The statistics of fluctuations in amorphous materials

There may be a general physical law behind the way many materials change irreversibly their own shape when pressed or pulled. This is what a group of scientists from the Center for Complexity and Biosystem (CC&B) of the University of Milan may have discovered while studying the deformation processes in amorphous solid materials.

The structure of most solids is crystalline, which means that their atoms or molecules are organised in a regular and periodic manner. On the other hand, liquids have a completely random structure. There is also an intermediate case, represented by amorphous solids: they lack the crystalline structure of many solids but, differently from liquids, their randomly arranged atoms cannot flow easily. The most famous examples of amorphous solid is glass, but the categories also includes gels, thin films and many polymers, some of which may consist of both crystalline and amorphous regions.

When an object is exposed to external forces, something happens within its atomic structure: a series of micro-events that eventually results in the deformation, or even the wreckage, of the object itself. Material scientists know this, and they also know that different materials deform in different ways. “There are two kinds of deformation, plastic and elastic”, explains Stefano Zapperi, professor of theoretical physics at the University of Milan, head of the CC&B and coordinator of the research, just published on Nature Communication. “A deformation is plastic when the shape of a material changes in an irreversible way but without breaking. Conversely, when a material can revert to the initial state, its deformation is called elastic. For this work, we chose to focus on plasticity in disordered solids”.

In 2011, Zapperi obtained an Advanced Grant from the European Research Council to conduct research on these topics, with a project called SIZEFFECTS. Within this project, he and his colleagues developed a computer model that mimics the deformation of an amorphous material following the exposure to different kinds of external forces, like tension and bending, with different intensities and directions.

“Our aim was to compare the material response at the microscopic scale to its deformation behaviour at bigger scale”, says Zapperi, “and to analyse this relationship from a statistical point of view”.

They measured how the atoms moved, how the structure changed and what patterns resulted from the different kinds of stress applied. All their findings were consistent with previous experimental studies and showed movements that occur as microscopic avalanches of atoms. Finally, they studied the distribution of these micro-events with a statistical approach and what they found is of great importance: regardless of the initial differences and the experimental conditions, all the deformation patterns shared a common statistical distribution.

“Our findings provide compelling evidence for generic dynamics of the statistics of fluctuations. Clearly, there is some sort of universality behind all these plastic deformation processes in amorphous materials, differently from previous explanations”, concludes Zapperi. “It is not different from what happens in earthquakes, where the sum of small and large events eventually results in the motion of a geological fault. We believe that our results might be of great help for future applications like materials engineering and design, especially for the production of metallic glasses”.

Universal features of amorphous plasticity
Zoe Budrikis, David Fernandez Castellanos, Stefan Sandfeld, Michael Zaiser & Stefano Zapperi
Nature Communications 8, Article number: 15928 (2017)

published on 7/4/2017