In reciprocal lattice sigma (100) is defined as 1/d(100) and sigma ( 200) as 2/d(100). This is fine. But can I write sigma(200) = 2/d(100) = 1/ d(200) ? I think there is no plane as (200) because this represents basically the second order diffraction maxima from the d(100) planes. Do I think in the right way ? Regards.
Respected Sir,
In order to calculate miller indices, we have to reduce the numbers to the minimum. Therefore, for cubic lattice right representation is 100. However, if we intentionally write 200 plane (there may be some atom situated at the midway) for the cubic lattice we will get the spacing equals to exactly half of d(100). The reason is as follows. There is no difference between 100 and 200 planes. They are equivalent. So, for the second case, one 100 plane is at 0, another 200 plane is at (1/2), another 100 plane is at 1. If we try to calculate the spacing we have to take the difference between one 100 plane ane tge adjacent 200 plane (because they are equivalent in all respect). Therefore, the answer is exactly half.
Hope, this is the right explanation.
Thanking you
Your obedient student,
Arka
Dear Arka, if (100) and (200) are equivalent planee then is it correct to designate these with two different indices , I mean (100) and (200) ?
I am confused .
Respected Sir,
If we consider simple cubic system with basis atoms situated only at vertices. 200 plane is absolutely imaginary. It has only mathematical existence. These planes are unoccupied. However, there are other simple cubic systems with multiple basis atoms per lattice point. For example, in case of caesium chloride we can consider the lattice as two interpenetrating simple cubic arrays where the corner of one cell sits at the body center of the other. Here, both 100 and 200 plane have real physical meanings. Because, here real atoms are situated at 0, 0.5, 1 .... .
Waiting for your insights about this.
Thanking you,
Your obedient student,
Arka
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