Mg21Sm3Sb16 crystallizes in the trigonal P-3m1 space group. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Sb(5,6) atoms to form MgSb6 octahedra that share corners with three equivalent Mg(3)Sb4 tetrahedra, corners with three equivalent Mg(4)Sb4 tetrahedra, corners with three equivalent Mg(8)Sb4 tetrahedra, corners with three equivalent Mg(9)Sb4 tetrahedra, edges with six equivalent Mg(1)Sb6 octahedra, edges with three equivalent Mg(8)Sb4 tetrahedra, and edges with three equivalent Mg(9)Sb4 tetrahedra. In the second Mg site, Mg(2) is bonded to three equivalent Sb(7) and three equivalent Sb(8) atoms to form MgSb6 octahedra that share corners with three equivalent Mg(10)Sb4 tetrahedra, corners with three equivalent Mg(11)Sb4 tetrahedra, corners with three equivalent Mg(5)Sb4 tetrahedra, corners with three equivalent Mg(6)Sb4 tetrahedra, edges with six equivalent Mg(2)Sb6 octahedra, edges with three equivalent Mg(10)Sb4 tetrahedra, and edges with three equivalent Mg(11)Sb4 tetrahedra. In the third Mg site, Mg(3) is bonded to one Sb(5,6) and three equivalent Sb(1) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(3)Sb4 tetrahedra, edges with three equivalent Sm(1)Sb6 octahedra, and edges with three equivalent Mg(8)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-59°. In the fourth Mg site, Mg(4) is bonded to one Sb(5,6) and three equivalent Sb(2) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(2)Sb6 octahedra, corners with six equivalent Mg(4)Sb4 tetrahedra, edges with three equivalent Sm(2)Sb6 octahedra, and edges with three equivalent Mg(9)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-59°. In the fifth Mg site, Mg(5) is bonded to one Sb(7) and three equivalent Sb(3) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(5)Sb4 tetrahedra, edges with three equivalent Sm(1)Sb6 octahedra, and edges with three equivalent Mg(10)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 13-58°. In the sixth Mg site, Mg(6) is bonded to one Sb(8) and three equivalent Sb(4) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Mg(7)Sb6 octahedra, corners with six equivalent Mg(6)Sb4 tetrahedra, edges with three equivalent Mg(7)Sb6 octahedra, and edges with three equivalent Mg(11)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-60°. In the seventh Mg site, Mg(7) is bonded to six equivalent Sb(4) atoms to form MgSb6 octahedra that share corners with six equivalent Mg(11)Sb4 tetrahedra, corners with six equivalent Mg(6)Sb4 tetrahedra, edges with six equivalent Mg(7)Sb6 octahedra, and edges with six equivalent Mg(6)Sb4 tetrahedra. In the eighth Mg site, Mg(8) is bonded to one Sb(1) and three equivalent Sb(5,6) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(8)Sb4 tetrahedra, edges with three equivalent Mg(1)Sb6 octahedra, and edges with three equivalent Mg(3)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-56°. In the ninth Mg site, Mg(9) is bonded to one Sb(2) and three equivalent Sb(5,6) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(2)Sb6 octahedra, corners with six equivalent Mg(9)Sb4 tetrahedra, edges with three equivalent Mg(1)Sb6 octahedra, and edges with three equivalent Mg(4)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-56°. In the tenth Mg site, Mg(10) is bonded to one Sb(3) and three equivalent Sb(7) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(10)Sb4 tetrahedra, edges with three equivalent Mg(2)Sb6 octahedra, and edges with three equivalent Mg(5)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 13-56°. In the eleventh Mg site, Mg(11) is bonded to one Sb(4) and three equivalent Sb(8) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Mg(7)Sb6 octahedra, corners with six equivalent Mg(11)Sb4 tetrahedra, edges with three equivalent Mg(2)Sb6 octahedra, and edges with three equivalent Mg(6)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 9-57°. There are two inequivalent Sm sites. In the first Sm site, Sm(1) is bonded to three equivalent Sb(1) and three equivalent Sb(3) atoms to form SmSb6 octahedra that share corners with three equivalent Mg(10)Sb4 tetrahedra, corners with three equivalent Mg(3)Sb4 tetrahedra, corners with three equivalent Mg(5)Sb4 tetrahedra, corners with three equivalent Mg(8)Sb4 tetrahedra, edges with six equivalent Sm(1)Sb6 octahedra, edges with three equivalent Mg(3)Sb4 tetrahedra, and edges with three equivalent Mg(5)Sb4 tetrahedra. In the second Sm site, Sm(2) is bonded to six equivalent Sb(2) atoms to form SmSb6 octahedra that share corners with six equivalent Mg(4)Sb4 tetrahedra, corners with six equivalent Mg(9)Sb4 tetrahedra, edges with six equivalent Sm(2)Sb6 octahedra, and edges with six equivalent Mg(4)Sb4 tetrahedra. There are seven inequivalent Sb sites. In the first Sb site, Sb(1) is bonded to one Mg(8), three equivalent Mg(3), and three equivalent Sm(1) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the second Sb site, Sb(2) is bonded to one Mg(9), three equivalent Mg(4), and three equivalent Sm(2) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the third Sb site, Sb(3) is bonded to one Mg(10), three equivalent Mg(5), and three equivalent Sm(1) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the fourth Sb site, Sb(4) is bonded to one Mg(11), three equivalent Mg(6), and three equivalent Mg(7) atoms to form a mixture of distorted edge and corner-sharing SbMg7 pentagonal bipyramids. In the fifth Sb site, Sb(5,6) is bonded in a 7-coordinate geometry to one Mg(3), three equivalent Mg(1), and three equivalent Mg(8) atoms. In the sixth Sb site, Sb(7) is bonded in a 7-coordinate geometry to one Mg(5), three equivalent Mg(10), and three equivalent Mg(2) atoms. In the seventh Sb site, Sb(8) is bonded to one Mg(6), three equivalent Mg(11), and three equivalent Mg(2) atoms to form distorted edge-sharing SbMg7 pentagonal bipyramids.
Mg21Sm3Sb16 crystallizes in the trigonal P-3m1 space group. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Sb(5,6) atoms to form MgSb6 octahedra that share corners with three equivalent Mg(3)Sb4 tetrahedra, corners with three equivalent Mg(4)Sb4 tetrahedra, corners with three equivalent Mg(8)Sb4 tetrahedra, corners with three equivalent Mg(9)Sb4 tetrahedra, edges with six equivalent Mg(1)Sb6 octahedra, edges with three equivalent Mg(8)Sb4 tetrahedra, and edges with three equivalent Mg(9)Sb4 tetrahedra. All Mg(1)-Sb(5,6) bond lengths are 3.13 Å. In the second Mg site, Mg(2) is bonded to three equivalent Sb(7) and three equivalent Sb(8) atoms to form MgSb6 octahedra that share corners with three equivalent Mg(10)Sb4 tetrahedra, corners with three equivalent Mg(11)Sb4 tetrahedra, corners with three equivalent Mg(5)Sb4 tetrahedra, corners with three equivalent Mg(6)Sb4 tetrahedra, edges with six equivalent Mg(2)Sb6 octahedra, edges with three equivalent Mg(10)Sb4 tetrahedra, and edges with three equivalent Mg(11)Sb4 tetrahedra. All Mg(2)-Sb(7) bond lengths are 3.16 Å. All Mg(2)-Sb(8) bond lengths are 3.09 Å. In the third Mg site, Mg(3) is bonded to one Sb(5,6) and three equivalent Sb(1) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(3)Sb4 tetrahedra, edges with three equivalent Sm(1)Sb6 octahedra, and edges with three equivalent Mg(8)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-59°. The Mg(3)-Sb(5,6) bond length is 2.90 Å. All Mg(3)-Sb(1) bond lengths are 2.86 Å. In the fourth Mg site, Mg(4) is bonded to one Sb(5,6) and three equivalent Sb(2) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(2)Sb6 octahedra, corners with six equivalent Mg(4)Sb4 tetrahedra, edges with three equivalent Sm(2)Sb6 octahedra, and edges with three equivalent Mg(9)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 14-59°. The Mg(4)-Sb(5,6) bond length is 2.90 Å. All Mg(4)-Sb(2) bond lengths are 2.86 Å. In the fifth Mg site, Mg(5) is bonded to one Sb(7) and three equivalent Sb(3) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(5)Sb4 tetrahedra, edges with three equivalent Sm(1)Sb6 octahedra, and edges with three equivalent Mg(10)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 13-58°. The Mg(5)-Sb(7) bond length is 2.87 Å. All Mg(5)-Sb(3) bond lengths are 2.87 Å. In the sixth Mg site, Mg(6) is bonded to one Sb(8) and three equivalent Sb(4) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Mg(7)Sb6 octahedra, corners with six equivalent Mg(6)Sb4 tetrahedra, edges with three equivalent Mg(7)Sb6 octahedra, and edges with three equivalent Mg(11)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-60°. The Mg(6)-Sb(8) bond length is 2.97 Å. All Mg(6)-Sb(4) bond lengths are 2.87 Å. In the seventh Mg site, Mg(7) is bonded to six equivalent Sb(4) atoms to form MgSb6 octahedra that share corners with six equivalent Mg(11)Sb4 tetrahedra, corners with six equivalent Mg(6)Sb4 tetrahedra, edges with six equivalent Mg(7)Sb6 octahedra, and edges with six equivalent Mg(6)Sb4 tetrahedra. All Mg(7)-Sb(4) bond lengths are 3.21 Å. In the eighth Mg site, Mg(8) is bonded to one Sb(1) and three equivalent Sb(5,6) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(8)Sb4 tetrahedra, edges with three equivalent Mg(1)Sb6 octahedra, and edges with three equivalent Mg(3)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-56°. The Mg(8)-Sb(1) bond length is 2.97 Å. All Mg(8)-Sb(5,6) bond lengths are 2.84 Å. In the ninth Mg site, Mg(9) is bonded to one Sb(2) and three equivalent Sb(5,6) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(1)Sb6 octahedra, corners with three equivalent Sm(2)Sb6 octahedra, corners with six equivalent Mg(9)Sb4 tetrahedra, edges with three equivalent Mg(1)Sb6 octahedra, and edges with three equivalent Mg(4)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 12-56°. The Mg(9)-Sb(2) bond length is 2.97 Å. All Mg(9)-Sb(5,6) bond lengths are 2.84 Å. In the tenth Mg site, Mg(10) is bonded to one Sb(3) and three equivalent Sb(7) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Sm(1)Sb6 octahedra, corners with six equivalent Mg(10)Sb4 tetrahedra, edges with three equivalent Mg(2)Sb6 octahedra, and edges with three equivalent Mg(5)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 13-56°. The Mg(10)-Sb(3) bond length is 2.98 Å. All Mg(10)-Sb(7) bond lengths are 2.83 Å. In the eleventh Mg site, Mg(11) is bonded to one Sb(4) and three equivalent Sb(8) atoms to form MgSb4 tetrahedra that share corners with three equivalent Mg(2)Sb6 octahedra, corners with three equivalent Mg(7)Sb6 octahedra, corners with six equivalent Mg(11)Sb4 tetrahedra, edges with three equivalent Mg(2)Sb6 octahedra, and edges with three equivalent Mg(6)Sb4 tetrahedra. The corner-sharing octahedral tilt angles range from 9-57°. The Mg(11)-Sb(4) bond length is 2.97 Å. All Mg(11)-Sb(8) bond lengths are 2.87 Å. There are two inequivalent Sm sites. In the first Sm site, Sm(1) is bonded to three equivalent Sb(1) and three equivalent Sb(3) atoms to form SmSb6 octahedra that share corners with three equivalent Mg(10)Sb4 tetrahedra, corners with three equivalent Mg(3)Sb4 tetrahedra, corners with three equivalent Mg(5)Sb4 tetrahedra, corners with three equivalent Mg(8)Sb4 tetrahedra, edges with six equivalent Sm(1)Sb6 octahedra, edges with three equivalent Mg(3)Sb4 tetrahedra, and edges with three equivalent Mg(5)Sb4 tetrahedra. All Sm(1)-Sb(1) bond lengths are 3.24 Å. All Sm(1)-Sb(3) bond lengths are 3.23 Å. In the second Sm site, Sm(2) is bonded to six equivalent Sb(2) atoms to form SmSb6 octahedra that share corners with six equivalent Mg(4)Sb4 tetrahedra, corners with six equivalent Mg(9)Sb4 tetrahedra, edges with six equivalent Sm(2)Sb6 octahedra, and edges with six equivalent Mg(4)Sb4 tetrahedra. All Sm(2)-Sb(2) bond lengths are 3.24 Å. There are seven inequivalent Sb sites. In the first Sb site, Sb(1) is bonded to one Mg(8), three equivalent Mg(3), and three equivalent Sm(1) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the second Sb site, Sb(2) is bonded to one Mg(9), three equivalent Mg(4), and three equivalent Sm(2) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the third Sb site, Sb(3) is bonded to one Mg(10), three equivalent Mg(5), and three equivalent Sm(1) atoms to form a mixture of distorted edge and corner-sharing SbSm3Mg4 pentagonal bipyramids. In the fourth Sb site, Sb(4) is bonded to one Mg(11), three equivalent Mg(6), and three equivalent Mg(7) atoms to form a mixture of distorted edge and corner-sharing SbMg7 pentagonal bipyramids. In the fifth Sb site, Sb(5,6) is bonded in a 7-coordinate geometry to one Mg(3), three equivalent Mg(1), and three equivalent Mg(8) atoms. In the sixth Sb site, Sb(7) is bonded in a 7-coordinate geometry to one Mg(5), three equivalent Mg(10), and three equivalent Mg(2) atoms. In the seventh Sb site, Sb(8) is bonded to one Mg(6), three equivalent Mg(11), and three equivalent Mg(2) atoms to form distorted edge-sharing SbMg7 pentagonal bipyramids.