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Materials Data on ZrTiMn4 by Materials Project

ZrTiMn4 is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. Zr is bonded in a 9-coordinate geometry to three equivalent Zr, one Ti, and twelve Mn atoms. All Zr–Zr bond lengths are 3.01 Å. The Zr–Ti bond length is 2.99 Å. There are a spread of Zr–Mn bond distances ranging from 2.85–2.97 Å. Ti is bonded in a 1-coordinate geometry to one Zr, three equivalent Ti, and twelve Mn atoms. All Ti–Ti bond lengths are 2.95 Å. There are a spread of Ti–Mn bond distances ranging from 2.77–2.84 Å. There are three inequivalent Mn sites. In the first Mn site, Mn is bonded to three equivalent Zr, three equivalent Ti, and six Mn atoms to form a mixture of corner, edge, and face-sharing MnZr3Ti3Mn6 cuboctahedra. There are a spread of Mn–Mn bond distances ranging from 2.35–2.53 Å. In the second Mn site, Mn is bonded to six equivalent Zr and six equivalent Mn atoms to form MnZr6Mn6 cuboctahedra that share corners with twelve equivalent MnZr3Ti3Mn6 cuboctahedra, edges with six equivalent MnZr6Mn6 cuboctahedra, and faces with twenty MnTi6Mn6 cuboctahedra. In the third Mn site, Mn is bonded to six equivalent Ti and six equivalent Mn atoms to form MnTi6Mn6 cuboctahedra that share corners with twelve equivalent MnZr3Ti3Mn6 cuboctahedra, edges with six equivalent MnTi6Mn6 cuboctahedra, and faces with twenty MnZr6Mn6 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on Zr3TiMn8 by Materials Project

Zr3TiMn8 crystallizes in the trigonal P3m1 space group. The structure is three-dimensional. there are three inequivalent Zr sites. In the first Zr site, Zr is bonded in a 12-coordinate geometry to one Zr, three equivalent Ti, and twelve Mn atoms. The Zr–Zr bond length is 3.09 Å. All Zr–Ti bond lengths are 2.98 Å. There are a spread of Zr–Mn bond distances ranging from 2.84–2.88 Å. In the second Zr site, Zr is bonded in a 12-coordinate geometry to four Zr and twelve Mn atoms. All Zr–Zr bond lengths are 3.01 Å. There are a spread of Zr–Mn bond distances ranging from 2.86–2.94 Å. In the third Zr site, Zr is bonded in a 9-coordinate geometry to three equivalent Zr, one Ti, and twelve Mn atoms. The Zr–Ti bond length is 3.00 Å. There are nine shorter (2.87 Å) and three longer (2.97 Å) Zr–Mn bond lengths. Ti is bonded in a 4-coordinate geometry to four Zr and twelve Mn atoms. There are a spread of Ti–Mn bond distances ranging from 2.85–2.88 Å. There are four inequivalent Mn sites. In the first Mn site, Mn is bonded to three equivalent Zr, three equivalent Ti, and six Mn atoms to form MnZr3Ti3Mn6 cuboctahedra that share corners with twelve MnZr4Ti2Mn6 cuboctahedra, edges with six equivalent MnZr3Ti3Mn6 cuboctahedra, and faces with twenty MnZr6Mn6 cuboctahedra. There are three shorter (2.45 Å) and three longer (2.48 Å) Mn–Mn bond lengths. In the second Mn site, Mn is bonded to six Zr and six Mn atoms to form MnZr6Mn6 cuboctahedra that share corners with twelve MnZr4Ti2Mn6 cuboctahedra, edges with six equivalent MnZr6Mn6 cuboctahedra, and faces with twenty MnZr3Ti3Mn6 cuboctahedra. All Mn–Mn bond lengths are 2.52 Å. In the third Mn site, Mn is bonded to four Zr, two equivalent Ti, and six Mn atoms to form MnZr4Ti2Mn6 cuboctahedra that share corners with eighteen MnZr3Ti3Mn6 cuboctahedra, edges with six MnZr5TiMn6 cuboctahedra, and faces with eighteen MnZr3Ti3Mn6 cuboctahedra. There are two shorter (2.40 Å) and two longer (2.47 Å) Mn–Mn bond lengths. In the fourth Mn site, Mn is bonded to five Zr, one Ti, and six Mn atoms to form MnZr5TiMn6 cuboctahedra that share corners with eighteen MnZr3Ti3Mn6 cuboctahedra, edges with six MnZr5TiMn6 cuboctahedra, and faces with eighteen MnZr3Ti3Mn6 cuboctahedra. There are two shorter (2.38 Å) and two longer (2.49 Å) Mn–Mn bond lengths.

36 MATERIALS SCIENCE↗