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Two new articles by Dr A. Zaccone in Physical Review Letters unveil the mechanisms of solid-liquid phase transitions

last modified Mar 03, 2017 02:28 PM
Dr Alessio Zaccone

Melting is a phase transition by which a solid material turns into liquid. This is something we experience every day when we dissolve a grain of sugar in our cup of tea, or a cube of ice in our drink. Melting has uncountable applications, from the industrial processing of materials to environmental science where ice melting is a key topic of contemporary research. Yet, how much do we actually know about the melting of a crystal or a glass into a liquid?

This is a longstanding hard problem in physics. For example, a satisfactory theory of melting in 2D came only in the 1970s and is due to Kosterlitz and Thouless who were awarded the Nobel prize in physics in 2016 for this achievement. A comparable theory for defect-free crystal melting in 3D is still missing.  Writing in Physical Review Letters, Dr Alessio Zaccone from CEB, together with Prof. David Weitz and collaborators at the Physics Department of Harvard University, presented experiments and theory on the example of colloidal crystals (defect-free) where, unlike in atomic or molecular crystals, individual motions of the building blocks (the colloidal particles forming the crystal) can be tracked precisely using a confocal microscope, see Figure 1 below.

Figure 1. Phase diagram of colloidal crystals as a function of volume fraction as observed with confocal microscopy, in both real space (top panels) and reciprocal space (bottom panels), from

In this work, it has been shown that in many systems (including most elemental metals) where the crystal phase undergoing melting is a bcc (body-centered cubic) crystal, like in the colloidal system considered, the melting transition is a weak first-order transition. This means that while formally being a transition with a discontinuous jump of the density, it shares significant features with second-order phase transitions where large-scale correlated density fluctuations appear, which are power-law correlated in space (hence they have a fractal structure) and also in time. Furthermore, Dr Zaccone and co-workers presented a new theory of melting which takes these large-scale fluctuations into account to describe how the transverse elastic constant (the shear modulus) of the crystal vanishes upon approaching the transition. The previous theory was developed by Max Born in 1939 and predicted a discontinuous vanishing of the shear modulus at melting. The problem here is that the Born melting theory was based on so-called affine elasticity, which assumes that, upon applying a small shear deformation, all the particles move proportionally to the macroscopic deformation. This is certainly true for all perfect crystals with low thermal fluctuations. However, close to melting, the thermal fluctuations are indeed very large, which implies that every particle effectively experiences a locally disordered environment due to the large spatio-temporal fluctuations of the nearest neighbours. Building on Dr Zaccone’s theoretical framework of nonaffine lattice dynamics in disordered solids, a new theory taking the large thermal fluctuations into account has been developed, which matches the experimental data in a parameter-free way (all physical parameters entering the theory were measured experimentally with confocal microscopy), as shown in Figure 2 below.

Figure 2. The shear elastic constant as predicted by the new theory (red solid line) and as measured experimentally (grey circles). The blue squares are points calculated based on the old Born theory. Again taken from

The new theory correctly predicts the smooth continuous vanishing of the shear elastic constant upon approaching the melting point in excellent agreement with experimental data, whereas the old Born theory predicts a discontinuous jump at the transition, which is at odds with the experimental data.

A second article ( has been recently published, also in Phys. Rev. Lett., presenting results of another collaboration led by Dr Alessio Zaccone, this time with experimental collaborators from the Heinrich-Heine University of Duesseldorf in Germany. This time a different type of melting has been studied, which occurs when a solid glass is subjected to a ramped-up deformation which increases linearly with time. The material initially responds like a solid, with a linear stress-strain relation (Hooke’s law) but then at some point deviates from linearity and starts to flow like a viscous liquid (Newtonian-like plateau). The problem has been studied experimentally using a colloidal glass where, also in this case, the individual particles trajectories can be precisely recorded using a confocal microscope. In particular, it has been possible to precisely measure and quantify the so-called nonaffine motions, which arise because the nearest-neighbours of every particle move in order to find their new positions in the strained frame, and in doing so they transmit forces to the tagged particle which could only vanish if the lattice were centrosymmetric (which clearly is not the case in a disordered glass). The info about these motions are used by Dr Zaccone’s theory to compute the nonlinear stress-strain curve, and for the first time, to precisely determine the point at which the material yields and starts to flow in a liquid-like way, in agreement with rheological data. This theory, and its experimental validation shown in Figure 3 below, represent the starting point to developing predictive calculations of material failure in various contexts, from soft materials to metallurgy.

Figure 3. Experimental measurements (symbols) and theory (solid lines) of yielding and crossover from solid-like to liquid-like behaviour in colloidal glasses subjected to a ramp of shear strain. From .


Some recent 2017 papers from the Statistical Physics Group:

  • J. Krausser, A. Lagiogianni, K. Samwer, A. Zaccone.
    Disentangling interatomic repulsion and anharmonicity in the viscosity and fragility of glasses.
    Physical Review B, accepted, in press.
  •  J. Sprakel, A. Zaccone, F. Spaepen, P. Schall, D. A. Weitz.
    Direct observation of entropic stabilization of bcc crystals near melting.
    Physical Review Letters 118, 088003 (2017). doi: 10.1103/PhysRevLett.118.088003
  • B. Cui, R. Milkus, and A. Zaccone.
    Direct link between boson-peak modes and dielectric alpha-relaxation in glasses.
    Physical Review E 95, 022603 (2017). doi: 10.1103/PhysRevE.95.022603
  • R. Milkus and A. Zaccone.
    Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids.
    Physical Review E 95, 023001 (2017). doi: 10.1103/PhysRevE.95.023001
  • M. Laurati, P. Masshoff, K.J. Mutch, S.U. Egelhaaf, A. Zaccone.
    Long-lived neighbors determine the rheological response of glasses.
    Physical Review Letters 118, 018002 (2017). doi: 10.1103/PhysRevLett.118.018002
  • B. Cui, R. Milkus, A. Zaccone.
    The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems.
    Physics Letters A 381, 446 (2017). doi: 10.1016/j.physleta.2016.12.003
  • W.Y. Chen, L. Young, M. Lu, Meng, A. Zaccone, F. Ströhl, N. Yu, G. Kaminski Schierle, C. Kaminski.
    Fluorescence self-quenching from reporter dyes informs on the structural properties of amyloid clusters formed in vitro and in cells.
    Nano Letters 17, 143 (2017). doi: 10.1021/acs.nanolett.6b03686


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