Quantitative Prediction of Structure and Properties of Nd³⁺-Doped Phosphate Laser Glass

Nd³⁺-doped phosphate glasses, utilizing the ⁴F_3/2 → ⁴I_11/2 energy-level transition of Nd³⁺ ions, achieve 1.06 μm luminescence and have critical applications in optical communications, biomedical engineering, and defense technologies. However, the development of laser glasses depends on empirical trial-and-error approaches, requiring extensive experimentation to generate limited data. This paradigm suffers from inefficiency, prolonged cycles, high costs, and a lack of theoretical guidance. Moreover, the luminescent properties of rare-earth-doped glasses are closely tied to the local structure of the rare-earth ions. The intricate relationship between structure and performance renders most computational models for glass properties ineffective, severely hindering the rapid advancement of laser glasses. It is thus necessary to develop cross-scale computational methods that combine physical interpretability and extrapolation capabilities to enable accurate prediction and inverse design of luminescent properties for broad-composition Nd³⁺-doped phosphate glasses.

In this study, Nd³⁺-doped Li₂O-MgO-Al₂O₃-P₂O₅ glasses were prepared. The local microstructure of Nd³⁺ in the glass as a statistical ensemble of its local environments in neighboring glassy compounds (NGCs) was described. Based on this theoretical framework, an NGCs model was proposed to quantitatively predict the luminescent properties of Nd³⁺-doped phosphate laser glasses, positing that the glass’s luminescent properties could be equal to the statistical average of the corresponding properties of its NGCs. This work could provide a theoretical foundation for quantitatively calculating the local structure and luminescent properties of rare-earth-doped laser glasses.

In rare-earth-doped laser glasses, the luminescent properties were determined via the analysis of the local structure of the rare-earth ions. The local structure of rare-earth ions in multicomponent laser glasses as a statistical ensemble of their configurations in NGCs was simulated based on the broken ergodicity theory. The NGCs in the compositional space (i.e., Li₂O·Al₂O₃·4P₂O₅, 9Li₂O·3 Al₂O₃·8P₂O₅, P₂O₅, Li₂O·P₂O₅, Al₂O₃·3P₂O₅, Li₂O·2MgO·P₂O₅, MgO·P₂O₅, Li₂O·6MgO·3P₂O₅, Al₂O₃·P₂O₅, MgO·2P₂O₅ and 2MgO·Al₂O₃·P₂O₅) were identified via querying the Materials Project database for the quaternary phosphate system (i.e., Li₂O-MgO-Al₂O₃-P₂O₅). The local microstructure and luminescent properties of all glass compositions in this system were derived from these 11 NGCs by the NGCs model.

The molecular dynamics (MD) simulations were performed by the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The Morse potential, suitable for modeling short-range interactions in rare-earth-doped glasses, was employed. The long-range interactions were treated by the Ewald summation method (cutoff radius: 12.0 Å), while the short-range interactions were truncated at 8.0 Å. The glass quenching process was simulated at a fixed timestep of 2 fs. The initial structure was thermalized at 5000 K for 1.0 ns to eliminate memory effects. The system was then cooled to 3000 K in the canonical (NVT) ensemble at 5 K/ps. To simulate the experimental conditions, the system was equilibrated in the isothermal-isobaric (NPT) ensemble at 3000 K for 1.0 ns, allowing simultaneous relaxation of the simulation box dimensions and atomic positions. The further cooling to 300 K was conducted in the NPT ensemble at 0.5 K/ps, with intermediate equilibration steps at 2500, 2000, 1500, 1000 K, and 300 K (1 ns each), respectively. Finally, a 1 ns equilibration in the microcanonical (NVE) ensemble was performed, with atomic coordinates recorded every 5000 steps during the last 500 ps.

The radial distribution function g(r) and structure factor S(q), representing short- and medium-range structural orders, were calculated by both the NGCs model and MD simulations. The results from these methods have remarkable consistency, indicating the NGCs model’s capability to quantitatively determine the local structural features of Nd³⁺ in Li₂O-MgO-Al₂O₃-P₂O₅ glasses. Since the luminescent properties of rare-earth-doped glasses are governed by the local coordination environment, this agreement validates the NGCs model for predicting luminescent performance.

The NGCs model is further applied to calculate key luminescent properties, i.e., the emission cross-section (σ_e) and fluorescence lifetime (τ) of the ⁴F_3/2→⁴I_11/2 transition. The σ_e values increase monotonically with Li₂O content, showing a maximum relative deviation of 1.72% from experimental data. For τ that is influenced by non-structural factors such as hydroxyl quenching and Nd³⁺ clustering, the maximum relative error is 6.19%. These results underscore the model’s accuracy in predicting luminescent properties. A robust composition-property mapping is established via leveraging this model, enabling efficient screening of high-performance Nd³⁺-doped phosphate glass compositions.

A comprehensive analysis of 11,355 valid glass compositions within the glass-forming region reveals an inverse correlation between σ_e and τ, i.e., compositions with a higher σ_e typically exhibit a shorter τ. However, the model identifies a subset of optimized compositions with both high σ_e and extended τ, corresponding to Al₂O₃ (0-7%), MgO (10%-18%), and Li₂O (1%-7%).

This study applied the NGCs model to analyze the local structure and luminescent properties of Nd³⁺-doped Li₂O-MgO-Al₂O₃-P₂O₅ glasses. The calculated g_Re (r) and S_Re(q), reflecting short- and medium-range orders, aligned closely with the MD simulation results, indicating the model’s precision in characterizing Nd³⁺ local structures. The model achieved exceptional accuracy in predicting luminescent properties, with maximum relative errors of 1.72% for σ_e and 6.19% for τ, compared to the experimental data. The systematic screening of the glass-forming region identified optimal compositional ranges (i.e., Al₂O₃: 0-7%, MgO: 10%-18%, Li₂O: 1%-7%) that could simultaneously maximize σ_e and τ.

The NGCs model could provide a groundbreaking approach for designing advanced Nd³⁺-doped phosphate laser glasses via establishing a quantitative link between atomic-scale structures and macroscopic performance. This methodology could accelerate material discovery and reduce reliance on costly experimental iterations, paving an efficient way for the development of next-generation laser mate rials.