NationMaster - Encyclopedia: Bragg's law

In physics, Bragg's law is the result of experiments into the diffraction of X-rays or neutrons off crystal surfaces at certain angles, derived by physicists Sir W.H. Bragg and his son Sir W.L. Bragg in 1912, and first presented on 1912-11-11 to the Cambridge Philosophical Society. Although simple, Bragg's law confirmed the existence of real particles at the atomic scale, as well as providing a powerful new tool for studying crystals in the form of X-ray and neutron diffraction. The Braggs were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS, and diamond. Physics (from the Greek, (phÃºsis), nature and (phusikÃ©), knowledge of nature) is the science concerned with the discovery and understanding of the fundamental laws which govern matter, energy, space, and time. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... Neutron diffraction is a crystallography technique that uses neutrons to determine the atomic structure of a material. ... For other senses of this word, see crystal (disambiguation). ... Sir William Henry Bragg OM, Cantab, OKW (Westward, Cumbria, England July 2, 1862 â€“ March 10, 1942) was an English physicist and chemist, educated at King Williams College, Isle of Man, and Trinity College, Cambridge. ... Sir William Lawrence Bragg CH, FRS, (31 March 1890 â€“ 1 July 1971) was an Australian physicist who shared the Nobel Prize in Physics in 1915 with his father Sir William Henry Bragg. ... 1912 (MCMXII) was a leap year starting on Monday in the Gregorian calendar (or a leap year starting on Tuesday in the 13-day-slower Julian calendar). ... 1912 (MCMXII) was a leap year starting on Monday in the Gregorian calendar (or a leap year starting on Tuesday in the 13-day-slower Julian calendar). ... November 11 is the 315th day of the year (316th in leap years) in the Gregorian Calendar, with 50 days remaining. ... The Cambridge Philosophical Society (CPS) is a scientific society at University of Cambridge. ... A subatomic particle is a particle smaller than an atom: it may be elementary or composite. ... For other senses of this word, see crystal (disambiguation). ... X-ray crystallography is a technique in crystallography in which the pattern produced by the diffraction of x-rays through the closely spaced lattice of atoms in a crystal is recorded and then analyzed to reveal the nature of that lattice. ... Neutron diffraction is a crystallography technique that uses neutrons to determine the atomic structure of a material. ... Nobel Prize medal. ... Physics (from the Greek, (phÃºsis), nature and (phusikÃ©), knowledge of nature) is the science concerned with the discovery and understanding of the fundamental laws which govern matter, energy, space, and time. ... 1915 (MCMXV) was a common year starting on Friday (see link for calendar). ... Sodium chloride, also known as common salt, table salt, or halite, is a chemical compound with the formula NaCl. ... Zinc sulfide (or zinc sulphide) is a chemical compound with the formula ZnS. Zinc sulfide is a white to yellow colored powder or crystal. ... // A scattering of round-brilliant cut diamonds shows off the many reflecting facets. ...

When X-rays hit an atom, they make the electronic cloud move as does any electromagnetic wave. The movement of these charges re-radiates waves with the same frequency (blurred slightly due to a variety of effects); this phenomenon is known as the Rayleigh scattering (or elastic scattering). A similar process occurs upon scattering neutron waves from the nuclei or by a coherent spin interaction with an unpaired electron. These re-emitted wave fields interfere with each other either constructively or destructively (overlapping waves either add together to produce stronger peaks or subtract from each other to some degree), producing a diffraction pattern on a detector or film. The resulting wave interference pattern is the basis of diffraction analysis. Both neutron and X-ray wavelengths are comparable with inter-atomic distances (~150 pm) and thus are an excellent probe for this length scale. In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... For other uses, see Atom (disambiguation). ... The electron is a fundamental subatomic particle that carries an electric charge. ... Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ... Look up movement in Wiktionary, the free dictionary The term Movement has a variety of different meanings related to motion: Physical movement between points in space (A to B). The amount of movement is called distance. ... A WAVES Photographer 3rd Class The WAVES were a World War II era division of the U.S. Navy that consisted entirely of women. ... Sine waves of various frequencies; the bottom waves have higher frequencies than those above. ... Rayleigh scattering causing a reddened sky at sunset Rayleigh scattering (named after Lord Rayleigh) is the scattering of light, or other electromagnetic radiation, by particles much smaller than the wavelength of the light. ... Process (lat. ... In particle physics, scattering is a class of phenomena by which particles are deflected by collisions with other particles. ... A semi-accurate depiction of the helium atom. ... Coherence is from Latin cohaerere = stick together, to be connected with). ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... The electron is a fundamental subatomic particle that carries an electric charge. ... In communications, interference is anything which alters, modifies, or disrupts a message; as it travels along a channel, between a source and a receiver. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ... A pattern is a form, template, or model (or, more abstractly, a set of rules) which can be used to make or to generate things or parts of a thing, especially if the things that are generated have enough in common for the underlying pattern to be inferred or discerned... To meet Wikipedias quality standards, this article or section may require cleanup. ... This article or section does not cite its references or sources. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... To help compare different orders of magnitude this page lists lengths between 1 pm and 10 pm (10-12 m and 10-11 m). ... In physics, length scale is a particular value of length or distance determined with the precision of one order (or a few orders) of magnitude. ...

The interference is constructive when the phase shift is proportional to 2π; this condition can be expressed by Bragg's law:

According to the 2θ deviation, the phase shift causes constructive (left figure) or destructive (right figure) interferences The wavelength is the distance between repeating units of a wave pattern. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... The electron is a fundamental subatomic particle that carries an electric charge. ... // For alternative meanings see proton (disambiguation). ... This article or section does not cite its references or sources. ... Wikipedia does not have an article with this exact name. ...

Note that moving particles, including electrons, protons and neutrons, have an associated wavelength, as determined by Louis de Broglie (see De Broglie wavelength). The electron is a fundamental subatomic particle that carries an electric charge. ... // For alternative meanings see proton (disambiguation). ... This article or section does not cite its references or sources. ... The wavelength is the distance between repeating units of a wave pattern. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892â€“March 19, 1987), was a French physicist and Nobel Prize laureate. ... The wavelength is the distance between repeating units of a wave pattern. ...

Alternate Derivation

A single monochromatic wave, of any type, is incident on aligned planes of lattice points, with separation d, at angle θ, as shown below. Something which is monochromatic has a single color. ... The ordinary meaning of lattice is the basis for several technical usages A cherry lattice pastry A mathematical lattice that is a type of partially ordered set. ...

There will be a path difference between the 'ray' that gets reflected along AC' and the ray that gets transmitted, then reflected along AB and BC paths respectively. This path difference is: Image File history File links Download high-resolution version (1600x1280, 17 KB) Made by Mark Ryan RMIT - Applied Physics Melbourne , Australia I, the creator of this work, hereby release it into the public domain. ...

If this path difference is equal to any integer value of the wavelength then the two separate waves will arrive at a point with the same phase, and hence undergo constructive interference. Expressed mathematically: The wavelength is the distance between repeating units of a wave pattern. ... A WAVES Photographer 3rd Class The WAVES were a World War II era division of the U.S. Navy that consisted entirely of women. ... Look up Phase in Wiktionary, the free dictionary Phase may refer to: Phase (matter), a physically distinctive form of a substance, such as the solid, liquid, and gaseous states of ordinary matter Phase (waves), the time position (or angle in the complex plane) within a cycle of a periodic waveform... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...

Using the Pythagorean theorem it is easily shown that: In mathematics, the Pythagorean theorem or Pythagoras theorem is a relation in Euclidean geometry among the three sides of a right triangle. ...

Putting everything together and using known identities for sinusoidal functions:

References

W.L. Bragg, "The Diffraction of Short Electromagnetic Waves by a Crystal", Proceedings of the Cambridge Philosophical Society, 17 (1912), 43–57.

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See also

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