Topological Constraint Theory Research Articles

Understanding the molecular origin of aging in the three topological phases of network glasses

ABSTRACT Network glasses composed of chalcogenide and modified oxides display three topological phases: the flexible, intermediate, and stressed-rigid. Modulated-DSC experiments, Raman scattering, and molar volume measurements along with topological constraint theory have shown that glass compositions in the flexible and stressed-rigid phases display glass transitions that age with time. The change of the enthalpy of relaxation (ΔHnr ) at the glass transition temperature (Tg ) steadily evolves with waiting time which can be traced to the presence of Open Degrees of Freedom (ODF). In the isostatically constrained intermediate phase (IP), glasses possess an enthalpy of relaxation which is substantially reduced in aging due to a lack of ODF. IP glasses are composed of self-organised Isostatically Rigid Local Structures (ISRLSs) which have no ODF. The melt fragility index (m) across the three topological phases displays a Gaussian-like global minimum of m = 15 near the IP centre composition, illustrating a super-strong melt behaviour leading to the realisation of the ideal Phillips glass condition where glass forming tendency is globally optimised as demonstrated in the present work. For melt compositions away from the IP centre and into the flexible and stressed-rigid phases, the fragility index steadily increases due to the increased presence of non-ISRLSs. The non-ISRLSs admix with the ISRLSs formed near the mid IP composition, thus promoting the melt networks to relax, age, and diffuse as one goes away from IP centre composition.

Topological understanding of the influence of mixed alkali components on the structure and properties of aluminosilicate glass

Herein, aluminosilicate (AS) glasses exhibit varying trends in Vickers hardness (HV), coefficient of thermal expansion, softening temperature (Ts) and glass transition temperature owing to the mixed alkali effect. To elucidate the mechanism of the mixed alkali effect, the glass structure was characterised using multiple methods. Employing temperature-dependent topological constraint theory, the variations in HV and Ts were investigated, and the constraint strengths of sodium (Na) and lithium (Li) in AS glasses were calculated. The findings indicated that an increase in alkali metal–ion content elevates the proportion of non-bridging oxygen, leading to a progressive decrease in constraint strength and the depolymerisation of the glass structure. For AS glasses with mixed alkali components, as the content of Li2O replacing Na2O increases, the constraint strength of the glass structure below the critical temperature (Tc) gradually rises, while above Tc, it undergoes unconventional changes. These alterations lead to non-linear variations in glass properties.

Application of topological constraint theory to alkali borate and silicate glass systems

Principles of Topological Constraint Theory (TCT) were applied to alkali borate and silicate glass systems using intermediate range structural models over wide compositional ranges. The structural model for lithium borate was derived from the Feller, Dell, and Bray model [1] and extended to the terminal composition at R=3 where R is the molar ratio of lithium oxide to borate. The sodium borate structural model was built using both NMR [2] and Raman [3] data, and also included carbonate retention in the glass [4]. This model was extended to R=3 similarly to the lithium borate system. The silicate system models were created from 29Si NMR data [5] and also incorporated carbonate retention where necessary [6].Constraint models considered the effect of intermediate range structures on the system, and also incorporated the effect of “loose” alkali which is not directly associated with a non-bridging oxygen. Constraint models of the alkali borate, silicate, and borosilicate systems were then used to predict properties such as glass transition temperature and fragility.

Development of physics-based compositional parameters for predicting the reactivity of amorphous aluminosilicates in alkaline environments

The reactivity of amorphous aluminosilicates in alkaline environments is important for many applications, including blended Portland cements and alkali-activated materials (AAMs). Here, two physics-based compositional parameters are derived to describe the relative reactivity of CaO-Al2O3-SiO2 and CaO-MgO-Al2O3-SiO2 glasses in alkaline environments: (i) a modified average metal oxide dissociation energy (AMODE) parameter developed from molecular dynamics simulations; and (ii) a topology constraint parameter derived from topological constraint theory. Both parameters are seen to generally outperform existing compositional parameters from the literature for a wide range of aluminosilicate glasses. Given that both the modified AMODE and topology constraint parameters can be calculated directly from chemical compositions, this study represents a major step forward in connecting aluminosilicate glass compositions with their reactivity in alkaline environments. The limitations of these compositional parameters, including their inability to capture the impact of Ca versus Mg on glass reactivity, have also been discussed.

Study of correlations between glass-transition temperature and local structure of Ge-As-Se, Ge-As-Se-S chalcogenide glasses

ABSTRACT The local structure and glass transition of Ge-As-Se, Ge-As-Se-Schalcogenide glasses have been studied by X-ray diffraction and differential scanning calorimetry. By applying the theory of topological constraints and considering chemically ordered network models, it has been determined that Ge10As20S10Se60 (average coordination number = 2.4), Ge25As10S25Se40 ( = 2.6) are the compositions associated with the more stable glasses. This result is related to the larger differences between the glass transition (Tg ) and crystallization-transition (Tcr ) temperatures (ΔTg-cr ∼ 38 and 43 K) at these compositions. Relatively high values of short-range (d∼5.7–6.34 Å) and medium-range (L∼26.59–33.74 Å) order parameters of the local structure in the glass compositions satisfying the mentioned conditions affect the glass-transition temperature (Tg ) and cause its value to increase (Tg ∼589–689 K). As a result of comparative analyses of X-ray diffraction and differential scanning calorimetry curves it has been determined that there is a correlation between the glass-transition temperature (Tg ) with the short range (d) and medium range order (L) parameters of the local structure.

Room temperature plasticity in amorphous SiO2 and amorphous Al[formula omitted]O[formula omitted]: A computational and topological study

Requirements for room temperature plasticity in oxides glasses have been only recently established. While atomistic mechanisms of this type of plasticity have been reported, it remains challenging to translate this knowledge between different structures and predict what other oxide glasses can be ductile and by which principle. Here we show that a coarse-grained analysis at the polyhedral level gives valuable information to accompany the atomistic characterization of plasticity, and we propose the analysis of polyhedral neighbor change events (PNCE) as a tool to allow comparison of the room temperature plasticity in various oxide glasses. Classical atomistic simulations with around 1 million atoms provided primitive data for coarse-grained analysis. Based on the PNCE analysis, the edge-sharing polyhedra are found to be up to 2 orders of magnitude more active in enabling plasticity, and combined with the occurrence of edge-sharing polyhedra, is shown to explain the brittle to ductile transition in a-SiO2 and the intrinsically high ductility of a-Al2O3. Finally, the coarse-grained analysis enables the benefit of using additional topological constraint theory analysis to yield more in-depth information regarding the ductile features of each glass structure. Quantitative comparison between amorphous Al2O3 and SiO2 shows a consistent trend between the materials and shows that the approach can be extended to the designing of other damage tolerant oxide glass materials.

The Crystallization of Disordered Materials under Shock Is Governed by Their Network Topology.

When the shock load is applied, materials experience incredibly high temperature and pressure conditions on picosecond timescales, usually accompanied by remarkable physical or chemical phenomena. Understanding the underlying physics that governs the kinetics of shocked materials is of great importance for both physics and materials science. Here, combining experiment and large-scale molecular dynamics simulation, the ultrafast nanoscale crystal nucleation process in shocked soda-lime silicate glass is investigated. By adopting topological constraints theory, this study finds that the propensity of nucleation is governed by the connectivity of the atomic network. The densification of local networks, which appears once the crystal starts to grow, results in the underconstrained shell around the crystal and prevents further crystallization. These results shed light on the nanoscale crystallization mechanism of shocked materials from the viewpoint of topological constraint theory.

Glass transition, topology, and elastic models of Se‐based glasses

AbstractFeatures intrinsic to disorder and network aspects are ubiquitous in structural glasses. Among this important class of materials, chalcogenide glasses are special—they are built of short‐range covalent forces, making them simpler than silicate glasses that possess mixed ionic and covalent forces. Selenium‐based glasses also display complex elastic phase transitions that have been described from various models, including mean‐field approaches to molecular simulations. These point to the presence of two sharply defined elastic phase transitions, a rigidity and stress transition that are non‐mean‐field in character, and separate the three distinct topological phases of flexible, isostatically rigid, and stressed‐rigid. This article reviews the physics of these glassy networks. The elastic phases and glass transition temperature are explained on a molecular level in terms of topological constraint theory (TCT), connectivity, and the open degrees of freedom. The broader aspects of TCT in relation to phase change materials, high‐k dielectrics, and cements are also commented upon.

The brittle-to-ductile transition in aluminosilicate glasses is driven by topological and dynamical heterogeneity

Amorphous materials can exhibit varying degrees of nanoscale ductility depending on their atomic structure. Despite its critical importance for applications, the physical origin that controls ductility remains largely unknown. Here, by using molecular dynamics simulations, we investigate the ductile-to-brittle transition of oxide glasses as a function of the connectivity of the atomic network. Interestingly, based on topological constraint theory, we show that the structural origin of the ductile-to-brittle transition is the rigidity transition caused by the percolation of stressed-rigid atomic clusters. Our further analysis of four-point correlation functions reveals that, similar to the case of supercooled liquids, the plastic dynamics of oxide glasses at room temperature are strongly correlated and spatially heterogeneous. Surprisingly, the dynamical length scale of plastic events significantly decreases when the stressed-rigid cluster percolates, resulting in a narrower transient plastic rearrangement region. These results provide physical insights into the relationship between the topological features of atomic structure, fracture behavior, and stress-induced dynamical heterogeneity of glasses.

Predicting initial dissolution rates using structural features from molecular dynamics simulations

AbstractPredicting the chemical durability of glass materials is important for various applications from daily life such as cell phone screens and kitchenware to advanced technologies such as nuclear waste disposal and biomedicine. In this work, we explored the prediction of the initial glass dissolution rates using structural features from molecular dynamics (MD) simulations for a series of glass compositions (total 28), including ZrO2‐ and V2O5‐containing boroaluminosilicate, borosilicate, and aluminosilicate glasses. The initial dissolution rates (r0) measured experimentally at 90°C with varying solution conditions were correlated with structural features (e.g., polyhedral linkages and non‐bridging oxygen species) obtained from MD simulations, either from this study or from literature. As hydrolysis of the glass network through breaking of the network former linkages (e.g., Si–O–Si, Si–O–Al, etc.) is a critical step of network glass dissolution, the statistics of these linkages obtained from MD were also correlated to r0 through linear regression, where the coefficients of determination (R2) and root mean square error are found to be 0.949 and 0.681, respectively. This model was compared and discussed with existing models developed by various approaches, including machine learning, the kinetic rate equation, topological constraint theory, and other descriptors from MD simulations. The discussion provides insights on future model improvements to predict glass dissolution. In addition, as the effect of V2O5 on glass dissolution was not well studied comparing to ZrO2, the impact of V2O5 was emphasized in this paper, suggesting that the impact is not the same across all glass compositions and test conditions.

Structure--property relationship and chemical durability of magnesium-containing borosilicate glasses with insight from topological constraints

The initial dissolution rate of a series of multicomponent glasses is studied in order to discuss the influence of increasing magnesium content in the glass on this alteration regime and to highlight differences in behavior between calcium- and magnesium-bearing glasses. The application of MD-based topological constraint theory (TCT) is confronted to glass transition temperature (Tg) and initial dissolution rate (r0) on a glass series containing the main oxides of a French nuclear glass (AVM). In addition, a comparison between a reference magnesium-containing nuclear waste glass, AVMV4 and a proposed derived simplified composition N19M8 is performed regarding r0 values. Results indicate a similar behavior in this alteration regime for the two glasses, suggesting that this simple glass might be a good analogue to the complex one. Substituting calcium for magnesium decreases the initial dissolution rate by a factor two in the series, while an overall increase of magnesium leads to an increased dissolution rate. Analyses performed with TCT suggests that magnesium environment is better defined than calcium or sodium and may behave as an intermediate species. Finally, a correlation between the number of constraints per atom and Tg is established, while the model failed to link structural features to r0.

Evaluating Ovonic Threshold Switching Materials with Topological Constraint Theory.

The physical properties of ovonic threshold switching (OTS) materials are of great interest due to the use of OTS materials as selectors in cross-point array nonvolatile memory systems. Here, we show that the topological constraint theory (TCT) of chalcogenide glasses provides a robust framework to describe the physical properties of sputtered thin film OTS materials and electronic devices. Using the mean coordination number (MCN) of an OTS alloy as a comparative metric, we show that changes in data trends from several measurements are signatures of the transition from a floppy to a rigid glass network as described by TCT. This approach provides a means to optimize OTS selector materials for device applications using film-level measurements.

Topological hardening through oxygen triclusters in calcium aluminosilicate glasses

AbstractMolecular dynamics simulations and topological constraint theory are used to study the impact of oxygen triclusters in the calcium aluminosilicate glass system at ratios of 0.6, 1, 1.5, 2, and 4 [Al2O3]/[CaO]. Negligible percentages (less than ~3%) of five‐coordinated Al structures are found at all ratios. Up to ~27% three‐coordinated oxygens, also known as triclusters, are found at the highest ratio of [Al2O3]/[CaO]. A topological constraint model, which considers additional constraints provided by triclusters, is created to predict the glass transition temperature, hardness, and Young's modulus. The models are used to elucidate the role of triclusters in glass properties. Analysis of topological constraints shows that triclusters can potentially increase the glass hardness within the calcium aluminosilicate system. The results are also compared to oxynitride glasses. Triclusters show the same ability as nitrogen to increase the glass hardness but are less effective at increasing the Young's modulus.

Structural and optical properties of amorphous Si\u2013Ge\u2013Te thin films prepared by combinatorial sputtering

The lack of order in amorphous chalcogenides offers them novel properties but also adds increased challenges in the discovery and design of advanced functional materials. The amorphous compositions in the Si–Ge–Te system are of interest for many applications such as optical data storage, optical sensors and Ovonic threshold switches. But an extended exploration of this system is still missing. In this study, magnetron co-sputtering is used for the combinatorial synthesis of thin film libraries, outside the glass formation domain. Compositional, structural and optical properties are investigated and discussed in the framework of topological constraint theory. The materials in the library are classified as stressed-rigid amorphous networks. The bandgap is heavily influenced by the Te content while the near-IR refractive index dependence on Ge concentration shows a minimum, which could be exploited in applications. A transition from a disordered to a more ordered amorphous network at 60 at% Te, is observed. The thermal stability study shows that the formed crystalline phases are dictated by the concentration of Ge and Te. New amorphous compositions in the Si–Ge–Te system were found and their properties explored, thus enabling an informed and rapid material selection and design for applications.

Search for a possible flexible-to-rigid transition in models of phase change materials

Structural models of the prototypal phase change material Ge-Sb-Te are generated from first-principles molecular dynamics simulations with a particular attention to the ${\mathrm{Ge}}_{x}{\mathrm{Sb}}_{x}{\mathrm{Te}}_{100\ensuremath{-}2x}$ join. Constraint counting algorithms permit us to analyze the obtained amorphous networks within the framework of topological constraint (rigidity) theory. A flexible-to-rigid transition is found at $x\ensuremath{\simeq}8.5$% which satisfies the Maxwell isostatic criterion and is characterized by an important topological disorder with large amounts of mixed geometries and miscoordinations. The angular constraint count furthermore leads to the identification of tetrahedral Ge sites whose population decreases with growing Ge/Sb content and is about 55% for ${\mathrm{Ge}}_{2}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{5}$. Sb sites change from a dominant pyramidal geometry typical of Group V chalcogenides to a defect octahedral one which is reminiscent of the crystalline polymorph of ${\mathrm{Ge}}_{2}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{5}$.

Melt dynamics, nature of glass transition and topological phases of equimolar GexAsxS100−2x ternary glasses

• Flexible, Intermediate and Stressed-Rigid Phases of Ge x As x S 100−2x glasses observed. • Abrupt Rigidity- and Stress- Elastic Phase Transitions observed near x = 9.0% and 16.0%. • Melt Fragility index, m, are< 20 in the Intermediate Phase (IP) but> 20 outside the IP. • Kinetics of melt/glass homogenization slow down as x increases to the IP compositions. • Ge- and As centered Local Structures of Ge x As x S 100−2x glasses deduced from Raman scattering. The Topological Phases (TPs) in specially homogenized equimolar Ge x As x S 100−2x ternary glasses are established here by performing detailed Raman scattering, together with Modulated-DSC and Volumetric measurements over a wide range of compositions, 5%< x < 25%. Our results show the presence of an Intermediate Phase (IP) residing in the 9.0%< x < 16.0% range, with compositions x < 9.0% in the flexible phase, and compositions x > 16% in the stressed-rigid phase. The novel use of ex-situ Raman profiling on the entire batch of compositions indicates very slow dynamics that is tracked with time and composition and reveals the impact of homogenization on physico-chemical properties of glasses. Stressed-Rigid glasses exceeding the chemical threshold composition are all found to be nanoscale phase separated. In the presently synthesized specially homogenized melts/glasses, we observe (i) evidence for the elusive 537 cm −1 Raman active mode of the S = As stretch in quasi-tetrahedral S = As(S 1/2 ) 3 local structure, (ii) a square-well like variation of the non-reversing enthalpy of relaxation ∆H nr (x) at T g displaying the Reversibility window and defining the Intermediate Phase (IP), (ii) a square-well like variation of molar volumes, V m (x) coinciding with the IP composition range defining a Volumetric window, (iii) Melt fragility index, m(x), variation showing a global minimum in the IP compositions with m(x)< 20, and with the fragility index, m(x)> 20 for non-IP compositions, defining a Fragility Anomaly, and finally a variation in the specific heat jump near T g , ∆C p (x), that tracks part of the observed anomalies in m(x) and ∆H nr (x). The location of each of these anomalies/windows coinciding with those of the IP highlights the privileged nature of the window edge compositions that represent respectively rigidity- (x r = 9.0%)- and the stress- (x s = 16.0%) elastic phase transitions determined within the Topological Constraint Theory of glasses.

Thermal conductivity of densified borosilicate glasses

In this work, we study the thermal conductivity of densified soda lime borosilicate glasses with varying B2O3/SiO2 ratio. Densification is induced by hot compression up to 2 GPa at the glass transition temperature. We find that the structural and mechanical properties of the glasses exhibit a similar response to hot compression as other oxide glasses, including increasing density, elastic moduli, and fraction of four-coordinated boron across the full compositional range. Generally, we find that thermal conductivity increases upon densification, but with a pronounced composition dependence, as silica-rich glasses exhibit only a minor increase (~8-10%) while borate-rich glasses exhibit a significant increase (>50%). We rationalize these variations in terms of topological constraint theory by showing a connection between the contribution of propagative vibrational modes to heat transfer and the volumetric constraint density across both as-made and densified samples. These findings thus provide insights into the linkages between structure and thermal conductivity.

Topological origin of phase separation in hydrated gels

HypothesisDepending on their composition, hydrated gels can be homogeneous or phase-separated, which, in turn, affects their dynamical and mechanical properties. However, the nature of the structural features, if any, that govern the propensity for a given gel to phase-separate remains largely unknown. Here, we argue that the propensity for hydrated gels to phase-separate is topological in nature. SimulationsWe employ reactive molecular dynamics simulations to model the early-age precipitation of calcium–alumino–silicate–hydrate (CASH) gels with varying compositions, i.e., (CaO)1.7(Al2O3)x(SiO2)1 –x(H2O)3.7 +x. By adopting topological constraint theory, we investigate the structural origin of phase separation in hydrated gels. FindingsWe report the existence of a homogeneous-to-phase-separated transition, wherein Si-rich (x ≤ 0.10) CASH gels are homogeneous, whereas Al-rich (x > 0.10) CASH gels tend to phase-separate. Furthermore, we demonstrate that this transition is correlated to a topological flexible-to-rigid transition within the atomic network. We reveal that the propensity for topologically-overconstrained gels to phase-separate arises from the existence of some internal stress within their atomic network, which acts as an energy penalty that drives phase separation.

Rigidity theory of glass: Determining the onset temperature of topological constraints by molecular dynamics

Topological constraint theory has been extensively used to describe how the composition and structure of glasses and glass-forming melts control their properties. This approach relies on an accurate enumeration of the topological constraints acting in the atomic network. Such direct enumeration is challenging since constraints can be active or thermally-broken depending on temperature. Here, based on molecular dynamics simulations, we present a generic method aiming to predict the onset temperature below which constraints become active. We illustrate this method by considering the example of a series of binary calcium silicate glasses. We find that inter-polytope angular bond-bending constraints are associated with a lower onset temperature than intra-polytope angular constraints. Based on this, we show that the differing values of these two onset temperatures largely govern the glasses’ fictive temperature.

Lithium ion sites and their contribution to the ionic conductivity of RLi2O-B2O3 glasses with R ≤ 1.85

The ionic conductivity in lithium borate glasses RLi2O-B2O3 is believed to be related to the number of loose lithium ions, calculated using the topological constraint theory, increasing significantly when 0 ≤ R ≤ 0.5 and reaching a plateau when 0.5 ≤ R ≤ 1.0, and increasing once again when R ≥ 1.0. To test this new proposed approach, high content lithium oxide glasses were prepared (up to R = 1.85) without any signs of heterogeneity by using a fast quenching technique. Results show that instead of being related to the number of loose lithium ions, the ionic conductivity is mostly likely related to the different boron species which act as lithium sites, given that the number of non-bridging oxygens increases proportionally to the lithium to boron ratio when R ≥ 0.5, the region where the plateau in electrical properties is observed.