Bridge Rectifier: Explained with Working Principle, Diagram & Examples

X-ray reflection, in accordance with Bragg's Law, is a fundamental concept in the study of crystallography and material characterization. When X-rays strike a crystal, they are scattered by the orderly arrangement of atoms within the crystal's lattice. Under specific conditions, these scattered X-rays interfere constructively, producing sharp reflection peaks known as Bragg peaks. 

This phenomenon is governed by Bragg's Law, which relates the angle of incidence, wavelength of the X-rays, and the spacing between the atomic planes in a crystal.

Understanding Bragg's Law

Bragg's Law provides the condition for constructive interference of X-rays reflecting off different layers of atoms within a crystal. The law is mathematically stated as:

Where:

• n = integer (order of reflection)
• λ = wavelength of the incident X-ray
• d = interplanar spacing (distance between atomic planes in the crystal)
• θ = angle of incidence (also called Bragg angle)

This relationship forms the basis for analyzing the crystal structure using incident X-rays.

Application of Bragg's Law in X-ray Diffraction (XRD)

In X-ray diffraction (XRD), a known wavelength of X-rays is directed at a crystal. The angle at which constructive interference (a Bragg reflection) occurs is measured. By substituting the measured angle and known wavelength into Bragg's Law, the value of d (the spacing between lattice planes) is calculated.

Repeated measurements produce a set of d-spacings, which acts like a fingerprint, uniquely identifying the crystal's internal structure.

Step-by-Step Approach for Applying Bragg's Law

1. Determine the wavelength (λ) of incident X-rays being used in the experiment.
2. Expose the crystal to the X-ray beam and gradually change the angle of incidence (θ).
3. Identify the angle(s) at which maximum reflected intensity occurs (Bragg peaks).
4. Apply Bragg’s Law formula to solve for the interplanar spacing (d):
   nλ = 2d sinθ
5. Repeat the process for various planes (multiple values of n) to get a complete set of d-spacings.

Key Table: Bragg's Law Variables and Their Significance

Bragg's Law in Material Characterization

The set of all possible reflections, created by different atomic planes in a crystal, provides a detailed profile that allows accurate identification of an unknown crystal. Crystals with high symmetry have fewer unique atomic planes and thus fewer reflection peaks; crystals with lower symmetry show more peaks because of their complex atomic arrangements.

Special Cases: Spectrometric Methods Using Bragg's Law

Bragg’s Law is also used in techniques like wavelength dispersive spectrometry (WDS) and X-ray fluorescence spectroscopy (XRF).

• In these techniques, crystals with known d-spacings serve as analyzing elements within a spectrometer.
• The position of the sample and detector is fixed, but the crystal's angle is adjusted to reflect X-rays of a specific wavelength into the detector.
• Each element produces X-rays at fixed wavelengths corresponding to energy differences between its atomic orbitals; by matching the wavelength to a unique angle via Bragg’s law, precise quantitative analysis of elements is achieved.

Example Problem: Calculation Using Bragg's Law

Suppose an X-ray beam of wavelength 1.54 Å is incident on a crystal and produces a maximum at an angle of 20°. Given that n = 1 (first-order reflection), the interplanar spacing d can be calculated as:

Common Physics Applications of Bragg’s Law

• Identification and structural analysis of crystals using XRD
• Quantitative elemental analysis in WDS and XRF
• Determining symmetry and atomic arrangement in materials science

Next Steps and Related Learning

• Study more about Electric circuits and circuit components
• Practice problems on Optics and Reflection

Understanding and applying Bragg’s Law will help you master topics in spectroscopy, crystallography, and modern physics. Explore official course materials for regular practice and in-depth learning.