Bonding Forces and Energies

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Bonding Forces and Energies

• Cassy Cortez
• E 106
• Prof Spjut
• January 19, 2007

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Motivation

• Lecture Problem 2.12
• - Given the expression for Net Potential
  Energy, determine an expression for Bonding
  Energy, E0.
• Material performance
• Function of material properties.
• Furthermore, material properties is a function of
  material structure.
• Interatomic forces present in atomic bonding can
  predict many physical properties of materials (
  i.e. melting temperature, elasticity, thermal
  expansion, and strength).

The four components of the discipline of
materials engineering and their linear
interrelationship
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Atomic Bonding
Anion
Cation

• As two ions approach each other, each atom
  exerts forces on the other.
• Magnitude of Forces is a function of interatomic
  distance
• Interatomic Forces
• - Attractive Force, Fa
• Repulsive Force, Fr

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Energy vs. interatomic separation, r
Net Potential Energy between two adjacent ions
Materials Science and Engineering, 2nd edition,
pg 20
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Bonding Energy

• Expression for Net Energy in terms of
  interatomic forces, Fr and Fa
• 1st Principle

Bonding Energy, E0
( Coulombs Law)
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Lecture Problem 2.12
Having the expression for Net Potential Energy,
we can find Bonding energy by taking the
derivative and setting it 0.
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Summary

• In assessing the performance of materials, its
  IMPORTANT to draw attention to the relationship
  between material properties and structural
  elements.
• Finding the minimum of a Potential Energy Curve
  corresponds to the energy released when two ions
  form a bond, Bonding Energy.
• - to find the equilibrium interionic spacing,
  r0, set
• and solve for r0.
• - to find Bonding Energy E0, simply plug r0
  into Net Energy expression.
• Bonding Energy and shape of Potential Energy
  Curve vs. r varies from material to material.
• - Number of material properties depend on E0.