Metallic –Electropositive: give up electrons Ionic –Electronegative/Electropositive Colavent –Electronegative: want electrons –Shared electrons along bond direction Types of Primary Chemical Bonds Isotropic, filled outer shells e- Close-packed structures

mirror plane (glide plane) a1a1 a2a2 high symmetry locations are good candidates for lattice points unit cell not a unit cell 6-fold rotation axis 2-fold rotation axes 3-fold rotation axes Definitions Lattice point Unit cell Lattice parameters Atoms per unit cell Symmetry operations Fractional coordinates Coordination number

A B

A C

ABABBABABA….A

ACACCACACA….A

ABABABCABC….C

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

ABABBABABA….A

A B C A A at (0,0) B at (2/3, 1/3) C at (1/3, 2/3) let atomic radius be R | a 1 | = | a 2 | = 2R A What are the unit cell dimensions? A A 2R2R R 3R3R  face diagonal = 2  3R = AA A AB = 1/3 (face diagonal) c a2a2 a1a1 ABCA { ½c½c 2R2R 2-D fractional coordinates

Hexagonal Close-packed Structure | a 1 | = | a 2 | = 2R  1 =  2 = 90°;  = 120° ideal: atoms per unit cell? coordination number? lattice points per unit cell? a unit cell with only one lattice point is a primitive cell 12 atoms per lattice point? reminder: the hexagon is not an acceptable unit cell shape HCP lattice type of HCP is called “primitive hexagonal”

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

ABABABCABC….C

What are the unit cell dimensions? face diagonal is close-packed direction a | a 1 | = | a 2 | = | a 3 |  1 =  2 =  3 = 90°

Cubic Close-packed Structure only one cell parameter to be specified | a 1 | = | a 2 | = | a 3 |  1 =  2 =  3 atoms per unit cell? coordination number? lattice points per unit cell? a unit cell with more than one lattice point is a non-primitive cell 12 atoms per lattice point? CCP structure is often simply called the FCC structure (misleading) lattice type of CCP is called “face-centered cubic” CCP

Cubic “Loose-packed” Structure Body-centered cubic (BCC) body diagonal is closest- packed direction a | a 1 | = | a 2 | = | a 3 |  1 =  2 =  3 = 90° atoms per unit cell? coordination number? lattice points per unit cell? 8 atoms per lattice point? another example of a non-primitive cell no common name that distinguishes lattice type from structure type lattice type of ‘CLP’ is “body-centered cubic”

Summary: Common Metal Structures hcp ccp (fcc) bcc ABABAB ABCABCnot close-packed Hexagonal unit cell Specify: a, c Hexagonal implies: | a 1 | = | a 2 | = a  = 120°;  =  = 90° Cubic unit cells Specify: a Cubic implies: | a 1 | = | a 2 | = | a 3 | = a  =  =  = 90°

Metals