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Bragg's law

physical science Maturity 11-13 Next article →

Bragg's law is a fundamental principle in physics used to understand how waves interact with crystals.

Bragg's law
Bragg's law

It describes a specific condition for the coherent scattering of waves from a large crystal lattice. This lattice is a repeating, ordered arrangement of atoms. When waves hit these atoms, they scatter in various directions. Bragg's law identifies the exact angles where these scattered waves reinforce one another. This phenomenon is essential for scientists to map the internal structures of different materials. It provides a mathematical bridge between the observed angles of scattered waves and the physical spacing of atoms.

The mechanism relies on the concept of constructive interference.

Bragg diffraction 2
Bragg diffraction 2

Imagine a crystal as a series of discrete, parallel atomic planes separated by a constant distance, known as the interplanar spacing, or "d". When a wave, such as an X-ray, hits these planes at a glancing angle, theta, it scatters off different layers. The waves hitting the deeper planes must travel a longer distance than the waves hitting the surface. This extra distance is calculated as 2d sin(theta). For the waves to emerge in phase and undergo constructive interference, this extra path must be an integer multiple of the wavelength, lambda. If this condition is met, the waves add together to create intense signals called Bragg peaks.

Braggs Law2
Braggs Law2

Bragg's law is not limited to X-rays. It applies to all types of matter waves, provided there are enough atoms to create a lattice. This includes neutron waves and electron waves. For these particles, the wavelengths are often comparable to the inter-atomic distances, which are roughly 150 picometers.

Diffusion rayleigh et diffraction
Diffusion rayleigh et diffraction

The law even explains the behavior of visible light in certain materials. In colloidal crystals, large particles form an ordered array. The spaces between these particles act as a natural diffraction grating for visible light. This is why objects like precious opals display a brilliant play of colors through iridescence.

The history of this discovery is tied to the Bragg family. Lawrence Bragg first presented his formulation to the Cambridge Philosophical Society on November 11, 1912. While some sources attribute the discovery to both Lawrence and his father, William Henry Bragg, official biographies state that Lawrence alone derived the law. The Braggs were awarded the Nobel Prize in physics in 1915 for their work on crystal structures. They successfully solved the structures of substances like sodium chloride, zinc sulfide, and diamond. They remain the only father and son team to jointly win a Nobel Prize.

Mathematically, the law is expressed by the equation n * lambda = 2d sin(theta). In this formula, "n" represents the diffraction order, which is an integer like 1, 2, or 3. The angle theta is the glancing angle, which is measured from the atomic planes rather than the surface normal. This equation allows researchers to calculate the "d" spacing of a crystal by measuring the angles where peaks occur. In many real materials, many atomic planes participate in the scattering. This causes the resulting Bragg peaks to be very sharp and distinct in a diffraction pattern.

DifraccionElectronesMET
DifraccionElectronesMET

Different types of radiation interact with matter in unique ways. X-rays and neutrons scatter relatively weakly, often requiring crystals that are at least 100 nanometers in size. Electrons, however, interact much more strongly with solids. Because of this intense interaction, samples used for electron diffraction must be much thinner. While Bragg's law provides a great approximation for electron diffraction, the patterns often show a complex lattice of spots. These spots are related to the reciprocal lattice, which is a mathematical representation of the crystal's structure. In some cases, such as high-energy electron diffraction, the results appear as rings of spots.

Bragg's law also finds modern applications in advanced technology. Volume Bragg gratings, or VBGs, use a periodic change in the refractive index to manipulate light. These gratings can be designed to reflect or transmit specific wavelengths. By changing the incident angle, scientists can tune the output wavelength by several hundred nanometers. This capability is used to create highly tunable laser sources and for hyperspectral imagery. By mastering the way waves interfere with ordered structures, we can continue to develop precise optical and physical tools.

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File:Diffusion rayleigh et diffraction.svg
Diffusion rayleigh et diffraction.svg
File:Braggs Law2.svg
Braggs Law2.svg
File:Bragg diffraction 2.svg
Bragg diffraction 2.svg
File:Bragg's law.svg
Bragg's law.svg
File:DifraccionElectronesMET.jpg
DifraccionElectronesMET.jpg
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