Symmetry and Structure of SrTiO3 Nanotubes

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Symmetry and Structure of SrTiO3 Nanotubes

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Symmetry and Structure of SrTiO3 Nanotubes Robert Evarestov1
1Department of Quantum Chemistry, St. Petersburg State University, Russia e-mail of presenting author: [email protected]
The line symmetry group L=ZP ( a product of one axial point group P and one infinite cyclic group Z of generalized translations ) of single-walled (SW) and double-walled (DW) SrTiO3 nanotubes (NT) is considered. The nanotube is defined by the square lattice translation vector L = l1a + l2b and chiral vector R = n1a + n2b, (l1, l2, n1 and n2 are integers). The nanotube of the chirality (n1, n2) is obtained by folding the (001) layer (with the layer group P4mm) in a way that the chiral vector R becomes circumference of the nanotube.
For SW (n,0) NTs the line symmetry groups belong to family 11 (T^Dnh ) and are n/mmm or 2n 2m for even and odd n, respectively. For SW (n,n) NTs the line symmetry groups (2n)n/mcm belong to family 13 (T2n1Dnh).
The line symmetry group of a double-wall nanotube can be found as intersection L2 = Z2P2 = (L ∩ L′) of the symmetry groups L and L′ of its single-wall constituents as earlier considered for DW CNTs [1,2].
In particular case of the commensurate (n,n)@M(n,n) and (n,0)@M(n,0) DW perovskite nanotubes with square morphology the DW NT symmetry group depends on the parity of M. For DW NTs with odd M, the line symmetry groups are the same as for their SW constituents and belong to families 13 and 11 respectively. For even M, the rotations about screw axis of order 2M are changed by rotations around pure rotation axis of order M so that DW NT line symmetry groups belong to family 11 for both chiralities.
The results of the first principles LCAO-PBE0 calculations of SW and DW SrTiO3 NTs are presented. CRYSTAL-09 computer code [3] is used, the rod subgroups of line groups are applied allowing the large scale computations for NTs. The DW nanotubes strain energy is estimated relatively to the sum of their constituents energies.
The author is grateful for the support of Saint-Petersburg State University, grant for fundamental research.
[1] Damnjanovic, M.; Milosevic, I.; Vukovic, T.; Sredanovic, R. Phys Rev B 1999, 60, 2728. [2] Damnjanovic, M.; Dobradzic, E.; Milosevic, I.; Vukovic, T.; Nicolic, B. New J. Phys. 2003, 5, 148. [3] R. Dovesi, et al., CRYSTAL09 User's Manual, University of Torino, Torino, 2010.