scholarly journals Geometric frustration and compatibility conditions for two-dimensional director fields

Soft Matter ◽  
2018 ◽  
Vol 14 (3) ◽  
pp. 424-431 ◽  
Author(s):  
Idan Niv ◽  
Efi Efrati
Keyword(s):  
Orientational Order ◽  
Two Dimensional ◽  
Compatibility Conditions ◽  
Geometric Frustration ◽  
Curved Objects

Packing curved objects in the plane cannot be performed uniformly and inevitably leads to frustration. In this work we establish what types of orientational order are possible in a general two-dimensional setting.

scholarly journals Correction: Geometric frustration and compatibility conditions for two-dimensional director fields

Soft Matter ◽  
2018 ◽  
Vol 14 (6) ◽  
pp. 1068-1068
Author(s):  
Idan Niv ◽  
Efi Efrati
Keyword(s):  
Soft Matter ◽  
Two Dimensional ◽  
Compatibility Conditions ◽  
Geometric Frustration

Correction for ‘Geometric frustration and compatibility conditions for two-dimensional director fields’ by Idan Niv et al., Soft Matter, 2018, DOI: 10.1039/c7sm01672g.

Crystal to Glass Transition and Melting in Two Dimensions

1993 ◽  
Vol 321 ◽  
Author(s):  
M. Li ◽  
W. L. Johnson ◽  
W. A. Goddard
Keyword(s):  
Glass Transition ◽  
Intermediate Phase ◽  
Orientational Order ◽  
Finite Size ◽  
Two Dimensions ◽  
Size Difference ◽  
Two Dimensional ◽  
Atomic Size ◽  
Bond Orientational Order ◽  
Dynamics Simulations

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.

Chiral spiral cyclic twins

2022 ◽  
Vol 78 (1) ◽  
Author(s):  
Wolfgang Hornfeck
Keyword(s):  
Long Range ◽  
Orientational Order ◽  
Two Dimensional ◽  
Point Sets ◽  
Degenerate Cases

A formula is presented for the generation of chiral m-fold multiply twinned two-dimensional point sets of even twin modulus m > 6 from an integer inclination sequence; in particular, it is discussed for the first three non-degenerate cases m = 8, 10, 12, which share a connection to the aperiodic crystallography of axial quasicrystals exhibiting octagonal, decagonal and dodecagonal long-range orientational order and symmetry.

scholarly journals On regular and random two-dimensional packing of crosses

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Ralf Stannarius ◽  
Jonas Schulze
Keyword(s):  
Correlation Functions ◽  
Short Range ◽  
Orientational Order ◽  
Simple Relation ◽  
Random Packing ◽  
Spatial Distributions ◽  
Two Dimensional ◽  
Packing Problems ◽  
Aspect Ratios ◽  
Local Correlations

AbstractPacking problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packing structures are known. The packing of 2D crosses does not yet belong to the category of solved problems. We demonstrate in experiments with crosses of different aspect ratios (arm width to length) which packing fractions are actually achieved by random packing, and we compare them to densest regular packing structures. We determine local correlations of the orientations and positions after ensembles of randomly placed crosses were compacted in the plane until they jam. Short-range orientational order is found over 2 to 3 cross lengths. Similarly, correlations in the spatial distributions of neighbors extend over 2 to 3 crosses. There is no simple relation between the geometries of the crosses and the peaks in the spatial correlation functions, but some features of the orientational correlations can be traced to typical local configurations.

Reliability of Orientational Order Parameters Determined from Two-dimensional X-ray Diffraction Patterns: A Simulation Study

ChemPhysChem ◽  
2016 ◽  
Vol 17 (11) ◽  
pp. 1568-1572 ◽  
Author(s):  
Frank Jenz ◽  
Stefan Jagiella ◽  
Matthew A. Glaser ◽  
Frank Giesselmann
Keyword(s):  
Simulation Study ◽  
Orientational Order ◽  
Order Parameters ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Patterns

scholarly journals Two-Dimensional Ordering of Solute Nanoclusters at a Close-Packed Stacking Fault: Modeling and Experimental Analysis

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Hajime Kimizuka ◽  
Shu Kurokawa ◽  
Akihiro Yamaguchi ◽  
Akira Sakai ◽  
Shigenobu Ogata
Keyword(s):  
Materials Science ◽  
Orientational Order ◽  
Stacking Fault ◽  
Coarse Grained ◽  
Scanning Tunneling ◽  
Two Dimensional ◽  
Tunneling Microscopy ◽  
Solute Cluster ◽  
Entropic Effect ◽  
High Degree

Abstract Predicting the equilibrium ordered structures at internal interfaces, especially in the case of nanometer-scale chemical heterogeneities, is an ongoing challenge in materials science. In this study, we established an ab-initio coarse-grained modeling technique for describing the phase-like behavior of a close-packed stacking-fault-type interface containing solute nanoclusters, which undergo a two-dimensional disorder-order transition, depending on the temperature and composition. Notably, this approach can predict the two-dimensional medium-range ordering in the nanocluster arrays realized in Mg-based alloys, in a manner consistent with scanning tunneling microscopy-based measurements. We predicted that the repulsively interacting solute-cluster system undergoes a continuous evolution into a highly ordered densely packed morphology while maintaining a high degree of six-fold orientational order, which is attributable mainly to an entropic effect. The uncovered interaction-dependent ordering properties may be useful for the design of nanostructured materials utilizing the self-organization of two-dimensional nanocluster arrays in the close-packed interfaces.

scholarly journals Fluctuations of orientational order and clustering in a two-dimensional colloidal system under quenched disorder

2013 ◽  
Vol 88 (6) ◽  
Author(s):  
Tobias Horn ◽  
Sven Deutschländer ◽  
Hartmut Löwen ◽  
Georg Maret ◽  
Peter Keim
Keyword(s):  
Orientational Order ◽  
Quenched Disorder ◽  
Colloidal System ◽  
Two Dimensional
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