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Title: Shape and Symmetry Determine Two-Dimensional Melting Transitions of Hard Regular Polygons

Authors:
; ; ; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1349978
Grant/Contract Number:
AC05-00OR22725
Resource Type:
Journal Article: Published Article
Journal Name:
Physical Review X
Additional Journal Information:
Journal Volume: 7; Journal Issue: 2; Related Information: CHORUS Timestamp: 2017-04-05 22:14:19; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Anderson, Joshua A., Antonaglia, James, Millan, Jaime A., Engel, Michael, and Glotzer, Sharon C. Shape and Symmetry Determine Two-Dimensional Melting Transitions of Hard Regular Polygons. United States: N. p., 2017. Web. doi:10.1103/PhysRevX.7.021001.
Anderson, Joshua A., Antonaglia, James, Millan, Jaime A., Engel, Michael, & Glotzer, Sharon C. Shape and Symmetry Determine Two-Dimensional Melting Transitions of Hard Regular Polygons. United States. doi:10.1103/PhysRevX.7.021001.
Anderson, Joshua A., Antonaglia, James, Millan, Jaime A., Engel, Michael, and Glotzer, Sharon C. Wed . "Shape and Symmetry Determine Two-Dimensional Melting Transitions of Hard Regular Polygons". United States. doi:10.1103/PhysRevX.7.021001.
@article{osti_1349978,
title = {Shape and Symmetry Determine Two-Dimensional Melting Transitions of Hard Regular Polygons},
author = {Anderson, Joshua A. and Antonaglia, James and Millan, Jaime A. and Engel, Michael and Glotzer, Sharon C.},
abstractNote = {},
doi = {10.1103/PhysRevX.7.021001},
journal = {Physical Review X},
number = 2,
volume = 7,
place = {United States},
year = {Wed Apr 05 00:00:00 EDT 2017},
month = {Wed Apr 05 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevX.7.021001

Citation Metrics:
Cited by: 4works
Citation information provided by
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  • The melting of ordered monolayers of n-hexane, n-octane, and n-decane adsorbed on Pt(111) has been studied by reflection-absorption infrared spectroscopy (RAIRS). Each alkane forms an overlayer at low temperatures (<160 K) that is characterized by both quasi-long-range translational and orientational order. Specifically there are two RAIR-allowed methylene v{sub C-H} stretching modes: one which largely involves motion of the methylene C-H bond that projects away from the surface (the distal C-H bond) and another that largely involves motion of the near-surface (i.e., proximal) C-H bond. At higher temperatures, a transition occurs to a one-dimensionally ordered (possibly `hexatic`) phase in which translationalmore » order has been lost along the long axis of the molecules but orientational ordering is maintained; the approximate 2D {yields} 1D transition temperatures are 187 K for n-hexane, 212 K for n-octane, and 225 K for n-decane. As expected for true phase transitions all changes noted by RAIRS are reversed when the samples are cooled. The conformational dynamics seen on a Pt(111) surface are compared with those that occur in the premelting and melting transitions of bulk n-alkane crystals. The present data also answer a long standing question about the mechanism of mode softening: the line widths of soft modes are defined largely by the degree of site homogeneity and thus are acutely sensitive to the conformational, rotational, and translational order of the adsorbate overlayer. 55 refs., 8 figs., 4 tabs.« less
  • A two dimensional lattice gas model of a bicrystal has been used previously to study the phase transitions and the atomic configuration near a ..sigma.. = 5 grain boundary. In previous work the authors studied the disordering and melting transitions in the boundary for the ordering system assuming always a fully symmetrical boundary with no rigid body translation of one crystal with respect to the other. It was found that for high temperatures the grain boundary regions is increasingly more disordered than the bulk and that for temperatures close to the melting point a layer forms in the boundary thatmore » has increasingly liquid-like properties. In this note the authors report simulations based on the same model that were performed to study the influence of the grain boundary rigid body displacement on these transitions. The introduction of a rigid body displacement of one crystal with respect to the other may result in the lack of coincident sites in the boundary, even if it is a low sigma boundary. It is expected that this lack of coincident sites will increase the tendency of formation of a liquid-like layer in the grain boundary region.« less
  • A two-dimensional lattice-gas model of a binary-ordering-alloy system was used to study the phase transitions and the atomic configuration near a ..sigma..=5 grain boundary. The cluster variation method was used to study order-disorder and melting transitions in the bulk alloys. The complete binary phase diagrams were constructed for two different sets of interaction-energy assumptions. Simulations based on the same model were performed to study these transitions in the grain-boundary region. In addition, the model also yields information on the segregation behavior of the alloying elements in the grain-boundary region.
  • Group-theoretical criteria which determine the possibility of group-subgroup phase transitions have been implemented on a computer. Lower-symmetry groups are determined by the subduction and chain criteria. We list all possible such symmetry-restricted transitions in two dimensions corresponding to k points of symmetry. We indicate relative origins and orientations of the prototype group and subgroup sufficient to obtain a wide class of useful experimental information.
  • A procedure is presented for the determination of geometric buckling for regular polygons. A new computation technique, the multiple reciprocity boundary element method (MRBEM), has been applied to solve the one-group neutron diffusion equation. The main difficulty in applying the ordinary boundary element method (BEM) to neutron diffusion problems has been the need to compute a domain integral, resulting from the fission source. The MRBEM has been developed for transforming this type of domain integral into an equivalent boundary integral. The basic idea of the MRBEM is to apply repeatedly the reciprocity theorem (Green's second formula) using a sequence ofmore » higher order fundamental solutions. The MRBEM requires discretization of the boundary only rather than of the domain. This advantage is useful for extensive survey analyses of buckling for complex geometries. The results of survey analyses have indicated that the general form of geometric buckling is B[sub g][sup 2] = (a[sub n]/R[sub c])[sup 2], where R[sub c] represents the radius of the circumscribed circle of the regular polygon under consideration. The geometric constant A[sub n] depends on the type of regular polygon and takes the value of [pi] for a square and 2.405 for a circle, an extreme case that has an infinite number of sides. Values of a[sub n] for a triangle, pentagon, hexagon, and octagon have been calculated as 4.190, 2.281, 2.675, and 2.547, respectively.« less