Formal Crystallography 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 a b c    space filling defined by 3 vectors parallelipiped arbitrary coord system lattice pts at corners +

6 or 7 crystal systems 14 lattices Can be redefined as a non- primitive hexagonal cell

Crystallographic notation Position: –x, y, z –fractional coordinates Direction: –x 2 -x 1, y 2 -y 1, z 2 -z 1 –no magnitude –specific: [t u v] –family:  t u v  x, y, z cubic system (x 1, y 1, z 1 ) (x 2, y 2, z 2 )

Specific vs. family square lattice a1a1 a2a2 specific: [1, 2] family: includes [1 2],[2 1], [1 2],[2 1]    [2 1],[1 2], [2 1],[1 2]    Do not include those permutations that imply a change in handedness Correction to lecture: family is distinct Generically: = [t, u], [u, -t], [-t, -u], [-u, t] also for planes

Crystallographic notation Plane –find intercepts –compute 1/intercept –clear fractions Example –(0 2 1) cubic system ½ axisinterceptinverseclear fractions a1a1  00 a2a2 ½22 a3a3 111 specific: (h k l) family: {h k l}

axisinterceptinverseclear fractions a1a1  00 a2a2 112 a3a3 2½1 Plane –find intercepts –compute 1/intercept –clear fractions Example –(0 2 1) Crystallographic notation cubic system ½

Plane –find intercepts –compute 1/intercept –clear fractions Example –(0 1 2) Crystallographic notation cubic system ½ axisinterceptinverseclear fractions a1a1  00 a2a2 2½1 a3a3 112

More examples front edge (2 0 2) (1 1 -2) (1 1 2) _

Specific vs. Family {2 0 2} cubic c tetragonal (2 0 2) (0 2 2) (2 2 0) (2 0 2) (2 0 2) (2 0 2) (0 2 2) (0 2 2) (0 2 2) (2 2 0) (2 2 0) (2 2 0)             X X X X {2 0 2}

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

H What’s Missing? Long chain molecules with repeated units Molecules formed by covalent bonds Secondary bonds link molecules into solids C C H H H methane C H many units

Polymer Synthesis Traditional synthesis –Initiation, using a catalyst that creates a free radical –Propagation –Termination R  + C=C R…… C – C  + C=C R…… C – C  +  C – C……R unpaired electron C=C H H H H  R – C – C   R……C – C – C – C   R –(C-C) n – R

Polydispersity Traditional synthesis  large variation in chain length number average # of polymer chains molecular weight # of polymer chains of M i total number of chains molecular weight weight average weight of polymer chains of M i total weight of all chains width is a measure of polydispersity = weight fraction Degree of polymerization –Average # of mer units/chain Average chain molecular weight by number by weight mer molecular weight

New modes of synthesis “Living polymerization” –Initiation occurs instantaneously –Chemically eliminate possibility of random termination –Polymer chains grow until monomer is consumed –Each grows for a fixed (identical) period

Polymers Homopolymer –Only one type of ‘mer’ Copolymer –Two or more types of ‘mers’ Block copolymer –Long regions of each type of ‘mer’ Bifunctional mer –Can make two bonds, e.g. ethylene  linear polymer Trifunctional mer –Can make three bonds  branched polymer

Polymers Linear Branched Cross-linked C CCC C C CC C C = C H H H H

Polymers C CCC C C CC C C = C H H H H 109.5° H out H in Placement of side groups is fixed once polymer is formed Example side group: styrene R = R

C CCC C C CC C R RR R C = C H H Cl H Isotactic C CCC C C CC C R RRR Syndiotactic CCCC C C CC C R RR R Atactic

Thermal Properties –Thermoplastics Melt (on heating) and resolidify (on cooling) Linear polymers –Thermosets Soften, decompose irreversibly on heating Crosslinked Crystallinity Linear: more crystalline than branched or crosslinked Crystalline has higher density than amorphous