Question

When I am computing structure factor values of a lattice, I am confused as to how some of the planes are classified.

My book describes the conditions for for a given intensity value F^2 as a function of the sum of the hkl values (h + k + l).

It gives the equation for the F^2 value for different planes... then says "when h+k+l is an odd multiple of 2" or "when h+k+l is an even multiple of 2".

I don't get what it means by an "odd multiple of 2". In the example, the plane (200) is considered plane with an h+k+l that is "an odd multiple of 2" I get how it is a multiple of 2 but what does it mean by odd? It also says the (220) is an even multiple of 2, and (400) is also an even multiple of 2.

Can someone explain what it means when (h+k+l) for a plane is an "odd multiple of 2"?

Answer 1

For a plane h, k and l represent the miller indices for the reciprocal lattice.

Consider the plane (200)

Here h = 2, k =0 and l=0

Hence

Now lets look at another plane (220)

here h =k = 2, l=0

So how they are differen?

In the first case, 2 is multiplied by 1 (1 is odd, thus h+k+l is an odd multiple of 2)

In the second case, h+k+l = 4 which is 2 multiplied by 2 (2 is even, hence h+k+l is even multiple of 2)

Lets take another exmaple.

Let the miller indices of the plane be,

h=h,

k=k,

l=l

Then, h+k+l = h+k+l . If h+k+l equals , where x is even, then h+k+l is an even multiple of 2.

If h+k+l equals where x is odd, then h+k+l is an odd multiple of 2.

Now, illustrate this with a different example to what you provided.

let the plane be (464)

Then

Let the plane be (4 2 2)