Abstract:
matter diffusion experiments are carried out in hexagonal columnar phases of mesogenic disk-like and polycatenar compounds. the diffusion characteristics of two dyes of different sizes diffused into these mesophases are determined by measuring the diffusion coefficients along the columns and perpendicularly to them. the nature of diffusion versus the structure of these mesophases in discussed in comparison with previous results obtained in nematic and smectic systems.

Abstract:
Matter diffusion experiments are carried out in hexagonal columnar phases of mesogenic disk-like and polycatenar compounds. The diffusion characteristics of two dyes of different sizes diffused into these mesophases are determined by measuring the diffusion coefficients along the columns and perpendicularly to them. The nature of diffusion versus the structure of these mesophases in discussed in comparison with previous results obtained in nematic and smectic systems.

Abstract:
We present a model that explains the origin and predicts the statistical properties of columnar quasi-hexagonal crack patterns, as observed in the columnar jointing of basaltic lava flows. Irregular fractures appear at the surface of the material, induced by temperature gradients during cooling. At later times fractures penetrate into the material, and tend to form polygonal patterns. We show that this ordering can be described as a tendency to minimize an energy functional. Atomistic simulations confirm this interpretation. Numerical simulations based on a phenomenological implementation of this principle generate patterns that have remarkably good statistical agreement with real ones.

Abstract:
A hexagonal columnar crystal undergoes a shear-melting transition above a critical shear rate or stress. We combine the analysis of the shear-thinning regime below the melting with that of synchrotron X-ray scattering data under shear and propose the melting to be due to a proliferation of dislocations, whose density is determined by both techniques to vary as a power law of the shear rate with a 2/3 exponent, as expected for a creep model of crystalline solids. Moreover, our data suggest the existence under shear of a line hexatic phase, between the columnar crystal and the liquid phase.

Abstract:
Columnar crystals contain defects in the form of vacancy/interstitial loops or strings of vacancies and interstitials bounded by column ``heads'' and ``tails''. These defect strings are oriented by the columnar lattice and can change size and shape by movement of the ends and forming kinks along the length. Hence an analysis in terms of directed living polymers is appropriate to study their size and shape distribution, volume fraction, etc. If the entropy of transverse fluctuations overcomes the string line tension in the crystalline phase, a string proliferation transition occurs, leading to a supersolid phase. We estimate the wandering entropy and examine the behaviour in the transition regime. We also calculate numerically the line tension of various species of vacancies and interstitials in a triangular lattice for power-law potentials as well as for a modified Bessel function interaction between columns as occurs in the case of flux lines in type-II superconductors or long polyelectrolytes in an ionic solution. We find that the centered interstitial is the lowest energy defect for a very wide range of interactions; the symmetric vacancy is preferred only for extremely short interaction ranges.

Abstract:
We report a new method for growing hexagonal columnar nanograin structured silicon carbide (SiC) thin films on silicon substrates by using graphene–graphitic carbon nanoflakes (GGNs) templates from solid carbon sources. The growth was carried out in a conventional low pressure chemical vapor deposition system (LPCVD). The GGNs are small plates with lateral sizes of around 100 nm and overlap each other, and are made up of nanosized multilayer graphene and graphitic carbon matrix (GCM). Long and straight SiC nanograins with hexagonal shapes, and with lateral sizes of around 200–400 nm are synthesized on the GGNs, which form compact SiC thin films.

Abstract:
In this paper, the physical parameters Y elastic constants mewly proposed in our previous paper are applied to polycrystalline materials with hexagonal structure to deduce Y elastic constants thereof and to compare with the x-ray elastic constants of polycrystalline materials of hexagonal structure through calculation of examples. Though the expressions of mechanical elastic constants of polycrystalline materials deduced from the application of Y elastic constants are different from the conclusions of Kneer, the calculaled results for concrete materials are in full compliance.

Abstract:
We have performed accurate ab initio total energy calculations using the full-potential linearized augmented plane wave (FP-LAPW) method with the generalized gradient approximation (GGA) for the exchange-correlation potential to systematically investigate elastic properties of 18 stable, meta-stable and hypothetical hexagonal (AlB2-like) metal diborides MB2, where M = Na, Be, Mg, Ca, Al, Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Ag and Au. For monocrystalline MB2 the optimized lattice parameters, independent elastic constants (Cij), bulk modules (B), shear modules (G) are obtained and analyzed in comparison with the available theoretical and experimental data. For the first time numerical estimates of a set of elastic parameters of the polycrystalline MB2 ceramics (in the framework of the Voigt-Reuss-Hill approximation), namely bulk and shear modules, compressibility, Young's modules, Poisson's ratio, Lame's coefficients are performed.

Abstract:
Columnar joints are three-dimensional fracture networks that form in cooling basalt and several other media. The network organizes itself into ordered, mostly hexagonal columns. The same pattern can be observed on a smaller scale in desiccating starch. We show how surface boundary conditions in the desiccation of starch affect the formation of columnar joints. Under constant drying power conditions, we find a power law dependence of columnar cross-sectional area with depth, while under constant drying rate conditions this coarsening is eventually halted. Discontinuous transitions in pattern scale can be observed under constant external conditions, which may prompt a reinterpretation of similar transitions found in basalt. Starch patterns are statistically similar to those found in basalt, suggesting that mature columnar jointing patterns contain inherent residual disorder, but are statistically scale invariant.

Abstract:
Columnar jointing is a fracture pattern common in igneous rocks in which cracks self-organize into a roughly hexagonal arrangement, leaving behind an ordered colonnade. We report observations of columnar jointing in a laboratory analog system, desiccated corn starch slurries. Using measurements of moisture density, evaporation rates, and fracture advance rates as evidence, we suggest an advective-diffusive system is responsible for the rough scaling behavior of columnar joints. This theory explains the order of magnitude difference in scales between jointing in lavas and in starches. We investigated the scaling of average columnar cross-sectional areas due to the evaporation rate, the analog of the cooling rate of igneous columnar joints. We measured column areas in experiments where the evaporation rate depended on lamp height and time, in experiments where the evaporation rate was fixed using feedback methods, and in experiments where gelatin was added to vary the rheology of the starch. Our results suggest that the column area at a particular depth is related to both the current conditions, and hysteretically to the geometry of the pattern at previous depths. We argue that there exists a range of stable column scales allowed for any particular evaporation rate.