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 t o an orientationally twinned crystalline nanodomain structure is deriv ed. Mapping the atomic positions of the quasicrystal onto the correspo nding positions of its (4,6)-approximant leads to a patchwork-like arr angement of crystalline nanodomains. The atomic displacements necessar y to transform the quasicrystal into the nanodomain structure are dete rmined locally. The optimum orientation of the approximant unit cells building the nanodomains is obtained by minimizing the sum of the corr esponding displacements. Approximately 50% of the resulting atomic shi fts 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 t o a one-dimensional quasicrystal. It is interpreted within the approac h of a linear growth model. Slight changes of the approximant lattice parameters as induced by temperature strongly influence domain size an d distribution. Correlations between the nanodomains are referred to t he discrete periodic average structure common to both the decagonal ph ase and the approximant structure.