Bonding in Solids:
Metals, Insulators, and Semiconductors
• Properties of metals can be explained by bonding in
metals.
• Metals are:
– Malleable - worked into useful shapes or foils.
– Ductile - pulled into wires
– Good conductors of heat and electricity.
• The bonding in metals cannot be explained in terms of
ionic or covalent bonding.
– There is little electronegativity difference from element to element
so metals and alloys do not form ionic bonds.
– The outermost subshells are not filled, so a large number of
covalent bonds would be needed to satisfy the octet rule.
Bonding Models for Metals
Electron Sea Model: A regular array of metals in a “sea” of
electrons.
Band (Molecular Orbital) Model: Electrons assumed to travel
around metal crystal in MOs formed from valence atomic
orbitals of metal atoms.
Models of Metallic Bonding
• The sea of electrons model is the first and
simplest qualitative explanation of metallic
bonding.
– The valence electrons are delocalized and move
freely throughout the solid.
• Allows for the conduction of electricity
– Explains malleability, ductility, and
conductivity properties of metals.
Electron Sea Model.
The electron sea model for metals postulates a regular array of cations in a "sea" of
valence electrons.
(a) Representation of an alkali metal (Group 1A) with one valence electron.
(b) Representation of an alkaline earth metal (Group 2A) with two valence electrons.
Models of Metallic Bonding
•
•
When a force is applied to a metal, the positively charged cores respond to the
stress, deforming the metal.
The free flow of electrons maintains the bonding throughout the process.
Models of Metallic Bonding
• Band theory is a quantitative model of bonding in solids.
– The wave functions of the valence electrons interact with each
other.
– Bonding molecular orbitals result from constructive interference.
– Antibonding molecular orbitals result from destructive
interference.
• The number of molecular orbitals formed equals the
number of atomic orbitals involved.
– For every bonding molecular orbital formed, one antibonding
molecular orbital is also formed.
– For odd number of bonding atoms, a nonbonding molecular orbital
is formed.
– The molecular orbitals formed belong to the entire set of atoms
Bonding in Metals –Molecular Orbitals of Solids
Band Theory
• Extension of MO
theory
– Valence orbitals on N
atoms combine to form
N molecular orbitals
– for large N, the energies
of the MO’s are closely
spaced
– Each valence orbital will
generate a band with
different energy range
Empty MO
Filled MO
•N/2 are filled.
•The valence band.
•N/2 are empty.
•The conduction band.
Band Theory and Conductivity
• Electrons fill the lowest energy band first.
• The energy difference between the filled and empty bands
determines the electrical properties of the bulk material.
• The band populated by valence electrons is the valence band.
• The empty band above the valence band is the conduction band.
• The energy difference between the valence and conduction band
is the band gap.
• Current flows when electrons move from the valence band to the
conduction band.
– Conductors have small band gaps. A very small amount of energy is
required to move electrons to the conduction band.
– Insulators have large band gaps. A large amount of energy is required to
move electrons to the conduction band.
– Semiconductors have band gap intermediate of conductors and insulators.
Band Theory
•
•
•
•
The valence e- fill in these MO’s
Depending on the substance, bands are partially or completely full
A partial filled band allows conduction
For a filled band to conduct, e- must be promoted from the highest occupied
MO to the lowest unoccupied MO
• The amount of energy required to promote these will determine how well the
substance conducts
Material
Conductivity
Type
Copper
106 S/cm
Conductor
Silicon
10-6 S/cm
Semiconductor
Silicon dioxide
10-12 S/cm
Insulator
Be Atoms to Solid Be with Considering Only the Valence
s Orbitals
Consider 1 mole of Be atoms each with a [He] 2s2 electron
configuration.
• The NA atoms with have NA 2s orbitals which will combine to give ½ NA
bonding orbitals (bonding band) and ½NA antibonding orbitals
(antibonding band).
• The 2 NA valence electrons will NA orbitals
• completely fill the bonding band orbitals
• completely fill the antibonding band orbitals
What is wrong with this argument?
•
•
Same number of occupied bonding and antibonding orbitals gives a bond
order of 0 (i.e. Solid Be would not form)
This predicts a large band gap between the highest occupied orbital and
lowest unoccupied orbital. Therefore, Be would be a poor conductor of
electricity.
Be Atoms to Solid for Be with Considing Only the Valence
s Orbitals
Be Atoms to Solid Be with Considing Both the Valence
s Orbitals and p Orbitals
Consider 1 mole of Be atoms each with a [He] 2s2 electron
configuration.
– The NA atoms with have NA 2s orbitals which will combine to give
½ NA bonding orbitals and ½NA antibonding orbitals.
– The NA atoms with have 3NA 2p orbitals which will combine to
give 3/2 NA bonding orbitals and 3/2 NA antibonding orbitals.
– Together the 2s and 2p orbitals give 2NA bonding orbitals (bonding
band) and 2NA antibonding orbitals (antibonding band).
This results in:
– The 2NA valence electrons will only partially fill the bonding band
orbitals (bond order = NA)
– This predicts a very small band gap between the highest occupied
orbital and lowest unoccupied orbital. Therefore, Be would be a
good conductor of electricity.
Be Atoms to Solid Be with Considing Both the Valence
s Orbitals and p Orbitals
Magnesium Metal
A representation of the energy levels (bands) in a magnesium
crystal.
Carbon Atoms to Diamond
Results in a completely filled bonding band. Therefore, the a lot of energy
is needed to promote an electron into the next higher energy level. So
diamond is a very poor conductor of electricity (it is an insulator)
Molecular Orbital Energies
Partial representation of the molecular orbital energies in
(a) diamond and (b) a typical metal.
Band Gap in
Group IVA
Diamondstructure
Solids
Overlap as a Function of Atomic Distance
•
(Left column) Two
hydrogen atoms
approaching with 1s orbitals
in phase result in an
enhanced amplitude in the
internuclear space
•
(Right column) Out-ofphase orbitals in the two
approaching hydrogen
atoms cancel each out in the
internuclear space, resulting
in diminished amplitude
(a node) between the atoms
Factors Affecting Band Gap Energy
• Band gap energy increases with overlap of the atomic
orbitals
– As the size of the atoms decrease they can get closer together so
their orbital interaction increases and the band gap energy
increases
• The band gap energy increases as the electronegativity
difference between the atoms increases
– As the difference increases the electrons are more “confined”
• In the bonding orbital the electron is located preferentially on the more
electronegative atom
• In the antibonding orbital the electron is located preferentially on the less
electronegative atom
• This results in greater difference energy between the bonding and antibonding
orbitals (greater band gap energy)
Atomic Radii
for Selected
Atoms