1.
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
2.
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
3.
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
4.
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
5.
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
6.
X-ray reflectivity
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X-ray reflectivity is a surface-sensitive analytical technique used in chemistry, physics, and materials science to characterize surfaces, thin films and multilayers. It is related to the techniques of neutron reflectometry and ellipsometry. The basic idea behind the technique is to reflect a beam of x-rays from a flat surface, if the interface is not perfectly sharp and smooth then the reflected intensity will deviate from that predicted by the law of Fresnel reflectivity. The deviations can then be analyzed to obtain the density profile of the normal to the surface. The technique appears to have first been applied to x-rays by Lyman G. Parratt in 1954, parratts initial work explored the surface of copper-coated glass, but since that time the technique has been extended to a wide range of both solid and liquid interfaces. The basic mathematical relationship which describes specular reflectivity is fairly straightforward, for films with multiple layers, X-ray reflectivity may show oscillations with wavelength, analogous to the Fabry-Pérot effect. These oscillations can be used to infer layer thicknesses and other properties, for example using the Abeles matrix formalism
[cond-mat.mtrl-sci].
