semiconductor physics and Devices

Week 6: Bonding in Solids (Part 2)

Lecture Topics:

1. Van der Waals Bonding

   • Weak, non-covalent interactions between molecules or atoms due to induced dipoles (e.g., noble gases like argon, molecular solids like iodine).

   • Characteristics: Low melting and boiling points, soft and easily deformed solids, poor electrical conductivity.

   • Types of van der Waals forces:

     • London dispersion forces: Arising from instantaneous dipoles in atoms and molecules.

     • Dipole-dipole interactions: Occurring between polar molecules.

     • Dipole-induced dipole interactions: Between polar and non-polar molecules.

2. Hydrogen Bonding

   • Special case of dipole-dipole interaction, where hydrogen atoms bond with highly electronegative atoms like oxygen, nitrogen, or fluorine (e.g., water, ammonia).

   • Characteristics: Stronger than van der Waals forces but weaker than covalent or ionic bonds.

   • Role of hydrogen bonding in determining properties of substances, such as the high boiling point of water and the structure of ice.

3. Cohesive Energy of Solids

   • Definition of cohesive energy: The energy required to separate a solid into individual atoms or ions.

   • Relation between bonding types and cohesive energy: Covalently bonded solids have higher cohesive energies compared to van der Waals bonded solids.

   • Calculation of cohesive energy in ionic solids using the Born-Haber cycle.

   • Comparison of cohesive energies for ionic, covalent, metallic, and van der Waals solids.

4. Madelung Constant and Lattice Energy

   • Review of the Madelung constant for ionic crystals and its significance in determining lattice energy.

   • Calculation of lattice energy using the Born-Landé equation

where MMM is the Madelung constant, z1z_1z1​ and z2z_2z2​ are the charges of the ions, r0r_0r0​ is the equilibrium separation, and nnn is the Born exponent.

1. • Example calculation of lattice energy for NaCl.

Examples:

• Compare the bonding in water (hydrogen bonding) and iodine (van der Waals bonding) and explain the differences in their physical properties.

• Calculate the lattice energy for an ionic solid using the Born-Landé equation.

• Estimate the cohesive energy of a van der Waals solid like argon using experimental data.

Homework/Exercises:

1. Compare and contrast van der Waals bonding and hydrogen bonding. Provide examples of materials where these bonds are important.

2. Use the Born-Haber cycle to calculate the cohesive energy of NaCl.

3. Calculate the lattice energy for KCl using the Born-Landé equation, given the necessary constants.

Suggested Reading:

• Charles Kittel, Introduction to Solid State Physics, Chapter 3: Crystal Binding (continued).

Key Takeaways:

• Van der Waals and hydrogen bonds are weaker than ionic, covalent, and metallic bonds, but they play crucial roles in determining the properties of molecular solids.

• Cohesive energy measures the strength of bonds in solids, with ionic and covalent bonds generally having higher cohesive energies than van der Waals forces.

• Lattice energy can be calculated using the Madelung constant and is crucial for understanding the stability of ionic solids.

This week builds on the previous content by introducing weaker bonding types, like van der Waals and hydrogen bonds, and discussing cohesive energy and lattice energy, further linking bonding to material properties.