The crystal structure described by Li31Zr2P13 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(3), one P(4), and three equivalent P(3) atoms to form distorted LiLi3P4 tetrahedra that share  a cornercorner with one Li(11)Li4P4 tetrahedra, corners with three equivalent Li(8)Li4P4 tetrahedra, corners with three equivalent Li(5)LiP4 tetrahedra, corners with three equivalent Zr(2)P4 tetrahedra, edges with three equivalent Li(4)Li4P4 tetrahedra, edges with six equivalent Li(1)Li3P4 tetrahedra, faces with three equivalent Li(8)Li4P4 tetrahedra, and faces with three equivalent Li(5)LiP4 tetrahedra. In the second Li site, Li(2) is bonded to one P(1) and three equivalent P(2) atoms to form distorted LiP4 tetrahedra that share  a cornercorner with one Li(27)Li4P4 tetrahedra, corners with three equivalent Li(31)Li3P4 tetrahedra, corners with three equivalent Li(5)LiP4 tetrahedra, corners with three equivalent Zr(2)P4 tetrahedra, corners with six equivalent Li(2)P4 tetrahedra, edges with three equivalent Zr(1)LiP4 tetrahedra, and edges with three equivalent Zr(2)P4 tetrahedra. In the third Li site, Li(3) is bonded in a 14-coordinate geometry to one Li(4), one Li(5), three equivalent Li(1), three equivalent Li(8), three equivalent P(3), and three equivalent P(4) atoms. In the fourth Li site, Li(4) is bonded to one Li(3), three equivalent Li(6), one P(6), and three equivalent P(4) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(5)LiP4 tetrahedra, corners with three equivalent Li(11)Li4P4 tetrahedra, corners with three equivalent Li(8)Li4P4 tetrahedra, edges with three equivalent Li(1)Li3P4 tetrahedra, edges with three equivalent Li(7)Li4P4 tetrahedra, edges with six equivalent Li(4)Li4P4 tetrahedra, faces with three equivalent Li(11)Li4P4 tetrahedra, and faces with three equivalent Li(8)Li4P4 tetrahedra. In the fifth Li site, Li(5) is bonded to one Li(3), one P(2), and three equivalent P(3) atoms to form distorted LiLiP4 tetrahedra that share  a cornercorner with one Li(4)Li4P4 tetrahedra,  a cornercorner with one Zr(1)LiP4 tetrahedra, corners with three equivalent Li(1)Li3P4 tetrahedra, corners with three equivalent Li(2)P4 tetrahedra, corners with six equivalent Li(5)LiP4 tetrahedra, edges with three equivalent Li(8)Li4P4 tetrahedra, edges with three equivalent Zr(2)P4 tetrahedra, and faces with three equivalent Li(1)Li3P4 tetrahedra. In the sixth Li site, Li(6) is bonded in a 11-coordinate geometry to one Li(7), one Li(8), three equivalent Li(11), three equivalent Li(4), and three equivalent P(6) atoms. In the seventh Li site, Li(7) is bonded to one Li(6), three equivalent Li(10), one P(5), and three equivalent P(6) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(8)Li4P4 tetrahedra,  a cornercorner with one Li(15)P4 tetrahedra, corners with three equivalent Li(11)Li4P4 tetrahedra, edges with three equivalent Li(4)Li4P4 tetrahedra, edges with three equivalent Li(9)LiP4 tetrahedra, edges with six equivalent Li(7)Li4P4 tetrahedra, and faces with three equivalent Li(11)Li4P4 tetrahedra. In the eighth Li site, Li(8) is bonded to one Li(6), three equivalent Li(3), one P(3), and three equivalent P(4) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(7)Li4P4 tetrahedra,  a cornercorner with one Zr(2)P4 tetrahedra, corners with three equivalent Li(1)Li3P4 tetrahedra, corners with three equivalent Li(4)Li4P4 tetrahedra, edges with three equivalent Li(11)Li4P4 tetrahedra, edges with three equivalent Li(5)LiP4 tetrahedra, edges with six equivalent Li(8)Li4P4 tetrahedra, faces with three equivalent Li(1)Li3P4 tetrahedra, and faces with three equivalent Li(4)Li4P4 tetrahedra. In the ninth Li site, Li(9) is bonded to one Li(10), one P(7), and three equivalent P(5) atoms to form distorted LiLiP4 tetrahedra that share  a cornercorner with one Li(11)Li4P4 tetrahedra,  a cornercorner with one Li(17)P4 tetrahedra, corners with three equivalent Li(12)P4 tetrahedra, corners with six equivalent Li(9)LiP4 tetrahedra, edges with three equivalent Li(7)Li4P4 tetrahedra, and edges with three equivalent Li(15)P4 tetrahedra. In the tenth Li site, Li(10) is bonded in a 11-coordinate geometry to one Li(11), one Li(9), three equivalent Li(13), three equivalent Li(7), and three equivalent P(5) atoms. In the eleventh Li site, Li(11) is bonded to one Li(10), three equivalent Li(6), one P(4), and three equivalent P(6) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(1)Li3P4 tetrahedra,  a cornercorner with one Li(9)LiP4 tetrahedra, corners with three equivalent Li(4)Li4P4 tetrahedra, corners with three equivalent Li(7)Li4P4 tetrahedra, edges with three equivalent Li(8)Li4P4 tetrahedra, edges with six equivalent Li(11)Li4P4 tetrahedra, faces with three equivalent Li(4)Li4P4 tetrahedra, and faces with three equivalent Li(7)Li4P4 tetrahedra. In the twelfth Li site, Li(12) is bonded to one P(8) and three equivalent P(7) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(19)P4 tetrahedra, corners with three equivalent Li(9)LiP4 tetrahedra, corners with three equivalent Li(14)P4 tetrahedra, corners with three equivalent Li(15)P4 tetrahedra, corners with six equivalent Li(12)P4 tetrahedra, edges with three equivalent Li(15)P4 tetrahedra, and edges with three equivalent Li(17)P4 tetrahedra. In the thirteenth Li site, Li(13) is bonded in a 3-coordinate geometry to three equivalent Li(10), one P(6), and three equivalent P(5) atoms. In the fourteenth Li site, Li(14) is bonded to one P(9) and three equivalent P(8) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(20)LiP4 tetrahedra, corners with three equivalent Li(12)P4 tetrahedra, corners with three equivalent Li(16)P4 tetrahedra, corners with three equivalent Li(17)P4 tetrahedra, corners with six equivalent Li(14)P4 tetrahedra, edges with three equivalent Li(17)P4 tetrahedra, and edges with three equivalent Li(19)P4 tetrahedra. In the fifteenth Li site, Li(15) is bonded to one P(5) and three equivalent P(7) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(7)Li4P4 tetrahedra, corners with three equivalent Li(12)P4 tetrahedra, corners with three equivalent Li(17)P4 tetrahedra, corners with six equivalent Li(15)P4 tetrahedra, edges with three equivalent Li(9)LiP4 tetrahedra, and edges with three equivalent Li(12)P4 tetrahedra. In the sixteenth Li site, Li(16) is bonded to one P(11) and three equivalent P(9) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(25)Li4P4 tetrahedra, corners with three equivalent Li(14)P4 tetrahedra, corners with three equivalent Li(19)P4 tetrahedra, corners with six equivalent Li(16)P4 tetrahedra, edges with three equivalent Li(20)LiP4 tetrahedra, and edges with three equivalent Li(19)P4 tetrahedra. In the seventeenth Li site, Li(17) is bonded to one P(7) and three equivalent P(8) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(9)LiP4 tetrahedra, corners with three equivalent Li(14)P4 tetrahedra, corners with three equivalent Li(15)P4 tetrahedra, corners with three equivalent Li(19)P4 tetrahedra, corners with six equivalent Li(17)P4 tetrahedra, edges with three equivalent Li(12)P4 tetrahedra, and edges with three equivalent Li(14)P4 tetrahedra. In the eighteenth Li site, Li(18) is bonded in a 3-coordinate geometry to three equivalent Li(21), one P(10), and three equivalent P(11) atoms. In the nineteenth Li site, Li(19) is bonded to one P(8) and three equivalent P(9) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(12)P4 tetrahedra, corners with three equivalent Li(20)LiP4 tetrahedra, corners with three equivalent Li(16)P4 tetrahedra, corners with three equivalent Li(17)P4 tetrahedra, corners with six equivalent Li(19)P4 tetrahedra, edges with three equivalent Li(14)P4 tetrahedra, and edges with three equivalent Li(16)P4 tetrahedra. In the twentieth Li site, Li(20) is bonded to one Li(21), one P(9), and three equivalent P(11) atoms to form distorted LiLiP4 tetrahedra that share  a cornercorner with one Li(22)Li4P4 tetrahedra,  a cornercorner with one Li(14)P4 tetrahedra, corners with three equivalent Li(19)P4 tetrahedra, corners with six equivalent Li(20)LiP4 tetrahedra, edges with three equivalent Li(25)Li4P4 tetrahedra, and edges with three equivalent Li(16)P4 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(25), and three equivalent P(11) atoms. In the twenty-second Li site, Li(22) is bonded to one Li(21), three equivalent Li(23), one P(12), and three equivalent P(10) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(30)Li4P4 tetrahedra,  a cornercorner with one Li(20)LiP4 tetrahedra, corners with three equivalent Li(25)Li4P4 tetrahedra, corners with three equivalent Li(28)Li4P4 tetrahedra, edges with three equivalent Li(24)Li4P4 tetrahedra, edges with six equivalent Li(22)Li4P4 tetrahedra, faces with three equivalent Li(25)Li4P4 tetrahedra, and faces with three equivalent Li(28)Li4P4 tetrahedra. In the twenty-third Li site, Li(23) is bonded in a 11-coordinate geometry to one Li(24), one Li(25), three equivalent Li(22), three equivalent Li(28), and three equivalent P(10) atoms. In the twenty-fourth Li site, Li(24) is bonded to one Li(23), three equivalent Li(26), one P(13), and three equivalent P(12) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(31)Li3P4 tetrahedra,  a cornercorner with one Li(25)Li4P4 tetrahedra, corners with three equivalent Li(28)Li4P4 tetrahedra, corners with three equivalent Li(30)Li4P4 tetrahedra, edges with three equivalent Li(22)Li4P4 tetrahedra, edges with three equivalent Li(27)Li4P4 tetrahedra, edges with six equivalent Li(24)Li4P4 tetrahedra, faces with three equivalent Li(28)Li4P4 tetrahedra, and faces with three equivalent Li(30)Li4P4 tetrahedra. In the twenty-fifth Li site, Li(25) is bonded to one Li(23), three equivalent Li(21), one P(11), and three equivalent P(10) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(24)Li4P4 tetrahedra,  a cornercorner with one Li(16)P4 tetrahedra, corners with three equivalent Li(22)Li4P4 tetrahedra, edges with three equivalent Li(28)Li4P4 tetrahedra, edges with three equivalent Li(20)LiP4 tetrahedra, edges with six equivalent Li(25)Li4P4 tetrahedra, and faces with three equivalent Li(22)Li4P4 tetrahedra. In the twenty-sixth Li site, Li(26) is bonded in a 11-coordinate geometry to one Li(27), one Li(28), three equivalent Li(24), three equivalent Li(30), and three equivalent P(12) atoms. In the twenty-seventh Li site, Li(27) is bonded to one Li(26), three equivalent Li(29), one P(1), and three equivalent P(13) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(28)Li4P4 tetrahedra,  a cornercorner with one Li(2)P4 tetrahedra, corners with three equivalent Li(31)Li3P4 tetrahedra, corners with three equivalent Li(30)Li4P4 tetrahedra, edges with three equivalent Li(24)Li4P4 tetrahedra, edges with three equivalent Zr(1)LiP4 tetrahedra, edges with six equivalent Li(27)Li4P4 tetrahedra, faces with three equivalent Li(31)Li3P4 tetrahedra, and faces with three equivalent Li(30)Li4P4 tetrahedra. In the twenty-eighth Li site, Li(28) is bonded to one Li(26), three equivalent Li(23), one P(10), and three equivalent P(12) atoms to form a mixture of distorted edge, face, and corner-sharing LiLi4P4 tetrahedra. In the twenty-ninth Li site, Li(29) is bonded in a 11-coordinate geometry to one Li(30), three equivalent Li(27), three equivalent Li(31), one Zr(1), and three equivalent P(13) atoms. In the thirtieth Li site, Li(30) is bonded to one Li(29), three equivalent Li(26), one P(12), and three equivalent P(13) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(22)Li4P4 tetrahedra,  a cornercorner with one Zr(1)LiP4 tetrahedra, corners with three equivalent Li(24)Li4P4 tetrahedra, corners with three equivalent Li(27)Li4P4 tetrahedra, edges with three equivalent Li(31)Li3P4 tetrahedra, edges with three equivalent Li(28)Li4P4 tetrahedra, edges with six equivalent Li(30)Li4P4 tetrahedra, faces with three equivalent Li(24)Li4P4 tetrahedra, and faces with three equivalent Li(27)Li4P4 tetrahedra. In the thirty-first Li site, Li(31) is bonded to three equivalent Li(29), one P(13), and three equivalent P(1) atoms to form LiLi3P4 tetrahedra that share  a cornercorner with one Li(24)Li4P4 tetrahedra, corners with three equivalent Li(27)Li4P4 tetrahedra, corners with three equivalent Li(2)P4 tetrahedra, corners with three equivalent Zr(1)LiP4 tetrahedra, edges with three equivalent Li(30)Li4P4 tetrahedra, edges with six equivalent Li(31)Li3P4 tetrahedra, faces with three equivalent Li(27)Li4P4 tetrahedra, and faces with three equivalent Zr(1)LiP4 tetrahedra. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to one Li(29), one P(2), and three equivalent P(1) atoms to form distorted ZrLiP4 tetrahedra that share  a cornercorner with one Li(30)Li4P4 tetrahedra,  a cornercorner with one Li(5)LiP4 tetrahedra, corners with three equivalent Li(31)Li3P4 tetrahedra, corners with three equivalent Zr(2)P4 tetrahedra, corners with six equivalent Zr(1)LiP4 tetrahedra, edges with three equivalent Li(27)Li4P4 tetrahedra, edges with three equivalent Li(2)P4 tetrahedra, and faces with three equivalent Li(31)Li3P4 tetrahedra. In the second Zr site, Zr(2) is bonded to one P(3) and three equivalent P(2) atoms to form distorted ZrP4 tetrahedra that share  a cornercorner with one Li(8)Li4P4 tetrahedra, corners with three equivalent Li(1)Li3P4 tetrahedra, corners with three equivalent Li(2)P4 tetrahedra, corners with three equivalent Zr(1)LiP4 tetrahedra, corners with six equivalent Zr(2)P4 tetrahedra, edges with three equivalent Li(5)LiP4 tetrahedra, and edges with three equivalent Li(2)P4 tetrahedra. There are thirteen inequivalent P sites. In the first P site, P(1) is bonded in a body-centered cubic geometry to one Li(2), one Li(27), three equivalent Li(31), and three equivalent Zr(1) atoms. In the second P site, P(2) is bonded in a body-centered cubic geometry to one Li(5), three equivalent Li(2), one Zr(1), and three equivalent Zr(2) atoms. In the third P site, P(3) is bonded in a body-centered cubic geometry to one Li(8), three equivalent Li(1), three equivalent Li(3), three equivalent Li(5), and one Zr(2) atom. In the fourth P site, P(4) is bonded in a 11-coordinate geometry to one Li(1), one Li(11), three equivalent Li(3), three equivalent Li(4), and three equivalent Li(8) atoms. In the fifth P site, P(5) is bonded in a 11-coordinate geometry to one Li(15), one Li(7), three equivalent Li(10), three equivalent Li(13), and three equivalent Li(9) atoms. In the sixth P site, P(6) is bonded in a 11-coordinate geometry to one Li(13), one Li(4), three equivalent Li(11), three equivalent Li(6), and three equivalent Li(7) atoms. In the seventh P site, P(7) is bonded in a body-centered cubic geometry to one Li(17), one Li(9), three equivalent Li(12), and three equivalent Li(15) atoms. In the eighth P site, P(8) is bonded in a body-centered cubic geometry to one Li(12), one Li(19), three equivalent Li(14), and three equivalent Li(17) atoms. In the ninth P site, P(9) is bonded in a body-centered cubic geometry to one Li(14), one Li(20), three equivalent Li(16), and three equivalent Li(19) atoms. In the tenth P site, P(10) is bonded in a 11-coordinate geometry to one Li(18), one Li(28), three equivalent Li(22), three equivalent Li(23), and three equivalent Li(25) atoms. In the eleventh P site, P(11) is bonded in a 11-coordinate geometry to one Li(16), one Li(25), three equivalent Li(18), three equivalent Li(20), and three equivalent Li(21) atoms. In the twelfth P site, P(12) is bonded in a 8-coordinate geometry to one Li(22), one Li(30), three equivalent Li(24), three equivalent Li(26), and three equivalent Li(28) atoms. In the thirteenth P site, P(13) is bonded in a 11-coordinate geometry to one Li(24), one Li(31), three equivalent Li(27), three equivalent Li(29), and three equivalent Li(30) atoms. is represented by the CIF file [CIF]
data_Li31Zr2P13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.183
_cell_length_b   4.183
_cell_length_c   55.107
_cell_angle_alpha   60.413
_cell_angle_beta   60.413
_cell_angle_gamma   60.040
_symmetry_Int_Tables_number   1
_cell_volume   686.123
_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  0.266  0.266  0.169  1.0
  Li  Li1  1  0.742  0.742  0.060  1.0
  Li  Li2  1  0.486  0.486  0.196  1.0
  Li  Li3  1  0.251  0.251  0.250  1.0
  Li  Li4  1  0.737  0.737  0.138  1.0
  Li  Li5  1  0.493  0.493  0.271  1.0
  Li  Li6  1  0.253  0.253  0.326  1.0
  Li  Li7  1  0.747  0.747  0.212  1.0
  Li  Li8  1  0.239  0.239  0.406  1.0
  Li  Li9  1  0.487  0.487  0.349  1.0
  Li  Li10  1  0.750  0.750  0.289  1.0
  Li  Li11  1  0.248  0.248  0.481  1.0
  Li  Li12  1  0.732  0.732  0.370  1.0
  Li  Li13  1  0.247  0.247  0.558  1.0
  Li  Li14  1  0.758  0.758  0.441  1.0
  Li  Li15  1  0.242  0.242  0.637  1.0
  Li  Li16  1  0.753  0.753  0.519  1.0
  Li  Li17  1  0.269  0.269  0.707  1.0
  Li  Li18  1  0.752  0.752  0.596  1.0
  Li  Li19  1  0.761  0.761  0.671  1.0
  Li  Li20  1  0.514  0.514  0.728  1.0
  Li  Li21  1  0.251  0.251  0.788  1.0
  Li  Li22  1  0.510  0.510  0.805  1.0
  Li  Li23  1  0.253  0.253  0.865  1.0
  Li  Li24  1  0.747  0.747  0.751  1.0
  Li  Li25  1  0.513  0.513  0.882  1.0
  Li  Li26  1  0.259  0.259  0.940  1.0
  Li  Li27  1  0.750  0.750  0.827  1.0
  Li  Li28  1  0.526  0.526  0.956  1.0
  Li  Li29  1  0.756  0.756  0.902  1.0
  Li  Li30  1  0.749  0.749  0.981  1.0
  Zr  Zr31  1  0.236  0.236  0.022  1.0
  Zr  Zr32  1  0.240  0.240  0.099  1.0
  P  P33  1  0.002  0.002  1.000  1.0
  P  P34  1  0.990  0.990  0.079  1.0
  P  P35  1  0.995  0.995  0.155  1.0
  P  P36  1  0.010  0.010  0.228  1.0
  P  P37  1  0.015  0.015  0.381  1.0
  P  P38  1  0.011  0.011  0.305  1.0
  P  P39  1  0.997  0.997  0.462  1.0
  P  P40  1  0.000  0.000  0.538  1.0
  P  P41  1  0.003  0.003  0.615  1.0
  P  P42  1  0.988  0.988  0.772  1.0
  P  P43  1  0.985  0.985  0.696  1.0
  P  P44  1  0.992  0.992  0.848  1.0
  P  P45  1  0.995  0.995  0.924  1.0
[/CIF]
.
The crystal structure described by Li31Zr2P13 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(3), one P(4), and three equivalent P(3) atoms to form distorted LiLi3P4 tetrahedra that share  a cornercorner with one Li(11)Li4P4 tetrahedra, corners with three equivalent Li(8)Li4P4 tetrahedra, corners with three equivalent Li(5)LiP4 tetrahedra, corners with three equivalent Zr(2)P4 tetrahedra, edges with three equivalent Li(4)Li4P4 tetrahedra, edges with six equivalent Li(1)Li3P4 tetrahedra, faces with three equivalent Li(8)Li4P4 tetrahedra, and faces with three equivalent Li(5)LiP4 tetrahedra. In the second Li site, Li(2) is bonded to one P(1) and three equivalent P(2) atoms to form distorted LiP4 tetrahedra that share  a cornercorner with one Li(27)Li4P4 tetrahedra, corners with three equivalent Li(31)Li3P4 tetrahedra, corners with three equivalent Li(5)LiP4 tetrahedra, corners with three equivalent Zr(2)P4 tetrahedra, corners with six equivalent Li(2)P4 tetrahedra, edges with three equivalent Zr(1)LiP4 tetrahedra, and edges with three equivalent Zr(2)P4 tetrahedra. In the third Li site, Li(3) is bonded in a 14-coordinate geometry to one Li(4), one Li(5), three equivalent Li(1), three equivalent Li(8), three equivalent P(3), and three equivalent P(4) atoms. In the fourth Li site, Li(4) is bonded to one Li(3), three equivalent Li(6), one P(6), and three equivalent P(4) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(5)LiP4 tetrahedra, corners with three equivalent Li(11)Li4P4 tetrahedra, corners with three equivalent Li(8)Li4P4 tetrahedra, edges with three equivalent Li(1)Li3P4 tetrahedra, edges with three equivalent Li(7)Li4P4 tetrahedra, edges with six equivalent Li(4)Li4P4 tetrahedra, faces with three equivalent Li(11)Li4P4 tetrahedra, and faces with three equivalent Li(8)Li4P4 tetrahedra. In the fifth Li site, Li(5) is bonded to one Li(3), one P(2), and three equivalent P(3) atoms to form distorted LiLiP4 tetrahedra that share  a cornercorner with one Li(4)Li4P4 tetrahedra,  a cornercorner with one Zr(1)LiP4 tetrahedra, corners with three equivalent Li(1)Li3P4 tetrahedra, corners with three equivalent Li(2)P4 tetrahedra, corners with six equivalent Li(5)LiP4 tetrahedra, edges with three equivalent Li(8)Li4P4 tetrahedra, edges with three equivalent Zr(2)P4 tetrahedra, and faces with three equivalent Li(1)Li3P4 tetrahedra. In the sixth Li site, Li(6) is bonded in a 11-coordinate geometry to one Li(7), one Li(8), three equivalent Li(11), three equivalent Li(4), and three equivalent P(6) atoms. In the seventh Li site, Li(7) is bonded to one Li(6), three equivalent Li(10), one P(5), and three equivalent P(6) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(8)Li4P4 tetrahedra,  a cornercorner with one Li(15)P4 tetrahedra, corners with three equivalent Li(11)Li4P4 tetrahedra, edges with three equivalent Li(4)Li4P4 tetrahedra, edges with three equivalent Li(9)LiP4 tetrahedra, edges with six equivalent Li(7)Li4P4 tetrahedra, and faces with three equivalent Li(11)Li4P4 tetrahedra. In the eighth Li site, Li(8) is bonded to one Li(6), three equivalent Li(3), one P(3), and three equivalent P(4) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(7)Li4P4 tetrahedra,  a cornercorner with one Zr(2)P4 tetrahedra, corners with three equivalent Li(1)Li3P4 tetrahedra, corners with three equivalent Li(4)Li4P4 tetrahedra, edges with three equivalent Li(11)Li4P4 tetrahedra, edges with three equivalent Li(5)LiP4 tetrahedra, edges with six equivalent Li(8)Li4P4 tetrahedra, faces with three equivalent Li(1)Li3P4 tetrahedra, and faces with three equivalent Li(4)Li4P4 tetrahedra. In the ninth Li site, Li(9) is bonded to one Li(10), one P(7), and three equivalent P(5) atoms to form distorted LiLiP4 tetrahedra that share  a cornercorner with one Li(11)Li4P4 tetrahedra,  a cornercorner with one Li(17)P4 tetrahedra, corners with three equivalent Li(12)P4 tetrahedra, corners with six equivalent Li(9)LiP4 tetrahedra, edges with three equivalent Li(7)Li4P4 tetrahedra, and edges with three equivalent Li(15)P4 tetrahedra. In the tenth Li site, Li(10) is bonded in a 11-coordinate geometry to one Li(11), one Li(9), three equivalent Li(13), three equivalent Li(7), and three equivalent P(5) atoms. In the eleventh Li site, Li(11) is bonded to one Li(10), three equivalent Li(6), one P(4), and three equivalent P(6) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(1)Li3P4 tetrahedra,  a cornercorner with one Li(9)LiP4 tetrahedra, corners with three equivalent Li(4)Li4P4 tetrahedra, corners with three equivalent Li(7)Li4P4 tetrahedra, edges with three equivalent Li(8)Li4P4 tetrahedra, edges with six equivalent Li(11)Li4P4 tetrahedra, faces with three equivalent Li(4)Li4P4 tetrahedra, and faces with three equivalent Li(7)Li4P4 tetrahedra. In the twelfth Li site, Li(12) is bonded to one P(8) and three equivalent P(7) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(19)P4 tetrahedra, corners with three equivalent Li(9)LiP4 tetrahedra, corners with three equivalent Li(14)P4 tetrahedra, corners with three equivalent Li(15)P4 tetrahedra, corners with six equivalent Li(12)P4 tetrahedra, edges with three equivalent Li(15)P4 tetrahedra, and edges with three equivalent Li(17)P4 tetrahedra. In the thirteenth Li site, Li(13) is bonded in a 3-coordinate geometry to three equivalent Li(10), one P(6), and three equivalent P(5) atoms. In the fourteenth Li site, Li(14) is bonded to one P(9) and three equivalent P(8) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(20)LiP4 tetrahedra, corners with three equivalent Li(12)P4 tetrahedra, corners with three equivalent Li(16)P4 tetrahedra, corners with three equivalent Li(17)P4 tetrahedra, corners with six equivalent Li(14)P4 tetrahedra, edges with three equivalent Li(17)P4 tetrahedra, and edges with three equivalent Li(19)P4 tetrahedra. In the fifteenth Li site, Li(15) is bonded to one P(5) and three equivalent P(7) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(7)Li4P4 tetrahedra, corners with three equivalent Li(12)P4 tetrahedra, corners with three equivalent Li(17)P4 tetrahedra, corners with six equivalent Li(15)P4 tetrahedra, edges with three equivalent Li(9)LiP4 tetrahedra, and edges with three equivalent Li(12)P4 tetrahedra. In the sixteenth Li site, Li(16) is bonded to one P(11) and three equivalent P(9) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(25)Li4P4 tetrahedra, corners with three equivalent Li(14)P4 tetrahedra, corners with three equivalent Li(19)P4 tetrahedra, corners with six equivalent Li(16)P4 tetrahedra, edges with three equivalent Li(20)LiP4 tetrahedra, and edges with three equivalent Li(19)P4 tetrahedra. In the seventeenth Li site, Li(17) is bonded to one P(7) and three equivalent P(8) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(9)LiP4 tetrahedra, corners with three equivalent Li(14)P4 tetrahedra, corners with three equivalent Li(15)P4 tetrahedra, corners with three equivalent Li(19)P4 tetrahedra, corners with six equivalent Li(17)P4 tetrahedra, edges with three equivalent Li(12)P4 tetrahedra, and edges with three equivalent Li(14)P4 tetrahedra. In the eighteenth Li site, Li(18) is bonded in a 3-coordinate geometry to three equivalent Li(21), one P(10), and three equivalent P(11) atoms. In the nineteenth Li site, Li(19) is bonded to one P(8) and three equivalent P(9) atoms to form LiP4 tetrahedra that share  a cornercorner with one Li(12)P4 tetrahedra, corners with three equivalent Li(20)LiP4 tetrahedra, corners with three equivalent Li(16)P4 tetrahedra, corners with three equivalent Li(17)P4 tetrahedra, corners with six equivalent Li(19)P4 tetrahedra, edges with three equivalent Li(14)P4 tetrahedra, and edges with three equivalent Li(16)P4 tetrahedra. In the twentieth Li site, Li(20) is bonded to one Li(21), one P(9), and three equivalent P(11) atoms to form distorted LiLiP4 tetrahedra that share  a cornercorner with one Li(22)Li4P4 tetrahedra,  a cornercorner with one Li(14)P4 tetrahedra, corners with three equivalent Li(19)P4 tetrahedra, corners with six equivalent Li(20)LiP4 tetrahedra, edges with three equivalent Li(25)Li4P4 tetrahedra, and edges with three equivalent Li(16)P4 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(25), and three equivalent P(11) atoms. In the twenty-second Li site, Li(22) is bonded to one Li(21), three equivalent Li(23), one P(12), and three equivalent P(10) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(30)Li4P4 tetrahedra,  a cornercorner with one Li(20)LiP4 tetrahedra, corners with three equivalent Li(25)Li4P4 tetrahedra, corners with three equivalent Li(28)Li4P4 tetrahedra, edges with three equivalent Li(24)Li4P4 tetrahedra, edges with six equivalent Li(22)Li4P4 tetrahedra, faces with three equivalent Li(25)Li4P4 tetrahedra, and faces with three equivalent Li(28)Li4P4 tetrahedra. In the twenty-third Li site, Li(23) is bonded in a 11-coordinate geometry to one Li(24), one Li(25), three equivalent Li(22), three equivalent Li(28), and three equivalent P(10) atoms. In the twenty-fourth Li site, Li(24) is bonded to one Li(23), three equivalent Li(26), one P(13), and three equivalent P(12) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(31)Li3P4 tetrahedra,  a cornercorner with one Li(25)Li4P4 tetrahedra, corners with three equivalent Li(28)Li4P4 tetrahedra, corners with three equivalent Li(30)Li4P4 tetrahedra, edges with three equivalent Li(22)Li4P4 tetrahedra, edges with three equivalent Li(27)Li4P4 tetrahedra, edges with six equivalent Li(24)Li4P4 tetrahedra, faces with three equivalent Li(28)Li4P4 tetrahedra, and faces with three equivalent Li(30)Li4P4 tetrahedra. In the twenty-fifth Li site, Li(25) is bonded to one Li(23), three equivalent Li(21), one P(11), and three equivalent P(10) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(24)Li4P4 tetrahedra,  a cornercorner with one Li(16)P4 tetrahedra, corners with three equivalent Li(22)Li4P4 tetrahedra, edges with three equivalent Li(28)Li4P4 tetrahedra, edges with three equivalent Li(20)LiP4 tetrahedra, edges with six equivalent Li(25)Li4P4 tetrahedra, and faces with three equivalent Li(22)Li4P4 tetrahedra. In the twenty-sixth Li site, Li(26) is bonded in a 11-coordinate geometry to one Li(27), one Li(28), three equivalent Li(24), three equivalent Li(30), and three equivalent P(12) atoms. In the twenty-seventh Li site, Li(27) is bonded to one Li(26), three equivalent Li(29), one P(1), and three equivalent P(13) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(28)Li4P4 tetrahedra,  a cornercorner with one Li(2)P4 tetrahedra, corners with three equivalent Li(31)Li3P4 tetrahedra, corners with three equivalent Li(30)Li4P4 tetrahedra, edges with three equivalent Li(24)Li4P4 tetrahedra, edges with three equivalent Zr(1)LiP4 tetrahedra, edges with six equivalent Li(27)Li4P4 tetrahedra, faces with three equivalent Li(31)Li3P4 tetrahedra, and faces with three equivalent Li(30)Li4P4 tetrahedra. In the twenty-eighth Li site, Li(28) is bonded to one Li(26), three equivalent Li(23), one P(10), and three equivalent P(12) atoms to form a mixture of distorted edge, face, and corner-sharing LiLi4P4 tetrahedra. In the twenty-ninth Li site, Li(29) is bonded in a 11-coordinate geometry to one Li(30), three equivalent Li(27), three equivalent Li(31), one Zr(1), and three equivalent P(13) atoms. In the thirtieth Li site, Li(30) is bonded to one Li(29), three equivalent Li(26), one P(12), and three equivalent P(13) atoms to form distorted LiLi4P4 tetrahedra that share  a cornercorner with one Li(22)Li4P4 tetrahedra,  a cornercorner with one Zr(1)LiP4 tetrahedra, corners with three equivalent Li(24)Li4P4 tetrahedra, corners with three equivalent Li(27)Li4P4 tetrahedra, edges with three equivalent Li(31)Li3P4 tetrahedra, edges with three equivalent Li(28)Li4P4 tetrahedra, edges with six equivalent Li(30)Li4P4 tetrahedra, faces with three equivalent Li(24)Li4P4 tetrahedra, and faces with three equivalent Li(27)Li4P4 tetrahedra. In the thirty-first Li site, Li(31) is bonded to three equivalent Li(29), one P(13), and three equivalent P(1) atoms to form LiLi3P4 tetrahedra that share  a cornercorner with one Li(24)Li4P4 tetrahedra, corners with three equivalent Li(27)Li4P4 tetrahedra, corners with three equivalent Li(2)P4 tetrahedra, corners with three equivalent Zr(1)LiP4 tetrahedra, edges with three equivalent Li(30)Li4P4 tetrahedra, edges with six equivalent Li(31)Li3P4 tetrahedra, faces with three equivalent Li(27)Li4P4 tetrahedra, and faces with three equivalent Zr(1)LiP4 tetrahedra. There are two inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to one Li(29), one P(2), and three equivalent P(1) atoms to form distorted ZrLiP4 tetrahedra that share  a cornercorner with one Li(30)Li4P4 tetrahedra,  a cornercorner with one Li(5)LiP4 tetrahedra, corners with three equivalent Li(31)Li3P4 tetrahedra, corners with three equivalent Zr(2)P4 tetrahedra, corners with six equivalent Zr(1)LiP4 tetrahedra, edges with three equivalent Li(27)Li4P4 tetrahedra, edges with three equivalent Li(2)P4 tetrahedra, and faces with three equivalent Li(31)Li3P4 tetrahedra. In the second Zr site, Zr(2) is bonded to one P(3) and three equivalent P(2) atoms to form distorted ZrP4 tetrahedra that share  a cornercorner with one Li(8)Li4P4 tetrahedra, corners with three equivalent Li(1)Li3P4 tetrahedra, corners with three equivalent Li(2)P4 tetrahedra, corners with three equivalent Zr(1)LiP4 tetrahedra, corners with six equivalent Zr(2)P4 tetrahedra, edges with three equivalent Li(5)LiP4 tetrahedra, and edges with three equivalent Li(2)P4 tetrahedra. There are thirteen inequivalent P sites. In the first P site, P(1) is bonded in a body-centered cubic geometry to one Li(2), one Li(27), three equivalent Li(31), and three equivalent Zr(1) atoms. In the second P site, P(2) is bonded in a body-centered cubic geometry to one Li(5), three equivalent Li(2), one Zr(1), and three equivalent Zr(2) atoms. In the third P site, P(3) is bonded in a body-centered cubic geometry to one Li(8), three equivalent Li(1), three equivalent Li(3), three equivalent Li(5), and one Zr(2) atom. In the fourth P site, P(4) is bonded in a 11-coordinate geometry to one Li(1), one Li(11), three equivalent Li(3), three equivalent Li(4), and three equivalent Li(8) atoms. In the fifth P site, P(5) is bonded in a 11-coordinate geometry to one Li(15), one Li(7), three equivalent Li(10), three equivalent Li(13), and three equivalent Li(9) atoms. In the sixth P site, P(6) is bonded in a 11-coordinate geometry to one Li(13), one Li(4), three equivalent Li(11), three equivalent Li(6), and three equivalent Li(7) atoms. In the seventh P site, P(7) is bonded in a body-centered cubic geometry to one Li(17), one Li(9), three equivalent Li(12), and three equivalent Li(15) atoms. In the eighth P site, P(8) is bonded in a body-centered cubic geometry to one Li(12), one Li(19), three equivalent Li(14), and three equivalent Li(17) atoms. In the ninth P site, P(9) is bonded in a body-centered cubic geometry to one Li(14), one Li(20), three equivalent Li(16), and three equivalent Li(19) atoms. In the tenth P site, P(10) is bonded in a 11-coordinate geometry to one Li(18), one Li(28), three equivalent Li(22), three equivalent Li(23), and three equivalent Li(25) atoms. In the eleventh P site, P(11) is bonded in a 11-coordinate geometry to one Li(16), one Li(25), three equivalent Li(18), three equivalent Li(20), and three equivalent Li(21) atoms. In the twelfth P site, P(12) is bonded in a 8-coordinate geometry to one Li(22), one Li(30), three equivalent Li(24), three equivalent Li(26), and three equivalent Li(28) atoms. In the thirteenth P site, P(13) is bonded in a 11-coordinate geometry to one Li(24), one Li(31), three equivalent Li(27), three equivalent Li(29), and three equivalent Li(30) atoms. is represented by the CIF file [CIF]
data_Li31Zr2P13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.183
_cell_length_b   4.183
_cell_length_c   55.107
_cell_angle_alpha   60.413
_cell_angle_beta   60.413
_cell_angle_gamma   60.040
_symmetry_Int_Tables_number   1
_cell_volume   686.123
_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  0.266  0.266  0.169  1.0
  Li  Li1  1  0.742  0.742  0.060  1.0
  Li  Li2  1  0.486  0.486  0.196  1.0
  Li  Li3  1  0.251  0.251  0.250  1.0
  Li  Li4  1  0.737  0.737  0.138  1.0
  Li  Li5  1  0.493  0.493  0.271  1.0
  Li  Li6  1  0.253  0.253  0.326  1.0
  Li  Li7  1  0.747  0.747  0.212  1.0
  Li  Li8  1  0.239  0.239  0.406  1.0
  Li  Li9  1  0.487  0.487  0.349  1.0
  Li  Li10  1  0.750  0.750  0.289  1.0
  Li  Li11  1  0.248  0.248  0.481  1.0
  Li  Li12  1  0.732  0.732  0.370  1.0
  Li  Li13  1  0.247  0.247  0.558  1.0
  Li  Li14  1  0.758  0.758  0.441  1.0
  Li  Li15  1  0.242  0.242  0.637  1.0
  Li  Li16  1  0.753  0.753  0.519  1.0
  Li  Li17  1  0.269  0.269  0.707  1.0
  Li  Li18  1  0.752  0.752  0.596  1.0
  Li  Li19  1  0.761  0.761  0.671  1.0
  Li  Li20  1  0.514  0.514  0.728  1.0
  Li  Li21  1  0.251  0.251  0.788  1.0
  Li  Li22  1  0.510  0.510  0.805  1.0
  Li  Li23  1  0.253  0.253  0.865  1.0
  Li  Li24  1  0.747  0.747  0.751  1.0
  Li  Li25  1  0.513  0.513  0.882  1.0
  Li  Li26  1  0.259  0.259  0.940  1.0
  Li  Li27  1  0.750  0.750  0.827  1.0
  Li  Li28  1  0.526  0.526  0.956  1.0
  Li  Li29  1  0.756  0.756  0.902  1.0
  Li  Li30  1  0.749  0.749  0.981  1.0
  Zr  Zr31  1  0.236  0.236  0.022  1.0
  Zr  Zr32  1  0.240  0.240  0.099  1.0
  P  P33  1  0.002  0.002  1.000  1.0
  P  P34  1  0.990  0.990  0.079  1.0
  P  P35  1  0.995  0.995  0.155  1.0
  P  P36  1  0.010  0.010  0.228  1.0
  P  P37  1  0.015  0.015  0.381  1.0
  P  P38  1  0.011  0.011  0.305  1.0
  P  P39  1  0.997  0.997  0.462  1.0
  P  P40  1  0.000  0.000  0.538  1.0
  P  P41  1  0.003  0.003  0.615  1.0
  P  P42  1  0.988  0.988  0.772  1.0
  P  P43  1  0.985  0.985  0.696  1.0
  P  P44  1  0.992  0.992  0.848  1.0
  P  P45  1  0.995  0.995  0.924  1.0
[/CIF]
.