Chapter 3: Atomic Interactions in Solids

Question 1

What holds a solid together?

Answer 1

Electrostatic interactions

Question 2

Types of Bonds

(5 points)

Answer 2

• Van der Waals: between neutral, noble atoms
• Ionic bonds: between positive and negative ions
• Covalent bonds: between neutral, non-noble atoms due to overlap in electron clouds
• Metallic bonds: delocalized electrons; metals
• Hydrogren bonds: important in organic molecules

Question 3

Binding Energy, Melting Temperature, & Compressability
(4 points)

Answer 3

• The binding energy is the energy needed to remove atom from solid
• Melting energy proportional to binding energy
• Compressabiity proportional to binding energy
  
  • Small binding energy → soft bonds → high compressability

Question 4

Van der Waals Interactions

(3 points)

Answer 4

• Interaction between neutral, noble atoms
• Fluctuations of electron cloud induce dipoles
• Short-range interaction (1/r⁶)

Question 5

Lennard–Jones Potential

(7 points)

Answer 5

• Due to Pauli Exclusion Principle, atoms repel at close distance
  
  • V(r) = b/r¹² (empirically determined)
• Together with Van der Waals interaction (see image)
  
  • e,σ material specific
• Equilibrium separation r₀ given by dV/dr = 0
  
  • r₀ = 2^1/6σ
  • V(r₀) = -e

Question 6

Equilibrium Lattice Constant (from LJ)

Answer 6

Summing up LJ over all pairs and minimizing

Question 7

Born-Mayer Potential

Answer 7

• Used to describe potential between ionic bonds (see image)
• λ, ρ strength and range of interactions