MgDy4Ti2O10 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(3), one O(4), and one O(9) atom to form distorted MgO5 square pyramids that share  a cornercorner with one Dy(4)O6 octahedra, corners with two equivalent Dy(3)O6 octahedra,  a cornercorner with one Ti(1)O5 trigonal bipyramid,  an edgeedge with one Dy(3)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one Ti(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 43-82°. There are four inequivalent Dy sites. In the first Dy site, Dy(1) is bonded in a 6-coordinate geometry to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(9) atom. In the second Dy site, Dy(2) is bonded in a 6-coordinate geometry to one O(10), one O(2), one O(3), one O(6), one O(7), and one O(8) atom. In the third Dy site, Dy(3) is bonded to one O(1), one O(3), one O(4), one O(5), one O(8), and one O(9) atom to form distorted DyO6 octahedra that share corners with two equivalent Dy(4)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, corners with two equivalent Mg(1)O5 square pyramids,  a cornercorner with one Ti(1)O5 trigonal bipyramid,  an edgeedge with one Mg(1)O5 square pyramid, and  an edgeedge with one Ti(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 36-62°. In the fourth Dy site, Dy(4) is bonded to one O(10), one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form distorted DyO6 octahedra that share corners with two equivalent Dy(3)O6 octahedra,  a cornercorner with one Mg(1)O5 square pyramid, corners with three equivalent Ti(1)O5 trigonal bipyramids, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(10), one O(3), one O(7), and one O(8) atom to form distorted TiO5 trigonal bipyramids that share  a cornercorner with one Dy(3)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with three equivalent Dy(4)O6 octahedra,  a cornercorner with one Mg(1)O5 square pyramid,  an edgeedge with one Dy(3)O6 octahedra, and  an edgeedge with one Mg(1)O5 square pyramid. The corner-sharing octahedral tilt angles range from 40-66°. In the second Ti site, Ti(2) is bonded to one O(2), one O(4), one O(5), one O(6), one O(7), and one O(9) atom to form TiO6 octahedra that share corners with three equivalent Dy(3)O6 octahedra,  a cornercorner with one Ti(1)O5 trigonal bipyramid, edges with two equivalent Dy(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 square pyramid. The corner-sharing octahedral tilt angles range from 36-51°. There are ten inequivalent O sites. In the first O site, O(1) is bonded in a distorted see-saw-like geometry to one Mg(1), one Dy(1), one Dy(3), and one Ti(1) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Dy(2), one Dy(4), and one Ti(2) atom. In the third O site, O(3) is bonded to one Mg(1), one Dy(1), one Dy(2), one Dy(3), and one Ti(1) atom to form distorted ODy3MgTi trigonal bipyramids that share  a cornercorner with one O(4)Dy2MgTi trigonal pyramid,  a cornercorner with one O(9)Dy2MgTi trigonal pyramid,  a cornercorner with one O(8)Dy3Ti trigonal pyramid, corners with two equivalent O(6)Dy3Ti trigonal pyramids,  an edgeedge with one O(4)Dy2MgTi trigonal pyramid,  an edgeedge with one O(9)Dy2MgTi trigonal pyramid,  an edgeedge with one O(5)Dy3Ti trigonal pyramid, and  an edgeedge with one O(8)Dy3Ti trigonal pyramid. In the fourth O site, O(4) is bonded to one Mg(1), one Dy(1), one Dy(3), and one Ti(2) atom to form ODy2MgTi trigonal pyramids that share  a cornercorner with one O(3)Dy3MgTi trigonal bipyramid,  a cornercorner with one O(5)Dy3Ti trigonal pyramid,  a cornercorner with one O(8)Dy3Ti trigonal pyramid, corners with two equivalent O(9)Dy2MgTi trigonal pyramids,  an edgeedge with one O(3)Dy3MgTi trigonal bipyramid,  an edgeedge with one O(9)Dy2MgTi trigonal pyramid,  an edgeedge with one O(5)Dy3Ti trigonal pyramid, and  an edgeedge with one O(6)Dy3Ti trigonal pyramid. In the fifth O site, O(5) is bonded to one Dy(1), one Dy(3), one Dy(4), and one Ti(2) atom to form ODy3Ti trigonal pyramids that share  a cornercorner with one O(4)Dy2MgTi trigonal pyramid,  a cornercorner with one O(9)Dy2MgTi trigonal pyramid,  a cornercorner with one O(6)Dy3Ti trigonal pyramid, corners with two equivalent O(8)Dy3Ti trigonal pyramids,  an edgeedge with one O(3)Dy3MgTi trigonal bipyramid,  an edgeedge with one O(4)Dy2MgTi trigonal pyramid,  an edgeedge with one O(9)Dy2MgTi trigonal pyramid, and  an edgeedge with one O(6)Dy3Ti trigonal pyramid. In the sixth O site, O(6) is bonded to one Dy(1), one Dy(2), one Dy(4), and one Ti(2) atom to form ODy3Ti trigonal pyramids that share corners with two equivalent O(3)Dy3MgTi trigonal bipyramids,  a cornercorner with one O(5)Dy3Ti trigonal pyramid, corners with two equivalent O(9)Dy2MgTi trigonal pyramids,  an edgeedge with one O(4)Dy2MgTi trigonal pyramid,  an edgeedge with one O(5)Dy3Ti trigonal pyramid, and  an edgeedge with one O(8)Dy3Ti trigonal pyramid. In the seventh O site, O(7) is bonded in a distorted see-saw-like geometry to one Dy(2), one Dy(4), one Ti(1), and one Ti(2) atom. In the eighth O site, O(8) is bonded to one Dy(2), one Dy(3), one Dy(4), and one Ti(1) atom to form distorted ODy3Ti trigonal pyramids that share  a cornercorner with one O(3)Dy3MgTi trigonal bipyramid,  a cornercorner with one O(4)Dy2MgTi trigonal pyramid,  a cornercorner with one O(9)Dy2MgTi trigonal pyramid, corners with two equivalent O(5)Dy3Ti trigonal pyramids,  an edgeedge with one O(3)Dy3MgTi trigonal bipyramid, and  an edgeedge with one O(6)Dy3Ti trigonal pyramid. In the ninth O site, O(9) is bonded to one Mg(1), one Dy(1), one Dy(3), and one Ti(2) atom to form ODy2MgTi trigonal pyramids that share  a cornercorner with one O(3)Dy3MgTi trigonal bipyramid,  a cornercorner with one O(5)Dy3Ti trigonal pyramid,  a cornercorner with one O(8)Dy3Ti trigonal pyramid, corners with two equivalent O(4)Dy2MgTi trigonal pyramids, corners with two equivalent O(6)Dy3Ti trigonal pyramids,  an edgeedge with one O(3)Dy3MgTi trigonal bipyramid,  an edgeedge with one O(4)Dy2MgTi trigonal pyramid, and  an edgeedge with one O(5)Dy3Ti trigonal pyramid. In the tenth O site, O(10) is bonded in a distorted see-saw-like geometry to one Mg(1), one Dy(2), one Dy(4), and one Ti(1) atom.
MgDy4Ti2O10 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(3), one O(4), and one O(9) atom to form distorted MgO5 square pyramids that share  a cornercorner with one Dy(4)O6 octahedra, corners with two equivalent Dy(3)O6 octahedra,  a cornercorner with one Ti(1)O5 trigonal bipyramid,  an edgeedge with one Dy(3)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one Ti(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 43-82°. The Mg(1)-O(1) bond length is 2.34 Å. The Mg(1)-O(10) bond length is 1.98 Å. The Mg(1)-O(3) bond length is 2.12 Å. The Mg(1)-O(4) bond length is 1.98 Å. The Mg(1)-O(9) bond length is 2.04 Å. There are four inequivalent Dy sites. In the first Dy site, Dy(1) is bonded in a 6-coordinate geometry to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(9) atom. The Dy(1)-O(1) bond length is 2.24 Å. The Dy(1)-O(3) bond length is 2.66 Å. The Dy(1)-O(4) bond length is 2.28 Å. The Dy(1)-O(5) bond length is 2.38 Å. The Dy(1)-O(6) bond length is 2.17 Å. The Dy(1)-O(9) bond length is 2.20 Å. In the second Dy site, Dy(2) is bonded in a 6-coordinate geometry to one O(10), one O(2), one O(3), one O(6), one O(7), and one O(8) atom. The Dy(2)-O(10) bond length is 2.19 Å. The Dy(2)-O(2) bond length is 2.20 Å. The Dy(2)-O(3) bond length is 2.34 Å. The Dy(2)-O(6) bond length is 2.27 Å. The Dy(2)-O(7) bond length is 2.38 Å. The Dy(2)-O(8) bond length is 2.54 Å. In the third Dy site, Dy(3) is bonded to one O(1), one O(3), one O(4), one O(5), one O(8), and one O(9) atom to form distorted DyO6 octahedra that share corners with two equivalent Dy(4)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, corners with two equivalent Mg(1)O5 square pyramids,  a cornercorner with one Ti(1)O5 trigonal bipyramid,  an edgeedge with one Mg(1)O5 square pyramid, and  an edgeedge with one Ti(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 36-62°. The Dy(3)-O(1) bond length is 2.29 Å. The Dy(3)-O(3) bond length is 2.34 Å. The Dy(3)-O(4) bond length is 2.26 Å. The Dy(3)-O(5) bond length is 2.23 Å. The Dy(3)-O(8) bond length is 2.35 Å. The Dy(3)-O(9) bond length is 2.23 Å. In the fourth Dy site, Dy(4) is bonded to one O(10), one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form distorted DyO6 octahedra that share corners with two equivalent Dy(3)O6 octahedra,  a cornercorner with one Mg(1)O5 square pyramid, corners with three equivalent Ti(1)O5 trigonal bipyramids, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. The Dy(4)-O(10) bond length is 2.23 Å. The Dy(4)-O(2) bond length is 2.22 Å. The Dy(4)-O(5) bond length is 2.22 Å. The Dy(4)-O(6) bond length is 2.41 Å. The Dy(4)-O(7) bond length is 2.31 Å. The Dy(4)-O(8) bond length is 2.38 Å. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(10), one O(3), one O(7), and one O(8) atom to form distorted TiO5 trigonal bipyramids that share  a cornercorner with one Dy(3)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with three equivalent Dy(4)O6 octahedra,  a cornercorner with one Mg(1)O5 square pyramid,  an edgeedge with one Dy(3)O6 octahedra, and  an edgeedge with one Mg(1)O5 square pyramid. The corner-sharing octahedral tilt angles range from 40-66°. The Ti(1)-O(1) bond length is 2.04 Å. The Ti(1)-O(10) bond length is 2.27 Å. The Ti(1)-O(3) bond length is 2.16 Å. The Ti(1)-O(7) bond length is 1.94 Å. The Ti(1)-O(8) bond length is 1.97 Å. In the second Ti site, Ti(2) is bonded to one O(2), one O(4), one O(5), one O(6), one O(7), and one O(9) atom to form TiO6 octahedra that share corners with three equivalent Dy(3)O6 octahedra,  a cornercorner with one Ti(1)O5 trigonal bipyramid, edges with two equivalent Dy(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 square pyramid. The corner-sharing octahedral tilt angles range from 36-51°. The Ti(2)-O(2) bond length is 1.95 Å. The Ti(2)-O(4) bond length is 2.19 Å. The Ti(2)-O(5) bond length is 2.12 Å. The Ti(2)-O(6) bond length is 2.12 Å. The Ti(2)-O(7) bond length is 2.10 Å. The Ti(2)-O(9) bond length is 2.14 Å. There are ten inequivalent O sites. In the first O site, O(1) is bonded in a distorted see-saw-like geometry to one Mg(1), one Dy(1), one Dy(3), and one Ti(1) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Dy(2), one Dy(4), and one Ti(2) atom. In the third O site, O(3) is bonded to one Mg(1), one Dy(1), one Dy(2), one Dy(3), and one Ti(1) atom to form distorted ODy3MgTi trigonal bipyramids that share  a cornercorner with one O(4)Dy2MgTi trigonal pyramid,  a cornercorner with one O(9)Dy2MgTi trigonal pyramid,  a cornercorner with one O(8)Dy3Ti trigonal pyramid, corners with two equivalent O(6)Dy3Ti trigonal pyramids,  an edgeedge with one O(4)Dy2MgTi trigonal pyramid,  an edgeedge with one O(9)Dy2MgTi trigonal pyramid,  an edgeedge with one O(5)Dy3Ti trigonal pyramid, and  an edgeedge with one O(8)Dy3Ti trigonal pyramid. In the fourth O site, O(4) is bonded to one Mg(1), one Dy(1), one Dy(3), and one Ti(2) atom to form ODy2MgTi trigonal pyramids that share  a cornercorner with one O(3)Dy3MgTi trigonal bipyramid,  a cornercorner with one O(5)Dy3Ti trigonal pyramid,  a cornercorner with one O(8)Dy3Ti trigonal pyramid, corners with two equivalent O(9)Dy2MgTi trigonal pyramids,  an edgeedge with one O(3)Dy3MgTi trigonal bipyramid,  an edgeedge with one O(9)Dy2MgTi trigonal pyramid,  an edgeedge with one O(5)Dy3Ti trigonal pyramid, and  an edgeedge with one O(6)Dy3Ti trigonal pyramid. In the fifth O site, O(5) is bonded to one Dy(1), one Dy(3), one Dy(4), and one Ti(2) atom to form ODy3Ti trigonal pyramids that share  a cornercorner with one O(4)Dy2MgTi trigonal pyramid,  a cornercorner with one O(9)Dy2MgTi trigonal pyramid,  a cornercorner with one O(6)Dy3Ti trigonal pyramid, corners with two equivalent O(8)Dy3Ti trigonal pyramids,  an edgeedge with one O(3)Dy3MgTi trigonal bipyramid,  an edgeedge with one O(4)Dy2MgTi trigonal pyramid,  an edgeedge with one O(9)Dy2MgTi trigonal pyramid, and  an edgeedge with one O(6)Dy3Ti trigonal pyramid. In the sixth O site, O(6) is bonded to one Dy(1), one Dy(2), one Dy(4), and one Ti(2) atom to form ODy3Ti trigonal pyramids that share corners with two equivalent O(3)Dy3MgTi trigonal bipyramids,  a cornercorner with one O(5)Dy3Ti trigonal pyramid, corners with two equivalent O(9)Dy2MgTi trigonal pyramids,  an edgeedge with one O(4)Dy2MgTi trigonal pyramid,  an edgeedge with one O(5)Dy3Ti trigonal pyramid, and  an edgeedge with one O(8)Dy3Ti trigonal pyramid. In the seventh O site, O(7) is bonded in a distorted see-saw-like geometry to one Dy(2), one Dy(4), one Ti(1), and one Ti(2) atom. In the eighth O site, O(8) is bonded to one Dy(2), one Dy(3), one Dy(4), and one Ti(1) atom to form distorted ODy3Ti trigonal pyramids that share  a cornercorner with one O(3)Dy3MgTi trigonal bipyramid,  a cornercorner with one O(4)Dy2MgTi trigonal pyramid,  a cornercorner with one O(9)Dy2MgTi trigonal pyramid, corners with two equivalent O(5)Dy3Ti trigonal pyramids,  an edgeedge with one O(3)Dy3MgTi trigonal bipyramid, and  an edgeedge with one O(6)Dy3Ti trigonal pyramid. In the ninth O site, O(9) is bonded to one Mg(1), one Dy(1), one Dy(3), and one Ti(2) atom to form ODy2MgTi trigonal pyramids that share  a cornercorner with one O(3)Dy3MgTi trigonal bipyramid,  a cornercorner with one O(5)Dy3Ti trigonal pyramid,  a cornercorner with one O(8)Dy3Ti trigonal pyramid, corners with two equivalent O(4)Dy2MgTi trigonal pyramids, corners with two equivalent O(6)Dy3Ti trigonal pyramids,  an edgeedge with one O(3)Dy3MgTi trigonal bipyramid,  an edgeedge with one O(4)Dy2MgTi trigonal pyramid, and  an edgeedge with one O(5)Dy3Ti trigonal pyramid. In the tenth O site, O(10) is bonded in a distorted see-saw-like geometry to one Mg(1), one Dy(2), one Dy(4), and one Ti(1) atom.