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Surface partition of large clusters.

K A Bugaev1, L Phair, J B Elliott

  • 1Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine and Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
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This study analytically derives the surface partition for large clusters using a statistical model and Laplace-Fourier transforms. A "hills and dales model" accurately approximates surface entropy and degeneracy prefactors for large clusters.

Area of Science:

  • Statistical Mechanics
  • Physical Chemistry
  • Surface Science

Background:

  • Understanding the surface partition of clusters is crucial for predicting their thermodynamic properties.
  • Existing models provide approximations for surface entropy, particularly for large clusters.

Purpose of the Study:

  • To analytically derive the surface partition function for large clusters using a simple statistical model.
  • To introduce and validate a
  • hills and dales model
  • for cluster surface properties.

Main Methods:

  • Laplace-Fourier transformation method applied to a statistical model.
  • Analytical derivation of the surface partition function.
  • Comparison with established theoretical results (e.g., Fisher's).

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Main Results:

  • The derived surface partition function for large clusters is presented.
  • The
  • hills and dales model
  • accurately reproduces the leading term of Fisher's surface entropy for small deformations (within a few percent).
  • The model successfully predicts the degeneracy prefactor for large clusters.

Conclusions:

  • The analytical approach and the
  • hills and dales model
  • offer a robust method for studying cluster surface properties.
  • The findings contribute to a deeper understanding of the thermodynamics of finite and large clusters.
  • The study validates theoretical predictions and provides a new model for surface entropy calculations.