The two dimensional plane can be filled with rhombuses, so as to generate non-periodic tilings with 4, 6, 8, 10 and 12-fold symmetries. Some representative tilings constructed using the rule of inflation are shown. The numerically computed diffraction patterns for the corresponding tilings are also shown to facilitate a comparison with possible X-ray or electron diffraction pictures.

The diffraction patterns from Fibonacci quasilattices have been calculated. Finite-size effects are evaluated for weak and strong peaks. For a smaller number of scatterers (<100) there are fluctuations in the intensities of weak and strong peaks. The fluctuations in weak peaks are greater than that in strong peaks. The fluctuations in intensities of weak and strong peaks near the origin are larger than in the corresponding cases of weak and strong peaks far away from the origin. Small shifts in peak-positions are unexpectedly found, the shifts being proportional toN^−3/2 for a large number of scatterers. The diffraction pattern of a one-dimensional crystal and random structure is compared with that of the Fibonacci quasilattice. The strong peaks observed in the diffraction pattern of 1-d crystal show negligible peak-shifts, they being comparable with computational errors even when the number of scatterers is as small as 5. The implications for analysing the experiments are briefly indicated.

We have studied the electrical conductivity of well aligned samples of hexahexylthiotriphenylene (HHTT) in the pure as well as doped states. The dopant used was a small concentration (0.62 mole %) of the electron acceptor trinitrofluorenone (TNF). In the columnar phases, doping causes the AC(1 kHz) conductivity along the columnar axis (σ_‖) to increase by a factor of 10⁷ or more relative to that in undoped samples; σ_‖ attains a value of 10⁻²S/m, which was the maximum measurable limit of our experimental set up. On the other hand, in the isotropic phase doping makes hardly any difference to the conductivity. The frequency dependence of the conductivity has been investigated. The DC conductivity of doped samples exhibits an enormous anisotropy, σ_‖/σ_⊥ ≥ 10¹⁰, which is 7 orders higher than that reported for any liquid crystalline system, and, to our knowledge, the largest observed in an organic conductor.

We also report the first thermoelectric power studies on these ‘molecular wires’. The sign of the thermoelectric power is in conformity with the expected nature of the charge carriers, namely, holes.