Keith Mack
Bragg's Law, also known as the Wulff-Bragg condition or Laue-Bragg interference, is a law in physics that describes the relationship between the angle at which a beam of X-rays interacts with the parallel planes of atoms in a crystal lattice and the resulting scattering of waves. This law was formulated by Lawrence Bragg and his father, William Henry Bragg, in 1913, and it has become one of the most well-known equations in science. Bragg's Law is particularly useful for predicting and understanding the behaviour of X-rays in crystal structures, which has applications in fields such as medicine and materials science. By utilising Bragg's Law, scientists can make precise energy measurements of X-rays, determine lattice spacings of crystals, and even create widely tunable laser sources.
| Characteristics | Values |
|---|---|
| Equation | sin Θ = nλ / 2d |
| Variables | Θ (angle between incident or reflected beam and crystal plane), λ (wavelength of radiation), d (inter-planar spacing), n (integer) |
| Predicts | When diffraction will occur |
| Application | Measuring wavelengths, determining lattice spacings of crystals, X-ray reflection, electron diffraction, and microscopy |
| Use | To study crystals, measure precise energy of X-rays and low-energy gamma rays |
| Relation | Between the angle of incidence, wavelength, and distance between crystal planes |
| Validity | For large crystals, not for visible light |
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What You'll Learn
The history of Bragg's Law
Bragg's Law, also known as the Wulff-Bragg condition or Laue-Bragg interference, is a special case of Laue diffraction. It describes the relationship between the wavelength and scattering angle of waves interacting with a large crystal lattice. This law was formulated for X-rays, but it is also applicable to other types of matter waves, including neutron and electron waves, as well as visible light with artificial periodic microscale lattices.
The equation for Bragg's Law is given as nλ = 2d sin θ, where n is the order of diffraction, λ is the wavelength of the radiation, d is the inter-planar spacing, and θ is the angle between the incident ray and the crystal planes. This equation predicts when diffraction will occur and provides valuable insights into the behaviour of waves when interacting with crystalline structures.
The significance of Bragg's Law in science, particularly in the fields of electron diffraction, microscopy, and crystallography, is undeniable. It has enabled scientists to confirm the existence of real particles at the atomic scale and provided a powerful tool for studying crystals and their structures. By utilising Bragg's Law, researchers can determine the lattice spacings of crystals and make precise energy measurements of X-rays, low-energy gamma rays, and neutrons.
Additionally, Bragg's Law has found applications in various modern technologies. For instance, Volume Bragg Gratings (VBG) or Volume Holographic Gratings (VHG) use the principles of Bragg's Law to transmit or reflect specific wavelengths of light. This technology has been employed in the development of widely tunable laser sources and global hyperspectral imagery systems.
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Bragg's Law and X-ray reflection
The phenomenon of X-ray reflection is explained by Bragg's Law, which is a special case of Laue diffraction. It determines the angles of coherent and incoherent scattering from a crystal lattice. When an X-ray is incident on a crystal surface, its angle of incidence, θ, will reflect with the same angle of scattering, θ. This is the basis of the relationship between an X-ray light shooting and its reflection from a crystal surface.
Bragg's Law is 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. In X-ray diffraction (XRD), the interplanar spacing (d-spacing) of a crystal is used for identification and characterization purposes. The wavelength of the incident X-ray is known, and measurement is made of the incident angle (Θ) at which constructive interference occurs.
Bragg's Law is useful for measuring wavelengths and for determining the lattice spacings of crystals. In the case of X-ray fluorescence spectroscopy (XRF) or wavelength dispersive spectrometry (WDS), crystals of known d-spacings are used for analyzing crystals in the spectrometer. By using a spectrometer crystal (with fixed d-spacing) and positioning the crystal at a unique and fixed angle (Θ), it is possible to detect and quantify elements of interest based on the characteristic X-ray wavelengths produced by each element.
Bragg's Law also has applications in the field of optics, where it can be used to understand the behaviour of light waves. For example, in the case of precious opal, a type of colloidal crystal with optical effects, Bragg's Law can be used to explain the brilliant iridescence (or play of colours) exhibited by the crystal. This occurs due to the diffraction and constructive interference of visible light waves when the interstitial spacing between the particles is similar to the wavelength of the incident light wave.
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Diffraction patterns and Bragg's Law
Diffraction patterns are an important tool in the study of crystallography, and Bragg's law is a key principle in this field. The law was first proposed by Lawrence Bragg and his father, William Henry Bragg, in 1913 after they discovered that crystalline solids produced distinct patterns of reflected X-rays.
Bragg's law, also known as the Wulff-Bragg condition or Laue-Bragg interference, is a special case of Laue diffraction. It provides the angles for the coherent scattering of waves from a large crystal lattice, establishing a strict relationship between the wavelength and the scattering angle. This relationship is described by the equation:
> nλ = 2d sin(θ)
Where λ is the wavelength of the radiation used, d is the inter-planar spacing, θ is the angle between the incident ray and the crystal planes, and n is the order of diffraction.
The law is not limited to X-rays, but also applies to other matter waves such as neutron and electron waves, as well as visible light with artificial periodic microscale lattices. In the case of electrons, low-energy electron diffraction results in electrons being reflected back from a surface, while high-energy electron diffraction typically produces rings of diffraction spots.
The principle of Bragg's law is applied in the construction of instruments such as the Bragg spectrometer, which is used to study the structure of crystals and molecules. By understanding and utilising Bragg's law, scientists can gain valuable insights into the nature and behaviour of crystalline materials.
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Bragg's Law and constructive interference
Although Laue is credited with the discovery of diffraction, it was W.H.Bragg who devised an equation that predicted when diffraction would take place. This equation, known as Bragg's Law, is one of the most well-known equations in science.
Bragg's Law is a special case of Laue diffraction that gives the angles for the coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength and scattering angle. This law was initially formulated for X-rays, but it also applies to all types of matter waves, including neutron and electron waves, and even to visible light with artificial periodic microscale lattices.
The law is particularly useful in the study of crystals and was first proposed by Lawrence Bragg and his father, William Henry Bragg, in 1913 after their discovery that crystalline solids produced surprising patterns of reflected X-rays. Lawrence Bragg explained this result by modelling the crystal as a set of discrete parallel planes separated by a constant parameter 'd'. He proposed that incident X-ray radiation would produce a Bragg peak if reflections off the various planes interfered constructively.
Constructive interference in Bragg's Law refers to the phenomenon where waves diffracted at the Bragg angle result in a stronger and clearer diffraction pattern. This occurs when the difference in path lengths, represented by the Bragg equation, is an integer multiple of the wavelength. The interference is constructive when the phase difference between the wave reflected off different atomic planes is a multiple of 2π. This condition was first presented by Lawrence Bragg in 1912 to the Cambridge Philosophical Society.
The so-called Bragg's Law for constructive interference is given by the equation: nλ = 2dsin(θ), where n is an integer, λ is the wavelength, and d is the distance between the layers in the crystal.
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Bragg's Law and crystal structures
In many scientific fields, Bragg's law, also known as Wulff–Bragg's condition or Laue–Bragg interference, is a special case of Laue diffraction that gives the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength and scattering angle.
Bragg's law was initially formulated for X-rays by Lawrence Bragg and his father, William Henry Bragg, in 1913 after they discovered that crystalline solids produced distinct patterns of reflected X-rays. Lawrence Bragg modelled the crystal as a set of discrete parallel planes separated by a constant parameter d. He proposed that incident X-ray radiation would produce a Bragg peak if reflections off the various planes interfered constructively. The interference is constructive when the phase difference between the wave reflected off different atomic planes is a multiple of 2π. This simple law confirmed the existence of real particles at the atomic scale and provided a powerful new tool for studying crystals.
Bragg's law is useful for measuring wavelengths and determining the lattice spacings of crystals. To measure a particular wavelength, the radiation beam and the detector are set at an arbitrary angle θ. The angle is then modified until a strong signal is received. The Bragg angle then gives the wavelength directly from Bragg's law. This is the main method for making precise energy measurements of X-rays and low-energy gamma rays.
Bragg diffraction occurs when radiation of a wavelength λ comparable to atomic spacings is scattered in a specular fashion by planes of atoms in a crystalline material and undergoes constructive interference. When the scattered waves are incident at a specific angle, they remain in phase and constructively interfere. The glancing angle θ, wavelength λ, and the "grating constant" d of the crystal are connected by a mathematical relation.
Bragg's law can be used to determine crystal structure. For example, it can be used to obtain the lattice spacing of a particular cubic system. It can also be used to determine the crystallinity of a material. By bombarding a sample with X-rays while rotating, diffraction patterns are generated that can be used to describe sample crystallinity. X-ray diffraction (XRD) follows Bragg's law in that the reflected X-rays from different crystal layers with long-range order undergo constructive interference, causing high-intensity peaks in the spectrum.
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Frequently asked questions
Bragg's Law, also known as the Wulff-Bragg condition or Laue-Bragg interference, is a law in physics that explains the relationship between the angle at which a beam of X-rays falls on the parallel planes of atoms in a crystal and the wavelength and distance between the crystal planes.
Bragg's Law confirmed the existence of real particles at the atomic scale and provided a powerful tool for studying crystals. It also led to the development of new technologies such as widely tunable laser sources and global hyperspectral imagery.
The equation for Bragg's Law is nλ = 2d sin θ, where n is an integer, λ is the wavelength of the radiation used, d is the distance between crystal planes, and θ is the angle between the incident beam and the crystal plane.
Bragg's Law is used to measure wavelengths and determine the lattice spacings of crystals. It is also used in X-ray diffraction experiments to study the crystallinity of materials and in electron diffraction and microscopy.
