# How are allowed and forbidden reflections calculated?

• ScareCrow271828
In summary, the rules of reflection for different cubic lattices (SC, BCC, FCC) based on the Bragg's law state that for incident X-rays, constructive interference occurs when the planes satisfy the equation 2dsin(θ)=nγ. For SC, any combination of h, k, and l can lead to constructive reflection. For BCC, the sum of h, k, and l must be even, while for FCC, all three must be either odd or even. The calculation involves finding the distance between planes (d) using the equation d=a/√(h^2+k^2+l^2) and the wavelength of the incident X-rays (λ). The equation sin2(θ
ScareCrow271828
Question:
Explain the rules of reflection for different cubic lattices (SC, BCC, FCC)
based on the Bragg ́s law. Help: If we have incident of X-rays, which planes have constructive/ distractive reflection? Why? Please calculate it for the following crystal planes. 001, 011, 111, 200, 210, 211

Equations:
2dsin(θ)=nγ
d=a/√(h^2+k^2+l^2)
γ=lambda (cant find the symbol sorry)

sin2(θ)=(γ2/4a2)*(h2+l2+k2)Attempt At Solution:
I know the rules. SC=any h,k,l BCC=h+k+l=even. FCC=h,k,l= all odd or even. And that it has to do with the satisfaction of Bragg's law that leads to constructive interference which leads to normal reflection. Although, I'm having trouble understanding exactly what to calculate. Any help would be greatly appreciated, If I could be pointed in the right direction or given an example for just one calculation that would be great.

Perhaps "calculate" is a bad choice of wording. I believe the question is asking you to state whether each of the given planes for each of the lattices exhibits constructive or destructive interference and explain your reasons. The explanation part will require some calculation involving h, k and l.

## 1. How are allowed and forbidden reflections determined?

The allowed and forbidden reflections are determined by the symmetry of the crystal lattice and the wavelength of the incident X-ray beam. The symmetry dictates the possible diffraction patterns that can occur, while the wavelength determines which of those patterns will be observed.

## 2. What is the difference between allowed and forbidden reflections?

Allowed reflections are those that follow the symmetry of the crystal lattice and produce observable diffraction patterns. Forbidden reflections do not follow the symmetry of the lattice and therefore do not produce observable diffraction patterns. However, they may still have a weak intensity and can provide valuable information about the structure of the crystal.

## 3. How is the symmetry of a crystal lattice determined?

The symmetry of a crystal lattice can be determined through techniques such as X-ray crystallography, neutron diffraction, or electron diffraction. These methods involve analyzing the diffraction patterns produced by the crystal and using mathematical algorithms to determine the symmetry of the lattice.

## 4. Are all reflections allowed in a crystal lattice?

No, not all reflections are allowed in a crystal lattice. The symmetry of the lattice restricts the possible diffraction patterns, and therefore only certain reflections will be allowed. These are known as systematic absences and are an important factor in determining the crystal structure.

## 5. How are forbidden reflections used in crystallography?

Although forbidden reflections do not produce observable diffraction patterns, they can still provide valuable information about the crystal structure. By analyzing the intensity and location of these reflections, scientists can gain insights into the symmetry and arrangement of atoms within the crystal lattice.

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