Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “K edge”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Materials Data on K3I2Br by Materials Project

K3I2Br is Caswellsilverite-like structured and crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. there are two inequivalent K1+ sites. In the first K1+ site, K1+ is bonded to six equivalent I1- atoms to form KI6 octahedra that share corners with six equivalent KI3Br3 octahedra and edges with twelve KI6 octahedra. The corner-sharing octahedral tilt angles are 0°. All K–I bond lengths are 3.56 Å. In the second K1+ site, K1+ is bonded to three equivalent I1- and three equivalent Br1- atoms to form a mixture of edge and corner-sharing KI3Br3 octahedra. The corner-sharing octahedral tilt angles are 0°. All K–I bond lengths are 3.58 Å. All K–Br bond lengths are 3.41 Å. I1- is bonded to six K1+ atoms to form IK6 octahedra that share corners with three equivalent IK6 octahedra, corners with three equivalent BrK6 octahedra, edges with three equivalent BrK6 octahedra, and edges with nine equivalent IK6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. Br1- is bonded to six equivalent K1+ atoms to form BrK6 octahedra that share corners with six equivalent IK6 octahedra, edges with six equivalent IK6 octahedra, and edges with six equivalent BrK6 octahedra. The corner-sharing octahedral tilt angles are 4°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KCu4(AsO4)3 by Materials Project

KCu4(AsO4)3 is Esseneite-like structured and crystallizes in the monoclinic C2/c space group. The structure is three-dimensional. K1+ is bonded to eight O2- atoms to form distorted KO8 hexagonal bipyramids that share corners with two equivalent AsO4 tetrahedra, edges with two equivalent KO8 hexagonal bipyramids, edges with four equivalent CuO6 octahedra, and edges with three AsO4 tetrahedra. There are a spread of K–O bond distances ranging from 2.68–2.80 Å. There are three inequivalent Cu2+ sites. In the first Cu2+ site, Cu2+ is bonded to six O2- atoms to form distorted CuO6 octahedra that share corners with six AsO4 tetrahedra, edges with two equivalent KO8 hexagonal bipyramids, and an edgeedge with one CuO6 octahedra. There are a spread of Cu–O bond distances ranging from 1.95–2.57 Å. In the second Cu2+ site, Cu2+ is bonded in a square co-planar geometry to four O2- atoms. There is two shorter (1.92 Å) and two longer (1.94 Å) Cu–O bond length. In the third Cu2+ site, Cu2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Cu–O bond distances ranging from 1.99–2.59 Å. There are two inequivalent As5+ sites. In the first As5+ site, As5+ is bonded to four O2- atoms to form AsO4 tetrahedra that share a cornercorner with one KO8 hexagonal bipyramid, corners with four equivalent CuO6 octahedra, and an edgeedge with one KO8 hexagonal bipyramid. The corner-sharing octahedra tilt angles range from 39–60°. There are a spread of As–O bond distances ranging from 1.72–1.76 Å. In the second As5+ site, As5+ is bonded to four O2- atoms to form AsO4 tetrahedra that share corners with four equivalent CuO6 octahedra and an edgeedge with one KO8 hexagonal bipyramid. The corner-sharing octahedra tilt angles range from 56–61°. There is two shorter (1.71 Å) and two longer (1.79 Å) As–O bond length. There are six inequivalent O2- sites. In the first O2- site, O2- is bonded to two equivalent K1+, one Cu2+, and one As5+ atom to form a mixture of distorted corner and edge-sharing OK2CuAs trigonal pyramids. In the second O2- site, O2- is bonded in a distorted bent 120 degrees geometry to two equivalent Cu2+ and one As5+ atom. In the third O2- site, O2- is bonded in a distorted trigonal planar geometry to two Cu2+ and one As5+ atom. In the fourth O2- site, O2- is bonded in a distorted trigonal planar geometry to two Cu2+ and one As5+ atom. In the fifth O2- site, O2- is bonded in a 2-coordinate geometry to one K1+, two Cu2+, and one As5+ atom. In the sixth O2- site, O2- is bonded in a 4-coordinate geometry to one K1+, two Cu2+, and one As5+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Cd by Materials Project

K3Cd is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Cd atoms to form distorted KK8Cd4 cuboctahedra that share corners with twelve equivalent KK8Cd4 cuboctahedra, edges with eight equivalent CdK12 cuboctahedra, edges with sixteen equivalent KK8Cd4 cuboctahedra, faces with four equivalent CdK12 cuboctahedra, and faces with fourteen equivalent KK8Cd4 cuboctahedra. All K–K bond lengths are 4.21 Å. All K–Cd bond lengths are 4.21 Å. Cd is bonded to twelve equivalent K atoms to form CdK12 cuboctahedra that share corners with twelve equivalent CdK12 cuboctahedra, edges with twenty-four equivalent KK8Cd4 cuboctahedra, faces with six equivalent CdK12 cuboctahedra, and faces with twelve equivalent KK8Cd4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KBiO3 by Materials Project

KBiO3 crystallizes in the cubic Pn-3 space group. The structure is three-dimensional. there are two inequivalent K1+ sites. In the first K1+ site, K1+ is bonded in a distorted hexagonal planar geometry to six equivalent O2- atoms. All K–O bond lengths are 2.75 Å. In the second K1+ site, K1+ is bonded in a distorted hexagonal planar geometry to six O2- atoms. There are three shorter (2.75 Å) and three longer (3.06 Å) K–O bond lengths. Bi5+ is bonded to six O2- atoms to form a mixture of corner and edge-sharing BiO6 octahedra. The corner-sharing octahedral tilt angles are 54°. There are a spread of Bi–O bond distances ranging from 2.13–2.18 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 2-coordinate geometry to two equivalent K1+ and two equivalent Bi5+ atoms. In the second O2- site, O2- is bonded to two K1+ and two equivalent Bi5+ atoms to form a mixture of distorted corner and edge-sharing OK2Bi2 tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Tl by Materials Project

K3Tl is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Tl atoms to form distorted KK8Tl4 cuboctahedra that share corners with twelve equivalent KK8Tl4 cuboctahedra, edges with eight equivalent TlK12 cuboctahedra, edges with sixteen equivalent KK8Tl4 cuboctahedra, faces with four equivalent TlK12 cuboctahedra, and faces with fourteen equivalent KK8Tl4 cuboctahedra. All K–K bond lengths are 4.18 Å. All K–Tl bond lengths are 4.18 Å. Tl is bonded to twelve equivalent K atoms to form TlK12 cuboctahedra that share corners with twelve equivalent TlK12 cuboctahedra, edges with twenty-four equivalent KK8Tl4 cuboctahedra, faces with six equivalent TlK12 cuboctahedra, and faces with twelve equivalent KK8Tl4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Mn by Materials Project

K3Mn is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Mn atoms to form distorted KK8Mn4 cuboctahedra that share corners with twelve equivalent KK8Mn4 cuboctahedra, edges with eight equivalent MnK12 cuboctahedra, edges with sixteen equivalent KK8Mn4 cuboctahedra, faces with four equivalent MnK12 cuboctahedra, and faces with fourteen equivalent KK8Mn4 cuboctahedra. All K–K bond lengths are 4.06 Å. All K–Mn bond lengths are 4.06 Å. Mn is bonded to twelve equivalent K atoms to form MnK12 cuboctahedra that share corners with twelve equivalent MnK12 cuboctahedra, edges with twenty-four equivalent KK8Mn4 cuboctahedra, faces with six equivalent MnK12 cuboctahedra, and faces with twelve equivalent KK8Mn4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Th by Materials Project

K3Th is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Th atoms to form distorted KK8Th4 cuboctahedra that share corners with twelve equivalent KK8Th4 cuboctahedra, edges with eight equivalent ThK12 cuboctahedra, edges with sixteen equivalent KK8Th4 cuboctahedra, faces with four equivalent ThK12 cuboctahedra, and faces with fourteen equivalent KK8Th4 cuboctahedra. All K–K bond lengths are 4.26 Å. All K–Th bond lengths are 4.26 Å. Th is bonded to twelve equivalent K atoms to form ThK12 cuboctahedra that share corners with twelve equivalent ThK12 cuboctahedra, edges with twenty-four equivalent KK8Th4 cuboctahedra, faces with six equivalent ThK12 cuboctahedra, and faces with twelve equivalent KK8Th4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Zr by Materials Project

K3Zr is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Zr atoms to form distorted KK8Zr4 cuboctahedra that share corners with twelve equivalent KK8Zr4 cuboctahedra, edges with eight equivalent ZrK12 cuboctahedra, edges with sixteen equivalent KK8Zr4 cuboctahedra, faces with four equivalent ZrK12 cuboctahedra, and faces with fourteen equivalent KK8Zr4 cuboctahedra. All K–K bond lengths are 4.20 Å. All K–Zr bond lengths are 4.20 Å. Zr is bonded to twelve equivalent K atoms to form ZrK12 cuboctahedra that share corners with twelve equivalent ZrK12 cuboctahedra, edges with twenty-four equivalent KK8Zr4 cuboctahedra, faces with six equivalent ZrK12 cuboctahedra, and faces with twelve equivalent KK8Zr4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3U by Materials Project

K3U is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent U atoms to form distorted KK8U4 cuboctahedra that share corners with twelve equivalent KK8U4 cuboctahedra, edges with eight equivalent UK12 cuboctahedra, edges with sixteen equivalent KK8U4 cuboctahedra, faces with four equivalent UK12 cuboctahedra, and faces with fourteen equivalent KK8U4 cuboctahedra. All K–K bond lengths are 4.33 Å. All K–U bond lengths are 4.33 Å. U is bonded to twelve equivalent K atoms to form UK12 cuboctahedra that share corners with twelve equivalent UK12 cuboctahedra, edges with twenty-four equivalent KK8U4 cuboctahedra, faces with six equivalent UK12 cuboctahedra, and faces with twelve equivalent KK8U4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Lu by Materials Project

K3Lu is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Lu atoms to form distorted KK8Lu4 cuboctahedra that share corners with twelve equivalent KK8Lu4 cuboctahedra, edges with eight equivalent LuK12 cuboctahedra, edges with sixteen equivalent KK8Lu4 cuboctahedra, faces with four equivalent LuK12 cuboctahedra, and faces with fourteen equivalent KK8Lu4 cuboctahedra. All K–K bond lengths are 4.30 Å. All K–Lu bond lengths are 4.30 Å. Lu is bonded to twelve equivalent K atoms to form LuK12 cuboctahedra that share corners with twelve equivalent LuK12 cuboctahedra, edges with twenty-four equivalent KK8Lu4 cuboctahedra, faces with six equivalent LuK12 cuboctahedra, and faces with twelve equivalent KK8Lu4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K2CoO3 by Materials Project

K2CoO3 crystallizes in the orthorhombic Cmce space group. The structure is three-dimensional. there are two inequivalent K1+ sites. In the first K1+ site, K1+ is bonded to seven O2- atoms to form distorted KO7 pentagonal bipyramids that share corners with four equivalent KO7 pentagonal bipyramids, a cornercorner with one CoO4 tetrahedra, edges with three equivalent KO7 pentagonal bipyramids, and edges with four equivalent CoO4 tetrahedra. There are a spread of K–O bond distances ranging from 2.76–2.94 Å. In the second K1+ site, K1+ is bonded in a 5-coordinate geometry to five O2- atoms. There are a spread of K–O bond distances ranging from 2.77–2.94 Å. Co4+ is bonded to four O2- atoms to form CoO4 tetrahedra that share a cornercorner with one KO7 pentagonal bipyramid, corners with two equivalent CoO4 tetrahedra, and edges with four equivalent KO7 pentagonal bipyramids. There is two shorter (1.76 Å) and two longer (1.86 Å) Co–O bond length. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded in a distorted bent 150 degrees geometry to two equivalent K1+ and two equivalent Co4+ atoms. In the second O2- site, O2- is bonded in a 1-coordinate geometry to five K1+ and one Co4+ atom. In the third O2- site, O2- is bonded to five K1+ and one Co4+ atom to form a mixture of distorted edge and corner-sharing OK5Co octahedra. The corner-sharing octahedral tilt angles are 16°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3In by Materials Project

K3In is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent In atoms to form distorted KK8In4 cuboctahedra that share corners with twelve equivalent KK8In4 cuboctahedra, edges with eight equivalent InK12 cuboctahedra, edges with sixteen equivalent KK8In4 cuboctahedra, faces with four equivalent InK12 cuboctahedra, and faces with fourteen equivalent KK8In4 cuboctahedra. All K–K bond lengths are 4.12 Å. All K–In bond lengths are 4.12 Å. In is bonded to twelve equivalent K atoms to form InK12 cuboctahedra that share corners with twelve equivalent InK12 cuboctahedra, edges with twenty-four equivalent KK8In4 cuboctahedra, faces with six equivalent InK12 cuboctahedra, and faces with twelve equivalent KK8In4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Hf by Materials Project

K3Hf is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Hf atoms to form distorted KK8Hf4 cuboctahedra that share corners with twelve equivalent KK8Hf4 cuboctahedra, edges with eight equivalent HfK12 cuboctahedra, edges with sixteen equivalent KK8Hf4 cuboctahedra, faces with four equivalent HfK12 cuboctahedra, and faces with fourteen equivalent KK8Hf4 cuboctahedra. All K–K bond lengths are 4.09 Å. All K–Hf bond lengths are 4.09 Å. Hf is bonded to twelve equivalent K atoms to form HfK12 cuboctahedra that share corners with twelve equivalent HfK12 cuboctahedra, edges with twenty-four equivalent KK8Hf4 cuboctahedra, faces with six equivalent HfK12 cuboctahedra, and faces with twelve equivalent KK8Hf4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3TlAu5 by Materials Project

K3Au5Tl crystallizes in the orthorhombic Imma space group. The structure is three-dimensional. there are two inequivalent K sites. In the first K site, K is bonded in a 2-coordinate geometry to ten Au and one Tl atom. There are a spread of K–Au bond distances ranging from 3.41–3.82 Å. The K–Tl bond length is 3.78 Å. In the second K site, K is bonded in a 6-coordinate geometry to six equivalent Au atoms. There are two shorter (3.61 Å) and four longer (3.65 Å) K–Au bond lengths. There are three inequivalent Au sites. In the first Au site, Au is bonded to six equivalent K and six Au atoms to form a mixture of edge and face-sharing AuK6Au6 cuboctahedra. There are four shorter (2.86 Å) and two longer (2.92 Å) Au–Au bond lengths. In the second Au site, Au is bonded in a distorted q6 geometry to four equivalent K and six Au atoms. There are two shorter (2.84 Å) and two longer (2.89 Å) Au–Au bond lengths. In the third Au site, Au is bonded in a 1-coordinate geometry to six K, three Au, and one Tl atom. The Au–Tl bond length is 2.79 Å. Tl is bonded in a distorted water-like geometry to two equivalent K and two equivalent Au atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Cr by Materials Project

K3Cr is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Cr atoms to form distorted KK8Cr4 cuboctahedra that share corners with twelve equivalent KK8Cr4 cuboctahedra, edges with eight equivalent CrK12 cuboctahedra, edges with sixteen equivalent KK8Cr4 cuboctahedra, faces with four equivalent CrK12 cuboctahedra, and faces with fourteen equivalent KK8Cr4 cuboctahedra. All K–K bond lengths are 4.18 Å. All K–Cr bond lengths are 4.18 Å. Cr is bonded to twelve equivalent K atoms to form distorted CrK12 cuboctahedra that share corners with twelve equivalent CrK12 cuboctahedra, edges with twenty-four equivalent KK8Cr4 cuboctahedra, faces with six equivalent CrK12 cuboctahedra, and faces with twelve equivalent KK8Cr4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Na by Materials Project

K3Na is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Na atoms to form distorted KK8Na4 cuboctahedra that share corners with twelve equivalent KK8Na4 cuboctahedra, edges with eight equivalent NaK12 cuboctahedra, edges with sixteen equivalent KK8Na4 cuboctahedra, faces with four equivalent NaK12 cuboctahedra, and faces with fourteen equivalent KK8Na4 cuboctahedra. All K–K bond lengths are 4.46 Å. All K–Na bond lengths are 4.46 Å. Na is bonded to twelve equivalent K atoms to form distorted NaK12 cuboctahedra that share corners with twelve equivalent NaK12 cuboctahedra, edges with twenty-four equivalent KK8Na4 cuboctahedra, faces with six equivalent NaK12 cuboctahedra, and faces with twelve equivalent KK8Na4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on K3Cu by Materials Project

K3Cu is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. K is bonded to eight equivalent K and four equivalent Cu atoms to form distorted KK8Cu4 cuboctahedra that share corners with twelve equivalent KK8Cu4 cuboctahedra, edges with eight equivalent CuK12 cuboctahedra, edges with sixteen equivalent KK8Cu4 cuboctahedra, faces with four equivalent CuK12 cuboctahedra, and faces with fourteen equivalent KK8Cu4 cuboctahedra. All K–K bond lengths are 4.11 Å. All K–Cu bond lengths are 4.11 Å. Cu is bonded to twelve equivalent K atoms to form distorted CuK12 cuboctahedra that share corners with twelve equivalent CuK12 cuboctahedra, edges with twenty-four equivalent KK8Cu4 cuboctahedra, faces with six equivalent CuK12 cuboctahedra, and faces with twelve equivalent KK8Cu4 cuboctahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on KHfMg30O31 by Materials Project

KMg30HfO31 crystallizes in the orthorhombic Pmm2 space group. The structure is three-dimensional. K is bonded to six O atoms to form KO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of K–O bond distances ranging from 2.36–2.38 Å. There are sixteen inequivalent Mg sites. In the first Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with two equivalent KO6 octahedra, corners with two equivalent HfO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–1°. There are a spread of Mg–O bond distances ranging from 1.95–2.19 Å. In the second Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, and edges with twelve MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.95–2.23 Å. In the third Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent KO6 octahedra, corners with two equivalent MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 1.96–2.21 Å. In the fourth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, and edges with eight MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are three shorter (2.12 Å) and two longer (2.19 Å) Mg–O bond lengths. In the fifth Mg site, Mg is bonded to six O atoms to form a mixture of edge and corner-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.12–2.17 Å. In the sixth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with two equivalent MgO6 octahedra, corners with two equivalent HfO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Mg–O bond distances ranging from 2.14–2.16 Å. In the seventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, an edgeedge with one HfO6 octahedra, edges with seven MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 3–14°. There are a spread of Mg–O bond distances ranging from 2.13–2.22 Å. In the eighth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, edges with nine MgO6 octahedra, and edges with three MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–3°. There are a spread of Mg–O bond distances ranging from 2.15–2.18 Å. In the ninth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one KO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–11°. There are a spread of Mg–O bond distances ranging from 2.15–2.20 Å. In the tenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 2–6°. There are a spread of Mg–O bond distances ranging from 2.10–2.22 Å. In the eleventh Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 1–10°. There are a spread of Mg–O bond distances ranging from 2.14–2.19 Å. In the twelfth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one HfO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 2–6°. There are a spread of Mg–O bond distances ranging from 2.11–2.22 Å. In the thirteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one KO6 octahedra, edges with nine MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.15–2.19 Å. In the fourteenth Mg site, Mg is bonded to five O atoms to form MgO5 square pyramids that share corners with four MgO6 octahedra, corners with five MgO5 square pyramids, an edgeedge with one HfO6 octahedra, and edges with seven MgO6 octahedra. The corner-sharing octahedral tilt angles are 3°. There are a spread of Mg–O bond distances ranging from 2.13–2.22 Å. In the fifteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with six MgO6 octahedra, an edgeedge with one KO6 octahedra, and edges with eleven MgO6 octahedra. The corner-sharing octahedra tilt angles range from 0–11°. There are a spread of Mg–O bond distances ranging from 2.15–2.19 Å. In the sixteenth Mg site, Mg is bonded to six O atoms to form MgO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, an edgeedge with one HfO6 octahedra, edges with nine MgO6 octahedra, and edges with two MgO5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are a spread of Mg–O bond distances ranging from 2.12–2.21 Å. Hf is bonded to six O atoms to form HfO6 octahedra that share corners with four MgO6 octahedra, corners with two equivalent MgO5 square pyramids, edges with ten MgO6 octahedra, and edges with two equivalent MgO5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Hf–O bond distances ranging from 2.09–2.17 Å. There are seventeen inequivalent O sites. In the first O site, O is bonded to one K and five Mg atoms to form a mixture of edge and corner-sharing OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the second O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the third O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the fourth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with six OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fifth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with four OKMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 1–5°. In the sixth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the seventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°. In the eighth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the ninth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 2–5°. In the tenth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with six OHfMg5 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the eleventh O site, O is bonded to five Mg and one Hf atom to form OHfMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the twelfth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with eleven OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the thirteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fourteenth O site, O is bonded to one K and five Mg atoms to form OKMg5 octahedra that share corners with six OHfMg5 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the fifteenth O site, O is bonded to five Mg and one Hf atom to form a mixture of edge and corner-sharing OHfMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–9°. In the sixteenth O site, O is bonded to six Mg atoms to form OMg6 octahedra that share corners with six OMg6 octahedra and edges with twelve OKMg5 octahedra. The corner-sharing octahedra tilt angles range from 0–7°. In the seventeenth O site, O is bonded to six Mg atoms to form a mixture of edge and corner-sharing OMg6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°.

36 MATERIALS SCIENCE↗