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The trigonal/bcc orientation relationships (ORs) and their likelihood of occurrence are extensively studied using dispersed Y 4 Zr 3 O 12 (δ) nano-precipitates in bcc Fe (α) matrix by means of transmission electron microscopy, image simulations and a crystallographic model. Two orientation relationships related by a rotation:[1 20] δ ||[111] α with (21 2) δ ||( 110) α and [1 20] δ ||[111] α with (00 3) δ ||( 110) α , are established and periodic arrays of misfit dislocation doublets are identified at the strained interface in (110) α for both ORs. Further eighteen energetically feasible ORs in Y 4 Zr 3 O 12 /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 interface with a minimum number of dislocation doublets is the most frequent.