Composition dependence of glass transition temperature and fragility. II. A topological model of alkali borate liquids

Revealing the relationship between liquid fragility and medium-range order in silicate glasses

Despite decades of studies, the nature of the glass transition remains elusive. In particular, the sharpness of the dynamical arrest of a melt at the glass transition is captured by its fragility. Here, we reveal that fragility is governed by the medium-range order structure. Based on neutron-diffraction data for a series of aluminosilicate glasses, we propose a measurable structural parameter that features a strong inverse correlation with fragility, namely, the average medium-range distance (MRD). We use in-situ high-temperature neutron-scattering data to discuss the physical origin of this correlation. We argue that glasses exhibiting low MRD values present an excess of small network rings. Such rings are unstable and deform more readily with changes in temperature, which tends to increase fragility. These results reveal that the sharpness of the dynamical arrest experienced by a silicate glass at the glass transition is surprisingly encoded into the stability of rings in its network.

Densification in transparent SiO2 glasses prepared by spark plasma sintering

Recently, spark plasma sintering (SPS) has become an attractive method for the preparation of solid-state ceramics. As SPS is a pressure-assisted low-temperature process, it is important to examine the effects of temperature and pressure on the structural properties of the prepared samples. In the present study, we examined the correlation between the preparation conditions and the physical and structural properties of SiO₂ glasses prepared by SPS. Compared with the conventional SiO₂ glass, the SPS-SiO₂ glasses exhibit a higher density and elastic modulus, but a lower-height first sharp diffraction peak of the X-ray total structure factor. Micro-Raman and micro-IR spectra suggest the formation of heterogeneous regions at the interface between the SiO₂ powders and graphite die. Considering the defect formation observed in optical absorption spectra, reduction reaction mainly affects the densification of SPS-SiO₂ glass. Hence, the reaction at the interface is important for tailoring the structure and physical properties of solid-state materials prepared by the SPS technique.

Beyond the Average: Spatial and Temporal Fluctuations in Oxide Glass-Forming Systems

Atomic structure dictates the performance of all materials systems; the characteristic of disordered materials is the significance of spatial and temporal fluctuations on composition-structure-property-performance relationships. Glass has a disordered atomic arrangement, which induces localized distributions in physical properties that are conventionally defined by average values. Quantifying these statistical distributions (including variances, fluctuations, and heterogeneities) is necessary to describe the complexity of glass-forming systems. Only recently have rigorous theories been developed to predict heterogeneities to manipulate and optimize glass properties. This article provides a comprehensive review of experimental, computational, and theoretical approaches to characterize and demonstrate the effects of short-, medium-, and long-range statistical fluctuations on physical properties (e.g., thermodynamic, kinetic, mechanical, and optical) and processes (e.g., relaxation, crystallization, and phase separation), focusing primarily on commercially relevant oxide glasses. Rigorous investigations of fluctuations enable researchers to improve the fundamental understanding of the chemistry and physics governing glass-forming systems and optimize structure-property-performance relationships for next-generation technological applications of glass, including damage-resistant electronic displays, safer pharmaceutical vials to store and transport vaccines, and lower-attenuation fiber optics. We invite the reader to join us in exploring what can be discovered by going beyond the average.

Atomistic Understanding of Ion Exchange Strengthening of Boroaluminosilicate Glasses: Insights from Molecular Dynamics Simulations and QSPR Analysis

Ion exchange (IOX) is an effective and widely used method to enhance mechanical properties of various glass products ranging from the touch screen of consumer electronics to window shields of airplanes and spacecrafts. IOX or chemical strengthening is achieved through the creation of a compressive surface layer on the glass product. Although widely studied experimentally, the fundamental understanding of the IOX strengthening process is still limited. In this work, we have applied large-scale atomistic simulations to understand IOX-induced mechanical property changes and their relation to the glass composition and structural characteristics. Two series of borosilicate glasses are studied to elucidate the composition effect, with boron oxide for silica and alumina for silica substitutions, respectively, on the mechanical properties of different levels of K⁺ to Na⁺ ion exchanges by using molecular dynamics (MD) simulations with a set of recently developed effective partial charge potentials. The linear network dilation coefficient (LNDC), a common measure of IOX behaviors, was calculated for each of the glass compositions. Quantitative structural property relationship (QSPR) analysis based on the MD-generated structural features was used to establish the structure-property correlations of mechanical and other properties. The results show strong composition dependence of the LNDC, hence the suitability of IOX strengthening. This behavior is discussed based on glass structure features of the glasses. It was found that glass compositions with a higher amount of mixed glass formers, higher network connectivity, and less complex components tend to show higher calculated LNDC and higher surface compressive stress. MD simulations, in combination with QSPR analysis, can thus provide atomistic insights into how the glass composition and structural characteristics affect IOX behaviors.

Configurational Entropy Relaxation of Silica Glass-Molecular Dynamics Simulations

Vitreous silica was modelled using molecular dynamics (MD). The glass structure was transferred into an undirected graph and decomposed into disjoint structural units that were ideally mixed to calculate the configurational entropy. The Debye relaxation model was suggested to simulate the evolution of entropy during the cooling of the system. It was found that the relaxation of the configurational entropy of MD corresponds to the effective cooling rate of 6.3 × 10⁶ Ks⁻¹ and its extrapolation to 0.33 Ks⁻¹ mimics the glass transition with T_g; close to the experimental value. Debye relaxation correctly describes the observed MD evolution of configurational entropy and explains the existence of freezing-in temperature and the shape of the curve in the transition region.

Unveiling the strong dependence of the α-relaxation dispersion on mixing thermodynamics in binary glass-forming liquids

Structural α-relaxation dispersion in binary molecular glass forming mixtures with distinct mixing enthalpy ΔHmix was investigated using enthalpic and dielectric relaxation measurements across the entire composition range. This study focused on the dependence of the relaxation dispersion on the mixing thermodynamics by determining the non-exponential exponent β, and its composition dependence. The β values determined by the enthalpic and dielectric relaxations agree well. Remarkably, it is found that the systems with positive enthalpy of mixing (exothermic, ΔHmix >0) have positive deviations in the composition dependence of β from the linear averaging of the two β values of the pure components, while negative deviations are observed for the systems with negative enthalpy of mixing (endothermic, ΔHmix <0). Furthermore, the relation between the non-exponential behaviors and entropy of mixing is discussed, revealing that the positive or negative deviation of β in its composition dependence on mixing is accompanied by the same sign of the excess entropy of mixing relative to the ideal one.

Lithium Borates from the Glass to the Melt: A Temperature-Induced Structural Transformation Viewed from the Boron and Oxygen Atoms

A multiedge study of the local structure of lithium borate glasses and melts has been carried out using X-ray Raman scattering (XRS) as a function of temperature. Thanks to a wide range of compositions, from pure B₂O₃ up to the metaborate composition, we are able to finely interpret the modifications of the local environment of both the boron and oxygen atoms in terms of boron coordination number, formation of nonbridging oxygens (NBOs), and polymerization degree of the borate framework as a function of temperature and composition. A temperature-induced ^[4]B to ^[3]B conversion is observed above the glass transition temperature (T_g) from the glass to the melt from the triborate composition up to the metaborate composition. Two distinct melt structures are reported: a well-polymerized borate network-with few NBOs-below the triborate composition and a depolymerized borate network above the diborate composition with a rapid increase of the number of NBOs when Li₂O is added. These two structurally distinct melts allow explaining the two dynamic regimes observed for lithium ion diffusion.

Predicting the onset temperature (Tg) of GexSe1-x glass transition: a feature selection based two-stage support vector regression method

Despite the usage of both experimental and topological methods, realizing a rapid and accurate measurement of the onset temperature (T_g) of Ge_xSe_1-x glass transition remains an open challenge. In this paper, a predictive model for the T_g in Ge_xSe_1-x glass system is presented by a machine learning method named feature selection based two-stage support vector regression (FSTS-SVR). Firstly, Pearson correlation coefficient (PCC) is used to select features highly correlated with T_g from the candidate features of Ge_xSe_1-x glass system. Secondly, in order to simulate the two-stage characteristic of T_g which is caused by structural variation with a turning point at x = 0.33 via the structural analysis, SVR is utilized to build predictive models for two stages separately and then the two achieved models are synthesized using a minimum error based model for T_g prediction. Compared with the topological and other methods based on SVR, the FSTS-SVR gives the highest predictive accuracy with the root mean square error (RMSE) and mean absolute percentage error (MAPE) of 10.64 K and 2.38%, respectively. This method is also expected to be more efficient for the prediction of T_g of other glass systems with the multi-stage characteristic.

Topological Origins of the Mixed Alkali Effect in Glass

The mixed alkali effect, the deviation from expected linear property changes when alkali ions are mixed in a glass, remains a point of contention in the glass community. While several earlier models have been proposed to explain mixed alkali effects on ionic motion, models based on or containing discussion of structural aspects of mixed-alkali glasses remain rare by comparison. However, the transition-range viscosity depression effect is many orders in magnitude for mixed-alkali glasses, and the original observation of the effect (then known as the Thermometer Effect) concerned the highly anomalous temperature dependence of stress and structural relaxation time constants. With this in mind, a new structural model based on topological constraint theory is proposed herein which elucidates the origin of the mixed alkali effect as a consequence of network strain due to differing cation radii. Discussion of literature models and data alongside new molecular dynamics simulations and experimental data are presented in support of the model, with good agreement.

Topological Control of Water Reactivity on Glass Surfaces: Evidence of a Chemically Stable Intermediate Phase

Glass surfaces are of considerable interest due to their disproportionately large influence on the performance of glass articles in many applications. However, the behavior of glass surfaces has proven difficult to model and predict due to their complex structure and interactions with the environment. Here, the effects of glass network topology on the surface reactivity of glasses have been investigated using reactive and nonreactive force field-based molecular dynamics simulations as well as density functional theory. A topological constraint-based description for surface reactivity is developed, allowing for improved understanding of the physical and chemical origins of surface reactivity. Results show evidence for the existence of a chemically stable intermediate phase on the surface of the glass where the glass network is mechanically isostatic.

Statistical Mechanical Modeling of Borate Glass Structure and Topology: Prediction of Superstructural Units and Glass Transition Temperature

Predicting the compositional evolution of the atomic-scale structure and properties of oxide glasses is important for designing new materials for advanced applications. A statistical mechanics-based approach has recently been applied to predict the composition-structure evolution in binary phosphate glasses, while topological constraint theory (TCT) has been applied in the last decade to predict the structure-property evolution in various oxide and nonoxide glass systems. In this work, we couple these two approaches to enable quantitative predictions of the compositional dependence of glass transition temperature and the population of superstructural units. The object of the study is the lithium borate glass system because they feature interesting structural characteristics (e.g., boron anomaly), and ample structure and property data are available. In these glasses, the average coordination number of boron first increases when lithium modifiers are added and then later decreases accompanied by network depolymerization. First, on the basis of ¹⁰B nuclear magnetic resonance spectroscopy data from literature, we present a statistical description of the structural evolution in lithium borate glasses by accounting for the relative enthalpic and entropic contributions to the bonding preferences. We show that the entire glass structure evolution (both short- and intermediate-range) can be predicted based on experimental structural information for only a few glass compositions. We then show that the developed structural model can be combined with a previously established TCT model to predict the compositional evolution of the glass transition temperature. This work thus opens a new avenue for the computational design of glasses with tailored properties.

Modifier clustering and avoidance principle in borosilicate glasses: A molecular dynamics study

Oxide glasses are typically described as having a random, disordered skeleton of network-forming polyhedra that are depolymerized by network-modifying cations. However, the existence of local heterogeneity or clustering within the network-forming and network-modifying species remains unclear. Here, based on molecular dynamics simulations, we investigate the atomic structure of a series of borosilicate glasses. We show that the network-modifying cations exhibit some level of clustering that depends on composition-in agreement with Greaves' modified random network model. In addition, we demonstrate the existence of some mutual avoidance among network-forming atoms, which echoes the Loewenstein avoidance principle typically observed in aluminosilicate phases. Importantly, we demonstrate that the degree of heterogeneity in the spatial distribution of the network modifiers is controlled by the level of ordering in the interconnectivity of the network formers. Specifically, the mutual avoidance of network formers is found to decrease the propensity for modifier clustering.

Prediction of the Glass Transition Temperatures of Zeolitic Imidazolate Glasses through Topological Constraint Theory

A topological constraint model is developed to predict the compositional scaling of glass transition temperature ( T_g) in a metal-organic framework glass, a_gZIF-62 [Zn(Im_{2- x}bIm _x)]. A hierarchy of bond constraints is established using a combination of experimental results and molecular dynamic simulations with ReaxFF. The model can explain the topological origin of T_g as a function of the benzimidazolate concentration with an error of 3.5 K. The model is further extended to account for the effect of 5-methylbenzimidazolate, enabling calculation of a ternary diagram of T_g with a mixture of three organic ligands in an as-yet unsynthesized, hypothetical framework. We show that topological constraint theory is an effective tool for understanding the properties of metal-organic framework glasses.

Structural Compromise between High Hardness and Crack Resistance in Aluminoborate Glasses

Alkali aluminoborate glasses have recently been shown to exhibit a high threshold for indentation cracking compared to other bulk oxide glasses. However, to enable the use of these materials in engineering applications, there is a need to improve their hardness by tuning the chemical composition. In this study, we substitute alkaline earth for alkali network-modifying species at fixed aluminoborate base glass composition and correlate it with changes in the structure, mechanical properties, and densification behavior. We find that the increase in field strength (i.e., the charge-to-size ratio) achieved by substituting alkaline earth oxide from BaO to MgO manifests itself in a monotonic increase in several properties, such as atomic packing density, glass-transition temperature, densification ability, indentation hardness, and crack resistance. Although the use of alkaline earth oxides as modifier enables higher hardness values (increasing from 2.0 GPa for Cs to 5.8 GPa for Mg), their crack resistance is generally lower than that of the corresponding alkali aluminoborate glasses. We discuss the origin of this compromise between hardness and crack resistance in terms of the ability of the glass networks to undergo structural transformations and self-adapt under stress. We show that the extent of volume densification scales linearly with the number of pressure-induced coordination number changes of B and Al.

Revealing the Effect of Irradiation on Cement Hydrates: Evidence of a Topological Self-Organization

Despite the crucial role of concrete in the construction of nuclear power plants, the effects of radiation exposure (i.e., in the form of neutrons) on the calcium-silicate-hydrate (C-S-H, i.e., the glue of concrete) remain largely unknown. Using molecular dynamics simulations, we systematically investigate the effects of irradiation on the structure of C-S-H across a range of compositions. Expectedly, although C-S-H is more resistant to irradiation than typical crystalline silicates, such as quartz, we observe that radiation exposure affects C-S-H's structural order, silicate mean chain length, and the amount of molecular water that is present in the atomic network. By topological analysis, we show that these "structural effects" arise from a self-organization of the atomic network of C-S-H upon irradiation. This topological self-organization is driven by the (initial) presence of atomic eigenstress in the C-S-H network and is facilitated by the presence of water in the network. Overall, we show that C-S-H exhibits an optimal resistance to radiation damage when its atomic network is isostatic (at Ca/Si = 1.5). Such an improved understanding of the response of C-S-H to irradiation can pave the way to the design of durable concrete for radiation applications.

Assessing the network connectivity of modifier ions in metaphosphate glass melts: A dynamic light scattering study of Na-Zn mixtures

Photon correlation spectroscopy conducted on polymeric metaphosphate melts [NaPO₃]_1-y[Zn(PO₃)₂]_y shows a systematic decrease in glass fragility as the more strongly bonding Zn cation replaces the more weakly bonding Na cation as a crosslinking agent between PO₃ chains. This decrease is similar to that observed previously in Na-Al melts and the decrease in fragility for both systems is shown to be fully consistent with a recently reported universal pattern of fragility in network forming glasses as a function of network connectivity. Unique to the Na-Zn system is the appearance of an ultraslow relaxation in the dynamic structure factor (slower than the viscoelastic decay) that is not present in either Na-Al or Na-Li metaphosphate mixtures. This relaxation appears to originate from the diffusion of the Zn cation within the melt which is partially coupled to the oxide network. Taken together, these results underscore the need to distinguish between network-forming cations of high ionic bond strength that contribute to the connectivity of the oxide network and those of lower bond strength that do not contribute.

Modifier cation effects on (29)Si nuclear shielding anisotropies in silicate glasses

We have examined variations in the (29)Si nuclear shielding tensor parameters of SiO4 tetrahedra in a series of seven alkali and alkaline earth silicate glass compositions, Cs2O·4.81 SiO2, Rb2O·3.96 SiO2, Rb2O·2.25 SiO2, K2O·4.48 SiO2, Na2O·4.74 SiO2, BaO·2.64 SiO2, and SrO·2.36 SiO2, using natural abundance (29)Si two-dimensional magic-angle flipping (MAF) experiments. Our analyses of these 2D spectra reveal a linear dependence of the (29)Si nuclear shielding anisotropy of Q((3)) sites on the Si-non-bridging oxygen bond length, which in turn depends on the cation potential and coordination of modifier cations to the non-bridging oxygen. We also demonstrate how a combination of Cu(2+) as a paramagnetic dopant combined with echo train acquisition can reduce the total experiment time of (29)Si 2D NMR measurements by two orders of magnitude, enabling higher throughput 2D NMR studies of glass structure.

Relaxation and physical aging in network glasses: a review

Recent progress in the description of glassy relaxation and aging are reviewed for the wide class of network-forming materials such as GeO2, Ge x Se1-x , silicates (SiO2-Na2O) or borates (B2O3-Li2O), all of which have an important usefulness in domestic, geological or optoelectronic applications. A brief introduction of the glass transition phenomenology is given, together with the salient features that are revealed both from theory and experiments. Standard experimental methods used for the characterization of the slowing down of the dynamics are reviewed. We then discuss the important role played by aspects of network topology and rigidity for the understanding of the relaxation of the glass transition, while also permitting analytical predictions of glass properties from simple and insightful models based on the network structure. We also emphasize the great utility of computer simulations which probe the dynamics at the molecular level, and permit the calculation of various structure-related functions in connection with glassy relaxation and the physics of aging which reveal the non-equilibrium nature of glasses. We discuss the notion of spatial variations of structure which leads to the concept of 'dynamic heterogeneities', and recent results in relation to this important topic for network glasses are also reviewed.

Revealing the role of molecular rigidity on the fragility evolution of glass-forming liquids

If quenched fast enough, a liquid is able to avoid crystallization and will remain in a metastable supercooled state down to the glass transition, with an important increase in viscosity upon further cooling. There are important differences in the way liquids relax as they approach the glass transition, rapid or slow variation in dynamic quantities under moderate temperature changes, and a simple means to quantify such variations is provided by the concept of fragility. Here, we report molecular dynamics simulations of a typical network-forming glass, Ge-Se, and find that the relaxation behaviour of the supercooled liquid is strongly correlated to the variation of rigidity with temperature and the spatial distribution of the corresponding topological constraints, which ultimately connect to the fragility minima. This permits extending the fragility concept to aspects of topology/rigidity, and to the degree of homogeneity of the atomic-scale interactions for a variety of structural glasses.

Ultrahigh-Temperature Regeneration of Long Period Gratings (LPGs) in Boron-Codoped Germanosilicate Optical Fibre

The regeneration of UV-written long period gratings (LPG) in boron-codoped germanosilicate "W" fibre is demonstrated and studied. They survive temperatures over 1000 °C. Compared with regenerated FBGs fabricated in the same type of fibre, the evolution curves of LPGs during regeneration and post-annealing reveal even more detail of glass relaxation. Piece-wise temperature dependence is observed, indicating the onset of a phase transition of glass in the core and inner cladding at ~500 °C and ~250 °C, and the melting of inner cladding between 860 °C and 900 °C. An asymmetric spectral response with increasing and decreasing annealing temperature points to the complex process dependent material system response. Resonant wavelength tuning by adjusting the dwell temperature at which regeneration is undertaken is demonstrated, showing a shorter resonant wavelength and shorter time for stabilisation with higher dwell temperatures. All the regenerated LPGs are nearly strain-insensitive and cannot be tuned by applying loads during annealing as done for regenerated FBGs.

Comment on "A model for phosphate glass topology considering the modifying ion sub-network" [J. Chem. Phys. 140, 154501 (2014)]

In a recent paper, Hermansen, Mauro, and Yue [J. Chem. Phys. 140, 154501 (2014)] applied the temperature-dependent constraint theory to model both the glass transition temperature, Tg, and fragility, m, of a series of binary alkali phosphate glasses of the form R2OxP2O5 1-x, where R represents an alkali species. Key to their success seems to be the retention of linear constraints between the alkali ion (R(+)) and the non-bridging oxygens near Tg, which allows the model to mimic a supposed minimum for both Tg(x) and m(x) located near x = 0.2. However, the authors have overlooked several recent studies that clearly show there is no minimum in m(x). We argue that the retention of the alkali ion constraints at these temperatures is unjustified and question whether the model calculations can be revised to meet the actual experimental data. We also discuss alternative interpretations for the fragility based on two-state thermodynamics that can accurately account for its compositional dependence.

Composition-structure-properties relationship of strontium borate glasses for medical applications

We have synthesized TiO2 doped strontium borate glasses, 70B2O3-(30-x)SrO-xTiO2 and 70B2 O3 -20SrO(10-x)Na2 O-xTiO2 . The composition dependence of glass structure, density, thermal properties, durability, and cytotoxicity of degradation products was studied. Digesting the glass in mineral acid and detecting the concentrations of various ions using an ICP provided the actual compositions that were 5-8% deviated from the theoretical values. The structure was investigated by means of (11)B magic angle spinning (MAS) NMR spectroscopy. DSC analyses provided the thermal properties and the degradation rates were measured by measuring the weight loss of glass disc-samples in phosphate buffered saline at 37°C in vitro. Finally, the MTT assay was used to analyze the cytotoxicity of the degradation products. The structural analysis revealed that replacing TiO2 for SrO or Na2 O increased the BO3/BO4 ratio suggesting the network-forming role of TiO2 . Thermal properties, density, and degradation rates also followed the structural changes. Varying SrO content predominantly controlled the degradation rates, which in turn controlled the ion release kinetics. A reasonable control (2-25% mass loss in 21 days) over mass loss was achieved in current study. Even though, very high concentrations (up to 5500 ppm B, and 1200 ppm Sr) of ions were released from the ternary glass compositions that saturated the degradation media in 7 days, the degradation products from ternary glass system was found noncytotoxic. However, quaternary glasses demonstrated negative affect on cell viability due to very high (7000 ppm) Na ion concentration. All the glasses investigated in current study are deemed fast degrading with further control over degradation rates, release kinetics desirable.

Topological principles of borosilicate glass chemistry

Borosilicate glasses display a rich complexity of chemical behavior depending on the details of their composition and thermal history. Noted for their high chemical durability and thermal shock resistance, borosilicate glasses have found a variety of important uses from common household and laboratory glassware to high-tech applications such as liquid crystal displays. In this paper, we investigate the topological principles of borosilicate glass chemistry covering the extremes from pure borate to pure silicate end members. Based on NMR measurements, we present a two-state statistical mechanical model of boron speciation in which addition of network modifiers leads to a competition between the formation of nonbridging oxygen and the conversion of boron from trigonal to tetrahedral configuration. Using this model, we derive a detailed topological representation of alkali-alkaline earth-borosilicate glasses that enables the accurate prediction of properties such as glass transition temperature, liquid fragility, and hardness. The modeling approach enables an understanding of the microscopic mechanisms governing macroscopic properties. The implications of the glass topology are discussed in terms of both the temperature and thermal history dependence of the atomic bond constraints and the influence on relaxation behavior. We also observe a nonlinear evolution of the jump in isobaric heat capacity at the glass transition when substituting SiO(2) for B(2)O(3), which can be accurately predicted using a combined topological and thermodynamic modeling approach.