1.
X-ray
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X-radiation is a form of electromagnetic radiation. Most X-rays have a wavelength ranging from 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz, X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays. Spelling of X-ray in the English language includes the variants x-ray, xray, X-rays with high photon energies are called hard X-rays, while those with lower energy are called soft X-rays. Due to their ability, hard X-rays are widely used to image the inside of objects, e. g. in medical radiography. The term X-ray is metonymically used to refer to an image produced using this method. Since the wavelengths of hard X-rays are similar to the size of atoms they are useful for determining crystal structures by X-ray crystallography. By contrast, soft X-rays are easily absorbed in air, the length of 600 eV X-rays in water is less than 1 micrometer. There is no consensus for a definition distinguishing between X-rays and gamma rays, one common practice is to distinguish between the two types of radiation based on their source, X-rays are emitted by electrons, while gamma rays are emitted by the atomic nucleus. This definition has problems, other processes also can generate these high-energy photons. One common alternative is to distinguish X- and gamma radiation on the basis of wavelength, with radiation shorter than some arbitrary wavelength, such as 10−11 m and this criterion assigns a photon to an unambiguous category, but is only possible if wavelength is known. Occasionally, one term or the other is used in specific contexts due to precedent, based on measurement technique. Thus, gamma-rays generated for medical and industrial uses, for radiotherapy, in the ranges of 6–20 MeV. X-ray photons carry enough energy to ionize atoms and disrupt molecular bonds and this makes it a type of ionizing radiation, and therefore harmful to living tissue. A very high radiation dose over a period of time causes radiation sickness. In medical imaging this increased risk is generally greatly outweighed by the benefits of the examination. The ionizing capability of X-rays can be utilized in treatment to kill malignant cells using radiation therapy. It is also used for material characterization using X-ray spectroscopy, hard X-rays can traverse relatively thick objects without being much absorbed or scattered. For this reason, X-rays are widely used to image the inside of visually opaque objects, the most often seen applications are in medical radiography and airport security scanners, but similar techniques are also important in industry and research
2.
Diffraction
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Diffraction refers to various phenomena that occur when a wave encounters an obstacle or a slit. It is defined as the bending of light around the corners of an obstacle or aperture into the region of shadow of the obstacle. In classical physics, the phenomenon is described as the interference of waves according to the Huygens–Fresnel principle. These characteristic behaviors are exhibited when a wave encounters an obstacle or a slit that is comparable in size to its wavelength. Similar effects occur when a wave travels through a medium with a varying refractive index. Diffraction occurs with all waves, including sound waves, water waves, since physical objects have wave-like properties, diffraction also occurs with matter and can be studied according to the principles of quantum mechanics. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record observations of the phenomenon in 1660. If the obstructing object provides multiple, closely spaced openings, a pattern of varying intensity can result. This is due to the addition, or interference, of different parts of a wave that travel to the observer by different paths, the formalism of diffraction can also describe the way in which waves of finite extent propagate in free space. For example, the profile of a laser beam, the beam shape of a radar antenna. The effects of diffraction are often seen in everyday life and this principle can be extended to engineer a grating with a structure such that it will produce any diffraction pattern desired, the hologram on a credit card is an example. Diffraction in the atmosphere by small particles can cause a ring to be visible around a bright light source like the sun or the moon. A shadow of an object, using light from a compact source. The speckle pattern which is observed when laser light falls on a rough surface is also a diffraction phenomenon. When deli meat appears to be iridescent, that is diffraction off the meat fibers, all these effects are a consequence of the fact that light propagates as a wave. Diffraction can occur with any kind of wave, ocean waves diffract around jetties and other obstacles. Sound waves can diffract around objects, which is why one can hear someone calling even when hiding behind a tree. Diffraction can also be a concern in some applications, it sets a fundamental limit to the resolution of a camera, telescope
3.
Materials science
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The interdisciplinary field of materials science, also commonly termed materials science and engineering, involves the discovery and design of new materials, with an emphasis on solids. Materials science still incorporates elements of physics, chemistry, and engineering, as such, the field was long considered by academic institutions as a sub-field of these related fields. Materials science is a syncretic discipline hybridizing metallurgy, ceramics, solid-state physics and it is the first example of a new academic discipline emerging by fusion rather than fission. Many of the most pressing scientific problems humans currently face are due to the limits of the materials that are available, thus, breakthroughs in materials science are likely to affect the future of technology significantly. Materials scientists emphasize understanding how the history of a material influences its structure, the understanding of processing-structure-properties relationships is called the § materials paradigm. This paradigm is used to advance understanding in a variety of areas, including nanotechnology, biomaterials. Such investigations are key to understanding, for example, the causes of various accidents and incidents. The material of choice of a given era is often a defining point, phrases such as Stone Age, Bronze Age, Iron Age, and Steel Age are great examples. Originally deriving from the manufacture of ceramics and its putative derivative metallurgy, materials science is one of the oldest forms of engineering, modern materials science evolved directly from metallurgy, which itself evolved from mining and ceramics and the use of fire. Materials science has driven, and been driven by, the development of technologies such as rubbers, plastics, semiconductors. Before the 1960s, many materials science departments were named metallurgy departments, reflecting the 19th, a material is defined as a substance that is intended to be used for certain applications. There are a myriad of materials around us—they can be found in anything from buildings to spacecraft, Materials can generally be divided into two classes, crystalline and non-crystalline. The traditional examples of materials are metals, semiconductors, ceramics, New and advanced materials that are being developed include nanomaterials and biomaterials, etc. The basis of science involves studying the structure of materials. Once a materials scientist knows about this structure-property correlation, they can go on to study the relative performance of a material in a given application. The major determinants of the structure of a material and thus of its properties are its constituent chemical elements and these characteristics, taken together and related through the laws of thermodynamics and kinetics, govern a materials microstructure, and thus its properties. As mentioned above, structure is one of the most important components of the field of materials science, Materials science examines the structure of materials from the atomic scale, all the way up to the macro scale. Characterization is the way materials scientists examine the structure of a material, structure is studied at various levels, as detailed below
4.
Metallurgy
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The production of metals involves the processing of ores to extract the metal they contain, and the mixture of metals, sometimes with other elements, to produce alloys. Metallurgy is distinguished from the craft of metalworking, although metalworking relies on metallurgy, as medicine relies on medical science, Metallurgy is subdivided into ferrous metallurgy and non-ferrous metallurgy or colored metallurgy. Ferrous metallurgy involves processes and alloys based on iron while non-ferrous metallurgy involves processes, the production of ferrous metals accounts for 95 percent of world metal production. The roots of metallurgy derive from Ancient Greek, μεταλλουργός, metallourgós, worker in metal, from μέταλλον, métallon, metal + ἔργον, érgon, in the late 19th century it was extended to the more general scientific study of metals, alloys, and related processes. In English, the pronunciation is the more common one in the UK. The /ˈmetələrdʒi/ pronunciation is the common one in the USA. The earliest recorded metal employed by humans appears to be gold, small amounts of natural gold have been found in Spanish caves used during the late Paleolithic period, c.40,000 BC. Silver, copper, tin and meteoric iron can also be found in native form, egyptian weapons made from meteoric iron in about 3000 BC were highly prized as daggers from heaven. Certain metals, notably tin, lead and copper, can be recovered from their ores by simply heating the rocks in a fire or blast furnace, a process known as smelting. The first evidence of this extractive metallurgy dates from the 5th and 6th millennia BC and was found in the sites of Majdanpek, Yarmovac and Plocnik. To date, the earliest evidence of copper smelting is found at the Belovode site, other signs of early metals are found from the third millennium BC in places like Palmela, Los Millares, and Stonehenge. However, the ultimate beginnings cannot be ascertained and new discoveries are both continuous and ongoing. These first metals were single ones or as found, about 3500 BC, it was discovered that by combining copper and tin, a superior metal could be made, an alloy called bronze, representing a major technological shift known as the Bronze Age. The extraction of iron from its ore into a metal is much more difficult than for copper or tin. The process appears to have been invented by the Hittites in about 1200 BC, the secret of extracting and working iron was a key factor in the success of the Philistines. Historical developments in ferrous metallurgy can be found in a variety of past cultures. A 16th century book by Georg Agricola called De re metallica describes the highly developed and complex processes of mining metal ores, metal extraction, Agricola has been described as the father of metallurgy. Extractive metallurgy is the practice of removing valuable metals from an ore, in order to convert a metal oxide or sulphide to a purer metal, the ore must be reduced physically, chemically, or electrolytically
5.
X-ray generator
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An X-ray generator is a device that produces X-rays. It is commonly used in a variety of applications including medicine, fluorescence, electronic assembly inspection, in medical applications, X-ray generators are used by radiographers to acquire x-ray images of the internal structures of living organisms, and also in sterilization. X-rays are typically generated by an X-ray tube, when the electrons collide with the target, about 1% of the resulting energy is emitted as X-rays, with the remaining 99% released as heat. Due to the energy of the electrons that reach relativistic speeds the target is usually made of tungsten even if other material can be used particularly in XRF applications. A cooling system is necessary to cool the anode, many X-ray generators use water or oil recirculating systems, the discovery of X-rays came from experimenting with Crookes tubes, an early experimental electrical discharge tube invented by English physicist William Crookes around 1869-1875. In 1895, Wilhelm Röntgen discovered X-rays emanating from Crookes tubes, one of the first X-ray photographs was made of the hand of Röntgens wife. The image displayed both her wedding ring and bones, on January 18,1896 an X-ray machine was formally displayed by H. L. Smith. A fully functioning unit was introduced to the public at the 1904 Worlds Fair by Clarence Dally, in the 1940s and 1950s, X-ray machines were used in stores to help sell footwear. These were known as Shoe-fitting fluoroscopes, however, as the harmful effects of X-ray radiation were properly considered, they finally fell out of use. Shoe-fitting use of the device was first banned by the state of Pennsylvania in 1957, together with Robert J. Van de Graaff, John G. Trump developed one of the first million-volt X-ray generators. X-ray photons are produced by a beam that is accelerated to a very high speed. The electrons that make up the beam are emitted from a cathode filament. The electrons are focused and accelerated by an electrical field towards an angled anode target. The point where the beam strikes the target is called the focal spot. Most of the energy contained in the electron beam is converted to heat, but around 1% of the energy is converted into X-ray photons. There is a round window in the X-ray tube directly above the angled target. This window allows the X-rays to exit the tube with little attenuation while maintaining a vacuum seal required for the X-ray tube operation. Other than the tube window or port the remaining portion of the x-ray tube housing is lined with lead to absorb all remaining x-rays not usable for image creation
6.
University of California, Santa Barbara
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The University of California, Santa Barbara is a public research university and one of the 10 campuses of the University of California system. The main campus is located on a 1, 022-acre site near Goleta, California, tracing its roots back to 1891 as an independent teachers college, UCSB joined the University of California system in 1944 and is the third-oldest general-education campus in the system. UCSB is one of Americas Public Ivy universities, which recognizes top public universities in the United States. The university is a doctoral university and is organized into five colleges. UCSB was ranked 37th among National Universities, 8th among U. S. public universities, the university was also ranked 48th worldwide for 2016-17 by the Times Higher Education World University Rankings and 42nd worldwide by the Academic Ranking of World Universities in 2016. UC Santa Barbara is a high activity research university with twelve national research centers. UCSB was the No.3 host on the ARPAnet and was elected to the Association of American Universities in 1995, the UC Santa Barbara Gauchos compete in the Big West Conference of the NCAA Division I. The Gauchos have won NCAA national championships in soccer and mens water polo. UCSB traces its origins back to the Anna Blake School which was founded in 1891 and offered training in home economics and industrial arts. The Anna Blake School was taken over by the state in 1909 and became the Santa Barbara State Normal School, the State College system sued to stop the takeover, but the Governor did not support the suit. A state initiative was passed, however, in 1946 to stop subsequent conversions of State Colleges to University of California campuses, from 1944 to 1958 the school was known as Santa Barbara College of the University of California, before taking on its current name. When the vacated Marine Corps training station in Goleta was purchased for the growing college. Originally, the Regents envisioned a small, several thousand-student liberal arts college, chronologically, UCSB is the third general-education campus of the University of California, after Berkeley and UCLA. The original campus the Regents acquired in Santa Barbara was located on only 100 acres of largely unusable land on a seaside mesa, all of this change was done in accordance with the California Master Plan for Higher Education. In 1959, UCSB professor Douwe Stuurman hosted the English writer Aldous Huxley as the universitys first visiting professor, Huxley delivered a lectures series called The Human Situation. In the late 1960s and early 1970s UCSB became nationally known as a hotbed of anti-Vietnam War activity, a bombing at the schools faculty club in 1969 killed the caretaker, Dover Sharp. UCSBs anti-Vietnam activity impelled then Governor Ronald Reagan to impose a curfew, weapon-carrying guardsmen were a common sight on campus and in Isla Vista during this time. On May 23,2014, a killing spree occurred in Isla Vista, California, all six people killed during the rampage were students at UCSB
7.
X-ray crystallography
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By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder. The method also revealed the structure and function of biological molecules, including vitamins, drugs, proteins. X-ray crystallography is still the method for characterizing the atomic structure of new materials. In a single-crystal X-ray diffraction measurement, a crystal is mounted on a goniometer, the goniometer is used to position the crystal at selected orientations. The crystal is illuminated with a finely focused monochromatic beam of X-rays, poor resolution or even errors may result if the crystals are too small, or not uniform enough in their internal makeup. X-ray crystallography is related to other methods for determining atomic structures. Similar diffraction patterns can be produced by scattering electrons or neutrons, for all above mentioned X-ray diffraction methods, the scattering is elastic, the scattered X-rays have the same wavelength as the incoming X-ray. By contrast, inelastic X-ray scattering methods are useful in studying excitations of the sample, Crystals, though long admired for their regularity and symmetry, were not investigated scientifically until the 17th century. Johannes Kepler hypothesized in his work Strena seu de Nive Sexangula that the symmetry of snowflake crystals was due to a regular packing of spherical water particles. The Danish scientist Nicolas Steno pioneered experimental investigations of crystal symmetry, hence, William Hallowes Miller in 1839 was able to give each face a unique label of three small integers, the Miller indices which remain in use today for identifying crystal faces. In the 19th century, a catalog of the possible symmetries of a crystal was worked out by Johan Hessel, Auguste Bravais, Evgraf Fedorov, Arthur Schönflies. Wilhelm Röntgen discovered X-rays in 1895, just as the studies of crystal symmetry were being concluded, physicists were initially uncertain of the nature of X-rays, but soon suspected that they were waves of electromagnetic radiation, in other words, another form of light. Single-slit experiments in the laboratory of Arnold Sommerfeld suggested that X-rays had a wavelength of about 1 angstrom, however, X-rays are composed of photons, and thus are not only waves of electromagnetic radiation but also exhibit particle-like properties. Albert Einstein introduced the concept in 1905, but it was not broadly accepted until 1922. Therefore, these properties of X-rays, such as their ionization of gases. Nevertheless, Braggs view was not broadly accepted and the observation of X-ray diffraction by Max von Laue in 1912 confirmed for most scientists that X-rays were a form of electromagnetic radiation, Crystals are regular arrays of atoms, and X-rays can be considered waves of electromagnetic radiation. Atoms scatter X-ray waves, primarily through the atoms electrons and this phenomenon is known as elastic scattering, and the electron is known as the scatterer
8.
Mineralogy
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Mineralogy is a subject of geology specializing in the scientific study of chemistry, crystal structure, and physical properties of minerals and mineralized artifacts. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, the German Renaissance specialist Georgius Agricola wrote works such as De re metallica and De Natura Fossilium which began the scientific approach to the subject. Systematic scientific studies of minerals and rocks developed in post-Renaissance Europe, the modern study of mineralogy was founded on the principles of crystallography and to the microscopic study of rock sections with the invention of the microscope in the 17th century. Nicholas Steno first observed the law of constancy of interfacial angles in quartz crystals in 1669 and this was later generalized and established experimentally by Jean-Baptiste L. Romé de lIslee in 1783. In 1814, Jöns Jacob Berzelius introduced a classification of minerals based on their chemistry rather than their crystal structure, james D. Dana published his first edition of A System of Mineralogy in 1837, and in a later edition introduced a chemical classification that is still the standard. It, however, retains a focus on the structures commonly encountered in rock-forming minerals. An initial step in identifying a mineral is to examine its physical properties and these can be classified into density, measures of mechanical cohesion, macroscopic visual properties, magnetic and electric properties, radioactivity and solubility in hydrogen chloride. If the mineral is crystallized, it will also have a distinctive crystal habit that reflects the crystal structure or internal arrangement of atoms. It is also affected by crystal defects and twinning. Many crystals are polymorphic, having more than one crystal structure depending on factors such as pressure and temperature. ”Examples of polymorphs are calcite and aragonite - two minerals with identical chemical composition, distinguished by their crystallography, calcite is rhombohedral and aragonite is orthorhombic. The crystal structure is the arrangement of atoms in a crystal and it is represented by a lattice of points which repeats a basic pattern, called a unit cell, in three dimensions. The lattice can be characterized by its symmetries and by the dimensions of the unit cell and these dimensions are represented by three Miller indices. The lattice remains unchanged by certain symmetry operations about any point in the lattice, reflection, rotation, inversion, and rotary inversion. Together, they make up an object called a crystallographic point group or crystal class. There are 32 possible crystal classes, in addition, there are operations that displace all the points, translation, screw axis, and glide plane. In combination with the point symmetries, they form 230 possible space groups, most geology departments have X-ray powder diffraction equipment to analyze the crystal structures of minerals. X-rays have wavelengths that are the order of magnitude as the distances between atoms. In a sample that is ground to a powder, the X-rays sample a random distribution of all crystal orientations, powder diffraction can distinguish between minerals that may appear the same in a hand sample, for example quartz and its polymorphs tridymite and cristobalite
9.
Resonant inelastic X-ray scattering
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Resonant Inelastic X-ray Scattering is an x-ray spectroscopy technique used to investigate the electronic structure of molecules and materials. Inelastic X-ray Scattering is a fast developing experimental technique in which one scatters high energy and it is a photon-in/photon-out spectroscopy where one measures both the energy and momentum change of the scattered photon. The energy and momentum lost by the photon are transferred to intrinsic excitations of the material under study, the RIXS process can also be described as a Resonant X-ray Raman or Resonant X-ray Emission process. RIXS is a resonant technique because the energy of the incident photon is chosen such that it coincides with, the resonance can greatly enhance the inelastic scattering cross section, sometimes by many orders of magnitude The RIXS event can be thought of as a two-step process. Starting from the state, absorption of an incident photon leads to creation of an excited intermediate state. From this state, emission of a leads to the final state. In a simplified picture the absorption process gives information of the empty electronic states, in the RIXS experiment these two pieces of information come together in a convolved manner, strongly perturbed by the core-hole potential in the intermediate state. RIXS studies can be performed using both soft and hard x-rays, the scattering phase space of x-rays is therefore without equal. RIXS is element and orbital specific, chemical sensitivity arises by tuning to the edges of the different types of atoms in a material.1 micrometre in the soft x-ray regime. RIXS needs only small volumes, the photon-matter interaction is relatively strong. This makes RIXS possible on very small samples, thin films, surfaces and nano-objects. In principle RIXS can probe a very broad class of intrinsic excitations of the system under study—as long as the excitations are overall charge neutral and this constraint arises from the fact that in RIXS the scattered photons do not add or remove charge from the system under study. In addition magnetic excitations are also symmetry-allowed in RIXS, because the momentum that the photons carry can in principle be transferred to the electrons spin moment. The energy and momentum resolution of RIXS do not depend on the core-hole that is present in the intermediate state, in general the natural linewidth of a spectral feature is determined by the life-times of initial and final states. In x-ray absorption and non-resonant emission spectroscopy, the resolution is limited by the relatively short life-time of the final state core-hole. As in RIXS a high energy core-hole is absent in final state, at the same time, RIXS experiments keep the advantages of x-ray probes, e. g. element specificity. The elemental specificity of the experiments comes from tuning the incident x-ray energy to the energy of a core level of the element of interest. One of the technical challenges in RIXS experiments is selecting the monochromator and energy analyzer which produce, at the desired energy
10.
Compton scattering
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Compton scattering, discovered by Arthur Holly Compton, is the inelastic scattering of a photon by a charged particle, usually an electron. It results in a decrease in energy of the photon, called the Compton effect, part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering exists, in which a charged particle transfers part of its energy to a photon, Compton scattering is an example of inelastic scattering of light by a free charged particle, where the wavelength of the scattered light is different from that of the incident radiation. In Comptons original experiment, the energy of the X ray photon was very much larger than the energy of the atomic electron. The amount by which the wavelength changes is called the Compton shift. Although nuclear Compton scattering exists, Compton scattering usually refers to the interaction involving only the electrons of an atom. The Compton effect was observed by Arthur Holly Compton in 1923 at Washington University in St. Louis, Compton earned the 1927 Nobel Prize in Physics for the discovery. The effect is significant because it demonstrates that light cannot be explained purely as a wave phenomenon, thus, light must behave as if it consists of particles, if we are to explain low-intensity Compton scattering. Comptons experiment convinced physicists that light can behave as a stream of particle-like objects, if the scattered photon still has enough energy, the process may be repeated. In this scenario, the electron is treated as free or loosely bound, experimental verification of momentum conservation in individual Compton scattering processes by Bothe and Geiger as well as by Compton and Simon has been important in disproving the BKS theory. If the photon is of low but sufficient energy, it can eject an electron from its host atom entirely, high energy photons may be able to bombard the nucleus and cause an electron and a positron to be formed, a process called pair production. By the early 20th century, research into the interaction of X-rays with matter was well under way and it was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle θ and emerge at a different wavelength related to θ. In 1923, Compton published a paper in the Physical Review that explained the X-ray shift by attributing particle-like momentum to light quanta, the energy of light quanta depends only on the frequency of the light. The quantity h⁄mec is known as the Compton wavelength of the electron, the wavelength shift λ′ − λ is at least zero and at most twice the Compton wavelength of the electron. Compton found that some X-rays experienced no wavelength shift despite being scattered through large angles, thus the magnitude of the shift is related not to the Compton wavelength of the electron, but to the Compton wavelength of the entire atom, which can be upwards of 10 000 times smaller. A photon γ with wavelength λ collides with an e in an atom. The collision causes the electron to recoil, and a new photon γ with wavelength λ emerges at angle θ from the photons incoming path, let e denote the electron after the collision. If m c 2 = h f, the equivalent photon mass must be h f / c 2, the photons momentum is then simply this effective mass times the photons frame-invariant velocity c
11.
Crystal structure
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In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles in the material that constitutes the pattern is the unit cell of the structure. The unit cell completely defines the symmetry and structure of the crystal lattice. The repeating patterns are said to be located at the points of the Bravais lattice, the lengths of the principal axes, or edges, of the unit cell and the angles between them are the lattice constants, also called lattice parameters. The symmetry properties of the crystal are described by the concept of space groups, all possible symmetric arrangements of particles in three-dimensional space may be described by the 230 space groups. The crystal structure and symmetry play a role in determining many physical properties, such as cleavage, electronic band structure. The crystal structure of a material can be described in terms of its unit cell, the unit cell is a box containing one or more atoms arranged in three dimensions. The unit cells stacked in three-dimensional space describe the arrangement of atoms of the crystal. Commonly, atomic positions are represented in terms of fractional coordinates, the atom positions within the unit cell can be calculated through application of symmetry operations to the asymmetric unit. The asymmetric unit refers to the smallest possible occupation of space within the unit cell and this does not, however imply that the entirety of the asymmetric unit must lie within the boundaries of the unit cell. Symmetric transformations of atom positions are calculated from the group of the crystal structure. Vectors and planes in a lattice are described by the three-value Miller index notation. It uses the indices ℓ, m, and n as directional parameters, which are separated by 90°, by definition, the syntax denotes a plane that intercepts the three points a1/ℓ, a2/m, and a3/n, or some multiple thereof. That is, the Miller indices are proportional to the inverses of the intercepts of the plane with the unit cell, if one or more of the indices is zero, it means that the planes do not intersect that axis. A plane containing a coordinate axis is translated so that it no longer contains that axis before its Miller indices are determined, the Miller indices for a plane are integers with no common factors. Negative indices are indicated with horizontal bars, as in, in an orthogonal coordinate system for a cubic cell, the Miller indices of a plane are the Cartesian components of a vector normal to the plane. Likewise, the planes are geometric planes linking nodes
12.
Scattering
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In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections that undergo scattering are often called diffuse reflections and unscattered reflections are called specular reflections, scattering may also refer to particle-particle collisions between molecules, atoms, electrons, photons and other particles. The effects of such features on the path of almost any type of propagating wave or moving particle can be described in the framework of scattering theory. Particle-particle scattering theory is important in such as particle physics, atomic, molecular. When radiation is scattered by one localized scattering center, this is called single scattering. It is very common that scattering centers are grouped together, in cases, radiation may scatter many times. This type of scattering would be exemplified by an electron being fired at an atomic nucleus. In this case, the exact position relative to the path of the electron is unknown and would be unmeasurable. Single scattering is often described by probability distributions. This is exemplified by a beam passing through thick fog. Multiple scattering is highly analogous to diffusion, and the multiple scattering. Optical elements designed to produce multiple scattering are thus known as diffusers, coherent backscattering, an enhancement of backscattering that occurs when coherent radiation is multiply scattered by a random medium, is usually attributed to weak localization. Not all single scattering is random, however, a well-controlled laser beam can be exactly positioned to scatter off a microscopic particle with a deterministic outcome, for instance. Such situations are encountered in radar scattering as well, where the targets tend to be macroscopic objects such as people or aircraft, similarly, multiple scattering can sometimes have somewhat random outcomes, particularly with coherent radiation. The random fluctuations in the scattered intensity of coherent radiation are called speckles. Speckle also occurs if multiple parts of a coherent wave scatter from different centers, in certain rare circumstances, multiple scattering may only involve a small number of interactions such that the randomness is not completely averaged out. These systems are considered to be some of the most difficult to model accurately, the description of scattering and the distinction between single and multiple scattering are tightly related to wave–particle duality. Scattering theory is a framework for studying and understanding the scattering of waves and particles, prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow
[cond-mat.mtrl-sci].
