. A strong absorption band observed in the region of ~1100–1000 cm⁻¹ is attributed to the asymmetric stretching vibration (ν₃) of S–O bonds in the SO₄ ²⁻ units. Another prominent band appearing near ~600–650 cm⁻¹ corresponds to the bending vibration mode (ν ₄) of the sulfate group. The presence of these well‐defined sulfate‐related bands verifies the structural integrity of SO₄ tetrahedra within the host lattice [29]. Weak features detected around ~950–900 cm⁻¹ may be associated with symmetric stretching (ν ₁) modes of the SO₄ ²⁻ group, which often appear with low intensity due to symmetry constraints. Minor broad absorption in the higher wavenumber region can be linked to surface‐adsorbed moisture or hydroxyl‐related species, which is common in powder samples exposed to ambient conditions. No additional impurity‐related peaks are observed, indicating the phase purity of the synthesized material.

FIGURE 4.

FTIR analysis of LiNaSO₄ phosphor.

3.4. Photoluminescence Investigation

The photoluminescence excitation and emission characteristics of Eu³⁺‐incorporated LiNaSO₄ phosphors are illustrated in Figures 5, 6, 7. As shown in Figure 5, the excitation spectrum monitored at an emission wavelength of 614 nm exhibits distinct excitation bands centered at 395 and 465 nm. These excitation peaks are attributed to the intra‐4f electronic transitions of Eu³⁺ ions, corresponding to the ⁷F₀→ ⁵L₆ and ⁷F₀ → ⁵D₂ transitions, respectively [3, 30, 31]. Upon excitation at 395 nm, the emission spectrum of the Eu³⁺‐doped LiNaSO₄ phosphor (Figure 6) displays two prominent emission lines located at 593 and 614 nm. These emissions originate from the ⁵D₀ → ⁷F₁ magnetic dipole transition and the ⁵D₀ → ⁷F₂ electric dipole transition of Eu³⁺ ions, respectively. Similarly, excitation at 465 nm produces identical emission features with variations in intensity, as shown in Figure 7, confirming that the emission behavior is independent of the excitation wavelength. The relatively stronger intensity of the electric dipole transition at 614 nm compared to the magnetic dipole transition at 593 nm suggests that Eu³⁺ ions occupy crystallographic sites lacking inversion symmetry within the LiNaSO₄ host lattice [32, 33, 34, 35, 36, 37].

FIGURE 5.

PL excitation spectra of Eu³⁺‐activated LiNaSO₄ phosphor at emission of 614 nm.

FIGURE 6.

PL emission spectra of Eu³⁺‐activated LiNaSO₄ phosphor at excitation of 395 nm.

FIGURE 7.

PL emission spectra of Eu³⁺‐activated LiNaSO₄ phosphor at excitation of 465 nm.

In the Eu³⁺‐doped LiNaSO₄ phosphors, the emission intensity increases steadily with increasing dopant concentration and reaches a maximum at 0.8 mol%. When the Eu³⁺ content exceeds this optimum value, a gradual decrease in luminescence intensity is observed, which signifies the onset of concentration quenching [38, 39, 40, 41]. Such behavior is commonly reported in rare‐earth‐activated phosphor systems and arises from nonradiative interactions between closely spaced activator ions. In general, concentration quenching can occur through several pathways, including cross‐relaxation between neighboring activator ions, energy migration among excited ions followed by transfer to impurity centers, energy transfer to lattice defects, and trapping of excitation energy by intrinsic defects such as color centers or hydroxyl groups. In the present LiNaSO₄ host lattice, Eu³⁺ ions are proposed to occupy Na⁺ sites owing to the closer match in ionic radius and coordination environment. The aliovalent substitution of Eu³⁺ for Na⁺ requires charge compensation, which is most likely achieved through the formation of sodium vacancies (VNa). These vacancy defects introduce localized lattice disorder and can serve as nonradiative trapping centers. Although Eu³⁺ ions possess fewer efficient cross‐relaxation channels than many other rare‐earth activators, cross‐relaxation cannot be completely ruled out at elevated dopant concentrations. As the Eu³⁺ concentration increases, excitation energy can migrate among neighboring Eu³⁺ ions and become trapped at defect centers associated with charge compensation, resulting in enhanced nonradiative relaxation and concentration quenching. Therefore, the observed quenching is attributed primarily to energy migration‐assisted defect trapping, with a possible secondary contribution from cross‐relaxation processes. The concentration quenching process is governed by interactions occurring over a critical energy transfer distance, which can be estimated using the Blasse model [42, 43]:

$$R_C=2{\left(\frac{3V}{4\prod X_{C}N}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$$ (5)

The critical energy transfer distance (RCR_CRC) was estimated using the critical activator concentration (XCX_CXC), the unit cell volume (VVV), and the number of activator sites per unit cell (NNN). Rietveld refinement of the crystal structure yielded a unit cell volume of 496.62 ų with one available activator site per unit cell. The critical concentration was fixed at 0.8 mol%, corresponding to the maximum emission intensity observed for all rare‐earth‐doped compositions. Based on these parameters, the RCR_CRC value for Eu³⁺ ions was calculated to be 5.8255 Å. This relatively large critical distance indicates that concentration quenching is not governed by exchange interactions but is instead dominated by multipolar interactions, leading to nonradiative energy transfer between neighboring Eu³⁺ ions mediated by the host lattice.

The nature of the electric multipolar interaction responsible for concentration quenching can be further examined by analyzing the variation of emission intensity arising from the energy levels involved in the interaction process [44, 45, 46, 47, 48]. Under conditions of high activator ion concentration, the relationship between the luminescence intensity (I) and the activator concentration (X) can be described by the following expression:

$$\frac{I}{x}=k{\left[1+\beta .x^{\frac{\theta }{3}}\right]}^{-1}$$ (6)

This equation is fairly accurate to

$$\mathit{log}\frac{1}{x}=c-\frac{\theta }{3}\mathit{log}x$$ (7)

For a given host lattice, the parameters kkk, βββ, and ccc are assumed to remain constant under identical excitation conditions. According to Van Uitert's theory, the value of θ\thetaθ provides insight into the nature of the electric multipolar interaction responsible for concentration quenching, where θ = 3\theta = 3θ = 3 corresponds to exchange interaction, θ = 6\theta = 6θ = 6 to dipole–dipole interaction, θ = 8\theta = 8θ = 8 to dipole–quadrupole interaction, and θ = 10\theta = 10θ = 10 to quadrupole–quadrupole interaction [49]. For Eu³⁺‐doped compositions investigated in this study, the dependence of log(I/x) on log(x) is depicted in Figure 8. Owing to the inherent complexity of ion–ion interactions at higher dopant concentrations, only three representative data points are included in the plot to clearly illustrate the dominant interaction mechanism governing concentration quenching in the system [41, 50, 51].

FIGURE 8.

Linear plot of log (x) versus log (I/x) of Eu³⁺ activated LiNaSO₄ phosphor.

The slopes obtained from the log(I/x) versus log(x) plots for Eu³⁺‐activated LiNaSO₄ phosphors were determined to be −0.2079 and −0.0781 for the emission bands centered at 593 and 614 nm, respectively. Using these slope values, the corresponding θ parameters were calculated to be 0.6237 for the 593‐nm transition and 0.2343 for the 614‐nm transition. The slopes obtained from the log(I/x) versus log(x) plots for the 593‐ and 614‐nm emission bands were found to be relatively small, yielding θ values that do not correspond to the standard theoretical values associated with exchange interaction (θ = 3) or multipolar interactions (θ = 6, 8, and 10). Therefore, a definitive assignment of the quenching mechanism based solely on the van Uitert analysis is not possible in the present study. Furthermore, the limited number of concentration points available in the quenching region reduces the reliability of the fitted slopes. Nevertheless, the critical energy transfer distance (R _c  = 5.83 Å) exceeds the typical limit for exchange interactions, suggesting that concentration quenching is more likely governed by multipolar energy transfer processes rather than short‐range exchange interactions. Accordingly, the van Uitert analysis is considered qualitative, whereas the Blasse critical distance criterion provides the more reliable indication of the dominant quenching mechanism in the present phosphor system.

3.5. CIE Chromaticity

The chromatic properties of the LiNaSO₄:Eu³⁺ phosphor series were evaluated using the Commission Internationale de l'Éclairage (Commission Internationale de l'Éclairage, CIE) chromaticity coordinates derived from the photoluminescence emission spectra, as shown in Figure 9 [52]. CIE coordinates are a crucial parameter for assessing the color performance and applicability of phosphor materials in solid‐state lighting. The calculated chromaticity coordinates are summarized in Table 1. As evident from Figure 9, the CIE chromaticity coordinates of the LiNaSO₄ ³⁺ phosphors are located within the red–orange region and exhibit only modest variations with increasing Eu³⁺ concentration. The observed changes in chromaticity reflect subtle variations in the relative intensities of the characteristic Eu³⁺ emission transitions, particularly the dominant ⁵D₀ → ⁷F₂ red emission band. Overall, the phosphors maintain highly saturated red emission throughout the investigated concentration range. Furthermore, the color purity of the phosphors is found to be strongly dependent on the Eu³⁺ concentration, as listed in Table 1. The color purity was evaluated using the standard relation based on the distance of the chromaticity coordinates from the white point and the dominant wavelength, providing a quantitative measure of the color saturation achieved in the Eu³⁺‐activated LiNaSO₄ phosphors [51, 52, 53, 54];

$$\mathit{\text{Colorpurity}}=\frac{\sqrt{{\left(X-X_i\right)}^2+{\left(Y-Y_i\right)}^2}}{\sqrt{{\left(X_d-X_i\right)}^2+{\left(Y_d-Y_i\right)}^2}}*100\%$$ (8)

FIGURE 9.

CIE chromaticity diagram of LiNaSO₄:Eu³⁺ phosphor.

TABLE 1.

Overview of CIE color coordinates and other parameters.

Sr. No.	Sample	X	Y	X d	Y d	CCT (K)	Color purity (%)
A.	LiNaSO4: 0.2 mol% Eu3+	0.5973	0.4020	0.6125	0.3842	5674.49	95.3706
B.	LiNaSO4: 0.4 mol% Eu3+	0.6380	0.3616	0.6125	0.3842	5460.40	96.1810
C.	LiNaSO4: 0.6 mol% Eu3+	0.6221	0.3774	0.6125	0.3842	3713.84	98.4250
D.	LiNaSO4: 0.8 mol% Eu3+	0.6088	0.3906	0.6125	0.3842	4368.79	98.9353
E.	LiNaSO4: 1.0 mol% Eu3+	0.6149	0.3845	0.6125	0.3842	3553.91	98.6712

Here, (x, y) and (x _i , y _i ) denote the color coordinates of the sample and the CIE equal‐energy illuminant, respectively, whereas (x _d , y _d ) represents the chromaticity coordinates corresponding to the dominant wavelength of the source.

The correlated color temperature (CCT) was derived from the following expression [55]:

$$\mathit{CCT}=-499n^3+3525n^2-6823.3n+5520.33$$ (9)

$$n=\frac{x-x_e}{y-y_e}$$ (10)

where x _e and y _e  = (0.332, 0.186).

Table 1 shows that the LiNaSO₄ phosphor doped with 0.2 mol% Eu³⁺ exhibits relatively low color purity. As shown in Table 1, the color purity generally increases with Eu³⁺ concentration and remains above 95% for all compositions. The CCT exhibits an overall decreasing trend toward the warm‐white region, although some nonmonotonic variation is observed among intermediate compositions. These results confirm that LiNaSO₄ ³⁺ phosphors exhibit highly saturated red emission characteristics suitable for warm‐white LED applications.

3.6. Judd‐Ofelt Parameters

The optical behavior of rare earth ions in solid‐state host lattices is governed by intra‐4f electronic transitions, which are shielded by outer 5s and 5p orbitals. As a result, their spectral lines are sharp and only weakly affected by the crystal field compared to transition metals. However, the intensities of these transitions are strongly influenced by the surrounding ligand environment. J‐O theory provides a quantitative model to describe the intensities of electric dipole transitions in rare earth ions embedded in crystalline hosts. Originally developed independently by Judd and Ofelt, the theory explains how parity‐forbidden 4f–4f transitions become partially allowed through odd‐parity components of the crystal field [56, 57, 58, 59].

In free ions, 4f–4f transitions obey the Laporte selection rule and are strictly forbidden as electric dipole transitions. Inside a crystal lattice, mixing of opposite parity states induced by the crystal field breaks inversion symmetry, allowing forced electric dipole transitions. J‐O theory expresses the electric dipole line strength of a transition between initial state ∣J⟩ and final state ∣J′⟩ as

$$S_{\mathit{ed}}\left(J\to J^{\prime }\right)=\sum _{\lambda =2,4,6}{\Omega }_{\lambda }{\left|⟨\mathit{\phi J}\Vert U^{\lambda }\Vert {\phi }^{\prime }{J}^{\prime }⟩\right|}^2$$ (11)

where Ω ₂, Ω ₄, and Ω ₆ are phenomenological intensity parameters dependent on the host lattice and ${\left|⟨\mathit{\phi J}\Vert U^{\lambda }\Vert {\phi }^{\prime }{J}^{\prime }⟩\right|}^2$ are reduced matrix elements that depend only on the rare earth ion. These parameters contain structural information about the environment of the dopant ion. The parameter Ω ₂ is highly sensitive to local symmetry and covalency, whereas Ω ₄ and Ω ₆ reflect long‐range interactions and rigidity of the host lattice [60, 61].

The spontaneous emission probability for an electric dipole transition is expressed as follows:

$$f_{J\to J\prime }=\frac{64{\pi }^4{e}^2}{3h\left(2J+1\right){\lambda }^3}\frac{n{\left(n^2+2\right)}^2}{9}{S}_{\mathit{ed}}$$ (12)

where n is the refractive index and λ is emission wavelength. For Eu³⁺ ions, the emission primarily originates from the ⁵D₀ level. The transition ⁵D₀ → ⁷F₁ is magnetic dipole in nature and nearly independent of host symmetry, and its probability is given by

$$A_{\mathit{md}}=14.65n^3\left({\mathrm{s}}^{-1}\right)$$

This transition is used as an internal reference for determining electric dipole probabilities. The ratio of integrated intensities of the hypersensitive transition ⁵D₀ → ⁷F₂ to the magnetic dipole transition is known as the asymmetry ratio.

$$R=\frac{I\left({{}^{5}D}_0\to {{}^{7}F}_2\right)}{I\left({{}^{5}D}_0\to {{}^{7}F}_1\right)}$$ (13)

which provides direct evidence of local site symmetry.

For LiNaSO₄:0.8 mol% Eu³⁺ phosphor excited at 395 nm, the integrated emission areas of the ⁵D₀ → ⁷F₁ and ⁵D₀ → ⁷F₂ transitions were obtained as 10255.03 and 21182.31, respectively. Substituting these values gives R = 2.07 indicating that Eu³⁺ ions occupy noncentrosymmetric lattice sites with considerable crystal field distortion. Assuming a refractive index n = 1.5n = 1.5n = 1.5, the magnetic dipole transition probability becomes A _md  = 14.65(1.5)³ = 49.4 s⁻¹.

Because emission intensity is proportional to transition probability,

Using the emission wavelength of 614 nm, the electric dipole line strength is obtained as follows:

$$\mathit{SED}=4.59\times {10}^{-20}{\mathrm{cm}}^2.$$

For Eu³⁺, the squared reduced matrix element for this transition is ∣U ⁽²⁾∣² = 0.0032. Therefore, the J‐O intensity parameter becomes

$${\Omega }_{\lambda }=\frac{S_{\mathit{ed}}}{{\left|U^{\left(2\right)}\right|}^2}=1.43\times {10}^{-20}{\mathrm{cm}}^2$$

The relatively large asymmetry ratio and significant Ω ₂ value confirm that Eu³⁺ ions experience strong crystal field interaction and occupy distorted lattice sites in LiNaSO₄. Enhanced hypersensitive transition intensity demonstrates increased covalent character of Eu–O bonding, which favors intense red emission. Such optical characteristics are beneficial for phosphor applications in solid‐state lighting, where strong red emission contributes to improved color rendering. Table 2 gives overview of all J‐O parameters.

TABLE 2.

Overview of J‐O parameters for LiNaSO₄ phosphor.

Parameter	Value	Unit
Asymmetry ratio (R)	2.07	—
Magnetic dipole probability (A md )	49.4	s−1
Electric dipole probability (A ed )	102.3	s−1
JO intensity parameter (Ω 2)	1.43 × 10−20	cm2

In the present study, only the Ω ₂ intensity parameter was evaluated because the emission spectrum was dominated by the hypersensitive ⁵D₀ → ⁷F₂ transition, whereas the remaining Eu³⁺ transitions exhibited comparatively weak intensities and limited spectral resolution. Consequently, reliable determination of the higher order J‐O intensity parameters (Ω ₄ and Ω ₆) was not feasible within the experimental uncertainty. Therefore, the J‐O analysis has been restricted to Ω ₂, which is widely used to assess the local symmetry and covalency around Eu³⁺ ions. A more comprehensive J‐O treatment, including Ω ₄, Ω ₆, and lifetime analysis, would require higher resolution spectra and additional spectroscopic measurements, which are beyond the scope of the present work.

4. Conclusion

In summary, Eu³⁺‐activated LiNaSO₄ phosphors were successfully synthesized by a sol–gel method and exhibited a phase‐pure trigonal structure, high crystallinity, and stable lattice framework as confirmed by XRD and Rietveld refinement, whereas FTIR and SEM analyses supported the structural integrity and favorable morphology of the material. Photoluminescence studies revealed characteristic Eu³⁺ red emission dominated by the electric dipole ⁵D₀ → ⁷F₂ transition, demonstrating that Eu³⁺ ions occupy distorted, low‐symmetry sites within the host lattice, with optimum emission intensity achieved at 0.8 mol% Eu³⁺, due to balanced activator concentration before the onset of concentration quenching through energy migration among Eu³⁺ ions and subsequent nonradiative relaxation at defect‐related centers. Chromaticity coordinates were located within the red–orange region with high color purity, whereas the CCT showed an overall decreasing tendency with minor variations among intermediate compositions, indicating the potential of the phosphor for warm white LED devices. J‐O analysis provided quantitative insight into the local environment, where the asymmetry ratio (R = 2.07) and Ω ₂ = 1.43 × 10⁻²⁰ cm² indicate strong crystal field distortion and significant Eu–O covalent interaction, explaining the enhanced hypersensitive transition intensity of the Eu³⁺ ions. Overall, the favorable structural, luminescent, and colorimetric properties suggest that LiNaSO₄:Eu³⁺ is a potential red‐emitting phosphor for solid‐state lighting applications. However, additional investigations on photoluminescence quantum yield, thermal stability, and luminescence lifetime are required to comprehensively evaluate its suitability for practical LED devices.

Author Contributions

R. B. Aurade: writing – review and editing, investigation, methodology. Gajanan S. Solanke: writing – review and editing. Mukesh V. Bhoge: writing – review and editing. Milind L. Turukmane: writing – review and editing. S. L. Dhondge: writing – review and editing. Abhijeet R. Kadam: writing – original draft, visualization, validation, methodology, conceptualization, investigation, data curation, formal analysis, funding acquisition, resources.

Funding

The authors have nothing to report.

Ethics Statement

The authors have nothing to report.

Conflicts of Interests

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.