We provide an overview of the field of rigidity theory applied at the atomic scale. This theoretical approach, initially designed for macroscopic structures such as bridges or buildings, has gained renewed interest in the past few years thanks to new methodological developments and to attractive applications in a variety of materials, such as scratch-resistant glassy sheets for mobile phones, phase-change memory, tough cement, dielectrics, and photonic devices. In parallel, basic phenomena associated with the onset of rigidity have been discovered, which have challenged our current understanding of the structural modification induced by changes in composition. This has led to the identification of “smart” glasses with multiple functionalities and superior mechanical performances. Topological prediction and engineering of physical properties are also enabling intelligent design of new disordered materials.

The nature of glass transitions in chalcogenides and modified oxides depends on the network mean coordination number $\langle r\rangle$. These display systematic trends when spanning across the three topological phases: flexible, intermediate, and stressed-rigid. Trends in the glass-transition temperature Tg($\langle r\rangle$) show a monotonic increase with $\langle r\rangle$, but the nonreversing enthalpy of relaxation at Tg, ΔHnr($\langle r\rangle$), shows a deep- and square-well-like minimum with the walls representing the rigidity and stress transitions with increasing $\langle r\rangle$, respectively. In the well, the ΔHnr($\langle r\rangle$) term remains minuscule (∼0) corresponding to the isostatically rigid intermediate phase (IP). The melt fragility index (m) shows rather low values, m($\langle r\rangle$) < 20 for IP compositions, but increases outside the IP. Glass compositions in the IP show absence of network stress, form compacted networks, possess thermally reversing glass transitions, and display high glass-forming tendency—functionalities that have attracted widespread interest in understanding the physics of glasses and applications of the new IP formed.

The properties and functionalities of inorganic glasses can be tuned by adjusting their chemical composition and, in turn, their atomic-scale structure. However, accurate prediction of glass properties from composition has traditionally been impossible. Recent progress in temperature-dependent constraint theory paves the way for the design of new multicomponent glasses with tailored properties. Atoms in network glasses are constrained by their chemical bonds and bond angles, and the strength of these constraints depends on the local topology and the chemical nature of the elements. By counting the number of constraints around both network-forming and network-modifying atoms as a function of both composition and temperature, it is possible to make quantitative connections among composition, structure, and certain macroscopic properties. Here, we review recent developments in glass-structure determination and modeling. We then demonstrate how the structural information is used as input for topological predictions of glass properties such as viscosity and hardness. These predictions enable the design of novel industrial glasses with desired properties and manufacturing attributes.

The development of doped photonic glass is of fundamental importance for various applications, including telecommunication, lasers, and photovoltaics. Despite the great advances in doping techniques, a long-standing barrier remains concerning how to gain better control over the properties of active dopants in disordered systems. Here, we provide a brief overview of recent progress on the engineering of the chemical environment and chemical state of dopants in glass by tuning the topological features, including sublattices and packing manner of the network. The methods allow us to finely tune the chemical state of active dopants over a wide range of length scales, from dispersed ions to aggregated clusters to nanoparticles, and also offer new opportunities to engineer the local crystal field around active dopants. This inherent structure-based strategy leads to intriguing optical phenomena such as tunable luminescence and notable enhancements in radiative transition probability.

We explore some aspects of the optimization of amorphous semiconductors as well as low- and high-dielectric-constant (low-/high-k) materials viewed purely from the perspective of percolation and topological constraint theories. We specifically illustrate how percolation, constraint theory, and mean network coordination, 〈r〉, play underlying roles in determining the electrical and mechanical properties of amorphous semiconducting and dielectric materials as well as interfaces that are important for modern micro-/nanoelectronic devices.

Rigidity theory is an extraordinary tool to understand glasses. This article demonstrates how this model can help in understanding the link between structure, dynamics, and subtler properties such as drift and aging, in particular, in phase-change materials (PCMs). First, a map of flexible/rigid regions in the Ge-(Sb)-Te system is drawn on the basis of atomistic structures modeled either by ab initio or reverse Monte Carlo techniques. A clear link between the flexible/rigid nature of the glass and its aging behavior is shown through resistivity drift as a function of composition measurements in amorphous GexTe100–x. In the particular case of amorphous GeTe, application of rigidity theory indicates that the average number of mechanical constraints decreases during aging, making the glass less stressed-rigid. Finally, the stability of PCMs also depends on the topology of the materials. The increasing number of constraints in GeTe when doped with C or N results in increased stability of the PCM.

Topological constraint theory is a convenient theoretical framework to predict structure–property relationships in glasses and identify optimal compositions featuring targeted macroscopic properties. Although introduced for chalcogenide glasses, molecular rigidity concepts have since been applied with great success to new families of materials, such as silicate glasses, phase-change materials, and proteins. Here, we review recent developments in the extension of rigidity theory to concrete, which is by far the most heavily manufactured material in the world. By capturing the important atomic topology while filtering out less relevant structural details of calcium–silicate–hydrate, the binding phase of concrete, topological constraint theory was used to nanoengineer concrete from the atomic scale by predicting the compositional dependence of hardness, toughness, and creep. As such, rigidity concepts represent a promising tool to accelerate the discovery of new materials with tailored properties.

Historical pipe organs offer rich insights into the relationships between materials and music in the past, and they represent a laboratory for contemporary materials science. Recent cross-disciplinary research has explored problems of conservation and corrosion in old organ pipes. The ability of some notable European Baroque organs to produce sound is threatened by atmospheric corrosion of their lead-tin alloy pipes. Organic acids emitted from the wood of organ cases are corrosive agents for lead-rich pipes. Laboratory exposure experiments were used to study the roles of humidity and alloy composition in the susceptibility to organic acid attack. The rates of growth, as well as the compositions and morphologies of the corrosion products were studied using gravimetry, x-ray diffraction, and scanning electron microscopy of surfaces and cross sections. This interdisciplinary project provides one model for the interplay of scientific and humanities research in addressing materials problems in cultural heritage.