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Announcement

Announcement. Subject to change. Close-packed Structures. Metallic materials have isotropic bonding In 2-D close-packed spheres generate a hexagonal array In 3-D, the close-packed layers can be stacked in all sorts of sequences Most common are A B A B A B .. A B C A B C A B C ….

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Announcement

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  1. Announcement Subject to change

  2. Close-packed Structures • Metallic materials have isotropic bonding • In 2-D close-packed spheres generate a hexagonal array • In 3-D, the close-packed layers can be stacked in all sorts of sequences • Most common are • ABABAB.. • ABCABCABC… Hexagonal close-packed Cubic close-packed

  3. AB C ABCABC…. Cubic???

  4. What are the unit cell dimensions? a face diagonal is close-packed direction |a1| = |a2| = |a3| a1 = a2 = a3 = 90°

  5. Cubic Close-packed Structure |a1| = |a2| = |a3| a1 = a2 = a3 only one cell parameter to be specified coordination number? 12 atoms per unit cell? 4 lattice points per unit cell? 4 CCP atoms per lattice point? 1 a unit cell with more than one lattice point is a non-primitive cell lattice type of CCP is called “face-centered cubic” CCP structure is often simply called the FCC structure (misleading)

  6. Cubic “Loose-packed” Structure Body-centered cubic (BCC) 8 coordination number? 2 atoms per unit cell? a 2 lattice points per unit cell? 1 atoms per lattice point? another example of a non-primitive cell body diagonal is closest-packed direction lattice type of ‘CLP’ is “body-centered cubic” no common name that distinguishes lattice type from structure type |a1| = |a2| = |a3| a1 = a2 = a3 = 90°

  7. Summary: Common Metal Structures hcp bcc ccp (fcc) ABCABC not close-packed ABABAB c • space filling • defined by 3 vectors • parallelipiped • arbitrary coord system • lattice pts at corners + Unit Cell a b b g a

  8. c a b b g a The Crystalline State • Crystalline • Periodic arrangement of atoms • Pattern is repeated by translation • Three translation vectors define: • Coordinate system • Crystal system • Unit cell shape • Lattice points • Points of identical environment • Related by translational symmetry • Lattice = array of lattice points

  9. 6 or 7 crystal systems 14 lattices

  10. Ionic Bonding & Structures Isotropic bonding; alternate anions and cations Which is more stable?  – – – – – – + – – + – – – – – – – + – – – Just barely stable

  11. Ionic Bonding & Structures • Isotropic bonding • Maximize # of bonds, subject to constraints • Maintain stoichiometry • Alternate anions and cations • Like atoms should not touch • ‘Radius Ratio Rules’ – rather, guidelines • Develop assuming rc < RA • But inverse considerations also apply • n-fold coordinated atom must be at least some size

  12. central atom drawn smaller than available space for clarity http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/Lecture3/Lec3.html#anchor4

  13. Radius Ratio Rules Consider: CN = 6, 8 12

  14. rc + RA 2RA rc + RA 2RA Octahedral Coordination: CN=6 a

  15. 2(rc + RA) 2RA Cubic Coordination: CN = 8 a

  16. 2RA rc + RA Cuboctahedral: CN = 12 rc + RA = 2RA rc = RA rc/RA = 1

  17. Radius Ratio Rules if rc is smaller than fRA, then the space is too big and the structure is unstable

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