Unravelling the crystallization mechanism and structural evolution of Yb/Er-doped SiO₂-GdF₃ nano-glass ceramics

Abstract

The crystallization mechanism of Yb/Er-doped GdF₃ nanocrystals in silica nano-glass ceramics was analyzed using model-free and model-fitting methods and thermal analysis data in correlation with structural data. The formation of GdF₃ nanocrystals occurs at around 300 °C, and their size is temperature dependent, ranging from 14 to 40 nm, depending on the processing temperature. A similar trend is observed for cell volume, where a contraction of up to ≈2.3% (at 600 °C) was assigned to the gradual incorporation of Li and Yb,Er dopants. Model-free analysis showed an increase in activation energy (E_a) and the preexponential factor (log A) up to 175 kJ mol⁻¹ and 14.8 s⁻¹, respectively, until the completion of crystallization. Model-fitting analysis indicated a crystallization process controlled by an autocatalytic-type reaction where a second metastable phase (LiF) acts as a catalyst and facilitates a rapid and self-accelerated crystallization of the main GdF₃ nanocrystalline phase. The ceramization process boosted UC luminescence up to values comparable to those of NaYF₄:18Yb/2Er.

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1. Introduction

A novel class of nanostructured materials is represented by nano-glass-ceramics (or glass ceramics), where partial precipitation of a specific nanocrystalline phase within the amorphous glass is reached; nucleation and growth of nanocrystals occur in the parent glass matrix during subsequent thermal processing of the glass.¹ The sol–gel approach represents an easy and controllable method for the preparation of transparent nano-glass ceramics, where optically active nanocrystals are embedded in a glass matrix, and optical transparency is assured by the small size of the nanocrystals.^2,3

The optical properties of glass ceramics are widely recognized to be significantly influenced by their microstructure, which is directly related to the crystallization process. While these materials have been widely studied for their properties, only a limited number of studies have investigated their crystallization mechanisms and the relationship between these mechanisms and their optical properties.^4,5 For the design of novel and/or improved application-based glass ceramic phosphors, a comprehensive study on the crystallization mechanism is complex but crucial as it can provide valuable insights into their structure and microstructure, as well as into how their structural and optical properties can be controlled through processing. It has been shown that formation of nano-glass ceramics involves a thermally activated chemical decomposition reaction of metal trifluoroacetates precursors, followed by the precipitation and growth of nanocrystals at high temperatures.^2–5 Therefore, the nanocrystal formation process indicates thermal behaviors that can be analyzed through complex thermal analysis, which should include not only TG-DSC measurements but also thermokinetic analysis. The crystallization mechanism under non-isothermal conditions has been investigated through DTA or DSC analysis, based on models such as Avrami's theory, along with modified formulations of the Ozawa, Friedman, Matusita, or Kissinger equations.^6–8 Non-isothermal crystallization kinetic analysis of the β-PbF₂ or YF₃ crystalline phase in silicate glass ceramics indicated a diffusion-controlled process of three-dimensional growth with decreasing nucleation.^4,5 In contrast, we showed that BaF₂ nanocrystal precipitation in a glass matrix is controlled by a homogeneous crystallization mechanism: nucleation centers resulting from thermal decomposition of Ba–trifluoroacetate grow into BaF₂ nanocrystals at higher temperatures—a process revealing a distinct crystallization peak at high temperatures.⁹ Later, the same approach was used for the analysis of the crystallization mechanism of an SiO₂-LaF₃ xerogel, and a chemical decomposition reaction followed by the fast precipitation of crystals was proposed instead of a diffusion-controlled nucleation and growth process.¹⁰

The synthesis and optical/luminescence properties of glass ceramics with rare-earth doped GdF₃ nanocrystals have been of keen interest for multicolor emitting phosphor applications¹¹ owing to several advantages such as efficient energy transfer between Gd and RE-ions,^12,13 and the low phonons energy of GdF₃ (around 300 cm⁻¹)¹⁴ that assures reduced multi-phonon relaxation rates, all of which lead to highly efficient luminescence properties. In addition, considering their desirable feature, such as low phonon energy,¹⁴ Yb/Er-doped GdF₃ nanocrystals have been investigated for up-conversion (UC) luminescence properties;^15,16 sequential absorption of two or more low energy photons (in infrared range) leads to light emission in the visible range, i.e. UC luminescence. However, the Yb/Er-doped GdF₃ nanocrystals showed a tendency to aggregate and exhibited relatively poor UC properties, with enhancement being observed only after Li doping.^15,16 Hence, in order to obtain higher UC luminescence efficiency, it is necessary to choose a proper synthesis method for nanoparticle dispersion along with low phonon energy host for high RE³⁺ ion luminescence efficiency.

A viable way may be to use a sol–gel chemistry approach useful for a wide range of compositions, assuring uniform distribution of optically active nanocrystals within the sample volume (through a thermally activated reaction) without agglomeration effects and with a high transparency degree due to their small size (tens of nm size).^2,3 Investigations into RE³⁺-doped SiO₂-GdF₃ glass ceramics have demonstrated the precipitation of GdF₃ nanocrystals in a silica matrix.^11,13,17 The crystallization process of GdF₃ nanocrystals (showing hexagonal or orthorhombic structure) is related to the gadolinium trifluoroacetate Gd(CF₃COO)₃ decomposition chemical reaction¹² and driven by Li ion dopants.¹⁷ Our investigations highlighted an autocatalytic process where a second metastable phase (lithium fluoride) acts as a catalyst for the GdF₃ crystallization process. Hence, the crystallization mechanism seems to be different compared with metal halide^4,5 nanocrystal precipitation in glass crystallization, but it nevertheless remains incompletely understood.

The aim of this study is to extend our previous knowledge on crystallization processes of GdF₃ nanocrystals in a silica glass matri¹⁷ and the UC luminescence properties using a deep and quantitative approach in order to provide further information that could either complement or confirm it. Model-free and model fitting methods were used to compute the kinetic parameters and propose a reaction model function using differential scanning calorimetry (DSC) data in correlation with data obtained from X-ray diffraction measurements. The absolute quantum yield QY of UC-luminescence of the Yb/Er-doped SiO₂-GdF₃ is also investigated.

2. Materials and methods

2.1. Sample preparation

For the preparation of the undoped and 4Yb³⁺/1Er³⁺-doped 90SiO₂-5GdF₃ (mol%) xerogels and those co-doped with Li, we used the sol–gel synthesis route¹⁷ and reagent-grade tetraethylorthosilicate (TEOS), trifluoroacetic acid (TFA), ethyl-alcohol, metal acetates, acetic acid and deionized water as starting materials. In the first step, TEOS was hydrolyzed under constant stirring with a mixed solution (8.2 mL) of ethanol and water and using glacial acetic acid as catalyst; molar ratio was 1 : 4 : 3.5 : 0.5. A second solution (3 mL) of Yb(CH₃COO)₃, Er(CH₃COO)₃, Li(CH₃COO), Gd(CH₃COO)₃ and TFA with a Yb : Er : Li : Gd : F molar ratio of 3 : 0.7 : 3.6 : 3.6 : 89 was prepared, mixed and added dropwise to the first solution. After an additional vigorous stirring for 1 h at room temperature, the mixed solution was aged at room temperature for a week in a Petri dish. The wet gels were dried up to 120 °C during 1 week to form the xerogel, and glass ceramization was achieved after thermal calcination in air for 60 min at 525 °C, and the glass ceramic samples were denoted as GCLiYb/Er.

2.2. Characterization methods

The thermal behaviour of the xerogel was investigated using a Netzsch STA 449 F3 Jupiter simultaneous thermal analyser in the TG-DSC mode. Approximately 25 mg sample was measured in synthetic air (80% N₂, 20% O₂) at heating rates of 5, 10, 15, 20, and 25 °C min⁻¹ from room temperature to 900 °C. Experiments were conducted in open alumina crucibles at a gas flow rate of 20 mL min⁻¹. Heat flux sensitivity was ±0.001 mW, and temperature accuracy was ±0.01 °C. Non-isothermal kinetic analysis of the DSC data was performed using Netzsch Thermokinetics 3.1 software (version 072010).

The structural characterization of the materials was performed using X-ray diffractometry (XRD) and a BRUKER D8 ADVANCE type X-ray diffractometer, in focusing geometry, equipped with a copper target X-ray tube and LynxEye one-dimensional detector, in the 15°–65° range with a 0.05° step and 2 s integration time. For the analysis of the XRD patterns, we used PowerCell dedicated software.¹⁸

Photoluminescence and reflectance spectra were recorded at room temperature using a FluoroMax 4P spectrophotometer and its accessories. Up-conversion (UC) luminescence spectra were recorded under laser light pumping at 980 nm from a laser module (200 mW). For the quantitative measurements of UC luminescence efficiency, we used a 50 mm diameter Thorlabs integrating sphere coupled to a commercial spectrophotometer (Ocean Optics usb2000) (see ESI†).

3. Theoretical background

The kinetics of xerogel crystallization were evaluated using model-free and model-fitting approaches. The model-free method allows the determination of activation energy and the preexponential factor without assuming a specific kinetic model for the crystallization process. In this study, the Friedman model was used. This model plots the natural logarithm of the conversion rate (ln(dα/dt)) against 1/T for measurements at different heating rates (β).¹⁹ According to theoretical studies,²⁰ the equation that describes the relationship between the reaction rate, reacted fraction, and temperature, independent of the thermal sequence used for experiments, has the following form:where α represents the reacted fraction, A is the Arrhenius pre-exponential factor, R is the gas constant, E_a is the activation energy, f(x) is the kinetic model (which is constant in the model-free analysis), and T is the temperature of the process. In logarithmic form, eqn (1) can be written as follows:

At a constant value of x, eqn (2) can be written as follows:

According to eqn (3), activation energy (E_a) can be determined from the slope of the plot of versus the inverse of temperature. The model fitting approach facilitates the identification of the crystallization reaction mechanism by minimizing the differences between experimental and calculated values. Using the kinetic parameters derived from the model-free analysis, the reaction model (f(x)), can be determined. The experimental data are then fitted to simulated curves, and through a statistical comparison of the fit for various models, the most suitable model along with its corresponding set of parameters is selected.²¹

4. Results and discussion

4.1. Thermal analysis

The TG-DSC curves of the Yb³⁺/Er³⁺-doped SiO₂-GdF₃ xerogel co-doped with Li measured in synthetic air with a heating rate of 10 °C min⁻¹ are shown in Fig. 1(a). The DSC curve shows four peaks of different intensities, accompanied by a mass loss, as shown in the TG curve. The first endothermic peak, with a maximum at a temperature of 92 °C, is associated with a minor weight loss of approximately 10 wt%, which is attributed to the evaporation of water and residual organic fragments.

Fig. 1 TG-DSC curves of the Yb³⁺/Er³⁺-doped SiO₂-GdF₃ xerogel co-doped with Li, measured in synthetic air at a heating rate of 10 °C min⁻¹ (a) and the crystallization peak highlighted at five different heating rates: 5, 10, 15, 20, and 25 °C min⁻¹ (b).

The main process revealed by thermal analysis is the thermolysis of metal (M) trifluoroacetate,²² and the reaction is characterized by a distinct exothermic DSC peak around 300 °C and a weight loss of approximately 38 wt%. A possible mechanism for this reaction involves the breaking of the C–F bond in trifluoroacetate ligands during thermal processing, leading to the formation of new M–F bonds and subsequent growth of MF₃ nanocrystals.²³ The 300 °C peak was assigned to gadolinium trifluoroacetate Gd(CF₃COO)₃ thermolysis with subsequent GdF₃ nanocrystalline phase precipitation^11,17 and overlaps with lithium and RE-trifluoroacetate decomposition, which occurs in the same temperature range.²²

A much weaker exothermic DSC peak at 550 °C is attributed to the crystallization of the LiGdF₄ phase, and the small DSC peak at 810 °C is likely associated with glass melting. At higher heating rates, the crystallization maxima shifted to higher temperatures, and their surface areas increased, as shown in Fig. 1(b). This occurs because faster heating leads to the production of a higher number of crystals within the same time.¹⁰

4.2. Structural and morphological characterization

The XRD pattern analysis allows tracking structural modifications during the annealing of the Yb³⁺/Er³⁺-doped SiO₂-GdF₃ xerogel (Fig. 2). The initial dried xerogel annealed up to 250 °C shows a broad background that is characteristic of the amorphous structure of the silica matrix, but as the annealing temperature increases, extra-diffraction peaks assigned to the nanocrystalline GdF₃ fluoride phase precipitation start to develop. The occurrence of GdF₃ nanocrystals dispersed in the amorphous glassy matrix was confirmed using transmission electron microscopy as well.¹⁷ As is known, GdF₃ exhibits two crystalline structures, orthorhombic (space group Pnma (no. 62)) and hexagonal (space group P6₃/mcm (no. 193)), which differ significantly in terms of coordination number, lattice volume, and other parameters. The crystallization of the orthorhombic GdF₃ nanocrystals (PDF 012-0788) can be observed in the 225–350 °C temperature range and agrees very well with the strong DSC peak at 300 °C from thermal analysis measurements (Fig. 1). At higher temperatures (600 °C), LiGdF₄ phase crystallization is observed, accompanied by weaker SiO₂ peaks.

Fig. 2 XRD patterns of GCLiYb/Er glass-ceramic samples after annealing at different temperatures; the XRD pattern of orthorhombic GdF₃ (PDF 012-0788) is included.

The XRD pattern analysis of the GCLiYb/Er sample annealed at different temperatures according to the TG/DSC curves (Fig. 1) indicates a strong lattice relaxation effect compared with GdF₃ (PDF 012-0788), revealed by the shift to higher angles (Fig. 2), along with a steady increase in the nanocrystals size, up to about 40 nm (Table 1). The ionic radii of 8-fold coordinated Yb³⁺ ions (105.3 pm) and Er³⁺ ions (100.4 pm) are much smaller than that of 8-fold coordinated Gd³⁺ ions (119 pm),²⁴ and the contraction effect (about 2.3% at 600 °C) was assigned to the Li⁺ and Yb³⁺, Er³⁺ ion incorporation in the lattice. The contraction effect solely related to Yb/Er doping is about 1.4%,²⁵ and therefore, the additional contraction up to 2.3% is related to Li doping. The contraction effect follows nanocrystal growth, with the unit cell volume decreasing by approximately 1.7% at 300 °C and up to 2.3% at 600 °C, relative to orthorhombic GdF₃ (as shown in Table 1). Hence, we suppose that the contraction effect is due to the incorporation of Li and Yb,Er ions into the lattice during the nanocrystal growth, most likely through the Ostwald ripening mechanism, where the growth of large nanocrystals occurs through the coalescence of smaller ones.

Table 1 Results of the X-ray diffraction (XRD) pattern analysis of GCLiYb/Er glass-ceramic samples annealed at different temperatures; the lattice parameters for GdF₃ (PDF 012-0788) are included for comparison

Temperature (°C)/lattice parameters	a (Å)	b (Å)	c (Å)	Cell volume (Å)^3	D (nm)
275	6.471	6.951	4.430	199.2	14
300	6.471	6.932	4.416	198.1	14
350	6.471	6.933	4.423	198.4	16
525	6.471	6.915	4.407	197.2	25
600	6.471	6.918	4.398	196.9	40
Orth-GdF3 (PDF file)	6.571	6.984	4.393	201.6	—

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4.3. Thermokinetic analysis

4.3.1. Model-free thermokinetic analysis. The activation energy and preexponential factor estimated using Friedman analysis are shown in the Fig. 3.

Fig. 3 Friedman analysis of the crystallization of the Yb³⁺/Er³⁺-doped SiO₂-GdF₃ xerogel co-doped with Li (a). Dependence of activation energy and the pre-exponential factor on the crystallization fraction according to the Friedman method (b).

Model-free analysis indicates that activation energy (E_a) and the preexponential factor (log A) gradually increase up to a partial area (x) of 0.4, reaching values of approximately 171 kJ mol⁻¹ and 14.2 s⁻¹, respectively. These parameters remain constant until x reaches 0.8, after which a slow increase is observed. At the end of crystallization (x = 1), we obtained an E_a of approximately 175 kJ mol⁻¹ and a log A of about 14.8 s⁻¹. These values are comparable to those reported for YF₃–SiO₂ glass-ceramics, where E_a values of approximately 129 and 139 kJ mol⁻¹ were obtained using Kissinger's and Chen's methods, respectively.⁵ Similar values of activation energy for PbF₂ crystallization were calculated using the Kissinger method to be about 162 kJ mol⁻¹ and 167 kJ mol⁻¹ for x = 0 and x = 1, respectively.⁴ In contrast, the E_a value for 80SiO₂-90LaF₂ glass-ceramics is significantly higher, of about 293 kJ mol⁻¹.¹⁰

4.3.2. Model-fitting analysis. The DSC curves recorded at different heating rates were analyzed and fitted to several reaction models²⁶ using multivariate least squares regression with the Thermokinetics program. According to Fig. 4, the best-fitted reaction model for the xerogel is the autocatalytic Prout-Tompkins model (Bna).

Fig. 4 Experimental data for the Yb³⁺/Er³⁺-doped SiO₂-GdF₃ xerogel co-doped with Li and the fitting curve of the 300 °C crystallization peak.

Previous investigations have shown the Prout-Tompkins autocatalytic model to be useful for describing a crystallization mechanism in which the crystallization rate is influenced by two key factors—the degree of conversion and the presence of catalytic compounds—both of which contribute to accelerating the crystallization process.^26,27 The mathematical representation of this model²⁸ is given by the following equation:

where n is the order of reaction, and a is the is the autocatalytic constant. The kinetic parameters are listed in Table 2: F_exp. is the experimental form of the reaction model (f(x)), obtained from DSC data, and the model with an F_exp-value of 1 has the least deviation out of all the models compared; F_crit is the critical value (quantile), obtained from F-distribution at a significance level of 0.05; t_crit is the critical value, obtained from t-distribution, and is defined for a given significance level and degrees of freedom.

Table 2 Kinetic model parameters resulting from non-linear regression analysis

Parameters	Values
Log A (s^−1)	12.25 ± 0.67
Ea (kJ mol^−1)	157.50 ± 2.73
React. Ord. 1	1.574 ± 0.09
Exponent a	0.211 ± 0.006
Fexp	1
Fcrit (0.95)	1.08
Statistical parameters
Correlation coefficient	0.994
Durbin–Watson factor	2.41
Rel. precision	0.00100
t-Critic (0.95; 136)	1.969

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According to this model, the amorphous xerogel sample shows rapid self-accelerated crystallization, which occurs through the simultaneous formation of Li-related metastable phases, resulting from the thermal decomposition of metal trifluoroacetates at temperatures around 300 °C. Although these phases are not detected in XRD patterns at this temperature—likely because of their low crystallinity, nanoscale dimensions, or limited concentration²⁹ —they play a crucial catalytic role in the crystallization process. Li⁺ ion doping is favorable for the formation of metastable phases that can act as diffusion barriers or phase interfaces, preventing uncontrolled crystallization kinetics (e.g., by delaying the crystallization of stable phases, blocking volatile pathways that would intensify autocatalysis, modifying diffusion in the solid state, etc.). By lowering the activation energy, they facilitate the crystallization of the Yb³⁺/Er³⁺-doped SiO₂-GdF₃ phase, thus promoting rapid phase formation. Furthermore, a reaction order value (n) greater than 1 (with n ≈ 1.57) suggests an accelerated nucleation and crystallite growth rate. This leads to a nonlinear increase in the crystallization rate, which can result in the formation of larger crystallites or rapid development of the crystalline phase. However, if not properly controlled, such conditions may also introduce issues, including structural defects or incomplete crystallization. Statistical parameters indicate that the model fits well, showing a strong correlation, no significant autocorrelation in the residuals, high precision, and statistical significance in the parameter estimates. This is supported by the Durbin–Watson statistic, which tests for autocorrelation in the residuals. A value near 2 indicates no significant autocorrelation.²⁹ Since the value of 2.41 is close to 2, it suggests that the residuals are independent, which is a positive indication.

4.4. Up-conversion luminescence properties

We observed that Li-ion co-dopant influence is not limited only to crystallization behavior (see above) but also on structural properties (for higher doping levels²⁵) accompanied by optical property improvements.^17,25 Under 980 nm IR light pumping, the GCLiYb/Er glass ceramic sample showed UC luminescence of Er³⁺ ions, caused by the energy transfer Yb–Er within the GdF₃ nanocrystals (Fig. 5).

Fig. 5 Normalized UC luminescence spectra recorded for GCLiYb/Er glass-ceramic (after calcination at 525 °C) and β-NaYF₄:18Yb/2Er polycrystalline powder recorded under 980 laser light pumping and the possible mechanism with the RE energy levels involved (inset).

The substitutional Li⁺ ions tailor the crystal field symmetry and alter the environment of Er³⁺,^15,16 leading to an increase in UC luminescence.²⁵ The UC mechanism has been extensively investigated in various host Yb³⁺/Er³⁺-doped nanocrystalline host materials, including GdF₃,^15,16 and oxyfluoride glass ceramics.^30–33 It is based on highly efficient IR light absorption by Yb³⁺ ions at around 1000 nm (²F_7/2 → ²F_5/2 transition). For unsaturated up-conversion processes, the UC luminescence intensity is proportional to the nth power of the incident pump power. The value of n, corresponding to the number of pump photons required for the population of the emitting level,³⁴ can be extracted from a double logarithmic plot, luminescence intensity vs. incident pump intensity, where n is the slope of this dependence (see ESI†). The Er³⁺ emitting levels are feed by the two-photon energy transfer (ET) process, accompanied by multi-phonon and cross-relaxation (Yb³⁺–Er³⁺) processes, followed by the characteristic green ((²H_11/2, ⁴S_3/2) → ⁴I_15/2) and red (⁴F_9/2 → ⁴I_15/2) luminescence (Fig. 5 inset); for “uv-blue” up-conversion luminescence (⁴G_11/2, ²H_9/2 → ⁴I_15/2), three-photon energy transfer processes are involved.^30,33

The quantitative measurement of the absolute quantum yield (QY) of up-conversion is challenging; therefore, we used the method proposed by J. C. Boyer et al.³⁵ For comparison and verification, we measured β-NaYF₄:18Yb/2Er polycrystalline powder, known to show the best luminescence property among UC luminescent materials. We obtained a QY of 0.2 ± 0.1% for GCLiYb/Er glass ceramic, and 0.3 ± 0.1% for the β-NaYF₄:18Yb/2Er, which matches well with the values reported in the literature;³⁵ QY can increase under higher power density.³⁶ For applications, optical transparency is a very important parameter. In the present case, GCLiYb/Er glass ceramic shows good optical transparency in the blue to red spectral optical range (300–700 nm), as shown by the high reflectance values of about 0.75; the small dips at 377, 485, 519 and 650 nm are assigned to the Er³⁺ ions characteristic absorptions from the ground state ⁴I_15/2 to ⁴G_11/2,9/2, ⁴F_7/2, ²H_11/2 and ⁴F_9/2, respectively (see ESI†).

5. Conclusion

Complex thermal analysis, correlated with structural data, showed that the precipitation of GdF₃ nanocrystals results from the thermolysis of gadolinium-trifluoroacetate at approximately 300 °C. The crystallization mechanism was found to be autocatalytic, with Li-based metastable phases acting as catalysts by lowering activation energy barriers for nanocrystal nucleation and growth. Thermokinetic analysis also indicated an accelerated rate of crystal nucleation and growth, influencing the material structure and microstructure. This behavior was confirmed by the evolution of optical properties, which showed enhanced UC luminescence, reaching values comparable to those of the NaYF4:18Yb/2Er phosphor while maintaining the optical transparency of the material.

Conflicts of interest

There are no conflicts to declare.

Data availability

The experimental data that support the findings of this study will be available on request.

Acknowledgements

The authors acknowledge funding by the Core Program of the National Institute of Materials Physics (NIMP), granted by the Romanian Ministry of Research, Innovation and Digitization through the Project PC3-PN23080303. The help of Dr Silviu Polosan for the Up-Conversion luminescence set-up and efficiency measurements is gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ma00377f

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