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Investigate the feasibility of using piezoelectric sensors/actuators for subscale GEnx composite fan blade damping at target modes.
One aspect of the present invention is a double sided hybrid crystal structure including a trigonal Sapphire wafer containing a (0001) C-plane and having front and rear sides. The Sapphire wafer is substantially transparent to light in the visible and infrared spectra, and also provides insulation with respect to electromagnetic radio frequency noise. A layer of crystalline Si material having a cubic diamond structure aligned with the cubic <111> direction on the (0001) C-plane and strained as rhombohedron to thereby enable continuous integration of a selected (SiGe) device onto the rear side of the Sapphire wafer. The double sided hybrid crystal structure further includes an integrated III-Nitride crystalline layer on the front side of the Sapphire wafer that enables continuous integration of a selected III-Nitride device on the front side of the Sapphire wafer.
One aspect of the present invention is a double sided hybrid crystal structure including a trigonal Sapphire wafer containing a (0001) C-plane and having front and rear sides. The Sapphire wafer is substantially transparent to light in the visible and infrared spectra, and also provides insulation with respect to electromagnetic radio frequency noise. A layer of crystalline Si material having a cubic diamond structure aligned with the cubic <111> direction on the (0001) C-plane and strained as rhombohedron to thereby enable continuous integration of a selected (SiGe) device onto the rear side of the Sapphire wafer. The double sided hybrid crystal structure further includes an integrated III-Nitride crystalline layer on the front side of the Sapphire wafer that enables continuous integration of a selected III-Nitride device on the front side of the Sapphire wafer.
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A tunable level, phase change material-based metasurface near IR optical filter on a transmissive doped silicon-on-insulator platform is demonstrated. This type of filter is non-volatile, non-mechanical, with switching being enabled by Joule heating via current pulses.
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Discussed herein are systems and methods for fabrication of MgSnGe-based thermoelectric materials for applications from room temperature and near room temperature to high temperature applications. The TE materials may be fabricated by hand or ball milling a powder to a predetermined particle size and hot-pressing the milled powder to form a thermoelectric component with desired properties including a figure of merit (ZT) over a temperature range. The TE materials fabricated may be disposed in thermoelectric devices for varying applications.
Y3Ru4Ge13 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are six inequivalent Y sites. In the first Y site, Y is bonded in a 12-coordinate geometry to four Ru and twelve Ge atoms. There are two shorter (3.18 Å) and two longer (3.19 Å) Y–Ru bond lengths. There are a spread of Y–Ge bond distances ranging from 3.14–3.19 Å. In the second Y site, Y is bonded in a 12-coordinate geometry to four Ru and twelve Ge atoms. There are two shorter (3.18 Å) and two longer (3.19 Å) Y–Ru bond lengths. There are a spread of Y–Ge bond distances ranging from 3.15–3.19 Å. In the third Y site, Y is bonded in a 12-coordinate geometry to four Ru and twelve Ge atoms. There are two shorter (3.18 Å) and two longer (3.19 Å) Y–Ru bond lengths. There are a spread of Y–Ge bond distances ranging from 3.16–3.19 Å. In the fourth Y site, Y is bonded in a 12-coordinate geometry to four Ru and twelve Ge atoms. There are two shorter (3.18 Å) and two longer (3.19 Å) Y–Ru bond lengths. There are a spread of Y–Ge bond distances ranging from 3.15–3.19 Å. In the fifth Y site, Y is bonded in a 12-coordinate geometry to four Ru and twelve Ge atoms. There are two shorter (3.18 Å) and two longer (3.19 Å) Y–Ru bond lengths. There are a spread of Y–Ge bond distances ranging from 3.15–3.19 Å. In the sixth Y site, Y is bonded in a 12-coordinate geometry to four Ru and twelve Ge atoms. There are two shorter (3.18 Å) and two longer (3.19 Å) Y–Ru bond lengths. There are a spread of Y–Ge bond distances ranging from 3.15–3.19 Å. There are eight inequivalent Ru sites. In the first Ru site, Ru is bonded in a 6-coordinate geometry to three Y and six Ge atoms. There are five shorter (2.47 Å) and one longer (2.48 Å) Ru–Ge bond lengths. In the second Ru site, Ru is bonded in a 6-coordinate geometry to three Y and six Ge atoms. There are four shorter (2.47 Å) and two longer (2.48 Å) Ru–Ge bond lengths. In the third Ru site, Ru is bonded in a 6-coordinate geometry to three Y and six Ge atoms. There are two shorter (2.47 Å) and four longer (2.48 Å) Ru–Ge bond lengths. In the fourth Ru site, Ru is bonded in a 6-coordinate geometry to three Y and six Ge atoms. There are four shorter (2.47 Å) and two longer (2.48 Å) Ru–Ge bond lengths. In the fifth Ru site, Ru is bonded in a 6-coordinate geometry to three Y and six Ge atoms. There are three shorter (2.47 Å) and three longer (2.48 Å) Ru–Ge bond lengths. In the sixth Ru site, Ru is bonded in a 6-coordinate geometry to three Y and six Ge atoms. All Ru–Ge bond lengths are 2.47 Å. In the seventh Ru site, Ru is bonded in a 6-coordinate geometry to three Y and six Ge atoms. There are four shorter (2.47 Å) and two longer (2.48 Å) Ru–Ge bond lengths. In the eighth Ru site, Ru is bonded in a 6-coordinate geometry to three Y and six Ge atoms. All Ru–Ge bond lengths are 2.47 Å. There are twenty-six inequivalent Ge sites. In the first Ge site, Ge is bonded in a 6-coordinate geometry to three Y, two Ru, and two Ge atoms. There are one shorter (2.72 Å) and one longer (3.09 Å) Ge–Ge bond lengths. In the second Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. There are one shorter (2.71 Å) and one longer (3.08 Å) Ge–Ge bond lengths. In the third Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. There are one shorter (2.72 Å) and one longer (3.07 Å) Ge–Ge bond lengths. In the fourth Ge site, Ge is bonded in a cuboctahedral geometry to twelve Ge atoms. There are a spread of Ge–Ge bond distances ranging from 3.06–3.09 Å. In the fifth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. The Ge–Ge bond length is 2.72 Å. In the sixth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and one Ge atom. In the seventh Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and one Ge atom. The Ge–Ge bond length is 3.05 Å. In the eighth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. There are one shorter (2.72 Å) and one longer (3.07 Å) Ge–Ge bond lengths. In the ninth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. The Ge–Ge bond length is 2.72 Å. In the tenth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and one Ge atom. In the eleventh Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. In the twelfth Ge site, Ge is bonded in a 6-coordinate geometry to three Y, two Ru, and two Ge atoms. The Ge–Ge bond length is 3.08 Å. In the thirteenth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. The Ge–Ge bond length is 3.08 Å. In the fourteenth Ge site, Ge is bonded in a 6-coordinate geometry to three Y, two Ru, and two Ge atoms. The Ge–Ge bond length is 3.09 Å. In the fifteenth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. The Ge–Ge bond length is 2.72 Å. In the sixteenth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and one Ge atom. The Ge–Ge bond length is 3.06 Å. In the seventeenth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. There are one shorter (2.72 Å) and one longer (3.07 Å) Ge–Ge bond lengths. In the eighteenth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and one Ge atom. The Ge–Ge bond length is 3.07 Å. In the nineteenth Ge site, Ge is bonded in a 6-coordinate geometry to three Y, two Ru, and two Ge atoms. In the twentieth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and one Ge atom. In the twenty-first Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. In the twenty-second Ge site, Ge is bonded in a cuboctahedral geometry to twelve Ge atoms. There are one shorter (3.08 Å) and one longer (3.09 Å) Ge–Ge bond lengths. In the twenty-third Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. In the twenty-fourth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and two Ge atoms. In the twenty-fifth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and one Ge atom. In the twenty-sixth Ge site, Ge is bonded in a 2-coordinate geometry to three Y, two Ru, and one Ge atom.
Rb4Ge23 crystallizes in the cubic Pm-3n space group. The structure is three-dimensional. there are six inequivalent Rb sites. In the first Rb site, Rb is bonded in a 8-coordinate geometry to twenty Ge atoms. There are eight shorter (3.57 Å) and twelve longer (3.67 Å) Rb–Ge bond lengths. In the second Rb site, Rb is bonded in a 8-coordinate geometry to twenty Ge atoms. There are eight shorter (3.57 Å) and twelve longer (3.67 Å) Rb–Ge bond lengths. In the third Rb site, Rb is bonded in a 12-coordinate geometry to twelve Ge atoms. There are eight shorter (3.78 Å) and four longer (3.95 Å) Rb–Ge bond lengths. In the fourth Rb site, Rb is bonded in a 12-coordinate geometry to twelve Ge atoms. There are eight shorter (3.78 Å) and four longer (3.95 Å) Rb–Ge bond lengths. In the fifth Rb site, Rb is bonded in a 12-coordinate geometry to twelve Ge atoms. There are eight shorter (3.78 Å) and four longer (3.95 Å) Rb–Ge bond lengths. In the sixth Rb site, Rb is bonded in a 12-coordinate geometry to twelve Ge atoms. There are eight shorter (3.78 Å) and four longer (3.95 Å) Rb–Ge bond lengths. There are twenty-four inequivalent Ge sites. In the first Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.57–2.67 Å. In the second Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.57–2.67 Å. In the third Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are two shorter (2.57 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the fourth Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are two shorter (2.57 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the fifth Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.57–2.67 Å. In the sixth Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.57–2.67 Å. In the seventh Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are two shorter (2.57 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the eighth Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are two shorter (2.57 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the ninth Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.57–2.67 Å. In the tenth Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.57–2.67 Å. In the eleventh Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are two shorter (2.57 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the twelfth Ge site, Ge is bonded in a 7-coordinate geometry to three Rb and four Ge atoms. There are two shorter (2.57 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the thirteenth Ge site, Ge is bonded to four Rb and four Ge atoms to form distorted corner-sharing GeRb4Ge4 tetrahedra. In the fourteenth Ge site, Ge is bonded in a distorted body-centered cubic geometry to four Rb and four Ge atoms. In the fifteenth Ge site, Ge is bonded in a distorted body-centered cubic geometry to four Rb and four Ge atoms. In the sixteenth Ge site, Ge is bonded in a distorted body-centered cubic geometry to four Rb and four Ge atoms. In the seventeenth Ge site, Ge is bonded in a 5-coordinate geometry to one Rb and four Ge atoms. The Ge–Ge bond length is 2.53 Å. In the eighteenth Ge site, Ge is bonded in a 5-coordinate geometry to one Rb and four Ge atoms. The Ge–Ge bond length is 2.53 Å. In the nineteenth Ge site, Ge is bonded in a 5-coordinate geometry to one Rb and four Ge atoms. The Ge–Ge bond length is 2.53 Å. In the twentieth Ge site, Ge is bonded in a 5-coordinate geometry to one Rb and four Ge atoms. The Ge–Ge bond length is 2.53 Å. In the twenty-first Ge site, Ge is bonded in a 5-coordinate geometry to one Rb and four Ge atoms. The Ge–Ge bond length is 2.53 Å. In the twenty-second Ge site, Ge is bonded in a 5-coordinate geometry to one Rb and four Ge atoms. The Ge–Ge bond length is 2.53 Å. In the twenty-third Ge site, Ge is bonded in a 5-coordinate geometry to one Rb and four Ge atoms. All Ge–Ge bond lengths are 2.57 Å. In the twenty-fourth Ge site, Ge is bonded in a 5-coordinate geometry to one Rb and four Ge atoms. All Ge–Ge bond lengths are 2.57 Å.
La6Ge11 crystallizes in the triclinic P-1 space group. The structure is three-dimensional. there are twelve inequivalent La sites. In the first La site, La is bonded in a 10-coordinate geometry to ten Ge atoms. There are a spread of La–Ge bond distances ranging from 3.19–3.31 Å. In the second La site, La is bonded in a 11-coordinate geometry to eleven Ge atoms. There are a spread of La–Ge bond distances ranging from 3.13–3.47 Å. In the third La site, La is bonded in a 11-coordinate geometry to eleven Ge atoms. There are a spread of La–Ge bond distances ranging from 3.13–3.70 Å. In the fourth La site, La is bonded in a 11-coordinate geometry to eleven Ge atoms. There are a spread of La–Ge bond distances ranging from 3.14–3.49 Å. In the fifth La site, La is bonded in a 10-coordinate geometry to ten Ge atoms. There are a spread of La–Ge bond distances ranging from 3.20–3.34 Å. In the sixth La site, La is bonded in a 10-coordinate geometry to ten Ge atoms. There are a spread of La–Ge bond distances ranging from 3.20–3.34 Å. In the seventh La site, La is bonded in a 11-coordinate geometry to eleven Ge atoms. There are a spread of La–Ge bond distances ranging from 3.14–3.47 Å. In the eighth La site, La is bonded in a 11-coordinate geometry to eleven Ge atoms. There are a spread of La–Ge bond distances ranging from 3.13–3.70 Å. In the ninth La site, La is bonded in a 11-coordinate geometry to eleven Ge atoms. There are a spread of La–Ge bond distances ranging from 3.15–3.49 Å. In the tenth La site, La is bonded in a 11-coordinate geometry to eleven Ge atoms. There are a spread of La–Ge bond distances ranging from 3.15–3.68 Å. In the eleventh La site, La is bonded in a 10-coordinate geometry to ten Ge atoms. There are a spread of La–Ge bond distances ranging from 3.18–3.31 Å. In the twelfth La site, La is bonded in a 11-coordinate geometry to eleven Ge atoms. There are a spread of La–Ge bond distances ranging from 3.15–3.68 Å. There are twenty-two inequivalent Ge sites. In the first Ge site, Ge is bonded in a 6-coordinate geometry to six La and two Ge atoms. There are one shorter (2.62 Å) and one longer (2.64 Å) Ge–Ge bond lengths. In the second Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.56–2.58 Å. In the third Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.52–2.66 Å. In the fourth Ge site, Ge is bonded in a 6-coordinate geometry to six La and two Ge atoms. There are one shorter (2.62 Å) and one longer (2.64 Å) Ge–Ge bond lengths. In the fifth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. There are one shorter (2.60 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the sixth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.52–2.66 Å. In the seventh Ge site, Ge is bonded in a 8-coordinate geometry to six La and two Ge atoms. Both Ge–Ge bond lengths are 2.59 Å. In the eighth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. There are one shorter (2.47 Å) and one longer (2.58 Å) Ge–Ge bond lengths. In the ninth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. There are one shorter (2.47 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the tenth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.48–2.63 Å. In the eleventh Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.55–2.58 Å. In the twelfth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. In the thirteenth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. The Ge–Ge bond length is 2.61 Å. In the fourteenth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. In the fifteenth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. The Ge–Ge bond length is 2.47 Å. In the sixteenth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. There are one shorter (2.59 Å) and one longer (2.63 Å) Ge–Ge bond lengths. In the seventeenth Ge site, Ge is bonded in a 6-coordinate geometry to four La and two Ge atoms. In the eighteenth Ge site, Ge is bonded in a 6-coordinate geometry to four La and two Ge atoms. In the nineteenth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. In the twentieth Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. In the twenty-first Ge site, Ge is bonded in a 9-coordinate geometry to six La and three Ge atoms. The Ge–Ge bond length is 2.58 Å. In the twenty-second Ge site, Ge is bonded in a 8-coordinate geometry to six La and two Ge atoms.
Ba7Ge39 crystallizes in the orthorhombic Cmc2_1 space group. The structure is three-dimensional. there are four inequivalent Ba sites. In the first Ba site, Ba is bonded in a 10-coordinate geometry to fifteen Ge atoms. There are a spread of Ba–Ge bond distances ranging from 3.45–3.80 Å. In the second Ba site, Ba is bonded in a 4-coordinate geometry to fourteen Ge atoms. There are a spread of Ba–Ge bond distances ranging from 3.46–3.67 Å. In the third Ba site, Ba is bonded in a 3-coordinate geometry to fifteen Ge atoms. There are a spread of Ba–Ge bond distances ranging from 3.46–3.78 Å. In the fourth Ba site, Ba is bonded in a 4-coordinate geometry to fourteen Ge atoms. There are a spread of Ba–Ge bond distances ranging from 3.44–3.71 Å. There are twenty-two inequivalent Ge sites. In the first Ge site, Ge is bonded to three Ba and four Ge atoms to form distorted corner-sharing GeBa3Ge4 hexagonal pyramids. There are a spread of Ge–Ge bond distances ranging from 2.55–2.64 Å. In the second Ge site, Ge is bonded in a 6-coordinate geometry to two equivalent Ba and four Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.55–2.60 Å. In the third Ge site, Ge is bonded in a 6-coordinate geometry to three Ba and three Ge atoms. Both Ge–Ge bond lengths are 2.59 Å. In the fourth Ge site, Ge is bonded in a 7-coordinate geometry to three Ba and four Ge atoms. Both Ge–Ge bond lengths are 2.66 Å. In the fifth Ge site, Ge is bonded in a distorted pentagonal planar geometry to two equivalent Ba and three Ge atoms. Both Ge–Ge bond lengths are 2.62 Å. In the sixth Ge site, Ge is bonded to three Ba and four Ge atoms to form a mixture of distorted edge, face, and corner-sharing GeBa3Ge4 hexagonal pyramids. There are a spread of Ge–Ge bond distances ranging from 2.61–2.65 Å. In the seventh Ge site, Ge is bonded in a 6-coordinate geometry to three Ba and three Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.58–2.64 Å. In the eighth Ge site, Ge is bonded in a 7-coordinate geometry to three Ba and four Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.59–2.61 Å. In the ninth Ge site, Ge is bonded in a 6-coordinate geometry to two Ba and four Ge atoms. There are one shorter (2.51 Å) and one longer (2.65 Å) Ge–Ge bond lengths. In the tenth Ge site, Ge is bonded to three Ba and four Ge atoms to form a mixture of distorted edge, face, and corner-sharing GeBa3Ge4 hexagonal pyramids. There are a spread of Ge–Ge bond distances ranging from 2.56–2.62 Å. In the eleventh Ge site, Ge is bonded to three Ba and four Ge atoms to form a mixture of distorted edge, face, and corner-sharing GeBa3Ge4 hexagonal pyramids. There are one shorter (2.55 Å) and one longer (2.63 Å) Ge–Ge bond lengths. In the twelfth Ge site, Ge is bonded in a 6-coordinate geometry to two Ba and four Ge atoms. There are one shorter (2.54 Å) and one longer (2.57 Å) Ge–Ge bond lengths. In the thirteenth Ge site, Ge is bonded in a 6-coordinate geometry to two Ba and four Ge atoms. There are one shorter (2.55 Å) and one longer (2.64 Å) Ge–Ge bond lengths. In the fourteenth Ge site, Ge is bonded in a 5-coordinate geometry to two Ba and four Ge atoms. The Ge–Ge bond length is 3.08 Å. In the fifteenth Ge site, Ge is bonded in a 6-coordinate geometry to two Ba and four Ge atoms. There are one shorter (2.52 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the sixteenth Ge site, Ge is bonded to three Ba and four Ge atoms to form a mixture of distorted edge and corner-sharing GeBa3Ge4 hexagonal pyramids. The Ge–Ge bond length is 2.55 Å. In the seventeenth Ge site, Ge is bonded to three Ba and four Ge atoms to form a mixture of distorted edge, face, and corner-sharing GeBa3Ge4 hexagonal pyramids. There are one shorter (2.62 Å) and one longer (2.69 Å) Ge–Ge bond lengths. In the eighteenth Ge site, Ge is bonded in a 6-coordinate geometry to two Ba and four Ge atoms. The Ge–Ge bond length is 2.70 Å. In the nineteenth Ge site, Ge is bonded in a 7-coordinate geometry to three Ba and four Ge atoms. The Ge–Ge bond length is 2.65 Å. In the twentieth Ge site, Ge is bonded in a 5-coordinate geometry to three Ba and four Ge atoms. The Ge–Ge bond length is 3.12 Å. In the twenty-first Ge site, Ge is bonded in a 7-coordinate geometry to two Ba and five Ge atoms. In the twenty-second Ge site, Ge is bonded in a 6-coordinate geometry to three Ba and three Ge atoms.
Ce7Pd4Ge2 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are twenty-eight inequivalent Ce sites. In the first Ce site, Ce is bonded in a 2-coordinate geometry to one Ce, four Pd, and one Ge atom. The Ce–Ce bond length is 2.86 Å. There are a spread of Ce–Pd bond distances ranging from 2.80–3.25 Å. The Ce–Ge bond length is 3.45 Å. In the second Ce site, Ce is bonded in a 3-coordinate geometry to one Ce, four Pd, and two Ge atoms. The Ce–Ce bond length is 2.77 Å. There are a spread of Ce–Pd bond distances ranging from 2.87–3.78 Å. There are one shorter (3.17 Å) and one longer (3.29 Å) Ce–Ge bond lengths. In the third Ce site, Ce is bonded in a 4-coordinate geometry to three Pd and two Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.75–3.14 Å. There are one shorter (2.94 Å) and one longer (2.96 Å) Ce–Ge bond lengths. In the fourth Ce site, Ce is bonded in a 2-coordinate geometry to one Ce, five Pd, and one Ge atom. The Ce–Ce bond length is 3.03 Å. There are a spread of Ce–Pd bond distances ranging from 2.83–3.44 Å. The Ce–Ge bond length is 3.12 Å. In the fifth Ce site, Ce is bonded in a 5-coordinate geometry to four Pd and three Ge atoms. There are a spread of Ce–Pd bond distances ranging from 3.11–3.89 Å. There are a spread of Ce–Ge bond distances ranging from 3.09–3.19 Å. In the sixth Ce site, Ce is bonded in a 2-coordinate geometry to one Ce, four Pd, and one Ge atom. The Ce–Ce bond length is 2.85 Å. There are a spread of Ce–Pd bond distances ranging from 2.80–3.26 Å. The Ce–Ge bond length is 3.43 Å. In the seventh Ce site, Ce is bonded in a 5-coordinate geometry to four Pd and three Ge atoms. There are a spread of Ce–Pd bond distances ranging from 3.11–3.90 Å. There are a spread of Ce–Ge bond distances ranging from 3.08–3.18 Å. In the eighth Ce site, Ce is bonded in a 4-coordinate geometry to three Pd and two Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.76–3.13 Å. There are one shorter (2.93 Å) and one longer (2.96 Å) Ce–Ge bond lengths. In the ninth Ce site, Ce is bonded in a 6-coordinate geometry to six Pd and three Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.95–3.65 Å. There are a spread of Ce–Ge bond distances ranging from 3.13–3.21 Å. In the tenth Ce site, Ce is bonded in a 6-coordinate geometry to six Pd and three Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.95–3.65 Å. There are a spread of Ce–Ge bond distances ranging from 3.13–3.21 Å. In the eleventh Ce site, Ce is bonded in a 2-coordinate geometry to one Ce, four Pd, and one Ge atom. The Ce–Ce bond length is 2.89 Å. There are a spread of Ce–Pd bond distances ranging from 2.81–3.25 Å. The Ce–Ge bond length is 3.44 Å. In the twelfth Ce site, Ce is bonded in a 8-coordinate geometry to three Ce, four Pd, and one Ge atom. There are one shorter (2.77 Å) and one longer (2.86 Å) Ce–Ce bond lengths. There are a spread of Ce–Pd bond distances ranging from 3.11–3.40 Å. The Ce–Ge bond length is 3.01 Å. In the thirteenth Ce site, Ce is bonded in a 3-coordinate geometry to one Ce, four Pd, and two Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.88–3.78 Å. There are one shorter (3.18 Å) and one longer (3.30 Å) Ce–Ge bond lengths. In the fourteenth Ce site, Ce is bonded in a 3-coordinate geometry to one Ce, four Pd, and one Ge atom. There are a spread of Ce–Pd bond distances ranging from 2.81–3.26 Å. The Ce–Ge bond length is 3.44 Å. In the fifteenth Ce site, Ce is bonded in a 4-coordinate geometry to three Pd and two Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.76–3.13 Å. There are one shorter (2.94 Å) and one longer (2.95 Å) Ce–Ge bond lengths. In the sixteenth Ce site, Ce is bonded in a 5-coordinate geometry to four Pd and three Ge atoms. There are a spread of Ce–Pd bond distances ranging from 3.11–3.90 Å. There are a spread of Ce–Ge bond distances ranging from 3.08–3.18 Å. In the seventeenth Ce site, Ce is bonded in a 8-coordinate geometry to three Ce, four Pd, and one Ge atom. There are one shorter (2.77 Å) and one longer (3.05 Å) Ce–Ce bond lengths. There are a spread of Ce–Pd bond distances ranging from 3.10–3.40 Å. The Ce–Ge bond length is 3.02 Å. In the eighteenth Ce site, Ce is bonded in a 8-coordinate geometry to three Ce, four Pd, and one Ge atom. The Ce–Ce bond length is 3.03 Å. There are a spread of Ce–Pd bond distances ranging from 3.11–3.39 Å. The Ce–Ge bond length is 3.02 Å. In the nineteenth Ce site, Ce is bonded in a 6-coordinate geometry to six Pd and three Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.95–3.64 Å. There are a spread of Ce–Ge bond distances ranging from 3.13–3.21 Å. In the twentieth Ce site, Ce is bonded in a 5-coordinate geometry to four Pd and three Ge atoms. There are a spread of Ce–Pd bond distances ranging from 3.11–3.89 Å. There are a spread of Ce–Ge bond distances ranging from 3.08–3.19 Å. In the twenty-first Ce site, Ce is bonded in a 8-coordinate geometry to three Ce, four Pd, and one Ge atom. There are one shorter (2.77 Å) and one longer (3.04 Å) Ce–Ce bond lengths. There are a spread of Ce–Pd bond distances ranging from 3.10–3.40 Å. The Ce–Ge bond length is 3.02 Å. In the twenty-second Ce site, Ce is bonded in a 6-coordinate geometry to six Pd and three Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.95–3.64 Å. There are a spread of Ce–Ge bond distances ranging from 3.13–3.20 Å. In the twenty-third Ce site, Ce is bonded in a 3-coordinate geometry to one Ce, four Pd, and two Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.86–3.79 Å. There are one shorter (3.16 Å) and one longer (3.30 Å) Ce–Ge bond lengths. In the twenty-fourth Ce site, Ce is bonded in a 2-coordinate geometry to one Ce, five Pd, and one Ge atom. There are a spread of Ce–Pd bond distances ranging from 2.82–3.43 Å. The Ce–Ge bond length is 3.12 Å. In the twenty-fifth Ce site, Ce is bonded in a 3-coordinate geometry to one Ce, four Pd, and two Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.87–3.78 Å. There are one shorter (3.17 Å) and one longer (3.30 Å) Ce–Ge bond lengths. In the twenty-sixth Ce site, Ce is bonded in a 4-coordinate geometry to three Pd and two Ge atoms. There are a spread of Ce–Pd bond distances ranging from 2.75–3.13 Å. Both Ce–Ge bond lengths are 2.95 Å. In the twenty-seventh Ce site, Ce is bonded in a 2-coordinate geometry to one Ce, five Pd, and one Ge atom. There are a spread of Ce–Pd bond distances ranging from 2.82–3.44 Å. The Ce–Ge bond length is 3.13 Å. In the twenty-eighth Ce site, Ce is bonded in a 2-coordinate geometry to one Ce, five Pd, and one Ge atom. There are a spread of Ce–Pd bond distances ranging from 2.82–3.42 Å. The Ce–Ge bond length is 3.12 Å. There are sixteen inequivalent Pd sites. In the first Pd site, Pd is bonded in a 10-coordinate geometry to eight Ce and two Ge atoms. There are one shorter (2.64 Å) and one longer (2.88 Å) Pd–Ge bond lengths. In the second Pd site, Pd is bonded in a 5-coordinate geometry to seven Ce, one Pd, and two Ge atoms. The Pd–Pd bond length is 2.94 Å. There are one shorter (2.61 Å) and one longer (3.12 Å) Pd–Ge bond lengths. In the third Pd site, Pd is bonded in a 10-coordinate geometry to eight Ce and two Ge atoms. There are one shorter (2.64 Å) and one longer (2.88 Å) Pd–Ge bond lengths. In the fourth Pd site, Pd is bonded in a 9-coordinate geometry to six Ce and two Pd atoms. The Pd–Pd bond length is 2.92 Å. In the fifth Pd site, Pd is bonded in a 10-coordinate geometry to eight Ce and two Ge atoms. There are one shorter (2.64 Å) and one longer (2.88 Å) Pd–Ge bond lengths. In the sixth Pd site, Pd is bonded in a 4-coordinate geometry to nine Ce and one Pd atom. The Pd–Pd bond length is 2.92 Å. In the seventh Pd site, Pd is bonded in a 4-coordinate geometry to nine Ce and one Pd atom. The Pd–Pd bond length is 2.92 Å. In the eighth Pd site, Pd is bonded in a 10-coordinate geometry to nine Ce and one Pd atom. In the ninth Pd site, Pd is bonded in a 4-coordinate geometry to nine Ce and one Pd atom. The Pd–Pd bond length is 2.92 Å. In the tenth Pd site, Pd is bonded in a 10-coordinate geometry to eight Ce and two Ge atoms. There are one shorter (2.64 Å) and one longer (2.87 Å) Pd–Ge bond lengths. In the eleventh Pd site, Pd is bonded in a 9-coordinate geometry to six Ce and three Pd atoms. There are one shorter (2.94 Å) and one longer (2.97 Å) Pd–Pd bond lengths. In the twelfth Pd site, Pd is bonded in a 5-coordinate geometry to seven Ce, one Pd, and two Ge atoms. There are one shorter (2.61 Å) and one longer (3.11 Å) Pd–Ge bond lengths. In the thirteenth Pd site, Pd is bonded in a 9-coordinate geometry to six Ce and three Pd atoms. The Pd–Pd bond length is 2.94 Å. In the fourteenth Pd site, Pd is bonded in a 9-coordinate geometry to six Ce and two Pd atoms. The Pd–Pd bond length is 2.94 Å. In the fifteenth Pd site, Pd is bonded in a 5-coordinate geometry to seven Ce, one Pd, and two Ge atoms. There are one shorter (2.62 Å) and one longer (3.12 Å) Pd–Ge bond lengths. In the sixteenth Pd site, Pd is bonded in a 5-coordinate geometry to seven Ce, one Pd, and two Ge atoms. There are one shorter (2.61 Å) and one longer (3.12 Å) Pd–Ge bond lengths. There are eight inequivalent Ge sites. In the first Ge site, Ge is bonded in a 10-coordinate geometry to seven Ce, two Pd, and one Ge atom. The Ge–Ge bond length is 2.58 Å. In the second Ge site, Ge is bonded in a 10-coordinate geometry to seven Ce, two Pd, and one Ge atom. The Ge–Ge bond length is 2.58 Å. In the third Ge site, Ge is bonded in a 9-coordinate geometry to six Ce, two Pd, and one Ge atom. The Ge–Ge bond length is 2.59 Å. In the fourth Ge site, Ge is bonded in a 9-coordinate geometry to six Ce, two Pd, and one Ge atom. In the fifth Ge site, Ge is bonded in a 10-coordinate geometry to seven Ce, two Pd, and one Ge atom. In the sixth Ge site, Ge is bonded in a 9-coordinate geometry to six Ce, two Pd, and one Ge atom. The Ge–Ge bond length is 2.59 Å. In the seventh Ge site, Ge is bonded in a 10-coordinate geometry to seven Ce, two Pd, and one Ge atom. In the eighth Ge site, Ge is bonded in a 9-coordinate geometry to six Ce, two Pd, and one Ge atom.
Mg5Yb15Ge16 is Magnesium tetraboride-derived structured and crystallizes in the monoclinic Pc space group. The structure is three-dimensional. there are five inequivalent Mg sites. In the first Mg site, Mg is bonded in a 4-coordinate geometry to four Ge atoms. There are a spread of Mg–Ge bond distances ranging from 2.81–3.15 Å. In the second Mg site, Mg is bonded in a distorted rectangular see-saw-like geometry to four Ge atoms. There are a spread of Mg–Ge bond distances ranging from 2.85–2.94 Å. In the third Mg site, Mg is bonded in a 4-coordinate geometry to six Ge atoms. There are a spread of Mg–Ge bond distances ranging from 2.80–3.19 Å. In the fourth Mg site, Mg is bonded in a distorted rectangular see-saw-like geometry to four Ge atoms. There are a spread of Mg–Ge bond distances ranging from 2.79–3.00 Å. In the fifth Mg site, Mg is bonded in a 4-coordinate geometry to four Ge atoms. There are a spread of Mg–Ge bond distances ranging from 2.79–3.10 Å. There are fifteen inequivalent Yb sites. In the first Yb site, Yb is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.08–3.33 Å. In the second Yb site, Yb is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.09–3.42 Å. In the third Yb site, Yb is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.05–3.56 Å. In the fourth Yb site, Yb is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.06–3.50 Å. In the fifth Yb site, Yb is bonded in a 6-coordinate geometry to six Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.96–3.11 Å. In the sixth Yb site, Yb is bonded in a 6-coordinate geometry to six Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.94–3.10 Å. In the seventh Yb site, Yb is bonded in a 6-coordinate geometry to six Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.94–3.13 Å. In the eighth Yb site, Yb is bonded in a 6-coordinate geometry to six Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.96–3.10 Å. In the ninth Yb site, Yb is bonded in a 6-coordinate geometry to six Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.89–3.04 Å. In the tenth Yb site, Yb is bonded in a 6-coordinate geometry to six Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.93–3.11 Å. In the eleventh Yb site, Yb is bonded in a 6-coordinate geometry to six Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.95–3.06 Å. In the twelfth Yb site, Yb is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.06–3.46 Å. In the thirteenth Yb site, Yb is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.99–3.44 Å. In the fourteenth Yb site, Yb is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.04–3.27 Å. In the fifteenth Yb site, Yb is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.03–3.30 Å. There are sixteen inequivalent Ge sites. In the first Ge site, Ge is bonded in a 8-coordinate geometry to two Mg, five Yb, and one Ge atom. The Ge–Ge bond length is 2.50 Å. In the second Ge site, Ge is bonded in a 8-coordinate geometry to two Mg, five Yb, and one Ge atom. The Ge–Ge bond length is 2.57 Å. In the third Ge site, Ge is bonded in a 9-coordinate geometry to one Mg, seven Yb, and one Ge atom. The Ge–Ge bond length is 2.54 Å. In the fourth Ge site, Ge is bonded in a 8-coordinate geometry to one Mg, six Yb, and one Ge atom. The Ge–Ge bond length is 2.57 Å. In the fifth Ge site, Ge is bonded in a 8-coordinate geometry to seven Yb and one Ge atom. The Ge–Ge bond length is 2.51 Å. In the sixth Ge site, Ge is bonded in a 9-coordinate geometry to two Mg, six Yb, and one Ge atom. The Ge–Ge bond length is 2.50 Å. In the seventh Ge site, Ge is bonded in a 9-coordinate geometry to two Mg, six Yb, and one Ge atom. The Ge–Ge bond length is 2.55 Å. In the eighth Ge site, Ge is bonded in a 9-coordinate geometry to two Mg, six Yb, and one Ge atom. The Ge–Ge bond length is 2.52 Å. In the ninth Ge site, Ge is bonded in a 9-coordinate geometry to three Mg, five Yb, and one Ge atom. In the tenth Ge site, Ge is bonded in a 9-coordinate geometry to two Mg, six Yb, and one Ge atom. In the eleventh Ge site, Ge is bonded in a 8-coordinate geometry to seven Yb and one Ge atom. In the twelfth Ge site, Ge is bonded in a 9-coordinate geometry to one Mg, seven Yb, and one Ge atom. In the thirteenth Ge site, Ge is bonded in a 9-coordinate geometry to one Mg, seven Yb, and one Ge atom. In the fourteenth Ge site, Ge is bonded in a 8-coordinate geometry to one Mg, six Yb, and one Ge atom. In the fifteenth Ge site, Ge is bonded in a 8-coordinate geometry to one Mg, six Yb, and one Ge atom. In the sixteenth Ge site, Ge is bonded in a 8-coordinate geometry to one Mg, six Yb, and one Ge atom.
Na2Li18Ge17 crystallizes in the trigonal P31m space group. The structure is three-dimensional. there are three inequivalent Na sites. In the first Na site, Na is bonded in a 4-coordinate geometry to four Ge atoms. There are a spread of Na–Ge bond distances ranging from 2.90–3.19 Å. In the second Na site, Na is bonded in a distorted single-bond geometry to four Ge atoms. There are one shorter (3.01 Å) and three longer (3.37 Å) Na–Ge bond lengths. In the third Na site, Na is bonded in a 1-coordinate geometry to four Ge atoms. There are one shorter (3.04 Å) and three longer (3.35 Å) Na–Ge bond lengths. There are thirteen inequivalent Li sites. In the first Li site, Li is bonded in a 12-coordinate geometry to four Li and twelve Ge atoms. There are a spread of Li–Li bond distances ranging from 2.97–3.04 Å. There are a spread of Li–Ge bond distances ranging from 2.98–3.10 Å. In the second Li site, Li is bonded in a 9-coordinate geometry to one Li and nine Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.95–3.05 Å. In the third Li site, Li is bonded in a 9-coordinate geometry to one Li and nine Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.87–3.07 Å. In the fourth Li site, Li is bonded in a 8-coordinate geometry to one Li and eight Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.88–3.02 Å. In the fifth Li site, Li is bonded in a 6-coordinate geometry to six Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.79–2.86 Å. In the sixth Li site, Li is bonded in a 4-coordinate geometry to four Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.55–2.69 Å. In the seventh Li site, Li is bonded to four Ge atoms to form distorted corner-sharing LiGe4 tetrahedra. There are a spread of Li–Ge bond distances ranging from 2.74–2.92 Å. In the eighth Li site, Li is bonded in a 12-coordinate geometry to six Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.78–3.12 Å. In the ninth Li site, Li is bonded in a 4-coordinate geometry to four Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.60–2.88 Å. In the tenth Li site, Li is bonded in a 4-coordinate geometry to five Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.80–3.14 Å. In the eleventh Li site, Li is bonded in a 4-coordinate geometry to four Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.57–2.74 Å. In the twelfth Li site, Li is bonded in a 7-coordinate geometry to seven Ge atoms. There are a spread of Li–Ge bond distances ranging from 2.89–2.98 Å. In the thirteenth Li site, Li is bonded to four Ge atoms to form a mixture of distorted edge and corner-sharing LiGe4 tetrahedra. There are a spread of Li–Ge bond distances ranging from 2.60–2.95 Å. There are twelve inequivalent Ge sites. In the first Ge site, Ge is bonded in a 10-coordinate geometry to one Na and nine Li atoms. In the second Ge site, Ge is bonded in a 1-coordinate geometry to one Na, six Li, and three Ge atoms. There are two shorter (2.60 Å) and one longer (2.61 Å) Ge–Ge bond lengths. In the third Ge site, Ge is bonded in a 10-coordinate geometry to one Na, six Li, and three equivalent Ge atoms. In the fourth Ge site, Ge is bonded in a 11-coordinate geometry to one Na, seven Li, and three Ge atoms. There are one shorter (2.61 Å) and two longer (2.62 Å) Ge–Ge bond lengths. In the fifth Ge site, Ge is bonded in a 7-coordinate geometry to one Na, six Li, and three equivalent Ge atoms. In the sixth Ge site, Ge is bonded in a 10-coordinate geometry to seven Li and three Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.52–2.70 Å. In the seventh Ge site, Ge is bonded in a 9-coordinate geometry to six Li and three Ge atoms. There are one shorter (2.53 Å) and one longer (2.60 Å) Ge–Ge bond lengths. In the eighth Ge site, Ge is bonded in a 9-coordinate geometry to six Li and three Ge atoms. There are one shorter (2.60 Å) and one longer (2.73 Å) Ge–Ge bond lengths. In the ninth Ge site, Ge is bonded in a 10-coordinate geometry to one Na, six Li, and three Ge atoms. The Ge–Ge bond length is 2.53 Å. In the tenth Ge site, Ge is bonded in a 9-coordinate geometry to one Na, five Li, and three Ge atoms. The Ge–Ge bond length is 2.51 Å. In the eleventh Ge site, Ge is bonded in a 1-coordinate geometry to seven Li and three Ge atoms. Both Ge–Ge bond lengths are 2.62 Å. In the twelfth Ge site, Ge is bonded in a 10-coordinate geometry to seven Li and three Ge atoms. The Ge–Ge bond length is 2.63 Å.
LiYb8Ge13 crystallizes in the monoclinic P2_1/c space group. The structure is three-dimensional. Li is bonded in a 8-coordinate geometry to one Yb and eight Ge atoms. The Li–Yb bond length is 3.30 Å. There are a spread of Li–Ge bond distances ranging from 2.69–2.86 Å. There are eight inequivalent Yb sites. In the first Yb site, Yb is bonded in a 9-coordinate geometry to nine Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.07–3.39 Å. In the second Yb site, Yb is bonded in a 10-coordinate geometry to ten Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.04–3.50 Å. In the third Yb site, Yb is bonded in a 11-coordinate geometry to one Li and ten Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.10–3.42 Å. In the fourth Yb site, Yb is bonded in a 9-coordinate geometry to nine Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.04–3.27 Å. In the fifth Yb site, Yb is bonded in a 5-coordinate geometry to nine Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.96–3.33 Å. In the sixth Yb site, Yb is bonded in a 9-coordinate geometry to nine Ge atoms. There are a spread of Yb–Ge bond distances ranging from 3.02–3.22 Å. In the seventh Yb site, Yb is bonded in a 8-coordinate geometry to eight Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.88–3.16 Å. In the eighth Yb site, Yb is bonded in a 9-coordinate geometry to nine Ge atoms. There are a spread of Yb–Ge bond distances ranging from 2.93–3.25 Å. There are thirteen inequivalent Ge sites. In the first Ge site, Ge is bonded in a 8-coordinate geometry to six Yb and two Ge atoms. There are one shorter (2.50 Å) and one longer (2.57 Å) Ge–Ge bond lengths. In the second Ge site, Ge is bonded in a 9-coordinate geometry to one Li, six Yb, and two Ge atoms. There are one shorter (2.52 Å) and one longer (2.69 Å) Ge–Ge bond lengths. In the third Ge site, Ge is bonded in a 9-coordinate geometry to one Li, six Yb, and two Ge atoms. The Ge–Ge bond length is 2.68 Å. In the fourth Ge site, Ge is bonded in a 8-coordinate geometry to one Li, five Yb, and two Ge atoms. There are one shorter (2.59 Å) and one longer (2.79 Å) Ge–Ge bond lengths. In the fifth Ge site, Ge is bonded in a 9-coordinate geometry to two equivalent Li, four Yb, and three Ge atoms. There are a spread of Ge–Ge bond distances ranging from 2.59–2.86 Å. In the sixth Ge site, Ge is bonded in a 9-coordinate geometry to one Li, five Yb, and three Ge atoms. The Ge–Ge bond length is 2.60 Å. In the seventh Ge site, Ge is bonded in a 9-coordinate geometry to seven Yb and two Ge atoms. The Ge–Ge bond length is 2.57 Å. In the eighth Ge site, Ge is bonded in a 9-coordinate geometry to one Li, five Yb, and three Ge atoms. The Ge–Ge bond length is 2.57 Å. In the ninth Ge site, Ge is bonded in a 8-coordinate geometry to six Yb and two Ge atoms. There are one shorter (2.58 Å) and one longer (2.63 Å) Ge–Ge bond lengths. In the tenth Ge site, Ge is bonded in a 8-coordinate geometry to six Yb and two Ge atoms. The Ge–Ge bond length is 2.59 Å. In the eleventh Ge site, Ge is bonded in a 8-coordinate geometry to six Yb and two Ge atoms. In the twelfth Ge site, Ge is bonded in a 8-coordinate geometry to six Yb and two Ge atoms. In the thirteenth Ge site, Ge is bonded in a 9-coordinate geometry to one Li, five Yb, and three Ge atoms.
Li13Zn11Ge12 crystallizes in the trigonal P3m1 space group. The structure is three-dimensional. there are eleven inequivalent Li sites. In the first Li site, Li is bonded in a hexagonal planar geometry to three equivalent Zn and three equivalent Ge atoms. All Li–Zn bond lengths are 2.58 Å. All Li–Ge bond lengths are 2.58 Å. In the second Li site, Li is bonded in a hexagonal planar geometry to three equivalent Zn and three equivalent Ge atoms. All Li–Zn bond lengths are 2.58 Å. All Li–Ge bond lengths are 2.58 Å. In the third Li site, Li is bonded in a hexagonal planar geometry to three equivalent Zn and three equivalent Ge atoms. All Li–Zn bond lengths are 2.58 Å. All Li–Ge bond lengths are 2.58 Å. In the fourth Li site, Li is bonded in a distorted trigonal planar geometry to three equivalent Ge atoms. All Li–Ge bond lengths are 2.58 Å. In the fifth Li site, Li is bonded in a distorted trigonal planar geometry to three equivalent Ge atoms. All Li–Ge bond lengths are 2.58 Å. In the sixth Li site, Li is bonded in a distorted hexagonal planar geometry to three equivalent Zn and three equivalent Ge atoms. All Li–Zn bond lengths are 2.62 Å. All Li–Ge bond lengths are 2.60 Å. In the seventh Li site, Li is bonded in a distorted hexagonal planar geometry to three equivalent Zn and three equivalent Ge atoms. All Li–Zn bond lengths are 2.62 Å. All Li–Ge bond lengths are 2.60 Å. In the eighth Li site, Li is bonded in a distorted hexagonal planar geometry to three equivalent Zn and three equivalent Ge atoms. All Li–Zn bond lengths are 2.63 Å. All Li–Ge bond lengths are 2.60 Å. In the ninth Li site, Li is bonded in a distorted hexagonal planar geometry to three equivalent Zn and three equivalent Ge atoms. All Li–Zn bond lengths are 2.64 Å. All Li–Ge bond lengths are 2.61 Å. In the tenth Li site, Li is bonded in a distorted hexagonal planar geometry to three equivalent Zn and three equivalent Ge atoms. All Li–Zn bond lengths are 2.63 Å. All Li–Ge bond lengths are 2.60 Å. In the eleventh Li site, Li is bonded in a distorted hexagonal planar geometry to three equivalent Zn and three equivalent Ge atoms. All Li–Zn bond lengths are 2.64 Å. All Li–Ge bond lengths are 2.61 Å. There are eleven inequivalent Zn sites. In the first Zn site, Zn is bonded to three equivalent Li and four Ge atoms to form distorted ZnLi3Ge4 hexagonal pyramids that share a cornercorner with one ZnLi3Ge4 hexagonal pyramid, corners with three equivalent GeLi3Zn3Ge hexagonal pyramids, edges with three equivalent GeLi3Zn3Ge hexagonal pyramids, and edges with six equivalent ZnLi3Ge4 hexagonal pyramids. There are one shorter (2.67 Å) and three longer (2.70 Å) Zn–Ge bond lengths. In the second Zn site, Zn is bonded to three equivalent Li and four Ge atoms to form distorted ZnLi3Ge4 hexagonal pyramids that share a cornercorner with one ZnLi3Ge4 hexagonal pyramid, corners with six GeLi3Zn3Ge hexagonal pyramids, edges with three equivalent GeLi3Zn3Ge hexagonal pyramids, and edges with six equivalent ZnLi3Ge4 hexagonal pyramids. All Zn–Li bond lengths are 2.62 Å. There are one shorter (2.67 Å) and three longer (2.69 Å) Zn–Ge bond lengths. In the third Zn site, Zn is bonded to three equivalent Li and four Ge atoms to form distorted ZnLi3Ge4 hexagonal pyramids that share a cornercorner with one ZnLi3Ge4 hexagonal pyramid, corners with six GeLi3Zn3Ge hexagonal pyramids, edges with three equivalent GeLi3Zn3Ge hexagonal pyramids, and edges with six equivalent ZnLi3Ge4 hexagonal pyramids. All Zn–Li bond lengths are 2.62 Å. All Zn–Ge bond lengths are 2.69 Å. In the fourth Zn site, Zn is bonded to three equivalent Li and four Ge atoms to form distorted ZnLi3Ge4 hexagonal pyramids that share a cornercorner with one ZnLi3Ge4 hexagonal pyramid, corners with three equivalent GeLi3Zn3Ge hexagonal pyramids, and edges with six equivalent ZnLi3Ge4 hexagonal pyramids. There are one shorter (2.52 Å) and three longer (2.74 Å) Zn–Ge bond lengths. In the fifth Zn site, Zn is bonded to three equivalent Li and four Ge atoms to form distorted ZnLi3Ge4 hexagonal pyramids that share a cornercorner with one ZnLi3Ge4 hexagonal pyramid, corners with six GeLi3Zn3Ge hexagonal pyramids, edges with three equivalent GeLi3Zn3Ge hexagonal pyramids, and edges with six equivalent ZnLi3Ge4 hexagonal pyramids. There are three shorter (2.69 Å) and one longer (2.71 Å) Zn–Ge bond lengths. In the sixth Zn site, Zn is bonded to three equivalent Li and four Ge atoms to form distorted ZnLi3Ge4 hexagonal pyramids that share a cornercorner with one ZnLi3Ge4 hexagonal pyramid, corners with six GeLi3Zn3Ge hexagonal pyramids, edges with three equivalent GeLi3Zn3Ge hexagonal pyramids, and edges with six equivalent ZnLi3Ge4 hexagonal pyramids. There are three shorter (2.69 Å) and one longer (2.70 Å) Zn–Ge bond lengths. In the seventh Zn site, Zn is bonded to three equivalent Li and four Ge atoms to form distorted ZnLi3Ge4 hexagonal pyramids that share a cornercorner with one ZnLi3Ge4 hexagonal pyramid, corners with three equivalent GeLi3Zn3Ge hexagonal pyramids, edges with three equivalent GeLi3Zn3Ge hexagonal pyramids, and edges with six equivalent ZnLi3Ge4 hexagonal pyramids. There are one shorter (2.69 Å) and three longer (2.70 Å) Zn–Ge bond lengths. In the eighth Zn site, Zn is bonded to three equivalent Li and four Ge atoms to form distorted ZnLi3Ge4 hexagonal pyramids that share a cornercorner with one ZnLi3Ge4 hexagonal pyramid, corners with three equivalent GeLi3Zn3Ge hexagonal pyramids, and edges with six equivalent ZnLi3Ge4 hexagonal pyramids. There are one shorter (2.52 Å) and three longer (2.74 Å) Zn–Ge bond lengths. In the ninth Zn site, Zn is bonded in a hexagonal planar geometry to three equivalent Li and three equivalent Ge atoms. All Zn–Ge bond lengths are 2.58 Å. In the tenth Zn site, Zn is bonded in a hexagonal planar geometry to three equivalent Li and three equivalent Ge atoms. All Zn–Ge bond lengths are 2.58 Å. In the eleventh Zn site, Zn is bonded in a hexagonal planar geometry to three equivalent Li and three equivalent Ge atoms. All Zn–Ge bond lengths are 2.58 Å. There are ten inequivalent Ge sites. In the first Ge site, Ge is bonded to three equivalent Li, three equivalent Zn, and one Ge atom to form distorted GeLi3Zn3Ge hexagonal pyramids that share corners with three equivalent GeLi3Zn5 hexagonal bipyramids, corners with six ZnLi3Ge4 hexagonal pyramids, edges with three equivalent ZnLi3Ge4 hexagonal pyramids, and edges with six equivalent GeLi3Zn3Ge hexagonal pyramids. The Ge–Ge bond length is 2.52 Å. In the second Ge site, Ge is bonded to three equivalent Li, three equivalent Zn, and one Ge atom to form distorted GeLi3Zn3Ge hexagonal pyramids that share corners with three equivalent GeLi3Zn5 hexagonal bipyramids, corners with six ZnLi3Ge4 hexagonal pyramids, edges with three equivalent ZnLi3Ge4 hexagonal pyramids, and edges with six equivalent GeLi3Zn3Ge hexagonal pyramids. The Ge–Ge bond length is 2.54 Å. In the third Ge site, Ge is bonded to three equivalent Li, three equivalent Zn, and one Ge atom to form distorted GeLi3Zn3Ge hexagonal pyramids that share corners with three equivalent GeLi3Zn5 hexagonal bipyramids, corners with six ZnLi3Ge4 hexagonal pyramids, edges with three equivalent ZnLi3Ge4 hexagonal pyramids, and edges with six equivalent GeLi3Zn3Ge hexagonal pyramids. In the fourth Ge site, Ge is bonded in a 7-coordinate geometry to three equivalent Li, three equivalent Zn, and one Ge atom. The Ge–Ge bond length is 2.52 Å. In the fifth Ge site, Ge is bonded to three equivalent Li, three equivalent Zn, and one Ge atom to form distorted GeLi3Zn3Ge hexagonal pyramids that share corners with three equivalent GeLi3Zn5 hexagonal bipyramids, corners with six ZnLi3Ge4 hexagonal pyramids, edges with three equivalent ZnLi3Ge4 hexagonal pyramids, and edges with six equivalent GeLi3Zn3Ge hexagonal pyramids. In the sixth Ge site, Ge is bonded in a 7-coordinate geometry to three equivalent Li, three equivalent Zn, and one Ge atom. In the seventh Ge site, Ge is bonded to three equivalent Li and five Zn atoms to form GeLi3Zn5 hexagonal bipyramids that share corners with six GeLi3Zn3Ge hexagonal pyramids and edges with six equivalent GeLi3Zn5 hexagonal bipyramids. In the eighth Ge site, Ge is bonded to three equivalent Li and five Zn atoms to form GeLi3Zn5 hexagonal bipyramids that share corners with six equivalent GeLi3Zn3Ge hexagonal pyramids and edges with six equivalent GeLi3Zn5 hexagonal bipyramids. In the ninth Ge site, Ge is bonded to three equivalent Li and five Zn atoms to form GeLi3Zn5 hexagonal bipyramids that share corners with six GeLi3Zn3Ge hexagonal pyramids and edges with six equivalent GeLi3Zn5 hexagonal bipyramids. In the tenth Ge site, Ge is bonded to six Li and two Zn atoms to form edge-sharing GeLi6Zn2 hexagonal bipyramids.