Interatomic Bonding
Bonding Forces and Energies
Equilibrium atomic spacing
Minimization of bonding energy
Embedded Atom Method (EAM)
Types of Bonding
Ionic
Covalent
Secondary
Metallic
Bonding Forces and
Energy
Interatomic Forces
attractive forces (Fa)
repulsive forces (Fr)
When the atoms reach a critical distance
(r0), the attractive and repulsive forces
cancel each other and the atoms are at
their equilibrium distance.
Bonding Forces and
Energy
Bonding Forces and
Energy
Sometimes it is easier to deal with
potential energies (E) rather than forces.
The relation of Energy to Force is as
follows: r
EN 

FN dr

 EA  E R
Equilibrium is reached by minimizing EN
Bonding Forces and
Energy
Embedded Atom Method
Potentials also calculated through the
embedded atom method (EAM)
potentials are calculated as a sum of pairwise
(interactions between a pair of atoms)
contributions and a many body term.
E   V (rij )   F (  i )
i, j
 i    (rij )
j
i
Embedded Atom Method
If a ternary system is being studied, EAM
potentials may be defined by considering
the three individual binary systems that
make up the ternary system.
As long as the interatomic interaction used
for each of the pure components is the same
in the description of the two binaries.
The volume term is calculated as the
embedding energy of a local electron
density.
Embedded Atom Method
Effective pairs
equivalent potentials where the various
contributions (pair and volume) are not the
same but add up to the same total energy for
all possible simulations.
Called the effective pair scheme, it is defined
as when the first derivative of the embedding
function is taken as zero.
Embedded Atom Method
Potentials converted to Effective pair
scheme:
F (  )  F (  )  F (  0 )
eff
V ( R)  V (r )  2  ( R) F (  0 )
eff
Transformation where mixed potentials
are originally derived:
eff
VAB
(r )  VAB (r )   A (r ) F (  0 B )   B (r ) F (  0 A )
EAM Potentials
Some examples of EAM functions for
various metals
Ag:
EAM Potentials
Al:
Au:
EAM Potentials
Veff for various pure elements:
Ionic Bonding
Most common bonding in metal-nonmetal
compounds.
Atoms give up/receive electrons from other
atoms in the compound to form stable
electron configurations
Because of net electrical charge in each ion,
they attract each other and bond via
coulombic forces.
Ionic Bonding
Attractive and repulsive energies are
functions of interatomic distance and may
be represented as follows:
A
EA  
r
B
EB  n
r
A and B are constants depending upon the
system. The value of n is usually taken as
12.
Ionic Bonding
Properties of ionic bonding
nondirectional: magnitude of bond is equal in
all directions around the ion.
High bonding energies (~600 - 1500 kJ/mol)
reflected in high melting temperatures
generally hard and brittle materials
most common bonding for ceramic materials
electrically and thermally insulative materials
Covalent Bonding
Stable configurations are obtained by the
sharing of valence electrons by 2 or more
atoms.
Typical in nonmetallic compounds (CH4, H20)
Number of possible bonds per atom is
determined by the number of valence
electrons in the following formula:
number of bonds = 8 - (valence electrons)
Bonds also are angle dependent
Covalent Bonding
Properties of covalent bonding
can be either very strong or very weak
bonds, depending upon the atoms involved in
the bond. This is also reflected in the melting
temperature of the compound
ex: diamond (strong bond) -- Tm> 3350°C
bismuth (weak bond) -- Tm ~ 270°C
most common form of bonding in polymers
Secondary Bonding
Van der Waals bonding
weak bonds in comparison with other forms
of bonding (~10 kJ/mol)
evident between all atoms, including inert
gases and especially between covalently
bonded molecules.
Bonds are created through both atomic and
molecular dipoles
Secondary Bonding
Hydrogen bonding
special type of secondary bond between
molecules with permenant dipoles and
hydrogen in the compound.
Ex: HF, H2O, NH3
these secondary bonds can have strengths as
high as ~50 kJ/mol and will cause increases
in melting temperature above those normally
expected.
Metallic Bonding
Most common in bonding of metals and
their alloys.
Proposed model of metallic bonding
metals usually have, at most, 3 valence
electrons, all of which form an “electron sea”,
which drift through the entire metal.
Base electrons form net-positive ion cores,
which attract the free electrons from the
“sea” as needed to maintain neutrality.
Metallic Bonding
Bonding may be weak or strong,
depending upon atoms involved.
Ex: Hg bonding energy = 68 kJ/mol
W bonding energy = 850 kJ/mol
Metallic Bonding
Potentials for metallic bonding are most
commonly calculated via the EAM,
especially in alloys and intermetallics
Link to Paper by Dr. Farkas