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A universal law for glassy matter

Glass transition

In a paper published in the journal "Nature Physics", a team of researchers including Alessio Zaccone of our Department, reported on the discovery of an unexpected universal relation between the coefficient of thermal expansion and the glass transition temperature in systems that undergo the transition from liquid state to solid glass.

Matter in the vitreous or glassy state represents a fascinating mystery for chemists and physicists, because glasses are solid materials, in all respects, but in their interior the atoms are arranged in a fully disordered way. This is a feature they share with liquids (from which they originate upon cooling), but which makes them very different from ordinary crystalline solids where the atoms are arranged in an extremely ordered way on the crystal lattice. According to Nobel laureate Phil W. Anderson, the nature of the phase transition from liquid to glass still represents one of the deepest unsolved problems in physics. In particular, it remains an impossible task to quantitatively predict the temperature at which the liquid to glass transition, known as „glass transition temperature“, occurs.

The new study, in which Alessio Zaccone from our Department took part together with German colleagues Alois Loidl and Peter Lunkenheimer from University of Augsburg, Konrad Samwer from University of Göttingen and Birte Riechers from the Bundesanstalt für Materialforschung und -prüfung in Berlin, has unveiled a universal correlation between the glass transition temperature and the thermal expansion coefficient of the glass (the latter quantifies how much the volume of the glass increases upon increasing the temperature). The relationship is valid across more than 200 materials and involves a third physical quantity, known as „fragility“ of the glass, which represents the curvature of the dependency of the liquid viscosity upon temperature, as the temperature is lowered towards the glass transition.
Besides being universal, the new relation discovered in this study is also supported by a theoretical framework: it can be justified and recovered within the atomic model of liquid viscosity referred to in the literature as the Krausser-Samwer-Zaccone (KSZ) model.

A similar relation between melting temperature and thermal expansion coefficient was known for crystalline solids since the 1910’s due to the work of Lindemann at that time.

In that case, however, the inverse proportionality between the two quantities is not mediated by the fragility, contrary to what has now been found for glasses. This fact is quite important because it shows that, in glasses, differently from what happens in crystals, the melting process is not simply due to the amplitude of thermal vibrations of the atoms, which increases with temperature and becomes larger than the lattice constant, but rather represents a much more cooperative process that involves coordinated and strongly correlated motions of a significant number of atoms. Furthermore, the study reveals a surprising correlation between thermal expansion in the solid glass and in the liquid, which also can be interpreted by means of the atomic model.

This discovery may lead to the synthesis of new materials with superior thermo-mechanical properties for various technological applications. The work at La Statale has been financially supported by the ERC Consoloditator Grant „Multimech“ and by funding from the Army Research Office of the USA.

07 February 2023
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