Missing Reflections in FCC/BCC Crystals: Bragg Model Inadequate?

[aaaa202]

I noticed that using the Laue equations reflections from some of the planes in the fcc and bcc crystal are not allowed. Now using the (maybe too naive?) Bragg model we can always find Bragg peaks whichever plane we hit with waves. So is the Bragg model too simple for these planes? And what is it physically that accounts for the missing reflections that was not incorporated into the Bragg model?

 

[UltrafastPED]

The missing spots are due to interference; it is called the "structure factor".
For example FCC crystals have spots for F_hkl where h,k,l are all even or all odd ... else the spot is missing.
The Bragg equation only depends on the distance between the hkl planes; the structure factor is independent.

The derivations are done here:
http://bama.ua.edu/~mweaver/courses/MTE583/MTE%20583_Class_18b.pdf

This site covers additional information:
http://www.xtal.iqfr.csic.es/Cristalografia/parte_05-en.html

 

[member 392791]

There are rules associated with when you can or can't use them, like the above poster stated. They are called reflection rules of x-ray diffraction

 

[DrDu]

UltrafastPED already explained why some reflections aren't observed in these lattices. However I don't believe that Laue and Bragg equations give different results in this respect.
I also disagree on the statement that the Laue equations would prohibit generally reflections from some planes.
You should elaborate on that.

 

[aaaa202]

I just meant that for for instance the fcc the Laue conditions tell us that no diffraction can occur from planes for which the integers are partly even and off. But the Bragg equation sure tells us that any plane would give constructive interference at some angle?

 

[DrDu]

I just meant that for for instance the fcc the Laue conditions tell us that no diffraction can occur from planes for which the integers are partly even and off. But the Bragg equation sure tells us that any plane would give constructive interference at some angle?

What does "even and off" mean?
Your formulation of Braggs condition is certainly true. The systematic absences for some angles mentioned certainly do not mean that the planes don't reflect for any angle, just not for a special subset.

 

[UltrafastPED]

He means all even or all odd Miller indices ... but neither the Laue conditions, nor the Bragg equation provides this insight. Instead we must calculate the structure factor for the unit cell for each Miller index.

@aaaa202 - why do you think the Laue conditions can give you this information? The only say that for a diffraction spot to occur the refelcted wave vector must be going in the direction of one of the crystal planes.

Here is another nice tutorial: physics.valpo.edu/courses/p440/Diffraction_Crystal_Structure.ppt

 

[nasu]

It may be OP's confusion between "Laue's equations" referring to the specific conditions for and the equations for scattering factor from "Laue's theory of diffraction".
The last one ends with an expression for the scattering factor which allows to predict which peaks will have zero intensity (based on the structure factor).

 

[aaaa202]

I meant even and odd. Diffraction from some planes are absent, but would they be if you used the bragg law?

 

[DrDu]

Maybe you are mixing up the Miller indices of the planes and those of points in the reciprocal lattice?

 

[M Quack]

Bragg's law tells you what the scattering angle is for a certain lattice plane spacing. It does not tell you anything about the intensity you can expect - in particular it does not tell you if the intensity will be zero.

If you have another set of planes half way in between the planes you use for Bragg's law, then the scattering from the two sets of planes will cancel. This is why the (100) in FCC or BCC lattices vanishes.

The systematic way to get an idea about intensities is to calculate structure factors, as was already pointed out above. There are some rules to tell you about systematic absences, these are called extinction rules.