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

Metals single element, fairly electropositive elements similar in electronegativity

cation anion Ionic Compounds elements differing in electronegativity

Covalent Compounds s2p2s2p2 s2p1s2p1 s2p3s2p3 sp 3 s2s2 s2p4s2p4

Hybridized Bonds one s + three p orbitals  4 (x 2) electron states (resulting orbital is a combination) sp 3 hybridization             diamond also methane: CH 4 Elemental carbon (no other elements)

Covalent Structures Recall: zinc blende  both species tetrahedral ZnS:+2 -2 GaAs:+3 -3 or sp 3 single element: C or Si or Sn diamond S Zn

Another way to hybridize Elemental carbon (no other elements) sp 2 hybridization     graphite                                     one s + two p orbitals  3 (x 2) electron states (resulting orbital is a combination) one unchanged p orbital trigonal symmetry

Forms of carbon with sp 2 bonds Nobel Prize Physics, 2010 Nobel Prize Chemistry, 1996 Graphene Fullerene Nanotube source: Wikipedia Graphite* *

Structural Characteristics Metals –Close-packed structures (CN = 12) –Slightly less close-packed (CN = 8) Ionic structures –Close-packed with constraints –CN = 4 to 8, sometimes 12 Covalent structures –Not close-packed, bonding is directional Any can be strongly or weakly bonded (T m )

Diamond vs. CCP 8 atoms/cell, CN = 44 atoms/cell, CN = 12 ½ tetrahedral sites filled

Computing density Establish unit cell contents Compute unit cell mass Compute unit cell volume –Unit cell constant, a, given (or a and c, etc.) –Or estimate based on atomic/ionic radii Compute mass/volume, g/cc Example: NaCl –Contents = 4 Na + 4 Cl –Mass = 4(atom mass Na + atomic mass Cl)/N o –Vol = a 3 –Units = Avogardo’s # Cl Na

Single Crystal vs. Polycrystalline Rb 3 H(SO 4 ) 2 Ba(Zr,Y)O 3-  Periodicity extends uninterrupted throughout entirety of the sample External habit often reflects internal symmetry Regions of uninterrupted periodicity amalgamated into a larger compact = grains delineated by grain boundaries Quartz (SiO 2 ) Diamond

Isotropic vs. Anisotropic * graphite*diamond polycrystalline averaging

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

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

Polymer Configurations 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

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 +

hcp ccp (fcc) bcc 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° But the two types of cubic unit cells are different!

6 or 7 crystal systems 14 lattices a, b, c, , ,  – all arbitrary a, b, c – arbitrary a, c – arbitrary b = a  =  = 90 a – arbitrary; a = b = c  – arbitrary;  =  =  C or A centered for  = arbitrary a, c – arbitrary a – arbitrary a, b, c – arbitrary  =  = 90

Centered Lattices b a b a b a conventional choice unconventional choice a b both are primitive cells unconventional is primitive conventional is centered unconventional choice conventional choice

More on Lattices X

X

Lattice types of some structures

Lattice types? BCC Metal CsCl Structure How many lattice points per unit cell?

Lattice types? Zinc blende (sphaelerite) Fluorite

Lattice types? Diamond Perovskite: AMO 3 A M O