  The trigonal/bcc orientation relationships (ORs) and their likelihood of
occurrence are extensively studied using dispersed Y4Zr3O12nano-precipitates in
bcc Fe matrix by means of transmission electron microscopy, image simulations,
and a crystallographic model. Two orientation relationships related by a
rotation:[1-20]||[111] with (21-2)||(-110) and [1-20]||[111] with
(00-3)||(-110), are established and periodic arrays of misfit dislocation
doublets are identified at the strained interface in (110) for both ORs.
Further eighteen energetically feasible ORs in Y4Zr3O12/bcc system are deduced
by combining stereographic projections, which include the two predominant ORs
in this study and other ORs in literature. The orientation relationship which
generates the interface with a minimum number of dislocation doublets is the
most frequent.
