Judd–Ofelt Analysis and Laser Optical Properties of Nd³⁺-Doped S-FAP Nanocrystals as Precursors for Transparent Laser Ceramics

Abstract

Nd:S-FAP (Nd³⁺-doped Sr₅(PO₄)₃F) is a high-performance laser material recognized for its large stimulated emission cross-section and broad absorption bands, which are highly desirable for achieving efficient optical gain at the nanoscale. In this work, 5% Nd-doped Nd:S-FAP nanocrystals with an average grain size of approximately 9.2 nm were successfully synthesized via an improved hot-injection method. The results show that the fluorescence lifetime of the nanocrystals is 66 μs (166.56 μs for the ceramic), the quantum yield is 19.7% (69.6% for the ceramic), and the stimulated emission cross-section is 2.29 × 10⁻²⁰ cm² (5.74 × 10⁻²⁰ cm² for the ceramic). These discrepancies are primarily governed by surface-to-volume ratio variation-related surface effects, lattice distortions, and the weakening of non-radiative f–f transition processes due to quantum confinement at the nanoscale. This study reports for the first time the laser optical parameters of Nd:S-FAP nanocrystals, providing an experimental basis for the optimization of precursors for transparent laser ceramics and holding significant importance for the design of laser materials.

1. Introduction

Nd:S-FAP, a hexagonal apatite-structured laser crystal, possesses a large emission cross-section, broad absorption band, and high damage threshold, making it an ideal gain medium for high-power solid-state lasers [1,2,3,4]. However, with the growing demand for large-size, high-optical-uniformity, and high-doping-concentration media in laser systems, bulk single crystals have increasingly revealed bottlenecks such as compositional segregation, core bubbles, cleavage cracking, and excessively long growth cycles [5,6]. To overcome the physical and thermodynamic limitations of single-crystal growth, colloidal nanocrystals and transparent ceramics—two morphologically distinct yet physically closely related materials—have emerged as frontier research directions in optical materials science.

On one hand, Nd:S-FAP transparent ceramics prepared by hot-pressing or spark plasma sintering retain the excellent spectral properties of single crystals while achieving size scalability, superior mechanical fracture toughness, and the possibility of gradient doping [7,8,9]. On the other hand, with the rapid development of nanotechnology, Nd:S-FAP nanocrystals at quantum-confined or mesoscopic scales (typically <100 nm) exhibit unique quantum and surface effects in biomedical near-infrared fluorescence imaging, flexible optoelectronic detectors, and high-sensitivity nanoscale temperature sensing [10,11,12]. In these nanosystems, the extremely high specific surface area and lattice distortions significantly alter the local coordination environment of luminescent ions, leading to excitation and decay dynamics that differ markedly from those of bulk materials.

The evolution from single crystals to nanocrystals is essentially a transition from an ideal crystal with infinite three-dimensional periodicity to a highly disordered system rich in surface defects and grain-boundary networks. In bulk single crystals, acute lattice strain severely restricts the maximum permissible Nd³⁺ doping threshold, inevitably triggering detrimental compositional segregation and structural cleavage. Transparent ceramics, composed of numerous randomly oriented micro-crystals connected by dense grain boundaries, achieve macroscopic averaging of anisotropy and can accommodate higher doping concentrations without macroscopic segregation. For dispersed nanocrystals, structural characteristics are dominated by the extremely high specific surface area; a large number of atoms are located on or near the particle surface, resulting in abundant dangling bonds and surface reconstruction. Organic ligands (such as oleic acid and oleylamine) used in synthesis further modify the local dielectric environment [13]. Although the structural parameters, absorption cross-sections, and fluorescence lifetimes of bulk transparent ceramic Nd:S-FAP have subsequently been well documented in the literature by Zhang et al. [14], systematic studies on the laser-relevant optical properties and transition dynamics of its colloidally dispersed nanocrystal precursors remain highly insufficient.

Herein, a 5% Nd³⁺ doping concentration was prescribed for the Sr₅(PO₄)₃F nanocrystals to navigate the unique luminescent dynamics at the nanoscale. Unlike bulk single crystals or transparent ceramics that suffer from severe concentration quenching via energy migration to killer sites at this doping level, sub-10 nm nanocrystals are inherently governed by ultrafast non-radiative decay channels tied to surface defects and ligand vibrations. Therefore, elevating the doping level to 5% becomes imperative to maintain a sufficient density of luminescent centers and yield robust emission, decoupling the conventional trade-off between active ion maximization and concentration-induced quenching. This paper provides a comprehensive comparison of the luminescent properties of Nd:S-FAP nanocrystals and transparent ceramics, including absorption/emission spectra, fluorescence characteristics, quantum yield, and stimulated emission cross-section, laying the foundation for the development of next-generation non-cubic high-power laser ceramics.

2. Materials and Methods

2.1. Materials

All operations were performed under a high-purity argon (Ar) atmosphere(with a constant flow rate of 150 sccm) to prevent oxidation and hydrolysis. The chemical reagents used included strontium acetate Sr(CH₃COO)₂ (99.5%), neodymium acetate Nd(CH₃COO)₃ (99.99%), 1-octadecene (ODE, >90%), oleic acid (OA, 99.7%), oleylamine (OM, analytical grade), triethyl phosphate (99.5%), and cyclohexane (AR, 99.7%), all the above reagents were purchased from Innochem (Beijing, China). Strontium trifluoroacetate Sr(CF₃COO)₂ was prepared in the laboratory. Anhydrous ethanol was purchased from Chongqing Chuandong Chemical Co., Ltd., Chongqing, China, and ultrapure water was used. All solvents were used without further purification.

2.2. Precursor Solution Preparation

(Each precursor was prepared in a 1000 mL three-neck flask): Precursor 1 (cation solution containing Nd³⁺): 114 mmol Sr(CH₃COO)₂ and 6 mmol Nd(CH₃COO)₃ were added to a 1000 mL three-neck flask, followed by 280 mL OA, 40 mL OM, and 280 mL ODE. The mixture was stirred magnetically under argon, heated to 150 °C, held for 45 min until completely clear, and cooled to room temperature. Precursor 2 (anion solution): 20 mmol Sr(CF₃COO)₂ and 120 mmol triethyl phosphate were added, followed by 300 mL OA and 300 mL ODE. The mixture was stirred under argon, heated to 125 °C, held for 45 min, and cooled. Precursor 3 (supplementary cation solution): 120 mmol Sr(CH₃COO)₂ was added, followed by 280 mL OA, 40 mL OM, and 280 mL ODE. The mixture was stirred under argon, heated to 150 °C, held for 45 min until clear, and cooled.

2.3. Hot-Injection Synthesis of Nanocrystals

(This was carried out in a 1000 mL three-neck flask): 25 mL OA and 40 mL OM were added to the flask. The mixture was stirred under argon and heated to 150 °C for 30 min to remove trace moisture and oxygen. The injection was carried out in three stages using a syringe pump(Yuanhang Power, Yancheng, China): Stage 1: The system was heated to 310 °C; 90 mL of precursor 1 was injected rapidly and held at 310 °C for 20 min. The temperature was lowered to 280 °C, and 60 mL of precursor 2 was injected slowly at 1 mL/min and held for 30 min. Stage 2: 180 mL of precursor 1 was injected, the temperature was raised to 300 °C and held for 30 min; 120 mL of precursor 2 was then injected at 2 mL/min and held for 30 min. Stage 3: 135 mL of precursor 3 was injected and held at 300 °C for 30 min; 90 mL of precursor 2 was injected at 4 mL/min and held for 30 min.

After the reaction, the mixture was cooled naturally to room temperature. Excess anhydrous ethanol (2–3 times the reaction volume) was added for precipitation. The precipitate was separated by centrifugation (8000 rpm, 10 min), redispersed in cyclohexane, precipitated again with an equal volume of ethanol, and washed three times. The final precipitate was dried in a vacuum oven (DZF-6050, China, Shanghai Jinghong Experimental Equipment Co., Ltd., Shanghai, China) at 60 °C for 12 h to obtain white Nd:S-FAP nanocrystal powder. The actual yield of the obtained nanocrystal powder was approximately 2.5 g, corresponding to a reaction yield of about 30.6%.

Compared with conventional one-pot hydrothermal or co-precipitation methods, the improved hot-injection methodology implemented in this work introduces a well-controlled, multi-stage programmed feeding strategy. In Stage 1, the rapid injection of the cation solution (Precursor 1) into the high-temperature matrix (310 °C) induces instantaneous thermodynamic supersaturation. This successfully triggers a ‘burst nucleation’ process, ensuring that all crystal nuclei form simultaneously within an extremely narrow time window. Subsequently, the strictly controlled, slow-dripping rate (1–4 mL/min) of the counter-ion solution (Precursor 2) across Stages 1 to 3 effectively decouples the subsequent crystal growth phase from the initial nucleation event. This kinetic restriction severely suppresses secondary nucleation and forces the existing nuclei into a ‘focusing growth’ regime. Such a tailored synthesis configuration is the fundamental reason for achieving the highly monodisperse, pure hexagonal-phase, and ultra-small spherical Nd:S-FAP nanocrystals with minimized structural heterogeneity.

2.4. Characterization

X-ray diffraction (XRD) data were collected on a Bruker D8 Advance diffractometer(Bruker AXS, Karlsruhe, Germany) with Cu Kα radiation. Morphology was observed using a Talos F200X G2 transmission electron microscope (TEM) (Thermo Fisher Scientific, Waltham, MA, USA). Absorption spectra were measured on a PerkinElmer Lambda 1050+ UV/Vis/NIR spectrophotometer(PerkinElmer, Waltham, MA, USA). Emission spectra and fluorescence decay curves were recorded on an Edinburgh FLS1000 fluorescence spectrometer(Edinburgh Instruments Ltd. Livingston, UK) equipped with a 450 W steady-state xenon lamp for steady-state spectra and a microsecond flashlamp (μs-pulse Xe lamp) for photoluminescence decay measurements, with the excitation wavelength monochromated to 794 nm. To establish a rigorous performance benchmark, all optical parameters and structural profiles for the reference bulk transparent ceramics utilized in this comparative study were adapted from the validated data reported by Zhang et al. [14]. The transparent ceramics with the same doping concentration of 5% were fabricated via vacuum hot-pressing sintering at 1100 °C under a hydrostatic pressure of 30 MPa for 2 h.

3. Results and Analysis

3.1. XRD and Micrograph

The phase purity and structural characteristics of the as-synthesized Nd:S-FAP nanocrystals were examined by X-ray diffraction (XRD) and transmission electron microscopy (TEM). As illustrated in Figure 1, the XRD pattern of the Nd:S-FAP nanocrystals matches the standard diffraction card of Sr₅(PO₄)₃F exactly, with no detectable impurity phases, confirming the formation of a pure hexagonal apatite structure. The corresponding TEM image (Figure 2) reveals that the nanocrystals are nearly spherical, uniformly dispersed, and possess an average particle diameter of approximately 9.2 nm. (Figure 3) This nanoscale dimension results in an exceptionally high surface-to-volume ratio, which is expected to profoundly influence the local coordination environment of the Nd³⁺ dopant ions.

3.2. Absorption and Emission Spectra

The UV/Vis/NIR absorption spectra of the Nd:S-FAP nanocrystals (dispersed in tetrachloroethylene) and the reference transparent ceramics are compared in Figure 4. The dominant absorption transitions in the nanocrystals occur at 582 nm (⁴I_9/2→⁴G_5/2+²G_7/2) and 802 nm (⁴I_9/2→⁴F_5/2+²H_9/2). Relative to the transparent ceramics [14], these peaks exhibit a consistent blue shift of 3–4 nm (ceramic peaks at 581.2 nm and 805.7 nm). This shift arises primarily from the inhomogeneous crystal field at the nanocrystal surfaces and the lattice strain induced by the finite-size effect. Moreover, the full width at half maximum (FWHM) of the absorption band near 800 nm is only 13 nm for the nanocrystals—significantly narrower than the 22 nm observed in the ceramics—yet the absolute absorption intensity is markedly lower.

Mechanistically, this size-induced lattice strain originates from the drastic modification of the boundary conditions as the particle dimension is reduced to the sub-10 nm regime. For ultra-small ~9.2 nm nanocrystals, the exceptionally high surface-to-volume ratio creates a tremendous inward hydrostatic pressure (often described as Laplace pressure), driven by the minimization of surface energy. This immense surface tension forces the interior crystal lattice to undergo global contraction, generating a pronounced macroscopic lattice strain. Concurrently, this comprehensive lattice strain translates into severe localized lattice distortion on the atomic scale. Consequently, the local chemical bond lengths (such as Sr–O and P–O bonds) are shortened, and the coordination polyhedra surrounding the Nd³⁺ ions experience varying degrees of asymmetric structural deformation and symmetry reduction. This micro-strain and the subsequent severe lattice distortion break the perfect structural periodicity of the host lattice, perturbing the local crystal field parameters. This ultimately adjusts the electronic energy-level splitting of the Nd³⁺ 4f³ configuration and induces the observed inhomogeneous spectral shifts.

The room-temperature steady-state emission spectra of the Nd³⁺:S-FAP nanocrystals and the reference transparent ceramic under 794 nm monochromated excitation are presented in Figure 5. The main emission peak of the nanocrystals is localized at 1056 nm, corresponding to the classic four-level laser transition of ⁴F_3/2→⁴I_11/2. Compared with the ceramic counterpart (1054 nm, FWHM = 20 nm [14]), the nanocrystal line exhibits a modest broadening (FWHM = 22 nm) and a slight 2 nm red shift, which is conventionally driven by the inhomogeneous crystal field and localized structural relaxation.

3.3. Fluorescence Decay

The fluorescence decay kinetics of the ⁴F_3/2 emitting level in the nanocrystals were analyzed by conforming to a biexponential profile, as expressed by [15]:

$$I\left(t\right)=I_0+A_{1}exp\left(-t/{\tau }_1\right)+A_{2}exp\left(-t/{\tau }_2\right)$$

(1)

where τ₁ and τ₂ are the short and long lifetime components, and A₁ and A₂ represent their respective amplitudes. To comprehensively evaluate the emission dynamics, the intensity-weighted average fluorescence lifetime (τ_ave) was mathematically derived using the equation:

$${\tau }_{ave}=\left(A_1{\tau }_1^2+A_2{\tau }_2^2\right)/\left(A_1{\tau }_1+A_2{\tau }_2\right)$$

(2)

A bi-exponential fit yields the intensity-weighted average lifetime of τ_ave = 66 μs (in Figure 6), which is only about 40% of the value reported for the transparent ceramics (166.56 μs [14]). This pronounced shortening demonstrates a significant enhancement of non-radiative decay channels. Although surface passivation by oleic acid and oleylamine ligands partially suppresses concentration quenching, the dominant contribution stems from the high density of surface states and dangling bonds inherent to the 9.2 nm particles, which facilitate multiphonon relaxation and energy-transfer processes.

3.4. Judd–Ofelt Parameters

The spectroscopic properties of Nd³⁺ ions in the S-FAP nanocrystals were analyzed using Judd–Ofelt (J–O) theory. Based on the absorption spectra, the experimental oscillator strengths (f_exp) of the absorption transitions were determined according to the equation provided in Ref. [16]. In the calculation of the theoretical oscillator strengths (f_cal), typically only the contributions from electric and magnetic dipoles are considered; thus, f_cal was evaluated using the formula from Ref. [17].

As shown in

Table 1. Nanocrystal absorption peak positions, experimental oscillator strengths, and theoretical oscillator strengths.

Nd: S-FAP Transition 4I9/2→	λ (nm)	${\mathit{f}}_{\mathit{exp}}$ (10−6 cm2)	${\mathit{f}}_{\mathit{cal}}$ (10−6 cm2)
4G7/2	525	2.4286	3.9350
4G5/2+2G7/2	582	8.3563	11.8398
4F7/2+2S3/2	745	2.9083	4.2368
4F5/2+2H9/2	802	5.3592	7.3096
4F3/2	870	1.2867	1.8127

, the experimental oscillator strengths of the Nd³⁺:S-FAP nanocrystals are systematically lower than those typically reported for bulk S-FAP crystals or transparent ceramics. In particular, the hypersensitive transition ⁴I_9/2 to ⁴G_5/2 +²G_7/2 at 582 nm exhibits a relatively high oscillator strength among the observed bands, consistent with its electric-dipole-dominated character. However, the overall reduced $f_{\mathit{exp}}$ values reflect the influence of the nanoscale environment, including surface effects, lattice distortion, and the modified local crystal field around Nd³⁺ ions. The good agreement between f_exp and f_cal, with the root–mean–square deviation (RMSD) typically being on the order of 10⁻⁶, validates the reliability of the Judd–Ofelt intensity parameters obtained in this study.

The line strengths were subsequently calculated following the methodology described in Refs. [17,18], with the required reduced matrix elements adopted from the same sources. ${\Omega }_t$ macroscopically describes the physical properties of the material [19], the three intensity parameters ${\Omega }_t$ (t = 2,4,6) can then be obtained by least-squares fitting of the experimental and theoretical oscillator strengths. The resulting intensity parameters Ω₂, Ω₄, and Ω₆ are listed in

Table 2. Judd—Ofelt intensity parameters for Nd³⁺-doped S-FAP nanocrystals and transparent ceramic.

Nd: S-FAP	Judd—Ofelt Parameters (×10−20 cm2)			Refs.
	${\mathit{\Omega }}_2$	${\mathit{\Omega }}_4$	${\mathit{\Omega }}_6$
nanocrystals	0.709	7.036	2.242	This work
transparent ceramic	0.856	9.966	11.284	[14]

.

The dramatically smaller Ω₂ values for the nanocrystals reflect a decrease in both the covalency of the Nd–ligand bonds and the overall asymmetry of the coordination polyhedra. These changes are direct consequences of the pronounced surface reconstruction, lattice contraction, and ligand-induced dielectric screening that dominate at the nanoscale. The lower Ω₄ and Ω₆ parameters further indicate reduced matrix rigidity and altered acid–base character of the host, both of which suppress the spontaneous emission probabilities.

The spontaneous emission transition probability between two energy levels, the total radiative lifetime${(\tau }_r)$and luminescence branch ratio $\left(\beta \right)$ of the ⁴F_3/2 energy level is then calculated [20], thus the quantum efficiency $\eta$ of the excited state is obtained [21]. Finally, the ⁴F_3/2→⁴I_11/2 energy level stimulated emission cross-section can be calculated [22]. The radiative transition probabilities (A_rad), quantum yield ($\eta$), and stimulated emission cross-section ($\sigma$) from the ⁴F_3/2 level are summarized in

Table 3. Measured radiative properties and emission cross-section from ⁴F_3/2 level of Nd³⁺ in S-FAP nanocrystals and transparent ceramic.

Nd: S-FAP		λ (nm)	Arad (s−1)	β (%)	$\mathit{\eta }$(%)	$\mathit{\sigma }\mathbf{(}{10}^{-20}\mathbf{cm}$2)	Refs.
nanocrystals	4F3/2→4I9/2	875	1768.54	0.6475	19.7	2.29
	4F3/2→4I11/2	1056	825.45	0.3022			This work
	4F3/2→4I13/2	1330	137.52	0.0503
transparent ceramic	4F3/2→4I9/2	890	1900	0.455	69.6	5.74
	4F3/2→4I11/2	1054	1820	0.435			[14]
	4F3/2→4I13/2	1337	460	0.11

.

As summarized in Table 3, the individual A_rad values for all observed transitions are consistently lower than those of the transparent ceramic counterpart, indicating a systematic suppression of radiative transition probabilities in the nanocrystalline system. This reduction is closely associated with the significantly smaller Judd–Ofelt intensity parameters (Ω₂, Ω₄, Ω₆) obtained for the nanocrystals. At the nanoscale, strong surface reconstruction, lattice distortion, and ligand-induced dielectric screening modify the local crystal-field environment around the Nd³⁺ ions and reduce the covalency and asymmetry of the Nd–ligand coordination. Consequently, the electric-dipole transition strength is weakened, leading to lower spontaneous emission probabilities compared with the highly crystalline transparent ceramic.

For the nanocrystals, the quantum yield of the ⁴F_3/2 level is only 19.7%, compared with 69.6% for the transparent ceramic. Correspondingly, the stimulated emission cross-section for the strongest laser transition (⁴F₃/₂ → ⁴I₁₁/₂ at 1056 nm) is 2.29 × 10⁻²⁰ cm²—approximately half of the ceramic value (5.74 × 10⁻²⁰ cm² [14]). Mechanistically, the fluorescence lifetime and the quantum yield are governed by the competition between the radiative transition rate (W_R) and the non-radiative relaxation rate (W_NR), expressed as τ_ave= 1/(W_R + W_NR) and $\eta =\tau$_ave/τ_rad. For the ultra-small Nd:S-FAP nanocrystals (~9.2 nm), their exceptionally high surface-to-volume ratio relocates a substantial fraction of Nd³⁺ ions to or near the particle surface. These surface-bound luminescent centers are exposed to a high density of coordinate imperfections, dangling bonds, and structural disordered defects, which introduce continuous mid-gap trapping states that act as highly efficient non-radiative ‘killer sites’. More detrimentally, the surface of the nanocrystals is capped with organic ligands (oleic acid and oleylamine), which possess high-frequency vibrational modes (such as C–H at 2900 cm⁻¹ and O–H/N–H at 3300 cm⁻¹). These high-energy phonons can easily bridge the relatively small energy gap of the Nd³⁺: ⁴F_3/2 metastable state via resonance-assisted multi-phonon relaxation, abruptly accelerating the non-radiative rate (W_NR). In sharp contrast, the macro-structured transparent ceramics are formed by high-temperature consolidation, which completely eliminates the organic capping ligands and severely expels surface dangling bonds through dense, highly crystalline grain boundary networks. Consequently, the Nd³⁺ ions inside the grains are well shielded by the rigid lattice host with much lower effective phonon energies, suppressing the non-radiative channels (W_NR→0). This dramatic mitigation of non-radiative losses leads to a prolonged fluorescence lifetime and a profoundly elevated quantum yield in the ceramic system.

These quantitative reductions in lifetime, quantum yield, and emission cross-section collectively demonstrate that surface effects and quantum-confinement-induced lattice distortions exert a dominant inhibitory influence on the luminescence dynamics of Nd:S-FAP at the nanoscale. The experimental data therefore provide the first comprehensive laser-relevant optical parameters for Nd:S-FAP nanocrystals and establish a clear performance benchmark relative to bulk transparent ceramics. Critically, the observed differences highlight the necessity of targeted surface-passivation strategies (e.g., core–shell architectures or optimized ligand exchange) to minimize non-radiative losses before the nanocrystals are consolidated into high-optical-quality transparent laser ceramics. Such precursor optimization is essential for realizing scalable, high-doping-level, gradient-doped laser gain media with superior mechanical and thermal properties.

4. Discussion

This paper systematically compares the optical properties of Nd:S-FAP nanocrystals and transparent ceramics, revealing the significant influence of surface effects and lattice distortion on the luminescence dynamics at the nanoscale. To the best of our knowledge, this is the first systematic report of the key laser optical parameters (fluorescence lifetime, quantum yield, and stimulated emission cross-section) for Nd:S-FAP nanocrystals. Although these values are lower than those of the bulk transparent ceramic, the obtained data provide critical experimental evidence for understanding the nanoscale effects in this system and offer an important reference for the optimization of nanocrystal precursors used in transparent laser ceramics. The systematic comparison presented herein not only elucidates the microscopic origins of the optical-property degradation in nanocrystalline Nd:S-FAP but also supplies valuable experimental guidance for bridging the gap between nanoscale precursors and macroscopic laser ceramics. Future work will focus on surface passivation strategies to further improve the optical performance of the nanocrystals and promote their application in high-power laser ceramics.