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Related Experiment Videos

Hard-sphere solids near close packing: testing theories for crystallization

Groh1, Mulder

  • 1FOM Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

Density-functional theory (DFT) accurately models hard-sphere crystals near close packing. Different DFT approximations yield varying predictions for crystal structure and free energy, with improved theories showing better agreement with simulations.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • Density-functional theory (DFT) is a powerful tool for studying phase transitions.
  • Hard spheres provide a fundamental model system for understanding crystallization.
  • Testing DFT in the close-packed limit rigorously evaluates its accuracy.

Purpose of the Study:

  • To evaluate density-functional theory (DFT) predictions for hard-sphere crystals at close packing.
  • To compare the Ramakrishnan-Yussouff (RY) approximation with variants of fundamental-measure theory (FMT).
  • To investigate the impact of non-Gaussian density profiles on DFT results.

Main Methods:

  • Analysis of density-functional theory (DFT) approximations: Ramakrishnan-Yussouff (RY) and fundamental-measure theory (FMT).

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  • Consideration of general density peak shapes beyond the Gaussian approximation.
  • Examination of crystalline structure and thermodynamics in the close-packing limit.

    • Main Results:

    • All DFT versions show peak width vanishing proportionally to inter-particle distance near close packing.
    • Free energy dependence on inter-particle distance is logarithmic across different DFTs.
    • RY theory predicts a closed loop of crystalline solutions; standard FMT yields steplike profiles, while improved FMT shows good agreement with simulations.

    Conclusions:

    • DFT accurately describes hard-sphere crystals near close packing, but approximations affect predictions.
    • Improved fundamental-measure theory (FMT) with tensor weighted densities shows excellent agreement with simulation data.
    • The close-packing limit serves as a critical test for the validity of liquid-state-based theories.