What is Bragg’s law?

Short Answer

Bragg’s law explains the condition under which X-rays are reflected strongly from the atomic planes of a crystal. According to this law, constructive interference occurs when the path difference between X-rays reflected from different layers of atoms is equal to an integer multiple of the wavelength. This produces bright diffraction lines.

Bragg’s law is written as:

It helps determine the spacing between crystal planes and is a fundamental principle in X-ray diffraction, crystallography, and the study of atomic structures.

Detailed Explanation :

Bragg’s law

Bragg’s law is a fundamental principle used to understand how X-rays interact with crystalline materials. When X-rays strike a crystal, they encounter a regular arrangement of atoms that act like layers or planes. As X-rays penetrate the crystal, some of the waves are scattered or reflected from one atomic plane, while others are reflected from deeper planes. These reflected waves can interfere with one another.

Bragg’s law gives the condition for constructive interference, meaning the reflected X-ray waves reinforce each other and produce a strong signal. This occurs when the extra distance travelled by one wave compared to another is exactly equal to a whole number (integer) multiple of the X-ray wavelength. If this condition is not met, the waves cancel out, resulting in weak or no diffraction.

This principle forms the basis of X-ray diffraction, which is used to determine atomic arrangements in solids.

Statement and formula

Bragg’s law is stated as:

Where:

  • n = order of diffraction (1, 2, 3, …)
  • λ (lambda) = wavelength of X-rays
  • d = spacing between atomic planes in the crystal
  • θ (theta) = angle of incidence at which X-rays strike the planes

This formula shows the exact condition for a bright diffraction line to appear.

Meaning of the Bragg’s law equation

The equation can be understood physically:

  • X-rays strike two parallel atomic planes.
  • One beam reflects from the top plane.
  • Another beam enters deeper and reflects from the lower plane.
  • The lower beam travels a longer distance.
  • If this extra distance equals nλ (one or more wavelengths), the waves reinforce each other.

This reinforcement produces a detectable diffraction peak.

If the extra distance is not equal to nλ, the waves cancel each other, and no peak appears.

Derivation concept (simple explanation)

Consider two parallel crystal planes separated by a distance d. When X-rays hit the planes at angle θ, the beam reflecting from the lower plane travels extra distance given by:

  • d sin θ entering
  • d sin θ leaving

So total extra path = 2d sin θ

For constructive interference:

This is Bragg’s law.

Importance of Bragg’s law

Bragg’s law is extremely important in studying crystals because:

  • It helps determine the spacing between atomic planes.
  • It reveals the internal structure of crystals.
  • It allows identification of unknown materials.
  • It helps understand symmetry and orientation of crystals.
  • It is fundamental in X-ray crystallography, a key scientific technique.

Modern technologies like material analysis, semiconductor research, mineralogy, and protein structure studies depend heavily on Bragg’s law.

Application in X-ray diffraction

X-ray diffraction experiments measure the angles and intensities of diffracted beams. Bragg’s law is used to:

  • calculate d, the distance between planes
  • determine crystal structure
  • identify phases of materials
  • study defects or impurities in solids

Even powdered samples give diffraction rings that follow Bragg’s law.

Role of Bragg’s law in crystallography

Crystallography uses Bragg’s law as a foundational tool. It helps scientists understand:

  • lattice structure
  • unit cells
  • atomic arrangement
  • symmetry in crystals

Using Bragg’s law and diffraction data, scientists build 3D models of crystals. It played a major role in identifying the double helical structure of DNA and in studying proteins, minerals, and metals.

Examples of Bragg’s law in real applications

  1. Mineral identification
    Each mineral has a unique diffraction pattern based on Bragg’s law.
  2. Metallurgy
    Engineers study grain structure and crystal defects.
  3. Semiconductor manufacturing
    Crystals used in computer chips are tested using Bragg diffraction.
  4. Pharmaceutical industry
    Drug molecules often form crystals, and XRD helps verify their structure.
  5. Biological research
    Protein structures are determined using X-ray crystallography.

Significance in scientific history

Bragg’s law was proposed in 1913 by Sir Lawrence Bragg and his father, William Henry Bragg. Their work showed how X-rays could be used to probe the atomic world. This discovery revolutionised solid-state physics and earned them the Nobel Prize in Physics in 1915.

Conclusion

Bragg’s law describes the condition under which X-rays reflected from different crystal planes interfere constructively. It is represented as . This law is the foundation of X-ray diffraction and is widely used to study the arrangement, spacing, and structure of atoms in crystals. Bragg’s law has immense applications in physics, chemistry, biology, materials science, and engineering, making it one of the most important principles in modern science.