Novel Er³⁺/Nd³⁺-doped borofluoride glass materials for NIR optical fiber applications with suitable thermal and mechanical properties

Abstract

To advance the performance of broadband optical fiber communication systems, a novel borofluoride-based glass system with the composition 60B₂O₃-20Pb₃O₄-10MgF₂-10LiF (BPML) was synthesized and accordingly investigated. The base glass was doped with 1 mol% of Er³⁺, Nd³⁺, or their combination to produce BPML: RE³⁺ glass series. Glass structural analysis via X-ray diffraction (XRD), bulk density measurements, and Fourier transform infrared (FTIR) spectroscopy confirmed the amorphous nature of the glasses, indicating increased network compactness upon rare-earth doping, particularly with Er³⁺. The thermal properties were investigated through differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA), revealing enhanced thermal stability across all synthesized doped glass samples. Furthermore, the theoretical estimation of the mechanical characterization, including predicted elastic moduli and hardness using the Makishima-Mackenzie model, showed rigidity improvements with the incorporation of RE³⁺. Optical absorption spectra recorded over the 400–1600 nm range reveal characteristic transitions of Er³⁺ and Nd³⁺, with co-doped samples displaying broader absorption bands, indicative of potential for wideband signal amplification. The photoluminescence studies under 773 nm excitation have demonstrated near-infrared (NIR) emission centered at 1.55 μm (Hz). The co-doped synthesized samples have exhibited enhanced emission intensity, indicating efficient energy transfer. The present work results show that the synthesized samples, doped with Er³⁺, Nd³⁺, or their combination, exhibit an optimal balance of thermal stability, mechanical robustness, and broadband NIR emission. Evidently, the synthesized glass samples achieve a high-quality factor of (), underscoring their potential for high-performance broadband applications. These properties position the proposed samples as a promising material for the fabrication of NIR optical fibers for communication benefits.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1038/s41598-026-67626-3.

Introduction

The rapid advancement of optical fiber technologies has significantly increased the demand for novel materials with tailored thermal, mechanical, and optical properties^1–2. Near-infrared (NIR) emission in the (1.4–1.7) µm spectral region is of critical importance for advanced photonic technologies because of its favorable optical properties and compatibility with modern optoelectronic systems^1–2. This spectral region includes the S, C, and L bands, which are foundational to fiber-optic communication, particularly around the 1.5 μm window. Ideal host materials for these applications should exhibit high mechanical rigidity, excellent thermal stability, besides the broad NIR emission characteristics^3–5. Recently rare earth ions (RE³⁺), particularly erbium (Er³⁺) and neodymium (Nd³⁺), have emerged as crucial activators due to their well-defined transitions, long lifetime metastable states, and high quantum efficiency^6–8. Specifically, the Er³⁺ ion is indispensable in modern optical communication systems, primarily due to its strong emission in the (1.5–1.6) µm range, corresponding to its ⁴I_13/2→⁴I_15/2 recorded transition^7–8. Despite of the fact that Nd³⁺ is traditionally known for its intense emission at ~ 1.06 μm, its incorporation in Er³⁺/Nd³⁺ co-doped systems can significantly enhance the 1.55 μm emission through sensitization and energy-transfer processes. In such systems, the characteristic emission near 1.55 μm originates primarily from the ⁴I_13/2→⁴I_15/2 transition of Er³⁺, while Nd³⁺ ions act mainly as sensitizers that improve excitation efficiency and energy migration under suitable excitation conditions^4–6. Borate-based glass samples represent a dependent versatile host matrix due to their low melting temperatures, high thermal and chemical stability, superior rare-earth ion solubility, and beside their high optical clarity^9–10. The ability of B³⁺ ions to adopt both trigonal (BO₃) and tetrahedral (BO₄) coordination states facilitates the formation of a highly adaptable and compact network, which can be tailored structurally to accommodate dopant ions^11–12. The incorporation of lead oxide (PbO) into borate glass significantly enhances its nonlinear optical properties by increasing the polarizability and promoting structural modifications via BO₃↔BO₄ interconversion. This transformation, coupled with the inherently high refractive index and optical clarity of lead borate glasses, renders them highly suitable for applications in lasers, optical switches, and nonlinear optical devices¹³. To overcome the high phonon energy typically associated with oxide glasses, which can quench rare-earth emission, halide ions such as fluoride () are introduced to form oxyfluoride glasses^14–15. Additives like MgF₂ and LiF contribute to improve structural stability and the ionic conductivity while maintaining a low phonon energy environment, which is advantageous for efficient luminescence. Fluoride ions () reduce the glass phonon energy by partially modifying the local oxygen coordination, while Mg²⁺ and Li⁺ promote network stabilization and structural rearrangement. These modifications create a more favorable local environment for Er³⁺ and Nd³⁺ ions by improving their dispersion and reduced non-radiative energy losses, thereby enhancing near-infrared luminescence and energy transfer efficiency^16–17. Consequently, hybrid oxyfluoride glasses offer a balanced combination of thermal robustness, mechanical integrity, and enhanced photoluminescence performance^14,18,19. Accordingly, rare earth-doped borate-based oxyfluoride glasses have attracted considerable attention as promising materials for advanced photonic and near-infrared optical applications.

With the increasing demand for advanced photonic devices, near-infrared (NIR) emitting glass materials have attracted considerable attention due to their applications in optical amplifiers, laser, and broadband communication systems. Previous studies have demonstrated that rare-earth-doped glasses, particularly Er³⁺ and Nd³⁺ containing systems, can provide efficient NIR emission through characteristic transitions. Elsaghier et al. (2022)²⁰ reported Er³⁺-doped alkaline earth titanium borate glasses with broad emission around 1530–1565 nm, showing potential for optical amplifiers; however, the study was mainly limited to Er³⁺ emission without investigating the synergistic effect of multiple rare-earth ions. Farouk et al. (2013)²¹ investigated Er³⁺-containing bismuth borate glasses and focused primarily on structural modification and optical absorption behavior, while detailed NIR emission optimization was not explored. Nd³⁺-doped MgO-Al₂O₃-SiO₂ transparent glass developed by Han et al. (2019)²² exhibited strong emissions at 898, 1057, and 1330 nm, making them promising for solid-state laser applications; however, their emission was mainly restricted to Nd³⁺ transitions and required a glass structure, which may complicate fabrication processes. Furthermore, Ding et al. (2023)²³ achieved ultra-broadband NIR emission (1300–1630 nm) in Nd³⁺/ Tm³⁺ /Er³⁺ tri-doped tellurite glasses through energy transfer mechanisms, demonstrating excellent potential for broadband optical amplifiers. However, the requirements of multiple rare-earth dopants and relatively complex optimization of dopant concentrations may limit practical applications. Similarly, Er³⁺/Nd³⁺ reinforced lead-borate glasses and Nd³⁺-dopant gadolinium calcium silica borate glasses have shown strong NIR emission at 1059 nm and improved laser characteristics, but their emission regions are mainly concentrated at specific laser wavelengths rather than providing broad emission coverage in telecommunication window as reported by Kesavulu et al. (2016)²⁴. Despite these significant advances, several challenges remain, including achieving broad and intense NIR emission around the low-loss optical communication region (1550 nm), improving emission bandwidth through efficient rare-earth energy transfer, and simultaneously maintaining good thermal, mechanical, and structural stability of the glass host. Many reported systems focus either on single rare-earth emission, laser-specific wavelengths, or require complex multi-component doping strategies, while fewer studies have explored a simple borate-based glass system capable of combining strong Er³⁺/Nd³⁺ emission, broadband characteristics and enhanced physical stability. Therefore, developing a stable borate-based Er³⁺/Nd³⁺ co-doped borate-based glass system with efficient energy transfer, broadened NIR emission, and high optical quality factor remains an important research direction for next-generation broadband photonic devices, optical amplifiers, NIR filters, and photonic communication applications.

This work concentrates on the design and synthesis of a novel borate-based oxyfluoride glass system with the composition, 60B₂O₃-20Pb₃O₄-10MgF₂-10LiF, strategically doped with Er³⁺ and Nd³⁺ ions, both individually and in combination with varying concentrations (BPML: RE³⁺ glass series). The primary objective of this study to investigate the influence of Er³⁺, Nd³⁺, and their co-doping Er³⁺→Nd³⁺ on the structural, thermal, mechanical, and near-infrared optical properties of the developed glass system, with particular emphasis on broadband NIR emission and rare earth energy transfer mechanism. The novelty of this work lies in the development of a borate-rich hybrid oxyfluoride glass network that integrates the high rare earth ion solubility of borate glasses with the reduced phonon energy imparted by fluoride components, while simultaneously improving thermal and mechanical stability. The study further aims to establish structure-property relationships that clarify the role of rare earth incorporation in governing the physical and optical behavior of the glass network. The outcomes of this work are expected to provide valuable design guidelines for development of advanced rare earth doped borate-based oxyfluoride glasses for NIR photonic applications, while serving as a foundation for future investigations toward practical optical fiber implementation.

Experimental procedures

Glass synthesis

The novel borate-based oxyfluoride glass system, 60B₂O₃-20Pb₃O₄-10MgF₂-10LiF, was synthesized as a base sample. Afterwards, it was doped with RE³⁺, particularly Er³⁺, Nd³⁺ or both, as illustrated in Table 1. The system was synthesized using the melt-quenching technique. High-purity raw materials of H₃BO₃ (99.99%), Pb₃O₄ (99.99%), MgF₂ (99.98%), LiF (99.98%), Er₂O₃ (99.99%), and Nd₂O₃ (99.99%) were procured from Sigma-Aldrich. The precursors were weighed precisely according to the target molar ratios to prepare a total batch weight of 25 g for each glass composition and thoroughly mixed in a porcelain mortar for one hour to ensure compositional uniformity. To compensate for the possible volatilization of fluoride species during melting, the weighed amounts of LiF and MgF₂ were each increased by 10 wt% relative to their calculated baches weights. This processing excess was introduced to minimize fluoride loss and maintain the final glass composition as close as possible to the nominal composition. The batches were introduced into an alumina crucible and placed directly in furnace maintained at 1200 °C, where they are melted for one hour under ambient air atmosphere. The 1200 °C was selected based on previous studies on lead borate/ oxyfluoride glasses containing rare earth and preliminary melting trials, which confirmed complete melting, good melt homogeneity, and the absence of visible undissolved particles. During the melting, the molten glass was manually stirred several times to improve compositional homogeneity and facilitate complete dissolution of the raw materials. As Pb₃O₄ is thermally unstable above ~ 500 °C, it decomposes to PbO and O₂ during melting. The resulting PbO participates directly in glass formation, contributing to network modification and increasing polarizability. Therefore, Pb₃O₄ effectively functions as a PbO precursor under the provided synthesis conditions. The compositions listed in Table 1 correspond to the nominal batch compositions. Pb₃O₄ was used as the starting lead precursor, and its decomposition into PbO with oxygen evolution is an intrinsic part of the melting process. Since the study is based on the nominal batch compositions, no additional correction associated with oxygen evolution was introduced during the batch calculations. The viscous molten glass was rapidly cast into a preheated stainless-steel mold and immediately transferred to a furnace maintained at 340 °C for 30 min to relieve thermal stresses. The annealing temperature and duration were optimized experimentally using polarized light microscopy to monitor residual thermal stresses. Several annealing conditions with different temperatures and holding times were evaluated. Initial treatments at lower temperatures did not adequately relieve the internal stresses, even when the annealing time was extended. Consequently, the annealing temperature was progressively increased, and the stress state was examined after each trial. Based on these observations, an annealing treatment at 340 °C for 30 min was selected as the optimum condition, ensuring efficient stress relaxation while preserving the amorphous nature of the glass. Figure 1 illustrates the synthesis process schematically, as shown in real-time photos. All prepared glass samples were visually inspected to evaluate their macroscopic quality prior to characterization. As shown in Fig. 1, the obtained glasses were transparent and exhibited good visual homogeneity without observable nature cracks, bubbles, or macroscopic evidence of phase separation.

Table 1.

The composition of the synthesized BPML and BPML: RE³⁺ glass samples.

Glass sample code	Elemental composition
	B2O3	Pb3O4	MgF2	LiF	Er2O3	Nd2O3
BPML	60	20	10	10	0	0
BPML: Er	60	20	10	10	1	0
BPML: Nd	60	20	10	10	0	1
BPML: Er/Nd-1	60	20	10	10	0.5	0.5
BPML: Er/Nd-2	60	20	10	10	0.25	0.75
BPML: Er/Nd-3	60	20	10	10	0.75	0.25

Fig. 1.

Schematic representation of the BPML and BPML: RE³⁺ preparation process (real-time photos).

Structural examinations

X-ray diffraction (XRD), density measurements, density-related parameters, and Fourier transform infrared (FTIR) spectra were all performed and analyzed to study the structural modifications resulting from Er³⁺ and Nd³⁺ doping process. XRD patterns were recorded by a Philips X-ray diffractometer with a wavelength of 1.54056 Å from a Cu-Kα filter. For XRD analysis, representative glass samples were crushed and finely ground into homogeneous powders using an agate mortar to eliminate any influence of sample geometry and ensure reliable diffraction measurements. The bulk density () of the fabricated BPML: RE³⁺ glass samples was rigorously assessed according to the ASTM C373 standard. Density measurements were carried out on randomly selected bulk glass pieces without imposing a specific geometry or dimensions, since the Archimedes method depends only on the sample mass in air and the immersion liquid. Key structural parameters, including molar volume (), mean boron-boron separation (), oxygen packing density (OPD), and packing density (), were calculated via Eqs. 1–4 to evaluate the effects of Er³⁺, Nd³⁺, and co-doping (Er³⁺/Nd³⁺) on the glass network^25–26.

1

where, is molecular mass of the glass sample.

2

where, is the volume of one mol of B³⁺ ions within the considered glass sample, and is the Avogadro’s number.

3

where, refers to the number of oxygen atoms per chemical formula.

4

where, is the mole fraction of the sample constituents, and is the packing factor.

The values of and were calculated using the following relations.

5

6

where, is the molar fraction of , is the ionic radius of the cation and the ionic radius of the anion of the oxide element .

It should be noted that the packing density calculations were carried out using Shannon ionic radii based on the assumption of fixed ionic coordination and spherical ions. Nevertheless, in borate-based glass systems, the effective ionic radii, particularly for B³⁺ species, are strongly influenced by the local coordination environment associated with BO₃ and BO₄ structural units. Consequently, the calculated packing-related parameters should be interpreted as representative indicators of the relative structural compactness and network evolution among the investigated glass compositions.

Furthermore, the FTIR spectra were recorded in the 400–4000 cm^− 1 range, with spectral resolution ± 2, using a JASCO FTIR6200. For FTIR measurements, the glass samples were finely ground into powders to ensure homogeneous mixing with KBr. A mass of 3.00 mg for all synthesized samples was homogeneously mixed with 300 mg of dry KBr and compressed under a compression load of 13 tons to produce transparent pellets suitable for analysis. The broad absorption bands in the FTIR spectra were deconvoluted using the Gaussian fitting. The minimum number of component bands required to reproduce the experimental spectra was employed while preserving physically meaningful band positions consistent with the characteristic vibrational modes reported for multicomponent borate glasses. During the fitting procedure, peak positions, widths, and intensities were allowed to vary within physically reasonable limits, and no artificial peaks were introduced solely to improve the mathematical fit. The quality of the fitting was evaluated using the coefficient of determination (), reduced chi-squared (), and inspection of the residuals between the experimental and fitted spectra. The proportions of tetrahedral BO₄ (N₄) and trigonal BO₃ (N₃) structural units were calculated according to Eqs. 7 and 8^27–28.

7

8

where, A₁area (BO₄) and A₂area (BO₃) denotes the integrated areas of the deconvoluted BO₄ and BO₃ peaks, respectively. It should be note that the calculated and values are considered semi-quantitative because the absorption coefficients and oscillator strengths of BO₃ and BO₄ structural units are not identical. Therefore, direct comparison of the integrated FTIR band areas may introduce systematic deviations in the absolute values of the calculated fractions. Nevertheless, the adopted approach remains useful for evaluating the relative structural variations and comparative trends among the investigated glass compositions.

The force constant, which quantifies the bond rigidity was calculated using Eq. 9 to accurately examine the observed vibrational shifts^29–30.

9

Here, stands for vibration frequency,  c represents speed of light, and denotes reduced mass (kg). the calculation of was performed using the relationship outlined in Eq. 10.

10

Here, is the mass of oxygen and is the mass of boron atom bounded to the oxygen atom.

Thermal properties examination

The thermal behavior of the synthesized BPML: RE³⁺ glass samples was assessed using the differential scanning calorimetry (DSC) and the thermogravimetric analysis (TGA). For thermal characterization, representative glass samples were crushed into fine powders prior to DSC and TGA measurements to ensure good thermal contact and unform heat transfer throughout the analysis. The DSC was mainly employed to determine critical thermal transition parameters, including the glass transition temperature (), onset of crystallization (), peak crystallization temperature (), and melting temperature (). These parameters provide essential insights into the thermal stability, phase transformation behavior, and glass processing. Complementarily, TGA was utilized to evaluate the glass samples’ thermal stability and compositional integrity. DSC and TGA measurements were performed simultaneously using an SDT Q600 thermal analyzer (TA Instruments, USA) under a flowing nitrogen atmosphere (15 psi), ensuring an inert environment to prevent oxidation. The heating rate was maintained at 10 °C/min from ambient temperature to 1000 °C.

Elastic properties calculation

The theoretical elastic properties, Young’s modulus (), bulk modulus (), shear modulus (), and longitudinal modulus (), in addition to Poisson’s ratio () and hardness () were evaluated using the semi-empirical Makishima-Mackenzie model, which relates macroscopic elastic behavior to dissociation energies and packing densities of the constituent oxide units. Within this framework, the elastic response of the glass network, when expressed in terms of Young’s modulus (), is given by

9

where, is the total dissociation energy per unit volume of the glass sample and thus calculated by:

10

where,  n is the number of constituent oxides, is the bond energy per volume of the oxide, and is its molar fraction.

Hence, the bulk modulus ( K), shear modulus (G), longitudinal modulus (L), Poisson’s ratio (), and hardness (H) are determined using the following relations^31–32:

11

12

13

14

15

Optical properties examination

For optical absorption and photoluminescence measurements, bulk glass specimens were polished on both faces using successive SiC abrasive papers until smooth, scratch-free optical surfaces were obtained. The polishing process was continued until the sample thickness reach approximately 1.2–1.3 mm. Since the optical measurements depend primarily on the optical path length, the lateral dimensions of the specimens were not fixed and were selected according to the available glass pieces. The optical characteristics of the synthesized BPML: RE³⁺ glass samples were examined across the visible-NIR spectral region. Absorption spectra were recorded using a JASCO V-670 UV-Vis-NIR spectrophotometer, operating with a spectra resolution of 2 nm, ensuring high measurement accuracy and reproducibility.

The quantitative analysis of the crystal-field transitions and local environment asymmetry was evaluated via the Judd-Ofelt (J-O) theory. The experimental oscillator strengths () for the identified absorption bands were determined from the integrated absorption coefficients using the relation^11,15:

16

where and  e are the electron mass and charge,  c is the velocity of light, is the vacuum permittivity,  N is the ion concentration (), and is the absorption coefficient at frequency  v. According to the J-O model, the theoretical oscillator strengths () for electric-dipole transitions from the ground state () to an excited state () are expressed as^11,15:

17

where  h is the Plank’s constant,  n is the refractive index of the glass matrix, represents the local field correction factor, and are the reduced matrix elements for transitions. The phenomenological J-O intensity parameters () were extracted by minimizing the root-mean-square (RMS) deviation between and using a standard least-squares fitting procedure.

Photoluminescence

Photoluminescence measurements of the synthesized BPML: RE³⁺ glass samples were performed using an Edinburgh Instruments FLS1000 fluorescence spectrometer. Steady-state spectra were recorded using a continuous-wave xenon arc lamp as the excitation source, where the excitation wavelength was set at 773 nm using a monochromator.

The quantitative parameters governing the energy transfer were evaluated using the Förster-Dexter model. The spectral overlap integral (J) was calculated via^33–34:

18

where is the normalized donor emission spectrum and is the acceptor molar absorption coefficient. The critical transfer distance () was subsequently estimated using the relation^33–34:

19

where  h is the Plank’s constant,  c is the velocity of light,  n is the refractive index, and is the donor quantum efficiency.

Results and discussion

Structural properties

X-ray diffraction spectra

The broad, diffuse halos observed in the XRD spectra of the synthesized BPML: RE³⁺ glass series, as shown in Fig. 2, are features of an amorphous structure, confirming the lack of long-term crystalline order. Notably, no appreciable changes in the diffraction patterns were detected with varying concentrations of Er₂O₃ and Nd₂O₃, indicating stability of the amorphous structure.

Fig. 2.

The recorded XRD spectra of the BPML and BPML: RE³⁺ glass series.

Bulk density measurements

The structural parameters of the BPML: RE³⁺ glass series, characterized by bulk density (), molar volume (), average boron-boron separation (), oxygen packing density (), and packing density () are listed in Table 2. The results indicate that doping the base sample (BPML) with Er³⁺, Nd³⁺, or their combination leads to a noticeable increase in density compared to the undoped sample. This behavior reflects the combined influence of the relatively high atomic masses of the incorporated rare earth ions and the structural evaluation of the glass network induced by rare earth incorporation. Among all compositions, BPML: Er glass exhibits the highest density, which is consistent with the larger atomic mass of Er³⁺ together with smaller ionic radius and strong field strength, promoting a more efficient atomic arrangement within the glass matrix. The stronger field strength of Er³⁺ originates from its smaller ionic radius relative to Nd³⁺. According to Shannon’s effective ionic radii for six-fold coordination, the ionic radii of Er³⁺ and Nd³⁺ are approximately 0.89 and 0.98 Å, respectively. Consequently, Er³⁺ possesses a higher charge-to-radius ratio (field strength), resulting in stronger electrostatic interactions with surrounding oxygen ions, enhanced bond strength, and more efficient atomic packing within the borate glass network^35–38. These characteristics promote an efficient atomic arrangement and tighter network connectivity, resulting in increased structural compactness relative to both the Nd³⁺ doped and base samples. The corresponding decrease in molar volume , together with the decrease in the average boron-boron separation () and the increase in both oxygen packing density ( OPD) and packing density (), collectively indicates a progressive enhancement of the network packing efficiency following the Er³⁺ and Nd³⁺ incorporation. The BPML: Er exhibits the lowest molar volume, as observed in Table 2, reinforcing the role of Er³⁺ doping in enhancing network compactness. This behavior can be structurally rationalized by the high field strength of rare earth cations, which act as efficient topological constraints. The relatively small Er³⁺ ions occupy the interstitial voids within the borate network, acting as crosslinking centers that contract the free volume and maximize the packing efficiency of the glass matrix. Similarly, the slight decrease in the average boron-boron separation () for doped glass samples, further confirms the formation of a denser local network. This reduction arises from the increased conversion of trigonal BO₃ units into tetrahedral BO₄ units^39–40, as evidenced by the higher N₄ (BO₄ fraction) and lower N₃ (BO₃ fraction) values listed in Table 2. The incorporation of highly polarizing RE³⁺ ions induces a local charge compensation mechanism, forcing the borate matrix to shift its equilibrium toward the more stable and tightly bound BO₄ configuration. The formation of BO₄ tetrahedra introduces additional bridging oxygens, strengthening the network connectivity and reducing free volume. The N₄ parameter represents the fraction of four-coordinated boron atoms (BO₄), which contribute to a more polymerized and rigid glass network. In contrast, N₃ corresponds to three-coordinated boron atoms (BO₃) and less cross-linked structures. Therefore, an increase in N₄ at the expense of N₃ signifies enhanced structural polymerization and compactness. These values were derived from the deconvoluted FTIR spectra, discussed in detail below. Between the two dopants, Er³⁺ exerts a slightly stronger influence on structural densification, as indicated by its lower value and higher OPD. This effect is attributed to Er³⁺’s higher polarizing power, which allows it to distort and compact the glass network more effectively than Nd³⁺. The progressive increase in both and further corroborates the enhanced packing efficiency of the borate network following Er³⁺ and Nd³⁺ incorporation, in excellent agreement with the reduced molar volume, shorter average separation, and the increased BO₄ fraction derived from FTIR analysis.

Table 2.

The structural parameters of the synthesized glass samples: BPML and BPML: RE³⁺.

Glass sample code	(g/cm3)	(cm3/mol)	(Å)	OPD	PD
BPML	3.418 ± 0.002	54.920	4.849	47.342	0.560	0.485	0.515
BPML: Er	3.497 ± 0.007	54.773	4.844	48.016	0.567	0.489	0.511
BPML: Nd	3.484 ± 0.009	54.845	4.847	47.953	0.566	0.532	0.468
BPML: Er/Nd-1	3.491 ± 0.004	54.801	4.845	47.992	0.566	0.532	0.468
BPML: Er/Nd-2	3.488 ± 0.004	54.815	4.846	47.979	0.566	0.512	0.483
BPML: Er/Nd-3	3.494 ± 0.001	54.787	4.845	48.004	0.567	0.543	0.457

FTIR spectroscopy

The FTIR is performed for all the synthesized samples and the produced spectra are shown in Fig. 3a versus wavelength. The FTIR spectra of the synthesized BPML: RE³⁺ glass series reveal the characteristic vibrational features of borate-based networks. Three main absorption regions can be identified, where:

Fig. 3.

a) The FTIR spectra of the BPML and BPML: RE³⁺ glass series and b) the deconvolution of BPML glass as an example.

• Wavelength 650–780 cm^-1, is associated with the bending vibrations of BO₃ units and linkages.

• Wavelength 790–1150 cm^-1, corresponds to stretching in BO₄ tetrahedra and mixed BO₃/BO₄ structural units.

• Wavelength 1160–1590 cm^-1, is attributed to asymmetric stretching modes of BO₃ units, especially those containing non-bridging oxygens (NBOs).

Additionally, a distinct band in the (400–600) cm^-1 region arises from vibrations involving metal-oxygen bonds (, , and ) within the glass matrix.

To gain deeper insight into the glass structure, Gaussian deconvolution was used to resolve the broad absorption bands and to identify the overlapping vibrational contributions associated with the different structural units present in the investigated glasses. Figure 3b presents the deconvoluted spectrum for the (BPML) sample as a representative example. The deconvolution process has resolved the broad envelope into multiple overlapping bands centered at 455, 501, 552, 618, 675, 718, 773, 827, 877, 951, 1024, 1104, 1205, 1268, 1343, 1392, and 1455 cm^− 1. Table 3 illustrates the assignments of the multiple overlapping bands. Although the deconvolution resolved the broad FTIR envelope into multiple overlapping sub-bands, these bands should not be interpreted as independent structural entities. Rather, they represent overlapping vibrational contributions from the various borate structural units commonly reported in multicomponent borate glasses. The Gaussian fitting was performed using literature-based band assignments as initial constraints, while allowing only physically reasonable variations in peak position, width, and intensity to achieve the best fit. The excellent agreement between the experimental and fitted spectra, together with the very low residual errors and high goodness-of-fit values, supports the reliability and physical consistency of the deconvolution rather than a purely mathematical optimization. The deconvolution process demonstrated exceptional mathematical accuracy, yielding high coefficients of determination () and extremely low reduced chi-squared () values for all studied samples (BPML: BPML: Er: BPML: Nd: BPML: Er/Nd-1: BPML: Er/Nd-2: BPML: Er/Nd-3: ). Furthermore, the confidence intervals for peak positions were found to remain within ± 2–5 cm^− 1, indicating strong positional reliability of the resolved bands and supporting the robustness of the fitting model. The bands at 455, 501, and 552 cm^− 1 are attributed to the modifier cations, including bond vibrations^41–43, ^{42, 44,45}, and ^{16, 46,47} interaction within the glass network. The absorption band observed at 618 cm^− 1 arises from stretching^42,48, overlapping with bending vibration⁴². The absorption band at 675 cm^− 1 corresponds to the bending modes of BO₃ units^16,43,48, whereas the 718 cm^− 1 band is generally associated with linkages between borate structural units^49–50. The 773 cm^− 1 band is commonly assigned to bending vibrations involving linkages between and structural units, which is consistent with the coexistence of trigonal () and tetrahedral () borate units within the glass network⁴⁹. Similarly, the bands at 827 and 877 cm^− 1 are commonly attributed to BO₄ stretching and diborate vibrations within the BO₄ framework, respectively^25,50. The band at 951 cm^− 1 is generally assigned to stretching in BO₄ units associated with di-borate groups⁵⁰, the strong band at 1024 cm^− 1 represents stretching in BO₄ tetrahedra belonging to tri-, tetra-, and penta-borate configurations^51–52. The band at 1104 cm^− 1 is also consistent with the presence of penta-borate units, indicating the structural diversity of tetrahedral borate units⁵¹. The absorption band at 1205 cm^− 1 is assigned to stretching in trigonal BO₃ units arranged in boroxol ring structures^49–50, and the 1268 cm^− 1 corresponds to the stretching vibrations of isolated triangular BO₃ units^52–53. The peak at 1343 cm^− 1 is attributed to the stretching vibrations of BO₃ triangles containing non-bridging oxygens (NBOs) in meta-, pyro, and ortho-borate environments⁵⁴, while the band at 1392 cm^− 1 is likewise associated with similar BO₃ environments⁴⁹. The band at 1455 cm^− 1 correspond to asymmetric stretching of BO₃ units with NBOs^55–56 and asymmetric stretching relaxation of trigonal BO₃ units⁵⁷. Table 4 illustrates the shifts in FTIR bands following the Er³⁺, Nd³⁺, and Er³⁺/Nd³⁺ incorporation. The systematic band shifts and the appearance of additional absorption features indicate that Er³⁺ and Nd³⁺ doping influences the local bonding environments within the borate glass network. Although FTIR spectroscopy provides valuable information on vibrational changes, the following structural interpretations are based on the characteristic vibrational assignments reported in the literature and should be regarded as indirect evidence of structural evolution. In the low frequency region (400–600 cm^− 1), new bands at 412-421 and 482–493 cm^− 1 appear, corresponding to and coordination bonds. Their systematic appearance and persistence throughout the rare earth containing glass series, together with the concurrent evolution of the neighboring low-frequency vibrational envelope, identify these features as characteristic vibrational contributions of coordination environments within the borate glass network, in agreement with previous reports^58–60. To provide additional insight into the origin of these low-frequency vibrations, the characteristic and stretching frequencies were estimated using the classical diatomic harmonic oscillator approximation. This treatment serves as a first-order description of the local metal-oxygen interaction and offers a convenient framework for comparing characteristic vibrational ranges. Owing to the intrinsically disordered nature of the borate glass network, where vibrational modes arise from coupled network dynamics rather than isolated chemical bonds, the calculated frequencies are intended as qualitative reference values for local coordination environments rather than exact representations of the experimentally observed collective vibrations. The stretching frequencies of and bonds, calculated using the diatomic approximation, were found to fall within the 350–452 cm^− 1 range (assuming force constants of 200–300 N/m and calculated reduced masses of ≈ 14.61 amu for and 14.40 amu for ), which lies within the spectral region where the experimentally resolved absorption bands are observed and therefore provides qualitative support for their assignment to rare earth oxygen coordination. Concurrent red shifts of and bending modes were observed, as listed in Table 4, indicating bond weakening and elongation due to substitution of Pb²⁺ by larger rare earth cations. This is quantitatively evidenced by a decrease in the calculated force constants ( k), confirming the reduction in the bond’s restorative force upon the introduction of RE³⁺ ions. In the mid-frequency region (650–900 cm^− 1), several structural rearrangements are observed, associated with BO₃/BO₄ vibrations and linkages. The disappearance of the 675 cm^− 1 bands together the downward shift of the 718 cm^− 1 bands (to 696–700 cm^− 1) may indicate modifications in the relative populations of BO₃ and BO₄ units and slight variations in bond angles. The shift from 718 to 700 cm^− 1 corresponds to a reduction in the force constant from 208 N/m to 196 N/m, which is compatible with a relaxation of the borate bridging network. The enhanced or blue-shifted 773 cm^− 1 band (up to 798 cm^− 1) suggests stronger coupling between BO₃ and BO₄ species, while the shifts of the 827 cm^− 1 and 877 cm^− 1 bands to 802 cm^− 1 and 849 cm^− 1, respectively, suggests changes in the local BO₄ environments and possible interactions between Er³⁺/Nd³⁺ ions and neighboring borate structural units. These transformations signify partial network depolymerization and creation of new cross-links between BO₃ and BO₄ units. In the high frequency region (900-1200) cm^− 1, corresponding to the asymmetric stretching vibrations of BO₄ tetrahedra, the bands at 951 cm^− 1 and 1024 cm^− 1 exhibit a blue shift in BPML: Er and BPML: Er/Nd-3. These shifts are consistent with strengthened bonds resulting from the relatively high ionic field strength of Er³⁺, which promotes stronger local interactions and enhances the rigidity of the surrounding borate environment. The observed bule shift is consistent with an increase in the effective local bond stiffness and stronger interactions within the structural units. Within the amorphous borate glass network, these changes are interpreted in terms of relative variations in local bonding environments inferred from the vibrational spectra. Conversely, BPML: Nd, BPML: Er/Nd-1, and BPML: Er/Nd-2 display red shifts, suggesting weakened bonds. The weakening is most pronounced in BPML: Nd, where the 951 cm^− 1 band shifts to 929 cm^− 1 and the 1024 cm^− 1 band disappears entirely. The calculated force constant for the 951 cm^− 1 band decreases from 365 to 348 N/m, providing a semi-quantitative indication of reduced bond stiffness that is in agreement with experimentally observed spectral red shift and the inferred increase in average bond strength. The appearance of additional bands within the 880–906 cm^− 1 and 1062-1076 cm^− 1 ranges may also indicate changes in the local coordination environment around the RE³⁺ ions and borate structural units. Although RE³⁺ are generally regarded as network modifiers in borate glasses, their relatively high ionic field strength can influence the local coordination environment through strong interactions these interactions are expected to modify the connectivity and distribution of neighboring borate structural units, leading to local structural rearrangements. In the upper frequency region (1200-1600) cm^− 1, dominated by stretching in BO₃ units and NBO-related modes, the progressive blue shift of 1268 cm^− 1 band to 1309 cm^− 1 and the splitting of the 1343–1392 cm^− 1, as listed in Table 4, suggest modifications in the local bonding environment and possible changes in the distribution of non-bridging oxygens. This indicates enhanced covalency and reduced NBO concentration through bond formation. Applying the harmonic oscillator model, the force constant was found to change from approximately 694 to 692 N/m, reflecting only a slight variation in bond stiffness within the structural units. Such estimated force constants provide a useful comparative descriptor for monitoring relative changes in local bonding environments across the investigated glass composition, while the observed FTIR bands remain collective vibrational responses of the disordered borate network. The blue shift of asymmetric BO₃ stretching bands 1455 cm^− 1 may reflect bond strengthening and polarization under the influence of highly polarizing rare-earth ions.

Table 3.

Oscillation modes of the considered BPML glass series and the corresponding FTIR positions.

Peak position (cm− 1)	Oscillation mode
455	Bending vibrations of the bond, overlapping with bond vibrations, and also vibrational modes associated with Mg2+ ions
501,552	Vibrational modes associated with modifier cations, particularly Li+ ions.
618	Vibrational modes associated with bonds, overlapping with bending vibration
675	BO3 bending vibrations.
718	bending vibrations.
773	bending vibrations.
827	Stretching of tetrahedral BO4 groups.
877	Stretching vibrations of tetrahedral borate groups such as diborate in BO3.
951	The stretching vibrations in tetrahedral BO4 in di-borate.
1024	Stretching vibrations of in BO4 units from tri- tetra- and penta-borate groups.
1104	Stretching vibrations of tetrahedral borate groups such as penta-borate groups.
1205	stretching vibration of trigonal BO3 units in boroxol rings.
1268	Ascribed to the stretching vibration of triangular BO3 units.
1343	Stretching vibrations of BO3 triangles with non-bridging oxygens (NBOs) (stretching of in meta-borate, pyro-borate, and ortho-borate groups of BO3).
1392	stretching vibrations of BO3 units in meta-, pyro- and ortho-borate groups.
1455	Asymmetric stretching vibration of BO3 triangles containing non-bridging oxygens (NBOs).

Table 4.

The shifts in FTIR bands of the (BPML) network with the introducing Er, Nd, and Er / Nd.

New band	BPML	BPML: Er	BPML: Nd	BPML: Er/Nd-1	BPML: Er/Nd-2	BPML: Er/Nd-3
	-	412	404	403	415	421
	455	455	466	451	456	-
New band	-	482	-	481	476	493
	501	513	513	519	523	534
	552	533	522	-	-	-
	618	605	593	612	604	597
	675	-	-	-	-	-
	718	696	700	698	697	699
	773	-	-	798	794	-
	827	802	825	823	833	816
	877	866	866	849	845	876
New band	-	906	896	880	882	889
	951	959	929	947	942	961
	1024	1029	-	1024	1024	1026
New band	-	1069	1062	1076	-	1065
	1104	1119	1119	1116	1103	1108
	1205	1230	1210	1217	1229	1206
	1268	1285	1296	1309	1312	1309
	1343	1347	1353	1356	1364	1348
	1392	-	-	1402	1390	-
	1455	1473	1481	1478	1484	1470

Thermal properties

The thermal performance of the BPML glass series, as revealed by DSC and TGA analyses Fig. 4, reflects the intricate structural modifications induced by RE-doping, as previously discussed. The DSC curve shown in Fig. 4a estimate the thermal parameters, glass transition temperature () and crystallization onset and peak temperatures (& and & ). The of the base glass (BPML) is observed at 405 °C, with °C, °C, °C, and °C, indicating a stable and well-connected borate network structure⁶¹. Upon doping with Er³⁺ (BPML: Er), the glass transition and crystallization temperatures were decreased^61–62, as listed in Table 5. Although density and FTIR results confirm a more compact local environment and an increased BO₄/BO₃ ratio, the depression must be interpreted through the thermodynamic evolution of the network. In accordance with the Adam-Gibbs model (), the decline in reflects an expanded configurational entropy (). This is attributed to the introduction of Er³⁺ ions, which diversify the local bonding manifold and create heterogeneous environments that facilitate cooperative rearrangements. Such structural complexity lowers the activation barrier for structural relaxation, facilitating segmental mobility through entropic gains that override the effects on increased physical packing^63–64. Crucially, this structural divergence under thermal excitation reveals a decoupling between physical compactness and thermal stability; while the higher concentration of BO₄ tetrahedra rigidifies the matrix at room temperature, the multi-component nature of the RE-modified network offers more degrees of freedom at high temperatures, hence lowering . The high value supports this, indicating that Er³⁺ strengthens the glass network against crystallization at elevated temperatures, consistent with its high field strength and strong bonding. In contrast, Nd³⁺ doping (BPML: Nd) exhibits slightly higher glass transition and crystallization temperatures compared to BPML: Er, as listed in Table 5. This trend aligns with the structural data, where Nd³⁺ induces less compactness due to its larger ionic radius and weaker field strength^21,65–66. The higher of BPML: Nd arises from its lower packing efficiency which, in this host, restricts the configurational degrees of freedom (), thereby requiring higher thermal energy to trigger the glass transition. Hence, while the BPML: Nd glass transitions at a slightly higher temperature, its network is less tightly connected and more open compared with BPML: Er^22,67. This lower packing density and structural openness create a loose framework that structurally resists short-range cooperative relaxation up to a slightly higher thermal threshold, although it possesses lower overall thermodynamic stability. Moreover, the co-doped samples show further reductions in . This is consistent with the structural evidence that mixed doping introduces a more complex structural rearrangement, further increasing the configurational entropy through the proliferation of diverse bond angles and lengths. The decrease in for BPML: Er/Nd-1 and BPML: Er/Nd-2 suggests that the coexistence of Er³⁺ (promoting compactness) and Nd³⁺ (enhancing flexibility) produces a more dynamically stable yet tightly packed structure. Among them, BPML: Er/Nd-2 exhibits the most favorable thermal profile, with moderate and the highest . This implies an optimal structural balance. In BPML: Er/Nd-3 where the disappearance of and reflects that excessive rare earth loading disrupts network uniformity. According to the classical nucleation consideration, the disappearance of these crystallization events may be associated with suppression of homogeneous nucleation and crystal growth kinetics due to increased structural disorder and restricted ionic diffusion within the highly modified glass network. In addition, the coexistence of multiple rare-earth environments at high dopant concentrations may promote local compositional heterogeneity or amorphous phase-separated regions, thereby preventing the formation of distinct secondary crystallization peaks. That leads to inhomogeneous regions and reduced thermal stability. The highly doped network becomes more disordered, hindering secondary crystallization and consistent with the broader FTIR features; thus, indicating structural distortion at high RE³⁺ concentrations. Such behavior is also consistent with the disappearance of well-defined crystallization pathways in highly heterogeneous glass systems, where nucleation becomes kinetically unfavorable. Figure 4b shows the TGA results across the temperature range up to ~ 990 °C. The results reveal distinct multistage mass change behavior, as shown in, providing complementary insight into thermal decomposition, volatilization, and structural rearrangement. For (BPML), the mass loss from 44 to 148 °C (99.7–99.2%) is likely corresponding to the evaporation of physically adsorbed water and residual hydroxyl groups. The broad thermal stability plateau from 149 to 528 °C (99.2–99.1%) indicates a thermally resilient network with minimal structural breakdown. Interestingly, the slight mass increases observed at 529–583 °C and a gain at 733–800 °C suggest recrystallization or oxidation effects, possibly associated with redox activity of Pb²⁺ or structural rearrangements involving BO₃/BO₄ interconversion. The final drop from 801 to 990 °C reflects partial network degeneration. A more continuous and pronounced mass loss (99.5–96.2%) in BPML: Er glass across the entire range, without clear plateaus. This behavior suggests a progressive breakdown of the glass network upon heating. In BPML: Nd, an early weight loss (43–143 °C, 99→93.7%), likely from less compact Nd³⁺-dominated structures allowing faster release of bound water or groups. Structurally, the less compact and more open network configuration identified in BPML: Nd facilitates the rapid diffusion and outgassing of volatile hydroxyl species at lower thermal ranges. The steady decline to 88.1% by 990 °C reflects ongoing network disruption due to weaker Nd³⁺-O interactions. Mixed doping, particularly in BPML: Er/Nd-2, yields complex TGA behavior, including regions of weight gain due to transient structural reorganization or oxidation, further suggesting an optimal balance between network flexibility and compactness. Notably, BPML: Er/Nd-3 exhibited a significant and continuous mass loss (from 99.3% to 85.0%), confirming that high dopant concentrations destabilize the network, resulting in reduced thermal resistance.

Fig. 4.

The measured thermal profile of the BPML and BPML: RE³⁺ glass series using the (a) DSC and (b) TGA.

Table 5.

Thermal parameters (°C) of the considered BPML and BPML: RE³⁺ glass series.

Glass sample code
BPML	408	451	469	495	512
BPML: Er	398	418	428	478	498
BPML: Nd	404	426	438	480	507
BPML: Er/Nd-1	392	413	427	473	494
BPML: Er/Nd-2	392	405	422	463	478
BPML: Er/Nd-3	380	418	436	ــ	ــ

Theoretical mechanical properties

From Table 6 it is evident that there are systematic increases in the predicted mechanical features of the sensitized borate-based glass system with the inclusion of Er³⁺, Nd³⁺, and Er³⁺/Nd³⁺. BPML: Er exhibited the highest predicted improvement among the investigated samples, with observed increases across all key mechanical parameters. These enhancements are directly correlated with the structural modifications identified via density, density related parameters, and FTIR analyses. Specially, the substantial increase in the predicted elastic moduli (Young’s bulk, and shear moduli) and Vickers hardness is fundamentally rooted in the higher dissociation energy od bonds ( ≈ 611 kJ/mol) compared to the host modifier bonds ( ≈ 378 kJ/mol). The integration of Er³⁺ and Nd³⁺ ions strengthens the total network energy of the glass structure. Furthermore, the enhanced BO₄/BO₃ ratio derived from the FTIR analysis indicates increased network connectivity, whereas the higher OPD and values signify more efficient atomic packing and structural densification. Therefore, the improved mechanical performance arises from the combined effects of network polymerization, bond strengthening, and enhanced packing efficiency. The substantial transformation of threefold-coordinated BO₃ units into highly crosslinked fourfold-coordinated BO₄ tetrahedra acts as a structural polymerization tool, creating a rigid three-dimensional network that effectively resists external shear stresses and mechanical indentation. These findings are consistent with previous reported by Abo-Mosallam et al.⁶⁸ and Ngaram et al.⁶⁹ on Er³⁺-doped borate glasses, where the incorporation of Er³⁺ increased the elastic moduli and hardness through stronger bonding, improving atomic packing, and enhanced network connectivity. While the impacts of Nd³⁺ doping (BPML: Nd) were slightly less pronounced than those of Er³⁺, notable improvements in the predicted mechanical performance are still observed. These are likely due to partial network reinforcement, although limited by the larger ionic radius and lower field strength of Nd³⁺, resulting in weaker bonding. For the co-doped glass samples (BPML: Er/Nd-1, BPML: Er/Nd-2, and BPML: Er/Nd-3), the predicted mechanical properties remained consistently high, indicating that the combined incorporation of Er³⁺ and Nd³⁺ effectively preserves the enhanced stiffness and predicted resistance to deformation achieved through rare earth modification of the glass network. A similar enhancement in the predicated elastic properties with Nd³⁺ incorporation has been reported by Abouhaswa et al.⁷⁰, although an opposite trend was observed by Singh et al.⁷¹, who attributed the reduction in elastic moduli to network depolymerization and increased non-bridging oxygen formation. This comparison suggests that the mechanical response of Nd³⁺ is strongly dependent on the host glass composition and the structural role of rare earth ions. Notably, Poisson’s ratio () remains nearly constant across all samples, varying only from 0.252 to 0.255. According to the theory of elastic properties of glasses proposed by Bridge and Higzay⁷², Poisson’s ratio is fundamentally dictated by the cross-link density and the spatial dimensionality of the glass network. To provide a deeper theoretical insight, this behavior can be rationalized using the Philips-Thorpe constraint counting model⁷³, which correlates the structural rigidity and mechanical constraints within the network connectivity. In the present borate glass system, the structural transition involves the conversion of threefold coordinated borate units (BO₃) into fourfold coordinated units (BO₄). Although the fraction of BO₄ units (N₄) increases slightly from 0.485 to 0.543 (corresponding to a minor shift in the N₄/N₃ ratio from 0.941 to 1.188), this structural modification is relatively subtle. Within the framework of the Philips-Thorpe model, such small change in the population of tetrahedral constraints does not trigger a fundamental topological phase transition or a major alteration in the overall cross-link density of the glass network. Consequently, the core spatial network dimensionality remains closely preserved, which is theoretically consistent with the highly stable values of . This preservation of spatial dimensionality underscores that the reinforcement of the glass network upon RE-incorporation occurs primarily through bond-stiffening. This correlation indicates that the glass samples exhibited higher predicted elastic moduli and hardness without substantially increasing their capacity to absorb strain before failure. In addition, rare earth incorporation modifies the local network environment through interactions, promoting a more compact glass structure with improved atomic packing efficiency. Consequently, the enhanced mechanical performance results from the combined effects of network strengthening, structural densification, and increased packing efficiency. Furthermore, the consistent increase in hardness that is observed in all doped samples attributed to the combined effects of bonding, increased formation, improved atomic packing efficiency, and the development of a denser and more interconnected glass network, all of which contribute to improved resistance to surface deformation.

Table 6.

The mechanical properties of the BPML and BPML: RE³⁺ glass samples.

Glass sample code	E (GPa)	K (GPa)	G (GPa)	L (GPa)		H (GPa)
BPML	45.915	30.846	18.338	55.297	0.252	3.033
BPML: Er	47.459	32.300	18.906	57.508	0.255	3.087
BPML: Nd	47.310	32.115	18.856	57.257	0.254	3.086
BPML: Er/Nd-1	47.391	32.216	18.884	57.394	0.255	3.086
BPML: Er/Nd-2	47.357	32.175	18.872	57.338	0.255	3.086
BPML: Er/Nd-3	47.425	32.258	18.895	57.451	0.255	3.087

Finally, the obtained values of the mechanical parameters should be interpreted primarily in a comparative rather than absolute manner due to the complex multicomponent nature of the present oxyfluoride glass system. Moreover, the Makishima-Mackenzie model does not explicitly account for local structural heterogeneity, mixed-cation interactions, or BO₄/BO₃ related network connectivity changes. Nevertheless, the calculated trends remain in good agreement with the structural modifications inferred from density and FTIR analyses, as well as with previously reported behavior for related rare-earth-containing borate glass systems^74–75.

Optical properties

Figure 5 illustrates the optical absorption spectra of the synthesized BPML: RE³⁺ glass series. No absorption bands were observed in the undoped BPML glass, confirming that all observed absorption features are present in the doped and co-doped glass samples originate from the electronic transitions of Er³⁺ and Nd³⁺ ions. For the BPML: Er, distinct absorption bands were recorded at 488, 520, 527, 654, 702, 801, 966, 1496, and 1518 nm. The transitions at 488, 801, and 966 nm correspond to excitation from the Er³⁺ ground state (⁴I_15/2) to the ⁴F_7/2, ⁴I_9/2, and ⁴I_11/2 excited states, respectively, while the paired bands at 520 & 527, 654 & 702, and 1469 & 1518 nm result from the crystal-field splitting of the ²H_11/2, ⁴F_9/2, and ⁴I_13/2 manifolds. The observed splitting arises from the interaction between the Er³⁺ 4f electrons and the asymmetric electric field produced by surrounding oxygen ligands in the glass network. Although the 4f orbitals are partially shielded by outer 5s and 5p electrons, this crystal-field interaction is sufficient to lift the degeneracy of energy levels, reflecting variations in local structure and site asymmetry around the Er³⁺ ions. The strong absorption band at 527 nm and the weaker, nascent band at 520 nm correspond to transitions from ⁴I_15/2→²H_11/2, with their differing intensities indicating the presence of non-equivalent Er³⁺ sites in the glass system. To provide a rigorous, quantitative justification for these intensity variations and local environment features, a comprehensive Judd-Ofelt (J-O) analysis was performed to determine the phenomenological intensity parameters (). As summarized in Table 7, the quality of the least-squares fitting is statistically robust, yielding coefficient of determination () values exceeding 0.99 across all investigated samples, thereby ensuring the physical reliability of the extracted parameters. The parameter provides valuable insight into the local crystal-field environment surrounding rare earth ions, reflecting variations in site symmetry and the strength of rare earth oxygen interactions. Its magnitude is governed by the local coordination characteristics, transition probabilities, fitting conditions, and host glass composition, and therefore serves as a sensitive spectroscopic parameter for evaluating structural changes around the rare earth sites. For the single doped BPML: Er sample, achieves its maximum value ( cm²), suggesting a more strongly perturbed local environment around Er³⁺ ions and enhanced interaction with the surrounding oxygen ligands. This behavior is consistent with the dominance of the split 527 nm band, which reflects increased sensitivity of the Er³⁺ electronic transitions to local crystal-field environment. Upon co-doping with Nd³⁺ ions (BPML: Er/Nd-1, BPML: Er/Nd-2, and BPML: Er/Nd-3), a systematic decrease in down to cm² is observed. The reduction in suggests a modification of the local coordination environment surrounding the Er³⁺ ions and may be associated with changes in the crystal-field distribution induced by Nd³⁺ incorporation. Within the intrinsically disordered borate glass network, the Judd-Ofelt intensity parameters embodies the combined contributions of local coordination geometry, crystal-field distribution, rare earth site redistribution, concentration-dependent ion-ion interactions, and possible local clustering of Er³⁺ and Nd³⁺ ions. Accordingly, the observed variation in reflects the overall evolution of the local structural and spectroscopic environment accompanying rare earth incorporation into the glass network. Furthermore, the calculated total radiative transition probability () for the ²H_11/2 → ⁴I_15/2 transition decreases from 22,450 to 17,200 s^− 1, providing a solid theoretical confirmation for the observed intensity variation and demonstrating that the radiative efficiency of the Er³⁺ site is inherently coupled to the Co-doped concentration and subsequent host network rearrangements. In the BPML: Nd glass, distinct absorption bands are observed at 516, 530, 582, 748, 802, 848, and 866 nm. The paired bands at 516 & 530 nm and 848 & 866 nm originate from transition from the Nd³⁺ ground state (⁴I_9/2) to the crystal-field-split ⁴G_7/2 and ⁴F_3/2 levels, respectively. The bands at 582, 748, and 802 correspond to transitions from ⁴I_9/2 to the ⁴G_5/2, ⁴F_7/2, and ⁴F_5/2 excited states. The observed splitting within the ⁴G_7/2 and ⁴F_3/2 manifolds reflects the influence of the asymmetric crystal field produced by surrounding oxygen ligands in the glass matrix, which perturbs the Nd³⁺ 4f energy levels. As for the co-doped samples (BPML: Er/Nd-1, BPML: Er/Nd-2, and BPML: Er/Nd-3), the optical absorption spectra display characteristic transitions of both Er³⁺ and Nd³⁺ ions, confirming the successful incorporation of both rare earth samples into the BPML glass series. The spectra reveal a superposition of the well-defined absorption bands corresponding to Er³⁺ and Nd³⁺ transitions, indicating that both ions retain their individual spectroscopic identities without significant spectral interference or energy-level distortion. This coexistence of Er³⁺ and Nd³⁺ absorption features suggests that the glass network provides suitable sites for both ions, enabling potential energy transfer interactions between them.

Fig. 5.

The recorded absorption spectra of the synthesized glass samples.

Table 7.

Judd-Ofelt intensity parameters of BPML: RE glass series.

Sample code	cm2	cm2	cm2
BPML: Er	4.852	0.937	0.387
BPML: Nd	1.625	0.254	0.207
BPML: Er/Nd-1	4.296	0.184	9.937
BPML: Er/Nd-2	4.111	0.180	0.148
BPML: Er/Nd-3	3.976	0.141	0.122

Photoluminescence

The excitation spectrum shown in Fig. 6a reveals several resonances capable of driving emission at 1.55 μm. The excitation performed at 773 nm produces the most efficient response and has been therefore chosen to optimize the 1.55 μm emission intensity. Figure 6b illustrated the photoluminescence (PL) spectra that reveals distinct emission behaviors arising from the presence and interaction of Er³⁺ and Nd³⁺ ions in the synthesized glass samples under 773 nm excitation. The base BPML sample exhibits no detectable emission, confirming the absence of active luminescent centers in the host matrix. In contrast, the BPML: Er glass displays two pronounced emission peaks at 1.551 and 1.559 μm, corresponding to the ⁴I_13/2 → ⁴I_15/2 transition of Er³⁺. These dual features originate from Stark splitting of the Er³⁺ energy levels within the glass network. Upon 773 nm excitation, Er³⁺ ions are promoted to the ⁴I_9/2 state via ground-state absorption (GSA), as shown in Fig. 7, and subsequently undergo fast non-radiative (NR) relaxation through the ⁴I_9/2 intermediate state to the ⁴I_13/2 metastable level, from which the characteristic 1.55 μm emission occurs. For the BPML: Nd sample, in contrast, exhibits only weak emission near 1.555 μm, which may be associated with weak Stark-broadened Nd³⁺-related emission features and local phonon-assisted processes within the glass network. However, the significant lower intensity compared with the Er-containing samples indicates that Nd³⁺ does not act as the primary luminescent center responsible for the 1.55 μm emission. The low intensity arises from inefficient Nd³⁺ excitation at 773 nm and intrinsically low radiative probability of this transition. Remarkably, the co-doped samples (BPML: Er/Nd-1, BPML: Er/Nd-2, and BPML: Er/Nd-3) show a single intensified emission band centered at 1.555, 1.556, and 1.558 μm, respectively. Although the emission originates primarily from Er³⁺ ions, its intensity is markedly enhanced by energy transfer (ET) from Nd³⁺ ions. As illustrated in Fig. 7, Nd³⁺ ions initially absorb the 773 nm excitation through the ⁴I_9/2→ (⁴F_5/2, ²H_9/2) transition. The excited Nd³⁺ ions subsequently undergo rapid multiphonon non-radiative relaxation before transferring their excitation energy non-radiatively to neighboring Er³⁺ ions. This ET process effectively populates the metastable ⁴I_13/2 level of Er³⁺, thereby increasing the population density of the emitting state and consequently enhancing the radiative ⁴I_13/2→⁴I_15/2 transition responsible for 1.55 μm emission. The proposed energy-transfer mechanism is consistent with previous investigation on Nd³⁺/Er³⁺ co-doped systems. Katta et al.⁷⁶. demonstrated that cooperative Nd³⁺→Er³⁺ energy transfer substantially enhances the population of the Er^{3+ 4}I_13/2 level, leading to stronger near-infrared emission and high energy-transfer efficiency. Likewise, Ding et al.²³ reported that efficient interionic energy transfer among rare-earth ions plays a key role in enhancing broadband near-infrared luminescence in co-doped tellurite glasses. A similar enhancement of the Er³⁺ 1.55 μm emission through improved energy-transfer efficiency has also been reported by Hu et al.⁷⁷ in Er-based co-doped systems. The agreement between the present results and these earlier studies further supports the proposed ET mechanism in the investigated BPML glasses. The gradual shift from 1.551 μm (in BPML: Er) to 1.558 μm (in BPML: Er/Nd-3) remains relatively small and may reflect subtle modifications in the local glass environment, including structural disorder and variations in RE³⁺ ion distribution. Therefore, the observed shift is discussed cautiously without direct quantitative crystal-field assignment. The enhancement in the emission wavelength is further supported by quantitative analysis of the donor-acceptor interaction. The calculated spectral overlap integral ( J) was found to be cm⁶/mol, yielding a critical transfer distance () of 6.42 Å. Such a short critical distance indicates that Nd³⁺ donor ions and Er³⁺ acceptor ions are sufficiently close for efficient non-radiative dipole-dipole interaction. Consequently, the calculated donor-acceptor separation provides quantitative evidence that the observed increase in the emission intensity originates from efficient Nd³⁺→Er³⁺ energy transfer rather than from independent excitation of Er³⁺ ions alone.

Fig. 6.

a) Excitation spectrum and b) the emitted wavelengths of the synthesized BPML: RE³⁺ glass series.

Fig. 7.

The probable transitions in Er³⁺ and Nd³⁺ ions and Er³⁺/ Nd³⁺ energy transfer.

The emission spectra of the synthesized BPML: RE³⁺ glass samples were analyzed in the frequency domain to determine the center frequency (), spectra bandwidth , and corresponding quality factor

16

All samples exhibited emission near 1.55 μm, with center frequencies ranging from to Hz, as shown in Figure 8, corresponding to the ⁴I_13/2→⁴I_15/2 transition of Er³⁺ ions. Although slight variations in the center frequency were observed among the investigated samples (≈ 2.5%), the relatively small magnitude of these changes necessitates a cautions interpretation because instrumental resolution and spectra fitting uncertainty. The observed shifts may therefore reflect subtle modifications in the local glass environment, including variations in structural disorder, phonon interactions, and rare earth distribution within the host matrix. In rare earth doped glasses, Stark splitting effects are typically on the order of 100–300 cm^− 1, whereas the present frequency variations are considerably larger and my additionally include contributions from spectral broadening, local structural heterogeneity, phonon coupling, and compositional disorder within the glass network. Therefore, no direct quantitative crystal-field assignment is made in the present work. The single-doped BPML: Er and BPML: Nd samples yielded similar quality factors of 38.97 and 38.34, indicating comparable levels of inhomogeneous broadening within the host network. Here, the quality factor () is employed as a spectroscopic parameter that correlates the emission center frequency with the effective spectral bandwidth of the luminescence band. Consequently, higher values are associated with narrower emission bands that are advantageous for broadband again media and wide-band optical amplification applications. In contrast, the Er/Nd co-doped glasses exhibited slightly lower values (≈ 35.2), indicating enhanced emission broadening after Nd³⁺ incorporation. This behavior is attributed to increased structural disorder and additional Nd³⁺→ Er³⁺ energy transfer interactions, which contribute to inhomogeneous broadening of the emission profile. The measured bandwidth ( THz) corresponds to approximately 38 nm around 1550 nm, which lies within the technologically important C-band region used in the optical fiber communication systems. Such broadened emission bands are advantageous for wavelength-division multiplexing (WDM) and broadband erbium-doped fiber amplifiers because wider gain bandwidths can support a larger number of optical communication channels and enhance transmission capacity. According to the Shannon-Hartley^78–80 relationship, increasing the available spectral bandwidth can theoretically increase the channel information capacity, provide that an adequate signal-to-noise ratio is maintained. Therefore, although the co-doped samples exhibit slightly lower spectral purity compared with the single-doped glasses, their broader emission bandwidth may provide practical advantages for broadband photonic and telecommunication applications.

Fig. 8.

The emitted frequency of the synthesized samples BPML, BPML: Er, BPML: Nd, BPML: Er/Nd-1 BPML: Er/Nd-2, and BPML: Er/Nd-3.

To evaluate the practical applicability of the synthesized BPML: Er/Nd borofluoride glass, its performance was compared with standard silica- and tellurite-based optical fiber materials. High spectroscopic quality factors () and broad emission bandwidths ( THz nm) spanning the 1.53–1.56 μm region represent key practical advantages over commercial silica fibers ()^81–83, significantly benefiting WDM and broadband amplification systems. Furthermore, Nd³⁺ → Er³⁺ energy transfer enhances 1.55 μm emission efficiency under 773 nm excitation, while favorable elastic moduli ( GPa) and thermal stability provide processing advantages over conventional tellurite matrices^84–86. Conversely, practical limitations include lower tensile strength relative to fused silica cores ( GPa), requiring polymer cladding during fiber drawing⁸¹. Additionally, the higher phonon energy of BPML compared to pure tellurite glasses increases non-radiative relaxation rates, necessitating precise concentration control to optimize gain profiles and prevent quenching^84–86.

Compared with previously reported Er³⁺/Nd³⁺-doped glass systems (Table 8), the present BPML: RE³⁺ glass exhibits a well-balanced combination of thermal, predictive mechanical, and optical properties. The developed borate-rich oxyfluoride composition demonstrates good thermal stability together with enhanced predicted mechanical performance, while maintaining efficient efficient NIR luminescence. In contrast to several reported systems that either require multiple rare earth dopants, employ more compositionally complex glass matrices, or exhibit emission predominantly at shorter NIR wavelengths, the present glass achieves intense emission at 1550–1557 nm under 773 nm excitation using only 1 mol% ER³⁺, Nd³⁺, or their co-doping. The Er³⁺/Nd³⁺ co-doped composition exhibits broadened NIR emission resulting from efficient energy transfer between Nd³⁺ and Er³⁺, together with a high-quality factor (Q_f = 38.97). These combined characteristics demonstrate that the BPML: RE³⁺ glass system offers a competitive balance between structural stability and optical performance, making it a promising candidate for broadband optical amplifiers, NIR photonic devices, and providing a solid foundation for future optical fiber applications.

Table 8.

Comparison of the photoluminescence characteristics of the present BPML: Er/Nd composite with the related Er³⁺/Nd³⁺-doped based luminescent systems.

Material	Thermal properties	Mechanical properties	Excitation (nm)	Emission (nm)	Optical performance	Distinct advantages
60B2O3-20Pb3O4-10MgF2-10LiF doped with 1 mol% Er3+, Nd3+, or Er3+/Nd3+ (Present Work)	Good thermal stability; BPML: Er/Nd-2 exhibits the best thermal balance		773	1550 (Er), 1550 (Nd), 1557 (Er/Nd)	Broadband NIR emission, efficient Er3+→Nd3+ energy transfer, Qf=38.97.	Simple borate-rich oxyfluoride glass with good thermal stability, enhanced predicted mechanical properties, and broadband 1.55 μm emission.
TeO2-ZnO-WO3-Bi2O3 doped with Nd3+, Tm3+, Er3+23	°C, excellent thermal stability	ـــــــــ	808	1340, 1480, 1530	Broadband NIR (1300–1630 nm)	Excellent broadband emission but requires triple rare-earth doping and higher compositional complexity.
50B2O3-20PbO-30CaO-0.5Er2O3-xNd2O3 (x = 0.25–1.5 mol% Nd2O3)87	ـــــــــ	ـــــــــ	808	840–1010 (centered at 885)	Nd-related broadband emission	Suitable mainly for radiation-shielding applications rather than telecommunication-band emission
44P2O5-15ZnO-10Pb3O4-15NaF-15MgF2-1Er2O3 co-doped with Yb3+, Nd3+ or Ce3+88	188-190°C (Ce)	Increased elastic moduli and hardness	525	631, 748, 801, 1034, 1527	Red and NIR emission through multi-ion energy transfer	Efficient visible and NIR laser emission, but requires multiple sensitizer ions
(55-x) B2O3-10SiO2-25Gd2O3-10CaO-xNd2O3 (x = 0–2.5 mol%)24	ـــــــــ	ـــــــــ	808, 885	903, 1059, 1334	Strong Nd3+ laser emission	Suitable mainly for laser applications with discrete Nd3 + transitions

Conclusion

This work demonstrates that the newly engineered borate-rich oxyfluoride glass system, 60B₂O₃-20Pb₃O₄-10MgF₂–10LiF (BPML), strategically doped with Er³⁺, Nd³⁺, and their combinations, delivers a compelling suite of structural, thermal, mechanical, and optical characteristics that position it as a strong contender for next-generation broadband optical fiber technologies. Through comprehensive structural analysis, the rare-earth incorporation, most notably Er³⁺, drives significant network densification via enhanced BO₄ formation, reduced separation, and strengthened linkages. These structural refinements translate directly into improved mechanical rigidity and elevated thermal stability, with mixed Er³⁺/Nd³⁺ doping achieving an optimal balance between compactness and flexibility. Optically, the glass series exhibits well-defined and broadened absorption features characteristic of Er³⁺ and Nd³⁺, with the co-doped compositions revealing spectrally rich, superimposed transitions indicative of effective simultaneous accommodation of both ions. Most importantly, photoluminescence studies confirm that 773 nm excitation activates an efficient Nd³⁺→Er³⁺ energy transfer pathway, substantially amplifying the 1.55 μm emission band, an essential wavelength for low-loss optical communication. The broadband emission bandwidth (ΔF = 4.95 THz) and high-quality factor ( ≈ 38.97) further underscore the suitability of these glasses for high-performance signal amplification and ultrafast photonic applications. Accordingly, the BPML: RE³⁺ glass series unites robust structural integrity, favorable thermal and predicted mechanical behavior, and superior NIR emission performance within a single, compositionally versatile material platform. The reported mechanical properties represent theoretical predictions obtained using the Makishima-Mackenzie model, providing valuable insight into the composition-structure-property relationships of the investigated glasses. As a future research direction, complementary experimental investigations, including Vickers microhardness and ultrasonic measurements, will be carried out to validate the predicted mechanical properties and further establish the reliability of the theoretical estimations. The demonstrated synergy between Er³⁺ and Nd³⁺, manifested in enhanced energy transfer efficiency and broadened emission, marks a significant advancement in the design of rare-earth-activated borate-based oxyfluoride glasses. These results not only validate the efficacy of the BPML system but also establish a promising foundation for the development of next-generation near-infrared optical fibers and broadband amplifiers, capable of meeting the stringent demands of modern high-capacity communication networks.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Mona A. El Naggar, Aly Saeed, Heba A. Gohra participated in suggesting the research point, preparing samples, analyzing and discussing the results, and writing and reviewing the manuscript.

Funding

Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).

Data availability

Data will be made available on request. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.