Bond Length vs Forces and Energy Plots

What 4 things can these graphs tell us?

1. Equilibrium bond length

2. Elastic Modulus

3. Melting Point

4. Coefficient of Thermal Expansion

What does it mean when the force equals zero?

• At equilibrium

• Equilibrium bond length is the distance at the point

Trend for Bonding energy (U)

• U becomes negative when getting closer

• At equilibrium, U is at its negative

What can we learn about stiffness from the bond-force curve?

Look at the slope of the curve around equilibrium

• Steep slope → High Stiffness

• Not steep slope → Low stiffness

What can we learn about stiffness from the bond-energy curve? (3 methods)

• The distance after the equilibrium point

  • Smaller distance → higher stiffness

  • Larger distance → lower stiffness

• Slope after equilibrium point

  • Steep slope → High Stiffness

  • Not steep slope → Low stiffness

• Look at curvature at the equilibrium point

  • Smaller radius → higher stiffness

  • Larger radius → lower stiffness

What can we learn about melting temperature from the bond-energy curve?

Energy to melt material: from equilibrium to the x-axis

• Deeper well ↔ higher melting temp

What can we learn about the thermal expansion coefficient from the bond-energy curve?

More symmetric ↔ smaller thermal expansion coefficient

• More asymmetric of the atomic bonding potential energy well leads to a larger CTE

• Rule of Thumb: Deeper potential energy wells are usually more symmetric and have lower CTE’s