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Physics of Important Developments That Predestined Graphene
Published in Andre U. Sokolnikov, Graphene for Defense and Security, 2017
At room temperature the coherence length is very high but at approximately the melting temperature (~ 49000 F), the coherence length is on the order of 50 µm. The Eq. (2.50) suggests that crumpling takes place only beyond ξp that equals a constant in an exponentially rising function. An introduction of a dislocation further promotes unbinding by reducing of the dislocation energy. The formation of a stable phase that has a six-fold orientation order is otherwise called a “hexatic” phase. The crystal orientation which is acquired helps to resist the thermal softening with an existing finite crumpling temperature.
The phase diagram and melting scenarios of two-dimensional Hertzian spheres
Published in Molecular Physics, 2018
Yu. D. Fomin, E. A. Gaiduk, E. N. Tsiok, V. N. Ryzhov
Phase transitions in two-dimensional () systems are of great interest for many reasons. This is a field where usual intuition can lead to wrong conclusions. Firstly, as shown by Landau [1] and Peierls [2,3], there are no crystals as we understand crystals in a three-dimensional () space. crystal structures do not demonstrate long-range translational order. However, there are still long-range orientational order and quasi-long-range translational order in crystals [4,5]. As a result, the melting of crystalline phases can occur not only as the first-order phase transition [6–10], as it always happens in , but a number of different scenarios are possible. In addition to the usual first-order phase transition, the melting of a crystal can appear as two continuous transitions of the Berezinskii–Kosterlitz–Thouless (BKT) type [11–15] (the Berezinskii–Kosterlitz–Thouless–Halperin–Nelson– Young (BKTHNY) scenario [5,13–23]). The BKTHNY scenario seems most popular now. According to this theory, solids melt through dissociation of bound dislocation pairs. As a result, long-range orientational order transforms into quasi-long-range order, and quasi-long-range positional order becomes short range. The new intermediate phase with quasi-long-range orientational order is called a hexatic phase (if melting of a square crystal is considered then it is a tetratic phase). It has zero shear rigidity and because of this it should be considered as a kind of ordered liquid. The hexatic phase transforms into an isotropic liquid phase having short-range orientational and positional orders through unbinding dislocation pairs. It should be noted that the BKTHNY theory only provides the limits of solid and hexatic phase stability.
Remarkable stabilisation of the intercalated smectic phases of nonsymmetric dimers by tert-butyl groups
Published in Liquid Crystals, 2022
Rebecca Walker, Damian Pociecha, Camilla Faidutti, Eva Perkovic, John M. D. Storey, Ewa Gorecka, Corrie T. Imrie
CBO11O.4 shows a rich smectic polymorphism, having the phase sequence on cooling: I-N-SmA-SmC-SmI-J-Cr. A characteristic schlieren texture was observed in the nematic phase, which on cooling became largely homeotropic with small regions of focal conic fans indicating a SmA phase, see Figure 6. The X-ray pattern of the smectic A phase contained a sharp low angle signal and a broad wide-angle signal. On cooling, the homeotropic regions developed a weakly birefringent schlieren texture characteristic of a SmC phase, and the X-ray diffraction pattern consisted of a sharp low angle and diffuse wide-angle signal reflecting the liquid-like arrangement of the molecules within the smectic layers. On cooling the smectic C phase, the schlieren texture becomes notably brighter and somewhat less well-defined, see Figure 6. The wide-angle reflection in the X-ray diffraction pattern narrows and splits, indicating a tilted hexatic phase. For an aligned sample, the pattern shows one of the wide-angle peaks is in an equatorial position with respect to the small-angle signals, indicating that the molecules are tilted towards nearest neighbours in the local in-plane hexagons, and hence the phase has been assigned as a SmI phase. On cooling the SmI phase, scratch-like defects appear on the texture and the birefringence changes. These changes are accompanied by a splitting of the wide-angle signal into a number of sharp peaks in the X-ray diffraction pattern suggesting this to be a crystal J phase. The layer spacings and the d/l ratios measured in each of the phases are listed in Table 2, and in each an intercalated arrangement of the molecules is evident. We also note that the position of the diffuse signal in the low angle region for the nematic phase is centred at around 21 Å suggesting a locally intercalated arrangement of the molecules. CBO11O.s4 and CBO11O.t4 show the same sequence of smectic phases but do not exhibit a nematic phase and instead show SmA-I isotropic transitions. The phase assignments were based on the observation of similar optical textures and X-ray diffraction patterns as described for CBO11O.4. The layer thicknesses measured in the SmA phase shown by CBO11.s4 and CBO11O.t4 are also listed in Table 2 and these reveal intercalated arrangements.