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LuB12 crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Lu is bonded in a 1-coordinate geometry to twenty-four equivalent B atoms. All Lu–B bond lengths are 2.77 Å. B is bonded in a 7-coordinate geometry to two equivalent Lu and five equivalent B atoms. There is one shorter (1.71 Å) and four longer (1.78 Å) B–B bond length.
Lu4V5B18 crystallizes in the monoclinic Pm space group. The structure is three-dimensional. there are sixteen inequivalent Lu3+ sites. In the first Lu3+ site, Lu3+ is bonded in a 6-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.62–2.66 Å. In the second Lu3+ site, Lu3+ is bonded in a 12-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.62–2.71 Å. In the third Lu3+ site, Lu3+ is bonded in a 12-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.62–2.71 Å. In the fourth Lu3+ site, Lu3+ is bonded in a 6-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.62–2.66 Å. In the fifth Lu3+ site, Lu3+ is bonded in a 2-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.61–2.72 Å. In the sixth Lu3+ site, Lu3+ is bonded in a 2-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.61–2.72 Å. In the seventh Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.59–2.71 Å. In the eighth Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.59–2.71 Å. In the ninth Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.60–2.71 Å. In the tenth Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.59–2.71 Å. In the eleventh Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.60–2.71 Å. In the twelfth Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B+1.33- atoms. There are a spread of Lu–B bond distances ranging from 2.60–2.72 Å. In the thirteenth Lu3+ site, Lu3+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.47–2.50 Å. In the fourteenth Lu3+ site, Lu3+ is bonded to twelve B+1.33- atoms to form LuB12 cuboctahedra that share edges with two equivalent VB12 cuboctahedra, a faceface with one VB12 cuboctahedra, and faces with two equivalent LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.47–2.51 Å. In the fifteenth Lu3+ site, Lu3+ is bonded to twelve B+1.33- atoms to form LuB12 cuboctahedra that share edges with two equivalent VB12 cuboctahedra, a faceface with one VB12 cuboctahedra, and faces with two equivalent LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.46–2.51 Å. In the sixteenth Lu3+ site, Lu3+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.47–2.50 Å. There are twenty inequivalent V+2.40+ sites. In the first V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.22–2.30 Å. In the second V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.22–2.29 Å. In the third V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.22–2.29 Å. In the fourth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.22–2.30 Å. In the fifth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.29 Å. In the sixth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.29 Å. In the seventh V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.30 Å. In the eighth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.24–2.29 Å. In the ninth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.24–2.29 Å. In the tenth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.24–2.29 Å. In the eleventh V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.28 Å. In the twelfth V+2.40+ site, V+2.40+ is bonded in a 10-coordinate geometry to ten B+1.33- atoms. There are a spread of V–B bond distances ranging from 2.25–2.28 Å. In the thirteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form VB12 cuboctahedra that share edges with two equivalent LuB12 cuboctahedra, a faceface with one LuB12 cuboctahedra, and faces with two equivalent VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.41–2.44 Å. In the fourteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form VB12 cuboctahedra that share edges with two equivalent LuB12 cuboctahedra, a faceface with one LuB12 cuboctahedra, and faces with two equivalent VB12 cuboctahedra. There are two shorter (2.41 Å) and ten longer (2.43 Å) V–B bond lengths. In the fifteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.39–2.45 Å. In the sixteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.40–2.45 Å. In the seventeenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.39–2.45 Å. In the eighteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.39–2.45 Å. In the nineteenth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.40–2.44 Å. In the twentieth V+2.40+ site, V+2.40+ is bonded to twelve B+1.33- atoms to form a mixture of edge and face-sharing VB12 cuboctahedra. There are a spread of V–B bond distances ranging from 2.40–2.44 Å. There are seventy-two inequivalent B+1.33- sites. In the first B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.75 Å) and two longer (1.76 Å) B–B bond length. In the second B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.74–1.76 Å. In the third B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.75–1.77 Å. In the fourth B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.74 Å) and one longer (1.75 Å) B–B bond length. In the fifth B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.74 Å) and one longer (1.75 Å) B–B bond length. In the sixth B+1.33- site, B+1.33- is bonded in a 3-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.74 Å) and one longer (1.75 Å) B–B bond length. In the seventh B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to six Lu3+ and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.80–1.97 Å. In the eighth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.72–1.87 Å. In the ninth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.72–1.88 Å. In the tenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to six Lu3+ and three B+1.33- atoms. There is one shorter (1.80 Å) and one longer (1.81 Å) B–B bond length. In the eleventh B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There is one shorter (1.72 Å) and one longer (1.88 Å) B–B bond length. In the twelfth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There is one shorter (1.71 Å) and one longer (1.88 Å) B–B bond length. In the thirteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.77–1.83 Å. In the fourteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.77–1.83 Å. In the fifteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There is two shorter (1.78 Å) and one longer (1.84 Å) B–B bond length. In the sixteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.77–1.83 Å. In the seventeenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.71–1.80 Å. In the eighteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.71–1.80 Å. In the nineteenth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.68–1.79 Å. In the twentieth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.68–1.79 Å. In the twenty-first B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.68–1.79 Å. In the twenty-second B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.68–1.79 Å. In the twenty-third B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There is one shorter (1.70 Å) and two longer (1.79 Å) B–B bond length. In the twenty-fourth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to two equivalent Lu3+, four V+2.40+, and three B+1.33- atoms. There are a spread of B–B bond distances ranging from 1.70–1.79 Å. In the twenty-fifth B+1.33- site, B+1.33- is bonded in a 9-coordinate geometry to four Lu3+,
LuB2 is hexagonal omega structure structured and crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Lu is bonded to twelve equivalent B atoms to form a mixture of edge and face-sharing LuB12 cuboctahedra. All Lu–B bond lengths are 2.64 Å. B is bonded in a 9-coordinate geometry to six equivalent Lu and three equivalent B atoms. All B–B bond lengths are 1.87 Å.
Lu2OsB6 crystallizes in the orthorhombic Pbam space group. The structure is three-dimensional. there are two inequivalent Lu3+ sites. In the first Lu3+ site, Lu3+ is bonded in a 12-coordinate geometry to fourteen B2- atoms. There are a spread of Lu–B bond distances ranging from 2.68–2.78 Å. In the second Lu3+ site, Lu3+ is bonded to twelve B2- atoms to form a mixture of edge and face-sharing LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.56–2.59 Å. Os6+ is bonded in a 10-coordinate geometry to ten B2- atoms. There are a spread of Os–B bond distances ranging from 2.32–2.38 Å. There are six inequivalent B2- sites. In the first B2- site, B2- is bonded in a 9-coordinate geometry to four equivalent Lu3+, two equivalent Os6+, and three B2- atoms. There are a spread of B–B bond distances ranging from 1.77–1.80 Å. In the second B2- site, B2- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent Os6+, and three B2- atoms. There is one shorter (1.79 Å) and one longer (1.80 Å) B–B bond length. In the third B2- site, B2- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent Os6+, and three B2- atoms. There is one shorter (1.73 Å) and one longer (1.82 Å) B–B bond length. In the fourth B2- site, B2- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent Os6+, and three B2- atoms. Both B–B bond lengths are 1.78 Å. In the fifth B2- site, B2- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent Os6+, and three B2- atoms. In the sixth B2- site, B2- is bonded in a 9-coordinate geometry to six Lu3+ and three B2- atoms. The B–B bond length is 2.08 Å.
Lu2B36Si7C(Si)2 crystallizes in the monoclinic Cm space group. The structure is three-dimensional and consists of four silicon molecules and one Lu2B36Si7C framework. In the Lu2B36Si7C framework, Lu3+ is bonded to twelve B+0.83- atoms to form corner-sharing LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.74–2.96 Å. There are twenty inequivalent B+0.83- sites. In the first B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to one Lu3+, five B+0.83-, and one Si+3.11+ atom. There are a spread of B–B bond distances ranging from 1.74–1.81 Å. The B–Si bond length is 2.05 Å. In the second B+0.83- site, B+0.83- is bonded in a 6-coordinate geometry to five B+0.83- and one Si+3.11+ atom. There are a spread of B–B bond distances ranging from 1.75–1.82 Å. The B–Si bond length is 2.02 Å. In the third B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to one Lu3+, five B+0.83-, and one Si+3.11+ atom. There are a spread of B–B bond distances ranging from 1.77–1.82 Å. The B–Si bond length is 2.09 Å. In the fourth B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to one Lu3+, five B+0.83-, and one Si+3.11+ atom. There is three shorter (1.79 Å) and one longer (1.82 Å) B–B bond length. The B–Si bond length is 2.04 Å. In the fifth B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to five B+0.83- and one Si+3.11+ atom. There are a spread of B–B bond distances ranging from 1.78–1.83 Å. The B–Si bond length is 2.01 Å. In the sixth B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to one Lu3+, five B+0.83-, and one Si+3.11+ atom. There is two shorter (1.80 Å) and two longer (1.82 Å) B–B bond length. The B–Si bond length is 2.07 Å. In the seventh B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to one Lu3+, five B+0.83-, and one Si+3.11+ atom. There is one shorter (1.75 Å) and two longer (1.77 Å) B–B bond length. The B–Si bond length is 2.04 Å. In the eighth B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to two equivalent Lu3+, five B+0.83-, and one Si+3.11+ atom. There is one shorter (1.75 Å) and two longer (1.78 Å) B–B bond length. The B–Si bond length is 2.09 Å. In the ninth B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to one Lu3+, five B+0.83-, and one Si+3.11+ atom. There is two shorter (1.81 Å) and one longer (1.87 Å) B–B bond length. The B–Si bond length is 2.05 Å. In the tenth B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to two equivalent Lu3+, five B+0.83-, and one Si+3.11+ atom. There is two shorter (1.81 Å) and one longer (1.87 Å) B–B bond length. The B–Si bond length is 2.10 Å. In the eleventh B+0.83- site, B+0.83- is bonded in a 6-coordinate geometry to six B+0.83- atoms. There are a spread of B–B bond distances ranging from 1.75–1.83 Å. In the twelfth B+0.83- site, B+0.83- is bonded in a 7-coordinate geometry to one Lu3+ and six B+0.83- atoms. There is one shorter (1.78 Å) and one longer (1.80 Å) B–B bond length. In the thirteenth B+0.83- site, B+0.83- is bonded in a 7-coordinate geometry to one Lu3+ and six B+0.83- atoms. There is one shorter (1.81 Å) and one longer (1.82 Å) B–B bond length. In the fourteenth B+0.83- site, B+0.83- is bonded in a 6-coordinate geometry to six B+0.83- atoms. There is one shorter (1.69 Å) and two longer (1.82 Å) B–B bond length. In the fifteenth B+0.83- site, B+0.83- is bonded in a 7-coordinate geometry to one Lu3+ and six B+0.83- atoms. There is one shorter (1.72 Å) and one longer (1.79 Å) B–B bond length. In the sixteenth B+0.83- site, B+0.83- is bonded in a 7-coordinate geometry to one Lu3+ and six B+0.83- atoms. There is one shorter (1.81 Å) and one longer (1.83 Å) B–B bond length. In the seventeenth B+0.83- site, B+0.83- is bonded in a 6-coordinate geometry to five B+0.83- and one Si+3.11+ atom. The B–Si bond length is 1.95 Å. In the eighteenth B+0.83- site, B+0.83- is bonded in a 1-coordinate geometry to five B+0.83- and one Si+3.11+ atom. The B–Si bond length is 1.94 Å. In the nineteenth B+0.83- site, B+0.83- is bonded in a distorted single-bond geometry to five B+0.83- and one C4- atom. The B–C bond length is 1.63 Å. In the twentieth B+0.83- site, B+0.83- is bonded in a distorted single-bond geometry to five B+0.83- and one C4- atom. The B–C bond length is 1.62 Å. There are five inequivalent Si+3.11+ sites. In the first Si+3.11+ site, Si+3.11+ is bonded in a trigonal non-coplanar geometry to three B+0.83- atoms. In the second Si+3.11+ site, Si+3.11+ is bonded in a trigonal non-coplanar geometry to three B+0.83- atoms. In the third Si+3.11+ site, Si+3.11+ is bonded in a trigonal non-coplanar geometry to three B+0.83- atoms. In the fourth Si+3.11+ site, Si+3.11+ is bonded in a trigonal non-coplanar geometry to three B+0.83- atoms. In the fifth Si+3.11+ site, Si+3.11+ is bonded in a distorted tetrahedral geometry to three B+0.83- and one C4- atom. The Si–C bond length is 1.84 Å. C4- is bonded in a tetrahedral geometry to three B+0.83- and one Si+3.11+ atom.
Lu2ReB6 crystallizes in the orthorhombic Pbam space group. The structure is three-dimensional. there are two inequivalent Lu3+ sites. In the first Lu3+ site, Lu3+ is bonded in a 10-coordinate geometry to fourteen B2- atoms. There are a spread of Lu–B bond distances ranging from 2.71–2.80 Å. In the second Lu3+ site, Lu3+ is bonded to twelve B2- atoms to form a mixture of edge and face-sharing LuB12 cuboctahedra. There are a spread of Lu–B bond distances ranging from 2.56–2.59 Å. Re6+ is bonded in a 10-coordinate geometry to ten B2- atoms. There are a spread of Re–B bond distances ranging from 2.34–2.39 Å. There are six inequivalent B2- sites. In the first B2- site, B2- is bonded in a 9-coordinate geometry to six Lu3+ and three B2- atoms. There are a spread of B–B bond distances ranging from 1.82–1.93 Å. In the second B2- site, B2- is bonded in a 9-coordinate geometry to four equivalent Lu3+, two equivalent Re6+, and three B2- atoms. There is one shorter (1.79 Å) and two longer (1.80 Å) B–B bond length. In the third B2- site, B2- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent Re6+, and three B2- atoms. The B–B bond length is 1.82 Å. In the fourth B2- site, B2- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent Re6+, and three B2- atoms. There is one shorter (1.74 Å) and one longer (1.81 Å) B–B bond length. In the fifth B2- site, B2- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent Re6+, and three B2- atoms. The B–B bond length is 1.80 Å. In the sixth B2- site, B2- is bonded in a 9-coordinate geometry to four Lu3+, two equivalent Re6+, and three B2- atoms.