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Crystalline Structure of Different Semiconductors
Published in Jyoti Prasad Banerjee, Suranjana Banerjee, Physics of Semiconductors and Nanostructures, 2019
Jyoti Prasad Banerjee, Suranjana Banerjee
Figure 1.13b shows one such special lattice, a square lattice having fourfold symmetry about an axis joining the midpoint of opposite pair of parallel faces. The other special lattices are rectangular lattice (Figure 1.13c), hexagonal lattice (Figure 1.10d), and centered rectangular lattice (Figure 1.13e). In case of a rectangular lattice, more than twofold rotational symmetry is not possible, but two orthogonal mirror planes of symmetry exist. The centered rectangular lattice has twofold rotational and reflection symmetries. The hexagonal lattice has sixfold rotation symmetry with the mirror reflection planes intersecting at an angle of 30°.
Star-shaped oligomers with truxenone centre and triphenylene branches: mesomorphism, optical and electronic properties
Published in Liquid Crystals, 2020
Wen Zhang, Wen-Hao Yu, Chun Feng, Shi-Kai Xiang, Bi-Qin Wang, Ke-Qing Zhao, Hai-Liang Ni, Ping Hu
XRD analysis was performed on three oligomers TrO[O(CH2)nOTP]3 (n = 6,8,10) to probe the precise bulk phase structure and molecular self-assembly properties in their mesophase (Figure S4 in ESI). The XRD data of the LC phases of three star-shaped oligomers are summarised in Table 2. It is noticed that the wide reflection signals of all diffraction patterns appearing on the left and right sides of the most prominent small angle reflection area are the background signal generated by the polymer foil carried by the instrument. For TrO[O(CH2)6OTP]3, the X-ray pattern recorded at 140°C (Figure 2) contains two sharp and intense Bragg reflections in the small-angle region and a broad amorphous halo with two relatively sharp shoulder peaks in the wide-angle region confirming the liquid nature of the mesophase. This sharpness of the small-angle reflections indicated the long-range correlation of the rectangular ordering and of the two-dimensional arrangement of the columns. There are five diffraction peaks at 2θ = 2.5°, 4.4°, 5.0°, 8.9° and 10.66° in the small-angle region, corresponding, respectively, to spacings of 35.6, 20.2, 17.7, 10.0 and 8.3 Å. The d-spacings of the first peak and the third peak are in the ratio of 1:1/2, which is in good agreement with (10) and (11) reflections of rectangular packing. The calculated two-dimensional rectangular lattice parameters are a = 35.6 Å and b = 20.3 Å [41,42]. The rectangular symmetry can be assigned to a distorted hexagonal lattice. This distortion could be related to the tilt of the discotic units with the shorter connecting chains. The broad amorphous halo corresponds to the average separation of aliphatic hydrocarbons, and the relatively shoulder peak can be divided into two small peaks. The d-spacings of the two small peaks were 3.4 and 3.5 Å, respectively, which resulted from the short-range π-π stacking interactions and are referred to the average distance between truxenone [30] or triphenylene [43,44] discs within a column. Taking into account the measured parameters of the rectangular columnar mesophase and assuming that the density of the material is close to 1 g·cm−3, we found that each unit cell of the main rectangular lattice contains an average of two discs in this case according to our calculation. Therefore, LC phase of TrO[O(CH2)6OTP]3 was identified as a rectangular columnar phase (Colr). A packing model for the organisation of the TrO[O(CH2)6OTP]3 in the mesophase is proposed in Figure 3, in which central truxenone cores and triphenylene arms are tightly coupled to form a supercolumn organised in a rectangular pattern.