NaGdF4 crystallizes in the triclinic P1 space group. There are three inequivalent Na sites. In the first Na site, Na(1) is bonded in a distorted octahedral geometry to one F(1), one F(11), one F(4), one F(6), one F(7), and one F(9) atom. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to one F(10), one F(12), one F(2), one F(3), one F(5), and one F(8) atom. In the third Na site, Na(3) is bonded in a 9-coordinate geometry to one F(1), one F(12), one F(2), one F(3), one F(4), one F(5), one F(6), one F(7), and one F(9) atom. There are three inequivalent Gd sites. In the first Gd site, Gd(1) is bonded in a 9-coordinate geometry to one F(10), one F(11), one F(12), one F(2), one F(4), one F(5), one F(7), one F(8), and one F(9) atom. In the second Gd site, Gd(2) is bonded in a 9-coordinate geometry to one F(1), one F(10), one F(11), one F(12), one F(3), one F(6), one F(7), one F(8), and one F(9) atom. In the third Gd site, Gd(3) is bonded in a 9-coordinate geometry to one F(1), one F(10), one F(11), one F(2), one F(3), one F(4), one F(5), one F(6), and one F(8) atom. There are twelve inequivalent F sites. In the first F site, F(1) is bonded to one Na(1), one Na(3), one Gd(2), and one Gd(3) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(12)Na2Gd2 tetrahedra, corners with two equivalent F(2)Na2Gd2 tetrahedra, corners with two equivalent F(8)NaGd3 tetrahedra, corners with three equivalent F(4)Na2Gd2 tetrahedra, corners with four equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra, and  an edgeedge with one F(11)NaGd3 tetrahedra. In the second F site, F(2) is bonded to one Na(2), one Na(3), one Gd(1), and one Gd(3) atom to form distorted FNa2Gd2 tetrahedra that share  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(4)Na2Gd2 tetrahedra,  a cornercorner with one F(10)NaGd3 tetrahedra,  a cornercorner with one F(8)NaGd3 tetrahedra, corners with two equivalent F(1)Na2Gd2 tetrahedra, corners with two equivalent F(7)Na2Gd2 tetrahedra, corners with two equivalent F(11)NaGd3 tetrahedra, corners with three equivalent F(3)Na2Gd2 tetrahedra, corners with four equivalent F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra,  an edgeedge with one F(8)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the third F site, F(3) is bonded to one Na(2), one Na(3), one Gd(2), and one Gd(3) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(1)Na2Gd2 tetrahedra,  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(5)Na2Gd2 tetrahedra,  a cornercorner with one F(10)NaGd3 tetrahedra,  a cornercorner with one F(8)NaGd3 tetrahedra, corners with two equivalent F(4)Na2Gd2 tetrahedra, corners with two equivalent F(7)Na2Gd2 tetrahedra, corners with two equivalent F(9)Na2Gd2 tetrahedra, corners with three equivalent F(2)Na2Gd2 tetrahedra, corners with three equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra,  an edgeedge with one F(11)NaGd3 tetrahedra, and  an edgeedge with one F(8)NaGd3 tetrahedra. In the fourth F site, F(4) is bonded to one Na(1), one Na(3), one Gd(1), and one Gd(3) atom to form distorted FNa2Gd2 tetrahedra that share  a cornercorner with one F(2)Na2Gd2 tetrahedra,  a cornercorner with one F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(3)Na2Gd2 tetrahedra, corners with two equivalent F(10)NaGd3 tetrahedra, corners with two equivalent F(8)NaGd3 tetrahedra, corners with three equivalent F(1)Na2Gd2 tetrahedra, corners with three equivalent F(5)Na2Gd2 tetrahedra,  a cornercorner with one F(6)Na2Gd2 trigonal pyramid,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra,  an edgeedge with one F(11)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the fifth F site, F(5) is bonded to one Na(2), one Na(3), one Gd(1), and one Gd(3) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(10)NaGd3 tetrahedra,  a cornercorner with one F(8)NaGd3 tetrahedra, corners with two equivalent F(9)Na2Gd2 tetrahedra, corners with two equivalent F(11)NaGd3 tetrahedra, corners with three equivalent F(4)Na2Gd2 tetrahedra, corners with four equivalent F(2)Na2Gd2 tetrahedra, corners with two equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra, and  an edgeedge with one F(8)NaGd3 tetrahedra. In the sixth F site, F(6) is bonded to one Na(1), one Na(3), one Gd(2), and one Gd(3) atom to form distorted FNa2Gd2 trigonal pyramids that share  a cornercorner with one F(4)Na2Gd2 tetrahedra,  a cornercorner with one F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(12)Na2Gd2 tetrahedra, corners with two equivalent F(5)Na2Gd2 tetrahedra, corners with two equivalent F(10)NaGd3 tetrahedra, corners with three equivalent F(3)Na2Gd2 tetrahedra, corners with four equivalent F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra,  an edgeedge with one F(11)NaGd3 tetrahedra, and  an edgeedge with one F(8)NaGd3 tetrahedra. In the seventh F site, F(7) is bonded to one Na(1), one Na(3), one Gd(1), and one Gd(2) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(1)Na2Gd2 tetrahedra,  a cornercorner with one F(4)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(2)Na2Gd2 tetrahedra, corners with two equivalent F(3)Na2Gd2 tetrahedra, corners with two equivalent F(8)NaGd3 tetrahedra, corners with three equivalent F(12)Na2Gd2 tetrahedra, corners with four equivalent F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(6)Na2Gd2 trigonal pyramid,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra,  an edgeedge with one F(11)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the eighth F site, F(8) is bonded to one Na(2), one Gd(1), one Gd(2), and one Gd(3) atom to form FNaGd3 tetrahedra that share  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(2)Na2Gd2 tetrahedra,  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(5)Na2Gd2 tetrahedra, corners with two equivalent F(1)Na2Gd2 tetrahedra, corners with two equivalent F(4)Na2Gd2 tetrahedra, corners with two equivalent F(7)Na2Gd2 tetrahedra, corners with three equivalent F(11)NaGd3 tetrahedra, corners with four equivalent F(10)NaGd3 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the ninth F site, F(9) is bonded to one Na(1), one Na(3), one Gd(1), and one Gd(2) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(1)Na2Gd2 tetrahedra,  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(4)Na2Gd2 tetrahedra, corners with two equivalent F(3)Na2Gd2 tetrahedra, corners with two equivalent F(5)Na2Gd2 tetrahedra, corners with two equivalent F(10)NaGd3 tetrahedra, corners with three equivalent F(11)NaGd3 tetrahedra, corners with four equivalent F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(6)Na2Gd2 trigonal pyramid,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(8)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the tenth F site, F(10) is bonded to one Na(2), one Gd(1), one Gd(2), and one Gd(3) atom to form FNaGd3 tetrahedra that share  a cornercorner with one F(2)Na2Gd2 tetrahedra,  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(5)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(4)Na2Gd2 tetrahedra, corners with two equivalent F(9)Na2Gd2 tetrahedra, corners with three equivalent F(12)Na2Gd2 tetrahedra, corners with four equivalent F(8)NaGd3 tetrahedra, corners with two equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra, and  an edgeedge with one F(11)NaGd3 tetrahedra. In the eleventh F site, F(11) is bonded to one Na(1), one Gd(1), one Gd(2), and one Gd(3) atom to form FNaGd3 tetrahedra that share  a cornercorner with one F(1)Na2Gd2 tetrahedra,  a cornercorner with one F(4)Na2Gd2 tetrahedra,  a cornercorner with one F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(10)NaGd3 tetrahedra, corners with two equivalent F(12)Na2Gd2 tetrahedra, corners with two equivalent F(2)Na2Gd2 tetrahedra, corners with two equivalent F(5)Na2Gd2 tetrahedra, corners with three equivalent F(9)Na2Gd2 tetrahedra, corners with three equivalent F(8)NaGd3 tetrahedra,  a cornercorner with one F(6)Na2Gd2 trigonal pyramid,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the twelfth F site, F(12) is bonded to one Na(2), one Na(3), one Gd(1), and one Gd(2) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(2)Na2Gd2 tetrahedra,  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(5)Na2Gd2 tetrahedra,  a cornercorner with one F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(8)NaGd3 tetrahedra, corners with two equivalent F(1)Na2Gd2 tetrahedra, corners with two equivalent F(11)NaGd3 tetrahedra, corners with three equivalent F(7)Na2Gd2 tetrahedra, corners with three equivalent F(10)NaGd3 tetrahedra, corners with two equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra, and  an edgeedge with one F(8)NaGd3 tetrahedra.
NaGdF4 crystallizes in the triclinic P1 space group. There are three inequivalent Na sites. In the first Na site, Na(1) is bonded in a distorted octahedral geometry to one F(1), one F(11), one F(4), one F(6), one F(7), and one F(9) atom. The Na(1)-F(1) bond length is 2.35 Å. The Na(1)-F(11) bond length is 2.31 Å. The Na(1)-F(4) bond length is 2.33 Å. The Na(1)-F(6) bond length is 2.43 Å. The Na(1)-F(7) bond length is 2.31 Å. The Na(1)-F(9) bond length is 2.23 Å. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to one F(10), one F(12), one F(2), one F(3), one F(5), and one F(8) atom. The Na(2)-F(10) bond length is 2.32 Å. The Na(2)-F(12) bond length is 2.23 Å. The Na(2)-F(2) bond length is 2.36 Å. The Na(2)-F(3) bond length is 2.38 Å. The Na(2)-F(5) bond length is 2.30 Å. The Na(2)-F(8) bond length is 2.24 Å. In the third Na site, Na(3) is bonded in a 9-coordinate geometry to one F(1), one F(12), one F(2), one F(3), one F(4), one F(5), one F(6), one F(7), and one F(9) atom. The Na(3)-F(1) bond length is 2.50 Å. The Na(3)-F(12) bond length is 2.34 Å. The Na(3)-F(2) bond length is 2.57 Å. The Na(3)-F(3) bond length is 2.53 Å. The Na(3)-F(4) bond length is 2.60 Å. The Na(3)-F(5) bond length is 2.50 Å. The Na(3)-F(6) bond length is 2.61 Å. The Na(3)-F(7) bond length is 2.32 Å. The Na(3)-F(9) bond length is 2.34 Å. There are three inequivalent Gd sites. In the first Gd site, Gd(1) is bonded in a 9-coordinate geometry to one F(10), one F(11), one F(12), one F(2), one F(4), one F(5), one F(7), one F(8), and one F(9) atom. The Gd(1)-F(10) bond length is 2.38 Å. The Gd(1)-F(11) bond length is 2.39 Å. The Gd(1)-F(12) bond length is 2.34 Å. The Gd(1)-F(2) bond length is 2.32 Å. The Gd(1)-F(4) bond length is 2.33 Å. The Gd(1)-F(5) bond length is 2.32 Å. The Gd(1)-F(7) bond length is 2.35 Å. The Gd(1)-F(8) bond length is 2.39 Å. The Gd(1)-F(9) bond length is 2.35 Å. In the second Gd site, Gd(2) is bonded in a 9-coordinate geometry to one F(1), one F(10), one F(11), one F(12), one F(3), one F(6), one F(7), one F(8), and one F(9) atom. The Gd(2)-F(1) bond length is 2.34 Å. The Gd(2)-F(10) bond length is 2.39 Å. The Gd(2)-F(11) bond length is 2.41 Å. The Gd(2)-F(12) bond length is 2.33 Å. The Gd(2)-F(3) bond length is 2.32 Å. The Gd(2)-F(6) bond length is 2.33 Å. The Gd(2)-F(7) bond length is 2.36 Å. The Gd(2)-F(8) bond length is 2.37 Å. The Gd(2)-F(9) bond length is 2.34 Å. In the third Gd site, Gd(3) is bonded in a 9-coordinate geometry to one F(1), one F(10), one F(11), one F(2), one F(3), one F(4), one F(5), one F(6), and one F(8) atom. The Gd(3)-F(1) bond length is 2.35 Å. The Gd(3)-F(10) bond length is 2.35 Å. The Gd(3)-F(11) bond length is 2.36 Å. The Gd(3)-F(2) bond length is 2.35 Å. The Gd(3)-F(3) bond length is 2.35 Å. The Gd(3)-F(4) bond length is 2.33 Å. The Gd(3)-F(5) bond length is 2.34 Å. The Gd(3)-F(6) bond length is 2.34 Å. The Gd(3)-F(8) bond length is 2.38 Å. There are twelve inequivalent F sites. In the first F site, F(1) is bonded to one Na(1), one Na(3), one Gd(2), and one Gd(3) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(12)Na2Gd2 tetrahedra, corners with two equivalent F(2)Na2Gd2 tetrahedra, corners with two equivalent F(8)NaGd3 tetrahedra, corners with three equivalent F(4)Na2Gd2 tetrahedra, corners with four equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra, and  an edgeedge with one F(11)NaGd3 tetrahedra. In the second F site, F(2) is bonded to one Na(2), one Na(3), one Gd(1), and one Gd(3) atom to form distorted FNa2Gd2 tetrahedra that share  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(4)Na2Gd2 tetrahedra,  a cornercorner with one F(10)NaGd3 tetrahedra,  a cornercorner with one F(8)NaGd3 tetrahedra, corners with two equivalent F(1)Na2Gd2 tetrahedra, corners with two equivalent F(7)Na2Gd2 tetrahedra, corners with two equivalent F(11)NaGd3 tetrahedra, corners with three equivalent F(3)Na2Gd2 tetrahedra, corners with four equivalent F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra,  an edgeedge with one F(8)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the third F site, F(3) is bonded to one Na(2), one Na(3), one Gd(2), and one Gd(3) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(1)Na2Gd2 tetrahedra,  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(5)Na2Gd2 tetrahedra,  a cornercorner with one F(10)NaGd3 tetrahedra,  a cornercorner with one F(8)NaGd3 tetrahedra, corners with two equivalent F(4)Na2Gd2 tetrahedra, corners with two equivalent F(7)Na2Gd2 tetrahedra, corners with two equivalent F(9)Na2Gd2 tetrahedra, corners with three equivalent F(2)Na2Gd2 tetrahedra, corners with three equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra,  an edgeedge with one F(11)NaGd3 tetrahedra, and  an edgeedge with one F(8)NaGd3 tetrahedra. In the fourth F site, F(4) is bonded to one Na(1), one Na(3), one Gd(1), and one Gd(3) atom to form distorted FNa2Gd2 tetrahedra that share  a cornercorner with one F(2)Na2Gd2 tetrahedra,  a cornercorner with one F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(3)Na2Gd2 tetrahedra, corners with two equivalent F(10)NaGd3 tetrahedra, corners with two equivalent F(8)NaGd3 tetrahedra, corners with three equivalent F(1)Na2Gd2 tetrahedra, corners with three equivalent F(5)Na2Gd2 tetrahedra,  a cornercorner with one F(6)Na2Gd2 trigonal pyramid,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra,  an edgeedge with one F(11)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the fifth F site, F(5) is bonded to one Na(2), one Na(3), one Gd(1), and one Gd(3) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(10)NaGd3 tetrahedra,  a cornercorner with one F(8)NaGd3 tetrahedra, corners with two equivalent F(9)Na2Gd2 tetrahedra, corners with two equivalent F(11)NaGd3 tetrahedra, corners with three equivalent F(4)Na2Gd2 tetrahedra, corners with four equivalent F(2)Na2Gd2 tetrahedra, corners with two equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra, and  an edgeedge with one F(8)NaGd3 tetrahedra. In the sixth F site, F(6) is bonded to one Na(1), one Na(3), one Gd(2), and one Gd(3) atom to form distorted FNa2Gd2 trigonal pyramids that share  a cornercorner with one F(4)Na2Gd2 tetrahedra,  a cornercorner with one F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(12)Na2Gd2 tetrahedra, corners with two equivalent F(5)Na2Gd2 tetrahedra, corners with two equivalent F(10)NaGd3 tetrahedra, corners with three equivalent F(3)Na2Gd2 tetrahedra, corners with four equivalent F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra,  an edgeedge with one F(11)NaGd3 tetrahedra, and  an edgeedge with one F(8)NaGd3 tetrahedra. In the seventh F site, F(7) is bonded to one Na(1), one Na(3), one Gd(1), and one Gd(2) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(1)Na2Gd2 tetrahedra,  a cornercorner with one F(4)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(2)Na2Gd2 tetrahedra, corners with two equivalent F(3)Na2Gd2 tetrahedra, corners with two equivalent F(8)NaGd3 tetrahedra, corners with three equivalent F(12)Na2Gd2 tetrahedra, corners with four equivalent F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(6)Na2Gd2 trigonal pyramid,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra,  an edgeedge with one F(11)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the eighth F site, F(8) is bonded to one Na(2), one Gd(1), one Gd(2), and one Gd(3) atom to form FNaGd3 tetrahedra that share  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(2)Na2Gd2 tetrahedra,  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(5)Na2Gd2 tetrahedra, corners with two equivalent F(1)Na2Gd2 tetrahedra, corners with two equivalent F(4)Na2Gd2 tetrahedra, corners with two equivalent F(7)Na2Gd2 tetrahedra, corners with three equivalent F(11)NaGd3 tetrahedra, corners with four equivalent F(10)NaGd3 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the ninth F site, F(9) is bonded to one Na(1), one Na(3), one Gd(1), and one Gd(2) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(1)Na2Gd2 tetrahedra,  a cornercorner with one F(12)Na2Gd2 tetrahedra,  a cornercorner with one F(4)Na2Gd2 tetrahedra, corners with two equivalent F(3)Na2Gd2 tetrahedra, corners with two equivalent F(5)Na2Gd2 tetrahedra, corners with two equivalent F(10)NaGd3 tetrahedra, corners with three equivalent F(11)NaGd3 tetrahedra, corners with four equivalent F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(6)Na2Gd2 trigonal pyramid,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(12)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(8)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the tenth F site, F(10) is bonded to one Na(2), one Gd(1), one Gd(2), and one Gd(3) atom to form FNaGd3 tetrahedra that share  a cornercorner with one F(2)Na2Gd2 tetrahedra,  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(5)Na2Gd2 tetrahedra,  a cornercorner with one F(11)NaGd3 tetrahedra, corners with two equivalent F(4)Na2Gd2 tetrahedra, corners with two equivalent F(9)Na2Gd2 tetrahedra, corners with three equivalent F(12)Na2Gd2 tetrahedra, corners with four equivalent F(8)NaGd3 tetrahedra, corners with two equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra, and  an edgeedge with one F(11)NaGd3 tetrahedra. In the eleventh F site, F(11) is bonded to one Na(1), one Gd(1), one Gd(2), and one Gd(3) atom to form FNaGd3 tetrahedra that share  a cornercorner with one F(1)Na2Gd2 tetrahedra,  a cornercorner with one F(4)Na2Gd2 tetrahedra,  a cornercorner with one F(7)Na2Gd2 tetrahedra,  a cornercorner with one F(10)NaGd3 tetrahedra, corners with two equivalent F(12)Na2Gd2 tetrahedra, corners with two equivalent F(2)Na2Gd2 tetrahedra, corners with two equivalent F(5)Na2Gd2 tetrahedra, corners with three equivalent F(9)Na2Gd2 tetrahedra, corners with three equivalent F(8)NaGd3 tetrahedra,  a cornercorner with one F(6)Na2Gd2 trigonal pyramid,  an edgeedge with one F(1)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(7)Na2Gd2 tetrahedra,  an edgeedge with one F(10)NaGd3 tetrahedra, and  an edgeedge with one F(6)Na2Gd2 trigonal pyramid. In the twelfth F site, F(12) is bonded to one Na(2), one Na(3), one Gd(1), and one Gd(2) atom to form FNa2Gd2 tetrahedra that share  a cornercorner with one F(2)Na2Gd2 tetrahedra,  a cornercorner with one F(3)Na2Gd2 tetrahedra,  a cornercorner with one F(5)Na2Gd2 tetrahedra,  a cornercorner with one F(9)Na2Gd2 tetrahedra,  a cornercorner with one F(8)NaGd3 tetrahedra, corners with two equivalent F(1)Na2Gd2 tetrahedra, corners with two equivalent F(11)NaGd3 tetrahedra, corners with three equivalent F(7)Na2Gd2 tetrahedra, corners with three equivalent F(10)NaGd3 tetrahedra, corners with two equivalent F(6)Na2Gd2 trigonal pyramids,  an edgeedge with one F(2)Na2Gd2 tetrahedra,  an edgeedge with one F(3)Na2Gd2 tetrahedra,  an edgeedge with one F(4)Na2Gd2 tetrahedra,  an edgeedge with one F(5)Na2Gd2 tetrahedra,  an edgeedge with one F(9)Na2Gd2 tetrahedra, and  an edgeedge with one F(8)NaGd3 tetrahedra.