When do amorphous solids lose their stability? Physicists at the University of Konstanz provide a model – with a box full of building blocks.

Why do avalanches start to slide? And what happens inside the "pile of snow"? If you ask yourself these questions, you are very close to a physical problem. This phenomenon not only occurs on mountain peaks and in snow masses, where it is rather uncontrolled. It is also studied in the laboratory at the microscopic level in materials with a disordered particle structure, for example in glasses, granular materials or foams. Their particles can "slide" in a similar way to avalanches, causing the structure to lose its stability and become deformable – and that even independently of a change in temperature. What happens inside such a shaky structure?

Physicist Matthias Fuchs from the University of Konstanz and his colleagues Florian Vogel and Philipp Baumgärtel are researching these disordered solids. Two years ago, they solved an old puzzle about glass vibrations by revisiting a forgotten theory. "Now we have continued the project to answer the question of when an 'irregular house of cards collapses'. We want to find out when an amorphous solid loses its stability and starts to slide like a pile of sand", says Fuchs. Based on the "Euclidean random matrix" (ERM) models, the researchers uncovered the rules behind this loss of stability and developed a theory to describe – and predict – the process. The observed effects are relevant for producing materials with improved properties, especially for granular systems and foams.

Like a box full of building blocks
Imagine the "inside" of a solid, i.e. its molecular particle structure, like a box full of building blocks. The blocks may be stacked neatly in rows, supporting each other. That is how ordered solids look like. Or the blocks are carelessly thrown into the box, wildly mixed up and with gaps in between – but still wedged into each other, which gives them a certain stability. This is the case in disordered solids.

If you shake the box, the neatly stacked building blocks will not move all that much. The blocks are "firmly in place", stabilize each other and return to their original position after minor vibrations. The messy box, on the other hand, is a different story. It is a jumble of building blocks, with empty spaces between them. This gives the individual blocks more scope to adopt a different position. With enough shaking, more and more of the supporting pillars destabilize until at some point the whole stack of building blocks collapses. The question is: At what threshold does this happen – and what exactly happens inside the box?

A look inside the box
Of course, it is not building blocks the Konstanz physicists are interested in. They want to answer the question of when disordered solids lose their molecular stability. To investigate the phenomenon, Matthias Fuchs and his team do not shake the symbolic "box" from the outside, but generate vibrations inside the particle system. They also ensure that there is no gravity that could destroy the unstable structure, and they check the spatial expansion of "stiff areas". What happens to the molecular structure when more and more of the stabilizing connections break? At what threshold value does the transition from stability to "sliding" occur? How large are the clusters of loose particles that are not attached to a solid structure? What rules can be derived from this?

"Our analyses show that the stability of the system is lost at a point where vibrations at a low frequency close to zero occur. That is where the speed of sound disappears", explains first author Florian Vogel. "The material structure is now malleable: When force is applied, the particles no longer return elastically to their original position, but start to slide. In this loose state, the particles move in clusters of increasing size".

Incidentally, temperature changes play no role in this process. So this project is not about heating a solid until it reaches a liquid state of aggregation. The loss of stability occurs at a constant temperature and is caused by a weakening of the stabilizing connections. The theory and simulations of the Konstanz research teams apply to, for example, molecular solids at a temperature close to absolute zero of -273 degrees Celsius or bulk materials such as sand or soil, where thermal fluctuations are negligible.

Meanwhile the project will continue, in fact, in outer space: The experiment GraSCha (Granular Sound Characterization) will test the theory on the International Space Station (ISS) under zero-gravity conditions in the fall of 2025; it is set up by the German Aerospace Center (DLR) in Cologne.

Collaborative Research Centre 1432
This research project is conducted in the context of the Collaborative Research Centre SFB 1432 "Fluctuations and Nonlinearities in Classical and Quantum Matter beyond Equilibrium" at the University of Konstanz. SFB 1432 explores the dynamics of physical systems far beyond their equilibrium, including quantum fluctuations and ultrafast electron processes, magnetism and nonlinear effects in nanomechanical systems.

Key facts: Original publication: Florian Vogel, Philipp Baumgärtel, and Matthias Fuchs, Self-consistent current response theory of unjamming and vibrational modes in low-temperature amorphous solids, Phys. Rev. X 15, 011030 DOI: https://doi.org/10.1103/PhysRevX.15.011030 Research in the context of the Collaborative Research Centre SFB 1432 "Fluctuations and Nonlinearities in Classical and Quantum Matter beyond Equilibrium" at the University of Konstanz. Professor Matthias Fuchs leads the Theory of Soft Matter research team at the University of Konstanz. He is project leader at SFB 1432. Doctoral researchers Philipp Baumgärtel and Florian Vogel are members of Matthias Fuchs' team.