Mg4Mn9O13 is Caswellsilverite-like structured and crystallizes in the trigonal R3m space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(6) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent Mn(5)O6 octahedra, corners with three equivalent Mn(7)O6 octahedra, edges with three equivalent Mn(5)O6 octahedra, edges with three equivalent Mn(7)O6 octahedra, and edges with six equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the second Mg site, Mg(2) is bonded to three equivalent O(10) and three equivalent O(9) atoms to form MgO6 octahedra that share corners with three equivalent Mn(8)O6 octahedra, corners with three equivalent Mn(9)O6 octahedra, edges with three equivalent Mn(8)O6 octahedra, edges with three equivalent Mn(9)O6 octahedra, and edges with six equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. In the third Mg site, Mg(3) is bonded to three equivalent O(11) and three equivalent O(12) atoms to form MgO6 octahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Mn(9)O6 octahedra, edges with three equivalent Mg(4)O6 octahedra, edges with three equivalent Mn(9)O6 octahedra, and edges with six equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the fourth Mg site, Mg(4) is bonded to three equivalent O(12) and three equivalent O(13) atoms to form MgO6 octahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, edges with three equivalent Mg(3)O6 octahedra, edges with three equivalent Mn(1)O6 octahedra, and edges with six equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. There are nine inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to three equivalent O(1) and three equivalent O(13) atoms to form MnO6 octahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra, edges with three equivalent Mg(4)O6 octahedra, edges with three equivalent Mn(3)O6 octahedra, and edges with six equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the second Mn site, Mn(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra are not tilted. In the third Mn site, Mn(3) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra are not tilted. In the fourth Mn site, Mn(4) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra are not tilted. In the fifth Mn site, Mn(5) is bonded to three equivalent O(5) and three equivalent O(6) atoms to form MnO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Mn(6)O6 octahedra, edges with three equivalent Mg(1)O6 octahedra, edges with three equivalent Mn(6)O6 octahedra, and edges with six equivalent Mn(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the sixth Mn site, Mn(6) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra are not tilted. In the seventh Mn site, Mn(7) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form MnO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Mn(8)O6 octahedra, edges with three equivalent Mg(1)O6 octahedra, edges with three equivalent Mn(8)O6 octahedra, and edges with six equivalent Mn(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the eighth Mn site, Mn(8) is bonded to three equivalent O(7) and three equivalent O(9) atoms to form MnO6 octahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Mn(7)O6 octahedra, edges with three equivalent Mg(2)O6 octahedra, edges with three equivalent Mn(7)O6 octahedra, and edges with six equivalent Mn(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the ninth Mn site, Mn(9) is bonded to three equivalent O(10) and three equivalent O(11) atoms to form MnO6 octahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Mg(3)O6 octahedra, edges with three equivalent Mg(2)O6 octahedra, edges with three equivalent Mg(3)O6 octahedra, and edges with six equivalent Mn(9)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Mn(1) and three equivalent Mn(3) atoms to form OMn6 octahedra that share corners with three equivalent O(13)Mg3Mn3 octahedra, corners with three equivalent O(2)Mn6 octahedra, edges with three equivalent O(13)Mg3Mn3 octahedra, edges with three equivalent O(2)Mn6 octahedra, and edges with six equivalent O(1)Mn6 octahedra. The corner-sharing octahedra are not tilted. In the second O site, O(2) is bonded to three equivalent Mn(2) and three equivalent Mn(3) atoms to form a mixture of corner and edge-sharing OMn6 octahedra. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to three equivalent Mn(2) and three equivalent Mn(4) atoms to form a mixture of corner and edge-sharing OMn6 octahedra. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded to three equivalent Mn(4) and three equivalent Mn(6) atoms to form a mixture of corner and edge-sharing OMn6 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to three equivalent Mn(5) and three equivalent Mn(6) atoms to form OMn6 octahedra that share corners with three equivalent O(6)Mg3Mn3 octahedra, corners with three equivalent O(4)Mn6 octahedra, edges with three equivalent O(6)Mg3Mn3 octahedra, edges with three equivalent O(4)Mn6 octahedra, and edges with six equivalent O(5)Mn6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to three equivalent Mg(1) and three equivalent Mn(5) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(8)Mg3Mn3 octahedra, corners with three equivalent O(5)Mn6 octahedra, edges with three equivalent O(8)Mg3Mn3 octahedra, edges with three equivalent O(5)Mn6 octahedra, and edges with six equivalent O(6)Mg3Mn3 octahedra. The corner-sharing octahedra are not tilted. In the seventh O site, O(7) is bonded to three equivalent Mn(7) and three equivalent Mn(8) atoms to form OMn6 octahedra that share corners with three equivalent O(8)Mg3Mn3 octahedra, corners with three equivalent O(9)Mg3Mn3 octahedra, edges with three equivalent O(8)Mg3Mn3 octahedra, edges with three equivalent O(9)Mg3Mn3 octahedra, and edges with six equivalent O(7)Mn6 octahedra. The corner-sharing octahedra are not tilted. In the eighth O site, O(8) is bonded to three equivalent Mg(1) and three equivalent Mn(7) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(6)Mg3Mn3 octahedra, corners with three equivalent O(7)Mn6 octahedra, edges with three equivalent O(6)Mg3Mn3 octahedra, edges with three equivalent O(7)Mn6 octahedra, and edges with six equivalent O(8)Mg3Mn3 octahedra. The corner-sharing octahedra are not tilted. In the ninth O site, O(9) is bonded to three equivalent Mg(2) and three equivalent Mn(8) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(10)Mg3Mn3 octahedra, corners with three equivalent O(7)Mn6 octahedra, edges with three equivalent O(10)Mg3Mn3 octahedra, edges with three equivalent O(7)Mn6 octahedra, and edges with six equivalent O(9)Mg3Mn3 octahedra. The corner-sharing octahedra are not tilted. In the tenth O site, O(10) is bonded to three equivalent Mg(2) and three equivalent Mn(9) atoms to form a mixture of corner and edge-sharing OMg3Mn3 octahedra. The corner-sharing octahedra are not tilted. In the eleventh O site, O(11) is bonded to three equivalent Mg(3) and three equivalent Mn(9) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(10)Mg3Mn3 octahedra, corners with three equivalent O(12)Mg6 octahedra, edges with three equivalent O(10)Mg3Mn3 octahedra, edges with three equivalent O(12)Mg6 octahedra, and edges with six equivalent O(11)Mg3Mn3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the twelfth O site, O(12) is bonded to three equivalent Mg(3) and three equivalent Mg(4) atoms to form OMg6 octahedra that share corners with three equivalent O(11)Mg3Mn3 octahedra, corners with three equivalent O(13)Mg3Mn3 octahedra, edges with three equivalent O(11)Mg3Mn3 octahedra, edges with three equivalent O(13)Mg3Mn3 octahedra, and edges with six equivalent O(12)Mg6 octahedra. The corner-sharing octahedral tilt angles are 1°. In the thirteenth O site, O(13) is bonded to three equivalent Mg(4) and three equivalent Mn(1) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(12)Mg6 octahedra, corners with three equivalent O(1)Mn6 octahedra, edges with three equivalent O(12)Mg6 octahedra, edges with three equivalent O(1)Mn6 octahedra, and edges with six equivalent O(13)Mg3Mn3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°.
Mg4Mn9O13 is Caswellsilverite-like structured and crystallizes in the trigonal R3m space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(6) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent Mn(5)O6 octahedra, corners with three equivalent Mn(7)O6 octahedra, edges with three equivalent Mn(5)O6 octahedra, edges with three equivalent Mn(7)O6 octahedra, and edges with six equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. All Mg(1)-O(6) bond lengths are 2.16 Å. All Mg(1)-O(8) bond lengths are 2.16 Å. In the second Mg site, Mg(2) is bonded to three equivalent O(10) and three equivalent O(9) atoms to form MgO6 octahedra that share corners with three equivalent Mn(8)O6 octahedra, corners with three equivalent Mn(9)O6 octahedra, edges with three equivalent Mn(8)O6 octahedra, edges with three equivalent Mn(9)O6 octahedra, and edges with six equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. All Mg(2)-O(10) bond lengths are 2.18 Å. All Mg(2)-O(9) bond lengths are 2.18 Å. In the third Mg site, Mg(3) is bonded to three equivalent O(11) and three equivalent O(12) atoms to form MgO6 octahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Mn(9)O6 octahedra, edges with three equivalent Mg(4)O6 octahedra, edges with three equivalent Mn(9)O6 octahedra, and edges with six equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. All Mg(3)-O(11) bond lengths are 2.17 Å. All Mg(3)-O(12) bond lengths are 2.19 Å. In the fourth Mg site, Mg(4) is bonded to three equivalent O(12) and three equivalent O(13) atoms to form MgO6 octahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, edges with three equivalent Mg(3)O6 octahedra, edges with three equivalent Mn(1)O6 octahedra, and edges with six equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. All Mg(4)-O(12) bond lengths are 2.19 Å. All Mg(4)-O(13) bond lengths are 2.17 Å. There are nine inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to three equivalent O(1) and three equivalent O(13) atoms to form MnO6 octahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra, edges with three equivalent Mg(4)O6 octahedra, edges with three equivalent Mn(3)O6 octahedra, and edges with six equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. All Mn(1)-O(1) bond lengths are 2.24 Å. All Mn(1)-O(13) bond lengths are 2.25 Å. In the second Mn site, Mn(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra are not tilted. All Mn(2)-O(2) bond lengths are 2.23 Å. All Mn(2)-O(3) bond lengths are 2.23 Å. In the third Mn site, Mn(3) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra are not tilted. All Mn(3)-O(1) bond lengths are 2.24 Å. All Mn(3)-O(2) bond lengths are 2.24 Å. In the fourth Mn site, Mn(4) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra are not tilted. All Mn(4)-O(3) bond lengths are 2.23 Å. All Mn(4)-O(4) bond lengths are 2.23 Å. In the fifth Mn site, Mn(5) is bonded to three equivalent O(5) and three equivalent O(6) atoms to form MnO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Mn(6)O6 octahedra, edges with three equivalent Mg(1)O6 octahedra, edges with three equivalent Mn(6)O6 octahedra, and edges with six equivalent Mn(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. All Mn(5)-O(5) bond lengths are 2.23 Å. All Mn(5)-O(6) bond lengths are 2.24 Å. In the sixth Mn site, Mn(6) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form a mixture of corner and edge-sharing MnO6 octahedra. The corner-sharing octahedra are not tilted. All Mn(6)-O(4) bond lengths are 2.23 Å. All Mn(6)-O(5) bond lengths are 2.23 Å. In the seventh Mn site, Mn(7) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form MnO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Mn(8)O6 octahedra, edges with three equivalent Mg(1)O6 octahedra, edges with three equivalent Mn(8)O6 octahedra, and edges with six equivalent Mn(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. All Mn(7)-O(7) bond lengths are 2.25 Å. All Mn(7)-O(8) bond lengths are 2.25 Å. In the eighth Mn site, Mn(8) is bonded to three equivalent O(7) and three equivalent O(9) atoms to form MnO6 octahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Mn(7)O6 octahedra, edges with three equivalent Mg(2)O6 octahedra, edges with three equivalent Mn(7)O6 octahedra, and edges with six equivalent Mn(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. All Mn(8)-O(7) bond lengths are 2.25 Å. All Mn(8)-O(9) bond lengths are 2.26 Å. In the ninth Mn site, Mn(9) is bonded to three equivalent O(10) and three equivalent O(11) atoms to form MnO6 octahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Mg(3)O6 octahedra, edges with three equivalent Mg(2)O6 octahedra, edges with three equivalent Mg(3)O6 octahedra, and edges with six equivalent Mn(9)O6 octahedra. The corner-sharing octahedral tilt angles are 3°. All Mn(9)-O(10) bond lengths are 2.26 Å. All Mn(9)-O(11) bond lengths are 2.26 Å. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Mn(1) and three equivalent Mn(3) atoms to form OMn6 octahedra that share corners with three equivalent O(13)Mg3Mn3 octahedra, corners with three equivalent O(2)Mn6 octahedra, edges with three equivalent O(13)Mg3Mn3 octahedra, edges with three equivalent O(2)Mn6 octahedra, and edges with six equivalent O(1)Mn6 octahedra. The corner-sharing octahedra are not tilted. In the second O site, O(2) is bonded to three equivalent Mn(2) and three equivalent Mn(3) atoms to form a mixture of corner and edge-sharing OMn6 octahedra. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to three equivalent Mn(2) and three equivalent Mn(4) atoms to form a mixture of corner and edge-sharing OMn6 octahedra. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded to three equivalent Mn(4) and three equivalent Mn(6) atoms to form a mixture of corner and edge-sharing OMn6 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to three equivalent Mn(5) and three equivalent Mn(6) atoms to form OMn6 octahedra that share corners with three equivalent O(6)Mg3Mn3 octahedra, corners with three equivalent O(4)Mn6 octahedra, edges with three equivalent O(6)Mg3Mn3 octahedra, edges with three equivalent O(4)Mn6 octahedra, and edges with six equivalent O(5)Mn6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to three equivalent Mg(1) and three equivalent Mn(5) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(8)Mg3Mn3 octahedra, corners with three equivalent O(5)Mn6 octahedra, edges with three equivalent O(8)Mg3Mn3 octahedra, edges with three equivalent O(5)Mn6 octahedra, and edges with six equivalent O(6)Mg3Mn3 octahedra. The corner-sharing octahedra are not tilted. In the seventh O site, O(7) is bonded to three equivalent Mn(7) and three equivalent Mn(8) atoms to form OMn6 octahedra that share corners with three equivalent O(8)Mg3Mn3 octahedra, corners with three equivalent O(9)Mg3Mn3 octahedra, edges with three equivalent O(8)Mg3Mn3 octahedra, edges with three equivalent O(9)Mg3Mn3 octahedra, and edges with six equivalent O(7)Mn6 octahedra. The corner-sharing octahedra are not tilted. In the eighth O site, O(8) is bonded to three equivalent Mg(1) and three equivalent Mn(7) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(6)Mg3Mn3 octahedra, corners with three equivalent O(7)Mn6 octahedra, edges with three equivalent O(6)Mg3Mn3 octahedra, edges with three equivalent O(7)Mn6 octahedra, and edges with six equivalent O(8)Mg3Mn3 octahedra. The corner-sharing octahedra are not tilted. In the ninth O site, O(9) is bonded to three equivalent Mg(2) and three equivalent Mn(8) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(10)Mg3Mn3 octahedra, corners with three equivalent O(7)Mn6 octahedra, edges with three equivalent O(10)Mg3Mn3 octahedra, edges with three equivalent O(7)Mn6 octahedra, and edges with six equivalent O(9)Mg3Mn3 octahedra. The corner-sharing octahedra are not tilted. In the tenth O site, O(10) is bonded to three equivalent Mg(2) and three equivalent Mn(9) atoms to form a mixture of corner and edge-sharing OMg3Mn3 octahedra. The corner-sharing octahedra are not tilted. In the eleventh O site, O(11) is bonded to three equivalent Mg(3) and three equivalent Mn(9) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(10)Mg3Mn3 octahedra, corners with three equivalent O(12)Mg6 octahedra, edges with three equivalent O(10)Mg3Mn3 octahedra, edges with three equivalent O(12)Mg6 octahedra, and edges with six equivalent O(11)Mg3Mn3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the twelfth O site, O(12) is bonded to three equivalent Mg(3) and three equivalent Mg(4) atoms to form OMg6 octahedra that share corners with three equivalent O(11)Mg3Mn3 octahedra, corners with three equivalent O(13)Mg3Mn3 octahedra, edges with three equivalent O(11)Mg3Mn3 octahedra, edges with three equivalent O(13)Mg3Mn3 octahedra, and edges with six equivalent O(12)Mg6 octahedra. The corner-sharing octahedral tilt angles are 1°. In the thirteenth O site, O(13) is bonded to three equivalent Mg(4) and three equivalent Mn(1) atoms to form OMg3Mn3 octahedra that share corners with three equivalent O(12)Mg6 octahedra, corners with three equivalent O(1)Mn6 octahedra, edges with three equivalent O(12)Mg6 octahedra, edges with three equivalent O(1)Mn6 octahedra, and edges with six equivalent O(13)Mg3Mn3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°.