Crystal melting and the glass transition obey the same physical law
The melting of crystals is the process by which an increase in temperature induces the disruption of the ordered crystalline lattice, leading to the disordered structure and highly fluctuating dynamic behavior of liquids. At the glass transition, where an amorphous solid (a glass) turns into a liquid, there is no obvious change in structure, and only the dynamics of the atoms change, going from strongly localized dynamics in space (in the glass state) to the highly fluctuating (diffusive) dynamics in the liquid.
The search for the atomic-scale mechanism of 3D crystal melting has a long history in physics, and famous physicists such as Max Born, Neville Mott and Frederick Lindemann proposed different ways to look at it. I have always had the impression that we still do not understand the melting of 3D crystals, which is a highly complicated cooperative process involving nonlinearly coupled dynamics of a huge number of atoms. This complexity I always found very fascinating.
Comparatively, the melting of 2D solids, mediated by dislocations-unbinding, is much better understood, and the theory that describes it led to the 2017 Nobel prize in physics for Kosterlitz and Thouless.
In recent work with my collaborators in Germany, I discovered that the temperature at which crystals melt and the temperature at which glasses turn into liquid are both proportional to the same quantity: This is the ratio between the fragility of the supercooled liquid (which measures how steeply the viscosity increases upon decreasing the temperature of the liquid) and the thermal expansion coefficient.
The latter measures how much the material dilates upon increasing the temperature, and therefore also how much farther apart two atoms move as temperature is increased. My colleagues and I discovered this fundamental law empirically by putting together experimental data for more than 100 different materials (polymers, atomic and molecular systems, metals, organic compounds).
However, in spite of its simplicity, the origin of this law has remained unexplained, because it could not be derived mathematically from a theory of the underlying atomic motions.
Working with my colleague Konrad Samwer at the University of Goettingen (Germany) during my Gauss visiting professorship there, I eventually managed to mathematically derive this law from the consideration of how atomic motions and interatomic interactions conspire to give the solid material its macroscopic rigidity (encoded in the shear modulus).
By extending the original melting criterion introduced by Born to include atomic motions that are due to lattice defects and thermal fluctuations, and combining this with a model of viscoelastic behavior due to Maxwell, my colleague and I showed that, indeed, both the melting temperature of the crystal and the glass transition temperature are directly proportional to the degree of cooperativity of the atomic dynamics in the liquid (the fragility) and inversely proportional to the thermal expansion of the solid. Our research is in The Journal of Chemical Â鶹ÒùÔºics.
These findings, besides providing a solution to a fundamental problem in physics that dates back more than 100 years, can be used for the materials-by-design of phase-change materials—materials with tunable switching between liquid and solid, which can be useful in many technological applications, from electronics to defense.
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More information: Alessio Zaccone et al, Fragility and thermal expansion control crystal melting and the glass transition, The Journal of Chemical Â鶹ÒùÔºics (2025). . On arXiv:
Bio:
Alessio Zaccone received his Ph.D. from the Department of Chemistry of ETH Zurich in 2010. From 2010 till 2014 he was an Oppenheimer Research Fellow at the Cavendish Laboratory, University of Cambridge.
After being on the faculty of Technical University Munich (2014–2015) and of University of Cambridge (2015–2018), he has been a full professor and chair of theoretical physics in the Department of Â鶹ÒùÔºics at the University of Milano since 2022. Awards include the ETH Silver Medal, the 2020 Gauss Professorship of the Göttingen Academy of Sciences, the Fellowship of Queens' College Cambridge, and an ERC Consolidator grant "Multimech").
Research contributions include the analytical solution to the jamming transition problem (Zaccone & Scossa-Romano PRB 2011), the analytical solution to the random close packing problem in 2d and 3d (Zaccone PRL 2022), the theory of thermally-activated reaction rate processes in shear flows (Zaccone et al PRE 2009), the theory of crystal nucleation under shear flow (Mura & Zaccone PRE 2016), the theoretical prediction of boson-like peaks in the vibrational spectra of crystals (Milkus & Zaccone PRB 2016; Baggioli & Zaccone PRL 2019), the theory of the glass transition in polymers (Zaccone & Terentjev PRL 2013), the theoretical and computational discovery of topological defects in glasses (Baggioli, Kriuchevskyi, Sirk, Zaccone PRL 2021), and the theoretical prediction of superconductivity enhancement effects due to phonon damping (Setty, Baggioli, Zaccone PRB 2020).
Research interests range from the statistical physics of disordered systems (random packings, jamming, glasses and the glass transition, colloids, nonequilibrium thermodynamics) to solid-state physics and superconductivity.
Journal information: Journal of Chemical Â鶹ÒùÔºics , arXiv
