MgTi4Pb2O9F2 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(2), one O(3), one O(8), and two equivalent O(9) atoms to form MgO5 trigonal bipyramids that share  a cornercorner with one Ti(3)O5 trigonal bipyramid, corners with two equivalent Mg(1)O5 trigonal bipyramids,  an edgeedge with one Ti(1)O5F octahedra, edges with two equivalent Ti(2)O5F octahedra, and edges with two equivalent Ti(4)O6 octahedra. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(3), one O(5), one O(8), two equivalent O(1), and one F(1) atom to form distorted TiO5F octahedra that share  a cornercorner with one Ti(2)O5F octahedra, corners with two equivalent Ti(1)O5F octahedra, corners with two equivalent Pb(1)O2F3 square pyramids, edges with two equivalent Ti(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 14-28°. In the second Ti site, Ti(2) is bonded to one O(4), one O(5), one O(9), two equivalent O(2), and one F(2) atom to form TiO5F octahedra that share  a cornercorner with one Ti(1)O5F octahedra,  a cornercorner with one Ti(4)O6 octahedra, corners with two equivalent Ti(2)O5F octahedra,  a cornercorner with one Pb(1)O2F3 square pyramid, edges with two equivalent Mg(1)O5 trigonal bipyramids, and edges with two equivalent Ti(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 8-25°. In the third Ti site, Ti(3) is bonded to one O(2), one O(6), one O(7), and two equivalent O(4) atoms to form distorted TiO5 trigonal bipyramids that share corners with two equivalent Pb(1)O2F3 square pyramids,  a cornercorner with one Mg(1)O5 trigonal bipyramid, corners with two equivalent Ti(3)O5 trigonal bipyramids,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(2)O5F octahedra. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(6), one O(7), one O(9), and two equivalent O(3) atoms to form TiO6 octahedra that share  a cornercorner with one Ti(2)O5F octahedra, corners with two equivalent Ti(4)O6 octahedra, corners with two equivalent Pb(1)O2F3 square pyramids, edges with two equivalent Ti(1)O5F octahedra,  an edgeedge with one Ti(3)O5 trigonal bipyramid, and edges with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 8-19°. There are two inequivalent Pb sites. In the first Pb site, Pb(1) is bonded to two equivalent O(7), one F(2), and two equivalent F(1) atoms to form distorted PbO2F3 square pyramids that share  a cornercorner with one Ti(2)O5F octahedra, corners with two equivalent Ti(1)O5F octahedra, corners with two equivalent Ti(4)O6 octahedra, corners with two equivalent Ti(3)O5 trigonal bipyramids, and edges with two equivalent Pb(1)O2F3 square pyramids. The corner-sharing octahedral tilt angles range from 42-82°. In the second Pb site, Pb(2) is bonded in a 5-coordinate geometry to one O(4), two equivalent O(6), and two equivalent O(8) atoms. There are nine inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Ti(4) and two equivalent Ti(1) atoms. In the second O site, O(2) is bonded to one Mg(1), one Ti(3), and two equivalent Ti(2) atoms to form corner-sharing OMgTi3 trigonal pyramids. In the third O site, O(3) is bonded to one Mg(1), one Ti(1), and two equivalent Ti(4) atoms to form distorted corner-sharing OMgTi3 trigonal pyramids. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Ti(2), two equivalent Ti(3), and one Pb(2) atom. In the fifth O site, O(5) is bonded in a linear geometry to one Ti(1) and one Ti(2) atom. In the sixth O site, O(6) is bonded in a distorted L-shaped geometry to one Ti(3), one Ti(4), and two equivalent Pb(2) atoms. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Ti(3), one Ti(4), and two equivalent Pb(1) atoms. In the eighth O site, O(8) is bonded in a distorted L-shaped geometry to one Mg(1), one Ti(1), and two equivalent Pb(2) atoms. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to two equivalent Mg(1), one Ti(2), and one Ti(4) atom. There are two inequivalent F sites. In the first F site, F(1) is bonded in a 3-coordinate geometry to one Ti(1) and two equivalent Pb(1) atoms. In the second F site, F(2) is bonded in a distorted bent 150 degrees geometry to one Ti(2) and one Pb(1) atom.
MgTi4Pb2O9F2 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(2), one O(3), one O(8), and two equivalent O(9) atoms to form MgO5 trigonal bipyramids that share  a cornercorner with one Ti(3)O5 trigonal bipyramid, corners with two equivalent Mg(1)O5 trigonal bipyramids,  an edgeedge with one Ti(1)O5F octahedra, edges with two equivalent Ti(2)O5F octahedra, and edges with two equivalent Ti(4)O6 octahedra. The Mg(1)-O(2) bond length is 2.02 Å. The Mg(1)-O(3) bond length is 2.01 Å. The Mg(1)-O(8) bond length is 1.99 Å. Both Mg(1)-O(9) bond lengths are 2.03 Å. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(3), one O(5), one O(8), two equivalent O(1), and one F(1) atom to form distorted TiO5F octahedra that share  a cornercorner with one Ti(2)O5F octahedra, corners with two equivalent Ti(1)O5F octahedra, corners with two equivalent Pb(1)O2F3 square pyramids, edges with two equivalent Ti(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 14-28°. The Ti(1)-O(3) bond length is 2.25 Å. The Ti(1)-O(5) bond length is 1.84 Å. The Ti(1)-O(8) bond length is 1.88 Å. Both Ti(1)-O(1) bond lengths are 2.00 Å. The Ti(1)-F(1) bond length is 2.25 Å. In the second Ti site, Ti(2) is bonded to one O(4), one O(5), one O(9), two equivalent O(2), and one F(2) atom to form TiO5F octahedra that share  a cornercorner with one Ti(1)O5F octahedra,  a cornercorner with one Ti(4)O6 octahedra, corners with two equivalent Ti(2)O5F octahedra,  a cornercorner with one Pb(1)O2F3 square pyramid, edges with two equivalent Mg(1)O5 trigonal bipyramids, and edges with two equivalent Ti(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 8-25°. The Ti(2)-O(4) bond length is 2.21 Å. The Ti(2)-O(5) bond length is 1.89 Å. The Ti(2)-O(9) bond length is 1.98 Å. Both Ti(2)-O(2) bond lengths are 1.99 Å. The Ti(2)-F(2) bond length is 2.13 Å. In the third Ti site, Ti(3) is bonded to one O(2), one O(6), one O(7), and two equivalent O(4) atoms to form distorted TiO5 trigonal bipyramids that share corners with two equivalent Pb(1)O2F3 square pyramids,  a cornercorner with one Mg(1)O5 trigonal bipyramid, corners with two equivalent Ti(3)O5 trigonal bipyramids,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(2)O5F octahedra. The Ti(3)-O(2) bond length is 2.06 Å. The Ti(3)-O(6) bond length is 1.92 Å. The Ti(3)-O(7) bond length is 1.83 Å. Both Ti(3)-O(4) bond lengths are 2.00 Å. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(6), one O(7), one O(9), and two equivalent O(3) atoms to form TiO6 octahedra that share  a cornercorner with one Ti(2)O5F octahedra, corners with two equivalent Ti(4)O6 octahedra, corners with two equivalent Pb(1)O2F3 square pyramids, edges with two equivalent Ti(1)O5F octahedra,  an edgeedge with one Ti(3)O5 trigonal bipyramid, and edges with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 8-19°. The Ti(4)-O(1) bond length is 2.10 Å. The Ti(4)-O(6) bond length is 1.99 Å. The Ti(4)-O(7) bond length is 2.11 Å. The Ti(4)-O(9) bond length is 2.20 Å. Both Ti(4)-O(3) bond lengths are 1.97 Å. There are two inequivalent Pb sites. In the first Pb site, Pb(1) is bonded to two equivalent O(7), one F(2), and two equivalent F(1) atoms to form distorted PbO2F3 square pyramids that share  a cornercorner with one Ti(2)O5F octahedra, corners with two equivalent Ti(1)O5F octahedra, corners with two equivalent Ti(4)O6 octahedra, corners with two equivalent Ti(3)O5 trigonal bipyramids, and edges with two equivalent Pb(1)O2F3 square pyramids. The corner-sharing octahedral tilt angles range from 42-82°. Both Pb(1)-O(7) bond lengths are 2.58 Å. The Pb(1)-F(2) bond length is 2.44 Å. Both Pb(1)-F(1) bond lengths are 2.47 Å. In the second Pb site, Pb(2) is bonded in a 5-coordinate geometry to one O(4), two equivalent O(6), and two equivalent O(8) atoms. The Pb(2)-O(4) bond length is 2.60 Å. Both Pb(2)-O(6) bond lengths are 2.54 Å. Both Pb(2)-O(8) bond lengths are 2.61 Å. There are nine inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Ti(4) and two equivalent Ti(1) atoms. In the second O site, O(2) is bonded to one Mg(1), one Ti(3), and two equivalent Ti(2) atoms to form corner-sharing OMgTi3 trigonal pyramids. In the third O site, O(3) is bonded to one Mg(1), one Ti(1), and two equivalent Ti(4) atoms to form distorted corner-sharing OMgTi3 trigonal pyramids. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Ti(2), two equivalent Ti(3), and one Pb(2) atom. In the fifth O site, O(5) is bonded in a linear geometry to one Ti(1) and one Ti(2) atom. In the sixth O site, O(6) is bonded in a distorted L-shaped geometry to one Ti(3), one Ti(4), and two equivalent Pb(2) atoms. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Ti(3), one Ti(4), and two equivalent Pb(1) atoms. In the eighth O site, O(8) is bonded in a distorted L-shaped geometry to one Mg(1), one Ti(1), and two equivalent Pb(2) atoms. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to two equivalent Mg(1), one Ti(2), and one Ti(4) atom. There are two inequivalent F sites. In the first F site, F(1) is bonded in a 3-coordinate geometry to one Ti(1) and two equivalent Pb(1) atoms. In the second F site, F(2) is bonded in a distorted bent 150 degrees geometry to one Ti(2) and one Pb(1) atom.