What is 2 $\theta$ in X-ray powder diffraction (XRD)?

Question

Why are we taking 2$\theta$ instead of $\theta$ in X-ray powder diffraction (XRD). I have found the forum post 2 theta in X-ray Powder Diffraction (XRD), but there is no answer. What is the explanation?

Answer 1

When you do diffraction, $\theta$ is the angle of incoming EM wave, as well as the angle of difracted EM in regard to Bragg's planes. So the total change in angle of the EM wave equals $2\theta$.

See images at http://en.wikipedia.org/wiki/Bragg%27s_law.

If this is not the answer you're looking for, maybe you should specify your question more clearly. (I was doing Bragg's experiments as a student decades ago, I naturally always halfed the angle, so I do not quite understand what is your problem.)

Answer 2

For the $\theta : 2\theta$ goniometer, the X-ray tube is stationary, the sample moves by the angle $\theta$ and the detector simultaneously moves by the angle $2\theta$. At high values of $\theta$, small or loosely packed samples may have a tendency to fall off the sample holder.

Answer 3

In x-ray powder diffraction, you have crystallites in all possible orientations. Only those crystallites whose bragg planes are at an angle θ with respect to the incident angle will diffract at an angle 2θ with respect to the incident beam (or at an angle θ with respect to the diffracting planes). So that is the reason, you always use 2θ instead of θ.

Answer 4

I think the angle $2 \theta$ is used because we can see diffracted pattern from incident beam so the angle of incident and reflected are combine to become $2 \theta$.

Answer 5

The 2θ convention comes from the way experiments are actually done, so-called θ−2θ scans. The Bragg diffraction condition contains only one factor of θ: 2dsinθ= nλ. In an XRD experiment, one is trying to learn about the crystal structure of a material by dividing the structure into 'planes' in every way possible and accessing every resultant inter-planar distance, d, by varying the incidence angle θ. In practice, it is easier to move the sample than the detector needs to simultaneously move. The detector traverses an arc subtending twice the angle that the sample has rotated in order to maintain the geometry sketched above. This is where 2θ comes from.