Crystal to Glass Transition and Melting in Two Dimensions

1993 ◽  
Vol 321 ◽  
Author(s):  
M. Li ◽  
W. L. Johnson ◽  
W. A. Goddard

ABSTRACTThermodynamic properties, structures, defects and their configurations of a two-dimensional Lennard-Jones (LJ) system are investigated close to crystal to glass transition (CGT) via molecular dynamics simulations. The CGT is achieved by saturating the LJ binary arrays below glass transition temperature with one type of the atoms which has different atomic size from that of the host atoms. It was found that for a given atomic size difference larger than a critical value, the CGT proceeds with increasing solute concentrations in three stages, each of which is characterized by distinct behaviors of translational and bond-orientational order correlation functions. An intermediate phase which has a quasi-long range orientational order but short range translational order has been found to exist prior to the formation of the amorphous phase. The destabilization of crystallinity is observed to be directly related to defects. We examine these results in the context of two dimensional (2D) melting theory. Finite size effects on these results, in particular on the intermediate phase formation, are discussed.

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.


2018 ◽  
Vol 30 (10) ◽  
pp. 104003 ◽  
Author(s):  
Alice L Thorneywork ◽  
Joshua L Abbott ◽  
Dirk G A L Aarts ◽  
Peter Keim ◽  
Roel P A Dullens

1993 ◽  
Vol 07 (26) ◽  
pp. 1661-1665
Author(s):  
M. MARSILI ◽  
G. JUG

The possibility of unusual leading logarithmic corrections to the asymptotic behavior of the percolation connectedness length ξ in two dimensions is explored through a finite-size transfer-matrix analysis on strips of widths L≤12. It is found that, for both square-site and triangular-site percolation problems, no such corrections arise and the accepted exact value of the critical exponent ν is recovered.


1992 ◽  
Vol 272 ◽  
Author(s):  
David R. Nelson

Flexible sheet polymers or “membranes” can be regarded as two-dimensional generalizations of linear polymer chains, for which there is a vigorous theoretical and experimental literature. Flexible membranes should exhibit even more richness and complexity, for two basic reasons. The first is that important geometric concepts like intrinsic curvature, orientability and genus, which have no direct analogue in linear polymers, appear naturally in discussions of two-dimensional macromolecules. Our understanding of the interplay between these concepts and the statistical mechanics of surfaces is still in its infancy. [1] The second reason is that surfaces can exist in a variety of different phases. The possibility of a two-dimensional shear modulus in planar membranes shows that we must distinguish between solids and liquids when these objects are allowed to crumple into three dimensions. Hexatic membranes, with extended six-fold bond orientational order, provide yet another important possibility. All three phases have quite distinctive properties. [2, 3] There are no such sharp distinctions for linear polymer chains.


2000 ◽  
Vol 138 ◽  
pp. 386-387 ◽  
Author(s):  
Takamichi Terao ◽  
Tsuneyoshi Nakayama

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