When you zoom in on a crystal, you will find an ordered array of atoms that are evenly spaced like the windows on the Empire State Building. But when you zoom in on a piece of glass, the picture looks a bit messier, more like a random pile of sand, or maybe be the windows on a Frank Gehry building.
With 30 pages of handwritten calculations, Duke postdoctoral fellow Sho Yaida has laid to rest a 30-year-old mystery about the nature of glass and “disordered” materials at low temperatures. They may in fact be a new state of matter. Credit: Irem Altan
The highly-ordered nature of crystals makes them quite simple to understand mathematically, and Physicists have created theories that capture all types of crystal properties, from how they absorb heat to what takes place when they break
However, the same can’t be said of amorphous, glassy or “disordered” materials such as frozen food, the glass in the windows and vases, and certain plastics. There are no widely accepted theories to describe their physical behavior.
For almost 30 years, Physicists have discussed whether a mysterious phase transition, present in theoretical models of disordered materials, could also exist in real-life glasses. Sho Yaida, a Postdoctoral Fellow at
Duke University, has laid this mystery to rest with the help of some mathematical wizardry borrowed from particle physics as well as dozens of pages of algebraic calculations done by hand.
Yaida’s understandings open up the possibility that some forms of glass could exist in a new state of matter at low temperatures and may influence how they respond to sound, heat and stress, and how and when they break.
We found hints of the transition that we didn’t dare say was evidence of the transition because part of the community said that it could not exist. What Sho shows is that it can exist.
Patrick Charbonneau, Associate Professor of Chemistry, Duke University
Charbonneau said that it may seem mind-boggling because the mathematics behind glasses and other disordered systems is, in fact, much easier to solve by presuming that these materials are present in a hypothetical infinite-dimensional universe. In infinite dimensions, their properties can be easily calculated, much like how the crystal properties can be calculated for three-dimensional universe.
“The question is whether this model has any relevance to the real world.” Charbonneau said. For Researchers who perform these calculations, “the gamble was that, as you change dimension, things change slowly enough that you can see how they morph as you go from an infinite number of dimensions to three,” he said.
One of the features of these infinite dimensional calculations is existence of the “Gardner transition”, a phase transition named after pioneering physicist Elizabeth Gardner, which, if present in glasses, it could considerably change their properties at low temperatures.
But did this phase transition, clearly present in infinite dimensions, can also exist in three? In the 1980s, a group of physicists made mathematical calculations showing that no, it could not exist. For three decades, the prevailing perspective remained that this transition, although theoretically interesting, was not relevant to the real world.
That is, until new experiments and simulations carried out by Charbonneau and other Researchers started showing hints of it in three-dimensional glasses.
The new drive to look at this is that, when attacking the problem of glass formation, they found a transition very much like the one that appeared in these studies. And in this context it can have significant materials applications.
Patrick Charbonneau , Associate Professor of Chemistry, Duke University
Yaida, who has experience in particle physics, took a second look at the previous mathematical proofs. These calculations did not find a “fixed point” in three dimensions, a requirement for the existence of a phase transition. However, if he took the calculation one more step further, he thought, the answer might change.
One month and 30 pages of calculations later, he had it.
Moments like these are the reason why I do science. It is just a point, but it means a lot to people in this field. It shows that this exotic thing that people found in the seventies and eighties does have a physical relevance to this three-dimensional world.
Sho Yaida, Postdoctoral Fellow, Duke University
After a year of checking and rechecking, plus an additional 60-odd pages of supporting calculations, the results were published in Physical Review Letters on May 26
“The fact that this transition might actually exist in three dimensions means that we can start looking for it seriously,” Charbonneau said. “It affects how sound propagates, how much heat can be absorbed, the transport of information through it. And if you start shearing the glass, how it will yield, how it will break."
“It changes profoundly how we understand amorphous materials in general, whether they be amorphous plastics or piles of sand or window glasses,” he said.
This research was supported by a grant from the Simons Foundation (#454937).