MgFe4(PO4)4 crystallizes in the monoclinic Pm space group. Mg(1) is bonded to one O(2), one O(4), and two equivalent O(6) atoms to form MgO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 pentagonal pyramids, corners with two equivalent P(1)O4 tetrahedra, and corners with two equivalent P(4)O4 tetrahedra. The corner-sharing octahedral tilt angles are 64°. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(11), one O(12), two equivalent O(3), and two equivalent O(8) atoms to form distorted FeO6 octahedra that share corners with four equivalent Fe(2)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent P(4)O4 tetrahedra, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 48-54°. In the second Fe site, Fe(2) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(8) atoms to form distorted FeO6 octahedra that share corners with four equivalent Fe(1)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, and  an edgeedge with one P(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 48-54°. In the third Fe site, Fe(3) is bonded to one O(10), one O(5), two equivalent O(6), and two equivalent O(7) atoms to form distorted FeO6 pentagonal pyramids that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra, and  an edgeedge with one P(1)O4 tetrahedra. In the fourth Fe site, Fe(4) is bonded in a 6-coordinate geometry to one O(4), one O(9), two equivalent O(6), and two equivalent O(7) atoms. There are four inequivalent P sites. In the first P site, P(1) is bonded to one O(11), one O(5), and two equivalent O(6) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 pentagonal pyramid, corners with two equivalent Mg(1)O4 tetrahedra, and  an edgeedge with one Fe(3)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 35°. In the second P site, P(2) is bonded to one O(1), one O(9), and two equivalent O(7) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra and corners with two equivalent Fe(3)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 51°. In the third P site, P(3) is bonded to one O(10), one O(12), and two equivalent O(8) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 pentagonal pyramid, and  an edgeedge with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 34-58°. In the fourth P site, P(4) is bonded to one O(2), one O(4), and two equivalent O(3) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, and  an edgeedge with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-58°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a bent 120 degrees geometry to one Fe(2) and one P(2) atom. In the second O site, O(2) is bonded in a trigonal planar geometry to one Mg(1), one Fe(2), and one P(4) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Fe(1), one Fe(2), and one P(4) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Mg(1), one Fe(4), and one P(4) atom. In the fifth O site, O(5) is bonded in a bent 150 degrees geometry to one Fe(3) and one P(1) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Mg(1), one Fe(3), one Fe(4), and one P(1) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Fe(3), one Fe(4), and one P(2) atom. In the eighth O site, O(8) is bonded in a distorted trigonal planar geometry to one Fe(1), one Fe(2), and one P(3) atom. In the ninth O site, O(9) is bonded in a bent 150 degrees geometry to one Fe(4) and one P(2) atom. In the tenth O site, O(10) is bonded in a bent 150 degrees geometry to one Fe(3) and one P(3) atom. In the eleventh O site, O(11) is bonded in a bent 150 degrees geometry to one Fe(1) and one P(1) atom. In the twelfth O site, O(12) is bonded in a bent 150 degrees geometry to one Fe(1) and one P(3) atom.
MgFe4(PO4)4 crystallizes in the monoclinic Pm space group. Mg(1) is bonded to one O(2), one O(4), and two equivalent O(6) atoms to form MgO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 pentagonal pyramids, corners with two equivalent P(1)O4 tetrahedra, and corners with two equivalent P(4)O4 tetrahedra. The corner-sharing octahedral tilt angles are 64°. The Mg(1)-O(2) bond length is 1.97 Å. The Mg(1)-O(4) bond length is 1.97 Å. Both Mg(1)-O(6) bond lengths are 2.09 Å. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(11), one O(12), two equivalent O(3), and two equivalent O(8) atoms to form distorted FeO6 octahedra that share corners with four equivalent Fe(2)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent P(4)O4 tetrahedra, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 48-54°. The Fe(1)-O(11) bond length is 2.00 Å. The Fe(1)-O(12) bond length is 1.93 Å. Both Fe(1)-O(3) bond lengths are 2.07 Å. Both Fe(1)-O(8) bond lengths are 2.13 Å. In the second Fe site, Fe(2) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(8) atoms to form distorted FeO6 octahedra that share corners with four equivalent Fe(1)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, and  an edgeedge with one P(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 48-54°. The Fe(2)-O(1) bond length is 2.03 Å. The Fe(2)-O(2) bond length is 2.19 Å. Both Fe(2)-O(3) bond lengths are 2.39 Å. Both Fe(2)-O(8) bond lengths are 2.09 Å. In the third Fe site, Fe(3) is bonded to one O(10), one O(5), two equivalent O(6), and two equivalent O(7) atoms to form distorted FeO6 pentagonal pyramids that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra, and  an edgeedge with one P(1)O4 tetrahedra. The Fe(3)-O(10) bond length is 1.97 Å. The Fe(3)-O(5) bond length is 2.04 Å. Both Fe(3)-O(6) bond lengths are 2.26 Å. Both Fe(3)-O(7) bond lengths are 1.98 Å. In the fourth Fe site, Fe(4) is bonded in a 6-coordinate geometry to one O(4), one O(9), two equivalent O(6), and two equivalent O(7) atoms. The Fe(4)-O(4) bond length is 2.16 Å. The Fe(4)-O(9) bond length is 1.93 Å. Both Fe(4)-O(6) bond lengths are 2.41 Å. Both Fe(4)-O(7) bond lengths are 2.12 Å. There are four inequivalent P sites. In the first P site, P(1) is bonded to one O(11), one O(5), and two equivalent O(6) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 pentagonal pyramid, corners with two equivalent Mg(1)O4 tetrahedra, and  an edgeedge with one Fe(3)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 35°. The P(1)-O(11) bond length is 1.52 Å. The P(1)-O(5) bond length is 1.52 Å. Both P(1)-O(6) bond lengths are 1.60 Å. In the second P site, P(2) is bonded to one O(1), one O(9), and two equivalent O(7) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra and corners with two equivalent Fe(3)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 51°. The P(2)-O(1) bond length is 1.50 Å. The P(2)-O(9) bond length is 1.52 Å. Both P(2)-O(7) bond lengths are 1.60 Å. In the third P site, P(3) is bonded to one O(10), one O(12), and two equivalent O(8) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 pentagonal pyramid, and  an edgeedge with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 34-58°. The P(3)-O(10) bond length is 1.54 Å. The P(3)-O(12) bond length is 1.53 Å. Both P(3)-O(8) bond lengths are 1.58 Å. In the fourth P site, P(4) is bonded to one O(2), one O(4), and two equivalent O(3) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, and  an edgeedge with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-58°. The P(4)-O(2) bond length is 1.55 Å. The P(4)-O(4) bond length is 1.58 Å. Both P(4)-O(3) bond lengths are 1.55 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a bent 120 degrees geometry to one Fe(2) and one P(2) atom. In the second O site, O(2) is bonded in a trigonal planar geometry to one Mg(1), one Fe(2), and one P(4) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Fe(1), one Fe(2), and one P(4) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Mg(1), one Fe(4), and one P(4) atom. In the fifth O site, O(5) is bonded in a bent 150 degrees geometry to one Fe(3) and one P(1) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Mg(1), one Fe(3), one Fe(4), and one P(1) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Fe(3), one Fe(4), and one P(2) atom. In the eighth O site, O(8) is bonded in a distorted trigonal planar geometry to one Fe(1), one Fe(2), and one P(3) atom. In the ninth O site, O(9) is bonded in a bent 150 degrees geometry to one Fe(4) and one P(2) atom. In the tenth O site, O(10) is bonded in a bent 150 degrees geometry to one Fe(3) and one P(3) atom. In the eleventh O site, O(11) is bonded in a bent 150 degrees geometry to one Fe(1) and one P(1) atom. In the twelfth O site, O(12) is bonded in a bent 150 degrees geometry to one Fe(1) and one P(3) atom.