00:01
Now it has been asked to derive in part a the planar density expressions for bcc 100 and 110 planes in terms of the atomic radius and in part b it has been asked to compute and compare the planar density values for the 100 and 110 planes of molybdenum.
00:47
Now let us draw the 100 and 110 planes in a bcc lattice.
00:58
So the 100 and 110 planes in a bcc lattice can be drawn as follows.
01:04
This is a bcc lattice and this is the 100 plane.
01:10
Any set of planes parallel to this is 100 plane.
01:16
The other one is this one is 110 plane.
01:22
Now this plane is 110 plane and this is the these are the coordinate axis of this unit cell.
01:34
So this is the x axis this is y this is z.
01:40
The dimensions of the bcc cell is the dimensions are all a so the lattice parameter is a along x y z direction.
01:52
The length of the one of the side of the 110 plane is along the body diagonal that is a root 2.
02:01
Coming to 100 plane the 100 plane for a bcc lattice can be redrawn separately as follows.
02:12
So this is the 100 plane its sides are a so it is a square lattice.
02:22
It is a the plane is in the form of a square.
02:27
Now one atom is present at each of the four corners of this plane and each corner atom is shared by four adjacent unit cells in the same plane.
02:48
Therefore the effective number of atoms in the 100 plane for a bcc lattice would be 4 times 1 by 4 that is equal to 1 atom.
03:07
Now area of this plane would be the area of the square of side a that is a square and for a bcc lattice we know that root 3 times a is equal to 4 r.
03:27
So a is related to atomic radius as 4 r by root 3 where r is the atomic radius...