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Bragg Reflections
In many areas of science, 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. This law was initially formulated for X-rays, but it also applies to all types of matter waves including neutron and electron waves if there are a large number of atoms, as well as to visible light with artificial periodic microscale lattices. History Bragg diffraction (also referred to as the Bragg formulation of X-ray diffraction) 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 (in contrast to those produced with, for instance, a liquid). They found that these crystal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georg Wulff
Georg Wulff, Georgy Wulff or Yuri Viktorovich Vulf () (22 June 1863, Nizhyn (Russian Empire, now Ukraine) – 25 December 1925, Moscow) was a pioneer Russian crystallography, crystallographer. Biography Wulff was born in Nizhyn, Chernigov province where his mother Lydia was daughter of teacher E. V. Gudim. His father Viktor Konstantinovich Vulf was a literature teacher at the 6th Warsaw Gymnasium. He grew up in Warsaw and graduated from the 6th Warsaw Gymnasium in 1880. He then went to the Imperial Warsaw University to study natural sciences. He studied under crystallographer Alexander Lagorio, A. E. Lagorio, and physicists N. G. Egorov and P. A. Zilov. In the third year, he studied the electrical properties of quartz for which he received a gold medal. In his fourth year he was assisting lectures of professor Zilov. He began to study the relationship of crystal structure and optical properties and in 1888 he published a paper on the "theory of rotatory polarization". He then wen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Diffraction
Electron diffraction is a generic term for phenomena associated with changes in the direction of electron beams due to elastic interactions with atoms. It occurs due to elastic scattering, when there is no change in the energy of the electrons. The negatively charged electrons are scattered due to Coulomb forces when they interact with both the positively charged atomic core and the negatively charged electrons around the atoms. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern, see for instance Figure 1. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in electron microscopes. This article provides an overview of electron diffraction and electron diffraction patterns, collective referred to by the generic name electron diffraction. This includes aspects of how in a general way electrons can act as waves, and diffract and interact with matter. It a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Lattice
In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as . It is one of the five types of two-dimensional lattices as classified by their symmetry groups; its symmetry group in IUC notation as , Coxeter notation as , and orbifold notation as . Two orientations of an image of the lattice are by far the most common. They can conveniently be referred to as the upright square lattice and diagonal square lattice; the latter is also called the centered square lattice.. They differ by an angle of 45°. This is related to the fact that a square lattice can be partitioned into two square sub-lattices, as is evident in the colouring of a checkerboard. Symmetry The square lattice's symmetry category is wallpaper group . A pattern with this lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself. An upright square lattice can be vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane Wave
In physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ..., a plane wave is a special case of a wave or field: a physical quantity whose value, at any given moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, the value of such a field can be written as F(\vec x,t) = G(\vec x \cdot \vec n, t), where \vec n is a unit-length vector, and G(d,t) is a function that gives the field's value as dependent on only two real parameters: the time t, and the scalar-valued displacement d = \vec x \cdot \vec n of the point \vec x along the direction \vec n. The displacement is constant over each plane perpendicular to \vec n. The values of the field F may be scalars, vectors, or any other physical or ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laue Equations
In crystallography and solid state physics, the Laue equations relate incoming waves to outgoing waves in the process of elastic scattering, where the photon energy or light temporal frequency does not change upon scattering by a crystal lattice. They are named after physicist Max von Laue (1879–1960). The Laue equations can be written as \mathbf= \mathbf_ - \mathbf_ = \mathbf as the condition of elastic wave scattering by a crystal lattice, where \mathbf is the scattering vector, \mathbf_, \mathbf k_ are incoming and outgoing ''wave vectors'' (to the crystal and from the crystal, by scattering), and \mathbf is a crystal ''reciprocal lattice vector''. Due to elastic scattering , \mathbf_, ^2=, \mathbf_, ^2, three vectors. \mathbf, \mathbf_, and -\mathbf_ , form a rhombus if the equation is satisfied. If the scattering satisfies this equation, all the crystal lattice points scatter the incoming wave toward the scattering direction (the direction along \mathbf k_). If the equatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffraction Order
In optics, a diffraction grating is an optical grating with a periodic structure that diffracts light, or another type of electromagnetic radiation, into several beams traveling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structural coloration. The directions or diffraction angles of these beams depend on the wave (light) incident angle to the diffraction grating, the spacing or periodic distance between adjacent diffracting elements (e.g., parallel slits for a transmission grating) on the grating, and the wavelength of the incident light. The grating acts as a dispersive element. Because of this, diffraction gratings are commonly used in monochromators and spectrometers, but other applications are also possible such as optical encoders for high-precision motion control and wavefront measurement. For typical applications, a reflective grating has ridges or ''rulings'' on its surface while a transmissive grating has tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Snell's Law
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index. The law states that, for a given pair of media, the ratio of the sines of angle of incidence \left(\theta_1 \right) and angle of refraction \left(\theta_2\right) is equal to the refractive index of the second medium with regard to the first (n_) which is equal to the ratio of the refractive indices \left(\tfrac\right) of the two media, or e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glancing Angle (optics)
The angle of incidence, in geometric optics, is the angle between a ray incident on a surface and the line perpendicular (at 90 degree angle) to the surface at the point of incidence, called the normal. The ray can be formed by any waves, such as optical, acoustic, microwave, and X-ray. In the figure below, the line representing a ray makes an angle θ with the normal (dotted line). The angle of incidence at which light is first totally internally reflected is known as the critical angle. The angle of reflection and angle of refraction are other angles related to beams. In computer graphics and geography, the angle of incidence is also known as the illumination angle of a surface with a light source, such as the Earth's surface and the Sun. It can also be equivalently described as the angle between the tangent plane of the surface and another plane at right angles to the light rays. This means that the illumination angle of a certain point on Earth's surface is 0° if the Sun i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interference (wave Propagation)
In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater amplitude (constructive interference) or lower amplitude (destructive interference) if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves. Etymology The word ''interference'' is derived from the Latin words ''inter'' which means "between" and ''fere'' which means "hit or strike", and was used in the context of wave superposition by Thomas Young in 1801. Mechanisms The principle of superposition of waves states that when two or more propagating waves of the same type are incident on the same point, the resultant amplitude at that point is equal to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specular Reflection
Specular reflection, or regular reflection, is the mirror-like reflection (physics), reflection of waves, such as light, from a surface. The law of reflection states that a reflected ray (optics), ray of light emerges from the reflecting surface at the same angle to the surface normal as the incident ray, but on the opposing side of the surface normal in the plane formed by the incident and reflected rays. The earliest known description of this behavior was recorded by Hero of Alexandria (Anno Domini, AD c. 10–70). Later, Ibn al-Haytham, Alhazen gave a complete statement of the law of reflection. He was first to state that the incident ray, the reflected ray, and the normal to the surface all lie in a same plane perpendicular to reflecting plane. Specular reflection may be contrasted with diffuse reflection, in which light is scattered away from the surface in a range of directions. Law of reflection When light encounters a boundary of a material, it is affected by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves), phase'' on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The multiplicative inverse, inverse of the wavelength is called the ''spatial frequency''. Wavelength is commonly designated by the Greek letter lambda (''λ''). For a modulated wave, ''wavelength'' may refer to the carrier wavelength of the signal. The term ''wavelength'' may also apply to the repeating envelope (mathematics), envelope of modulated waves or waves formed by Interference (wave propagation), interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed phase velocity, wave speed, wavelength is inversely proportion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
