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Distribution of Molecular Speeds

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
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Crystal Field Theory
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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
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Published on: September 17, 2021

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

Pak Yuen Chan1, Nigel Goldenfeld, Jon Dantzig

  • 1Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801-3080, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary

This study introduces a non-negative order parameter for the phase-field-crystal model, enabling precise atomic configurations and vacancy descriptions. This method allows for molecular dynamics simulations on diffusive timescales, revealing atomic motion and fluid properties.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Chemical Engineering

Background:

  • The phase-field-crystal (PFC) model is a powerful tool for simulating materials at atomic scales.
  • Existing PFC models often struggle to accurately represent discrete atomic configurations and vacancies.
  • Bridging atomistic and diffusive time scales in simulations remains a challenge.

Purpose of the Study:

  • To extend the phase-field-crystal model to incorporate exact atomic configurations and vacancies.
  • To develop a theoretical framework that dictates the number of atoms and describes their motion.
  • To enable molecular dynamics simulations on diffusive time scales using a partial differential equation.

Main Methods:

  • Modification of the phase-field-crystal model by enforcing a non-negative order parameter.
  • Derivation of a dynamical equation governing atomic configurations and motion.
  • Numerical solution of the derived partial differential equation.

Main Results:

  • The extended PFC model successfully accommodates exact atomic configurations and vacancies.
  • The theory accurately dictates the number of atoms and their dynamics.
  • The approach allows for molecular dynamics simulations on diffusive time scales.

Conclusions:

  • The non-negative order parameter extension of the PFC model provides a robust method for simulating atomic-level phenomena.
  • This method bridges the gap between atomistic simulations and diffusive processes.
  • The approach was validated by calculating the two-point correlation function of a fluid.