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Home/Optics & Light/Bragg’s Law (X-ray)

Bragg’s Law (X-ray)

Bragg's Law describes the condition for constructive interference when X-rays scatter off the periodic planes of atoms within a crystal. This simulator visualizes the core principle: when X-rays strike a crystal at a glancing angle θ, they reflect off parallel atomic planes separated by a distance d. For the reflected waves to reinforce each other, the path difference between rays reflecting from adjacent planes must be an integer multiple of the X-ray wavelength λ. This condition is expressed by the famous equation nλ = 2d sin θ, where n is the order of the diffraction. The simulator allows you to manipulate key parameters—the wavelength (λ), interplanar spacing (d), and angle of incidence (θ)—and observe in real-time how these changes affect the condition for a constructive 'Bragg peak.' A schematic diagram shows the crystal planes, incident and reflected beams, and the critical path difference. Key learnings include the geometric origin of the 2d sin θ term, the concept of diffraction orders, and how Bragg's Law is used to determine crystal structures. The model simplifies reality by treating the crystal as a set of perfect, infinite planes and the X-ray reflection as a purely elastic, specular process, ignoring absorption and thermal effects. By interacting, students build intuition for how crystallographers probe atomic arrangements and why only specific angles yield intense diffraction patterns.

Who it's for: Undergraduate students in solid-state physics, materials science, or chemistry courses studying crystallography and X-ray diffraction techniques.

Key terms

  • Bragg's Law
  • X-ray Diffraction
  • Constructive Interference
  • Interplanar Spacing
  • Glancing Angle
  • Diffraction Order
  • Crystal Lattice
  • Path Difference

Lattice & wavelength

0.25 nm
0.154 nm
1
12 °

Condition 2d sin θ = nλ (θ measured from the planes). X-ray crystallography uses this; Cu Kα is ~0.154 nm — play with θ until the green “match” lights up.

Measured values

2d sin θ0.1040 nm
nλ0.1540 nm
Bragg matchno

How it works

Specular reflection from parallel planes produces path differences that hit constructive interference when the Bragg condition holds.

Frequently asked questions

Why do the X-rays need to reflect off the atomic planes at such a specific angle?
The specific angle is required to satisfy the condition for constructive interference. If the path difference between waves reflecting from adjacent planes is not exactly an integer multiple of the wavelength, the waves arrive out of phase and destructively interfere, resulting in no detectable signal. This selectivity is what makes Bragg diffraction a powerful tool for analyzing crystal structure.
Is this process truly 'reflection' like from a mirror?
No, it is diffraction, not simple mirror-like reflection. The phenomenon occurs because X-rays scatter from individual electrons within the atoms. The regular, periodic arrangement of atoms creates many scattered wavelets that only constructively interfere in specific directions given by Bragg's Law. The term 'Bragg reflection' is a convenient but physically imprecise shorthand.
What does the integer 'n' (the order) represent physically?
The order n corresponds to the number of complete wavelengths in the path difference. For n=1, the path difference is exactly λ; for n=2, it is 2λ, and so on. Higher-order peaks occur at larger angles for the same set of crystal planes. In practice, the n=1 reflection from planes with spacing d/2 is physically equivalent to the n=2 reflection from planes with spacing d, which is why we often set n=1 and consider different families of planes.
What is a real-world application of Bragg's Law?
The primary application is X-ray crystallography, used to determine the atomic structure of crystals, from simple salts to complex proteins like DNA. By measuring the angles and intensities of Bragg peaks, scientists can calculate the distances between atomic planes and ultimately reconstruct the three-dimensional arrangement of atoms within the material.