Characterization and interpretation of twin related row-matching orientation relationships between Mg₂Sn precipitates and the Mg matrix

Two irrational orientation relationships (ORs) are newly observed between β-Mg₂Sn precipitates and the α-Mg matrix in an aged Mg–Sn-based alloy, namely OR9: [011]_β-9//_α, (100)_β-9 about −15.6° from (0001)_α and OR10: _β-10//_α, (100)_β-10 about 4.0° from _α. The ORs have a common reciprocal row-matching condition, which shows that rows of diffraction spots parallel to g_β-9 [or g_β-10] from lattice β match those parallel to g_α from lattice α. A twin relationship exists between OR9-type and OR10-type precipitates, of which the major side facets, parallel to the twinning plane, are invariably normal to the matching rows in reciprocal space. The reciprocal row matching of diffraction spots is proven to correspond to a real row matching of lattice sites in direct space. The real matching rows of lattice sites lie in the major side facets, resulting in periodically distributed good matching lattice bands in the facets, i.e. a singular interfacial structure. This explains why the irrational ORs are preferred. This study demonstrates an explicit association of geometric lattice matching with the ORs and the morphologies of precipitates developed during a phase transformation.