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Persistent homology and persistence diagram a The increasing sequence of spheres for input data (left). The persistence diagram (right) is obtained as a histogram counting the number of rings on the birth-death plane. b, c The appearance and disappearance of a ring for a regular hexagon/triangle. d The pairs of birth and death radii for a hexagon and triangle in the one-dimensional persistence diagram.
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Silicate glasses have evolved from basic structural materials to enabling materials for advanced applications. In this article, we unravel the origin of the mixed alkali effect for alkali silicate 22.7R2O–77.3SiO2 glasses (R = Na and/or K) by identifying the variation in the alkali ion location around the non-bridging oxygen atoms. To do so, we con...
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Single crystals of (K1.52Na0.48)Ca3Si3O10 [idealized (K1.5Na0.5)Ca3Si3O10, di(potassium, sodium) tricalcium trisilicate], were obtained from the crystallization of a glass with a molar oxide ratio of K2O:Na2O:CaO:SiO2 = 1.5:0.5:6:6 that was annealed at 1273 K. The crystal structure can be characterized as a mixed-anion oxidosilicate with isolated...
Citations
... PDF analysis provides the interatomic distances and average coordination numbers [10][11][12] . In several previous investigations, the PDF analysis with structural modeling techniques showed that the coordination number of a cation in a glass was different from that in a crystal [13][14][15][16][17] . For instance, Mg-O species adopted four, five, and six-coordination in silicate glass that contains insufficient network formers 13 ; ZnO x (average x < 4) polyhedra formed the network in Zn-rich binary phosphate glass 15 ; and K ions were trapped in highly coordinated K-O polyhedra, forming a correlated pair arrangement with Na-O polyhedra in silicate glass with the mixed alkali effect 16 . ...
... In several previous investigations, the PDF analysis with structural modeling techniques showed that the coordination number of a cation in a glass was different from that in a crystal [13][14][15][16][17] . For instance, Mg-O species adopted four, five, and six-coordination in silicate glass that contains insufficient network formers 13 ; ZnO x (average x < 4) polyhedra formed the network in Zn-rich binary phosphate glass 15 ; and K ions were trapped in highly coordinated K-O polyhedra, forming a correlated pair arrangement with Na-O polyhedra in silicate glass with the mixed alkali effect 16 . These cation coordination environments are characteristic of glasses and rarely derived solely by EXAFS because the EXAFS analysis of glassy materials is performed using a well-defined crystalline structure as a reference. ...
Understanding the nucleation mechanism in glass is crucial for the development of new glass-ceramic materials. Herein, we report the structure of a commercially important glass-ceramic ZrO2-doped lithium aluminosilicate system during its initial nucleation stage. We conducted an X-ray multiscale analysis, and this analysis was used to observe the structure from the atomic to the nanometer scale by using diffraction, small-angle scattering, absorption, and anomalous scattering techniques. The inherent phase separation between the Zr-rich and Zr-poor regions in the pristine glass was enhanced by thermal treatment without changing the spatial geometry at the nanoscale. Element-specific pair distribution function analysis using anomalous X-ray scattering data showed the formation of a liquid ZrO2-like local structural motif and edge sharing between the ZrOx polyhedra and (Si/Al)O4 tetrahedra during the initial nucleation stage. Furthermore, the local structure of the Zr⁴⁺ ions resembled a cubic or tetragonal ZrO2 crystalline phase and formed after 2 h of annealing the pristine glass. Therefore, the Zr-centric periodic structure formed in the early stage of nucleation was potentially the initial crystal nucleus for the Zr-doped lithium aluminosilicate glass-ceramic.
... In contrast, there is a clear discrepancy in a small peak at around 3-4 Å −1 . This peak is often referred to as the second principal peak [59]. To understand the reason for this difference, larger models comprising approximately 3000 atoms for B100, LB89, LB80, and LB67 glasses were constructed by conducting melt-quench simulations at a cooling rate of 10 K/ps. ...
Machine-learning potentials (MLPs) are advantageous in modeling boron coordination and three-membered rings (3-rings) in borate glasses. In this study, the prominent ability of MLP enables us to study how boron coordination varies during deformation, and the change in microstructure circumvents the overload stress in lithium borate and lithium borosilicate glasses via molecular dynamics simulations. Under uniaxial and triaxial compressive deformations, some of the threefold coordinated boron, B3, atoms were altered to be fourfold coordinated boron (B4) at a strain range beyond elastic deformations. According to the local deformation analysis, a microstructure at around B4 was determined to be rigid, specifically, that around B4 forming a 3-ring exhibited the least flexibility. Conversely, the local region at around B3 and oxygen atoms in nonring structures flexibly deformed following the entire deformation. As a result, nonbridging oxygen located in the vicinity of B3 was found to migrate to form B4 due to compression. Remarkably, most of the boron atoms became B4, and they formed abundant three membered rings in the borate glasses at a certain strain owing to the triaxial compression. Consequently, it is inferred that such a drastic structural variation can be the origin of high damage resistance of borate glasses.
... PH has been applied to study the structure of glasses, whereby the constituting atoms are considered as interconnected nodes, and their positions in metric space are used as the simplicial complex. However, the physical interpretation of PDs of glass ensembles is challenging [11,[20][21][22][23]. In particular, it is not possible to infer the structure of a unique simplex from individual birth-death datapoints due to high degeneracy: a single point in the PD could originate from a multitude of geometrically different structures. ...
... Persistence diagrams were obtained for the full set of atoms as well as for the individual Si and Na sub-sets, for one and two-dimensional simplices (denoted H 1 and H 2 , respectively; the index n = {1; 2} is the Betti number corresponding to the number of individual cycles in topological space). H 2 reflects cavity units as defined in PH graph analyses [20,41], using the atom positions as graph nodes. An example of representing the initial glass structure as such a graph, together with its associated PD, is shown in Fig. 1a. ...
Glasses are typically isotropic, but permanent or transient anisotropy can be induced by tensile strain. We use persistent homology (PH) analysis to explore the topological effects of such anisotropy in SiO 2-Na 2 O glass ensembles with variable alkali concentration as a function of frozen-in anisotropic strain. Statistical information was extracted on ring (H 1) and cavity (H 2) features, whereby anisotropic stretching was found to induce strong variations in the ring topology of the-O-Si-O-backbone, but only minor changes in the overall cavity statistics or in the Na distribution (the Na distribution was found to be governed by H 2 persistence). Tensile fracture led to total recovery of network topology relative to the pristine (isotropic) glass. In revealing such reactions, PH and persistence similarity analysis may help to differentiate purely entropic orientation and irreversible structural alterations leading to glass anisotropy.
... Reliable structures of amorphous materials can be described by reverse Monte Carlo (RMC) modelling based on a combination of experimental datasets, such as X-ray diffraction (XRD) and neutron diffraction, magic angle spinning nuclear magnetic resonance (MAS NMR), and extended XAFS (EXAFS) [32][33][34] . Because the raw data of Ag K-edge EXAFS is not suitable for fitting because of noise of signal due to the low concentration, back-Fourier transformed EXAFS data was used (Fig. S9). ...
Thermodynamically metastable glasses that can contain metastable species are important functional materials. X-ray absorption near-edge structure (XANES) spectroscopy is an effective technique for determining the valence states of cations, especially for the doping element in phosphors. Herein, we first confirm the valence change of silver cations from monovalent to trivalent in aluminophosphate glasses by X-ray irradiation using a combination of Ag L3-edge XANES, electron spin resonance, and simulated XANES spectra based on first-principles calculations. The absorption edge of the experimental and simulated XANES spectra demonstrate the spectral features of Ag(III), confirming that AgO exists as Ag(I)Ag(III)O2. A part of Ag(I) changes to Ag(III) by X-ray irradiation, and the generation of Ag(III) is saturated after high irradiation doses, in good agreement with conventional radiophotoluminescence (RPL) behaviour. The structural modelling based on a combination of quantum beam analysis suggests that the local coordination of Ag cations is similar to that of Ag(III), which is confirmed by density functional theory calculations. This demonstration of Ag(III) in glass overturns the conventional understanding of the RPL mechanism of silver cations, redefining the science of silver-related materials.
... This is called the mixed alkali-mediated bottleneck effect. [32,38] From the viewpoint of energy (Figure 1d), the introduction of mixed alkali ions can increase ΔG bottleneck , which in turn leads to an increase in the Li + migration barrier ΔG. As a result, the difference between ΔG Si/Al→Nb and ΔG Nb→Si/Al becomes small, and the migration tendency of Li + from the Nb-rich region to the Si/Al-rich region is reduced. ...
The rational control of intrinsic defects in materials can significantly enhance their scientific and technological potentials, but it remains a long‐standing challenge in nanocrystal‐in‐glass composites (NGCs). Herein, a defect engineering strategy mediated by the mixed alkali effect is proposed and experimentally demonstrated for NGCs. Interestingly, the hybridization of large alkali ions can effectively increase the barrier of Li⁺ migration and reduce the Li‐related defects in LiNbO3 NGC. As a result, a novel LiNbO3 NGC with greatly reduced Li‐related defects, high crystallinity of over 60%, and excellent optical transmission are successfully fabricated. This unique NGC configuration facilitates efficient transverse second harmonic generation (TSHG) in a broad wavelength region. Based on the above effects, a standard TSHG device is fabricated and implemented to monitor ultrashort optical pulses with duration in the order of ≈10⁻¹³ s over a broad wavelength region, down to 780 nm. The proposed strategy not only provides a new idea for defect engineering in materials science but also has great significance for boosting the practical applications of NGCs in ultrashort optical pulse monitoring.
... PH has been applied to study the structure of glasses, whereby the constituting atoms are considered as interconnected nodes, and their positions in metric space are used as the simplicial complex. However, the physical interpretation of PDs of glass ensembles is challenging [20][21][22][23][24]. In particular, it is not possible to infer the structure of a unique simplex from individual birth-death datapoints due to high degeneracy: a single point in the PD could originate from a multitude of geometrically different structures. ...
... Persistence diagrams were obtained for the full set of atoms as well as for the individual Si and Na sub-sets, for one and twodimensional simplices (denoted H 1 and H 2 , respectively). H 2 reflects cavity units as defined in PH graph analyses [20] [42], using the atom positions as graph nodes. An example of representing the initial glass structure as such a graph, together with its associated PD, is shown in Figure 1a. ...
... However, the analysis omits more complicated behavior, involving more than two structural units, such as the mixed alkali effect. 38) It should be noted that it is not sufficient to simply discuss cation-based compositions because the data should be organized according to the oxygen coordination number of each cation. Although the data presented in this study are very different from those used in various advanced machine learning studies, 1)10) this study provides a foundation for glass studies using data science. ...
Regression analysis was performed on the data of low-melting phosphate glasses extracted from a glass database. The data were categorized based on duplication, and the most commonly used components for each temperature range were extracted. The relationship between metal-oxide-based compositions and cation-based compositions was examined. Even though various compositions were included in the database, it was found that the average and standard deviation values of divalent or tetravalent cations in cation-based compositions were approximately 2/3 of those in oxide-based compositions. Multiple regression analysis suggested that cation-based analysis is more suitable than oxide-based analysis. Predictions using cations are expected to become more important in future structure-driven data analyses of glasses.
... The mixed alkali effect (MAE) refers to the phenomenon where the inclusion of two or more alkali metal ions (such as Na, K, and Li) in a glass composition can lead to an enhancement of the properties of BGs, such as improved thermal stability, electrical conductivity, and mechanical strength [14]. The effect is believed to arise from changes in the glass structure, as a result of the presence of multiple alkali cations and the difference in the atomic sizes and bonding of the ions [87]. The MAE has been extensively studied in various BG systems and has shown to be promising for enhancing the properties of BGs for biomedical applications. ...
Bioactive glasses (BGs) are promising materials for bone regeneration due to their ability to bond with living bone tissue. However, thermal stability and mechanical properties of BGs need improvement for better clinical performance. In this paper, we present an overview of the influence of different ions on the sintering and crystallization of BGs. Specifically, this review focuses on the impact of thermal treatments on the crystallization of 45S5 and other significant BG compositions. Potential applications of these thermally treated BGs, such as scaffolds, BG-based composites, and thermally sprayed coatings, are explored. Moreover, the substitution of ions has been investigated as a method to enhance the thermal properties of BGs. Notably, zinc, potassium, and strontium have been studied extensively and have demonstrated promising effects on both the thermal and the mechanical properties of BGs. However, it is important to note that research on ion inclusion in BGs is still in its early stages, and further investigation is necessary to fully comprehend the effects of different ions on sintering and crystallization. Therefore, future studies should focus on optimizing the ion substitution method to improve the thermal, mechanical, and even biological properties of BGs, thereby enhancing their potential for various biomedical applications.
... These and others have been used to characterize and probe the structures of glasses. More recently, persistent homology has attracted attention as a novel algorithm to analyze glassy topologies based on the vacancy distribution [14][15][16]. In terms of local structural environments, descriptors such as tetrahedral order of SiO 4 [17], Q speciation, and bond order for atoms [18] are used to represent the short-range coordination, while medium-range descriptors are still mostly limited to local strain [19] and potential energy [20,21]. ...
... The spatial periodicity indicates the distance between exchangeable ions, which corresponds to the average site positions of the alkali-metal ions. Previous studies have reported that the distances between alkali-metal ions in glass are 2−4 Å, 44 which suggests that the results of the MD calculation are reasonable. In general, when alkali-metal ions with large atomic numbers and large ionic radii are included in the glass, the distance between the nearestneighbor ions increases, [45][46][47] which was also reproduced in the MD calculations. ...
Oxide glasses are dielectric materials with potential applications in high‐frequency communications; hence, their dielectric properties in the gigahertz to terahertz frequency range should be investigated. In this study, the dielectric properties of silica glass and five single alkali silicate glasses were measured at 0.5–10 THz using terahertz time‐domain spectroscopy and far‐infrared spectroscopic ellipsometry. At 0.5–10 THz, the silica glass exhibited low dielectric dispersion with a low dielectric constant and loss. By contrast, the alkali silicate glasses exhibited high dielectric dispersion, and the dielectric constant and loss were higher than those of the silica glass. The shape of the dielectric dispersion profile depended on the alkali‐metal ions; it was broader for lighter ions such as Li ions and sharper for heavier ions such as Cs ions. The peak dielectric loss shifted toward a lower frequency as the weight of the alkali‐metal ions in the alkali‐silicate glass increased. To understand the dielectric dispersion, the complex permittivity was calculated using molecular dynamics simulations. The theoretical results qualitatively agreed with the experimental data. Ion dynamics analysis revealed that alkali‐metal ions vibrate and migrate under an applied electric field, which affects the dielectric constant and loss of alkali‐silicate glasses at gigahertz to terahertz frequencies. To fabricate filter devices at low temperatures, alkali metals should be added to silicate glass; therefore, a minimum amount of light alkali metals should be used to minimize the dielectric loss of the glass materials while maintaining productivity.
