Use of periodic approximants in the structure refinement of icosahedral AlCuFe

By exploiting the periodic cells which are approximants to the icosahedral phase, the problem of structure determination of the icosahedral phase can be converted to the standard crystallographic structure refinement problem. As larger approximants are used, structures are obtained which converge to that of the icosahedral phase. We refine the structure of the (hypothetical) 1/1 cubic approximant to icosahedral AlCuFe using this technique, with the aim of determining the structure of the icosahedral phase.