Structural Analysis of Erbium-Doped Silica-Based Glass-Ceramics Using Anomalous and Small-Angle X-Ray Scattering

Abstract

This study employs advanced structural characterization techniques, including anomalous small-angle X-ray scattering (ASAXS), small-angle X-ray scattering (SAXS), and X-ray photoelectron spectroscopy (XPS), to investigate erbium (Er³⁺)-doped silica-based glass-ceramic thin films synthesized via the sol–gel method. This research examines the SiO₂-TiO₂ and SiO₂-TiO₂-PO_2.5 systems, focusing on the formation, dispersion, and structural integration of Er³⁺-containing nanocrystals within the amorphous matrix under different thermal treatments. Synchrotron radiation tuned to the L_III absorption edge of erbium enabled ASAXS measurements, providing element-specific details about the localization of Er³⁺ ions. The findings confirm their migration into crystalline phases, such as erbium phosphate (EPO) and erbium titanate (ETO). SAXS and Guinier analysis quantified nanocrystal sizes, revealing trends influenced by their composition and heat treatment. Complementary XPS analysis of the Er 5p core-level states provided detailed information on the chemical and electronic environment of the Er³⁺ ions, confirming their stabilization within the crystalline structure. Transmission electron microscopy (TEM) highlighted the nanoscale morphology, verifying the aggregation of Er³⁺ ions into well-defined nanocrystals. The results offer a deeper understanding of their size, distribution, and interaction with the surrounding matrix.

1. Introduction

Recent advancements in photonic applications have increasingly focused on rare earth (RE) ion-doped materials due to their unique energy levels, which allow for a variety of radiative transitions across UV, visible, and NIR wavelengths. Common host materials include crystals, glasses, transparent ceramics, and nanocrystalline films. Among these, glass-ceramics (GCs)—amorphous matrices embedded with nanocrystals—are particularly promising, as they combine the properties of glass (like chemical durability and mechanical strength) with the optical properties of nanocrystals [1,2].

For free RE ions, intra-4f transitions are generally parity-forbidden, which leads to low transition probabilities and long luminescence lifetimes. These extended lifetimes are advantageous for applications such as upconversion lasers, where a sustained energy release is desirable [3]. Embedding RE ions in host materials can activate these transitions by introducing asymmetry in the surrounding crystal field, thereby increasing the luminescence intensity of lanthanide ions and enhancing their practical applicability [4]. However, a challenge with RE ions, particularly Er³⁺, is their low solubility in oxide materials, primarily due to mismatches between the ionic radii and the covalent bonds within the matrix. This mismatch often leads to ion clustering at higher concentrations, causing luminescence degradation via ion–ion coupling linked to erbium ion cross-relaxation processes in clustering Er–O–Er bonds [5] or the formation of optically inactive phases [1]. An alternative approach is to localize these ions within the nanocrystalline phase, which can significantly improve the material’s optical properties [1,2].

Among the GCs, silica–titania (ST) glass-ceramics have gained significant attention due to their compatibility with optical fibers and their tunable refractive index [6]. By adjusting the silica (SiO₂)–to–titania (TiO₂) ratio, the refractive index of ST glass-ceramics can be fine-tuned to enhance the light propagation and coupling efficiency in various optical circuits and photonic devices. This is critical for minimizing refractive index mismatches at interfaces, thereby reducing light scattering and improving the performance of components such as waveguides, amplifiers, and modulators used in integrated photonic systems.

The control of the nanocrystal size within the glass-ceramic matrix is critical for maintaining high transparency and minimizing optical losses caused by Rayleigh scattering. Ideally, nanocrystals should be kept below 100 nm in diameter [7]. Additionally, co-dopants like phosphorus (P) help form SiO₂–TiO₂–PO_2.5 (STP) oxide matrices, which support higher concentrations of Er³⁺ ions without aggregation [8]. This improves solubility, extends the excited-state lifetimes of Er³⁺ ions, and reduces quenching effects. For instance, the crystallization of ErPO₄ (EPO) in STP sol–gel glass matrices have shown enhanced fluorescence properties, attributed to the Er³⁺ ions’ environment within EPO crystallites [1]. Similarly, Er₂Ti₂O₇ (ETO) crystallites can form in ST matrices, further increasing fluorescence emissions [1,9]. Co-dopants help distribute fluorescent ions uniformly within nanocrystals, minimizing clustering and enhancing optical performance in devices such as optical amplifiers [2].

Upon the heat treatment of sol–gel films, RE ions tend to migrate toward smaller nanocrystals, decreasing the average inter-ion distance (R) and intensifying energy transfer interactions due to the R⁻⁶ dependence [10,11,12]. This effect is particularly significant in erbium-doped glass compositions, which exhibit a strong fluorescence peak at 1540 nm, crucial for telecommunications applications. However, maintaining a uniform Er³⁺ distribution at concentrations above 0.5% remains challenging, as higher concentrations can lead to clustering and fluorescence quenching. Abdullah et al. [13] demonstrated that at a 6% Er concentration, silicate materials exhibited luminescence intensities indicative of the formation of Er₂Si₂O₇ phases, contributing to enhanced luminescent properties. Meanwhile, Gao et al. [14] specifically highlighted that the γ-Er₂Si₂O₇ phase exhibited the highest luminescent activity.

Small-angle X-ray scattering (SAXS) is a powerful technique to probe local structures, especially in nanoparticle systems. Anomalous small-angle X-ray scattering (ASAXS) further enhances sensitivity to specific elements or phases, providing a detailed view of crystallization processes and nanoscale phase separations in glassy systems [15]. This approach has been effectively utilized to study crystallization processes and nanoscale phase separations in glassy systems. For example, Hoell et al. [16] demonstrated the core–shell structure of BaF₂ nanocrystals formed in phase-separated glasses, showcasing the utility of ASAXS for elucidating the structural evolution during crystallization. Gericke et al. [17] employed ASAXS in combination with absorption spectroscopy to observe nanostructural dynamics, providing detailed insights into compositional variations within the nanocrystals under heat treatment. Furthermore, Haas et al. [18] demonstrated the effectiveness of ASAXS in accessing the phase composition of oxyfluoride glass ceramics doped with Er³⁺/Yb³⁺, offering a nuanced understanding of the interplay between nanostructure and nanochemistry in these systems.

In this study, we employ both SAXS and ASAXS to investigate the dispersion of Er³⁺ ions in silica-based glass-ceramic thin films. The goal is to determine whether the Er³⁺ ions remain dispersed within the amorphous matrix, form clusters, or transition into ETO or EPO nanocrystals upon heat treatment. Specifically, we aim to perform the following:

• Examine the dispersion of Er³⁺ ions: Do they remain uniformly distributed in the amorphous matrix, form clusters, or migrate into nanocrystalline phases?
• Investigate how thermal treatments affect the distribution and structural organization of Er³⁺ ions, observed through SAXS and ASAXS.
• Explore the local electronic environment of Er³⁺ ions using XPS, focusing on their binding energies and phase composition.

This study builds upon preliminary results from an initial investigation, where the use of SAXS and ASAXS to analyze Er³⁺ dispersion in silica-based glass-ceramics was presented solely at the national conference Física2000 (Portugal) [19] and was not formally published. We revisit these findings with a more comprehensive analysis, incorporating new data from XRD and XPS measurements. By investigating the distribution of nanocrystals and the localization of Er³⁺ ions within the glass-ceramic matrix, this work seeks to demonstrate how structural characterization techniques like SAXS and ASAXS can provide critical insights into material organization. These findings lay the groundwork for further studies aimed at leveraging nanostructural control in the development of photonic devices.

2. SAXS and ASAXS to Study Erbium-Doped Nanocrystals Embedded Within Glass

Small-angle X-ray scattering (SAXS) and anomalous SAXS (ASAXS) are powerful techniques for studying the nanoscale structure of doped glass-ceramic matrices. SAXS measures the scattering intensity $\mathrm{I}\left(q\right)$ as a function of the scattering vector q, which provides information about the structural features within the sample. By measuring the scattering of X-rays at small angles, SAXS provides detailed information about the size, shape, and spatial distribution of nanostructures, such as nanoparticles, aerosols, micelles, minerals, and particles synthesized through sol–gel reactions, among others [15]. This method is highly valuable for examining structural inhomogeneities in thin films, polymers, and other complex systems.

In SAXS, the scattering intensity is represented as $\mathrm{I}\left(q\right)$, where q is the scattering vector, which provides information on the structural features within the sample. Here, the intensity depends solely on q, as SAXS is typically conducted at a fixed X-ray energy. The SAXS intensity $\mathrm{I}\left(q\right)$ is proportional to the electron density contrast $\mathsf{\Delta }\mathsf{\rho }$ between phases and follows:

$$\mathrm{I}\left(q\right)\propto {\mathsf{\Delta }\mathsf{\rho }}^2\mathrm{P}\left(q\right)\mathrm{S}\left(q\right)$$

(1)

where $\mathrm{P}\left(q\right)$ is the form factor related to the particle shape and size, and $\mathrm{S}\left(q\right)$ is the structure factor accounting for inter-particle correlations. This dependence on electron density contrast allows SAXS to characterize the size and spatial distribution of nanocrystals and amorphous regions.

Building on SAXS, anomalous SAXS (ASAXS) extends this technique by tuning the X-ray energy near the absorption edge of a target element. Therefore, the scattering intensity is represented as $\mathrm{I}(q,E)$, because it depends both on the scattering vector q and on the X-ray energy E. By tuning E near the absorption edge of a target element (Er, in this study), ASAXS selectively enhances the scattering contributions from that element. This method is particularly effective for studying composite samples with elements that exhibit spatial discontinuities, provided that the experimental setup can access the absorption edges of these elements [20]. This tuning provides element-specific contrast, isolating the Er³⁺ contribution to scattering, and thus allowing ASAXS to reveal details about Er³⁺ ’s localization, providing information about its local distribution within nanocrystalline and amorphous phases.

This energy tuning adjusts the anomalous scattering factor $f\prime \left(\mathrm{E}\right)$, selectively enhancing the scattering contribution from Er³⁺ ions. By plotting the square root of the summed scattering intensities ${\left(\mathsf{\Sigma }\mathrm{I}\right)}^{1/2}$ versus $f\prime \left(\mathrm{E}\right)$, one can separate element-specific contributions from the matrix background. This energy-dependent scattering approach allows us to isolate the contributions of erbium, providing quantitative information into Er³⁺ dispersion and nanocrystal formation. For instance, the thermal annealing of amorphous silicate glass resulted in the formation of cubic BaF₂ nanocrystals embedded within the glass matrix. ASAXS studies conducted near the Ba L_III edge demonstrated that these nanocrystals fell within the nanometer size range and were enveloped by nanoshells of lower electron-density glass [21]. A similar thermally induced nanocrystalline phase also occurred in Cd(S,Se)-doped glasses, where ASAXS conducted near the selenium K edge, was employed to investigate the stoichiometry of nanocrystals smaller than 10 nm [22]. In this research, ASAXS is applied to investigate Er³⁺-doped thin ST and STP films synthesized using the sol–gel method.

2.1. General Principles

ASAXS extends SAXS by incorporating an energy-dependent scattering factor for selective element analysis. While SAXS measures scattering at a constant energy, ASAXS uses an energy (E) close to the absorption edge of the target element—in this case, Er. As E nears erbium’s L_III absorption edge (8357 eV), variations in the scattering factor $f\left(\mathrm{E}\right)$ selectively enhance scattering from regions containing Er³⁺. This yields the ASAXS intensity $\mathrm{I}(q,E)$, with dual dependence on q and E. The scattering factor $f\left(\mathrm{E}\right)$ can be decomposed as:

$$f\left(\mathrm{E}\right)=\mathrm{Z}+f\prime \left(\mathrm{E}\right)+\mathrm{i}f″\left(\mathrm{E}\right)$$

(2)

where Z is the atomic number of Er, and $f\prime \left(\mathrm{E}\right)$ and $f″\left(\mathrm{E}\right)$ are the energy-dependent real and imaginary parts of the anomalous dispersion factor, respectively. Near the absorption edge, $f\prime \left(\mathrm{E}\right)$ and $f″\left(\mathrm{E}\right)$ undergo rapid changes, significantly altering the electron density contrast between Er³⁺ ions and the surrounding matrix, enhancing the sensitivity of ASAXS to Er³⁺, allowing it selective detection.

In ASAXS, the energy-dependent scattering intensity $\mathrm{I}(q,\mathrm{E})$, which depends on both the scattering vector q and the X-ray energy E, can be represented as:

$$I\left(q,E\right)={\left|f_{Er}\left(E\right)+f_{matrix}\left(q\right)\right|}^2.P\left(q\right)$$

(3)

where $f_{Er}\left(E\right)$ is the scattering factor specific to Er³⁺, which varies significantly with energy E near its absorption edge; $f_{matrix}\left(q\right)$ represents the constant scattering factor for the non-Er³⁺-containing matrix, which depends on q but does not vary with E; and $\mathrm{P}\left(q\right)$ represents the form factor, which is independent of E. Expanding this yields:

$$I\left(q,E\right)={\left|f_{Er}\left(q,E\right)\right|}^2+{\left|f_{matrix}\left(q\right)\right|}^2+2Re\left[f_{Er}\left(q,E\right)f_{matrix}^{\mathrm{*}}\left(q\right)\right].P\left(q\right)$$

(4)

The expanded form of the scattering intensity includes contributions from the Er³⁺ nanocrystals ${\left|f_{Er}\left(q,E\right)\right|}^2$, matrix-only scattering ${\left|f_{matrix}\left(q\right)\right|}^2$, and an interference term $2Re\left[f_{Er}\left(q,E\right)f_{matrix}^{\mathrm{*}}\left(q\right)\right]$.

Thus, the scattering intensity of Er³⁺-doped thin films combines the individual scattering from Er³⁺ nanocrystals and the matrix, along with an interference term representing the interactions between the two components. Here, $f_{Er}\left(q,E\right)$ varies with both the scattering vector q and the X-ray energy E, especially near Er’s absorption edge, which induces changes in both the real and imaginary parts of the scattering factor. In contrast, $f_{matrix}\left(q\right)$ remains constant with respect to energy.

The interference term $2Re\left[f_{Er}\left(q,E\right)f_{matrix}^{*}\left(q\right)\right]$ accounts for the interaction between Er³⁺ and the matrix scattering contributions. The factor of 2 arises because the interference is symmetric and includes contributions from both $f_{Er}\left(q,E\right)f_{matrix}^{*}\left(q\right)$ and its conjugate $f_{matrix}\left(q\right)f_{Er}^{*}\left(q,E\right)$, meaning it appears twice in the intensity calculation.

Only the real part of this product is physically measurable, representing the effective interference between Er³⁺ and matrix components.

The energy-dependent scattering intensity $\mathrm{I}(q, E)$ is essential for isolating the scattering contributions of Er³⁺ from other components in the material. Only the Er³⁺-specific terms $f\prime \left(\mathrm{E}\right)$ and $f″\left(\mathrm{E}\right)$ show significant changes near the L_III edge, while matrix scattering remains relatively stable. Standard references like [23] provide tabulated values of $f\prime \left(\mathrm{E}\right)$ and $f″\left(\mathrm{E}\right)$ for various elements, which are important for modeling scattering near absorption edges. Figure 1 illustrates the energy-dependent variations in $f\prime \left(\mathrm{E}\right)$ and $f″\left(\mathrm{E}\right)$ around Er’s L-edges (L_III, L_II, L_I) from 6 keV to 10 keV, showing abrupt shifts: $f\prime \left(\mathrm{E}\right)$ becomes more negative, and $f″\left(\mathrm{E}\right)$ more positive. These sharp transitions produce anomalous scattering effects that enhance Er’s contribution while reducing interference from other elements.

2.2. Energy-Dependent Scattering and the Linear Relationship ${\left(\Sigma I\right)}^{1/2}$ Versus $f\prime \left(E\right)$

A fundamental aspect of ASAXS analysis is understanding how the scattering intensity varies as a function of X-ray energy, particularly near the absorption edges of the elements in question. This variation is driven by the real part of the anomalous scattering factor, $f\prime \left(\mathrm{E}\right)$, which has a pronounced impact near the absorption edge, whereas the imaginary part, $f″\left(\mathrm{E}\right)$, contributes minimally in this region. In the case of Er³⁺-doped materials, this energy dependence allows for the selective isolation of the scattering contributions from the Er³⁺ ions and an understanding of how they are distributed—whether they are dispersed uniformly in the amorphous matrix or incorporated into nanocrystals.

To quantify this, we express the total scattering intensity $\mathrm{I}(q, E)$ as a function of $f\prime \left(\mathrm{E}\right)$, which is directly related to the scattering contributions from Er³⁺. By integrating the scattering intensities over a range of q-values, we obtain the total integrated intensity $\mathsf{\Sigma }\mathrm{I}$, which can be written as:

$$\mathsf{\Sigma }\mathrm{I}=\int I\left(E,q\right)dq ~ K{(\mathrm{A}f\prime \left(E)+\mathrm{B}\right)}^2$$

(5)

where K is a constant, A represents the contribution from Er³⁺ ions, and B accounts for the scattering from the matrix. Since the scattering from Er³⁺ depends on where it is located (whether within nanocrystals or dispersed in the amorphous matrix), the terms A and B will vary accordingly.

To simplify this, we take the square root of $\mathsf{\Sigma }\mathrm{I}$, which gives:

$${\left(\mathsf{\Sigma }\mathrm{I}\right)}^{1/2}=\sqrt{K}(\mathrm{A}f\prime \left(E)+\mathrm{B}\right)$$

(6)

This results in a linear relationship [19]:

$${\left(\mathsf{\Sigma }\mathrm{I}\right)}^{1/2}=\mathsf{\alpha }f\prime +\mathsf{\beta }$$

(7)

where $\alpha =\sqrt{K}\mathrm{A}$ and $\beta =\sqrt{K}\mathrm{B}$.

The term α reflects the scattering contribution from Er³⁺, with higher values of α indicating that Er³⁺ is more concentrated in nanocrystals, and lower values suggesting that Er³⁺ is more uniformly dispersed within the amorphous matrix. The intercept β corresponds to the matrix’s baseline scattering, independent of Er³⁺’s presence.

The ratio β/α is particularly useful, as it indicates the relative amounts of Er³⁺ in nanocrystals versus the amorphous matrix. A higher β/α ratio suggests that Er³⁺ is more evenly distributed within the matrix, whereas a lower ratio indicates a stronger scattering contribution from Er³⁺, typically associated with its concentration in nanocrystals. Thus, the linear relationship described by Equation (7) enables the assessment of the Er³⁺ distribution.

2.3. Guinier Analysis and Radius of Gyration

In our Er³⁺-doped samples, we use the Guinier approximation in SAXS to estimate the size of Er³⁺-containing clusters. This approach yields information about the overall size of scattering entities, helping to distinguish between phases with different structural characteristics, such as nanocrystalline and amorphous regions. The analysis is focused on the low-q region, where qR_g ≪ 1, which is particularly sensitive to the overall size of the scattering entities.

The Guinier plot (log $I\left(q\right) \mathrm{v}\mathrm{s}.$q²) enables us to determine the radius of gyration R_g of Er³⁺-containing regions, allowing us to estimate the size of these clusters. The Guinier equation, assuming an isotropic, approximately spherical distribution of scattering centers, is given by:

$$I\left(q\right)=I(0)exp\left(-{\displaystyle \frac{R_g^2{q}^2}{3}}\right)$$

(8)

where $I\left(q\right)$ is the scattering intensity at a given scattering vector q; $I\left(0\right)$ represents the extrapolated scattering intensity at zero angle (forward scattering); and $q={\displaystyle \frac{4\pi \mathrm{s}\mathrm{i}\mathrm{n}\left(\theta \right)}{\lambda }}$ with θ as the scattering angle and λ as the wavelength of the incident radiation.

In this equation, the radius of gyration R_g serves as an indicator of particle size, describing the distribution of the electron density within each scattering entity. This approximation holds for particles which are large compared to atomic scales but small enough to avoid inter-particle interference effects. Here, R_g effectively represents the average electron density distance from the particle’s center of mass.

From the linear region of the Guinier plot, we extract R_g by fitting the slope of log I(q) versus q², providing a quantitative measure of the size of Er³⁺-containing clusters. For spherical particles, the linearity observed in the Guinier plot is typically narrow [25], indicating that the scattering entities exhibit a uniform size distribution, consistent with the idealized model of spherical inhomogeneities. When Er³⁺ ions aggregate into larger regions within the amorphous matrix, an increase in R_g reflects the formation of Er³⁺-rich regions, though these may not form fully organized nanocrystals. In contrast, if thermal treatment leads to the formation of Er³⁺ nanocrystals, they will exhibit a characteristic R_g value, indicating a defined size and more regular distribution. Conversely, if Er³⁺ ions remain well dispersed in the amorphous phase, a smaller R_g value will suggest minimal clustering.

2.4. Synergistic Role of ASAXS and Guinier Analysis for Erbium Distribution

When combined, SAXS and ASAXS provide a comprehensive view of Er³⁺ clustering in these thin films. ASAXS isolates the energy-dependent contribution of Er³⁺ to the scattering intensity, focusing on Er³⁺-rich regions. Meanwhile, Guinier analysis quantifies the size of these regions. Together, they provide a comprehensive understanding of the distribution of Er³⁺ in GCs, revealing how different thermal treatments affect Er³⁺ clustering at the nanoscale.

3. Materials and Methods

Thin films were deposited on Si substrates within the SiO₂–TiO₂–ErO_1.5 and SiO₂–TiO₂–PO_2.5–ErO_1.5 systems using the sol–gel method, as described in [1]. The films were synthesized with target molar compositions, where SiO₂ and TiO₂ ratios were precisely controlled, and dopant levels were nominally set as follows:

A: 80SiO₂–20TiO₂ with 2 mol% ErO_1.5;

B: 80SiO₂–20TiO₂ with 10 mol% PO_2.5 and 2 mol% ErO_1.5;

C: 98SiO₂–2TiO₂ with 10 mol% PO_2.5 and 2 mol% ErO_1.5;

D: 98SiO₂–2TiO₂ with 2 mol% ErO_1.5.

The films, which were approximately 500 nm thick, underwent thermal treatments at 900 °C and 1000 °C for 30 and 60 min, respectively. For clarity, the samples are labeled based on treatment conditions (e.g., A1 for 900 °C/30 min, A2 for 1000 °C/60 min, etc.). These treatments produced transparent glass-ceramic films by precipitating nanocrystals without affecting their transparency.

3.1. SAXS and ASAXS Measurements

Measurements were conducted at the LURE facility (Orsay, Paris, France), now upgraded to the SWING beamline at the SOLEIL Synchrotron (Saint-Aubin, France), using synchrotron radiation at 1.85 GeV and a beam current of approximately 300 mA. Both SAXS and ASAXS measurements were performed on the same beamline. The primary distinction between the two techniques lies in the energy tuning used for ASAXS, which targets specific absorption edges for element-specific analysis, while SAXS uses a broader energy range. The D22 beamline spectrometer, equipped with a double-crystal monochromator (Ge(1,1,1) crystals), selected monochromatic radiation in the 5–15 keV range. For ASAXS, measurements were focused on energies from 8000 eV to 8347 eV, spanning 10 eV to 357 eV below the L_III absorption edge, enabling element-specific analysis. The experimental setup used a near-grazing incidence angle (0.3° ± 0.01°) and an energy resolution of 2 eV, ensuring precision in the measurements. The data acquisition setup was designed to ensure accurate measurements, supported by an adjustable aperture and guard slits to optimize the beam dimensions (H × V = 0.5 × 0.2 to 3 × 0.4 mm²) and minimize parasitic scattering [26].

The beam intensity was measured using Kapton foil-based monitors coupled with NaI scintillators, positioned both before and after the sample along the beam path. This setup ensured the accurate normalization of scattering intensities and compensated for variations in sample thickness and transmission. Calibration of the scattering vector (q) axis was achieved using crystalline samples with sharp Bragg peaks, while absolute intensity normalization utilized water as a reference, leveraging its known differential scattering cross-section of 1.65 × 10⁻² cm⁻¹ [26].

The experiments were conducted at room temperature, with the samples mounted in holders designed for solid materials. These holders ensured stable positioning and minimized mechanical vibrations during measurements. The vacuum chamber, equipped with a movable beamstop and a large output window, reduced background scattering and provided flexibility in detector configurations. Data collection utilized a linear position-sensitive detector capable of covering a q-range from 5 × 10⁻³ A˚⁻¹ to 0.4 A˚⁻¹, enabling efficient measurements without frequent adjustments [26]. More details about the standard protocols and advanced instrumentation that facilitated high-quality SAXS and ASAXS measurements at LURE-D22 can be found in [26].

Table 1. Diffusion factor $f\prime \left(\mathrm{E}\right)$ for each energy of the incident X-ray beam in the ASAXS measurements. λ is the wavelength associated with this energy, and ΔE is the energy variation relative to the L_III absorption edge of erbium (8357 eV) [19].

Energy (eV)	ΔE (eV)	λ (Å)	$\mathit{f}\mathbf{\prime }\left(\mathbf{E}\right)$
8000	357	1.5500	−9.584
8157	200	1.5200	−10.822
8211	146	1.5100	−11.487
8265	92	1.5001	−12.474
8289	68	1.4957	−13.105
8313	44	1.4914	−14.015
8324	33	1.4894	−14.625
8336	21	1.4874	−15.539
8341	16	1.4864	−16.095
8347	10	1.4853	−17.059

provides the specific energies, their shifts relative to the absorption edge, corresponding X-ray wavelengths, and the real part of the scattering factor for each energy.

This energy range enabled the comprehensive mapping of Er³⁺ scattering behavior, specifically targeting the anomalous scattering effects that reveal Er³⁺ distribution within the nanostructures of the films. The chosen energy steps (ΔE) allowed for the precise tracking of scattering intensity variations as the energy approached the L_III edge, revealing Er³⁺-rich nanostructures not visible at energies far from the absorption edge. The grazing incidence geometry enhanced the surface sensitivity and minimized the Si substrate contribution to less than 1% of the total signal.

3.2. Data Processing and Analysis

The real-time acquisition software applied automated corrections to the raw ASAXS data, accounting for detector response, absorption, and refraction effects [27]. The substrate signal, contributing less than 1% of the total, was excluded from these corrections. Scattered intensity I(q) was recorded as a function of the scattering vector q, and Guinier plots (log(I) vs. q²) were generated for each energy point. From these plots, the Guinier radius R_g was determined, providing an estimate of the average nanocrystal size, assuming spherical particles.

The integrated intensity (ΣI)^1/2 was plotted against the anomalous scattering factor $f\prime \left(\mathrm{E}\right)$ at each energy, following Equation (7). This linear relationship helped isolate Er³⁺’s contribution to the scattering intensity, revealing its distribution within the nanostructures—whether localized in nanocrystals or uniformly dispersed within the matrix.

To validate these results, complementary structural and morphological analyses were performed using grazing-incidence X-ray diffraction (GIXRD), X-ray photoelectron spectroscopy (XPS), and transmission electron microscopy (TEM). TEM micrographs, captured in bright-field mode using a Hitachi H-800 microscope (Hitachi, Tokyo, Japan) operating at 150 kV, allowed for a detailed examination of the sample morphology and nanocrystal distribution, revealing the structural characteristics of the samples. To analyze the diffraction pattern, the ODPIN online diffraction pattern indexing tool was utilized (https://www.odpin.com (accessed on 19 January 2025)). The crystal structure under investigation was modeled assuming a cubic system with the following unit cell parameters: a = 7.155 Å, b = 7.155 Å, c = 7.155 Å, and angles α = β = γ = 60° (https://legacy.materialsproject.org/materials/mp-5889 (accessed on 19 January 2025)). These parameters correspond to a cubic crystal system. The diffraction data were input into the ODPIN tool, which assisted in indexing the diffraction pattern and determining the corresponding crystallographic information based on the provided unit cell parameters.

GIXRD patterns of the films after heat treatment were recorded using a Siemens D-5000 diffractometer (Siemens, Munich, Germany) with CuKα radiation at a grazing incidence angle of 2°. The 2θ range was covered from 21° to 45° with a step size of 0.04°. The choice of the windows, at 21–37° and 25–45°, was deliberate. The first window captures the key diffraction peaks corresponding to a mix of the rutile phase (110) and ETO phase diffraction planes (311), (222), and (400). The second window isolates peaks corresponding only to the ETO phase diffraction planes (311), (222), (400), and the additional (331).

XPS measurements were conducted on an ESCALAB 250 spectrometer (Thermo Fisher Scientific K.K., Tokyo, Japan) with dual aluminum–magnesium anodes and monochromatic Al Kα radiation (hν = 1486.6 eV). Initially, a survey was performed exclusively on sample A1 to obtain an overview of its chemical composition. This survey was carried out with an energy resolution of 1 eV. Subsequently, detailed spectra were collected for the Er 5p peaks (5p_3/2 and 5p_1/2) in all selected samples using a higher energy resolution of 0.1 eV. All peaks were calibrated with respect to the C 1s peak, which was fixed at 284.4 eV. The procedure followed was as described in [28].

4. Results and Discussion

4.1. Crystallization Behavior

The samples analyzed in this study—labeled A, B, C, and D—consist of various compositions of SiO₂, TiO₂, PO_2.5, and ErO_1.5, selected for their established crystallization behavior and known phase formations during thermal treatments, as highlighted in prior research [1].

Table 2. Crystallization phases observed in samples A, B, C, and D.

Sample Composition	Crystallization Behavior		References
	900 °C	1000 °C
A: 80SiO2–20TiO2–2 mol% ErO1.5	am	R + ETO	[1], This work
B: 80SiO2–20TiO2–10 mol% PO2.5 and 2 mol% ErO1.5	am	R + EPO	[1]
C: 98SiO2–2TiO2–10 mol% PO2.5 and 2 mol% ErO1.5	EPO	EPO	[1]
D: 98SiO2–2TiO2 with 2 mol% ErO1.5	ETO	ETO	This work

am—amorphous; R—rutile (TiO₂); ETO—erbium titanate (Er₂Ti₂O₇); and EPO—erbium phosphate (ErPO₄).

provides a comparative overview of the crystallization phases observed in these samples following heat treatment. Sample A (80SiO₂–20TiO₂–2 mol% ErO_1.5) remains amorphous at 900 °C (A1) but undergoes a phase transformation to a mixture of rutile (R) and erbium titanate (ETO) at 1000 °C (A2). Sample B (80SiO₂–20TiO₂–10 mol% PO_2.5 and 2 mol% ErO_1.5) retains an amorphous state at 900 °C (B1) and forms anatase (A) and erbium phosphate (EPO) at 1000 °C (B2). The presence of phosphorus likely facilitates the crystallization of the anatase and rutile phases, which may coexist.

In contrast, sample C (98SiO₂–2TiO₂–10 mol% PO_2.5 and 2 mol% ErO_1.5), with a lower TiO₂ content, exhibits the crystallization of erbium phosphate (EPO), even at 900 °C (C1), and EPO becomes the dominant phase at 1000 °C (C2). Finaly, sample D (98SiO₂–2TiO₂ with 2 mol% ErO_1.5) forms only erbium titanate (ETO) crystallites at both 900 °C and 1000 °C.

The X-ray diffraction (XRD) patterns of the samples are presented in Figure 2. Panel (a) shows the XRD data for sample A at 900 °C (A1) and 1000 °C (A2), highlighting the phase transitions observed in this composition. Panel (b) displays the XRD patterns for sample D at 900 °C (D1) and 1000 °C (D2), confirming the crystallization of erbium titanate (ETO) at both temperatures.

The XRD patterns in panel (a) of Figure 2 show a peak at approximately 27.5°, which corresponds to the (110) plane of rutile TiO₂ (ICDD card no. 00-021-1276), confirming the presence of the rutile phase, a feature commonly observed in annealed sol–gel-derived ST glassy films [1]. Additional peaks were identified as belonging to Er₂Ti₂O₇ (Erbium Titanate, ETO), rather than Er₂O₃ (Erbium Oxide) or metallic Ti (Titanium). Specifically, the peaks at 2θ values of 29.6°, 30.8°, 35.9°, and 39° correspond to the crystallographic planes (311), (222), (400), and (331) of Er₂Ti₂O₇, as documented in ICDD card no. 01-073-1647, and are visible in both panels (a) and (b). As the annealing temperature increases, there is no significant shift in the position of the diffraction peaks, but the peak intensities increase notably, especially between 900 °C and 1000 °C. This increase in intensity suggests enhanced crystallinity and greater phase stability at higher temperatures. The sharp intensity of the (222) peak at 2θ = 29.6° specifically indicates a well-ordered matrix structure. This observation aligns with the findings from [9], which show that higher temperatures enhance atomic mobility, facilitating ion rearrangement into a more stable crystalline structure, as evidenced by sharper diffraction peaks. While the (222) peak shows a marked intensity increase, other weaker peaks exhibit a more modest rise with thermal treatment. This supports the conclusion that Er₂Ti₂O₇ is the dominant crystalline phase, rather than isolated erbium oxide or titanium [29,30,31]. The absence of peaks corresponding to SiO₂ and TiO₂ indicates that these components remain amorphous, consistent with the lack of anatase or rutile phases at either temperature, as shown in Table 2. This further supports the conclusion that in the D1 and D2 samples, Er₂Ti₂O₇ is the primary crystalline phase formed.

During the doping process, Er³⁺ ions likely bond with Ti in the presence of ambient oxygen, promoting the formation of erbium titanate (ETO). When Er and Ti are present in balanced proportions (e.g., sample D, 2% Er:2% Ti), only ETO crystallites form. This occurs because equal proportions of Er³⁺ and Ti⁴⁺ ions provide the stoichiometric balance and coordination environment required for ETO formation, in line with Pauling’s rules for ionic crystal stability [32]. Specifically, the balance between Er³⁺ and Ti⁴⁺ ions ensures proper coordination and charge neutrality, minimizing structural disorder. In this balanced system, each Er³⁺ ion is adequately coordinated by Ti⁴⁺ ions, stabilizing the crystalline lattice and following Pauling’s Coordination Principle (Rule 1), which describes how cations and anions arrange themselves for stable coordination.

In compositions where Ti > Er (e.g., sample A, 2% Er:20% Ti), a mixture of ETO and rutile (TiO₂) phases is observed. The excess Ti⁴⁺ ions favor the formation of rutile, while some Er³⁺ ions remain dispersed within the amorphous matrix. This dispersion can be attributed to their role as network modifiers, disrupting the glass structure by breaking bridging oxygens (BOs) and forming non-bridging oxygens (NBOs) [33]. Although Er³⁺ ions form strong bonds with oxygen [34], these bonds alone are insufficient to counteract the structural dominance of TiO₂, leading to the coexistence of rutile and dispersed Er³⁺ ions. The formation of rutile over ETO in Ti-rich compositions aligns with Pauling’s Electrostatic Valency Principle (Rule 2), where the excess Ti⁴⁺ ions dominate the lattice, creating a charge imbalance that destabilizes Er³⁺ coordination. These observations are consistent with previous studies [35], which emphasize the interplay between Ti⁴⁺ content and the stabilization of Er³⁺ crystalline structures.

The nanosized features of the investigated samples are clearly highlighted in the TEM micrographs presented in Figure 3, which provide bright-field images revealing the dispersion of nanoparticles within the samples. Panel (a) shows the microstructure of sample A annealed at 1000 °C (A2), while panel (b) displays sample D annealed at 1000 °C (D2).

The bright-field TEM images exhibit a strong contrast, with dark nanocrystals visible against the lighter amorphous matrix, confirming the presence of distinct nanocrystalline structures. Both panels reveal the predominance of spherical nanocrystals, which are relatively uniform in size, sub-100 nm, and exhibit some degree of clustering. In addition to the spherical particles, a smaller population of rod-shaped nanocrystals is evident, appearing elongated and less frequent. These rods are also sub-100 nm in size, suggesting a variation in growth mechanism or crystal orientation. These observations indicate that the annealing process at 1000 °C facilitated the nucleation and stabilization of spherical nanocrystals as the dominant phase, while the rod-shaped structures represent a minority phase, likely influenced by specific local conditions or compositional variations. The observed distribution and morphology are consistent with the processing conditions and annealing temperatures applied to the samples.

4.2. Nanostructure Characterization via SAXS

The SAXS measurements provided data on the size and distribution of nanocrystals in the sol–gel-derived thin films. Guinier plots were used to calculate the Guinier radius, which estimates the average size of the nanocrystals (Figure 4). The Guinier radii values for the various compositions, as summarized in

Table 3. Results of the linear fits and Guinier radii for various compositions. Adapted from [19].

Sample	A1	A2	B1	B2	C1	C2	D1	D2
β/α	230.9	56.9	73.6	86.1	57.5	56.5	51.5	65.9
$R_{\beta /\alpha }^2$	0.723	0.980	0.980	0.980	0.980	0.980	0.980	0.980
Rg (nm)	16.9	17.23	18.02	18.03	18.93	17.79	18.50	17.31

R² represents the square of the correlation coefficient r.

, show clear trends across the different compositions and thermal treatments.

The Guinier radii for all samples, extracted from the SAXS measurements (Figure 4), ranged from 16.9 nm to 18.9 nm, indicating the formation of nanocrystals after thermal treatment. Samples A1 and A2 exhibited the smallest R_g values, with A1 showing the smallest overall R_g (16.90 nm). Samples B1 and B2 showed intermediate R_g values, which were slightly larger for the 1000 °C annealing condition (B2, 18.03 nm). Sample C (C1 and C2) displayed the largest R_g values, with C2 reaching the highest value (18.93 nm), suggesting that the addition of phosphorus facilitated more effective nanocrystal growth. Sample D (D1 and D2) also exhibited intermediate R_g values, with D1 being slightly larger (18.50 nm) than D2 (17.31 nm). These results highlight the impact of annealing temperature and composition on nanocrystal growth. The increasing R_g values observed for the samples annealed at 1000 °C, as compared to those treated at 900 °C, suggest enhanced crystallization at higher temperatures. The larger nanocrystal sizes observed in sample C may indicate that phosphorus addition promotes more effective nanocrystal growth. These trends are consistent with previous studies [36], which confirm the formation of nanocrystalline phases and further support the findings presented here.

4.3. Interpretation of the β/α Ratio

The ASAXS measurements were conducted near the L_III absorption edge of Er (8357 eV), which allowed for the isolation of Er³⁺’s contribution to nanocrystal formation. Since the K-edges of other elements in the matrix, such as phosphorus (P) at around 2153 eV, silicon (Si) at approximately 1840 eV, and titanium (Ti) near 4966 eV [24], were significantly far from the Er L_III edge, their contributions did not interfere with the analysis of Er, ensuring that the observed scattering data exclusively reflected the behavior of Er³⁺ within the nanostructures.

The parameters α, β, and the ratio β/α were extracted as outlined in Equation (7), providing information about the distribution of Er³⁺ within the nanocrystals and its interactions with other matrix components. The β/α ratio directly reflects how Er³⁺ is localized in the nanostructures, serving as a diagnostic for its concentration in the nanocrystals.

For sample A1, the higher β/α ratio suggests that Er³⁺ ions are more evenly dispersed throughout the amorphous matrix rather than concentrated within the nanocrystals, consistent with XRD results indicating an amorphous phase for this sample. This diffuse distribution of Er³⁺ lowers the electron density contrast between Er³⁺ and the surrounding matrix, resulting in a weaker and more gradual increase in scattering intensity, as shown in Figure 5. Consequently, the X-ray scattering effect is less pronounced, as the lack of concentrated Er³⁺ clusters reduces the sharpness of the scattering contrast. In contrast, sample A2 exhibits a lower β/α ratio, indicating a higher concentration of Er³⁺ within the nanocrystals. This concentrated presence of Er³⁺ within nanocrystals increases the electron density contrast, leading to a sharper scattering contrast and stronger intensity near the absorption edge. These observations align with the XRD results, which reveal a more substantial presence of Er³⁺ in the crystalline phases for sample A2.

The β/α ratios for sample pairs C (C1 and C2) and D (D1 and D2) remain nearly constant, as supported by the data in Figure 6 and Figure 7, with values comparable to those of sample A2. This stability, regardless of thermal variation, suggests a consistent concentration of Er³⁺ within the nanocrystals. The lower β/α ratios indicate the efficient incorporation of Er³⁺ into specific nanocrystalline phases, leading to a denser distribution of Er³⁺ within the crystalline structure rather than remaining in the amorphous matrix. This behavior likely points to a saturation effect, where the Er³⁺ concentration in the nanocrystals reaches a threshold and remains stable despite further thermal treatment.

The XRD results support this by confirming the presence of Er³⁺-containing crystalline phases in these samples. For the samples in series C, erbium phosphate (EPO) is observed, while erbium titanate (ETO) forms in samples from series D. The phase distinction suggests that Er³⁺ incorporation is composition-dependent, with phosphorus inhibiting the formation of ETO and favoring EPO in the samples with a 2% Er:2% Ti ratio. This selective phase formation is consistent with the stable β/α ratios observed in series C, where phosphorus promotes a more uniform and concentrated Er³⁺ distribution within the EPO phase.

In the B samples (Figure 8), the β/α ratio remains relatively stable between B1 (900 °C) and B2 (1000 °C), with a slight increase observed in B2. This suggests a mild tendency for Er³⁺ to disperse in the matrix at higher temperatures, although the effect is less pronounced than in sample A1. The intermediate β/α ratios in B1 and B2—lower than A1’s but higher than those of A2 and pairs C and D—indicate that Er³⁺ tends to remain in the matrix. However, the interaction between phosphorus and the high Ti content (20% Ti with 2% Er) in B2 seems to favor the crystallization of TiO₂ phases, such as rutile, which competes with the incorporation of Er³⁺ into erbium phosphate (EPO) nanocrystals, thus influencing the distribution of Er³⁺. Interestingly, this competition is not fully reflected in the β/α ratio of 86 observed in B2, which is slightly higher than that of the other samples containing erbium crystallites.

Additionally, discrepancies arise between the XRD and ASAXS results, particularly for sample B1, which remains amorphous. Despite this, the β/α ratio of 73 for B1 is not comparable to that of sample A1, which underwent similar conditions. While XRD detects the crystallization of rutile in A2 and B1, ASAXS does not, as rutile lacks Er³⁺. This discrepancy can be attributed to the different detection principles of SAXS and ASAXS. SAXS depends primarily on the size and shape of nanostructures rather than their atomic structure, enabling it to detect features such as the formation of Er³⁺-free phases like rutile in B1, beyond just the ETO and EPO phases.

Notably, SAXS reveals a radius of gyration (R_g) of 16.9 nm for A1 and 18.02 nm for B1, even though both samples lack Er³⁺-rich precipitates or other crystalline phases. Given the sol–gel synthesis of these samples, these R_g values may correspond to residual porosity within the amorphous network rather than to crystalline precipitates. This suggests that SAXS is sensitive to early structural features, such as porosity, that may not be detectable by ASAXS, which is limited to detecting features containing Er³⁺.

This interpretation aligns with the findings in the literature; for example, reference [9] describes ETO films that retain sponge-like porosity even after high-temperature treatment, with pores around 10 nm persisting in thin film areas. This residual porosity, typical of sol–gel-derived films [8,37,38], could account for the SAXS-detected features in A1 and B1, underscoring SAXS’s ability to reveal subtle structural features such as pores. Further supporting this interpretation, a study in [25] examined activated carbon samples using SAXS. Similarly to our observations, SAXS detected residual porosity within the matrix of the carbon samples. The study reported spherical pores with sizes around 6 nm, suggesting that SAXS can reveal porosity in materials even in the absence of crystalline phases. This reinforces the idea that SAXS is sensitive to the structural features of the matrix, such as porosity, which are not necessarily captured by ASAXS, which focuses on crystalline phases.

4.4. X-Ray Photoelectron Spectroscopy (XPS) Analysis

X-ray photoelectron spectroscopy (XPS) is a crucial technique for probing the chemical state and electronic structure of Er in oxide materials, particularly for analyzing its 5p orbitals. These orbitals split into 5p_3/2 and 5p_1/2 due to spin–orbit coupling, resulting in two distinct binding energy peaks [39]. These peaks are sensitive to the Er’s chemical environment, which can vary in complex oxide matrices.

Erbium (Er) naturally prefers the +3 oxidation state due to its electron configuration. Like other rare earth elements, it has three electrons outside a stable, filled inner shell. By losing these three electrons, erbium attains a stable electronic configuration, making Er³⁺ the most chemically stable form. This is particularly true in oxygen-rich environments, such as oxides and silicates, which are commonly found in sol–gel glasses. The highly electronegative oxygen atoms in the glass matrix stabilize Er³⁺ because oxygen’s strong affinity for electrons makes further reductions unlikely. Additionally, the oxide network “locks” Er into the +3 oxidation state by forming stable Er–O bonds. To explore how changes in crystallinity and composition impact the electronic structure of Er³⁺, XPS was performed on four representative samples: A1, A2, D1, and D2. These samples were chosen to span a range of structural environments, from fully amorphous matrices to those containing the crystalline phases of TiO₂ (rutile) and erbium titanate (Er₂Ti₂O₇, ETO). Sample A1 was completely amorphous, A2 contained a mixture of rutile and ETO crystallites, D1 showed partial crystallization with remnants of ETO crystallites, and D2 contained well-developed nanocrystalline ETO within a glass matrix. This selection allowed for a comparative analysis of how varying crystallinity and phase composition influence the electronic environment and oxidation states of Er³⁺.

In general, the Er 5p_3/2 and 5p_1/2 peaks typically appear around 24.7 eV and 31.4 eV, respectively, as documented in the X-ray Data Booklet by Lawrence Berkeley National Laboratory [40]. Studies on Er-doped silicon have reported similar but slightly higher binding energies, with the 5p_3/2 peak at approximately 26 eV and the 5p_1/2 peak at 32 eV, due to variations in the local environment and matrix interactions [41]. These values provide a reference range for comparing Er-containing materials of varying crystallinity and coordination environments, as seen in our samples.

In panel (a) of Figure 9, a comprehensive survey scan of sample A1 was conducted, uncovering the key elements present, including the distinctive Er 5p peak. Building upon this initial finding, a more detailed XPS analysis was then performed, focusing specifically on the Er 5p peak (panel (b)) to delve deeper into the electronic properties of this element within the samples. The XPS spectra of the Er 5p_3/2 and 5p_1/2 peaks are displayed for samples A1, A2, D1, and D2, each showcasing the unique structural characteristics that significantly influence the local environment surrounding Er³⁺. Changes in the binding energies can reflect shifts in the chemical environment, crystallinity, oxidation state, and local bonding structure of Er in the different samples. For sample A1, the 5p_3/2 and 5p_1/2 peaks are broad, indicating the disordered environment of the amorphous matrix where Er atoms are randomly coordinated with oxygen. This broadening is indicative of the variability in local bonding, leading to a wider range of binding energies around the reference values. Additionally, the peaks are shifted to lower binding energies compared to other samples, reflecting the reduced electron density and weaker Er–O interactions in the disordered structure of A1. The broad peaks and lower binding energy suggest a less stable electronic environment around Er, and a weaker impact of spin–orbit coupling, as the disordered matrix likely diminishes the splitting of the 5p peaks. In contrast, sample A2, which contains both rutile and ETO crystallites, shows sharper 5p peaks, suggesting a more ordered local environment around the Er atoms. The binding energies observed in A2 are slightly higher than those in A1, indicating that the presence of crystalline phases, especially ETO, stabilizes the local electronic environment around Er³⁺, as the ordered lattice structure stabilizes the local electronic density around it, reducing the range of binding energy variations. The sharper peaks and higher binding energies in A2 suggest enhanced spin–orbit coupling, with better defined 5p_3/2 and 5p_1/2 peaks. Sample D1, which exhibits partial crystallization with remnants of ETO crystallites, shows 5p peaks that are partially resolved, lying between the broad profile of A1 and the sharper profile of A2. The binding energies in D1 are higher than in A1 but show slight variations due to the presence of both amorphous and crystalline regions. This partial crystallization introduces greater order into the structure, though some disordered regions still contribute to broader peaks. The higher binding energy in D1 compared to A1 and A2 may reflect a more stable oxidation state of Er³⁺, as the local environment around the ions becomes more crystalline.

Finally, sample D2, which contains well-developed nanocrystalline ETO within a glass matrix, exhibits the sharpest and most defined peaks of all samples, with the highest binding energies. The nanocrystalline environment around Er³⁺ ions provides a highly ordered structure, leading to consistent bonding with oxygen and, consequently, narrow XPS peaks due to the stable Er–O interactions.

This trend in binding energies (A1 < A2 < D1 < D2) reflects the progression from amorphous to increasingly crystalline matrices, accompanied by a rise in local structural order and stability in the oxidation state around Er³⁺ ions.

4.5. Corroboration with ASAXS and SAXS Analysis

The ASAXS and SAXS analyses corroborate the XPS findings by providing structural evidence for the varying degrees of order and crystallinity in each sample. The gradual increase in local structural order from A1 (fully amorphous) to D2 (nanocrystalline) is consistently reflected in both the scattering data and the XPS spectra, with each technique reinforcing the conclusion that crystallinity stabilizes the Er³⁺ electronic environment. This structural stability leads to narrower, higher binding energy peaks in the XPS spectra, underscoring the relationship between crystallinity, Er–O interaction strength, and electronic stability in sol–gel-derived glasses. This combined analysis provides valuable insights into the structural and chemical evolution of Er³⁺ within these materials as crystallinity increases.

5. Conclusions

This study provided a detailed analysis of erbium-doped silica-based glass-ceramic thin films synthesized via the sol–gel method, emphasizing the formation, dispersion, and stabilization of erbium-containing nanocrystals under varying thermal treatments. Advanced characterization techniques, including anomalous small-angle X-ray scattering (ASAXS), small-angle X-ray scattering (SAXS), X-ray photoelectron spectroscopy (XPS), and transmission electron microscopy (TEM), were employed to investigate the structural and chemical properties of the films.

The ASAXS results revealed distinct differences in the distribution of Er³⁺ ions across compositions and thermal conditions. The β/α ratios highlighted a higher concentration of Er³⁺ ions within nanocrystals for samples treated at higher temperatures and with specific dopant compositions, confirming their migration into crystalline phases such as erbium phosphate (EPO) and erbium titanate (ETO). The SAXS and Guinier analyses quantified the nanocrystal sizes, with the radii of gyration ranging from 16.9 nm to 18.9 nm, demonstrating the influence of phosphorus addition and annealing temperature on nanocrystal growth. TEM further validated these findings, showcasing the morphology and dispersion of spherical and rod-shaped nanocrystals within the amorphous matrix.

XPS provided detailed insights into the chemical environment and stabilization of Er³⁺ ions, confirming their incorporation into crystalline structures and their interaction with the surrounding matrix. The results demonstrated that thermal treatments and compositional adjustments play a crucial role in controlling the nanoscale organization and behavior of these systems.

This work advances the understanding of rare earth-doped glass-ceramics, offering a deeper understanding of the size, distribution, and interaction of erbium-containing nanocrystals within the amorphous matrix. The findings emphasize the importance of optimizing the composition and thermal treatment to achieve desirable nanostructural and chemical properties. These results lay the groundwork for the development of tailored glass-ceramic materials for advanced technological applications.