MgTi3WPb5O15 crystallizes in the tetragonal P4/nmm space group. Mg(1) is bonded to one O(2), one O(3), and four equivalent O(1) atoms to form MgO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with five equivalent W(1)O6 octahedra, faces with four equivalent Pb(1)O12 cuboctahedra, and faces with four equivalent Pb(2)O12 cuboctahedra. The corner-sharing octahedra are not tilted. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(3), one O(5), and four equivalent O(4) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, faces with four equivalent Pb(2)O12 cuboctahedra, and faces with four equivalent Pb(3)O12 cuboctahedra. The corner-sharing octahedra are not tilted. In the second Ti site, Ti(2) is bonded to one O(6), one O(7), and four equivalent O(4) atoms to form TiO6 octahedra that share  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one W(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, faces with four equivalent Pb(2)O12 cuboctahedra, and faces with four equivalent Pb(3)O12 cuboctahedra. The corner-sharing octahedra are not tilted. In the third Ti site, Ti(3) is bonded to one O(5), one O(6), and four equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with four equivalent Ti(3)O6 octahedra, and faces with eight equivalent Pb(3)O12 cuboctahedra. The corner-sharing octahedra are not tilted. W(1) is bonded to one O(2), one O(7), and four equivalent O(1) atoms to form WO6 octahedra that share  a cornercorner with one Ti(2)O6 octahedra, corners with five equivalent Mg(1)O6 octahedra, faces with four equivalent Pb(1)O12 cuboctahedra, and faces with four equivalent Pb(2)O12 cuboctahedra. The corner-sharing octahedra are not tilted. There are three inequivalent Pb sites. In the first Pb site, Pb(1) is bonded to four equivalent O(2) and eight equivalent O(1) atoms to form PbO12 cuboctahedra that share corners with four equivalent Pb(1)O12 cuboctahedra, corners with eight equivalent Pb(2)O12 cuboctahedra, faces with two equivalent Pb(2)O12 cuboctahedra, faces with four equivalent Pb(1)O12 cuboctahedra, faces with four equivalent Mg(1)O6 octahedra, and faces with four equivalent W(1)O6 octahedra. In the second Pb site, Pb(2) is bonded to two equivalent O(3), two equivalent O(7), four equivalent O(1), and four equivalent O(4) atoms to form distorted PbO12 cuboctahedra that share corners with four equivalent Pb(1)O12 cuboctahedra, corners with four equivalent Pb(2)O12 cuboctahedra, corners with four equivalent Pb(3)O12 cuboctahedra,  a faceface with one Pb(1)O12 cuboctahedra,  a faceface with one Pb(3)O12 cuboctahedra, faces with four equivalent Pb(2)O12 cuboctahedra, faces with two equivalent Mg(1)O6 octahedra, faces with two equivalent Ti(1)O6 octahedra, faces with two equivalent Ti(2)O6 octahedra, and faces with two equivalent W(1)O6 octahedra. In the third Pb site, Pb(3) is bonded to two equivalent O(5), two equivalent O(6), four equivalent O(4), and four equivalent O(8) atoms to form PbO12 cuboctahedra that share corners with four equivalent Pb(2)O12 cuboctahedra, corners with eight equivalent Pb(3)O12 cuboctahedra,  a faceface with one Pb(2)O12 cuboctahedra, faces with five equivalent Pb(3)O12 cuboctahedra, faces with two equivalent Ti(1)O6 octahedra, faces with two equivalent Ti(2)O6 octahedra, and faces with four equivalent Ti(3)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a linear geometry to one Mg(1), one W(1), two equivalent Pb(1), and two equivalent Pb(2) atoms. In the second O site, O(2) is bonded in a linear geometry to one Mg(1), one W(1), and four equivalent Pb(1) atoms. In the third O site, O(3) is bonded in a linear geometry to one Mg(1), one Ti(1), and four equivalent Pb(2) atoms. In the fourth O site, O(4) is bonded in a linear geometry to one Ti(1), one Ti(2), two equivalent Pb(2), and two equivalent Pb(3) atoms. In the fifth O site, O(5) is bonded in a linear geometry to one Ti(1), one Ti(3), and four equivalent Pb(3) atoms. In the sixth O site, O(6) is bonded in a linear geometry to one Ti(2), one Ti(3), and four equivalent Pb(3) atoms. In the seventh O site, O(7) is bonded in a linear geometry to one Ti(2), one W(1), and four equivalent Pb(2) atoms. In the eighth O site, O(8) is bonded in a linear geometry to two equivalent Ti(3) and four equivalent Pb(3) atoms.
MgTi3WPb5O15 crystallizes in the tetragonal P4/nmm space group. Mg(1) is bonded to one O(2), one O(3), and four equivalent O(1) atoms to form MgO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with five equivalent W(1)O6 octahedra, faces with four equivalent Pb(1)O12 cuboctahedra, and faces with four equivalent Pb(2)O12 cuboctahedra. The corner-sharing octahedra are not tilted. The Mg(1)-O(2) bond length is 2.07 Å. The Mg(1)-O(3) bond length is 2.06 Å. All Mg(1)-O(1) bond lengths are 2.08 Å. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(3), one O(5), and four equivalent O(4) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, faces with four equivalent Pb(2)O12 cuboctahedra, and faces with four equivalent Pb(3)O12 cuboctahedra. The corner-sharing octahedra are not tilted. The Ti(1)-O(3) bond length is 1.82 Å. The Ti(1)-O(5) bond length is 2.10 Å. All Ti(1)-O(4) bond lengths are 2.02 Å. In the second Ti site, Ti(2) is bonded to one O(6), one O(7), and four equivalent O(4) atoms to form TiO6 octahedra that share  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one W(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, faces with four equivalent Pb(2)O12 cuboctahedra, and faces with four equivalent Pb(3)O12 cuboctahedra. The corner-sharing octahedra are not tilted. The Ti(2)-O(6) bond length is 1.88 Å. The Ti(2)-O(7) bond length is 2.09 Å. All Ti(2)-O(4) bond lengths are 2.00 Å. In the third Ti site, Ti(3) is bonded to one O(5), one O(6), and four equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with four equivalent Ti(3)O6 octahedra, and faces with eight equivalent Pb(3)O12 cuboctahedra. The corner-sharing octahedra are not tilted. The Ti(3)-O(5) bond length is 1.88 Å. The Ti(3)-O(6) bond length is 2.08 Å. All Ti(3)-O(8) bond lengths are 2.01 Å. W(1) is bonded to one O(2), one O(7), and four equivalent O(1) atoms to form WO6 octahedra that share  a cornercorner with one Ti(2)O6 octahedra, corners with five equivalent Mg(1)O6 octahedra, faces with four equivalent Pb(1)O12 cuboctahedra, and faces with four equivalent Pb(2)O12 cuboctahedra. The corner-sharing octahedra are not tilted. The W(1)-O(2) bond length is 1.93 Å. The W(1)-O(7) bond length is 1.99 Å. All W(1)-O(1) bond lengths are 1.94 Å. There are three inequivalent Pb sites. In the first Pb site, Pb(1) is bonded to four equivalent O(2) and eight equivalent O(1) atoms to form PbO12 cuboctahedra that share corners with four equivalent Pb(1)O12 cuboctahedra, corners with eight equivalent Pb(2)O12 cuboctahedra, faces with two equivalent Pb(2)O12 cuboctahedra, faces with four equivalent Pb(1)O12 cuboctahedra, faces with four equivalent Mg(1)O6 octahedra, and faces with four equivalent W(1)O6 octahedra. All Pb(1)-O(2) bond lengths are 2.84 Å. All Pb(1)-O(1) bond lengths are 2.83 Å. In the second Pb site, Pb(2) is bonded to two equivalent O(3), two equivalent O(7), four equivalent O(1), and four equivalent O(4) atoms to form distorted PbO12 cuboctahedra that share corners with four equivalent Pb(1)O12 cuboctahedra, corners with four equivalent Pb(2)O12 cuboctahedra, corners with four equivalent Pb(3)O12 cuboctahedra,  a faceface with one Pb(1)O12 cuboctahedra,  a faceface with one Pb(3)O12 cuboctahedra, faces with four equivalent Pb(2)O12 cuboctahedra, faces with two equivalent Mg(1)O6 octahedra, faces with two equivalent Ti(1)O6 octahedra, faces with two equivalent Ti(2)O6 octahedra, and faces with two equivalent W(1)O6 octahedra. Both Pb(2)-O(3) bond lengths are 2.84 Å. Both Pb(2)-O(7) bond lengths are 2.84 Å. All Pb(2)-O(1) bond lengths are 2.87 Å. All Pb(2)-O(4) bond lengths are 2.78 Å. In the third Pb site, Pb(3) is bonded to two equivalent O(5), two equivalent O(6), four equivalent O(4), and four equivalent O(8) atoms to form PbO12 cuboctahedra that share corners with four equivalent Pb(2)O12 cuboctahedra, corners with eight equivalent Pb(3)O12 cuboctahedra,  a faceface with one Pb(2)O12 cuboctahedra, faces with five equivalent Pb(3)O12 cuboctahedra, faces with two equivalent Ti(1)O6 octahedra, faces with two equivalent Ti(2)O6 octahedra, and faces with four equivalent Ti(3)O6 octahedra. Both Pb(3)-O(5) bond lengths are 2.84 Å. Both Pb(3)-O(6) bond lengths are 2.84 Å. All Pb(3)-O(4) bond lengths are 2.84 Å. All Pb(3)-O(8) bond lengths are 2.82 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a linear geometry to one Mg(1), one W(1), two equivalent Pb(1), and two equivalent Pb(2) atoms. In the second O site, O(2) is bonded in a linear geometry to one Mg(1), one W(1), and four equivalent Pb(1) atoms. In the third O site, O(3) is bonded in a linear geometry to one Mg(1), one Ti(1), and four equivalent Pb(2) atoms. In the fourth O site, O(4) is bonded in a linear geometry to one Ti(1), one Ti(2), two equivalent Pb(2), and two equivalent Pb(3) atoms. In the fifth O site, O(5) is bonded in a linear geometry to one Ti(1), one Ti(3), and four equivalent Pb(3) atoms. In the sixth O site, O(6) is bonded in a linear geometry to one Ti(2), one Ti(3), and four equivalent Pb(3) atoms. In the seventh O site, O(7) is bonded in a linear geometry to one Ti(2), one W(1), and four equivalent Pb(2) atoms. In the eighth O site, O(8) is bonded in a linear geometry to two equivalent Ti(3) and four equivalent Pb(3) atoms.