Decagonal quasicrystals (periodicity of 1 center dot 24 nm and 3 center dot 72 nm) and their orthorhombic approximants in Al67Cr15Cu18

Decagonal quasicrystals with two different periodicities in the tenfold direction, 1.24 nm and 3.72 nm respectively, have been found in rapidly solidified Al67Cr25Cu18. On annealing at 800-950 degrees C, four orthorhombic approximants appeared by substituting rational ratios of two consecutive Fibonacci numbers (0, 1, 1, 2, 3, 5, 8, 13, ...) for the irrational tau in the two orthogonal, quasiperiodic, twofold directions in these decagonal quasicrystals. The (1/1,1/1) approximant has about the same lattice parameters as Al3Mn, whereas those of the (1/0,2/1) are the same as T-3-AlMnZn. The (1/0,2/1), (2/1,5/3) and (3/2,8/5) approximants form a family of approximants with a and c parameters in 1 : tau(2) : tau(3) ratios. Although the (2/1,5/3) approximant has a b parameter of 3.72 nm, all others have a b value of 1.24 nm.