X-rays are electromagnetic radiation such as visible light and as such has **interference effects**. This, however, cannot be detected with a typical single or double slit experiment, because due to the small wavelength, the gap distances would have to be extremely small.

In 1912, **Max von Laue** has the idea to use **crystals** for interference experiments. Their internal structure is like a grating, its ions are arranged at regular intervals \( d \).

The X-rays are diffracted by the electron shell of the irradiated atoms and interfere with each other. The path difference of the diffracted waves for a certain angle \( \alpha \) depends on the distance between the atoms in the crystal lattice and thus of the element-specific lattice spacing \( d \).

In the sketch, the red, green and purple line together form a right triangle with the hypotenuse \( d \). Using the sine definition we get the following expression:

$$ \delta = d \cdot \sin \alpha $$As can be seen in the sketch on the left, the path difference is the dual of \( \delta \):

$$ \Delta s = 2 \cdot \delta = 2d \cdot \sin \alpha $$
Constructive interference occurs when the path difference \( \Delta s \) is a **multiple of the wavelength**.

Thus applies to the \( k \)-th **maxima**:

In the rotational crystal experiment X-rays hit a crystal. The radiation interferes and then hits a detector. The crystal can be rotated so that you can change the angle of incidence \( \ alpha \) of the radiation.

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In this case, a **lithium fluoride crystal** and X-rays of an unknown wavelength \( \lambda \) are used. At the angles \( \alpha_1 = 0° \) \( \alpha_2 \approx 10° \) and \( \alpha_3 \approx 21° \) relative intensity maxima are observed. These angles are the so-called **Bragg angle** or **glancing angles**.

If one knows the lattice spacing of lithium fluorid \( d_L = 2.01 \times 10^{-10} \,\, m \), one can use any any of these angles in the Bragg equation and thereby calculate the wavelength of X-rays used in the experiment. For the first maximum the following holds:

$$ \lambda = 2 \cdot d \cdot \sin \alpha = 2 \cdot 2,01 \cdot 10^{-10} \,\, m \cdot \sin 10^\circ = 6,98 \cdot 10^{-11} \,\, m $$- Wikipedia: Article about "Bragg's law"

- Deutsche Version: Artikel über "Bragg-Gleichung"