Geochemical Instrumentation and Analysis
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X-ray reflection in accordance with Bragg's Law

Darrell Henry, Louisiana State University
Nelson Eby, University of Massachusetts - Lowell
John Goodge, University of Minnesota - Duluth
David Mogk, Montana State University

When a crystal is bombarded with X-rays of a fixed wavelength (similar to spacing of the atomic-scale crystal lattice planes) and at certain incident angles, intense reflected X-rays are produced when the wavelengths of the scattered X-rays interfere constructively. In order for the waves to interfere constructively, the differences in the travel path must be equal to integer multiples of the wavelength. When this constructive interference occurs, a diffracted beam of X-rays will leave the crystal at an angle equal to that of the incident beam.

Figure 1. Bragg's Law reflection. The diffracted X-rays exhibit constructive interference when the distance between paths ABC and A'B'C' differs by an integer number of wavelengths (λ).

To illustrate this feature, consider a crystal with crystal lattice planar distances d (right). Where the travel path length difference between the ray paths ABC and A'B'C' is an integer multiple of the wavelength, constructive interference will occur for a combination of that specific wavelength, crystal lattice planar spacing and angle of incidence (Θ). Each rational plane of atoms in a crystal will undergo refraction at a single, unique angle (for X-rays of a fixed wavelength).

The general relationship between the wavelength of the incident X-rays, angle of incidence and spacing between the crystal lattice planes of atoms is known as Bragg's Law, expressed as:

n λ = 2d sinΘ

where n (an integer) is the "order" of reflection, λ is the wavelength of the incident X-rays, d is the interplanar spacing of the crystal and Θ is the angle of incidence.

Applications of Bragg's Law.


Eby, G.N., 2004, Principles of Environmental Geochemistry. Brooks/Cole-Thomson Learning, p. 212-214.

Related Resources

Bragg's Law Applet Activity, Glenn Richard
This teaching activity provides an introduction to Bragg's Law and has students use a Java applet to explore and answer questions. The activity was developed for the On the Cutting Edge, Understanding the Deep Earth workshop.