Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.

A model potential-energy function comprising both twoand three-atom contributions is proposed to describe interactions in solid and liquid forms of Si. Implications of this potential are then explored by molecular-dynamics computer simulation, using 216 atoms with periodic boundary conditions. Starting with the diamond-structure crystal at low temperature, heating causes spontaneous nucleation and melting. The resulting liquid structurally resembles the real Si melt. By carrying out steepest-descent mappings of syste~ configurations onto potential-energy minima, two main conclusions emerge: (1) a temperature-independent inherent structure underlies the liquid phase, just as for "simple" liquids with only pair interactions; (2) the Lindemann melting criterion for the crystal apparently can be supplemented by a freezing criterion for the liquid, where both involve critical values of appropriately defined mean displacements from potential minima.

Various static and dynamic phenomena displayed by glass-forming liquids, particularly those near the so-called "fragile" limit, emerge as manifestations of the multidimensional complex topography of the collective potential energy function. These include non-Arrhenius viscosity and relaxation times, bifurcation between the alpha- and beta-relaxation processes, and a breakdown of the Stokes-Einstein relation for self-diffusion. This multidimensional viewpoint also produces an extension of the venerable Lindemann melting criterion and provides a critical evaluation of the popular "ideal glass state" concept.

Most materials attain a glassy state at low temperatures under suitable methods of preparation. This state exhibits the mechanical properties of a solid, but shows microscopic structural disorder 1,2 . A comprehensive understanding of the glassy state is, however, still lacking 3 . A widespread assumption is that the nonexponential relaxation processes observed in the dynamics of glasses-and also in protein dynamics, protein folding and population dynamics-are (in common with other manifestations of complex dynamics) strongly influenced by the underlying energy landscape associated with the structural configurations that the system may adopt. But concrete evidence for this in studies of glass formation has been scarce. Here we present such evidence, obtained from computer simulations of a model glassforming liquid. We demonstrate that the onset of non-exponential relaxation corresponds to a well defined temperature below which the depth of the potential-energy minima explored by the liquid increases with decreasing temperature, and above which it does not. At lower temperatures, we observe a sharp transition when the liquid gets trapped in the deepest accessible energy basin. This transition temperature depends on the cooling rate, in a manner analogous to the experimental glass transition. We also present evidence that the barrier heights separating potential-energy minima sampled by the liquid increase abruptly at a temperature above the glass transition but well below the onset of non-exponential relaxation. This identification of a relationship between static, topographic features of the energy landscape and complex dynamics holds letters to nature 554 NATURE | VOL 393 | 11 JUNE 1998 0.0 0.5 1.0 1.5 2.0 Temperature -7.05 -7.00 -6.95 -6.90 Energy Cooling rate = 1.08 ×10 -3 Cooling rate = 2.70 ×10 -4 Cooling rate = 8.33 ×10 -5Cooling rate = 3.33 ×10 -6 a Figure 1 Molecular dynamics simulations of a binary Lennard-Jones mixture 21 . 80% of the particles are of type A, 20% are type B, and Lennard-Jones parameters are e AA ¼ 1:0, e AB ¼ 1:5, e BB ¼ 0:5, j AA ¼ 1:0, j AB ¼ 0:8 and j BB ¼ 0:88. All quantities are in reduced units: length in units of j AA , temperature in units of e AA /k B , and time in units of (j 2 AA m/e AA ) 1/2 , where m is the mass of the particles. The density r in all cases is 1.2. The calculated pressures for the system remain positive except for T Ͻ 0:06, much below temperatures where the system forms a glass in all cases studied. The Lennard-Jones potential, with a quadratic cut-off and shifting of the potential at r ab c ¼ 2:5j ab (ref. 29), a; b ʦ A; B is used. Our cut-off procedure results in a potential minimum value which is ϳ4% smaller than that in ref. 21. The time step is dt ¼ 0:003. Each run was initialized by equilibration at a high temperature, followed by equilibration and data collection runs at a series of temperatures. The run length at each temperature, together with the number of temperatures chosen, determines the cooling rate. Equilibration was done at constant temperat...

Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction ϕ = π/ √ 18 ≈ 0.74. It is also well-known that certain random (amorphous) jammed packings have ϕ ≈ 0.64. Here we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely; up to ϕ = 0.68 − 0.71 for spheroids with an aspect ratio close to that of M&M'S r Candies, and even approach ϕ ≈ 0.74 for general ellipsoids. We suggest that the higher 1