Question

Determine linear atomic density along [001] direction of a FCC unit cell with lattice constant a (cube edge length).

Answer 1

Answer:

$LD=\dfrac{0.5}{ a}$

Explanation:

Given that

Unit cell is in FCC

Here given direction is not clear visible so we take direction [001].

We know that linear density(LD) given as

$LD=\dfrac{Number\ of\ atoms\ in\ the\ direction\ vector}{d_{[001]}}$

So the number of atom will be 1/2 in direction  [001]

In FCC

$a=2\sqrt2 \ r$

$LD=\dfrac{0.5}{ a}$

$LD=\dfrac{1}{2\sqrt2 \ r}$