Geometrical model of the phase transformation of decagonal Al-Co-Ni to its periodic approximant

Based on computer simulations in direct as well as in reciprocal space, a geometrical model for the transformation from decagonal Al-Co-Ni to an orientationally twinned crystalline nanodomain structure is derived. Mapping the atomic positions of the quasicrystal onto the corresponding positions of its (4,6)-approximant leads to a patchwork-like arrangement of crystalline nanodomains. The atomic displacements necessary to transform the quasicrystal into the nanodomain structure are determined locally. The optimum orientation of the approximant unit cells building the nanodomains is obtained by minimizing the sum of the corresponding displacements. Approximately 50% of the resulting atomic shifts are less than 1 Angstrom, and more than 90% less than 1.5 Angstrom. These results are verified by comparison with previous experimental observations. An intermediate state of the transformation is related to a one-dimensional quasicrystal. It is interpreted within the approach of a linear growth model. Slight changes of the approximant lattice parameters as induced by temperature strongly influence domain size and distribution. Correlations between the nanodomains are referred to the discrete periodic average structure common to both the decagonal phase and the approximant structure.