Twinning and the orientation relationships of icosahedral phase with the magnesium matrix

Five possible orientation relationships OR1 to OR5 of icosahedral quasicrystal with magnesium matrix are derived and experimental evidences are shown. In three of these, an icosahedral twofold axis occurs along the hexagonal axis of magnesium, symmetrically in the case of OR1 and OR2 and asymmetrically in OR5. A fivefold axis occurs along the magnesium hexagonal axis in OR3. An icosahedral "mirror" zone axis occurs along the hexagonal axis in OR4. These orientation relationships are related by {1 0 2} twinning of magnesium or twinning of the icosahedral phase. OR2 and OR3 can form from the OR1 by a {1 0 2} twinning of the matrix. At the same time, twinning of an icosahedral phase which makes OR1 with magnesium can create OR3 with the same matrix. OR4 forms on a particular twinning of the icosahedral phase in OR1 and OR2 while OR5 can be derived by a twinning of the icosahedral phase in OR3.