Kinetics of liquid crystal phase transitions:

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Modelling the Phase Diagram of Carbon
Luca M. Ghiringhelli, Van t Hoff Institute for
Molecular Sciences, Universiteit van
Amsterdam with Jan H. Los and Annalisa
Fasolino, Evert Jan Meijer and Daan Frenkel
Lyon, 17th October 2005
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• Outline
• Bond order potential(s)
• LCBOP(I)
• Calculating the phase diagram of carbon method
• Calculating the phase diagram of carbon results
• On the nature of liquid carbon
• Improving LCBOP(I) LCBOPII
• Summary and perspectives

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Carbon potential A Bond Order Potential
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Carbon potential LCBOP(I) Carbon Bond Order
Potential with intrinsic non-bonded interactions
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In depth angular interactions
Coordination three or more Coordination two or
less
G
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In depth torsional interactions
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Calculating Phase equilibria Thermodynamic
integration for free energy evaluation
Reference system for the liquid Lennard-Jones
liquid. Reference system for the solids harmonic
(Einstein) solid.
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From Helmoltz to Gibbs free-energy
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The calculated carbon phase diagram
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Liquid structure no LLPT
T 6000 K
T 6000 K
DF-MD (PBE) (Wu et al., PRL 2002)
Brenner potential (Glosli and Ree, PRL 1999)
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5000 K, 150 GPa
Unsatisfactory features of LCBOP(I).
Diamond (LCBOP(I)) Liquid (LCBOP(I)) Liquid
(DF-MD)
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• LCBOPII
• Extension of the angular dependency via a middle
  range (2.2 - 4 Å) potential, to account for
  dangling bonds

3HC
CH3
C
C
3HC
CH3
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• LCBOPII
• Extension of the angular dependency via a middle
  range (2.2 - 4 Å) potential, to account for
  dangling bonds
• Angular correlations flexibly coordination
  dependent

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• LCBOPII
• Extension of the angular dependency via a middle
  range (2.2 - 4 Å) potential, to account for
  dangling bonds
• Angular correlations flexibly coordination
  dependent
• New definition of torsion angles

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• LCBOPII
• Extension of the angular dependency via a middle
  range (2.2 - 4 Å) potential, to account for
  dangling bonds
• Angular correlations flexibly coordination
  dependent
• New definition of torsional angles
• New scheme for multidimensional smoothing

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LCBOPII radial distribution functions in the
liquid
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• In summary
• State-of-the-art bond order potential for carbon
  (LCBOPII !)
• Carbon phase diagram by free-energy calculation
• No first order liquid-liquid phase transition

Perspectives Surface reconstructions Size
dependent phase diagram Nano-materials
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This work was done in collaboration with


Jan H. Los, Radboud Universiteit Nijmegen

Annalisa Fasolino, Radboud Universiteit
Nijmegen and Universiteit van Amsterdam

Evert Jan
Meijer, Universiteit van Amsterdam
Daan Frenkel,
AMOLF and Universiteit van Amsterdam. Support
FOM and NCF
For more information LCBOP Los and Fasolino,
Phys. Rev. B 68, 024107 (2003) Diamond-like
liquid Ghiringhelli et al., Phys. Rev. B 69,
100101(R) (2004) Phase diagram Ghiringhelli et
al., Phys. Rev. Lett. 94, 145601 (2005) LCBOPII
(theory) Los, Ghiringhelli et al., accepted on
Phys. Rev. B LCBOPII (application) Ghiringhelli,
Los et al., accepted on Phys. Rev. B