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.
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. All Li(1)-Li(3) bond lengths are 2.69 Å. The Li(1)-P(4) bond length is 2.67 Å. All Li(1)-P(3) bond lengths are 2.50 Å. 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. The Li(2)-P(1) bond length is 2.72 Å. All Li(2)-P(2) bond lengths are 2.57 Å. 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. The Li(3)-Li(4) bond length is 2.45 Å. The Li(3)-Li(5) bond length is 2.63 Å. All Li(3)-Li(8) bond lengths are 2.53 Å. All Li(3)-P(3) bond lengths are 3.03 Å. All Li(3)-P(4) bond lengths are 2.83 Å. 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. All Li(4)-Li(6) bond lengths are 2.60 Å. The Li(4)-P(6) bond length is 2.51 Å. All Li(4)-P(4) bond lengths are 2.60 Å. 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. The Li(5)-P(2) bond length is 2.64 Å. All Li(5)-P(3) bond lengths are 2.54 Å. 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. The Li(6)-Li(7) bond length is 2.50 Å. The Li(6)-Li(8) bond length is 2.66 Å. All Li(6)-Li(11) bond lengths are 2.54 Å. All Li(6)-P(6) bond lengths are 2.87 Å. 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. All Li(7)-Li(10) bond lengths are 2.63 Å. The Li(7)-P(5) bond length is 2.49 Å. All Li(7)-P(6) bond lengths are 2.59 Å. 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. The Li(8)-P(3) bond length is 2.59 Å. All Li(8)-P(4) bond lengths are 2.52 Å. 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. The Li(9)-Li(10) bond length is 2.59 Å. The Li(9)-P(7) bond length is 2.53 Å. All Li(9)-P(5) bond lengths are 2.67 Å. 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. The Li(10)-Li(11) bond length is 2.74 Å. All Li(10)-Li(13) bond lengths are 2.59 Å. All Li(10)-P(5) bond lengths are 2.82 Å. 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. The Li(11)-P(4) bond length is 2.72 Å. All Li(11)-P(6) bond lengths are 2.53 Å. 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. The Li(12)-P(8) bond length is 2.59 Å. All Li(12)-P(7) bond lengths are 2.56 Å. 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. The Li(13)-P(6) bond length is 2.91 Å. All Li(13)-P(5) bond lengths are 2.47 Å. 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. The Li(14)-P(9) bond length is 2.55 Å. All Li(14)-P(8) bond lengths are 2.58 Å. 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. The Li(15)-P(5) bond length is 2.69 Å. All Li(15)-P(7) bond lengths are 2.61 Å. 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. The Li(16)-P(11) bond length is 2.68 Å. All Li(16)-P(9) bond lengths are 2.61 Å. 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. The Li(17)-P(7) bond length is 2.55 Å. All Li(17)-P(8) bond lengths are 2.58 Å. 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. All Li(18)-Li(21) bond lengths are 2.58 Å. The Li(18)-P(10) bond length is 2.93 Å. All Li(18)-P(11) bond lengths are 2.47 Å. 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. The Li(19)-P(8) bond length is 2.59 Å. All Li(19)-P(9) bond lengths are 2.56 Å. 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. The Li(20)-Li(21) bond length is 2.58 Å. The Li(20)-P(9) bond length is 2.53 Å. All Li(20)-P(11) bond lengths are 2.67 Å. 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. The Li(21)-Li(22) bond length is 2.74 Å. All Li(21)-Li(25) bond lengths are 2.63 Å. All Li(21)-P(11) bond lengths are 2.81 Å. 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. All Li(22)-Li(23) bond lengths are 2.54 Å. The Li(22)-P(12) bond length is 2.71 Å. All Li(22)-P(10) bond lengths are 2.52 Å. 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. The Li(23)-Li(24) bond length is 2.68 Å. The Li(23)-Li(25) bond length is 2.48 Å. All Li(23)-Li(28) bond lengths are 2.60 Å. All Li(23)-P(10) bond lengths are 2.85 Å. 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. All Li(24)-Li(26) bond lengths are 2.53 Å. The Li(24)-P(13) bond length is 2.70 Å. All Li(24)-P(12) bond lengths are 2.53 Å. 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. The Li(25)-P(11) bond length is 2.49 Å. All Li(25)-P(10) bond lengths are 2.60 Å. 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. The Li(26)-Li(27) bond length is 2.65 Å. The Li(26)-Li(28) bond length is 2.47 Å. All Li(26)-Li(30) bond lengths are 2.59 Å. All Li(26)-P(12) bond lengths are 2.85 Å. 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. All Li(27)-Li(29) bond lengths are 2.52 Å. The Li(27)-P(1) bond length is 2.69 Å. All Li(27)-P(13) bond lengths are 2.52 Å. 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. The Li(28)-P(10) bond length is 2.49 Å. All Li(28)-P(12) bond lengths are 2.60 Å. 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. The Li(29)-Li(30) bond length is 2.41 Å. All Li(29)-Li(31) bond lengths are 2.67 Å. The Li(29)-Zr(1) bond length is 3.02 Å. All Li(29)-P(13) bond lengths are 2.80 Å. 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. The Li(30)-P(12) bond length is 2.46 Å. All Li(30)-P(13) bond lengths are 2.61 Å. 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. The Li(31)-P(13) bond length is 2.57 Å. All Li(31)-P(1) bond lengths are 2.56 Å. 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. The Zr(1)-P(2) bond length is 2.57 Å. All Zr(1)-P(1) bond lengths are 2.63 Å. 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. The Zr(2)-P(3) bond length is 2.56 Å. All Zr(2)-P(2) bond lengths are 2.57 Å. 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.