A FAMILY OF TAU-INFLATED MONOCLINIC AL13CO4 PHASES

Monoclinic tau(2)-Al13Co4, tau(3)-Al13Co4 and tau(4)-Al13Co4 phases with a and c parameters about tau(2), tau(3) and tau(4) times [tau = (1 + 5(1/2))/2 = 1.61803, which is the golden number], respectively, greater than their counterparts in Al13Co4 (space group Cm, a = 1.5183, b = 0.8122, c = 1.2340 nm, beta = 107 degrees 54' [Hudd & Taylor (1962). Acta Cryst. 15, 441-442]) have been found by selected-area electron diffraction and high-resolution electron microscopy (HREM). The [010] HREM images showed that these tau-inflated phases have a similar pentagonal layer structure as Al13Co4, but the edge length of the pentagons is tau(2), tau(3) and tau(4) times larger, respectively, than that in Al13Co4. This explains why these tau-inflated phases have about the same beta angle (similar or equal to 108 degrees) and b representing a repeat unit of the stacking of these pentagonal layers. The tau(2) pentagon (1.23 nm) consists of six smaller pentagons (0.47 nm) existing in Al13Co4, one inverted and five of the same orientation as the tau(2) pentagon. Similarly, the tau(3) pentagon (2.00 nm) consists of six tau pentagons (0.76 nm), and the tau(4) pentagon (3.23 nm) of six tau(2) pentagons which in turn contain six 0.47 nm pentagons in each of them. The greater the inflation, the larger the unit-cell parameters, and the better the approximation of its structure to that of a decagonal quasicrystal (DQC). In other words, a DQC is considered to be the end member of this family of tau-inflated phases.