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Kikuchi Lines
Kikuchi lines are patterns of electrons formed by scattering. They pair up to form bands in electron diffraction from single crystal specimens, there to serve as "roads in orientation-space" for microscopists uncertain of what they are looking at. In transmission electron microscopes, they are easily seen in diffraction from regions of the specimen thick enough for multiple scattering. Unlike diffraction spots, which blink on and off as one tilts the crystal, Kikuchi bands mark orientation space with well-defined intersections (called zones or poles) as well as paths connecting one intersection to the next. Experimental and theoretical maps of Kikuchi band geometry, as well as their direct-space analogs e.g. bend contours, electron channeling patterns, and fringe visibility maps are increasingly useful tools in electron microscopy of crystalline and nanocrystalline materials. Because each Kikuchi line is associated with Bragg diffraction from one side of a single set of lattice p ...
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Photographic Film
Photographic film is a strip or sheet of transparent film base coated on one side with a gelatin emulsion containing microscopically small light-sensitive silver halide crystals. The sizes and other characteristics of the crystals determine the sensitivity, contrast, and resolution of the film. The emulsion will gradually darken if left exposed to light, but the process is too slow and incomplete to be of any practical use. Instead, a very short exposure to the image formed by a camera lens is used to produce only a very slight chemical change, proportional to the amount of light absorbed by each crystal. This creates an invisible latent image in the emulsion, which can be chemically developed into a visible photograph. In addition to visible light, all films are sensitive to ultraviolet light, X-rays, gamma rays, and high-energy particles. Unmodified silver halide crystals are sensitive only to the blue part of the visible spectrum, producing unnatural-looking rendition ...
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Beam Compass
A beam compass is a compass with a beam and sliding sockets or cursors for drawing and dividing circles larger than those made by a regular pair of compasses. The instrument can be as a whole, or made on the spot with individual sockets (called trammel points) and any suitable beam. Draftsman's beam compass A draftsman's beam compass consists of a set of points and holders, mounted on a plated brass, aluminum, or German 'silver' rod. One end is generally locked down at the end of the rod, while the other has both rough and fine adjustments, though some are opposite in construction. The locked tip holder consists of a needle, for the centre of the radius, and the other holds either a lead clutch, or an inking nib. There are older variants which use a wooden beam. Another similar type is a Machinist or Engineers beam compass, which uses scribing points only, similar to ones used by woodworkers, except that its fine adjustment is generally more refined. These beam compasses can ...
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Stereographic Projection
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the ''pole'' or ''center of projection''), onto a plane (the ''projection plane'') perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the entire plane. It maps circles on the sphere to circles or lines on the plane, and is conformal, meaning that it preserves angles at which curves meet and thus locally approximately preserves shapes. It is neither isometric (distance preserving) nor equiareal (area preserving). The stereographic projection gives a way to represent a sphere by a plane. The metric induced by the inverse stereographic projection from the plane to the sphere defines a geodesic distance between points in the plane equal to the spherical distance between the spherical points they represent. A two-dimensional coordinate system on the stereo ...
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Steradian
The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians, projected onto a circle, gives a ''length'' on the circumference, a solid angle in steradians, projected onto a sphere, gives an ''area'' on the surface. The name is derived from the Greek 'solid' + radian. The steradian, like the radian, is a dimensionless unit, the quotient of the area subtended and the square of its distance from the centre. Both the numerator and denominator of this ratio have dimension length squared (i.e. , dimensionless). It is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol "sr" is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian (W⋅sr−1). The steradian was formerly an SI supplementary unit, but th ...
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Selected Area Diffraction
Selected area (electron) diffraction (abbreviated as SAD or SAED), is a crystallographic experimental technique typically performed using a transmission electron microscope (TEM). It is a specific case of electron diffraction used primarily in material science and solid state physics as one of the most common experimental techniques. Especially with appropriate analytical software, SAD patterns (SADP) can be used to determine crystal orientation, measure lattice constants or examine its defects. Principle In transmission electron microscope, a thin crystalline sample is illuminated by parallel beam of electrons accelerated to energy of hundreds of kiloelectron volts. At these energies, even metallic samples are transparent for the electrons if the sample is thinned enough (typically less than 100  nm). Due to the wave–particle duality, the high-energetic electrons behave as waves with wavelength of a few thousandths of a nanometer. The relativistic wavelength ...
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Inelastic Mean Free Path
The inelastic mean free path (IMFP) is an index of how far an electron on average travels through a solid before losing energy. If a monochromatic primary beam of electrons is incident on a solid surface, the majority of incident electrons lose their energy because they interact strongly with matter, leading to plasmon excitation, electron-hole pair formation, and vibrational excitation. The intensity of the primary electrons, I_0, is damped as a function of the distance, ''d'', into the solid. The intensity decay can be expressed as follows: : I(d) = I_0 \ e^ where \textstyle I(d) is the intensity after the primary electron beam has traveled through the solid to a distance \textstyle d. The parameter \textstyle \lambda(E), termed the inelastic mean free path (IMFP), is defined as the distance an electron beam can travel before its intensity decays to \textstyle 1/e of its initial value. (Note that this is equation is closely related to the Beer–Lambert law.) The inelastic ...
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Bragg's Law
In physics and chemistry , Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a crystal lattice. It encompasses the superposition of wave fronts scattered by lattice planes, leading to a strict relation between wavelength and scattering angle, or else to the wavevector transfer with respect to the crystal lattice. Such law had initially been formulated for X-rays upon crystals. However, It applies to all sorts of quantum beams, including neutron and electron waves at atomic distances, as well as visible light at 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 in response to their discovery that crystalline solids produced surprising patterns of reflected X-rays (in contrast to that of, say, a liquid). The ...
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