The material structure described by AgCrTiS4 is Hausmannite-derived structured and crystallizes in the triclinic P-1 space group. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent S(1), two equivalent S(5), and two equivalent S(7) atoms to form TiS6 octahedra that share corners with four equivalent Cr(3)S6 octahedra, corners with two equivalent Ag(1)S4 tetrahedra, edges with two equivalent Ti(3)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, and edges with two equivalent Ag(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-46°. In the second Ti site, Ti(2) is bonded to two equivalent S(3), two equivalent S(6), and two equivalent S(8) atoms to form TiS6 octahedra that share corners with four equivalent Ti(3)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and edges with two equivalent Cr(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 45-46°. In the third Ti site, Ti(3) is bonded to one S(1), one S(2), one S(3), one S(4), one S(6), and one S(7) atom to form distorted TiS6 octahedra that share corners with two equivalent Ti(2)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with four equivalent Cr(3)S6 octahedra,  a cornercorner with one Ag(1)S4 tetrahedra,  an edgeedge with one Ti(1)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, and  an edgeedge with one Ag(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-48°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent S(2), two equivalent S(6), and two equivalent S(8) atoms to form CrS6 octahedra that share corners with four equivalent Ti(3)S6 octahedra, edges with two equivalent Ti(2)S6 octahedra, and edges with two equivalent Cr(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 46-47°. In the second Cr site, Cr(2) is bonded to two equivalent S(4), two equivalent S(5), and two equivalent S(7) atoms to form CrS6 octahedra that share corners with four equivalent Cr(3)S6 octahedra, corners with two equivalent Ag(1)S4 tetrahedra, edges with two equivalent Ti(1)S6 octahedra, edges with two equivalent Ti(3)S6 octahedra, and edges with two equivalent Ag(1)S4 tetrahedra. The corner-sharing octahedral tilt angles are 47°. In the third Cr site, Cr(3) is bonded to one S(1), one S(2), one S(3), one S(4), one S(5), and one S(8) atom to form distorted CrS6 octahedra that share corners with two equivalent Ti(1)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra, corners with four equivalent Ti(3)S6 octahedra, corners with three equivalent Ag(1)S4 tetrahedra,  an edgeedge with one Ti(2)S6 octahedra, and  an edgeedge with one Cr(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 45-48°. There are two inequivalent Ag sites. In the first Ag site, Ag(1) is bonded to one S(1), one S(4), one S(5), and one S(7) atom to form distorted AgS4 tetrahedra that share  a cornercorner with one Ti(1)S6 octahedra,  a cornercorner with one Ti(3)S6 octahedra,  a cornercorner with one Cr(2)S6 octahedra, corners with three equivalent Cr(3)S6 octahedra,  an edgeedge with one Ti(1)S6 octahedra,  an edgeedge with one Ti(3)S6 octahedra, and  an edgeedge with one Cr(2)S6 octahedra. The corner-sharing octahedral tilt angles range from 58-78°. In the second Ag site, Ag(2) is bonded in a distorted rectangular see-saw-like geometry to one S(2), one S(3), one S(6), and one S(8) atom. There are eight inequivalent S sites. In the first S site, S(1) is bonded in a distorted rectangular see-saw-like geometry to one Ti(1), one Ti(3), one Cr(3), and one Ag(1) atom. In the second S site, S(2) is bonded in a rectangular see-saw-like geometry to one Ti(3), one Cr(1), one Cr(3), and one Ag(2) atom. In the third S site, S(3) is bonded in a distorted rectangular see-saw-like geometry to one Ti(2), one Ti(3), one Cr(3), and one Ag(2) atom. In the fourth S site, S(4) is bonded in a rectangular see-saw-like geometry to one Ti(3), one Cr(2), one Cr(3), and one Ag(1) atom. In the fifth S site, S(5) is bonded in a rectangular see-saw-like geometry to one Ti(1), one Cr(2), one Cr(3), and one Ag(1) atom. In the sixth S site, S(6) is bonded in a rectangular see-saw-like geometry to one Ti(2), one Ti(3), one Cr(1), and one Ag(2) atom. In the seventh S site, S(7) is bonded to one Ti(1), one Ti(3), one Cr(2), and one Ag(1) atom to form distorted corner-sharing STi2CrAg trigonal pyramids. In the eighth S site, S(8) is bonded to one Ti(2), one Cr(1), one Cr(3), and one Ag(2) atom to form distorted corner-sharing STiCr2Ag trigonal pyramids. is represented by the CIF file [CIF]
data_TiCrAgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.140
_cell_length_b   7.036
_cell_length_c   12.073
_cell_angle_alpha   90.305
_cell_angle_beta   90.343
_cell_angle_gamma   91.151
_symmetry_Int_Tables_number   1
_cell_volume   521.480
_cell_formula_units_Z   4
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ti  Ti0  1  0.500  0.000  0.000  1.0
  Ti  Ti1  1  0.000  0.500  0.500  1.0
  Ti  Ti2  1  0.533  0.228  0.747  1.0
  Ti  Ti3  1  0.467  0.772  0.253  1.0
  Cr  Cr4  1  0.000  0.000  0.500  1.0
  Cr  Cr5  1  0.500  0.500  0.000  1.0
  Cr  Cr6  1  0.025  0.735  0.755  1.0
  Cr  Cr7  1  0.975  0.265  0.245  1.0
  Ag  Ag8  1  0.919  0.246  0.905  1.0
  Ag  Ag9  1  0.081  0.754  0.095  1.0
  Ag  Ag10  1  0.427  0.736  0.587  1.0
  Ag  Ag11  1  0.573  0.264  0.413  1.0
  S  S12  1  0.719  0.968  0.826  1.0
  S  S13  1  0.281  0.032  0.174  1.0
  S  S14  1  0.217  0.005  0.672  1.0
  S  S15  1  0.783  0.995  0.328  1.0
  S  S16  1  0.787  0.525  0.328  1.0
  S  S17  1  0.213  0.475  0.672  1.0
  S  S18  1  0.288  0.488  0.175  1.0
  S  S19  1  0.712  0.512  0.825  1.0
  S  S20  1  0.269  0.743  0.911  1.0
  S  S21  1  0.731  0.257  0.089  1.0
  S  S22  1  0.773  0.239  0.593  1.0
  S  S23  1  0.227  0.761  0.407  1.0
  S  S24  1  0.308  0.248  0.914  1.0
  S  S25  1  0.692  0.752  0.086  1.0
  S  S26  1  0.815  0.750  0.589  1.0
  S  S27  1  0.185  0.250  0.411  1.0
[/CIF]
.
The material structure described by AgCrTiS4 is Hausmannite-derived structured and crystallizes in the triclinic P-1 space group. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent S(1), two equivalent S(5), and two equivalent S(7) atoms to form TiS6 octahedra that share corners with four equivalent Cr(3)S6 octahedra, corners with two equivalent Ag(1)S4 tetrahedra, edges with two equivalent Ti(3)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, and edges with two equivalent Ag(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-46°. In the second Ti site, Ti(2) is bonded to two equivalent S(3), two equivalent S(6), and two equivalent S(8) atoms to form TiS6 octahedra that share corners with four equivalent Ti(3)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and edges with two equivalent Cr(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 45-46°. In the third Ti site, Ti(3) is bonded to one S(1), one S(2), one S(3), one S(4), one S(6), and one S(7) atom to form distorted TiS6 octahedra that share corners with two equivalent Ti(2)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with four equivalent Cr(3)S6 octahedra,  a cornercorner with one Ag(1)S4 tetrahedra,  an edgeedge with one Ti(1)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, and  an edgeedge with one Ag(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-48°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent S(2), two equivalent S(6), and two equivalent S(8) atoms to form CrS6 octahedra that share corners with four equivalent Ti(3)S6 octahedra, edges with two equivalent Ti(2)S6 octahedra, and edges with two equivalent Cr(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 46-47°. In the second Cr site, Cr(2) is bonded to two equivalent S(4), two equivalent S(5), and two equivalent S(7) atoms to form CrS6 octahedra that share corners with four equivalent Cr(3)S6 octahedra, corners with two equivalent Ag(1)S4 tetrahedra, edges with two equivalent Ti(1)S6 octahedra, edges with two equivalent Ti(3)S6 octahedra, and edges with two equivalent Ag(1)S4 tetrahedra. The corner-sharing octahedral tilt angles are 47°. In the third Cr site, Cr(3) is bonded to one S(1), one S(2), one S(3), one S(4), one S(5), and one S(8) atom to form distorted CrS6 octahedra that share corners with two equivalent Ti(1)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra, corners with four equivalent Ti(3)S6 octahedra, corners with three equivalent Ag(1)S4 tetrahedra,  an edgeedge with one Ti(2)S6 octahedra, and  an edgeedge with one Cr(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 45-48°. There are two inequivalent Ag sites. In the first Ag site, Ag(1) is bonded to one S(1), one S(4), one S(5), and one S(7) atom to form distorted AgS4 tetrahedra that share  a cornercorner with one Ti(1)S6 octahedra,  a cornercorner with one Ti(3)S6 octahedra,  a cornercorner with one Cr(2)S6 octahedra, corners with three equivalent Cr(3)S6 octahedra,  an edgeedge with one Ti(1)S6 octahedra,  an edgeedge with one Ti(3)S6 octahedra, and  an edgeedge with one Cr(2)S6 octahedra. The corner-sharing octahedral tilt angles range from 58-78°. In the second Ag site, Ag(2) is bonded in a distorted rectangular see-saw-like geometry to one S(2), one S(3), one S(6), and one S(8) atom. There are eight inequivalent S sites. In the first S site, S(1) is bonded in a distorted rectangular see-saw-like geometry to one Ti(1), one Ti(3), one Cr(3), and one Ag(1) atom. In the second S site, S(2) is bonded in a rectangular see-saw-like geometry to one Ti(3), one Cr(1), one Cr(3), and one Ag(2) atom. In the third S site, S(3) is bonded in a distorted rectangular see-saw-like geometry to one Ti(2), one Ti(3), one Cr(3), and one Ag(2) atom. In the fourth S site, S(4) is bonded in a rectangular see-saw-like geometry to one Ti(3), one Cr(2), one Cr(3), and one Ag(1) atom. In the fifth S site, S(5) is bonded in a rectangular see-saw-like geometry to one Ti(1), one Cr(2), one Cr(3), and one Ag(1) atom. In the sixth S site, S(6) is bonded in a rectangular see-saw-like geometry to one Ti(2), one Ti(3), one Cr(1), and one Ag(2) atom. In the seventh S site, S(7) is bonded to one Ti(1), one Ti(3), one Cr(2), and one Ag(1) atom to form distorted corner-sharing STi2CrAg trigonal pyramids. In the eighth S site, S(8) is bonded to one Ti(2), one Cr(1), one Cr(3), and one Ag(2) atom to form distorted corner-sharing STiCr2Ag trigonal pyramids. is represented by the CIF file [CIF]
data_TiCrAgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.140
_cell_length_b   7.036
_cell_length_c   12.073
_cell_angle_alpha   90.305
_cell_angle_beta   90.343
_cell_angle_gamma   91.151
_symmetry_Int_Tables_number   1
_cell_volume   521.480
_cell_formula_units_Z   4
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ti  Ti0  1  0.500  0.000  0.000  1.0
  Ti  Ti1  1  0.000  0.500  0.500  1.0
  Ti  Ti2  1  0.533  0.228  0.747  1.0
  Ti  Ti3  1  0.467  0.772  0.253  1.0
  Cr  Cr4  1  0.000  0.000  0.500  1.0
  Cr  Cr5  1  0.500  0.500  0.000  1.0
  Cr  Cr6  1  0.025  0.735  0.755  1.0
  Cr  Cr7  1  0.975  0.265  0.245  1.0
  Ag  Ag8  1  0.919  0.246  0.905  1.0
  Ag  Ag9  1  0.081  0.754  0.095  1.0
  Ag  Ag10  1  0.427  0.736  0.587  1.0
  Ag  Ag11  1  0.573  0.264  0.413  1.0
  S  S12  1  0.719  0.968  0.826  1.0
  S  S13  1  0.281  0.032  0.174  1.0
  S  S14  1  0.217  0.005  0.672  1.0
  S  S15  1  0.783  0.995  0.328  1.0
  S  S16  1  0.787  0.525  0.328  1.0
  S  S17  1  0.213  0.475  0.672  1.0
  S  S18  1  0.288  0.488  0.175  1.0
  S  S19  1  0.712  0.512  0.825  1.0
  S  S20  1  0.269  0.743  0.911  1.0
  S  S21  1  0.731  0.257  0.089  1.0
  S  S22  1  0.773  0.239  0.593  1.0
  S  S23  1  0.227  0.761  0.407  1.0
  S  S24  1  0.308  0.248  0.914  1.0
  S  S25  1  0.692  0.752  0.086  1.0
  S  S26  1  0.815  0.750  0.589  1.0
  S  S27  1  0.185  0.250  0.411  1.0
[/CIF]
.