# Order of diffraction pattern confusion in XRD experiment

Somewhere I came across this phrase:

"expected diffraction angle for first order reflection."

With respect to XRD do I take this as a rule of thumb that the diffraction will always be a first order one? I will quote some relatable lines:

"The Bragg equation can be used for determining the lattice parameters of cubic crystals. Let us first consider the value that n should be assigned. A second order reflection from (100) planes should satisfy the following Bragg equation. $$2\lambda=2d_{110}\sinθ$$ or $$\lambda=d_{100}\sin \theta$$. Similarly a first order reflection from (200) planes should satisfy the following condition $$\lambda=2d_{200}\sin \theta$$.

What do I consider the value of n as when this is given to me?

• Can you give us the source of the quote? It seems like it's talking about the expected diffraction angle for 1st order diffraction, not that every single XRD will be first order. Jan 14 at 16:20
• @NikeDattani I will quote some relatable lines.."The Bragg equation can be used for determining the lattice parameters of cubic crystals.Let us first consider the value that n should be assigned.A second order reflection from (100) planes should satisfy the following Bragg equation.$2 \lambda =2d_{110}sin \theta$ or $\lambda =2d_{200}sin \theta$. Similarly a first order reflection from (200) planes should satisfy the following condition $\lambda=2d_{200}sin \theta$. Jan 14 at 16:25
• @user586228 could you edit the question to include a longer quote, and write what you find confusing? Jan 14 at 17:32

In Bragg's law, $$n\lambda=2d\sin(\theta)$$. Here, $$n$$ is the order of the reflection, and corresponds to the path length difference between X-rays diffracted from two different layers of atoms, in terms of the number of wavelengths. So if the path lengths differ by exactly one wavelength, it is a first order reflection.
By convention, we treat all reflections as first order, and introduce a different "effective" lattice spacing. This avoids having to deal with reflection order explicitly. As an example from the comments on the original question, if you consider a second order reflection from (100) planes, the equation is $$2\lambda=2d_{100}\sin(\theta)$$ and a first order reflection from (200) planes is satisfied by $$\lambda=2d_{200}\sin(\theta)$$. But we know that $$2d_{200}=d_{100}$$, so these two conditions both correspond to the same diffraction angle in the material. Again, we just consider all reflections as first order by convention.