Question

The direction of greatest atomic density in aluminum (FCC structure) occurs along the diagonal of one face of the unit cell. If the atomic radius of aluminum is 0.143 nm, calculate:

a) The network parameter of Al.

b) The Burger vector of Al.

Answer 1

a) The network parameter of aluminum (Al) in the face-centered cubic (FCC) structure can be calculated using the formula:

Network parameter (a) = 4 * (Radius of Al) / √2

Given that the atomic radius of aluminum is 0.143 nm, we can substitute this value into the formula to find the network parameter:

a = 4 * 0.143 nm / √2

b) The Burgers vector (b) in a crystal lattice represents the magnitude and direction of the lattice distortion caused by a dislocation. For an FCC structure, the Burgers vector can be determined using the formula:

Burgers vector (b) = a / 2 * [hkl]

Where a is the network parameter and [hkl] represents the Miller indices of the dislocation line.

Since we're considering the diagonal of one face of the unit cell, the Miller indices [hkl] can be expressed as [1 0 0] or [0 1 0] or [0 0 1].

Let's assume [1 0 0] as the Miller indices for our calculation:

b = a / 2 * [1 0 0]

Substituting the value of a calculated in part (a), we can find the Burgers vector.