Bi2MgO4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Bi(4)O6 octahedra, and corners with six equivalent Bi(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-58°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(1)O6 octahedra, corners with three equivalent Bi(3)O6 octahedra, and corners with six equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-55°. In the third Mg site, Mg(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Bi(6)O4 tetrahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with three equivalent Bi(4)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(6) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(2)O6 octahedra, corners with three equivalent Bi(5)O6 octahedra, and corners with six equivalent Bi(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-56°. In the fifth Mg site, Mg(5) is bonded to one O(9) and three equivalent O(3) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(2)O6 octahedra, corners with three equivalent Bi(3)O6 octahedra, and corners with six equivalent Bi(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-55°. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(4)O6 octahedra, corners with three equivalent Bi(5)O6 octahedra, and corners with six equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-55°. There are six inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Bi(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Bi(3)O6 octahedra, and edges with four equivalent Bi(1)O6 octahedra. In the second Bi site, Bi(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Mg(5)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Bi(3)O6 octahedra,  an edgeedge with one Bi(5)O6 octahedra, and edges with four equivalent Bi(2)O6 octahedra. In the third Bi site, Bi(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form BiO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(5)O4 tetrahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with three equivalent Bi(2)O6 octahedra. In the fourth Bi site, Bi(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(4)O4 tetrahedra, corners with two equivalent Bi(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Bi(5)O6 octahedra, and edges with four equivalent Bi(4)O6 octahedra. In the fifth Bi site, Bi(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form BiO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Bi(2)O6 octahedra, and edges with three equivalent Bi(4)O6 octahedra. In the sixth Bi site, Bi(6) is bonded to one O(5) and three equivalent O(11) atoms to form BiO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Bi(1)O6 octahedra, and corners with six equivalent Bi(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-64°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(3), and two equivalent Bi(1) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(2) and three equivalent Bi(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(5), one Bi(3), and two equivalent Bi(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Bi(3), and two equivalent Bi(2) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Bi(6) and three equivalent Bi(1) atoms. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Mg(4) and three equivalent Bi(2) atoms. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Mg(6), one Bi(5), and two equivalent Bi(2) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Bi(5), and two equivalent Bi(4) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Mg(5) and three equivalent Bi(2) atoms. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Mg(1) and three equivalent Bi(4) atoms. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Mg(3), one Bi(6), and two equivalent Bi(4) atoms. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Mg(6) and three equivalent Bi(4) atoms.
Bi2MgO4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Bi(4)O6 octahedra, and corners with six equivalent Bi(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-58°. The Mg(1)-O(10) bond length is 2.05 Å. All Mg(1)-O(1) bond lengths are 2.18 Å. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(1)O6 octahedra, corners with three equivalent Bi(3)O6 octahedra, and corners with six equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-55°. The Mg(2)-O(2) bond length is 2.10 Å. All Mg(2)-O(4) bond lengths are 2.08 Å. In the third Mg site, Mg(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Bi(6)O4 tetrahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with three equivalent Bi(4)O6 octahedra. All Mg(3)-O(1) bond lengths are 2.25 Å. All Mg(3)-O(11) bond lengths are 2.16 Å. In the fourth Mg site, Mg(4) is bonded to one O(6) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(2)O6 octahedra, corners with three equivalent Bi(5)O6 octahedra, and corners with six equivalent Bi(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-56°. The Mg(4)-O(6) bond length is 2.06 Å. All Mg(4)-O(8) bond lengths are 2.06 Å. In the fifth Mg site, Mg(5) is bonded to one O(9) and three equivalent O(3) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(2)O6 octahedra, corners with three equivalent Bi(3)O6 octahedra, and corners with six equivalent Bi(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-55°. The Mg(5)-O(9) bond length is 2.06 Å. All Mg(5)-O(3) bond lengths are 2.07 Å. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Bi(4)O6 octahedra, corners with three equivalent Bi(5)O6 octahedra, and corners with six equivalent Bi(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-55°. The Mg(6)-O(12) bond length is 2.08 Å. All Mg(6)-O(7) bond lengths are 2.10 Å. There are six inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Bi(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Bi(3)O6 octahedra, and edges with four equivalent Bi(1)O6 octahedra. The Bi(1)-O(2) bond length is 2.39 Å. The Bi(1)-O(5) bond length is 2.43 Å. Both Bi(1)-O(1) bond lengths are 2.37 Å. Both Bi(1)-O(3) bond lengths are 2.47 Å. In the second Bi site, Bi(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Mg(5)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Bi(3)O6 octahedra,  an edgeedge with one Bi(5)O6 octahedra, and edges with four equivalent Bi(2)O6 octahedra. The Bi(2)-O(6) bond length is 2.41 Å. The Bi(2)-O(9) bond length is 2.41 Å. Both Bi(2)-O(4) bond lengths are 2.40 Å. Both Bi(2)-O(7) bond lengths are 2.44 Å. In the third Bi site, Bi(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form BiO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(5)O4 tetrahedra, edges with three equivalent Bi(1)O6 octahedra, and edges with three equivalent Bi(2)O6 octahedra. All Bi(3)-O(3) bond lengths are 2.40 Å. All Bi(3)-O(4) bond lengths are 2.46 Å. In the fourth Bi site, Bi(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form BiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(4)O4 tetrahedra, corners with two equivalent Bi(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Bi(5)O6 octahedra, and edges with four equivalent Bi(4)O6 octahedra. The Bi(4)-O(10) bond length is 2.45 Å. The Bi(4)-O(12) bond length is 2.40 Å. Both Bi(4)-O(11) bond lengths are 2.35 Å. Both Bi(4)-O(8) bond lengths are 2.44 Å. In the fifth Bi site, Bi(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form BiO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Bi(2)O6 octahedra, and edges with three equivalent Bi(4)O6 octahedra. All Bi(5)-O(7) bond lengths are 2.40 Å. All Bi(5)-O(8) bond lengths are 2.47 Å. In the sixth Bi site, Bi(6) is bonded to one O(5) and three equivalent O(11) atoms to form BiO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Bi(1)O6 octahedra, and corners with six equivalent Bi(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-64°. The Bi(6)-O(5) bond length is 2.17 Å. All Bi(6)-O(11) bond lengths are 2.30 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(3), and two equivalent Bi(1) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(2) and three equivalent Bi(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(5), one Bi(3), and two equivalent Bi(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Bi(3), and two equivalent Bi(2) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Bi(6) and three equivalent Bi(1) atoms. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Mg(4) and three equivalent Bi(2) atoms. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Mg(6), one Bi(5), and two equivalent Bi(2) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Bi(5), and two equivalent Bi(4) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Mg(5) and three equivalent Bi(2) atoms. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Mg(1) and three equivalent Bi(4) atoms. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Mg(3), one Bi(6), and two equivalent Bi(4) atoms. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Mg(6) and three equivalent Bi(4) atoms.