This document discusses carbon allotropes and band theory of solids. It describes how carbon can bond in different ways to form diamond, graphite, buckyballs and nanotubes. Diamond has a giant covalent structure from sp3 hybridization, making it very hard. Graphite has sheets of sp2 hybrid carbon rings, allowing for conductivity. Buckyballs and nanotubes also use sp2 hybridization and have interesting electrical and strength properties. The document then explains band theory, where atomic electron energy levels form bands in solids. Insulators have a large gap between valence and conduction bands, while conductors have overlap or a partially filled conduction band, allowing electron movement. Semiconductors have a small gap
3. Allotropes
• Carbon can bond with itself in at least three
different ways giving us 3 different materials
– Diamond
– Graphite
– Buckyballs and nanotubes
4. Diamond
• Carbons are bonded via
sp3 hybridization to 4
other carbon atoms
forming a giant network
covalent compound.
5. Properties of Diamond
• High melting point due to strong directional covalent
bonds (3550 C)
• Extremely hard because it is difficult to break atoms
apart or move them in relation to one another
• No electrical conductivity because electrons are
localized in specific bonds
• Insoluble in polar and non-polar solvents because
molecular bonds are stronger than any
intermolecular forces
6. Graphite
• Carbon atoms are
bonded via sp2
hybridization.
• Carbon atoms form
sheets of six sided rings
with p-orbitals
perpendicular from
plane of ring.
7. Graphite Structure
• Carbon has 4 valence e-
to bond with. 3 are
used for closest atoms
in rings. 1 is delocalized
in p-orbitals
• The presence of p-
orbitals allows for
strong van der waals
forces that hold the
sheets together
8. Properties of Graphite
• Different from Diamond
– Conducts electricity because of delocalized
electrons
– Slippery can be used as lubricant, sheets can
easily slip past each other (think of a deck of
cards)
• Same as Diamond
– High melting point (higher actually because of
delocalized e-, 3653C)
– Insoluble (same reason)
9. Fullerenes
• Buckyballs: spherical
• Nanotubes: tube
shaped
• Both have very
interesting properties
– Super strong
– Conduct electricity and
heat with low resistance
– Free radical scavenger
10. Buckyballs
• Carbon atoms bond in
units of 60 atoms (C-60)
forming a structure similar
to a soccerball with
interlocking six sided and
five sided rings.
• sp2 hybridization
• Extra p-orbitals form pi
bonds resulting in
– Electrical conductivity
– Stronger covalent
bonds, therefore
stronger materials
11. Band Theory of Solids In isolated atoms the
electrons are arranged in
energy levels
UNIT-I BAND THEORY OF SOLIDS
12. In solids the outer electron energy levels become
smeared out to form bands
The highest occupied band is called the VALENCE band.
This is full.
For conduction of electrical energy there must be
electrons in the CONDUCTION band. Electrons are free
to move in this band.
13. Insulators : There is a big energy gap between the
valence and conduction band. Examples are plastics, paper
…..
Conductors : There is an overlap between the valence and
conduction band hence electrons are free to move about.
Examples are copper, lead ….
Semiconductors : There is a small energy gap between
the two bands. Thermal excitation is sufficient to move
electrons from the valence to conduction band. Examples
are silicon ,germanium….
14. When a conductor is
heated its resistance
increases ; The atoms
vibrate more and the
electrons find it more
difficult to move
through the conductor.
R
T
R
But in a semiconductor the
resistance decreases with
an increase in temperature.
Electrons can be excited up
to the conduction band.
Conductivity increases
15. Valence band: Band occupied by the outermost electrons
Conduction: Lowest band with unoccupied states
Conductor: Valence band partially filled (half full) Cu.
or Conduction band overlaps the valence band
