Interatomic Bonding

1
Interatomic Bonding

• Bonding Forces and Energies
• 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 (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

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) -- Tmgt 3350C
  bismuth (weak bond) -- Tm 270C
• 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