The structure described by HfCrAgS4 crystallizes in the monoclinic Pm space group. There are four inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one S(10), one S(6), two equivalent S(14), and two equivalent S(5) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(3)S6 octahedra, corners with two equivalent Hf(2)S6 octahedra, corners with two equivalent Ag(2)S7 pentagonal bipyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and edges with two equivalent Cr(4)S6 octahedra. The corner-sharing octahedral tilt angles range from 54-60°. In the second Hf site, Hf(2) is bonded to one S(15), one S(5), two equivalent S(1), and two equivalent S(11) atoms to form HfS6 octahedra that share  a cornercorner with one Cr(1)S6 octahedra, corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Ag(2)S7 pentagonal bipyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Ag(2)S7 pentagonal bipyramid, and edges with two equivalent Ag(1)S7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 50-60°. In the third Hf site, Hf(3) is bonded to one S(16), one S(6), two equivalent S(12), and two equivalent S(2) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(1)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Ag(1)S7 pentagonal bipyramids, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Ag(1)S7 pentagonal bipyramid, and edges with two equivalent Ag(2)S7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 54-57°. In the fourth Hf site, Hf(4) is bonded to one S(13), one S(7), two equivalent S(3), and two equivalent S(9) atoms to form HfS6 octahedra that share  a cornercorner with one Cr(2)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra, corners with two equivalent Ag(1)S7 pentagonal bipyramids, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and  an edgeedge with one Ag(1)S7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 54-58°. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one S(5), one S(9), two equivalent S(13), and two equivalent S(6) atoms to form CrS6 octahedra that share  a cornercorner with one Hf(2)S6 octahedra, corners with two equivalent Hf(3)S6 octahedra, corners with two equivalent Ag(1)S7 pentagonal bipyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, and edges with two equivalent Cr(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 50-57°. In the second Cr site, Cr(2) is bonded to one S(11), one S(7), two equivalent S(15), and two equivalent S(8) atoms to form CrS6 octahedra that share  a cornercorner with one Hf(4)S6 octahedra, corners with two equivalent Cr(4)S6 octahedra, corners with two equivalent Ag(1)S7 pentagonal bipyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Ag(1)S7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 54-59°. In the third Cr site, Cr(3) is bonded to one S(12), one S(8), two equivalent S(16), and two equivalent S(7) atoms to form CrS6 octahedra that share  a cornercorner with one Cr(4)S6 octahedra, corners with two equivalent Hf(4)S6 octahedra, corners with two equivalent Ag(2)S7 pentagonal bipyramids, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Ag(2)S7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 54-58°. In the fourth Cr site, Cr(4) is bonded to one S(14), one S(8), two equivalent S(10), and two equivalent S(4) atoms to form CrS6 octahedra that share  a cornercorner with one Cr(3)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra, corners with two equivalent Ag(2)S7 pentagonal bipyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, and  an edgeedge with one Ag(2)S7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 54-59°. There are four inequivalent Ag sites. In the first Ag site, Ag(1) is bonded to one S(1), two equivalent S(15), two equivalent S(2), and two equivalent S(9) atoms to form distorted AgS7 pentagonal bipyramids that share corners with two equivalent Hf(3)S6 octahedra, corners with two equivalent Hf(4)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Hf(3)S6 octahedra,  an edgeedge with one Hf(4)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Ag(2)S7 pentagonal bipyramids, and faces with two equivalent Ag(1)S7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 13-60°. In the second Ag site, Ag(2) is bonded to one S(2), two equivalent S(1), two equivalent S(10), and two equivalent S(16) atoms to form distorted AgS7 pentagonal bipyramids that share corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Hf(2)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra, corners with two equivalent Cr(4)S6 octahedra,  an edgeedge with one Hf(2)S6 octahedra,  an edgeedge with one Cr(3)S6 octahedra,  an edgeedge with one Cr(4)S6 octahedra, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Ag(1)S7 pentagonal bipyramids, and faces with two equivalent Ag(2)S7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 15-67°. In the third Ag site, Ag(3) is bonded in a 7-coordinate geometry to one S(3), two equivalent S(11), two equivalent S(13), and two equivalent S(4) atoms. In the fourth Ag site, Ag(4) is bonded in a 7-coordinate geometry to one S(4), two equivalent S(12), two equivalent S(14), and two equivalent S(3) atoms. There are sixteen inequivalent S sites. In the first S site, S(1) is bonded to two equivalent Hf(2), one Ag(1), and two equivalent Ag(2) atoms to form distorted SHf2Ag3 square pyramids that share corners with two equivalent S(16)HfCr2Ag2 square pyramids, corners with two equivalent S(11)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(9)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(10)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(16)HfCr2Ag2 square pyramid, edges with two equivalent S(1)Hf2Ag3 square pyramids, edges with two equivalent S(2)Hf2Ag3 square pyramids, edges with two equivalent S(15)HfCr2Ag2 square pyramids,  an edgeedge with one S(11)Hf2CrAg2 trigonal bipyramid, and  an edgeedge with one S(10)HfCr2Ag2 trigonal bipyramid. In the second S site, S(2) is bonded to two equivalent Hf(3), one Ag(2), and two equivalent Ag(1) atoms to form distorted SHf2Ag3 square pyramids that share corners with two equivalent S(15)HfCr2Ag2 square pyramids, corners with two equivalent S(12)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(9)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(10)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(15)HfCr2Ag2 square pyramid, edges with two equivalent S(1)Hf2Ag3 square pyramids, edges with two equivalent S(2)Hf2Ag3 square pyramids, edges with two equivalent S(16)HfCr2Ag2 square pyramids,  an edgeedge with one S(12)Hf2CrAg2 trigonal bipyramid, and  an edgeedge with one S(9)Hf2CrAg2 trigonal bipyramid. In the third S site, S(3) is bonded to two equivalent Hf(4), one Ag(3), and two equivalent Ag(4) atoms to form distorted SHf2Ag3 square pyramids that share corners with two equivalent S(14)Hf2CrAg2 square pyramids, corners with two equivalent S(11)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(12)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(9)Hf2CrAg2 trigonal bipyramids,  an edgeedge with one S(14)Hf2CrAg2 square pyramid, edges with two equivalent S(4)Cr2Ag3 square pyramids, edges with two equivalent S(3)Hf2Ag3 square pyramids, edges with two equivalent S(13)HfCr2Ag2 square pyramids,  an edgeedge with one S(12)Hf2CrAg2 trigonal bipyramid, and  an edgeedge with one S(9)Hf2CrAg2 trigonal bipyramid. In the fourth S site, S(4) is bonded to two equivalent Cr(4), one Ag(4), and two equivalent Ag(3) atoms to form distorted SCr2Ag3 square pyramids that share corners with two equivalent S(13)HfCr2Ag2 square pyramids, corners with two equivalent S(11)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(12)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(10)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(13)HfCr2Ag2 square pyramid, edges with two equivalent S(4)Cr2Ag3 square pyramids, edges with two equivalent S(3)Hf2Ag3 square pyramids, edges with two equivalent S(14)Hf2CrAg2 square pyramids,  an edgeedge with one S(11)Hf2CrAg2 trigonal bipyramid, and  an edgeedge with one S(10)HfCr2Ag2 trigonal bipyramid. In the fifth S site, S(5) is bonded in a rectangular see-saw-like geometry to one Hf(2), two equivalent Hf(1), and one Cr(1) atom. In the sixth S site, S(6) is bonded in a rectangular see-saw-like geometry to one Hf(1), one Hf(3), and two equivalent Cr(1) atoms. In the seventh S site, S(7) is bonded in a rectangular see-saw-like geometry to one Hf(4), one Cr(2), and two equivalent Cr(3) atoms. In the eighth S site, S(8) is bonded in a rectangular see-saw-like geometry to one Cr(3), one Cr(4), and two equivalent Cr(2) atoms. In the ninth S site, S(9) is bonded to two equivalent Hf(4), one Cr(1), and two equivalent Ag(1) atoms to form distorted SHf2CrAg2 trigonal bipyramids that share corners with two equivalent S(1)Hf2Ag3 square pyramids, corners with two equivalent S(2)Hf2Ag3 square pyramids, corners with two equivalent S(3)Hf2Ag3 square pyramids, corners with two equivalent S(15)HfCr2Ag2 square pyramids,  an edgeedge with one S(2)Hf2Ag3 square pyramid,  an edgeedge with one S(3)Hf2Ag3 square pyramid,  an edgeedge with one S(15)HfCr2Ag2 square pyramid, edges with two equivalent S(13)HfCr2Ag2 square pyramids, and edges with two equivalent S(9)Hf2CrAg2 trigonal bipyramids. In the tenth S site, S(10) is bonded to one Hf(1), two equivalent Cr(4), and two equivalent Ag(2) atoms to form distorted SHfCr2Ag2 trigonal bipyramids that share corners with two equivalent S(4)Cr2Ag3 square pyramids, corners with two equivalent S(1)Hf2Ag3 square pyramids, corners with two equivalent S(2)Hf2Ag3 square pyramids, corners with two equivalent S(16)HfCr2Ag2 square pyramids,  an edgeedge with one S(4)Cr2Ag3 square pyramid,  an edgeedge with one S(1)Hf2Ag3 square pyramid,  an edgeedge with one S(16)HfCr2Ag2 square pyramid, edges with two equivalent S(14)Hf2CrAg2 square pyramids, and edges with two equivalent S(10)HfCr2Ag2 trigonal bipyramids. In the eleventh S site, S(11) is bonded to two equivalent Hf(2), one Cr(2), and two equivalent Ag(3) atoms to form distorted SHf2CrAg2 trigonal bipyramids that share corners with two equivalent S(4)Cr2Ag3 square pyramids, corners with two equivalent S(1)Hf2Ag3 square pyramids, corners with two equivalent S(3)Hf2Ag3 square pyramids, corners with two equivalent S(13)HfCr2Ag2 square pyramids,  an edgeedge with one S(4)Cr2Ag3 square pyramid,  an edgeedge with one S(1)Hf2Ag3 square pyramid,  an edgeedge with one S(13)HfCr2Ag2 square pyramid, edges with two equivalent S(15)HfCr2Ag2 square pyramids, and edges with two equivalent S(11)Hf2CrAg2 trigonal bipyramids. In the twelfth S site, S(12) is bonded to two equivalent Hf(3), one Cr(3), and two equivalent Ag(4) atoms to form distorted SHf2CrAg2 trigonal bipyramids that share corners with two equivalent S(4)Cr2Ag3 square pyramids, corners with two equivalent S(2)Hf2Ag3 square pyramids, corners with two equivalent S(3)Hf2Ag3 square pyramids, corners with two equivalent S(14)Hf2CrAg2 square pyramids,  an edgeedge with one S(2)Hf2Ag3 square pyramid,  an edgeedge with one S(3)Hf2Ag3 square pyramid,  an edgeedge with one S(14)Hf2CrAg2 square pyramid, edges with two equivalent S(16)HfCr2Ag2 square pyramids, and edges with two equivalent S(12)Hf2CrAg2 trigonal bipyramids. In the thirteenth S site, S(13) is bonded to one Hf(4), two equivalent Cr(1), and two equivalent Ag(3) atoms to form distorted SHfCr2Ag2 square pyramids that share corners with two equivalent S(4)Cr2Ag3 square pyramids, corners with two equivalent S(11)Hf2CrAg2 trigonal bipyramids,  an edgeedge with one S(4)Cr2Ag3 square pyramid, edges with two equivalent S(3)Hf2Ag3 square pyramids, edges with two equivalent S(13)HfCr2Ag2 square pyramids,  an edgeedge with one S(11)Hf2CrAg2 trigonal bipyramid, and edges with two equivalent S(9)Hf2CrAg2 trigonal bipyramids. In the fourteenth S site, S(14) is bonded to two equivalent Hf(1), one Cr(4), and two equivalent Ag(4) atoms to form distorted SHf2CrAg2 square pyramids that share corners with two equivalent S(3)Hf2Ag3 square pyramids, corners with two equivalent S(12)Hf2CrAg2 trigonal bipyramids,  an edgeedge with one S(3)Hf2Ag3 square pyramid, edges with two equivalent S(4)Cr2Ag3 square pyramids, edges with two equivalent S(14)Hf2CrAg2 square pyramids,  an edgeedge with one S(12)Hf2CrAg2 trigonal bipyramid, and edges with two equivalent S(10)HfCr2Ag2 trigonal bipyramids. In the fifteenth S site, S(15) is bonded to one Hf(2), two equivalent Cr(2), and two equivalent Ag(1) atoms to form SHfCr2Ag2 square pyramids that share corners with two equivalent S(2)Hf2Ag3 square pyramids, corners with two equivalent S(9)Hf2CrAg2 trigonal bipyramids,  an edgeedge with one S(2)Hf2Ag3 square pyramid, edges with two equivalent S(1)Hf2Ag3 square pyramids, edges with two equivalent S(15)HfCr2Ag2 square pyramids,  an edgeedge with one S(9)Hf2CrAg2 trigonal bipyramid, and edges with two equivalent S(11)Hf2CrAg2 trigonal bipyramids. In the sixteenth S site, S(16) is bonded to one Hf(3), two equivalent Cr(3), and two equivalent Ag(2) atoms to form distorted SHfCr2Ag2 square pyramids that share corners with two equivalent S(1)Hf2Ag3 square pyramids, corners with two equivalent S(10)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(1)Hf2Ag3 square pyramid, edges with two equivalent S(2)Hf2Ag3 square pyramids, edges with two equivalent S(16)HfCr2Ag2 square pyramids,  an edgeedge with one S(10)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(12)Hf2CrAg2 trigonal bipyramids. is represented by the CIF card [CIF]
data_HfCrAgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.097
_cell_length_b   3.609
_cell_length_c   12.382
_cell_angle_alpha   90.000
_cell_angle_beta   90.939
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   540.574
_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
  Hf  Hf0  1  0.893  0.750  0.913  1.0
  Hf  Hf1  1  0.164  0.250  0.693  1.0
  Hf  Hf2  1  0.845  0.750  0.294  1.0
  Hf  Hf3  1  0.347  0.750  0.210  1.0
  Cr  Cr4  1  0.107  0.250  0.077  1.0
  Cr  Cr5  1  0.401  0.750  0.578  1.0
  Cr  Cr6  1  0.607  0.250  0.431  1.0
  Cr  Cr7  1  0.650  0.250  0.799  1.0
  Ag  Ag8  1  0.136  0.750  0.416  1.0
  Ag  Ag9  1  0.857  0.250  0.588  1.0
  Ag  Ag10  1  0.381  0.250  0.911  1.0
  Ag  Ag11  1  0.626  0.750  0.084  1.0
  S  S12  1  0.038  0.750  0.624  1.0
  S  S13  1  0.956  0.250  0.384  1.0
  S  S14  1  0.452  0.250  0.119  1.0
  S  S15  1  0.550  0.750  0.880  1.0
  S  S16  1  0.042  0.250  0.882  1.0
  S  S17  1  0.969  0.750  0.118  1.0
  S  S18  1  0.471  0.750  0.391  1.0
  S  S19  1  0.531  0.250  0.618  1.0
  S  S20  1  0.201  0.250  0.253  1.0
  S  S21  1  0.779  0.750  0.743  1.0
  S  S22  1  0.301  0.750  0.752  1.0
  S  S23  1  0.700  0.250  0.248  1.0
  S  S24  1  0.228  0.750  0.034  1.0
  S  S25  1  0.762  0.250  0.966  1.0
  S  S26  1  0.276  0.250  0.525  1.0
  S  S27  1  0.730  0.750  0.469  1.0
[/CIF]
.
The structure described by HfCrAgS4 crystallizes in the monoclinic Pm space group. There are four inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one S(10), one S(6), two equivalent S(14), and two equivalent S(5) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(3)S6 octahedra, corners with two equivalent Hf(2)S6 octahedra, corners with two equivalent Ag(2)S7 pentagonal bipyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and edges with two equivalent Cr(4)S6 octahedra. The corner-sharing octahedral tilt angles range from 54-60°. In the second Hf site, Hf(2) is bonded to one S(15), one S(5), two equivalent S(1), and two equivalent S(11) atoms to form HfS6 octahedra that share  a cornercorner with one Cr(1)S6 octahedra, corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Ag(2)S7 pentagonal bipyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Ag(2)S7 pentagonal bipyramid, and edges with two equivalent Ag(1)S7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 50-60°. In the third Hf site, Hf(3) is bonded to one S(16), one S(6), two equivalent S(12), and two equivalent S(2) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(1)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Ag(1)S7 pentagonal bipyramids, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Ag(1)S7 pentagonal bipyramid, and edges with two equivalent Ag(2)S7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 54-57°. In the fourth Hf site, Hf(4) is bonded to one S(13), one S(7), two equivalent S(3), and two equivalent S(9) atoms to form HfS6 octahedra that share  a cornercorner with one Cr(2)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra, corners with two equivalent Ag(1)S7 pentagonal bipyramids, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and  an edgeedge with one Ag(1)S7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 54-58°. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one S(5), one S(9), two equivalent S(13), and two equivalent S(6) atoms to form CrS6 octahedra that share  a cornercorner with one Hf(2)S6 octahedra, corners with two equivalent Hf(3)S6 octahedra, corners with two equivalent Ag(1)S7 pentagonal bipyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, and edges with two equivalent Cr(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 50-57°. In the second Cr site, Cr(2) is bonded to one S(11), one S(7), two equivalent S(15), and two equivalent S(8) atoms to form CrS6 octahedra that share  a cornercorner with one Hf(4)S6 octahedra, corners with two equivalent Cr(4)S6 octahedra, corners with two equivalent Ag(1)S7 pentagonal bipyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Ag(1)S7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 54-59°. In the third Cr site, Cr(3) is bonded to one S(12), one S(8), two equivalent S(16), and two equivalent S(7) atoms to form CrS6 octahedra that share  a cornercorner with one Cr(4)S6 octahedra, corners with two equivalent Hf(4)S6 octahedra, corners with two equivalent Ag(2)S7 pentagonal bipyramids, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Ag(2)S7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 54-58°. In the fourth Cr site, Cr(4) is bonded to one S(14), one S(8), two equivalent S(10), and two equivalent S(4) atoms to form CrS6 octahedra that share  a cornercorner with one Cr(3)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra, corners with two equivalent Ag(2)S7 pentagonal bipyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, and  an edgeedge with one Ag(2)S7 pentagonal bipyramid. The corner-sharing octahedral tilt angles range from 54-59°. There are four inequivalent Ag sites. In the first Ag site, Ag(1) is bonded to one S(1), two equivalent S(15), two equivalent S(2), and two equivalent S(9) atoms to form distorted AgS7 pentagonal bipyramids that share corners with two equivalent Hf(3)S6 octahedra, corners with two equivalent Hf(4)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Hf(3)S6 octahedra,  an edgeedge with one Hf(4)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Ag(2)S7 pentagonal bipyramids, and faces with two equivalent Ag(1)S7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 13-60°. In the second Ag site, Ag(2) is bonded to one S(2), two equivalent S(1), two equivalent S(10), and two equivalent S(16) atoms to form distorted AgS7 pentagonal bipyramids that share corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Hf(2)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra, corners with two equivalent Cr(4)S6 octahedra,  an edgeedge with one Hf(2)S6 octahedra,  an edgeedge with one Cr(3)S6 octahedra,  an edgeedge with one Cr(4)S6 octahedra, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Ag(1)S7 pentagonal bipyramids, and faces with two equivalent Ag(2)S7 pentagonal bipyramids. The corner-sharing octahedral tilt angles range from 15-67°. In the third Ag site, Ag(3) is bonded in a 7-coordinate geometry to one S(3), two equivalent S(11), two equivalent S(13), and two equivalent S(4) atoms. In the fourth Ag site, Ag(4) is bonded in a 7-coordinate geometry to one S(4), two equivalent S(12), two equivalent S(14), and two equivalent S(3) atoms. There are sixteen inequivalent S sites. In the first S site, S(1) is bonded to two equivalent Hf(2), one Ag(1), and two equivalent Ag(2) atoms to form distorted SHf2Ag3 square pyramids that share corners with two equivalent S(16)HfCr2Ag2 square pyramids, corners with two equivalent S(11)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(9)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(10)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(16)HfCr2Ag2 square pyramid, edges with two equivalent S(1)Hf2Ag3 square pyramids, edges with two equivalent S(2)Hf2Ag3 square pyramids, edges with two equivalent S(15)HfCr2Ag2 square pyramids,  an edgeedge with one S(11)Hf2CrAg2 trigonal bipyramid, and  an edgeedge with one S(10)HfCr2Ag2 trigonal bipyramid. In the second S site, S(2) is bonded to two equivalent Hf(3), one Ag(2), and two equivalent Ag(1) atoms to form distorted SHf2Ag3 square pyramids that share corners with two equivalent S(15)HfCr2Ag2 square pyramids, corners with two equivalent S(12)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(9)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(10)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(15)HfCr2Ag2 square pyramid, edges with two equivalent S(1)Hf2Ag3 square pyramids, edges with two equivalent S(2)Hf2Ag3 square pyramids, edges with two equivalent S(16)HfCr2Ag2 square pyramids,  an edgeedge with one S(12)Hf2CrAg2 trigonal bipyramid, and  an edgeedge with one S(9)Hf2CrAg2 trigonal bipyramid. In the third S site, S(3) is bonded to two equivalent Hf(4), one Ag(3), and two equivalent Ag(4) atoms to form distorted SHf2Ag3 square pyramids that share corners with two equivalent S(14)Hf2CrAg2 square pyramids, corners with two equivalent S(11)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(12)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(9)Hf2CrAg2 trigonal bipyramids,  an edgeedge with one S(14)Hf2CrAg2 square pyramid, edges with two equivalent S(4)Cr2Ag3 square pyramids, edges with two equivalent S(3)Hf2Ag3 square pyramids, edges with two equivalent S(13)HfCr2Ag2 square pyramids,  an edgeedge with one S(12)Hf2CrAg2 trigonal bipyramid, and  an edgeedge with one S(9)Hf2CrAg2 trigonal bipyramid. In the fourth S site, S(4) is bonded to two equivalent Cr(4), one Ag(4), and two equivalent Ag(3) atoms to form distorted SCr2Ag3 square pyramids that share corners with two equivalent S(13)HfCr2Ag2 square pyramids, corners with two equivalent S(11)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(12)Hf2CrAg2 trigonal bipyramids, corners with two equivalent S(10)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(13)HfCr2Ag2 square pyramid, edges with two equivalent S(4)Cr2Ag3 square pyramids, edges with two equivalent S(3)Hf2Ag3 square pyramids, edges with two equivalent S(14)Hf2CrAg2 square pyramids,  an edgeedge with one S(11)Hf2CrAg2 trigonal bipyramid, and  an edgeedge with one S(10)HfCr2Ag2 trigonal bipyramid. In the fifth S site, S(5) is bonded in a rectangular see-saw-like geometry to one Hf(2), two equivalent Hf(1), and one Cr(1) atom. In the sixth S site, S(6) is bonded in a rectangular see-saw-like geometry to one Hf(1), one Hf(3), and two equivalent Cr(1) atoms. In the seventh S site, S(7) is bonded in a rectangular see-saw-like geometry to one Hf(4), one Cr(2), and two equivalent Cr(3) atoms. In the eighth S site, S(8) is bonded in a rectangular see-saw-like geometry to one Cr(3), one Cr(4), and two equivalent Cr(2) atoms. In the ninth S site, S(9) is bonded to two equivalent Hf(4), one Cr(1), and two equivalent Ag(1) atoms to form distorted SHf2CrAg2 trigonal bipyramids that share corners with two equivalent S(1)Hf2Ag3 square pyramids, corners with two equivalent S(2)Hf2Ag3 square pyramids, corners with two equivalent S(3)Hf2Ag3 square pyramids, corners with two equivalent S(15)HfCr2Ag2 square pyramids,  an edgeedge with one S(2)Hf2Ag3 square pyramid,  an edgeedge with one S(3)Hf2Ag3 square pyramid,  an edgeedge with one S(15)HfCr2Ag2 square pyramid, edges with two equivalent S(13)HfCr2Ag2 square pyramids, and edges with two equivalent S(9)Hf2CrAg2 trigonal bipyramids. In the tenth S site, S(10) is bonded to one Hf(1), two equivalent Cr(4), and two equivalent Ag(2) atoms to form distorted SHfCr2Ag2 trigonal bipyramids that share corners with two equivalent S(4)Cr2Ag3 square pyramids, corners with two equivalent S(1)Hf2Ag3 square pyramids, corners with two equivalent S(2)Hf2Ag3 square pyramids, corners with two equivalent S(16)HfCr2Ag2 square pyramids,  an edgeedge with one S(4)Cr2Ag3 square pyramid,  an edgeedge with one S(1)Hf2Ag3 square pyramid,  an edgeedge with one S(16)HfCr2Ag2 square pyramid, edges with two equivalent S(14)Hf2CrAg2 square pyramids, and edges with two equivalent S(10)HfCr2Ag2 trigonal bipyramids. In the eleventh S site, S(11) is bonded to two equivalent Hf(2), one Cr(2), and two equivalent Ag(3) atoms to form distorted SHf2CrAg2 trigonal bipyramids that share corners with two equivalent S(4)Cr2Ag3 square pyramids, corners with two equivalent S(1)Hf2Ag3 square pyramids, corners with two equivalent S(3)Hf2Ag3 square pyramids, corners with two equivalent S(13)HfCr2Ag2 square pyramids,  an edgeedge with one S(4)Cr2Ag3 square pyramid,  an edgeedge with one S(1)Hf2Ag3 square pyramid,  an edgeedge with one S(13)HfCr2Ag2 square pyramid, edges with two equivalent S(15)HfCr2Ag2 square pyramids, and edges with two equivalent S(11)Hf2CrAg2 trigonal bipyramids. In the twelfth S site, S(12) is bonded to two equivalent Hf(3), one Cr(3), and two equivalent Ag(4) atoms to form distorted SHf2CrAg2 trigonal bipyramids that share corners with two equivalent S(4)Cr2Ag3 square pyramids, corners with two equivalent S(2)Hf2Ag3 square pyramids, corners with two equivalent S(3)Hf2Ag3 square pyramids, corners with two equivalent S(14)Hf2CrAg2 square pyramids,  an edgeedge with one S(2)Hf2Ag3 square pyramid,  an edgeedge with one S(3)Hf2Ag3 square pyramid,  an edgeedge with one S(14)Hf2CrAg2 square pyramid, edges with two equivalent S(16)HfCr2Ag2 square pyramids, and edges with two equivalent S(12)Hf2CrAg2 trigonal bipyramids. In the thirteenth S site, S(13) is bonded to one Hf(4), two equivalent Cr(1), and two equivalent Ag(3) atoms to form distorted SHfCr2Ag2 square pyramids that share corners with two equivalent S(4)Cr2Ag3 square pyramids, corners with two equivalent S(11)Hf2CrAg2 trigonal bipyramids,  an edgeedge with one S(4)Cr2Ag3 square pyramid, edges with two equivalent S(3)Hf2Ag3 square pyramids, edges with two equivalent S(13)HfCr2Ag2 square pyramids,  an edgeedge with one S(11)Hf2CrAg2 trigonal bipyramid, and edges with two equivalent S(9)Hf2CrAg2 trigonal bipyramids. In the fourteenth S site, S(14) is bonded to two equivalent Hf(1), one Cr(4), and two equivalent Ag(4) atoms to form distorted SHf2CrAg2 square pyramids that share corners with two equivalent S(3)Hf2Ag3 square pyramids, corners with two equivalent S(12)Hf2CrAg2 trigonal bipyramids,  an edgeedge with one S(3)Hf2Ag3 square pyramid, edges with two equivalent S(4)Cr2Ag3 square pyramids, edges with two equivalent S(14)Hf2CrAg2 square pyramids,  an edgeedge with one S(12)Hf2CrAg2 trigonal bipyramid, and edges with two equivalent S(10)HfCr2Ag2 trigonal bipyramids. In the fifteenth S site, S(15) is bonded to one Hf(2), two equivalent Cr(2), and two equivalent Ag(1) atoms to form SHfCr2Ag2 square pyramids that share corners with two equivalent S(2)Hf2Ag3 square pyramids, corners with two equivalent S(9)Hf2CrAg2 trigonal bipyramids,  an edgeedge with one S(2)Hf2Ag3 square pyramid, edges with two equivalent S(1)Hf2Ag3 square pyramids, edges with two equivalent S(15)HfCr2Ag2 square pyramids,  an edgeedge with one S(9)Hf2CrAg2 trigonal bipyramid, and edges with two equivalent S(11)Hf2CrAg2 trigonal bipyramids. In the sixteenth S site, S(16) is bonded to one Hf(3), two equivalent Cr(3), and two equivalent Ag(2) atoms to form distorted SHfCr2Ag2 square pyramids that share corners with two equivalent S(1)Hf2Ag3 square pyramids, corners with two equivalent S(10)HfCr2Ag2 trigonal bipyramids,  an edgeedge with one S(1)Hf2Ag3 square pyramid, edges with two equivalent S(2)Hf2Ag3 square pyramids, edges with two equivalent S(16)HfCr2Ag2 square pyramids,  an edgeedge with one S(10)HfCr2Ag2 trigonal bipyramid, and edges with two equivalent S(12)Hf2CrAg2 trigonal bipyramids. is represented by the CIF card [CIF]
data_HfCrAgS4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.097
_cell_length_b   3.609
_cell_length_c   12.382
_cell_angle_alpha   90.000
_cell_angle_beta   90.939
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   540.574
_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
  Hf  Hf0  1  0.893  0.750  0.913  1.0
  Hf  Hf1  1  0.164  0.250  0.693  1.0
  Hf  Hf2  1  0.845  0.750  0.294  1.0
  Hf  Hf3  1  0.347  0.750  0.210  1.0
  Cr  Cr4  1  0.107  0.250  0.077  1.0
  Cr  Cr5  1  0.401  0.750  0.578  1.0
  Cr  Cr6  1  0.607  0.250  0.431  1.0
  Cr  Cr7  1  0.650  0.250  0.799  1.0
  Ag  Ag8  1  0.136  0.750  0.416  1.0
  Ag  Ag9  1  0.857  0.250  0.588  1.0
  Ag  Ag10  1  0.381  0.250  0.911  1.0
  Ag  Ag11  1  0.626  0.750  0.084  1.0
  S  S12  1  0.038  0.750  0.624  1.0
  S  S13  1  0.956  0.250  0.384  1.0
  S  S14  1  0.452  0.250  0.119  1.0
  S  S15  1  0.550  0.750  0.880  1.0
  S  S16  1  0.042  0.250  0.882  1.0
  S  S17  1  0.969  0.750  0.118  1.0
  S  S18  1  0.471  0.750  0.391  1.0
  S  S19  1  0.531  0.250  0.618  1.0
  S  S20  1  0.201  0.250  0.253  1.0
  S  S21  1  0.779  0.750  0.743  1.0
  S  S22  1  0.301  0.750  0.752  1.0
  S  S23  1  0.700  0.250  0.248  1.0
  S  S24  1  0.228  0.750  0.034  1.0
  S  S25  1  0.762  0.250  0.966  1.0
  S  S26  1  0.276  0.250  0.525  1.0
  S  S27  1  0.730  0.750  0.469  1.0
[/CIF]
.