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, (phúsis), nature and (phusiké), 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. ... Quartz crystal In chemistry and mineralogy, a crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ... Sir William Henry Bragg OM, Cantab, OKW (Westward, Cumbria, England July 2, 1862 – 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, (March 31, 1890 - July 1, 1971) was a Australian physicist who won the Nobel Prize in Physics in 1915. ... 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. ... Quartz crystal In chemistry and mineralogy, a crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ... 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, (phúsis), nature and (phusiké), 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. ...

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 dueto 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. 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. ... Sine waves of various frequencies; the lower 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. ... 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. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ... 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. ...

Wikipedia does not have an article with this exact name. ...

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

where

• n is an integer,
• λ is the wavelength of x-rays, and moving electrons, protons and neutrons,
• d is the spacing between the planes in the atomic lattice, and
• θ is the angle between the incident ray and the scattering planes

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. ... Properties [1][2] In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... 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. ... Properties [1][2] In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... 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, 1892–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 relfected along AB and BC paths respectively. This path difference is:

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: Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...

Where the same definition of n and λ apply from the article above

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. ...

and and

also it can be shown that:

Putting everything together and using known identities for sinusoidal functions:

Which simplifies to:

Bragg's Law

As it turns out λ< 2d or else that would force sin(θ) to be greater than 1 which it cannot be.

References

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

See also

• Bragg diffraction
• Dynamical theory of diffraction
• Crystal lattice
• Diffraction
  • Diffraction grating
• Distributed Bragg reflector
  • Fiber Bragg grating
• Photonic crystal fiber
• Wavelength
• X-ray crystallography