Materials Science: The Search for the Ideal Glass

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Amber | The yellowish material is a glass made from tree resin. This sample, found in the Baltic States, contains prehistoric flies. For physicists, amber offers a unique opportunity to study ancient glass whose structure has reorganized across geologic timescales.

The reason: the molecules on the surface of a substance are much more mobile than those that are covered by several layers. This mobility allows the glass to quickly find an optimal configuration. In 2007, Ediger and his colleagues were able to prove that the glass-like films are denser, more stable and more resistant – and also have a lower configuration entropy than glass, which formed as a result of the slow cooling of a liquid. Experts therefore call the substances obtained in this way »ultra stable«. According to recent measurements, the ultrastable films could have a transition temperature that differs from the mysterious Kauzmann temperature by only a few degrees, and are thus very close to the limit of the ideal glass.

Since 2007, several papers have shown that ultrastable materials are useful for numerous engineering applications. For example, the Oled displays of Samsung smartphones contain some components made of glass synthesized by vapor deposition. In 2017, a team from the University of Barcelona demonstrated that the technology discovered by Ediger increases the brightness and lifespan of Oled screens by more than 15 percent. Their higher performance indicates that the glasses have a better disordered configuration.

Ultra-stable glasses | Thanks to a sophisticated manufacturing technique that deposits molecules onto a substrate, ultra-stable materials exhibit the properties of very slowly cooled glass. Author Ludovic Berthier and his colleagues have developed a numerical simulation based on a Monte Carlo algorithm to model these substances. The latter randomly swaps the position of different molecules in the material. The process makes it possible to quickly calculate various arrangements and the energies involved. The researchers were able to show that the particles on the surface diffuse more easily than those on the inside, resulting in a stable state of equilibrium in the thin films. The three images are results of simulations performed for different temperatures: the lowest on the left, the highest on the right. The redder a ball, the more mobile it is.

Experimentally, it is still difficult to find direct evidence for a phase transition to ideal glass. However, the synthesis of ultrastable amorphous films provides convincing indirect evidence. The glass-like flat structures become liquid again as soon as they are heated. The transition thus resembles that of a heated solid (e.g. ice at plus temperatures). This supports the assumption that the ultra-stable glass phase represents a distinct amorphous state of matter – and not simply a liquid with extremely slow dynamics.

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To be on the safe side, physicists can use another tool: computer-aided simulations. Significant progress has also been made in this area in recent years. The approach has the advantage that each parameter can be perfectly controlled. In addition, one can look at the substances at the atomic level while at the same time examining the macroscopic behavior of the materials.

Ideal glass is a disordered material, devoid of any flaws: the perfect disorder!

By 2016, glass transition simulation techniques were at an impasse. The computing times were so considerable that the achievable cooling rates were around 100 million times faster than in laboratory tests. As a result, the simulated glasses were far less stable than those in classical experiments – which in turn were already far from the ideal glass. This left little hope for the numerical approach.

Simulations provide new clues

But that year the situation changed radically. Back then, at the Université de Montpellier, we introduced a new Monte Carlo algorithm that was based on a certain randomness in its execution. This approach closes the gap between simulations and experiments and makes it possible to examine model glasses on the computer. Even better, by further optimizing the program, we were able to model glasses that are significantly stronger and denser than experimentally produced materials. In doing so, we sometimes save more than twelve orders of magnitude in computing time – with two-dimensional structures it is even 40 orders of magnitude. The glasses produced in the simulation are therefore comparable to the ultra-stable films produced by Ediger’s research group.

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In particular, the numerical progress makes it possible to check whether the molecular field theory is also valid in three dimensions. Since 2016, numerous computer simulations have explored the physical behavior of liquids at temperatures never before computationally accessible. Several studies seem to confirm that the molecular field approach correctly describes three-dimensional model glasses. If the fluids are cooled down to as close as possible to the ideal glass transition, all theoretically predicted properties agree well with the measured values ​​of the simulated systems. Our computer models suggest that configurational entropy vanishes at a glass transition temperature. The transition has the same characteristics as a first-order phase transition—one that is abrupt, like the crystallization of water at zero degrees Celsius.

Defects in ultra-stable glasses

The specific heat of glass

Heat transport is a fundamental material property. In general, it depends on the »specific heat«. A large value for this means that a lot of energy can be stored at the expense of a small temperature increase. Specific heat is directly related to dissipation, where energy is converted into heat and is then no longer available. These effects have technical consequences that are particularly important for quantum computers.

At the beginning of the 20th century, Peter Debye and Albert Einstein formulated a theory of specific heat in periodic crystals. It is based on the quantization of the harmonic excitations of the crystal lattice. At low temperatures of around one Kelvin (about minus 272 degrees Celsius), the specific heat depends on the third power of the temperature.

In glasses, on the other hand, there is a linear relationship. At low temperatures, glass has a larger specific heat than a crystalline solid, suggesting that there are different excitations in glass that are not yet properly understood. In the 1970s, Phil Anderson and his colleagues proposed a model attributing the behavior to localized defects whose quantum behavior would explain the observations.

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Experiments with ultrastable amorphous films by Miguel Ramos from the Universidad Autónoma de Madrid and Frances Hellman from the University of California at Berkeley indicate that the number of such defects decreases in ultrastable glasses. In 2020, the authors of this article, Camille Scalliet and Ludovic Berthier, along with their colleagues, corroborated the results with computational simulations, in which they were able to identify the defects at the molecular level for the first time (red in figure). By systematically varying the stability of the modeled glasses, they were able to observe a drastic decrease in defects with increasingly stable glasses. All of these results suggest that the specific heat in quasi-ideal glasses can become as low as in a perfect crystal. Consequently, the energy dissipation in such materials is much smaller than in ordinary glass.

However, Miguel Ramos’ measurements in geological amber, whose structure has probably stabilized over millions of years, show that the energy dissipation is not significantly lower compared to young amber. It is not yet known why this is so. Thus, Bernstein remains a mystery to be solved.

These recent developments shed new light on the physical properties of glass. In order to examine this, one can, for example, vary the quality of the material produced. And as it turns out, the characteristics of ultra-stable materials (which resemble ideal glass) and those of ordinary glasses are different. We now understand that the thermal, thermodynamic and mechanical properties can be explained by a small cluster of defects. However, the existence of such defects is difficult to prove because the microscopic structure of glass is homogeneous and disordered. Finding the right tools to easily detect them remains difficult. Nevertheless, computer-aided simulations make it clear that glass only deforms in a few places when pressure is applied slowly. The closer you get to the ideal state, the smaller the number of fracture points. This suggests that ideal glass, as predicted by molecular field theory, is a disordered material, devoid of any defects: the perfect disorder!

A team led by physicist Frances Hellman from the University of California at Berkeley demonstrated another advantage of these materials in 2014: those defects that ensure dissipation, i.e. that energy within the glass is converted into heat and is thus “lost”, occur much less frequently in ultra-stable materials than in ordinary chilled glasses. Ramos and his collaborators have achieved similar results. Our computational study published in 2020 supports the experimental results and suggests that there is virtually no dissipation in the ideal glass. Hellman’s team is now working on ultra-stable glass coatings that can be used for the LIGO interferometer. Such materials with greatly reduced dissipation could also solve some of the problems in future quantum computers.

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