Learning Objectives for Today
After today’s class you should be able to:
• Define and compare ionic/covalent bonds
• Predict properties of materials with different kinds
of bonds
• Guess what kind of bonding should occur for
specific materials and back it up with things you’ve
learned about bonding
Reminder: More student talks Thursday and Tuesday
Comparing Charge Densities
• We have characterized metals versus insulators by
having partially full or full bands in k space
• Distinction in real space less clear (charge density)
• Covalent crystals have large interstitial charge density
called bonds
• Molecular crystals (noble gases) have filled shells, and
are extremely tight-binding solids (~spherical).
• Ionic crystals composed of a metallic and a
nonmetallic element and share electrons (also bond)
• Compare to metals (even distribution)
Bonding Type Affects Properties
Properties are determined to a great degree by type of bonding
– Ionic: involves transfer of an electron between two atoms,
resulting in a net electrostatic attractive force
– Covalent: involves sharing of an electron between atoms
The type of bonding is determined mainly by the degree of overlap
between the electronic wavefunctions of the atoms involved.
Covalent to Ionic Transition
Purely
Covalent
An ion is an atom in which the total number of electrons is not equal to the
total number of protons, giving the atom a net electrical charge.
Perovskites and
other structures
(oxygen cation
or anion?)
Cation: positive
ion
Anion: negative
ion
Purely
Ionic
Why do bonds form?
The binding energy is released when molecules form.
Binding energy = bond strength.
Bonding can be understood from coulomb energy
Assume that charge (one electron) is completely transferred in an ionic molecule:
-
+
R0  0.2 nm
1.44 eV nm
ke 2

 7 eV
U 
0.2 nm
R0
If this potential energy is greater in magnitude
than the energy required to ionize the atoms, a
molecule will tend to form
Ionic Solids
(Finding Binding Energy)
• Let’s find the energy required to transfer an electron
from Na to Cl and then to form a NaCl molecule
– To remove an electron from Na (ionize the atom) one needs to
“spend” 5.14eV (compare with the ionization energy of a
hydrogen atom?)
Na + 5.14eV  Na+ + e– When a Cl atom captures an electron, 3.62eV
of energy is released (electron affinity of atom)
X + e− → X− + energy
Cl + e-  Cl- + 3.62eV
The energy cost to transfer the electron from the
alkali to the halogen is
E  IE (Na)  EA(Cl)  5.1 eV  3.6 eV  1.5 eV
Reminder: k=1/4o
The Ionic Bond
E  Ionization Energy (alkali)  Electron Affinity (halogen)
E  IE (Na)  EA(Cl)  5.1 eV  3.6 eV  1.5 eV
+
Na+
R
Cl-
• Since E >0, this will not happen if the atoms are far away
• As the atoms move closer, forming an ionic bond becomes
energetically favorable due to coulomb potential energy
• Total energy of ion as a function of separation R is
ke 2
E ( R)  E 
R
The ionic bond will form when E(R) becomes negative.
With a partner, find this R for NaCl.
This happens when R is below the critical distance
ke 2
RC 
at which E(R) = 0.
E
The Ionic Bond
In reality, ions will not get infinitely close to each because ?
NaCl critical distance is RC  0.96 nm
•repulsion between nuclei
•electrons in the same region can not occupy the
same quantum states (Pauli exclusion principle),
thus increasing the energy of the ion
Effective potential
ke2 B
 
 n
r
r
•2nd term describes repulsion (two free
parameters: B and 6<n<10)
•This leads to a minimum energy as a
function of R which defines distance
between ions in molecule:
A good approximation for the binding energy can be obtained from R0:
ke2
BE  E ( R0 ) 
 E
R0
Ionic crystals
• 3D crystals can be produced in this manner.
• In NaCl, each chlorine atom is surrounded by
sodium neighbors, and vice versa.
• The exact structure is determined by the
optimal use of space for the given ionic radii
-
+
R0  0.2 nm
Impenetrable Spheres
• Ionic crystals are often modeled as hard spheres
Due to Pauli exclusion
Due to Coulomb attraction
If the spheres touch, the
sum of the two diameters is
approximately the lattice
parameter (may not touch if
size very different)
a
Types of Crystals Group IV prefer covalent.
I-VII ionic crystals
II-VI ionic crystals
III-V crystals are more covalent and
semiconducting.
Closed-shell
elements:
molecular
crystals
Closed-shell –plus one
(alkali) elements: reactive
due to loosely-bound outer
electron in s-shell
Closed-shell–minus-one elements (halogens):
elements with high electron affinity A (energy
gained when an additional electron is added to a
neutral atom); will easily form negative ions (take
additional electron) in remaining p-shell state due
to large nuclear charge; these elements are very
reactive (e.g., F- with e.a.=3.4 eV)
Ionic crystals have strong bonds
Property
Explanation
Melting point
and boiling point
The melting and boiling points of ionic compounds are
high because a large amount of thermal energy is
required to separate the ions which are bound by
strong electrical forces.
Electrical
conductivity
Solid ionic compounds do not conduct electricity when
a potential is applied because there are no mobile
charged particles.
No free electrons causes the ions to be firmly bound
and cannot carry charge by moving.
Hardness
(Scratchable?)
Most ionic compounds are hard; the surfaces of their
crystals are not easily scratched. This is because the
ions are bound strongly to the lattice and aren't easily
displaced.
Brittleness
(Bendable?)
Most ionic compounds are brittle; a crystal will shatter
if we try to distort it. This happens because distortion
causes ions of like charges to come close together then
sharply repel.
COVALENT BONDING
• The covalent bonding is formed by
sharing of outer shell electrons (i.e., s and
p electrons) between atoms rather than
by electron transfer.
• Thus, the interaction between nearest
neighbors is of prime importance!
Covalent Bonding of Multielectron Atoms
For multielectron atoms
covalent bonding is more likely
to occur if there are unpaired
electrons in an orbital
– Unpaired electrons can share the
same orbital with another
unpaired electron of opposite spin
Example
F: 1s22s22px22py22pz1
Fluorine has one unpaired electron, thus acts like
H in forming covalent bonds
e.g.: F2, HF
Covalent Bonding of Multielectron Atoms
N: 1s22s22px12py12pz1
• N in ground state has three unoccupied p-orbital states in order to
minimize repulsion energy between electrons
• Nitrogen therefore has three electrons available for covalent bonding and
can form molecules such as N2 and NH3 (ammonia)
In general, binding energy
increases with number of bonds:
F2
O2
N2
Molecule B (eV)
(1 bond)
(2 bonds)
(3 bonds)
1.6
5.1
9.8
The Oxygen Molecule
• (Group) Discuss the
electron configuration of
the oxygen molecule O2.
• What does this tell you
about the properties of
the molecule?
• The oxygen molecule is
formed when two half
filled 2p-orbitals of each
oxygen atom overlap
with the 2p-orbitals, of
the other oxygen atom
to form a double bond
Is oxygen atom happy?
What to do?
What would
that look
like?
Covalent Materials Also Strong Bonds
Property
Explanation
Melting point
and boiling point
Very high melting points because each atom is bound
by strong covalent bonds. Many covalent bonds must
be broken if the solid is to be melted and a large
amount of thermal energy is required for this.
Which do
you think is Electrical
more
conductivity
conducting?
Hardness
Brittleness
Poor conductors because electrons are held either on
the atoms or within covalent bonds. They cannot move
through the lattice.
They are hard because the atoms are strongly bound in
the lattice, and are not easily displaced.
Covalent network substances are brittle. If sufficient
force is applied to a crystal, covalent bond are broken
as the lattice is distorted. Shattering occurs rather than
deformation of a shape.
METALLIC BONDING
• Metallic bonding is when electrons
are accumulated between ion cores.
• Metallic bonding is the type of
bonding found in metal elements.
This is the electrostatic force of
attraction between positively charged
ions and delocalized outer electrons.
• In contrast to ionic bonds, the
electrons now have wavefunctions
that are very extended. (4s
wavefunction at large r.) Thus, many
neighbors are involved in bonding.
• The metallic bond is weaker than the
ionic and the covalent bonds.
Wave function amplitudes in Ni
METALLIC PROPERTIES
• All conduction e-s in a metal combine to form a sea of
electrons that move freely between cores  high electrical
and thermal conductivity.
• More electrons=stronger attraction. Means melting and
boiling points are higher, and metal is stronger and harder.
• The free electrons act as the bond (or a “glue”) between
the positive ions.
• This type of bonding is nondirectional and
+
+
+
rather insensitive to structure.
• As a result we have a high ductility of metals:
+
+
+
the “bonds” do not “break” when atoms are
rearranged – metals can experience a
+
+
+
significant degree of plastic deformation.
van der Waals Bond
• Arise from charge fluctuations in
atoms due to zero-point motion
(due to Heisenberg uncertainty
principle); these create dipole
moments that are attractive
• Depends on p2/r6, short ranged
• Always present, but significant only
when other types of bonding not
possible (closed electron shells,
saturated molecules)
• Typical strength of 0.2 eV/atom
~1% of other bonds
• Because force results from dipoledipole interactions, it is short
range, varying as r -6
graphite
Usually with oxygen,
fluorine or nitrogen
Hydrogen “Bonding”
• Comes from the fact that it’s really hard (13.6eV)
to completely remove an electron from hydrogen
• In H20, hydrogen covalently
bonds with nearby oxygen, but it
also has a hydrogen bond with
the next nearest neighbor.
• Since the electron is pulled
toward the closer oxygen, the
positive charge is on the outside
and attracted to other negative
oxygens.