Disordered solids such as glasses are in very high-dimensional rugged energy landscape with metastable minima. Glass ages as time goes by which indicates the glass system moves in the energy landscape as a result of thermal excitation, compression and so forth. Due to the vast number of metastable minima, however, to predict how system evolves neither by theoretical nor computational methods is pretty challenging.

In a study published in Physical Review Letters, XU Ning at University of Science and Technology of China, collaborating with Andrea J. Liu at University of Pennsylvania and Sidney R. Nagel at University of Chicago studied the new properties of glass modeled by a jammed packing of sphere when it approaches an instability, and found that instabilities contribute to both the density of vibrational states and the distribution of energy barriers, which lead to a refined understanding of marginal stability in jammed packings.

Their research focused on the instabilities in zero-temperature where a potential-energy barrier vanishes along some direction in configurational space to simplify this problem. They chose the easiest situation zero-temperature jammed sphere packing as their object.

Jammed packings are packings where the particles are packed tightly and cannot move freely due to the impenetrability constraints. The researchers first simulated the scaling of the lowest vibrational mode frequency and barrier height as the system is compressed or sheared towards the stress. The simulation is accurately in line with theoretical predictions named as fold instabilities.

Based on the distribution functions, they further studied density of states and energy barriers. It turned out that both compression and shear instabilities give rise to a cube of frequency contribution to the density.

They revealed that a finite-sized jammed solid is nearly marginally stable with respect to compression or shear and becomes marginally stable in the thermodynamic limit. In that limit an infinitesimal increase in either stress will lead to an instability and the vanishing of a mode frequency.

One interesting conclusion was that the nature of the ground states in jammed systems has universal anharmonic as well as harmonic properties. Harmonic properties such as the elastic moduli and density of vibrational states are universal in jammed packings of particles with repulsive, finite-ranged potentials and the existence of universal anharmonic features has been hinted at in jammed systems.

The anharmonic features studied here, however, are likely to be even more broadly universal because they originate from the scaling of the fold instability. This may provide the classical interpretation of abnormal heat capacity of glass at low temperature.

This work was supported by the National Natural Science Foundation of China.

The displacement field of two-dimensional Jammed Solid under compression (Left) and shear (Right) (Image by XU Ning's team)