2010
DOI: 10.1007/978-3-642-11172-3_2
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Line Groups Structure

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Cited by 6 publications
(19 citation statements)
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“…Since nanoribbons have translational symmetry in only one direction, we have to resort to the so called rod groups to describe their symmetry. The PGNRs studied in this work belong to the rod group labeled P 112 1 28 , 37 . It has the identity transformation plus a C 2 rotation around the periodic axis of the ribbon combined with a glide plane translation by 1/2 a , where a is the lattice constant vector in the direction with translational symmetry.…”
Section: Resultsmentioning
confidence: 99%
“…Since nanoribbons have translational symmetry in only one direction, we have to resort to the so called rod groups to describe their symmetry. The PGNRs studied in this work belong to the rod group labeled P 112 1 28 , 37 . It has the identity transformation plus a C 2 rotation around the periodic axis of the ribbon combined with a glide plane translation by 1/2 a , where a is the lattice constant vector in the direction with translational symmetry.…”
Section: Resultsmentioning
confidence: 99%
“…Hooke–Jeeves () algorithm is applied and helical and tubular geometrical parameters are varied together with the helical coordinates of atoms . Efficiency of the numerical code is substantially improved by implementing symmetry, described by the line groups of the 5th family . At temperatures T>0, instead of Brenner interatomic potential V , Helmholtz free energy A , defined as A=VitalicTS (where S is the entropy of the system at temperature T ) is optimized.…”
Section: Methodsmentioning
confidence: 99%
“…At temperatures T>0, instead of Brenner interatomic potential V , Helmholtz free energy A , defined as A=VitalicTS (where S is the entropy of the system at temperature T ) is optimized. The entropy S is calculated applying the local harmonic approximation (LHA): S=kBi=1nk=13ln2sinhωi,k2knormalBT, where kB is Boltzmann constant; indices i and k enumerate symcell () atoms and their coordinates, respectively; ωi,k is frequency of the oscillations (in k ‐direction) of the i th atom.…”
Section: Methodsmentioning
confidence: 99%
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“…Geometrical structure of HCCNTs is characterized by tubular diameter d , outer diameter of a helix D and helical step p . Symmetry of HCCNT is described by the line group generated by a helical transformation and π‐rotation around two fold horizontal axis .…”
Section: Introductionmentioning
confidence: 99%