Na4MgHfSi2SO12 is Pb (Zr_0.50 Ti_0.48) O_3-derived structured and crystallizes in the monoclinic Cc space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(2), one O(3), one O(5), one O(7), and one O(8) atom. In the second Na site, Na(2) is bonded in a 8-coordinate geometry to one O(11), one O(12), one O(5), one O(6), one O(7), one O(9), and two equivalent O(1) atoms. In the third Na site, Na(3) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(3), one O(8), one O(9), and two equivalent O(4) atoms. In the fourth Na site, Na(4) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(12), one O(7), one O(8), and one O(9) atom. Mg(1) is bonded to one O(1), one O(2), one O(3), one O(7), one O(8), and one O(9) atom to form MgO6 octahedra that share corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(2)O4 tetrahedra, and corners with two equivalent S(1)O4 tetrahedra. Hf(1) is bonded to one O(10), one O(11), one O(12), one O(4), one O(5), and one O(6) atom to form HfO6 octahedra that share corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(2)O4 tetrahedra, and corners with two equivalent S(1)O4 tetrahedra. There are two inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1), one O(10), one O(4), and one O(7) atom to form SiO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Hf(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 27-43°. In the second Si site, Si(2) is bonded to one O(12), one O(3), one O(5), and one O(8) atom to form SiO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Hf(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 24-42°. S(1) is bonded to one O(11), one O(2), one O(6), and one O(9) atom to form SO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Hf(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 28-35°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to two equivalent Na(2), one Mg(1), and one Si(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Na(1), one Mg(1), and one S(1) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Na(1), one Na(3), one Mg(1), and one Si(2) atom. In the fourth O site, O(4) is bonded in a bent 150 degrees geometry to two equivalent Na(3), one Hf(1), and one Si(1) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one Na(1), one Na(2), one Hf(1), and one Si(2) atom. In the sixth O site, O(6) is bonded in a distorted bent 150 degrees geometry to one Na(2), one Hf(1), and one S(1) atom. In the seventh O site, O(7) is bonded to one Na(1), one Na(2), one Na(4), one Mg(1), and one Si(1) atom to form distorted ONa3MgSi trigonal bipyramids that share  a cornercorner with one O(10)Na3HfSi trigonal bipyramid,  an edgeedge with one O(10)Na3HfSi trigonal bipyramid, and  a faceface with one O(8)Na3MgSi trigonal bipyramid. In the eighth O site, O(8) is bonded to one Na(1), one Na(3), one Na(4), one Mg(1), and one Si(2) atom to form distorted ONa3MgSi trigonal bipyramids that share corners with three equivalent O(10)Na3HfSi trigonal bipyramids and  a faceface with one O(7)Na3MgSi trigonal bipyramid. In the ninth O site, O(9) is bonded in a 5-coordinate geometry to one Na(2), one Na(3), one Na(4), one Mg(1), and one S(1) atom. In the tenth O site, O(10) is bonded to one Na(1), one Na(3), one Na(4), one Hf(1), and one Si(1) atom to form a mixture of distorted edge and corner-sharing ONa3HfSi trigonal bipyramids. In the eleventh O site, O(11) is bonded in a 5-coordinate geometry to one Na(1), one Na(2), one Na(4), one Hf(1), and one S(1) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Na(2), one Na(3), one Na(4), one Hf(1), and one Si(2) atom.
Na4MgHfSi2SO12 is Pb (Zr_0.50 Ti_0.48) O_3-derived structured and crystallizes in the monoclinic Cc space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a 7-coordinate geometry to one O(10), one O(11), one O(2), one O(3), one O(5), one O(7), and one O(8) atom. The Na(1)-O(10) bond length is 2.64 Å. The Na(1)-O(11) bond length is 2.74 Å. The Na(1)-O(2) bond length is 2.75 Å. The Na(1)-O(3) bond length is 2.88 Å. The Na(1)-O(5) bond length is 2.67 Å. The Na(1)-O(7) bond length is 2.36 Å. The Na(1)-O(8) bond length is 2.45 Å. In the second Na site, Na(2) is bonded in a 8-coordinate geometry to one O(11), one O(12), one O(5), one O(6), one O(7), one O(9), and two equivalent O(1) atoms. The Na(2)-O(11) bond length is 2.76 Å. The Na(2)-O(12) bond length is 2.49 Å. The Na(2)-O(5) bond length is 2.91 Å. The Na(2)-O(6) bond length is 2.99 Å. The Na(2)-O(7) bond length is 2.48 Å. The Na(2)-O(9) bond length is 2.63 Å. There is one shorter (2.35 Å) and one longer (3.02 Å) Na(2)-O(1) bond length. In the third Na site, Na(3) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(3), one O(8), one O(9), and two equivalent O(4) atoms. The Na(3)-O(10) bond length is 2.62 Å. The Na(3)-O(12) bond length is 2.65 Å. The Na(3)-O(3) bond length is 2.31 Å. The Na(3)-O(8) bond length is 2.35 Å. The Na(3)-O(9) bond length is 2.52 Å. There is one shorter (2.96 Å) and one longer (2.98 Å) Na(3)-O(4) bond length. In the fourth Na site, Na(4) is bonded in a 6-coordinate geometry to one O(10), one O(11), one O(12), one O(7), one O(8), and one O(9) atom. The Na(4)-O(10) bond length is 2.62 Å. The Na(4)-O(11) bond length is 2.80 Å. The Na(4)-O(12) bond length is 2.51 Å. The Na(4)-O(7) bond length is 2.39 Å. The Na(4)-O(8) bond length is 2.33 Å. The Na(4)-O(9) bond length is 2.64 Å. Mg(1) is bonded to one O(1), one O(2), one O(3), one O(7), one O(8), and one O(9) atom to form MgO6 octahedra that share corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(2)O4 tetrahedra, and corners with two equivalent S(1)O4 tetrahedra. The Mg(1)-O(1) bond length is 2.01 Å. The Mg(1)-O(2) bond length is 2.14 Å. The Mg(1)-O(3) bond length is 2.00 Å. The Mg(1)-O(7) bond length is 2.11 Å. The Mg(1)-O(8) bond length is 2.14 Å. The Mg(1)-O(9) bond length is 2.28 Å. Hf(1) is bonded to one O(10), one O(11), one O(12), one O(4), one O(5), and one O(6) atom to form HfO6 octahedra that share corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(2)O4 tetrahedra, and corners with two equivalent S(1)O4 tetrahedra. The Hf(1)-O(10) bond length is 2.01 Å. The Hf(1)-O(11) bond length is 2.28 Å. The Hf(1)-O(12) bond length is 2.09 Å. The Hf(1)-O(4) bond length is 1.95 Å. The Hf(1)-O(5) bond length is 2.01 Å. The Hf(1)-O(6) bond length is 2.25 Å. There are two inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1), one O(10), one O(4), and one O(7) atom to form SiO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Hf(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 27-43°. The Si(1)-O(1) bond length is 1.61 Å. The Si(1)-O(10) bond length is 1.68 Å. The Si(1)-O(4) bond length is 1.68 Å. The Si(1)-O(7) bond length is 1.62 Å. In the second Si site, Si(2) is bonded to one O(12), one O(3), one O(5), and one O(8) atom to form SiO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Hf(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 24-42°. The Si(2)-O(12) bond length is 1.68 Å. The Si(2)-O(3) bond length is 1.61 Å. The Si(2)-O(5) bond length is 1.67 Å. The Si(2)-O(8) bond length is 1.63 Å. S(1) is bonded to one O(11), one O(2), one O(6), and one O(9) atom to form SO4 tetrahedra that share corners with two equivalent Mg(1)O6 octahedra and corners with two equivalent Hf(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 28-35°. The S(1)-O(11) bond length is 1.50 Å. The S(1)-O(2) bond length is 1.47 Å. The S(1)-O(6) bond length is 1.50 Å. The S(1)-O(9) bond length is 1.48 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to two equivalent Na(2), one Mg(1), and one Si(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Na(1), one Mg(1), and one S(1) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Na(1), one Na(3), one Mg(1), and one Si(2) atom. In the fourth O site, O(4) is bonded in a bent 150 degrees geometry to two equivalent Na(3), one Hf(1), and one Si(1) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one Na(1), one Na(2), one Hf(1), and one Si(2) atom. In the sixth O site, O(6) is bonded in a distorted bent 150 degrees geometry to one Na(2), one Hf(1), and one S(1) atom. In the seventh O site, O(7) is bonded to one Na(1), one Na(2), one Na(4), one Mg(1), and one Si(1) atom to form distorted ONa3MgSi trigonal bipyramids that share  a cornercorner with one O(10)Na3HfSi trigonal bipyramid,  an edgeedge with one O(10)Na3HfSi trigonal bipyramid, and  a faceface with one O(8)Na3MgSi trigonal bipyramid. In the eighth O site, O(8) is bonded to one Na(1), one Na(3), one Na(4), one Mg(1), and one Si(2) atom to form distorted ONa3MgSi trigonal bipyramids that share corners with three equivalent O(10)Na3HfSi trigonal bipyramids and  a faceface with one O(7)Na3MgSi trigonal bipyramid. In the ninth O site, O(9) is bonded in a 5-coordinate geometry to one Na(2), one Na(3), one Na(4), one Mg(1), and one S(1) atom. In the tenth O site, O(10) is bonded to one Na(1), one Na(3), one Na(4), one Hf(1), and one Si(1) atom to form a mixture of distorted edge and corner-sharing ONa3HfSi trigonal bipyramids. In the eleventh O site, O(11) is bonded in a 5-coordinate geometry to one Na(1), one Na(2), one Na(4), one Hf(1), and one S(1) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Na(2), one Na(3), one Na(4), one Hf(1), and one Si(2) atom.