Bonding

State the equation for total interatomic force

F=F_A​+F_R​

When do repulsive forces become significant?

When electron clouds overlap.

Where is equilibrium atomic spacing assumed?

Where the net force is zero.

How is bond potential energy determined?

By integrating force with respect to distance. U=∫ Fdr

At what point is bond potential energy minimum?

At the equilibrium atomic spacing

Why do atoms settle at an equilibrium spacing?

Physical systems tend to minimise energy.

What is a common expression for bond potential energy?

U=−Ar^−m+Br⁻ⁿ

What do the constants A B m and n represent in the bond energy equation?

A and B are attraction and repulsion constants while m and n depend on the bond type.

How is interatomic force obtained from bond energy?

By differentiating bond energy with respect to r.​

What is the typical value of m for ionic, covalent and metallic bonds?

m = 1

m = 2 and n = 9

m = 1-4

How is equilibrium spacing ro determined?

By setting the net force equal to zero.

How is Young’s modulus related to atomic bonding?

Young’s modulus is related to the slope of the force-separation curve near equilibrium spacing.

What happens to atoms during elastic deformation?

Atoms move slightly away from their equilibrium spacing.

What part of the force-separation curve relates to Young’s modulus?

The initial slope of the force-separation curve

For which materials can Young’s modulus be predicted well using interatomic forces?

• metals

• elastic deformation comes mainly from stretching of atomic bonds

Why does the interatomic force model fail to predict polymer stiffness accurately

• polymer stiffness not controlled only by bond stretching

• uncoiling and straightening of long polymer chains

• stretching of weak secondary bonds

How do theoretical strengths compare with actual strengths

Theoretical strengths predicted from interatomic force data are much higher than actual measured strengths

What is the typical relationship between UTS and E for metals

Metals often show UTS values around E/100 to E/1000

Why can’t interatomic force data accurately predict metal strength

Because real metals contain defects and dislocations

Which physical property can be explained using the U-r diagram?

Thermal expansion