Question

The densest plane and direction in BCC and FCC structure

Answer 1

I draw the BCC structure and show the plane of highest density,

  

Here, the atomic arrangement of { 110 } planes in a BCC structure have the highest density. This arrangement shows the closed packed direction joins diagonally opposite corners of the BCC unit cell . Therefore, it has two ( 111 ) direction.

There will be 6 similar planes and each has two directions. So, there will be total of 12 possible combinations of { 110 } and ( 111 )

I draw the FCC structure and show the plane of highest density,

Here, the plane of { 111 } has the close packed planes and each of these planes has direction of ( 110 ). So, each has three direction . Since, there are four planes similar to the the close packed plane and and each has three direction.

So, there will be total of 12 possible combination of { 111 } and ( 110 ).