Question

derive linear density expressions for fcc [100] and [111] directions in terms of the atomic radius r?.compute and compare linear density values for these same two directions for copper cu?

Answer 1

The linear density expressions for the FCC [100] and [111] directions can be derived using the lattice constant and the atomic radius. The linear density values are approximately 1.110 nm^-1 and 0.812 nm^-1 for copper (Cu).

Step-by-step explanation:

In an FCC (face-centered cubic) structure, the linear density (LD) in the [100] direction can be calculated as LD = (2 / sqrt(2)) * (1 / a), where a is the lattice constant. In the [111] direction, the linear density can be calculated as LD = (2 / sqrt(3)) * (1 / a).

For copper (Cu), the atomic radius (r) is approximately 0.128 nm. The lattice constant (a) for Cu in the FCC structure is approximately 0.361 nm. Therefore, the linear density in the [100] direction is approximately 1.110 nm^-1, and the linear density in the [111] direction is approximately 0.812 nm^-1.