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Ian Snook: „Studies of crystallization of the hard sphere fluid - recent MD and MC studies and structure measures”
RMIT University, Melbourne, Australia

The simplest realistic system to show a liquid/solid transition is the hard sphere system and so this system has been extensively studied and used as a prototype for understanding the freezing transition. Pioneering work by Alder and Wainwright and by Hoover and Ree established that not only is the fluid to solid transition of a three dimensional system of hard spheres possible but that it is a first order transition. The thermodynamic properties of each phase and the freezing and melting densities are now very accurately known.

However, the mechanism by which this transition occurs and a detailed description of the processes involved in nucleation are still not fully known.

In this talk I will outline work on this transition which I have been involved in for several years now.

I shall attempt to show what can be learnt about this transition from several points of view i.e.

  1. A thermodynamic one based on the calculation of the exact free volume1
  2. A topological one based on ring statistics2
  3. One based on single particle dynamics and the velocity autocorrelation function3,4 and finally
  4. Studies of the actual dynamics in which nucleation is observed5,6


  1. B. O' Malley and I. Snook, "Cavity and Free Volume Distribution of the Dense Hard Sphere System and the Fluid/Solid Transition", to be submitted
  2. B. O' Malley and I. Snook, "Structure of the hard sphere fluid and precursor structures to crystallisation". J. Chem. Phys., 123 054511 (2005)
  3. S.R. Williams, P. McGlynn, G. Bryant, I.K. Snook and W. van Megen, "Dynamical signatures of freezing: Stable fluids, metastable fluids and crystals", Phys. Rev. E, 74 031204 (2006)
  4. S.R. Williams, G. Bryant, I.K. Snook and W. van Megen, "Velocity autocorrelation functions of hard-sphere liquids: Long-time tails upon undercooling", Phys. Rev. Letters, 96 087801 (2006)
  5. B. O' Malley, and I. Snook, "Crystal Nucleation in the Hard Sphere Fluid at Co-existence", Phys. Rev. Letters, 90 85702 (2003)
  6. T. Schilling, H.J. Schope, M. Oettel, G. Opletal and I. Snook, "Precursor-mediated crystallization process in suspensions of hard spheres", Phys. Rev. Letters, to appear 2010