Complete structural studies of long period stacking ordered (LPSO) phases in the Y-Ni-Mg system by 3D electron diffraction

The crystal structures of three Y-Ni-Mg LPSO phases were directly solved from diffraction data of X-rays ((Mg@Y 8 Ni 6 )Mg 18 , tI 66-Nd 8+x Ru 6 Mg 19-x ) and electrons ((Mg@Y 8 Ni 6 ) 16 Mg 505 and (Mg@Y 8 Ni 6 ) 3 Mg 154 )). The latter two are modulated structures described in 6D( Fm -3 m (α00)000(0α0)000(00α)000, q1 = 0.441(6) a*, q2 = 0.441(6) b* , and q3 = 0.441(6) c* ) and 5D ( R- 3 c (αα0)00(-2α,α0)00, q 1 = 0.1457(7) a* + 0.1457(7) b*, q 2 = -0.2915(7) a* + 0.1457(7) b* ) superspaces, respectively. The 3D electron diffraction was applied here for the first time to LPSO compounds, turning out to be the only method successfully overcoming the numerous problems hampering their complete structure solution. The structural analysis of these compounds resulted in a generalized description of Y-Ni-Mg LPSO phases in terms of Mg@Y 8 Ni 6 clusters more or less densely distributed in a Mg matrix, justifying the proposed formulas. LPSO classification based on the layer stacking modes is proposed, leading to fcc ( c -type) and hybrid fcc/hcp ( (h) n cc -type) subfamilies, the former being identified in this work and including (Mg@Y 8 Ni 6 )Mg 18 as well as (Mg@Y 8 Ni 6 ) 16 Mg 505 . The inter-clusters coordination in form of distorted anticuboctahedra or cuboctahedra is a further fingerprint of membership in either family. Increasing the magnesium content, the Mg@Y 8 Ni 6 units tend to form aggregates at characteristic inter-cluster distances, the distribution of which is at the origin of the structural modulation.