Two novel types of irrational orientation relationships(ORs)between β-Mg2Sn precipitates and theα-Mg matrix were observed in a Mg-4Sn alloy aged at 160℃.In contrast to that for the dominant β-Mg2Sn laths lying on the(0001)α basal plane of the matrix,the precipitates with the irrational ORs are inclined or normal to(0001)α.Specifically,the precipitates that adopt the OR of[011]β//[2(11)0]α,with((1)1(1))βdeviating approximately 4.7° from(0002)α,have a long axis parallel to[0001]α.The precipitates with the OR of[011]β//[2(11)0]α,with(11(1))βdeviating approximately 13.5° from(0002)α,exhibit a long axis of[02(2)1]α.Both types of precipitates have a habit plane(HP)of(2(11)0)α.The interface orientations of the precipitates associated with the irrational ORs are interpreted by a good matching sites(GMS)method.A thorough examination of the crystallographic features of the β-Mg2Sn precipitates in the literature shows that the precipitates with most rational ORs have a HP parallel to(0001)α,and those with most irrational ORs have a HP(or long axis)inclined or normal to(0001)α.The preferences of the precipitates with different irrational ORs have also been analyzed by examining the lattice matching condition across the interfaces between the precipitates and the matrix.