1. Interatomic Bonding Bonding Forces and Energies Types of Bonding
Equilibrium atomic spacing
Minimization of bonding energy
Embedded Atom Method (EAM)
Types of Bonding
Ionic
Covalent
Secondary
Metallic

2. 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.

3. Bonding Forces and Energy

4. 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

5. Bonding Forces and Energy

6. 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.

7. 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.

8. 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.

9. Embedded Atom Method Potentials converted to Effective pair scheme:
Transformation where mixed potentials are originally derived:

10. EAM Potentials
Some examples of EAM functions for various metals
Ag:

11. EAM Potentials
Al: Au:

12. EAM Potentials
Veff for various pure elements:

13. 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.

14. 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.

15. Ionic Bonding Properties of ionic bonding
nondirectional: magnitude of bond is equal in all directions around the ion.
High bonding energies (~ kJ/mol)
reflected in high melting temperatures
generally hard and brittle materials
most common bonding for ceramic materials
electrically and thermally insulative materials

16. 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

17. 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

18. 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

19. 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.

20. 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.

21. 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

22. Metallic Bonding
Potentials for metallic bonding are most commonly calculated via the EAM, especially in alloys and intermetallics
Link to Paper by Dr. Farkas