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Graphite

Allotropes of C. Graphite. Diamond. Buckminster Fullerene 1985. Graphene 2004. Carbon Nanotubes 1991. Graphite. Sp 2 hybridization  3 covalent bonds  Hexagonal sheets. a = 2 d cos 30° = √3 d. y. x. d = 1.42 Å a = 2.46 Å. =120. b=a. a. Graphite. a = 2.46 Å

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Graphite

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  1. Allotropes of C Graphite Diamond Buckminster Fullerene1985 Graphene2004 Carbon Nanotubes1991

  2. Graphite Sp2 hybridization  3 covalent bonds  Hexagonal sheets a = 2 d cos 30° = √3 d y x d = 1.42 Å a = 2.46 Å =120 b=a a

  3. Graphite a = 2.46 Å c = 6.70 Å Lattice: Simple Hexagonal Motif: 4 carbon atoms A c B y x A www.scifun.ed.ac.uk/

  4. Graphite Highly Anisotropic: Properties are very different in the a and c directions Uses: Solid lubricant Pencils (clay + graphite, hardness depends on fraction of clay) carbon fibre www.sciencemuseum.org.uk/

  5. Diamond Sp3 hybridization  4 covalent bonds  Tetrahedral bonding Location of atoms: 8 Corners 6 face centres 4 one on each of the 4 body diagonals

  6. Diamond Cubic Crystal: Lattice & motif? y 0,1 0,1 R M D C y M R L S N P Q Q T D 0,1 L S K C N K T A x B B A P x 0,1 0,1 Projection of the unit cell on the bottom face of the cube Diamond Cubic Crystal = FCC lattice + motif: 000; ¼¼¼

  7. Diamond Coordination number 4 Face Inside Corners Effective number of atoms in the unit cell = Relaton between lattice parameter and atomic radius Packing efficiency

  8. Diamond Cubic Crystal Structures C Si Ge Gray Sn a (Å) 3.57 5.43 5.65 6.46

  9. Equiatomic binary AB compounds having diamond cubic like structure y 0,1 0,1 IV-IV compound: SiC III-V compound: AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb II-VI compound: ZnO, ZnS, CdS, CdSe, CdTe I-VII compound: CuCl, AgI 0,1 S 0,1 0,1

  10. USES: Diamond Abrasive in polishing and grinding wire drawing dies Si, Ge, compounds: semiconducting devices SiC abrasives, heating elements of furnaces

  11. Allotropes of C Graphite Diamond Buckminster Fullerene1985 Graphene2004 Carbon Nanotubes1991

  12. C60 Buckminsterfullerene H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl and R.E. Smalley Nature 318 (1985) 162-163 Long-chain carbon molecules in interstellar space A carbon atom at each vertex 1996 Nobel Prize

  13. Americanarchitect, author, designer, futurist, inventor, and visionary. He was expelled from Harvard twice: 1. first for spending all his money partying with a Vaudeville troupe, 2. for his "irresponsibility and lack of interest". what he, as an individual, could do to improve humanity's condition, which large organizations, governments, and private enterprises inherently could not do.

  14. Montreal Biosphere in Montreal, Canada

  15. Truncated Icosahedron Icosahedron: A Platonic solid (a regular solid) Truncated Icosahedron: An Archimedean solid

  16. A regular polygon A polygon with all sides equal and all angles equal Square regular Rectangle unequal sides not regular Rhombusunequal angles not regular

  17. Regular Polygons: All sides equal all angles equal Triangle square pentagon hexagon… 3 4 5 6… A regular n-gon with any n >= 3 is possible There are infinitely many regular polygons

  18. 3D: Regular Polyhedra or Platonic Solids All faces regular congruent polygons, all corners identical. Tetrahedron Cube How many regular solids?

  19. There are 5 and only 5 Platonic or regular solids ! Tetrahedron Cube Octahedron Dodecahedron Icosahedron

  20. Tetrahedron 4 6 4 • Octahedron 6 12 8 • Cube 8 12 6 • Icosahedron 12 30 20 • Dodecahedron 20 30 12 Duals Duals Euler’s Polyhedron Formula V-E+F=2

  21. Duality Tetrahedron Self-Dual Octahedron-Cube Icosahedron-Dodecahedron

  22. Proof of Five Platonic Solids At any vertex at least three faces should meet The sum of polygonal angles at any vertex should be less the 360 Triangles (60) 3 Tetrahedron 4 Octahedron 5 Icosahedron 6 or more: not possible Square (90) 3 Cube 4 or more: not possible Pentagon (108) 3 Dodecahedron

  23. Dense packings of the Platonic and Archimedean solids S. Torquato & Y. Jiao Nature, Aug 13, 2009

  24. Truncated Icosahedron: V=60, E=90, F=32

  25. Synthesis of Fullerene

  26. Arc Evaporation of graphite in inert atmosphere M. CARAMAN, G. LAZAR, M. STAMATE, I. LAZAR

  27. Nature391, 59-62 (1 January 1998) Electronic structure of atomically resolved carbon nanotubes Jeroen W. G. Wilder, Liesbeth C. Venema, Andrew G. Rinzler, Richard E. Smalley & Cees Dekker

  28. Structural features of carbon nanotubes a1 zigzig (n,0) =chiral angle a2 wrapping vector (n,m)=(6,3) armchair (n,n)

  29. Source: wiki

  30. Electrical For a given (n,m) nanotube, if n = m, the nanotube is metallic; if n − m is a multiple of 3, then the nanotube is semiconducting with a very small band gap, otherwise the nanotube is a moderate semiconductor. Thus all armchair (n=m) nanotubes are metallic, and nanotubes (5,0), (6,4), (9,1), etc. are semiconducting. In theory, metallic nanotubes can carry an electrical current density of 4×109 A/cm2 which is more than 1,000 times greater than metals such as copper[23].

  31. While the fantasy of a space elevator has been around for about 100 years, the idea became slightly more realistic by the 1991 discovery of "carbon nanotubes,"

  32. The Space Engineering and Science Institute presents The 2009 Space Elevator Conference Pioneer the next frontier this summer with a four-day conference on the Space Elevator in Redmond, Washington at the Microsoft Conference Center. Thursday, August 13 through Sunday, August 16, 2009 Register Today!

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