Materials Data on K6Al32O51 by Materials Project

K6Al32O51 is beta indium sulfide-derived structured and crystallizes in the monoclinic Cm space group. The structure is three-dimensional. there are four inequivalent K sites. In the first K site, K is bonded in a 1-coordinate geometry to five O atoms. There are a spread of K–O bond distances ranging from 2.70–3.11 Å. In the second K site, K is bonded in a 5-coordinate geometry to five O atoms. There are a spread of K–O bond distances ranging from 2.52–3.08 Å. In the third K site, K is bonded in a 1-coordinate geometry to five O atoms. There are a spread of K–O bond distances ranging from 2.69–3.11 Å. In the fourth K site, K is bonded in a 5-coordinate geometry to five O atoms. There are a spread of K–O bond distances ranging from 2.52–3.08 Å. There are nineteen inequivalent Al sites. In the first Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with six AlO4 tetrahedra and edges with six AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.87–1.94 Å. In the second Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.85–2.03 Å. In the third Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.84–2.03 Å. In the fourth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.84–2.02 Å. In the fifth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with six AlO4 tetrahedra and edges with six AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.88–1.95 Å. In the sixth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 52–59°. There is three shorter (1.81 Å) and one longer (1.85 Å) Al–O bond length. In the seventh Al site, Al is bonded to four O atoms to form AlO4 tetrahedra that share corners with six AlO6 octahedra and a cornercorner with one AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 52–54°. There is three shorter (1.77 Å) and one longer (1.78 Å) Al–O bond length. In the eighth Al site, Al is bonded to four O atoms to form AlO4 tetrahedra that share corners with six AlO6 octahedra and a cornercorner with one AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 54–55°. There is one shorter (1.76 Å) and three longer (1.80 Å) Al–O bond length. In the ninth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 50–58°. There is one shorter (1.78 Å) and three longer (1.83 Å) Al–O bond length. In the tenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with four AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.74–2.10 Å. In the eleventh Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with four AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.74–2.10 Å. In the twelfth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.84–2.03 Å. In the thirteenth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 49–63°. There are a spread of Al–O bond distances ranging from 1.80–1.94 Å. In the fourteenth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 50–59°. There is one shorter (1.79 Å) and three longer (1.83 Å) Al–O bond length. In the fifteenth Al site, Al is bonded to four O atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedra tilt angles range from 54–55°. There is one shorter (1.67 Å) and three longer (1.82 Å) Al–O bond length. In the sixteenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.83–2.05 Å. In the seventeenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with four AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.74–2.11 Å. In the eighteenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.84–2.02 Å. In the nineteenth Al site, Al is bonded to six O atoms to form AlO6 octahedra that share corners with five AlO4 tetrahedra and edges with five AlO6 octahedra. There are a spread of Al–O bond distances ranging from 1.83–2.05 Å. There are thirty inequivalent O sites. In the first O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the second O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the third O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the fourth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the fifth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the sixth O site, O is bonded in a distorted tetrahedral geometry to one K and three Al atoms. In the seventh O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the eighth O site, O is bonded in a distorted tetrahedral geometry to one K and three Al atoms. In the ninth O site, O is bonded in a linear geometry to two Al atoms. In the tenth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the eleventh O site, O is bonded in a 4-coordinate geometry to one K and three Al atoms. In the twelfth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the thirteenth O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the fourteenth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the fifteenth O site, O is bonded in a distorted trigonal non-coplanar geometry to one K and two Al atoms. In the sixteenth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the seventeenth O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the eighteenth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the nineteenth O site, O is bonded in a 4-coordinate geometry to one K and three Al atoms. In the twentieth O site, O is bonded in a single-bond geometry to six K and one Al atom. In the twenty-first O site, O is bonded in a distorted tetrahedral geometry to one K and three Al atoms. In the twenty-second O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the twenty-third O site, O is bonded in a 3-coordinate geometry to one K and three Al atoms. In the twenty-fourth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the twenty-fifth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the twenty-sixth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the twenty-seventh O site, O is bonded in a distorted trigonal non-coplanar geometry to one K and two equivalent Al atoms. In the twenty-eighth O site, O is bonded in a distorted tetrahedral geometry to one K and three Al atoms. In the twenty-ninth O site, O is bonded in a rectangular see-saw-like geometry to four Al atoms. In the thirtieth O site, O is bonded in a 4-coordinate geometry to one K and three Al atoms.

K₆Al₃₂O₅₁为β-硫化铟衍生结构，结晶于单斜晶系Cm空间群，其结构为三维框架。该体系存在4个不等价的钾（K）位点：在第一个K位点中，K原子以1配位几何与5个氧原子成键，K-O键长分布范围为2.70~3.11 Å；在第二个K位点中，K原子以5配位几何与5个氧原子成键，K-O键长分布范围为2.52~3.08 Å；在第三个K位点中，K原子以1配位几何与5个氧原子成键，K-O键长分布范围为2.69~3.11 Å；在第四个K位点中，K原子以5配位几何与5个氧原子成键，K-O键长分布范围为2.52~3.08 Å。

该体系存在19个不等价的铝（Al）位点：
1. 第一个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与6个AlO₄四面体共享顶角，同时与6个AlO₆八面体共享棱边，Al-O键长分布范围为1.87~1.94 Å。
2. 第二个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与5个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.85~2.03 Å。
3. 第三个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与5个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.84~2.03 Å。
4. 第四个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与5个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.84~2.02 Å。
5. 第五个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与6个AlO₄四面体共享顶角，同时与6个AlO₆八面体共享棱边，Al-O键长分布范围为1.88~1.95 Å。
6. 第六个Al位点：Al原子与4个O原子配位形成AlO₄四面体，该四面体为顶角共享结构，其顶角共享八面体的倾斜角范围为52°~59°，Al-O键长包含3条较短键（1.81 Å）与1条较长键（1.85 Å）。
7. 第七个Al位点：Al原子与4个O原子配位形成AlO₄四面体，该四面体与6个AlO₆八面体共享顶角，同时与1个AlO₄四面体通过顶角-顶角相连，其顶角共享八面体的倾斜角范围为52°~54°，Al-O键长包含3条较短键（1.77 Å）与1条较长键（1.78 Å）。
8. 第八个Al位点：Al原子与4个O原子配位形成AlO₄四面体，该四面体与6个AlO₆八面体共享顶角，同时与1个AlO₄四面体通过顶角-顶角相连，其顶角共享八面体的倾斜角范围为54°~55°，Al-O键长包含1条较短键（1.76 Å）与3条较长键（1.80 Å）。
9. 第九个Al位点：Al原子与4个O原子配位形成顶角共享的AlO₄四面体，其顶角共享八面体的倾斜角范围为50°~58°，Al-O键长包含1条较短键（1.78 Å）与3条较长键（1.83 Å）。
10. 第十个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与4个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.74~2.10 Å。
11. 第十一个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与4个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.74~2.10 Å。
12. 第十二个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与5个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.84~2.03 Å。
13. 第十三个Al位点：Al原子与4个O原子配位形成顶角共享的AlO₄四面体，其顶角共享八面体的倾斜角范围为49°~63°，Al-O键长分布范围为1.80~1.94 Å。
14. 第十四个Al位点：Al原子与4个O原子配位形成顶角共享的AlO₄四面体，其顶角共享八面体的倾斜角范围为50°~59°，Al-O键长包含1条较短键（1.79 Å）与3条较长键（1.83 Å）。
15. 第十五个Al位点：Al原子与4个O原子配位形成顶角共享的AlO₄四面体，其顶角共享八面体的倾斜角范围为54°~55°，Al-O键长包含1条较短键（1.67 Å）与3条较长键（1.82 Å）。
16. 第十六个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与5个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.83~2.05 Å。
17. 第十七个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与4个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.74~2.11 Å。
18. 第十八个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与5个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.84~2.02 Å。
19. 第十九个Al位点：Al原子与6个O原子配位形成AlO₆八面体，该八面体与5个AlO₄四面体共享顶角，同时与5个AlO₆八面体共享棱边，Al-O键长分布范围为1.83~2.05 Å。

该体系存在30个不等价的氧（O）位点：
1. 第一个O位点：O原子以3配位几何与1个K原子和3个Al原子成键。
2. 第二个O位点：O原子以3配位几何与1个K原子和3个Al原子成键。
3. 第三个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
4. 第四个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
5. 第五个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
6. 第六个O位点：O原子以畸变四面体配位几何与1个K原子和3个Al原子成键。
7. 第七个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
8. 第八个O位点：O原子以畸变四面体配位几何与1个K原子和3个Al原子成键。
9. 第九个O位点：O原子以直线型配位几何与2个Al原子成键。
10. 第十个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
11. 第十一个O位点：O原子以4配位几何与1个K原子和3个Al原子成键。
12. 第十二个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
13. 第十三个O位点：O原子以3配位几何与1个K原子和3个Al原子成键。
14. 第十四个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
15. 第十五个O位点：O原子以畸变三角非共面配位几何与1个K原子和2个等价Al原子成键。
16. 第十六个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
17. 第十七个O位点：O原子以3配位几何与1个K原子和3个Al原子成键。
18. 第十八个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
19. 第十九个O位点：O原子以4配位几何与1个K原子和3个Al原子成键。
20. 第二十个O位点：O原子以单键配位几何与6个K原子和1个Al原子成键。
21. 第二十一个O位点：O原子以畸变四面体配位几何与1个K原子和3个Al原子成键。
22. 第二十二个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
23. 第二十三个O位点：O原子以3配位几何与1个K原子和3个Al原子成键。
24. 第二十四个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
25. 第二十五个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
26. 第二十六个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
27. 第二十七个O位点：O原子以畸变三角非共面配位几何与1个K原子和2个等价Al原子成键。
28. 第二十八个O位点：O原子以畸变四面体配位几何与1个K原子和3个Al原子成键。
29. 第二十九个O位点：O原子以矩形跷跷板状配位几何与4个Al原子成键。
30. 第三十个O位点：O原子以4配位几何与1个K原子和3个Al原子成键。