The structure described by Li31Zr2As13 crystallizes in the trigonal R3m space group. There are thirty-one inequivalent Li sites. In the first Li site, Li(1) is bonded to three equivalent Li(4), one As(4), and three equivalent As(3) atoms to form distorted LiLi3As4 tetrahedra that share  a cornercorner with one Li(10)Li4As4 tetrahedra, corners with three equivalent Li(7)Li4As4 tetrahedra, corners with three equivalent Li(3)LiAs4 tetrahedra, corners with three equivalent Zr(2)As4 tetrahedra, edges with three equivalent Li(5)Li4As4 tetrahedra, edges with six equivalent Li(1)Li3As4 tetrahedra, faces with three equivalent Li(7)Li4As4 tetrahedra, and faces with three equivalent Li(3)LiAs4 tetrahedra. In the second Li site, Li(2) is bonded to one As(1) and three equivalent As(2) atoms to form distorted LiAs4 tetrahedra that share  a cornercorner with one Li(28)Li4As4 tetrahedra, corners with three equivalent Li(31)Li3As4 tetrahedra, corners with three equivalent Li(3)LiAs4 tetrahedra, corners with three equivalent Zr(2)As4 tetrahedra, corners with six equivalent Li(2)As4 tetrahedra, edges with three equivalent Zr(2)As4 tetrahedra, and edges with three equivalent Zr(1)LiAs4 tetrahedra. In the third Li site, Li(3) is bonded to one Li(4), one As(2), and three equivalent As(3) atoms to form distorted LiLiAs4 tetrahedra that share  a cornercorner with one Li(5)Li4As4 tetrahedra,  a cornercorner with one Zr(1)LiAs4 tetrahedra, corners with three equivalent Li(2)As4 tetrahedra, corners with three equivalent Li(1)Li3As4 tetrahedra, corners with six equivalent Li(3)LiAs4 tetrahedra, edges with three equivalent Li(7)Li4As4 tetrahedra, edges with three equivalent Zr(2)As4 tetrahedra, and faces with three equivalent Li(1)Li3As4 tetrahedra. In the fourth Li site, Li(4) is bonded in a 14-coordinate geometry to one Li(3), one Li(5), three equivalent Li(1), three equivalent Li(7), three equivalent As(3), and three equivalent As(4) atoms. In the fifth Li site, Li(5) is bonded to one Li(4), three equivalent Li(8), one As(5), and three equivalent As(4) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(3)LiAs4 tetrahedra, corners with three equivalent Li(10)Li4As4 tetrahedra, corners with three equivalent Li(7)Li4As4 tetrahedra, edges with three equivalent Li(1)Li3As4 tetrahedra, edges with three equivalent Li(6)Li4As4 tetrahedra, edges with six equivalent Li(5)Li4As4 tetrahedra, faces with three equivalent Li(10)Li4As4 tetrahedra, and faces with three equivalent Li(7)Li4As4 tetrahedra. In the sixth Li site, Li(6) is bonded to one Li(8), three equivalent Li(9), one As(6), and three equivalent As(5) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(14)As4 tetrahedra,  a cornercorner with one Li(7)Li4As4 tetrahedra, corners with three equivalent Li(10)Li4As4 tetrahedra, edges with three equivalent Li(5)Li4As4 tetrahedra, edges with three equivalent Li(11)LiAs4 tetrahedra, edges with six equivalent Li(6)Li4As4 tetrahedra, and faces with three equivalent Li(10)Li4As4 tetrahedra. In the seventh Li site, Li(7) is bonded to one Li(8), three equivalent Li(4), one As(3), and three equivalent As(4) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(6)Li4As4 tetrahedra,  a cornercorner with one Zr(2)As4 tetrahedra, corners with three equivalent Li(1)Li3As4 tetrahedra, corners with three equivalent Li(5)Li4As4 tetrahedra, edges with three equivalent Li(10)Li4As4 tetrahedra, edges with three equivalent Li(3)LiAs4 tetrahedra, edges with six equivalent Li(7)Li4As4 tetrahedra, faces with three equivalent Li(1)Li3As4 tetrahedra, and faces with three equivalent Li(5)Li4As4 tetrahedra. In the eighth Li site, Li(8) is bonded in a 14-coordinate geometry to one Li(6), one Li(7), three equivalent Li(10), three equivalent Li(5), three equivalent As(4), and three equivalent As(5) atoms. In the ninth Li site, Li(9) is bonded in a 14-coordinate geometry to one Li(10), one Li(11), three equivalent Li(13), three equivalent Li(6), three equivalent As(5), and three equivalent As(6) atoms. In the tenth Li site, Li(10) is bonded to one Li(9), three equivalent Li(8), one As(4), and three equivalent As(5) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(1)Li3As4 tetrahedra,  a cornercorner with one Li(11)LiAs4 tetrahedra, corners with three equivalent Li(5)Li4As4 tetrahedra, corners with three equivalent Li(6)Li4As4 tetrahedra, edges with three equivalent Li(7)Li4As4 tetrahedra, edges with six equivalent Li(10)Li4As4 tetrahedra, faces with three equivalent Li(5)Li4As4 tetrahedra, and faces with three equivalent Li(6)Li4As4 tetrahedra. In the eleventh Li site, Li(11) is bonded to one Li(9), one As(7), and three equivalent As(6) atoms to form distorted LiLiAs4 tetrahedra that share  a cornercorner with one Li(16)As4 tetrahedra,  a cornercorner with one Li(10)Li4As4 tetrahedra, corners with three equivalent Li(12)As4 tetrahedra, corners with six equivalent Li(11)LiAs4 tetrahedra, edges with three equivalent Li(14)As4 tetrahedra, and edges with three equivalent Li(6)Li4As4 tetrahedra. In the twelfth Li site, Li(12) is bonded to one As(8) and three equivalent As(7) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(19)As4 tetrahedra, corners with three equivalent Li(14)As4 tetrahedra, corners with three equivalent Li(15)As4 tetrahedra, corners with three equivalent Li(11)LiAs4 tetrahedra, corners with six equivalent Li(12)As4 tetrahedra, edges with three equivalent Li(14)As4 tetrahedra, and edges with three equivalent Li(16)As4 tetrahedra. In the thirteenth Li site, Li(13) is bonded in a 4-coordinate geometry to three equivalent Li(9), one As(5), and three equivalent As(6) atoms. In the fourteenth Li site, Li(14) is bonded to one As(6) and three equivalent As(7) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(6)Li4As4 tetrahedra, corners with three equivalent Li(12)As4 tetrahedra, corners with three equivalent Li(16)As4 tetrahedra, corners with six equivalent Li(14)As4 tetrahedra, edges with three equivalent Li(12)As4 tetrahedra, and edges with three equivalent Li(11)LiAs4 tetrahedra. In the fifteenth Li site, Li(15) is bonded to one As(9) and three equivalent As(8) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(20)LiAs4 tetrahedra, corners with three equivalent Li(12)As4 tetrahedra, corners with three equivalent Li(16)As4 tetrahedra, corners with three equivalent Li(17)As4 tetrahedra, corners with six equivalent Li(15)As4 tetrahedra, edges with three equivalent Li(16)As4 tetrahedra, and edges with three equivalent Li(19)As4 tetrahedra. In the sixteenth Li site, Li(16) is bonded to one As(7) and three equivalent As(8) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(11)LiAs4 tetrahedra, corners with three equivalent Li(14)As4 tetrahedra, corners with three equivalent Li(15)As4 tetrahedra, corners with three equivalent Li(19)As4 tetrahedra, corners with six equivalent Li(16)As4 tetrahedra, edges with three equivalent Li(12)As4 tetrahedra, and edges with three equivalent Li(15)As4 tetrahedra. In the seventeenth Li site, Li(17) is bonded to one As(10) and three equivalent As(9) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(24)Li4As4 tetrahedra, corners with three equivalent Li(15)As4 tetrahedra, corners with three equivalent Li(19)As4 tetrahedra, corners with six equivalent Li(17)As4 tetrahedra, edges with three equivalent Li(19)As4 tetrahedra, and edges with three equivalent Li(20)LiAs4 tetrahedra. In the eighteenth Li site, Li(18) is bonded in a 3-coordinate geometry to three equivalent Li(21), one As(11), and three equivalent As(10) atoms. In the nineteenth Li site, Li(19) is bonded to one As(8) and three equivalent As(9) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(12)As4 tetrahedra, corners with three equivalent Li(16)As4 tetrahedra, corners with three equivalent Li(17)As4 tetrahedra, corners with three equivalent Li(20)LiAs4 tetrahedra, corners with six equivalent Li(19)As4 tetrahedra, edges with three equivalent Li(15)As4 tetrahedra, and edges with three equivalent Li(17)As4 tetrahedra. In the twentieth Li site, Li(20) is bonded to one Li(21), one As(9), and three equivalent As(10) atoms to form distorted LiLiAs4 tetrahedra that share  a cornercorner with one Li(15)As4 tetrahedra,  a cornercorner with one Li(22)Li4As4 tetrahedra, corners with three equivalent Li(19)As4 tetrahedra, corners with six equivalent Li(20)LiAs4 tetrahedra, edges with three equivalent Li(17)As4 tetrahedra, and edges with three equivalent Li(24)Li4As4 tetrahedra. In the twenty-first Li site, Li(21) is bonded in a 11-coordinate geometry to one Li(20), one Li(22), three equivalent Li(18), three equivalent Li(24), and three equivalent As(10) atoms. In the twenty-second Li site, Li(22) is bonded to one Li(21), three equivalent Li(25), one As(13), and three equivalent As(11) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(29)Li4As4 tetrahedra,  a cornercorner with one Li(20)LiAs4 tetrahedra, corners with three equivalent Li(24)Li4As4 tetrahedra, corners with three equivalent Li(26)Li4As4 tetrahedra, edges with three equivalent Li(23)Li4As4 tetrahedra, edges with six equivalent Li(22)Li4As4 tetrahedra, faces with three equivalent Li(24)Li4As4 tetrahedra, and faces with three equivalent Li(26)Li4As4 tetrahedra. In the twenty-third Li site, Li(23) is bonded to one Li(25), three equivalent Li(27), one As(12), and three equivalent As(13) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(31)Li3As4 tetrahedra,  a cornercorner with one Li(24)Li4As4 tetrahedra, corners with three equivalent Li(26)Li4As4 tetrahedra, corners with three equivalent Li(29)Li4As4 tetrahedra, edges with three equivalent Li(22)Li4As4 tetrahedra, edges with three equivalent Li(28)Li4As4 tetrahedra, edges with six equivalent Li(23)Li4As4 tetrahedra, faces with three equivalent Li(26)Li4As4 tetrahedra, and faces with three equivalent Li(29)Li4As4 tetrahedra. In the twenty-fourth Li site, Li(24) is bonded to one Li(25), three equivalent Li(21), one As(10), and three equivalent As(11) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(17)As4 tetrahedra,  a cornercorner with one Li(23)Li4As4 tetrahedra, corners with three equivalent Li(22)Li4As4 tetrahedra, edges with three equivalent Li(26)Li4As4 tetrahedra, edges with three equivalent Li(20)LiAs4 tetrahedra, edges with six equivalent Li(24)Li4As4 tetrahedra, and faces with three equivalent Li(22)Li4As4 tetrahedra. In the twenty-fifth Li site, Li(25) is bonded in a 14-coordinate geometry to one Li(23), one Li(24), three equivalent Li(22), three equivalent Li(26), three equivalent As(11), and three equivalent As(13) atoms. In the twenty-sixth Li site, Li(26) is bonded to one Li(27), three equivalent Li(25), one As(11), and three equivalent As(13) atoms to form a mixture of distorted face, corner, and edge-sharing LiLi4As4 tetrahedra. In the twenty-seventh Li site, Li(27) is bonded in a 14-coordinate geometry to one Li(26), one Li(28), three equivalent Li(23), three equivalent Li(29), three equivalent As(12), and three equivalent As(13) atoms. In the twenty-eighth Li site, Li(28) is bonded to one Li(27), three equivalent Li(30), one As(1), and three equivalent As(12) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(2)As4 tetrahedra,  a cornercorner with one Li(26)Li4As4 tetrahedra, corners with three equivalent Li(31)Li3As4 tetrahedra, corners with three equivalent Li(29)Li4As4 tetrahedra, edges with three equivalent Li(23)Li4As4 tetrahedra, edges with three equivalent Zr(1)LiAs4 tetrahedra, edges with six equivalent Li(28)Li4As4 tetrahedra, faces with three equivalent Li(31)Li3As4 tetrahedra, and faces with three equivalent Li(29)Li4As4 tetrahedra. In the twenty-ninth Li site, Li(29) is bonded to one Li(30), three equivalent Li(27), one As(13), and three equivalent As(12) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(22)Li4As4 tetrahedra,  a cornercorner with one Zr(1)LiAs4 tetrahedra, corners with three equivalent Li(23)Li4As4 tetrahedra, corners with three equivalent Li(28)Li4As4 tetrahedra, edges with three equivalent Li(31)Li3As4 tetrahedra, edges with three equivalent Li(26)Li4As4 tetrahedra, edges with six equivalent Li(29)Li4As4 tetrahedra, faces with three equivalent Li(23)Li4As4 tetrahedra, and faces with three equivalent Li(28)Li4As4 tetrahedra. In the thirtieth Li site, Li(30) is bonded in a 14-coordinate geometry to one Li(29), three equivalent Li(28), three equivalent Li(31), one Zr(1), three equivalent As(1), and three equivalent As(12) atoms. In the thirty-first Li site, Li(31) is bonded to three equivalent Li(30), one As(12), and three equivalent As(1) atoms to form distorted LiLi3As4 tetrahedra that share  a cornercorner with one Li(23)Li4As4 tetrahedra, corners with three equivalent Li(2)As4 tetrahedra, corners with three equivalent Li(28)Li4As4 tetrahedra, corners with three equivalent Zr(1)LiAs4 tetrahedra, edges with three equivalent Li(29)Li4As4 tetrahedra, edges with six equivalent Li(31)Li3As4 tetrahedra, faces with three equivalent Li(28)Li4As4 tetrahedra, and faces with three equivalent Zr(1)LiAs4 tetrahedra. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to one Li(30), one As(2), and three equivalent As(1) atoms to form distorted ZrLiAs4 tetrahedra that share  a cornercorner with one Li(29)Li4As4 tetrahedra,  a cornercorner with one Li(3)LiAs4 tetrahedra, corners with three equivalent Li(31)Li3As4 tetrahedra, corners with three equivalent Zr(2)As4 tetrahedra, corners with six equivalent Zr(1)LiAs4 tetrahedra, edges with three equivalent Li(2)As4 tetrahedra, edges with three equivalent Li(28)Li4As4 tetrahedra, and faces with three equivalent Li(31)Li3As4 tetrahedra. In the second Zr site, Zr(2) is bonded to one As(3) and three equivalent As(2) atoms to form distorted ZrAs4 tetrahedra that share  a cornercorner with one Li(7)Li4As4 tetrahedra, corners with three equivalent Li(2)As4 tetrahedra, corners with three equivalent Li(1)Li3As4 tetrahedra, corners with three equivalent Zr(1)LiAs4 tetrahedra, corners with six equivalent Zr(2)As4 tetrahedra, edges with three equivalent Li(2)As4 tetrahedra, and edges with three equivalent Li(3)LiAs4 tetrahedra. There are thirteen inequivalent As sites. In the first As site, As(1) is bonded in a body-centered cubic geometry to one Li(2), one Li(28), three equivalent Li(30), three equivalent Li(31), and three equivalent Zr(1) atoms. In the second As site, As(2) is bonded in a body-centered cubic geometry to one Li(3), three equivalent Li(2), one Zr(1), and three equivalent Zr(2) atoms. In the third As site, As(3) is bonded in a body-centered cubic geometry to one Li(7), three equivalent Li(1), three equivalent Li(3), three equivalent Li(4), and one Zr(2) atom. In the fourth As site, As(4) is bonded in a 8-coordinate geometry to one Li(1), one Li(10), three equivalent Li(4), three equivalent Li(5), three equivalent Li(7), and three equivalent Li(8) atoms. In the fifth As site, As(5) is bonded in a 11-coordinate geometry to one Li(13), one Li(5), three equivalent Li(10), three equivalent Li(6), three equivalent Li(8), and three equivalent Li(9) atoms. In the sixth As site, As(6) is bonded in a 11-coordinate geometry to one Li(14), one Li(6), three equivalent Li(11), three equivalent Li(13), and three equivalent Li(9) atoms. In the seventh As site, As(7) is bonded in a body-centered cubic geometry to one Li(11), one Li(16), three equivalent Li(12), and three equivalent Li(14) atoms. In the eighth As site, As(8) is bonded in a body-centered cubic geometry to one Li(12), one Li(19), three equivalent Li(15), and three equivalent Li(16) atoms. In the ninth As site, As(9) is bonded in a body-centered cubic geometry to one Li(15), one Li(20), three equivalent Li(17), and three equivalent Li(19) atoms. In the tenth As site, As(10) is bonded in a 11-coordinate geometry to one Li(17), one Li(24), three equivalent Li(18), three equivalent Li(20), and three equivalent Li(21) atoms. In the eleventh As site, As(11) is bonded in a 11-coordinate geometry to one Li(18), one Li(26), three equivalent Li(22), three equivalent Li(24), and three equivalent Li(25) atoms. In the twelfth As site, As(12) is bonded in a 11-coordinate geometry to one Li(23), one Li(31), three equivalent Li(27), three equivalent Li(28), three equivalent Li(29), and three equivalent Li(30) atoms. In the thirteenth As site, As(13) is bonded in a 8-coordinate geometry to one Li(22), one Li(29), three equivalent Li(23), three equivalent Li(25), three equivalent Li(26), and three equivalent Li(27) atoms. is represented by the CIF card [CIF]
data_Li31Zr2As13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.323
_cell_length_b   4.323
_cell_length_c   56.894
_cell_angle_alpha   60.367
_cell_angle_beta   60.367
_cell_angle_gamma   60.055
_symmetry_Int_Tables_number   1
_cell_volume   756.464
_cell_formula_units_Z   1
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
  Li  Li0  1  0.264  0.264  0.170  1.0
  Li  Li1  1  0.744  0.744  0.059  1.0
  Li  Li2  1  0.740  0.740  0.137  1.0
  Li  Li3  1  0.488  0.488  0.195  1.0
  Li  Li4  1  0.251  0.251  0.250  1.0
  Li  Li5  1  0.253  0.253  0.326  1.0
  Li  Li6  1  0.747  0.747  0.212  1.0
  Li  Li7  1  0.493  0.493  0.271  1.0
  Li  Li8  1  0.488  0.488  0.349  1.0
  Li  Li9  1  0.750  0.750  0.289  1.0
  Li  Li10  1  0.241  0.241  0.406  1.0
  Li  Li11  1  0.249  0.249  0.481  1.0
  Li  Li12  1  0.735  0.735  0.369  1.0
  Li  Li13  1  0.758  0.758  0.440  1.0
  Li  Li14  1  0.246  0.246  0.558  1.0
  Li  Li15  1  0.753  0.753  0.519  1.0
  Li  Li16  1  0.242  0.242  0.636  1.0
  Li  Li17  1  0.265  0.265  0.708  1.0
  Li  Li18  1  0.751  0.751  0.596  1.0
  Li  Li19  1  0.760  0.760  0.671  1.0
  Li  Li20  1  0.513  0.513  0.728  1.0
  Li  Li21  1  0.251  0.251  0.788  1.0
  Li  Li22  1  0.252  0.252  0.865  1.0
  Li  Li23  1  0.747  0.747  0.751  1.0
  Li  Li24  1  0.508  0.508  0.806  1.0
  Li  Li25  1  0.749  0.749  0.827  1.0
  Li  Li26  1  0.511  0.511  0.882  1.0
  Li  Li27  1  0.259  0.259  0.940  1.0
  Li  Li28  1  0.755  0.755  0.903  1.0
  Li  Li29  1  0.523  0.523  0.956  1.0
  Li  Li30  1  0.748  0.748  0.981  1.0
  Zr  Zr31  1  0.238  0.238  0.022  1.0
  Zr  Zr32  1  0.240  0.240  0.098  1.0
  As  As33  1  0.004  0.004  0.999  1.0
  As  As34  1  0.991  0.991  0.079  1.0
  As  As35  1  0.994  0.994  0.155  1.0
  As  As36  1  0.009  0.009  0.229  1.0
  As  As37  1  0.009  0.009  0.306  1.0
  As  As38  1  0.014  0.014  0.381  1.0
  As  As39  1  0.996  0.996  0.462  1.0
  As  As40  1  1.000  1.000  0.538  1.0
  As  As41  1  0.004  0.004  0.615  1.0
  As  As42  1  0.986  0.986  0.696  1.0
  As  As43  1  0.990  0.990  0.772  1.0
  As  As44  1  0.995  0.995  0.924  1.0
  As  As45  1  0.992  0.992  0.848  1.0
[/CIF]
.
The structure described by Li31Zr2As13 crystallizes in the trigonal R3m space group. There are thirty-one inequivalent Li sites. In the first Li site, Li(1) is bonded to three equivalent Li(4), one As(4), and three equivalent As(3) atoms to form distorted LiLi3As4 tetrahedra that share  a cornercorner with one Li(10)Li4As4 tetrahedra, corners with three equivalent Li(7)Li4As4 tetrahedra, corners with three equivalent Li(3)LiAs4 tetrahedra, corners with three equivalent Zr(2)As4 tetrahedra, edges with three equivalent Li(5)Li4As4 tetrahedra, edges with six equivalent Li(1)Li3As4 tetrahedra, faces with three equivalent Li(7)Li4As4 tetrahedra, and faces with three equivalent Li(3)LiAs4 tetrahedra. In the second Li site, Li(2) is bonded to one As(1) and three equivalent As(2) atoms to form distorted LiAs4 tetrahedra that share  a cornercorner with one Li(28)Li4As4 tetrahedra, corners with three equivalent Li(31)Li3As4 tetrahedra, corners with three equivalent Li(3)LiAs4 tetrahedra, corners with three equivalent Zr(2)As4 tetrahedra, corners with six equivalent Li(2)As4 tetrahedra, edges with three equivalent Zr(2)As4 tetrahedra, and edges with three equivalent Zr(1)LiAs4 tetrahedra. In the third Li site, Li(3) is bonded to one Li(4), one As(2), and three equivalent As(3) atoms to form distorted LiLiAs4 tetrahedra that share  a cornercorner with one Li(5)Li4As4 tetrahedra,  a cornercorner with one Zr(1)LiAs4 tetrahedra, corners with three equivalent Li(2)As4 tetrahedra, corners with three equivalent Li(1)Li3As4 tetrahedra, corners with six equivalent Li(3)LiAs4 tetrahedra, edges with three equivalent Li(7)Li4As4 tetrahedra, edges with three equivalent Zr(2)As4 tetrahedra, and faces with three equivalent Li(1)Li3As4 tetrahedra. In the fourth Li site, Li(4) is bonded in a 14-coordinate geometry to one Li(3), one Li(5), three equivalent Li(1), three equivalent Li(7), three equivalent As(3), and three equivalent As(4) atoms. In the fifth Li site, Li(5) is bonded to one Li(4), three equivalent Li(8), one As(5), and three equivalent As(4) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(3)LiAs4 tetrahedra, corners with three equivalent Li(10)Li4As4 tetrahedra, corners with three equivalent Li(7)Li4As4 tetrahedra, edges with three equivalent Li(1)Li3As4 tetrahedra, edges with three equivalent Li(6)Li4As4 tetrahedra, edges with six equivalent Li(5)Li4As4 tetrahedra, faces with three equivalent Li(10)Li4As4 tetrahedra, and faces with three equivalent Li(7)Li4As4 tetrahedra. In the sixth Li site, Li(6) is bonded to one Li(8), three equivalent Li(9), one As(6), and three equivalent As(5) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(14)As4 tetrahedra,  a cornercorner with one Li(7)Li4As4 tetrahedra, corners with three equivalent Li(10)Li4As4 tetrahedra, edges with three equivalent Li(5)Li4As4 tetrahedra, edges with three equivalent Li(11)LiAs4 tetrahedra, edges with six equivalent Li(6)Li4As4 tetrahedra, and faces with three equivalent Li(10)Li4As4 tetrahedra. In the seventh Li site, Li(7) is bonded to one Li(8), three equivalent Li(4), one As(3), and three equivalent As(4) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(6)Li4As4 tetrahedra,  a cornercorner with one Zr(2)As4 tetrahedra, corners with three equivalent Li(1)Li3As4 tetrahedra, corners with three equivalent Li(5)Li4As4 tetrahedra, edges with three equivalent Li(10)Li4As4 tetrahedra, edges with three equivalent Li(3)LiAs4 tetrahedra, edges with six equivalent Li(7)Li4As4 tetrahedra, faces with three equivalent Li(1)Li3As4 tetrahedra, and faces with three equivalent Li(5)Li4As4 tetrahedra. In the eighth Li site, Li(8) is bonded in a 14-coordinate geometry to one Li(6), one Li(7), three equivalent Li(10), three equivalent Li(5), three equivalent As(4), and three equivalent As(5) atoms. In the ninth Li site, Li(9) is bonded in a 14-coordinate geometry to one Li(10), one Li(11), three equivalent Li(13), three equivalent Li(6), three equivalent As(5), and three equivalent As(6) atoms. In the tenth Li site, Li(10) is bonded to one Li(9), three equivalent Li(8), one As(4), and three equivalent As(5) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(1)Li3As4 tetrahedra,  a cornercorner with one Li(11)LiAs4 tetrahedra, corners with three equivalent Li(5)Li4As4 tetrahedra, corners with three equivalent Li(6)Li4As4 tetrahedra, edges with three equivalent Li(7)Li4As4 tetrahedra, edges with six equivalent Li(10)Li4As4 tetrahedra, faces with three equivalent Li(5)Li4As4 tetrahedra, and faces with three equivalent Li(6)Li4As4 tetrahedra. In the eleventh Li site, Li(11) is bonded to one Li(9), one As(7), and three equivalent As(6) atoms to form distorted LiLiAs4 tetrahedra that share  a cornercorner with one Li(16)As4 tetrahedra,  a cornercorner with one Li(10)Li4As4 tetrahedra, corners with three equivalent Li(12)As4 tetrahedra, corners with six equivalent Li(11)LiAs4 tetrahedra, edges with three equivalent Li(14)As4 tetrahedra, and edges with three equivalent Li(6)Li4As4 tetrahedra. In the twelfth Li site, Li(12) is bonded to one As(8) and three equivalent As(7) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(19)As4 tetrahedra, corners with three equivalent Li(14)As4 tetrahedra, corners with three equivalent Li(15)As4 tetrahedra, corners with three equivalent Li(11)LiAs4 tetrahedra, corners with six equivalent Li(12)As4 tetrahedra, edges with three equivalent Li(14)As4 tetrahedra, and edges with three equivalent Li(16)As4 tetrahedra. In the thirteenth Li site, Li(13) is bonded in a 4-coordinate geometry to three equivalent Li(9), one As(5), and three equivalent As(6) atoms. In the fourteenth Li site, Li(14) is bonded to one As(6) and three equivalent As(7) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(6)Li4As4 tetrahedra, corners with three equivalent Li(12)As4 tetrahedra, corners with three equivalent Li(16)As4 tetrahedra, corners with six equivalent Li(14)As4 tetrahedra, edges with three equivalent Li(12)As4 tetrahedra, and edges with three equivalent Li(11)LiAs4 tetrahedra. In the fifteenth Li site, Li(15) is bonded to one As(9) and three equivalent As(8) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(20)LiAs4 tetrahedra, corners with three equivalent Li(12)As4 tetrahedra, corners with three equivalent Li(16)As4 tetrahedra, corners with three equivalent Li(17)As4 tetrahedra, corners with six equivalent Li(15)As4 tetrahedra, edges with three equivalent Li(16)As4 tetrahedra, and edges with three equivalent Li(19)As4 tetrahedra. In the sixteenth Li site, Li(16) is bonded to one As(7) and three equivalent As(8) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(11)LiAs4 tetrahedra, corners with three equivalent Li(14)As4 tetrahedra, corners with three equivalent Li(15)As4 tetrahedra, corners with three equivalent Li(19)As4 tetrahedra, corners with six equivalent Li(16)As4 tetrahedra, edges with three equivalent Li(12)As4 tetrahedra, and edges with three equivalent Li(15)As4 tetrahedra. In the seventeenth Li site, Li(17) is bonded to one As(10) and three equivalent As(9) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(24)Li4As4 tetrahedra, corners with three equivalent Li(15)As4 tetrahedra, corners with three equivalent Li(19)As4 tetrahedra, corners with six equivalent Li(17)As4 tetrahedra, edges with three equivalent Li(19)As4 tetrahedra, and edges with three equivalent Li(20)LiAs4 tetrahedra. In the eighteenth Li site, Li(18) is bonded in a 3-coordinate geometry to three equivalent Li(21), one As(11), and three equivalent As(10) atoms. In the nineteenth Li site, Li(19) is bonded to one As(8) and three equivalent As(9) atoms to form LiAs4 tetrahedra that share  a cornercorner with one Li(12)As4 tetrahedra, corners with three equivalent Li(16)As4 tetrahedra, corners with three equivalent Li(17)As4 tetrahedra, corners with three equivalent Li(20)LiAs4 tetrahedra, corners with six equivalent Li(19)As4 tetrahedra, edges with three equivalent Li(15)As4 tetrahedra, and edges with three equivalent Li(17)As4 tetrahedra. In the twentieth Li site, Li(20) is bonded to one Li(21), one As(9), and three equivalent As(10) atoms to form distorted LiLiAs4 tetrahedra that share  a cornercorner with one Li(15)As4 tetrahedra,  a cornercorner with one Li(22)Li4As4 tetrahedra, corners with three equivalent Li(19)As4 tetrahedra, corners with six equivalent Li(20)LiAs4 tetrahedra, edges with three equivalent Li(17)As4 tetrahedra, and edges with three equivalent Li(24)Li4As4 tetrahedra. In the twenty-first Li site, Li(21) is bonded in a 11-coordinate geometry to one Li(20), one Li(22), three equivalent Li(18), three equivalent Li(24), and three equivalent As(10) atoms. In the twenty-second Li site, Li(22) is bonded to one Li(21), three equivalent Li(25), one As(13), and three equivalent As(11) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(29)Li4As4 tetrahedra,  a cornercorner with one Li(20)LiAs4 tetrahedra, corners with three equivalent Li(24)Li4As4 tetrahedra, corners with three equivalent Li(26)Li4As4 tetrahedra, edges with three equivalent Li(23)Li4As4 tetrahedra, edges with six equivalent Li(22)Li4As4 tetrahedra, faces with three equivalent Li(24)Li4As4 tetrahedra, and faces with three equivalent Li(26)Li4As4 tetrahedra. In the twenty-third Li site, Li(23) is bonded to one Li(25), three equivalent Li(27), one As(12), and three equivalent As(13) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(31)Li3As4 tetrahedra,  a cornercorner with one Li(24)Li4As4 tetrahedra, corners with three equivalent Li(26)Li4As4 tetrahedra, corners with three equivalent Li(29)Li4As4 tetrahedra, edges with three equivalent Li(22)Li4As4 tetrahedra, edges with three equivalent Li(28)Li4As4 tetrahedra, edges with six equivalent Li(23)Li4As4 tetrahedra, faces with three equivalent Li(26)Li4As4 tetrahedra, and faces with three equivalent Li(29)Li4As4 tetrahedra. In the twenty-fourth Li site, Li(24) is bonded to one Li(25), three equivalent Li(21), one As(10), and three equivalent As(11) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(17)As4 tetrahedra,  a cornercorner with one Li(23)Li4As4 tetrahedra, corners with three equivalent Li(22)Li4As4 tetrahedra, edges with three equivalent Li(26)Li4As4 tetrahedra, edges with three equivalent Li(20)LiAs4 tetrahedra, edges with six equivalent Li(24)Li4As4 tetrahedra, and faces with three equivalent Li(22)Li4As4 tetrahedra. In the twenty-fifth Li site, Li(25) is bonded in a 14-coordinate geometry to one Li(23), one Li(24), three equivalent Li(22), three equivalent Li(26), three equivalent As(11), and three equivalent As(13) atoms. In the twenty-sixth Li site, Li(26) is bonded to one Li(27), three equivalent Li(25), one As(11), and three equivalent As(13) atoms to form a mixture of distorted face, corner, and edge-sharing LiLi4As4 tetrahedra. In the twenty-seventh Li site, Li(27) is bonded in a 14-coordinate geometry to one Li(26), one Li(28), three equivalent Li(23), three equivalent Li(29), three equivalent As(12), and three equivalent As(13) atoms. In the twenty-eighth Li site, Li(28) is bonded to one Li(27), three equivalent Li(30), one As(1), and three equivalent As(12) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(2)As4 tetrahedra,  a cornercorner with one Li(26)Li4As4 tetrahedra, corners with three equivalent Li(31)Li3As4 tetrahedra, corners with three equivalent Li(29)Li4As4 tetrahedra, edges with three equivalent Li(23)Li4As4 tetrahedra, edges with three equivalent Zr(1)LiAs4 tetrahedra, edges with six equivalent Li(28)Li4As4 tetrahedra, faces with three equivalent Li(31)Li3As4 tetrahedra, and faces with three equivalent Li(29)Li4As4 tetrahedra. In the twenty-ninth Li site, Li(29) is bonded to one Li(30), three equivalent Li(27), one As(13), and three equivalent As(12) atoms to form distorted LiLi4As4 tetrahedra that share  a cornercorner with one Li(22)Li4As4 tetrahedra,  a cornercorner with one Zr(1)LiAs4 tetrahedra, corners with three equivalent Li(23)Li4As4 tetrahedra, corners with three equivalent Li(28)Li4As4 tetrahedra, edges with three equivalent Li(31)Li3As4 tetrahedra, edges with three equivalent Li(26)Li4As4 tetrahedra, edges with six equivalent Li(29)Li4As4 tetrahedra, faces with three equivalent Li(23)Li4As4 tetrahedra, and faces with three equivalent Li(28)Li4As4 tetrahedra. In the thirtieth Li site, Li(30) is bonded in a 14-coordinate geometry to one Li(29), three equivalent Li(28), three equivalent Li(31), one Zr(1), three equivalent As(1), and three equivalent As(12) atoms. In the thirty-first Li site, Li(31) is bonded to three equivalent Li(30), one As(12), and three equivalent As(1) atoms to form distorted LiLi3As4 tetrahedra that share  a cornercorner with one Li(23)Li4As4 tetrahedra, corners with three equivalent Li(2)As4 tetrahedra, corners with three equivalent Li(28)Li4As4 tetrahedra, corners with three equivalent Zr(1)LiAs4 tetrahedra, edges with three equivalent Li(29)Li4As4 tetrahedra, edges with six equivalent Li(31)Li3As4 tetrahedra, faces with three equivalent Li(28)Li4As4 tetrahedra, and faces with three equivalent Zr(1)LiAs4 tetrahedra. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to one Li(30), one As(2), and three equivalent As(1) atoms to form distorted ZrLiAs4 tetrahedra that share  a cornercorner with one Li(29)Li4As4 tetrahedra,  a cornercorner with one Li(3)LiAs4 tetrahedra, corners with three equivalent Li(31)Li3As4 tetrahedra, corners with three equivalent Zr(2)As4 tetrahedra, corners with six equivalent Zr(1)LiAs4 tetrahedra, edges with three equivalent Li(2)As4 tetrahedra, edges with three equivalent Li(28)Li4As4 tetrahedra, and faces with three equivalent Li(31)Li3As4 tetrahedra. In the second Zr site, Zr(2) is bonded to one As(3) and three equivalent As(2) atoms to form distorted ZrAs4 tetrahedra that share  a cornercorner with one Li(7)Li4As4 tetrahedra, corners with three equivalent Li(2)As4 tetrahedra, corners with three equivalent Li(1)Li3As4 tetrahedra, corners with three equivalent Zr(1)LiAs4 tetrahedra, corners with six equivalent Zr(2)As4 tetrahedra, edges with three equivalent Li(2)As4 tetrahedra, and edges with three equivalent Li(3)LiAs4 tetrahedra. There are thirteen inequivalent As sites. In the first As site, As(1) is bonded in a body-centered cubic geometry to one Li(2), one Li(28), three equivalent Li(30), three equivalent Li(31), and three equivalent Zr(1) atoms. In the second As site, As(2) is bonded in a body-centered cubic geometry to one Li(3), three equivalent Li(2), one Zr(1), and three equivalent Zr(2) atoms. In the third As site, As(3) is bonded in a body-centered cubic geometry to one Li(7), three equivalent Li(1), three equivalent Li(3), three equivalent Li(4), and one Zr(2) atom. In the fourth As site, As(4) is bonded in a 8-coordinate geometry to one Li(1), one Li(10), three equivalent Li(4), three equivalent Li(5), three equivalent Li(7), and three equivalent Li(8) atoms. In the fifth As site, As(5) is bonded in a 11-coordinate geometry to one Li(13), one Li(5), three equivalent Li(10), three equivalent Li(6), three equivalent Li(8), and three equivalent Li(9) atoms. In the sixth As site, As(6) is bonded in a 11-coordinate geometry to one Li(14), one Li(6), three equivalent Li(11), three equivalent Li(13), and three equivalent Li(9) atoms. In the seventh As site, As(7) is bonded in a body-centered cubic geometry to one Li(11), one Li(16), three equivalent Li(12), and three equivalent Li(14) atoms. In the eighth As site, As(8) is bonded in a body-centered cubic geometry to one Li(12), one Li(19), three equivalent Li(15), and three equivalent Li(16) atoms. In the ninth As site, As(9) is bonded in a body-centered cubic geometry to one Li(15), one Li(20), three equivalent Li(17), and three equivalent Li(19) atoms. In the tenth As site, As(10) is bonded in a 11-coordinate geometry to one Li(17), one Li(24), three equivalent Li(18), three equivalent Li(20), and three equivalent Li(21) atoms. In the eleventh As site, As(11) is bonded in a 11-coordinate geometry to one Li(18), one Li(26), three equivalent Li(22), three equivalent Li(24), and three equivalent Li(25) atoms. In the twelfth As site, As(12) is bonded in a 11-coordinate geometry to one Li(23), one Li(31), three equivalent Li(27), three equivalent Li(28), three equivalent Li(29), and three equivalent Li(30) atoms. In the thirteenth As site, As(13) is bonded in a 8-coordinate geometry to one Li(22), one Li(29), three equivalent Li(23), three equivalent Li(25), three equivalent Li(26), and three equivalent Li(27) atoms. is represented by the CIF card [CIF]
data_Li31Zr2As13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.323
_cell_length_b   4.323
_cell_length_c   56.894
_cell_angle_alpha   60.367
_cell_angle_beta   60.367
_cell_angle_gamma   60.055
_symmetry_Int_Tables_number   1
_cell_volume   756.464
_cell_formula_units_Z   1
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
  Li  Li0  1  0.264  0.264  0.170  1.0
  Li  Li1  1  0.744  0.744  0.059  1.0
  Li  Li2  1  0.740  0.740  0.137  1.0
  Li  Li3  1  0.488  0.488  0.195  1.0
  Li  Li4  1  0.251  0.251  0.250  1.0
  Li  Li5  1  0.253  0.253  0.326  1.0
  Li  Li6  1  0.747  0.747  0.212  1.0
  Li  Li7  1  0.493  0.493  0.271  1.0
  Li  Li8  1  0.488  0.488  0.349  1.0
  Li  Li9  1  0.750  0.750  0.289  1.0
  Li  Li10  1  0.241  0.241  0.406  1.0
  Li  Li11  1  0.249  0.249  0.481  1.0
  Li  Li12  1  0.735  0.735  0.369  1.0
  Li  Li13  1  0.758  0.758  0.440  1.0
  Li  Li14  1  0.246  0.246  0.558  1.0
  Li  Li15  1  0.753  0.753  0.519  1.0
  Li  Li16  1  0.242  0.242  0.636  1.0
  Li  Li17  1  0.265  0.265  0.708  1.0
  Li  Li18  1  0.751  0.751  0.596  1.0
  Li  Li19  1  0.760  0.760  0.671  1.0
  Li  Li20  1  0.513  0.513  0.728  1.0
  Li  Li21  1  0.251  0.251  0.788  1.0
  Li  Li22  1  0.252  0.252  0.865  1.0
  Li  Li23  1  0.747  0.747  0.751  1.0
  Li  Li24  1  0.508  0.508  0.806  1.0
  Li  Li25  1  0.749  0.749  0.827  1.0
  Li  Li26  1  0.511  0.511  0.882  1.0
  Li  Li27  1  0.259  0.259  0.940  1.0
  Li  Li28  1  0.755  0.755  0.903  1.0
  Li  Li29  1  0.523  0.523  0.956  1.0
  Li  Li30  1  0.748  0.748  0.981  1.0
  Zr  Zr31  1  0.238  0.238  0.022  1.0
  Zr  Zr32  1  0.240  0.240  0.098  1.0
  As  As33  1  0.004  0.004  0.999  1.0
  As  As34  1  0.991  0.991  0.079  1.0
  As  As35  1  0.994  0.994  0.155  1.0
  As  As36  1  0.009  0.009  0.229  1.0
  As  As37  1  0.009  0.009  0.306  1.0
  As  As38  1  0.014  0.014  0.381  1.0
  As  As39  1  0.996  0.996  0.462  1.0
  As  As40  1  1.000  1.000  0.538  1.0
  As  As41  1  0.004  0.004  0.615  1.0
  As  As42  1  0.986  0.986  0.696  1.0
  As  As43  1  0.990  0.990  0.772  1.0
  As  As44  1  0.995  0.995  0.924  1.0
  As  As45  1  0.992  0.992  0.848  1.0
[/CIF]
.