HfNi3 is beta Cu3Ti-like structured and crystallizes in the trigonal R-3m space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to three Ni(2,2,2) and nine Ni(1,1,1,1) atoms to form HfNi12 cuboctahedra that share corners with six Ni(2,2,2)Hf4Ni8 cuboctahedra; corners with nine equivalent Hf(1)Ni12 cuboctahedra; edges with six Ni(2,2,2)Hf4Ni8 cuboctahedra; edges with fifteen Ni(1,1,1,1)Hf4Ni8 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with three Ni(2,2,2)Hf4Ni8 cuboctahedra; faces with four equivalent Hf(2)Ni12 cuboctahedra; and faces with nine Ni(1,1,1,1)Hf4Ni8 cuboctahedra. In the second Hf site, Hf(2) is bonded to six Ni(1,1,1) and six Ni(2,2,2) atoms to form HfNi12 cuboctahedra that share corners with six equivalent Hf(2)Ni12 cuboctahedra; corners with twelve Ni(1,1,1,1,1)Hf4Ni8 cuboctahedra; edges with six Ni(2,2,2)Hf4Ni8 cuboctahedra; edges with twelve Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with six Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with eight equivalent Hf(1)Ni12 cuboctahedra. There are twelve inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two equivalent Ni(2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Ni(2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra. In the second Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra. In the third Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1,1)Hf4Ni8 cuboctahedra. In the fourth Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1,1)Hf4Ni8 cuboctahedra. In the fifth Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1,1)Hf4Ni8 cuboctahedra. In the sixth Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1)Hf4Ni8 cuboctahedra. In the seventh Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1,1)Hf4Ni8 cuboctahedra. In the eighth Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra. In the ninth Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra. In the tenth Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1,1,1)Hf4Ni8 cuboctahedra. In the eleventh Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1,1,1,1)Hf4Ni8 cuboctahedra. In the twelfth Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra.
HfNi3 is beta Cu3Ti-like structured and crystallizes in the trigonal R-3m space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to three Ni(2,2,2) and nine Ni(1,1,1,1) atoms to form HfNi12 cuboctahedra that share corners with six Ni(2,2,2)Hf4Ni8 cuboctahedra; corners with nine equivalent Hf(1)Ni12 cuboctahedra; edges with six Ni(2,2,2)Hf4Ni8 cuboctahedra; edges with fifteen Ni(1,1,1,1)Hf4Ni8 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with three Ni(2,2,2)Hf4Ni8 cuboctahedra; faces with four equivalent Hf(2)Ni12 cuboctahedra; and faces with nine Ni(1,1,1,1)Hf4Ni8 cuboctahedra. All Hf(1)-Ni(2,2,2) bond lengths are 2.65 Å. There are six shorter (2.61 Å) and three longer (2.62 Å) Hf(1)-Ni(1,1,1,1) bond lengths. In the second Hf site, Hf(2) is bonded to six Ni(1,1,1) and six Ni(2,2,2) atoms to form HfNi12 cuboctahedra that share corners with six equivalent Hf(2)Ni12 cuboctahedra; corners with twelve Ni(1,1,1,1,1)Hf4Ni8 cuboctahedra; edges with six Ni(2,2,2)Hf4Ni8 cuboctahedra; edges with twelve Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with six Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with eight equivalent Hf(1)Ni12 cuboctahedra. All Hf(2)-Ni(1,1,1) bond lengths are 2.64 Å. All Hf(2)-Ni(2,2,2) bond lengths are 2.61 Å. There are twelve inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two equivalent Ni(2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Ni(2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra. The Ni(1)-Hf(2) bond length is 2.64 Å. There are two shorter (2.61 Å) and one longer (2.62 Å) Ni(1)-Hf(1) bond length. Both Ni(1)-Ni(2) bond lengths are 2.56 Å. There are a spread of Ni(1)-Ni(1,1,1) bond distances ranging from 2.44-2.78 Å. In the second Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra. The Ni(1)-Hf(2) bond length is 2.64 Å. Both Ni(1)-Ni(2,2) bond lengths are 2.56 Å. There are a spread of Ni(1)-Ni(1,1,1) bond distances ranging from 2.44-2.78 Å. In the third Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1,1)Hf4Ni8 cuboctahedra. Both Ni(1)-Ni(2,2) bond lengths are 2.56 Å. There are a spread of Ni(1)-Ni(1,1) bond distances ranging from 2.44-2.78 Å. In the fourth Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1,1)Hf4Ni8 cuboctahedra. Both Ni(1)-Ni(2,2) bond lengths are 2.56 Å. The Ni(1)-Ni(1) bond length is 2.58 Å. In the fifth Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1,1)Hf4Ni8 cuboctahedra. All Ni(2)-Ni(1,1,1) bond lengths are 2.56 Å. All Ni(2)-Ni(2,2) bond lengths are 2.61 Å. In the sixth Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1)Hf4Ni8 cuboctahedra. All Ni(2)-Ni(1,1) bond lengths are 2.56 Å. Both Ni(2)-Ni(2) bond lengths are 2.61 Å. In the seventh Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1,1)Hf4Ni8 cuboctahedra. The Ni(2)-Ni(1) bond length is 2.56 Å. In the eighth Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra. There is one shorter (2.44 Å) and one longer (2.78 Å) Ni(1)-Ni(1) bond length. In the ninth Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four Ni(2,2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra. The Ni(1)-Hf(2) bond length is 2.64 Å. There are two shorter (2.61 Å) and one longer (2.62 Å) Ni(1)-Hf(1) bond length. Both Ni(1)-Ni(2,2) bond lengths are 2.56 Å. There are a spread of Ni(1)-Ni(1,1) bond distances ranging from 2.44-2.78 Å. In the tenth Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1,1,1)Hf4Ni8 cuboctahedra. Both Ni(2)-Hf(1) bond lengths are 2.65 Å. Both Ni(2)-Hf(2) bond lengths are 2.61 Å. The Ni(2)-Ni(1) bond length is 2.56 Å. All Ni(2)-Ni(2,2) bond lengths are 2.61 Å. In the eleventh Ni site, Ni(2) is bonded to two equivalent Hf(1); two equivalent Hf(2); four Ni(1,1,1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with four equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(1)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with twelve Ni(1,1,1,1,1,1)Hf4Ni8 cuboctahedra. Both Ni(2)-Hf(1) bond lengths are 2.65 Å. Both Ni(2)-Hf(2) bond lengths are 2.61 Å. The Ni(2)-Ni(1) bond length is 2.56 Å. Both Ni(2)-Ni(2) bond lengths are 2.61 Å. In the twelfth Ni site, Ni(1) is bonded to one Hf(2); three equivalent Hf(1); two Ni(2,2); and six Ni(1,1,1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with nine Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with five equivalent Hf(1)Ni12 cuboctahedra; edges with ten Ni(1,1,1,1)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(2,2,2,2)Hf4Ni8 cuboctahedra; and faces with nine Ni(1,1,1)Hf4Ni8 cuboctahedra. The Ni(1)-Hf(2) bond length is 2.64 Å. There are two shorter (2.61 Å) and one longer (2.62 Å) Ni(1)-Hf(1) bond length. The Ni(1)-Ni(2) bond length is 2.56 Å. There are a spread of Ni(1)-Ni(1,1) bond distances ranging from 2.44-2.78 Å.