Bragg's Law Calculator

This Bragg's law calculator is the perfect tool to understand how an incident X-ray on a crystal relates to the wavelength of the reflected radiation and the distance between atoms in the crystal.

This tool is also called d-spacing calculator because you can easily find the interplanar spacing with it.

Keep reading to learn more about Bragg's diffraction law and Bragg's equation.

Bragg's law describes the condition for when the reflected radiation from X-rays incident on a crystal produces maximum constructive interference.

Two parallel X-rays interacting with different layers of the crystals separated by $d$ travel different lengths.

If this path length difference is equal to an integer multiple of the X-rays' wavelength, then both reflected waves interfere constructively. Otherwise, they interfere destructively.

The result is that we can observe peaks in the intensity of the scattered radiation at some angles. Bragg's equation expresses the relationship between these angles, wavelength, and distance between planes.

The extra distance that the beam in the lower layer travels is related to the distance between layers of molecules and angle of incidence by:

where:

• $d$ is the interplanar spacing or distance between layers of molecules.
• $\theta$ is the angle of incidence. Note: we will use both of these parameters in Bragg's equation.

As we said, maximum constructive interference will appear when this distance equals an integer multiple of the wavelength.

We summarize this condition in Bragg's equation:

where:

• $n$ is called the diffraction order; and
• $\lambda$ is the wavelength of the X-ray.

Our Bragg's law calculator is straightforward:

1. Input the wavelength $\lambda$.
2. Input the interplanar distance.
3. The diffraction order tells us how many times $\lambda$ fits within the space between molecules. Its maximum value is: (2 * d) / λ. Therefore, we should input every integer equal to or less than this maximum within this field (one at a time).
4. For each diffraction order, the calculator will output a different angle at which the scattered radiation's intensity will be maximum.

Alternatively, if we know the diffraction order, we can use this tool as a d-spacing calculator by filling every field and letting it complete the interplanar distance automatically!