Fivefold symmetry in real and reciprocal spaces

Tetrahedrally close-packed structures with juxtaposed pentagonal antiprisms, such as the μ, C14 Laves and the newly found C phases, were studied by means of HREM and SAD. It was found that each bright spot in the structural image corresponds to an antiprism. Differently oriented domains of these phases intergrow frequently with a fairly good match at the interphase boundary. All diffraction patterns of these phases show a fivefold distribution of spot-pairs, and it is shown that this fivefold symmetry comes from the pentagons and spot-pairs from two pentagonal prisms superposed in antisymmetrical positions.