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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
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Two-step melting in two dimensions: first-order liquid-hexatic transition.

Etienne P Bernard1, Werner Krauth

  • 1Laboratoire de Physique Statistique Ecole Normale Supérieure, UPMC, CNRS 24 rue Lhomond, 75231 Paris Cedex 05, France. etienne.bernard@lps.ens.fr

Physical Review Letters
|November 24, 2011
PubMed
Summary

Melting in two-dimensional systems, like thin films, was studied using a new Monte Carlo algorithm. The research reveals a two-step melting process, clarifying a long-standing physics problem.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Melting in two spatial dimensions (2D) is a complex phase transition, poorly understood even in fundamental models like hard disks.
  • The melting mechanism of the hard-disk model has been debated for 50 years, hindering progress in theoretical, computational, and experimental research.

Purpose of the Study:

  • To elucidate the melting mechanism in two-dimensional systems, specifically the hard-disk model.
  • To resolve the long-standing debate regarding the nature of phase transitions in 2D melting.

Main Methods:

  • Utilized a recent Monte Carlo algorithm to simulate large systems, enabling access to the thermodynamic regime.
  • Analyzed the phase transitions occurring in the hard-disk model under thermalization.

Main Results:

  • Demonstrated that melting in hard disks occurs in two distinct steps, involving solid, hexatic, and liquid phases.
  • Identified the hexatic-solid transition as continuous.
  • Surprisingly found the liquid-hexatic transition to be of the first order.

Conclusions:

  • The study resolves a fundamental model in statistical physics concerning 2D melting.
  • Provides a clear melting scenario for 2D systems, impacting related research fields.
  • Offers crucial insights into phase transitions at interfaces and in thin films.