Fluorescence Lifetime as a Ruler: Quantifying Sm³⁺ Doping Levels in Na₄La₂ (CO₃)₅ Crystals via Time-Resolved Luminescence Decay

Abstract

Hollow dendritic Na₄La₂(CO₃)₅ crystals doped with Sm³⁺ ions were synthesized with sodium carbonate using a hydrothermal method. The unique lifetime of Sm³⁺ enables the optical measurement of luminescent ion content. The X-ray diffraction spectrum indicates that the nanocrystals maintain structural stability with a hexagonal arrangement, even when the concentration of Sm³⁺ reaches 50 at.%. As the concentration of Sm³⁺ increases, the emission intensity of Na₄(La_1−xSm_x)₂(CO₃)₅ first rises and then falls. The maximum emission intensity of the fluorescent powder occurs at a Sm³⁺ concentration of 0.04. Beyond this concentration, concentration quenching takes place, primarily due to electric dipole–dipole interactions. Using an excitation wavelength of 404 nm and monitoring at 596 nm, the fluorescence lifetime of Na₄(La_1−xSm_x)₂(CO₃)₅ shows a strong dependence on Sm³⁺ concentration, which can be described by a precise equation. Over the range of Sm³⁺ concentrations from 0.005 to 1, the lifetime decreases from 3.126 ms to 0.023 ms. Therefore, optical monitoring of fluorescent powders is crucial for confirming the composition of coatings used in applications such as solid-state lighting and anti-counterfeiting, by utilizing the relationship between lifetime and doping concentration.

1. Introduction

Fluorescent materials can be developed into various high-performance optical sensors for temperature [1,2,3], pressure [4,5], stress [6], pH [7,8], methanol [9], acetone [10], Cd²⁺ [11], and DNA [12] measurements. Na₄La₂(CO₃)₅, a rare-earth carbonate, has a non-centrosymmetric hexagonal space group structure, which has been shown to be an effective nonlinear optical material and luminescent host [13,14,15]. This compound can be successfully synthesized using a hydrothermal method and exhibits a short UV cut-off edge, allowing for efficient excitation by UVA light [13]. The compound can be described by the general formula A₃B₃(CO₃)₅, where A represents Na⁺, and B can be either Na⁺ or rare-earth ions (RE³⁺) [16]. The duty ratios of various elements at three B sites in crystal structure are different, resulting in a variable Na⁺ to RE³⁺ ratio that is typically greater than 1 but smaller than 2. As the ionic arrangement of doping elements in B-sites is closely related to temperature, the exploration of A₃B₃(CO₃)₅ system can greatly expand the application of materials in optics and thermal management [16]. Additionally, since the three B lattice sites can be occupied by different elements, the variation among these elements often leads to rare-earth carbonates exhibiting monoclinic or pseudo-hexagonal structures [16,17]. Luo et al. successfully synthesized colorless hexagonal Na₄La₂(CO₃)₅ crystals using a hydrothermal reaction of NaF and Na₂CO₃ double salts at 220 °C in five days [13]. However, using the same experimental method, the crystal structure of Na₄La₂(CO₃)₅ doped with Eu³⁺ and Tb³⁺ is monoclinic [14,15]. Therefore, the research on the structure and optical properties of Na₄La₂(CO₃)₅-based materials is crucial for broadening the application fields of rare-earth carbonate functional materials.

Na₄La₂(CO₃)₅ serves as an excellent luminescent host, but its application for optical measurements of ion doping concentration has not yet been developed. This paper investigates the effects of Sm³⁺ doping on the synthesis conditions, lattice structure, luminescence intensity, and decay properties of Na₄La₂(CO₃)₅. Additionally, the potential application of Na₄ (La_1-xSm_x)₂(CO₃)₅ functional material in optical quantifying was discussed.

2. Materials and Methods

Na₄(La_1−xSm_x)₂(CO₃)₅ (labeled as NLC:xSm³⁺) were prepared using the hydrothermal method. La(NO₃)₃·6H₂O (99.99%), Sm(NO₃)₃·6H₂O (99.99%), and Na₂CO₃ (99.5%) were purchased from Shanghai Aladdin Bio-Chem Technology Co., Ltd., Shanghai, China. Firstly, 5 mmol of Na₂CO₃ was weighed and placed into a beaker. Then, 20 mL of deionized water was gradually added to the Na₂CO₃ while stirring with a magnetic stirrer until it fully dissolved. The pH of the dissolved Na₂CO₃ solution was adjusted to 9.6 using dilute nitric acid. Secondly, 1 mmol of lanthanum nitrate and samarium nitrate were weighed and dissolved in 3 mL of deionized water, ensuring thorough mixing to obtain a homogeneous nitrate solution. This mixed nitrate solution was then added dropwise to the sodium carbonate solution while continuously stirring to maintain the pH at 9.1. After stirring for 50 min, the reaction mixture was transferred to a reactor and heated to 220 °C for 18 h. After complete cooling, the precipitate was washed three times with ethanol and deionized water, and dried at 90 °C for 1 h to obtain hollow dendritic crystals NLC:Sm³⁺ phosphor.

The crystal structure of NLC:xSm³⁺ was analyzed using an X-ray diffractometer with a scanning range of 5–80° (PANalytic, Almelo, The Netherlands). The morphologies and energy dispersive spectrum of NLC:xSm³⁺ were imaged via cold field emission scanning electron microscopy (Regulus 8220, Hitachi High-Tech Co., Tokyo, Japan). The fluorescent spectra of NLC:xSm³⁺ were measured with a FLS920 fluorescence spectrophotometer equipped with a 450 W Xenon lamp (Edinburgh Instruments, Livingston, UK). The scanning range of the luminescent spectrum is 210–740 nm, and the slit widths of the excitation and emission grating were both set to 1 nm. The decay curves of NLC:xSm³⁺ (x = 0.005, 0.02, 0.04, 0.06, 0.08, 0.1, 0.3, 0.5, 0.7, 1) were recorded using a 60 W microsecond flashlamp (Edinburgh Instruments, Livingston, UK).

3. Results and Discussion

3.1. Crystal Structures

Figure 1 shows the X-ray diffraction patterns of NLC:xSm³⁺ (x = 0, 0.005, 0.04, 0.1, 0.5, and 1). The diffraction patterns revealed that as the proportion of Sm³⁺ increases from 0% to 50%, the number of diffraction peak positions in the spectra does neither increase or decrease, and the peak shape remains unchanged. This indicates that La³⁺ can be partially or completely substituted by Sm³⁺, leading to the formation of a new rare-earth luminescent material containing both Sm³⁺ and La³⁺. The Sm³⁺-doped NLC:xSm³⁺ prepared by this method exhibits a hexagonal phase structure, which is consistent with the crystal structure previously reported by Luo et al. [13]. When the doping concentration of Sm³⁺ reaches 100%, a few diffraction peaks appear in the X-ray diffraction spectrum at positions of 12.99° and 16.47°. The intensities of these diffraction peaks are quite similar to those of the standard monoclinic phase structure, suggesting that the highly doped material contains a small amount of NLC:xSm³⁺ in the monoclinic phase. For the doping process with various concentrations of Sm³⁺, it can be concluded that when the Sm³⁺ content is less than 50%, the NLC:xSm³⁺ is a pure hexagonal phase. However, when the Sm³⁺ content exceeds 50%, the substance consists of a large amount of hexagonal NLC:xSm³⁺ along with a smaller amount of monoclinic NLC:xSm³⁺. This polymorphism can be attributed to the similar ionic radii of Sm³⁺ (1.079 Å) and La³⁺ (1.160 Å) [18], which allows Sm³⁺ to effectively replace La³⁺ in the lattice, resulting in a stable NLC:xSm³⁺. A hydrothermal method using NaF and sodium carbonate as reactants can significantly affect the crystal lattice of rare-earth ion-doped Na₄La₂(CO₃)₅, allowing for the formation of either a hexagonal [13] or monoclinic phase [15]. This method enables the stable incorporation of Sm³⁺ ions into NLC in any proportion.

3.2. Morphologies and Element Distribution

Figure 2 shows the typical structure and energy spectrum analysis of Sm³⁺-doped NLC:xSm³⁺. In Figure 2a, the microstructure of NLC:0.04Sm³⁺ shows relatively uniform grains with a dendritic structure. Each grain consists of a root and several dendrites, where the root forms a polycrystalline bundle structure, while the dendrites appear as two-dimensional hexagonal hollow structures. The enlarged images of typical structures (1–4) are shown in Figure 2b–e. Figure 2a–d provide enlarged schematic diagrams of these hexagonal hollow structure grains. In Figure 2b,c, the cross-section of the two-dimensional dendrites is hexagonal and well-defined, indicating the integrity of the grains and high-quality growth. The observation of the hexagonal structure of the crystal is consistent with the results from X-ray diffraction. Figure 2d shows a top view of the dendritic structure, where each dendrite is hollow and distinctly separated from the others. Figure 2e depicts a side view of the dendritic structure. The figure demonstrates that the bottom ends of each dendrite merge into bundles, resembling the trunk of a tree. Each branch resembles a tree branch, clustered together but independent from one another. Figure 2f shows the energy spectrum and elemental analysis of NLC:0.04Sm³⁺. The graph indicates that the composition includes elements such as Na, La, Sm, C, and O. The ratio of Na to the combined content of La and Sm is 1.12, which is greater than 1 but less than 2. The ratio value indicates that Na not only occupies the Na sites in the Na₄La₂(CO₃)₅ structure, but also enters the La sites. This finding is consistent with literature reports indicating that Na can occupy the M position in Na₃M₃(CO₃)₅ (M = rare earth or Na) [16].

3.3. Luminescence Spectra

Figure 3 shows the excitation spectra of NLC:xSm³⁺ (x = 0.005, 0.02, 0.04, 0.06, 0.08, 0.10) phosphors at a monitoring wavelength of 593 nm. From the figure, the excitation peak positions of samples with different Sm³⁺ doping concentrations remain the same. In the wavelength range of 210–500 nm, the excitation spectrum consists of broadband excitation peaks and several narrowband excitation peaks. The broad excitation peak, located between 210 and 260 nm, corresponds to the charge transfer transition between Sm³⁺ and O²⁻ [19,20]. Several narrowband excitation peaks, arising from f-f transitions of 4f electrons in Sm³⁺, can be observed between 300 nm and 500 nm. These include peak positions at 318 nm (⁶H_5/2 → ⁴P_3/2), 346 nm (⁶H_5/2 → ⁴H_9/2), 363 nm (⁶H_5/2 → ⁴D_3/2), 376 nm (⁶H_5/2 → ⁴D_1/2), 404 nm (⁶H_5/2 → ⁴F_7/2), 418 nm (⁶H_5/2 → ⁴M_19/2), 441 nm (⁶H_5/2 → ⁴G_9/2), 463 nm (⁶H_5/2 → ⁴I_13/2), and 481 nm (⁶H_5/2 → 4M_15/2) [21,22], with the highest intensity observed at 404 nm. The intensity of these narrowband peaks is closely related to the Sm³⁺ doping concentration, peaking at 0.04.

Figure 4 shows the emission spectrum of NLC:0.04Sm³⁺ at an excitation wavelength of 404 nm. From the graph, the emission spectrum consists of four narrowband peaks in the 540–740 nm range: 560 nm (⁴G_5/2 → ⁶H_5/2), 593 nm (⁴G_5/2 → ⁶H_7/2), 641 nm (⁴G_5/2 → ⁶H_9/2), and 702 nm (⁴G_5/2 → ⁶H_11/2) [23,24]. The transition from ⁴G_5/2 to ⁶H_5/2, ⁶H_7/2, and ⁶H_9/2 correspond to the different dipole transitions. Literature research indicates that when Sm³⁺ is situated at the center of an inversion symmetry lattice, the emitted light appears as orange-red, and the transition is mainly magnetic dipole transition at 560 nm (⁴G_5/2 → ⁶H_5/2) [25]. Conversely, if Sm³⁺ is placed in the non-inversion symmetric lattice site, the emitted light remains orange-red, but the transitions predominantly involve electric dipole transitions at 593 nm (⁴G_5/2 → ⁶H_7/2) and 641 nm (⁴G_5/2 → ⁶H_9/2) [26]. In spectral testing, the strongest emission peak for NLC:Sm³⁺ fluorescent powder occurs at 593 nm (⁴G_5/2 → ⁶H_7/2), indicating that Sm³⁺ occupies a non-inversion symmetric lattice site within the NLC host.

There are two distinct emission peaks at 641 nm that nearly overlap. The emission wavelength of 641 nm results from the transition of an electron from the ⁴G_5/2 to the ⁶H_9/2 level. The energy levels adjacent to ⁶H_9/2 are ⁶H_7/2 and another level at ⁶H_11/2. There is a significant difference in the band gap between these levels. Therefore, the emission observed at 641 nm does not arise from transitions between two adjacent energy levels, but rather from energy resonance transfer between two neighboring Sm³⁺ ions. Furthermore, the emission intensity of Sm³⁺ initially increases with the increase in doping concentration. The luminescence intensity peaks at a doping concentration of 0.04, beyond which the emission strength weakens, illustrating a concentration quenching phenomenon. The quenching concentration for Sm³⁺ in NLC is similar to 0.05 in Li₆Y(BO₃)₃ host [22], 0.04 in LaSr₂AlO₅ host [27], and 0.02 in Sr₉Y₂W₄O₂₄ host [28].

Figure 5 illustrates the relationship between the emission intensity of NLC:xSm³⁺ and the concentration of Sm³⁺. From the graph, the peak emission intensities at 593 nm and 641 nm are significantly higher, approximately three times greater than those at 560 nm and 702 nm. As the concentration of Sm³⁺ increases, the number of luminescent centers also rises, which enhances the excitation intensity. The maximum emission intensity at 560, 593, 641, and 702 nm for NLC:xSm³⁺ also occurs at a Sm³⁺ concentration of 0.04. However, as the concentration of Sm³⁺ increases, the distances between adjacent Sm³⁺ ions decrease, raising the probability of concentration quenching and reducing luminescence intensity. Consequently, emission data indicates that for Sm³⁺ doping concentrations between 0.02 and 0.06, the emission efficiency of NLC:xSm³⁺ can exceed 65% of the maximum value, optimizing the utilization of rare-earth Sm³⁺.

3.4. Concentration Quenching

According to Dexter’s theory, concentration quenching can be described by an equation that represents the multipolar interactions [29].

$${\displaystyle \frac{I}{x}}={K[1+\beta (x^{{\displaystyle \frac{Q}{3}}})]}^{-1}$$

(1)

where K and β are constants on the same excited condition, I is emission intensity at different concentrations, x is ion doping concentration, and Q is the type of electrical multilevel interaction. When Q values are 6, 8, or 10, they correspond to the interaction mechanisms of dipole–dipole (d-d), dipole–quadrupole (d-q), and quadrupole–quadrupole (q-q), respectively. By applying a logarithmic transformation to the initial Equation (1), Equation (2) can be obtained [24].

$$\log \left({\displaystyle \frac{I}{x}}\right)=-{\displaystyle \frac{Q}{3}}\log \left(x\right)+C$$

(2)

Figure 6 depicts the relationship between the logarithm of fluorescence intensity (I/x) and the logarithm of the concentration (x) of NLC:xSm³⁺ (x = 0.04, 0.06, 0.08, 0.1). A linear analysis of the data reveals a slope of K = −1.76 and a corresponding Q value of 5.28, which is close to the threshold of 6. This finding suggests that the concentration-quenching mechanism for Sm³⁺ is consistent with the electric dipole–dipole interaction mechanisms observed in LiBaPO₄ [29].

3.5. Decay Curves and Element Quantifying

Figure 7 illustrates the decay curves of the NLC:xSm³⁺ samples measured at a monitoring wavelength of 593 nm under an excitation wavelength of 404 nm. The decay curves reveal that the radiative transitions of excited-state electrons are not independent. Instead, they involve multiple processes. The multi-stage decay of excited-state electrons can be attributed to several factors. Firstly, energy resonance transfer allows excited-state electrons to exchange between adjacent Sm³⁺ ions at excited-state energy levels, leading to a redistribution of electrons in the ⁴G_5/2 excited state. This process results in the emission spectrum displaying emission bands with varying peak shapes. Secondly, phonons play a role in facilitating non-radiative transitions for electrons at multiple excited-state levels, such as ⁴M_19/2, ⁴G_9/2, ⁴I_13/2, and 4M_15/2, which promotes their movement to the ⁴G_5/2 emission level. These transitions increase the effective number of excited-state electrons in the ⁴G_5/2 level by several factors. Moreover, due to electric dipole–dipole interactions, excited-state electrons can transfer between various excited-state energy levels. This transfer can lead to a reduction in the number of effective luminescent ions in the ⁴G_5/2 state. As a result of these processes, the decay of excited-state electrons can be characterized using multiple exponential functions in an Equation (3) [30]:

$$I_t=I_0+A_1\exp \left(-{\displaystyle \frac{t}{{\tau }_1}}\right)+A_2\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{t}{{\tau }_2}})+A_3\exp \left(-{\displaystyle \frac{t}{{\tau }_3}}\right)+A_4\exp \left(-{\displaystyle \frac{t}{{\tau }_4}}\right)$$

(3)

where t is the decay time, I_t and I₀ are the emission intensities at time t and time 0, respectively. A₁, A₂, A₃, and A₄ are constants, and τ₁, τ₂, τ₃, and τ₄ represent the fluorescence lifetimes of different processes. The formula for calculating the average lifetime is provided in Equation (4):

$$\overline{\tau }={\displaystyle \frac{(A_1{{\tau }_1}^2+A_2{{\tau }_2}^2+A_3{{\tau }_3}^2+A_4{{\tau }_4}^2)}{(A_1{\tau }_1+A_2{\tau }_2+A_3{\tau }_3+A_4{\tau }_4)}}$$

(4)

The decay process of the NLC:xSm³⁺ is fitted using Equation (3). The dashed line represents the fitted curve, while the solid line shows the measured data. In terms of intensity variation, the fittings of multiple exponential curves are very good with minimal error. The luminescence intensity of NLC:xSm³⁺ decays slowly at low Sm³⁺ concentrations. However, as the Sm³⁺ doping concentration increases, the concentration quenching effect intensifies, leading to a sharp decrease in intensity. The Adj.R-Square values for all fitted data exceed 0.99 and are close to 1, which can accurately characterize the emission decay of excited-state photons.

Table 1. Lifetimes of NLC:xSm³⁺ at different Sm³⁺ doping concentrations.

x	τ1 (μs)	A1	τ2 (μs)	A2	τ3 (μs)	A3	τ4 (μs)	A4	$\overline{\mathit{\tau }}$ (μs)
0.005	32.322	488.298	292.7593	464.171	1706.7059	1080.930	3701.5582	1431.482	3125.66079
0.02	53.552	579.622	413.7319	894.990	1549.2641	1447.263	3409.1107	1442.114	2697.0012
0.04	70.813	869.038	353.8018	733.283	1030.3673	1539.962	2861.9882	1292.322	2278.6158
0.06	43.810	968.308	251.8847	1017.717	848.2378	1577.200	2515.3235	981.195	1805.06070
0.08	26.816	1087.621	187.0909	1260.309	717.8652	1775.547	2235.8934	765.399	1472.29055
0.1	37.180	1103.463	168.8446	980.702	611.3864	1716.550	1976.5186	632.914	1253.93227
0.3	6.6347	43,534.801	36.5430	12,082.146	268.2743	5080.547	816.735	778.150	330.82171
0.5	3.4611	112,851.969	15.4604	49,054.973	125.0992	2797.744	364.8252	406.032	67.33125
0.7	2.3905	199,440.828	12.4428	18,546.146	103.2877	461.417	620.5405	36.692	29.64514
1	2.2751	219,636.656	12.6237	66,785.313	164.9922	216.890	1008.0468	14.475	23.25147

shows the lifetimes of NLC:xSm³⁺ (x = 0.005, 0.02, 0.04, 0.06, 0.08, 0.10, 0.30, 0.50, 0.70, 1.00) at different Sm³⁺ doping concentrations. The average lifetimes of NLC:Sm³⁺ decrease with increasing doping concentration. The maximum lifetime of 3.13 ms is observed in NLC:0.005Sm³⁺, while the minimum of 0.023 ms is found in NLC:1Sm³⁺. Compared to other hosts, the lifetime of NLC:0.005Sm³⁺ is similar to that of GdPO₄:0.01Sm³⁺ (3.86 ms) [19], higher than that of PbWO₄:0.02Sm³⁺ (0.524 ms) [23], and lower than that of YInGe₂O₇:0.01Sm³⁺ (4.5 ms) [31]. The decrease in lifetime is mainly attributed to the increased concentration of Sm³⁺ in the lattice, leading to a reduction in the distance between them. This proximity intensifies the cross-relaxation (CR) effect, resulting in a quicker depopulation of electrons from the excited-state energy level. The additional cross-relaxation leads to irregular changes in the decay curve.

Figure 8 shows the decay curve of Sm³⁺ emitted at 593 nm under the excitation at 560 nm. The decay curve at 593 nm reveals notable discrepancies when a single-exponential fitting is applied. In contrast, when a bi-exponential fitting is used, the error decreases, and is further minimized with a multi-exponential fitting. This precise fitting suggests that the luminescence process of Sm³⁺ involves not only the emission from individual Sm³⁺ ions, but also interactions with other Sm³⁺ ions. The reason is that the lowest excited-state energy level of Sm³⁺ is ⁴G_5/2 in the visible light range. Electrons at this level can transition to lower energy levels, such as ⁶H_5/2, ⁶H_7/2, ⁶H_9/2, and ⁶H_11/2, to emit visible light. In the absence of cross-relaxation between Sm³⁺, the decay curve of ⁴G_5/2 level could be described by a single-exponential equation. However, if the decay curve needs to be represented by multiple exponential equations, it indicates that the emission from the ⁴G_5/2 energy level in Sm³⁺ is not only a radiative transition process.

The depopulation process of excited-state electrons in Sm³⁺ can be illustrated using the energy level diagram in Figure 9. When Sm³⁺ is excited at a wavelength of 404 nm, electrons transition from the ⁶H_5/2 ground state to the ⁴F_7/2 excited state, and then relax to the ⁴G_5/2 luminescent state through a non-radiative transition. As the electrons return to the ground state, visible light is emitted at wavelengths of 560, 593, 641, and 702 nm, corresponding to the ⁴G_5/2 → ⁶H_5/2, ⁴G_5/2 → ⁶H_7/2, ⁴G_5/2 → ⁶H_9/2, and ⁴G_5/2 → ⁶H_11/2 transitions, respectively. According to the analysis of the fluorescence decay process at 593 nm, the number of excited-state electrons in ⁴G_5/2 is influenced by cross-relaxation. Cross-relaxation often occurs between Sm³⁺ ions, as demonstrated by Deopa et al. [21], Kumar et al. [29], and Ouertani et al. [19], where the ions interact via dipole–dipole interactions. The cross-relaxation processes can be expressed as follows [32]: ⁴G_5/2 + ⁶H_5/2 → ⁶F_5/2 + ⁶F_11/2, ⁴G_5/2 + ⁶H_5/2 → ⁶F_7/2 + ⁶F_9/2, ⁴G_5/2 + ⁶H_5/2 → ⁶F_9/2 + ⁶F_7/2, ⁴G_5/2 + ⁶H_5/2→⁶F_11/2 + ⁶F_5/2. These cross-relaxation processes can lead to a non-single-exponential change in the depopulation of excited-state electrons.

Figure 10 illustrates the relationship between the lifetimes of NLC:xSm³⁺ and the concentration of Sm³⁺. When excited by photons at 404 nm, Sm³⁺ generates four major emission bands corresponding to the ⁴G_5/2 energy level, with the maximum emission intensity observed at 593 nm. The lifetime at 593 nm shows the most regular variation, which is directly related to the concentration of Sm³⁺. After fitting, the relationship between the lifetime of 593 nm and the doping concentration can be expressed as Equation (5)

$$\tau =2.208\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{x}{0.075}}\right)+1.106\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{x}{0.203}}\right)+0.008$$

(5)

where x is the doping concentration of Sm³⁺ in NLC:xSm³⁺, and τ is the lifetime of 593 nm emission in NLC:xSm³⁺. The Adj.R-square of the fitted curve is 0.9986, which is very close to 1. This indicates that the equation effectively characterizes the relationship between the lifetime and the Sm³⁺ doping level in NLC:xSm³⁺. Therefore, when NLC:Sm³⁺ fluorescent materials are used in applications such as anti-counterfeiting coatings, fluorescent decorations, or solid-state lighting coatings in the future, the lifetime detection method is useful for identifying the composition and authenticity of these materials.

3.6. Chromaticity Coordinates

Figure 11 displays the chromaticity coordinates of NLC:xSm³⁺ under the 404 nm excitation. The chromaticity coordinates of the fluorescent samples, prepared with varying concentrations of Sm³⁺, are quite similar, yielding nearly identical coordinate points. All of the emitted light appears as orange-red. Notably, the color of the emitted light remains consistent regardless of the Sm³⁺ concentration. Based on the spectral data, the chromaticity coordinates for efficient NLC:xSm³⁺ at different concentrations (x = 0.005, 0.02, 0.04, 0.06, 0.08, and 0.10) were calculated as follows: (0.6051, 0.3942), (0.6065, 0.3929), (0.6056, 0.3938), (0.6060, 0.3934), (0.6055, 0.3939), and (0.6059, 0.3934). These chromaticity coordinates suggest that as the concentration of Sm³⁺ increases, the chromaticity coordinates of the fluorescent powder remain stable, demonstrating good optical stability. This finding suggests that variations in Sm³⁺ content in NLC does not affect the color properties of emission light, which is beneficial for applications in display and lighting technologies.

4. Conclusions

Hollow dendritic crystals of NLC:xSm³⁺ (x = 0, 0.005, 0.01, 0.02, 0.04, 0.06, 0.08, 0.10, 0.30, 0.50, 0.70, 1.00) were synthesized using the hydrothermal method at 220 °C for 18 h. The crystal structure was confirmed through X-ray diffraction and cold field emission scanning electron microscopy. The crystal structure of NLC:xSm³⁺ allows for the substitution of Sm³⁺ and La³⁺ ions in any ratio. Fluorescence studies revealed that the emission intensity peaks at a Sm³⁺ doping concentration of 0.04. The main factor contributing to fluorescence quenching is the electric dipole–electric dipole interaction among Sm³⁺ ions. Additionally, the lifetime of Sm³⁺ decreases as the doping concentration increases. The variation in lifetime can be precisely correlated with the Sm³⁺ doping concentration within the range of 0.005 to 1. Consequently, the relationship between lifetime and Sm³⁺ concentration can be utilized for identification purposes in applications such as fluorescent anti-counterfeiting and solid-state lighting coatings.