A simple approach to quasicrystal structure and phason defect formulation

The advantages of the cut or section method in describing quasicrystal structures and phason defects are given. The real and reciprocal quasilattice formulation is derived straightforwardly. It is shown that the linear phason strain which leads to the quasilattice distortion is equivalent to a rotation of physical space relative to the high-dimensional space. A continuous rotation of the physical space will make the quasilattice deviate from its idealized form and turn gradually into a periodic lattice. The derivation of a geometrical relationship between the icosahedral quasilattice and the corresponding b.c.c. lattice becomes simple and clear. This will be beneficial to the construction of a quasicrystal structure model by reference to the corresponding b.c.c. crystal structure.