Designing optical glasses by machine learning coupled with a genetic algorithm

Engineering new glass compositions have experienced a sturdy tendency to move forward from (educated) trial-and-error to data- and simulation-driven strategies. In this work, we developed a computer program that combines data-driven predictive models (in this case, neural networks) with a genetic algorithm to design glass compositions with desired combinations of properties. First, we induced predictive models for the glass transition temperature (T_g) using a dataset of 45,302 compositions with 39 different chemical elements, and for the refractive index (n_d) using a dataset of 41,225 compositions with 38 different chemical elements. Then, we searched for relevant glass compositions using a genetic algorithm informed by a design trend of glasses having high n_d (1.7 or more) and low T_g (500 °C or less). Two candidate compositions suggested by the combined algorithms were selected and produced in the laboratory. These compositions are significantly different from those in the datasets used to induce the predictive models, showing that the used method is indeed capable of exploration. Both glasses met the constraints of the work, which supports the proposed framework. Therefore, this new tool can be immediately used for accelerating the design of new glasses. These results are a stepping stone in the pathway of machine learning-guided design of novel glasses.     

Nepheline Crystallization in Nuclear Waste Glasses: Progress Toward Acceptance of High-Alumina Formulations

Historical data have been critically compiled and analyzed for investigating the quantity of nepheline (NaAlSiO₄) precipitated as a function of composition in simulated nuclear waste glasses. To understand compositional effects two primary methods were used: (1) investigating the Al₂O₃–SiO₂–Na₂O ternary while filtering for different B₂O₃ levels and (2) creating a quadrant system consisting of compositions reduced to two representations: (i) the nepheline discriminator (ND) which depends only on the SiO₂ content by weight normalized to the total weight of the Al₂O₃–SiO₂–Na₂O submixture and (ii) the optical basicity (OB) which contains contributions from all constituents in the glass. Nepheline precipitation is expected to be suppressed at high SiO₂ levels (ND > 0.62) or at low basicities (OB < 0.55–0.57). Changes in sodium aluminosilicate glass OB values due to additions of CaO and B₂O₃ correlate with the observed effects on nepheline formation. It is proposed that additional composition space is available for formulating high waste loading, high-Al₂O₃ nuclear waste glasses when consideration is given to location on the Al₂O₃–SiO₂–Na₂O submixture as well as OB.     

Submixture model to predict nepheline precipitation in waste glasses

High-alumina high-level waste (HLW) glasses are prone to nepheline precipitation during canister-centerline cooling (CCC). If sufficient nepheline forms, the chemical durability of the glass will be significantly impacted. Overly conservative constraints have been developed and used to avoid the deleterious effects of nepheline formation in U.S. HLW glasses. The constraints used have been shown to significantly limit the loading of waste in glass at Hanford and therefore the cost and schedule of cleanup. A 90-glass study was performed to develop an improved understanding of the impacts of glass composition on the formation of nepheline during CCC. The CCC crystallinity data from these glasses were combined with 657 glasses found in the literature. The trends showed significant effects of Na₂O, Al₂O₃, SiO₂, B₂O₃, CaO, Li₂O, and potentially K₂O on the propensity for nepheline formation. A pseudo-ternary submixture model was proposed to identify the glass composition region prone to nepheline precipitation. This pseudo-ternary with axes of SiO₂ + 1.98B₂O₃, Na₂O + 0.653Li₂O + 0.158CaO, and Al₂O₃ was found to divide glasses that precipitate nepheline during CCC from those that do not. Application of this constraint is anticipated to increase the loading of Hanford high-alumina HLWs in glass by roughly one-third.     

The effect of glass composition on the reactivity of synthetic glasses

The reactivity of synthetic glasses depends on their chemical compositions. In far from equilibrium dissolution experiments, the reactivity of Ca‐rich glasses with compositions similar to blast‐furnace slag is found to be much higher (up to ~60 wt.% after 7 days) compared to Si‐rich glasses with compositions similar to type F fly ash (up to ~20 wt.% after 7 days). Isothermal calorimetry and TGA experiments conducted on model systems containing portlandite and calcite and on glass‐blended Portland cement confirmed the higher reactivity of the Ca‐rich glasses. The degree of glass reaction after 91 days ranged from 7 to 20 wt.%. The results showed also a higher reactivity of the glasses containing more aluminum (both for Ca‐rich and Si‐rich glasses) indicating that not only calcium but also aluminum acted rather as network modifier than as network former. The results confirm a strong dependence of the glass reactivity on the degree of polymerization of the glass network.     

Accelerated Leach Testing of GLASS (ALTGLASS): I. Informatics approach to high level waste glass gel formation and aging

Glass corrosion data from the ALTGLASS^™ database were used to determine if gel compositions, which evolve as glass systems corrode, are correlated with the generation of zeolites and subsequent increase in the glass dissolution rate at long times. The gel compositions were estimated based on the difference between the elemental glass starting compositions and the measured elemental leachate concentrations from the long-term product consistency tests (ASTM C1285) at various stages of dissolution, ie, reaction progress. A well-characterized subset of high level waste glasses from the database was selected: these glasses had been leached for 15-20 years at reaction progresses up to ~80%. The gel composition data, at various reaction progresses, were subjected to a step-wise regression, which demonstrated that hydrogel compositions with Si^*/Al^* ratios of <1.0 did not generate zeolites and maintained low dissolution rates for the duration of the experiments. Glasses that formed hydrogel compositions with Si^*/Al^* ratios ≥1, generated zeolites accompanied by a resumption in the glass dissolution rate. The role of the gel Si/Al ratio, and the interactions with the leachate, provides the fundamental understanding needed to predict if and when the glass dissolution rate will increase due to zeolitization.     

Interpreting the optical properties of oxide glasses with machine learning and Shapely additive explanations

Due to their excellent optical properties, glasses are used for various applications ranging from smartphone screens to telescopes. Developing compositions with tailored Abbe number (V_d) and refractive index at 587.6 nm (n_d), two crucial optical properties, is a major challenge. To this extent, machine learning (ML) approaches have been successfully used to develop composition–property models. However, these models are essentially black boxes in nature and suffer from the lack of interpretability. In this paper, we demonstrate the use of ML models to predict the composition-dependent variations of V_d and n_d. Further, using Shapely additive explanations (SHAP), we interpret the ML models to identify the contribution of each of the input components toward target prediction. We observe that glass formers such as SiO₂, B₂O₃, and P₂O₅ and intermediates such as TiO₂, PbO, and Bi₂O₃ play a significant role in controlling the optical properties. Interestingly, components contributing toward increasing the n_d are found to decrease the V_d and vice versa. Finally, we develop the Abbe diagram, using the ML models, allowing accelerated discovery of new glasses for optical properties beyond the experimental pareto front. Overall, employing explainable ML, we predict and interpret the compositional control on the optical properties of oxide glasses.     

Thermodynamic assessment of the pseudoternary Na2O–Al2O3–SiO2 system

Vitrified high‐level radioactive waste that contains high concentrations of Na₂O and Al₂O₃, such as the waste stored at the Hanford site, can cause nepheline to precipitate in the glass upon cooling in the canisters. Nepheline formation removes oxides such as Al₂O₃ and SiO₂ from the host glass, which can reduce its chemical durability. Uncertainty in the extent of precipitated nepheline necessitates operating at an enhanced waste loading margin, which increases operational costs by extending the vitrification mission as well as increasing waste storage requirements. A thermodynamic evaluation of the Na₂O–Al₂O₃–SiO₂ system that forms nepheline was conducted by utilizing the compound energy formalism and ionic liquid model to represent the solid solution and liquid phases, respectively. These were optimized with experimental data and used to extrapolate phase boundaries into regions of temperature and composition where measurements are unavailable. The intent is to import the determined Gibbs energies into a phase field model to more accurately predict nepheline phase formation and morphology evolution in waste glasses to allow for the design of formulations with maximum loading.     

Structural dependence of crystallization in phosphorus-containing sodium aluminoborosilicate glasses

The article reports on the structural dependence of crystallization in Na₂O–Al₂O₃–B₂O₃–P₂O₅–SiO₂-based glasses over a broad compositional space. The structure of melt-quenched glasses has been investigated using ¹¹B, ²⁷Al, ²⁹Si, and ³¹P magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy, while the crystallization behavior has been followed using X-ray diffraction and scanning electron microscopy combined with energy dispersive spectroscopy. In general, the integration of phosphate into the sodium aluminoborosilicate network is mainly accomplished via the formation of Al–O–P and B–O–P linkages with the possibility of formation of Si–O–P linkages playing only a minor role. In terms of crystallization, at low concentrations (≤5 mol.%), P₂O₅ promotes the crystallization of nepheline (NaAlSiO₄), while at higher concentrations (≥10 mol.%), it tends to suppress (completely or incompletely depending on the glass chemistry) the crystallization in glasses. When correlating the structure of glasses with their crystallization behavior, the MAS NMR results highlight the importance of the substitution/replacement of Si–O–Al linkages by Al–O–P, Si–O–B, and B–O–P linkages in the suppression of nepheline crystallization in glasses. The results have been discussed in the context of (1) the problem of nepheline crystallization in Hanford high-level waste glasses and (2) designing vitreous waste forms for the immobilization of phosphate-rich dehalogenated Echem salt waste.     

Predicting and interpreting oxide glass properties by machine learning using large datasets

With the advent of powerful computer simulation techniques, it is time to move from the widely used knowledge-guided empirical methods to approaches driven by data science, mainly machine learning algorithms. We investigated the predictive performance of three machine learning algorithms for six different glass properties. For such, we used an extensive dataset of about 150,000 oxide glasses, which was segmented into smaller datasets for each property investigated. Using the decision tree induction, k-nearest neighbors, and random forest algorithms, selected from a previous study of six algorithms, we induced predictive models for glass transition temperature, liquidus temperature, elastic modulus, thermal expansion coefficient, refractive index, and Abbe number. Moreover, each model was induced with default and tuned hyperparameter values. We demonstrate that, apart from the elastic modulus (which had the smallest training dataset), the induced predictive models for the other five properties yield a comparable uncertainty to the usual data spread. However, for glasses with extremely low or high values of these properties, the prediction uncertainty is significantly higher. Finally, as expected, glasses containing chemical elements that are poorly represented in the training set yielded higher prediction errors. The method developed here calls attention to the success and possible pitfalls of machine learning algorithms. The analysis of the SHAP values indicated the key elements that increase or decrease the value of the modeled properties. It also estimated the maximum possible increase or decrease. Insights gained by this analysis can help empirical compositional tuning and computer-aided inverse design of glass formulations.     

The Fluxing Effect of Mineral Material – Cullet Compositions on Enamel Glass

Enamel glasses are synthesized based on the Na₂O – B₂O₃ – Co₂O₃ – SiO₂ system, including perlite, nepheline concentrate, and cullet. The physicochemical and technological properties of the resulting glasses and one-layer coatings based on these glasses are considered. A comparative analysis of the fluxing effect of the nepheline - cullet and perlite-cullet compositions on glasses is carried out. The reference composition areas are shown to be suitable for the development of one-coat powdered glass enamels.     

Derivation of the Structural Integrity of Residual (SIR) glass model for the enhancement of waste loading

A new model based on glass structure to allow for enhanced waste loading in nuclear waste glass while maintaining chemical durability is proposed. The model is derived by splitting the molar concentrations of the targeted starting glass composition into theoretical crystalline phases anticipated to be observed during devitrification and a residual glass. An empirically derived relationship based on maintaining the residual glass structure, determined from a calculated non-bridging oxygen content, was demonstrated to successfully screen glasses for acceptable durability. The proposed model can successfully identify durable glass compositions containing 20–35 wt% Al₂O₃, a concentration that would significantly increase the projected waste loading in glasses processed at the Hanford Tank Waste Treatment and Immobilization Plant.     

Density of fluoride glasses through artificial intelligence techniques

Artificial Intelligence techniques have been employed for the first time to train a dataset of 1258 distinct fluoride glasses collected from published literature to predict the density of novel oxy-fluoro glasses based on their chemical composition and ionic radii. The glass dataset was split based on the linear and non-linear variation to predict the glass density using various AI models like gradient descent, random forest regression and artificial neural networks. High concentration of boron in glass specimens resulted in scattering of datapoints in packing factor relation and density prediction. The random forest regression model fit the combined glass dataset with the highest R² of 0.980. In case of boron-rich glasses, their non-linear behavior restricted the R² for ANNs to 0.792 as optimum with the tanh activation function.     

Photosensitivity of barium germano-gallate glasses under femtosecond laser direct writing for Mid-IR applications

Barium germano-gallate glasses are attractive glass hosts for photonic applications in the mid-infrared region up to 6 μm. In this work, we investigate the photosensitivity of such glasses under femtosecond laser, with an emphasize on the formation of refractive index changes. Six glasses with varying compositions (including addition of K, Na, Y, and La) were studied. We observed several transformation regimes in the pulse energy – repetition rate landscape: Type I (isotropic refractive index change) and a spatial broadening regime with a phase shift Δϕ > 2π rad at 550 nm. This translates into refractive index changes Δn > 10⁻² and is comparable to values obtained in most chalcogenide glasses. The effect of glass composition on Δϕ appears correlated to the number of non-bridging oxygen presented in the glass and is brought to evidence by monitoring the Cations/GaO_3/2 ratio. This provides a way to design a range of germano-gallate glasses suitable to imprinting high refractive index contrast.     

Vitrification of a waste water flocculate from a petroleum catalyst manufacturer

Chemical and mineral compositions of a waste water flocculate generated in a manufacturer producing fluidized-bed catalytic cracking catalysts were analyzed. The flocculate was then calcined at 1200–1350 °C. X-ray diffraction analysis results indicate that the flocculate can be directly vitrified at 1350 °C without the addition of any other ingredients. The density and chemical durability of the directly vitrified product are comparable with commercial soda-lime-silicate glasses. However, the viscosity of directly vitrified glass melt was very high. Thus, the refining and shaping of the glass melt were difficult. With the addition of minerals such as limestone, dolomite and fluorite, workable glasses could be formed. The influence of MgO on the structure and properties of the obtained glasses is discussed. Results show that the density and hardness of the glass increase with the increase of MgO, whereas the chemical durability, transition and crystallization temperatures decrease. The present study provides a general way to utilize waste water flocculates in glass production.     

Rheology of simulated radioactive waste slurry and cold cap during vitrification

During the vitrification of radioactive waste in a Joule‐heated melter, aqueous melter feed slurry forms a cold cap, a reacting and melting material, which floats on the surface of the molten glass. The rheological behavior of the feed affects cold cap formation and shape, and is vital for modeling the feed‐to‐melt conversion process. We used slurry feed simulant and fast‐dried slurry solids representing the cold cap to investigate the rheological behavior of the feed as it transforms into glass. Both low‐temperature and high‐temperature rheometry were performed and a new scheme was applied to estimate the feed viscosity. This study shows that the conversion advances in four sequential stages that form distinct regions in the cold cap: (i) a fast‐spreading boiling slurry from which water evaporates, (ii) a porous solid region (viscosity > 10⁸ Pa s) containing reacting solids and molten salts, (iii) a plastic region in which glass‐forming melt connects the refractory solids (~10⁸ to ~10⁶ Pa s), and (iv) a viscous foam layer in which the viscosity drops from ~10⁵ to ~10¹ Pa s. The implications for the mathematical modeling of the cold cap are discussed.     

Structural dependence of crystallization in glasses along the nepheline (NaAlSiO4) ‐ eucryptite (LiAlSiO4) join

Lithium and sodium aluminosilicates are important glass‐forming systems for commercial glass‐ceramics, as well as being important model systems for ion transport in battery studies. In addition, uncontrolled crystallization of LiAlSiO₄ (eucryptite) in high‐Li₂O compositions, analogous to the more well‐known problem of NaAlSiO₄ (nepheline) crystallization, can cause concerns for long‐term chemical durability in nuclear waste glasses. To study the relationships between glass structure and crystallization, nine glasses were synthesized in the Li_xNa_1‐xAlSiO₄ series, from x = 0 to x = 1. Raman spectra, nuclear magnetic resonance (NMR) spectroscopy (Li‐7, Na‐23, Al‐27, Si‐29), and X‐ray diffraction were used to study the quenched and heat‐treated glasses. It was found that different LiAlSiO₄ and NaAlSiO₄ crystal phases crystallize from the glass depending on the Li/Na ratio. Raman and NMR spectra of quenched glasses suggest similar structures regardless of alkali substitution. Li‐7 and Na‐23 NMR spectra of the glass‐ceramics near the endmember compositions show evidence of several differentiable sites distinct from known Li_xNa_1‐xAlSiO₄ crystalline phases, suggesting that these measurements can reveal subtle chemical environment differences in mixed‐alkali systems, similar to what has been observed for zeolites.     

Flow regime identification in aerated stirred vessel using passive acoustic emission and machine learning

Smart at- or online process sensors, which employ machine learning (ML) to process data, have been the subject of extensive research in recent years, due to their potential for real-time process control. In this paper, a passive acoustic emission process sensor has been used to detect gas–liquid regimes within a stirred, aerated vessel using novel ML approaches. Pressure fluctuations (acoustic emissions) in an air-water system were recorded using a piezoelectric sensor installed on the external wall of three identical cylindrical tanks of diameter, T = 160 mm, filled to a volume of 5 L (height, H = 1.5 T). The tanks were made of either glass, steel, or aluminium, and each tank was equipped with a Rushton turbine of diameter, D = 0.35 T. The investigated flow regimes, flooding, loading, complete dispersion, and un-gassed, were obtained by changing the air feed flow rates and by varying the impeller speed. The acoustic spectra obtained were processed to select an optimal number of features characterizing each of the regimes, and these were used to train three different ML algorithms. The pre-processing includes a principal component analysis (PCA) step, which reduces the volume of data fed to the ML algorithms, saving computational time up to a factor of 5. The algorithms (decision tree, k-nearest neighbour, and support vector machines) were challenged to use these features to identify the correct flow regime. Accurate predictions of the three gas–liquid regimes of interest have been achieved. The accuracy of the prediction ranges from 90% to 99%, and this difference is related to the material used for the vessel.     

Influence of Al2O3/SiO2 ratio in multicomponent LNAS glasses and glass-ceramics on the crystallization behavior,microstructure and mechanical performance

Transparent glass-ceramics containing eucryptite and nepheline crystalline phases were prepared from alkali (Li, Na) aluminosilicate glasses with various mole substitutions of Al₂O₃ for SiO₂. The relationships between glass network structure and crystallization behavior of Li₂O–Na₂O–Al₂O₃–SiO₂ (LNAS) glasses were investigated. It was found that the crystallization of the eucryptite and nepheline in LNAS glasses significantly depended on the concentration of Al₂O₃. LNAS glasses with the addition of Al₂O₃ from 16 to 18 mol% exhibited increasing Q⁴ (mAl) structural units confirmed by NMR and Raman spectroscopy, which promoted the formation of eucryptite and nepheline crystalline phases. With the Al₂O₃ content increasing to 19–20 mol%, the formation of highly disordered (Li, Na)₃PO₄ phase which can serve as nucleation sites was inhibited and the crystallization mechanism of glass became surface crystallization. Glass-ceramics containing 18 mol% Al₂O₃ showed high transparency ～84% at 550 nm. Moreover, the microhardness, elastic modulus and fracture toughness are 8.56 GPa, 95.7 GPa and 0.78 MPa m^1/2 respectively. The transparent glass-ceramics with good mechanical properties show high potential in the applications of protective cover of displays.