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:

Equilibrium is reached by minimizing EN

RA

N

EE

dr FE

r

N

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.

jiji

ii

jiij

r

FrVE

)(

)()(,

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:

Transformation where mixed potentials are originally derived:

)()(2)()(

)()()(

0

0

FRrVRV

FFFeff

eff

)()()()()()( 00 ABBAABeff

AB FrFrrVrV

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 and B are constants depending upon the system. The value of n is usually taken as 12.

nr

BE

r

AE

B

A

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 materialsmost 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 compoundex: 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