Cr4Si4O13 crystallizes in the triclinic P-1 space group. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), one O(4), one O(6), and two equivalent O(5) atoms to form distorted CrO6 octahedra that share  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra,  a cornercorner with one Si(4)O4 tetrahedra, corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(3)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 57°. In the second Cr site, Cr(2) is bonded to one O(1), one O(2), one O(4), one O(5), and two equivalent O(6) atoms to form CrO6 octahedra that share  a cornercorner with one Si(2)O4 tetrahedra,  a cornercorner with one Si(3)O4 tetrahedra, corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(4)O4 tetrahedra,  a cornercorner with one Cr(3)O5 trigonal bipyramid,  an edgeedge with one Cr(2)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. In the third Cr site, Cr(3) is bonded to one O(1), one O(10), one O(9), and two equivalent O(8) atoms to form distorted CrO5 trigonal bipyramids that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Cr(4)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra, corners with two equivalent Si(4)O4 tetrahedra,  an edgeedge with one Cr(4)O6 octahedra,  an edgeedge with one Si(1)O4 tetrahedra, and  an edgeedge with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 50-69°. In the fourth Cr site, Cr(4) is bonded to one O(10), one O(3), one O(8), one O(9), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra,  a cornercorner with one Si(4)O4 tetrahedra, corners with two equivalent Si(3)O4 tetrahedra, corners with two equivalent Cr(3)O5 trigonal bipyramids,  an edgeedge with one Cr(4)O6 octahedra,  an edgeedge with one Si(1)O4 tetrahedra, and  an edgeedge with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 57°. There are four inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1), one O(2), one O(3), and one O(9) atom to form SiO4 tetrahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra,  an edgeedge with one Cr(4)O6 octahedra, and  an edgeedge with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 49-62°. In the second Si site, Si(2) is bonded to one O(10), one O(12), one O(13), and one O(4) atom to form SiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Si(3)O4 tetrahedra,  a cornercorner with one Si(4)O4 tetrahedra, and  a cornercorner with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 49-73°. In the third Si site, Si(3) is bonded to one O(11), one O(12), one O(5), and one O(7) atom to form SiO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(4)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra, and  a cornercorner with one Si(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 44-71°. In the fourth Si site, Si(4) is bonded to one O(11), one O(13), one O(6), and one O(8) atom to form SiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra,  a cornercorner with one Si(3)O4 tetrahedra, and corners with two equivalent Cr(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 50-62°. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Cr(2), one Cr(3), and one Si(1) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Cr(1), one Cr(2), and one Si(1) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Cr(1), one Cr(4), and one Si(1) atom. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Cr(1), one Cr(2), and one Si(2) atom. In the fifth O site, O(5) is bonded to one Cr(2), two equivalent Cr(1), and one Si(3) atom to form distorted edge-sharing OCr3Si tetrahedra. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Cr(1), two equivalent Cr(2), and one Si(4) atom. In the seventh O site, O(7) is bonded in a distorted trigonal planar geometry to two equivalent Cr(4) and one Si(3) atom. In the eighth O site, O(8) is bonded to one Cr(4), two equivalent Cr(3), and one Si(4) atom to form distorted edge-sharing OCr3Si tetrahedra. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Cr(3), one Cr(4), and one Si(1) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Cr(3), one Cr(4), and one Si(2) atom. In the eleventh O site, O(11) is bonded in a bent 150 degrees geometry to one Si(3) and one Si(4) atom. In the twelfth O site, O(12) is bonded in a distorted bent 120 degrees geometry to one Si(2) and one Si(3) atom. In the thirteenth O site, O(13) is bonded in a bent 120 degrees geometry to one Si(2) and one Si(4) atom.
Cr4Si4O13 crystallizes in the triclinic P-1 space group. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), one O(4), one O(6), and two equivalent O(5) atoms to form distorted CrO6 octahedra that share  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra,  a cornercorner with one Si(4)O4 tetrahedra, corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(3)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 57°. The Cr(1)-O(2) bond length is 2.20 Å. The Cr(1)-O(3) bond length is 2.04 Å. The Cr(1)-O(4) bond length is 2.36 Å. The Cr(1)-O(6) bond length is 2.52 Å. There is one shorter (2.18 Å) and one longer (2.30 Å) Cr(1)-O(5) bond length. In the second Cr site, Cr(2) is bonded to one O(1), one O(2), one O(4), one O(5), and two equivalent O(6) atoms to form CrO6 octahedra that share  a cornercorner with one Si(2)O4 tetrahedra,  a cornercorner with one Si(3)O4 tetrahedra, corners with two equivalent Si(1)O4 tetrahedra, corners with two equivalent Si(4)O4 tetrahedra,  a cornercorner with one Cr(3)O5 trigonal bipyramid,  an edgeedge with one Cr(2)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. The Cr(2)-O(1) bond length is 1.98 Å. The Cr(2)-O(2) bond length is 2.08 Å. The Cr(2)-O(4) bond length is 1.95 Å. The Cr(2)-O(5) bond length is 2.21 Å. There is one shorter (2.13 Å) and one longer (2.14 Å) Cr(2)-O(6) bond length. In the third Cr site, Cr(3) is bonded to one O(1), one O(10), one O(9), and two equivalent O(8) atoms to form distorted CrO5 trigonal bipyramids that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Cr(4)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra, corners with two equivalent Si(4)O4 tetrahedra,  an edgeedge with one Cr(4)O6 octahedra,  an edgeedge with one Si(1)O4 tetrahedra, and  an edgeedge with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 50-69°. The Cr(3)-O(1) bond length is 2.11 Å. The Cr(3)-O(10) bond length is 2.28 Å. The Cr(3)-O(9) bond length is 2.07 Å. There is one shorter (2.17 Å) and one longer (2.25 Å) Cr(3)-O(8) bond length. In the fourth Cr site, Cr(4) is bonded to one O(10), one O(3), one O(8), one O(9), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra,  a cornercorner with one Si(4)O4 tetrahedra, corners with two equivalent Si(3)O4 tetrahedra, corners with two equivalent Cr(3)O5 trigonal bipyramids,  an edgeedge with one Cr(4)O6 octahedra,  an edgeedge with one Si(1)O4 tetrahedra, and  an edgeedge with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 57°. The Cr(4)-O(10) bond length is 1.99 Å. The Cr(4)-O(3) bond length is 2.07 Å. The Cr(4)-O(8) bond length is 2.16 Å. The Cr(4)-O(9) bond length is 2.04 Å. There is one shorter (2.02 Å) and one longer (2.13 Å) Cr(4)-O(7) bond length. There are four inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1), one O(2), one O(3), and one O(9) atom to form SiO4 tetrahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra,  an edgeedge with one Cr(4)O6 octahedra, and  an edgeedge with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 49-62°. The Si(1)-O(1) bond length is 1.66 Å. The Si(1)-O(2) bond length is 1.64 Å. The Si(1)-O(3) bond length is 1.67 Å. The Si(1)-O(9) bond length is 1.67 Å. In the second Si site, Si(2) is bonded to one O(10), one O(12), one O(13), and one O(4) atom to form SiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra,  a cornercorner with one Si(3)O4 tetrahedra,  a cornercorner with one Si(4)O4 tetrahedra, and  a cornercorner with one Cr(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 49-73°. The Si(2)-O(10) bond length is 1.60 Å. The Si(2)-O(12) bond length is 1.63 Å. The Si(2)-O(13) bond length is 1.64 Å. The Si(2)-O(4) bond length is 1.63 Å. In the third Si site, Si(3) is bonded to one O(11), one O(12), one O(5), and one O(7) atom to form SiO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(4)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra, and  a cornercorner with one Si(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 44-71°. The Si(3)-O(11) bond length is 1.60 Å. The Si(3)-O(12) bond length is 1.61 Å. The Si(3)-O(5) bond length is 1.66 Å. The Si(3)-O(7) bond length is 1.64 Å. In the fourth Si site, Si(4) is bonded to one O(11), one O(13), one O(6), and one O(8) atom to form SiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Si(2)O4 tetrahedra,  a cornercorner with one Si(3)O4 tetrahedra, and corners with two equivalent Cr(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 50-62°. The Si(4)-O(11) bond length is 1.60 Å. The Si(4)-O(13) bond length is 1.61 Å. The Si(4)-O(6) bond length is 1.65 Å. The Si(4)-O(8) bond length is 1.66 Å. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Cr(2), one Cr(3), and one Si(1) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Cr(1), one Cr(2), and one Si(1) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Cr(1), one Cr(4), and one Si(1) atom. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Cr(1), one Cr(2), and one Si(2) atom. In the fifth O site, O(5) is bonded to one Cr(2), two equivalent Cr(1), and one Si(3) atom to form distorted edge-sharing OCr3Si tetrahedra. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Cr(1), two equivalent Cr(2), and one Si(4) atom. In the seventh O site, O(7) is bonded in a distorted trigonal planar geometry to two equivalent Cr(4) and one Si(3) atom. In the eighth O site, O(8) is bonded to one Cr(4), two equivalent Cr(3), and one Si(4) atom to form distorted edge-sharing OCr3Si tetrahedra. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Cr(3), one Cr(4), and one Si(1) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Cr(3), one Cr(4), and one Si(2) atom. In the eleventh O site, O(11) is bonded in a bent 150 degrees geometry to one Si(3) and one Si(4) atom. In the twelfth O site, O(12) is bonded in a distorted bent 120 degrees geometry to one Si(2) and one Si(3) atom. In the thirteenth O site, O(13) is bonded in a bent 120 degrees geometry to one Si(2) and one Si(4) atom.