Mg3(AsO4)2 crystallizes in the tetragonal I-4 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form MgO6 octahedra that share  a cornercorner with one Mg(3)O6 octahedra,  a cornercorner with one Mg(4)O6 octahedra,  a cornercorner with one As(1)O4 tetrahedra,  a cornercorner with one As(3)O4 tetrahedra, corners with two equivalent As(2)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra, and  an edgeedge with one As(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-60°. In the second Mg site, Mg(2) is bonded in a 8-coordinate geometry to four equivalent O(3) and four equivalent O(5) atoms. In the third Mg site, Mg(3) is bonded to two equivalent O(3), two equivalent O(5), and two equivalent O(6) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent As(3)O4 tetrahedra, corners with four equivalent As(2)O4 tetrahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 60°. In the fourth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent As(1)O4 tetrahedra, corners with four equivalent As(2)O4 tetrahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 56°. There are three inequivalent As sites. In the first As site, As(1) is bonded to four equivalent O(1) atoms to form AsO4 tetrahedra that share corners with four equivalent Mg(1)O6 octahedra and corners with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. In the second As site, As(2) is bonded to one O(2), one O(3), one O(4), and one O(5) atom to form AsO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(3)O6 octahedra, corners with two equivalent Mg(4)O6 octahedra, and  an edgeedge with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 42-53°. In the third As site, As(3) is bonded to four equivalent O(6) atoms to form AsO4 tetrahedra that share corners with four equivalent Mg(1)O6 octahedra and corners with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-51°. There are six inequivalent O sites. In the first O site, O(3) is bonded to one Mg(1), one Mg(2), one Mg(3), and one As(2) atom to form a mixture of distorted corner and edge-sharing OMg3As trigonal pyramids. In the second O site, O(4) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(4), and one As(2) atom. In the third O site, O(5) is bonded to one Mg(1), one Mg(2), one Mg(3), and one As(2) atom to form a mixture of corner and edge-sharing OMg3As tetrahedra. In the fourth O site, O(6) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(3), and one As(3) atom. In the fifth O site, O(1) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(4), and one As(1) atom. In the sixth O site, O(2) is bonded in a distorted T-shaped geometry to one Mg(1), one Mg(4), and one As(2) atom.
Mg3(AsO4)2 crystallizes in the tetragonal I-4 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form MgO6 octahedra that share  a cornercorner with one Mg(3)O6 octahedra,  a cornercorner with one Mg(4)O6 octahedra,  a cornercorner with one As(1)O4 tetrahedra,  a cornercorner with one As(3)O4 tetrahedra, corners with two equivalent As(2)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra, and  an edgeedge with one As(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-60°. The Mg(1)-O(1) bond length is 2.00 Å. The Mg(1)-O(2) bond length is 2.04 Å. The Mg(1)-O(3) bond length is 2.07 Å. The Mg(1)-O(4) bond length is 2.09 Å. The Mg(1)-O(5) bond length is 2.18 Å. The Mg(1)-O(6) bond length is 2.02 Å. In the second Mg site, Mg(2) is bonded in a 8-coordinate geometry to four equivalent O(3) and four equivalent O(5) atoms. All Mg(2)-O(3) bond lengths are 2.62 Å. All Mg(2)-O(5) bond lengths are 2.14 Å. In the third Mg site, Mg(3) is bonded to two equivalent O(3), two equivalent O(5), and two equivalent O(6) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent As(3)O4 tetrahedra, corners with four equivalent As(2)O4 tetrahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 60°. Both Mg(3)-O(3) bond lengths are 2.12 Å. Both Mg(3)-O(5) bond lengths are 2.10 Å. Both Mg(3)-O(6) bond lengths are 2.05 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent As(1)O4 tetrahedra, corners with four equivalent As(2)O4 tetrahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 56°. Both Mg(4)-O(1) bond lengths are 2.07 Å. Both Mg(4)-O(2) bond lengths are 2.21 Å. Both Mg(4)-O(4) bond lengths are 2.05 Å. There are three inequivalent As sites. In the first As site, As(1) is bonded to four equivalent O(1) atoms to form AsO4 tetrahedra that share corners with four equivalent Mg(1)O6 octahedra and corners with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. All As(1)-O(1) bond lengths are 1.69 Å. In the second As site, As(2) is bonded to one O(2), one O(3), one O(4), and one O(5) atom to form AsO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(3)O6 octahedra, corners with two equivalent Mg(4)O6 octahedra, and  an edgeedge with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 42-53°. The As(2)-O(2) bond length is 1.68 Å. The As(2)-O(3) bond length is 1.70 Å. The As(2)-O(4) bond length is 1.69 Å. The As(2)-O(5) bond length is 1.75 Å. In the third As site, As(3) is bonded to four equivalent O(6) atoms to form AsO4 tetrahedra that share corners with four equivalent Mg(1)O6 octahedra and corners with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-51°. All As(3)-O(6) bond lengths are 1.70 Å. There are six inequivalent O sites. In the first O site, O(3) is bonded to one Mg(1), one Mg(2), one Mg(3), and one As(2) atom to form a mixture of distorted corner and edge-sharing OMg3As trigonal pyramids. In the second O site, O(4) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(4), and one As(2) atom. In the third O site, O(5) is bonded to one Mg(1), one Mg(2), one Mg(3), and one As(2) atom to form a mixture of corner and edge-sharing OMg3As tetrahedra. In the fourth O site, O(6) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(3), and one As(3) atom. In the fifth O site, O(1) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(4), and one As(1) atom. In the sixth O site, O(2) is bonded in a distorted T-shaped geometry to one Mg(1), one Mg(4), and one As(2) atom.