Crystallographic point group
In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving the edges and faces of the crystal to the positions of features of the same size and shape. For a periodic crystal, the group must maintain the three-dimensional translational symmetry that defines crystallinity; the geometric properties of a crystal must look the same before and after applying any of the operations in its point group. In the classification of crystals, each point group defines a so-called crystal class. There are infinitely many three-dimensional point groups. However, the crystallographic restriction on the general point groups results in there being only 32 crystallographic point groups; these 32 point groups are one-and-the-same as the 32 types of morphological crystalline symmetries derived in 1830 by Johann Friedrich Christian Hessel from a consideration of observed crystal forms. The point group of a crystal determines, among other things, the directional variation of physical properties that arise from its structure, including optical properties such as birefringency, or electro-optical features such as the Pockels effect.
The point groups are named according to their component symmetries. There are several standard notations used by crystallographers and physicists. For the correspondence of the two systems below, see crystal system. In Schoenflies notation, point groups are denoted by a letter symbol with a subscript; the symbols used in crystallography mean the following: Cn indicates that the group has an n-fold rotation axis. Cnh is Cn with the addition of a mirror plane perpendicular to the axis of rotation. Cnv is Cn with the addition of n mirror planes parallel to the axis of rotation. S2n denotes a group with only a 2n-fold rotation-reflection axis. Dn indicates that the group has an n-fold rotation axis plus n twofold axes perpendicular to that axis. Dnh has, in a mirror plane perpendicular to the n-fold axis. Dnd has, in addition to the elements of Dn, mirror planes parallel to the n-fold axis; the letter T indicates. Td includes improper rotation operations, T excludes improper rotation operations, Th is T with the addition of an inversion.
The letter O indicates that the group has the symmetry of an octahedron, with or without improper operations. Due to the crystallographic restriction theorem, n = 1, 2, 3, 4, or 6 in 2- or 3-dimensional space. D4d and D6d are forbidden because they contain improper rotations with n=8 and 12 respectively; the 27 point groups in the table plus T, Td, Th, O and Oh constitute 32 crystallographic point groups. An abbreviated form of the Hermann–Mauguin notation used for space groups serves to describe crystallographic point groups. Group names are Molecular symmetry Point group Space group Point groups in three dimensions Crystal system Point-group symbols in International Tables for Crystallography. Vol. A, ch. 12.1, pp. 818-820 Names and symbols of the 32 crystal classes in International Tables for Crystallography. Vol. A, ch. 10.1, p. 794 Pictorial overview of the 32 groups
Transparency and translucency
In the field of optics, transparency is the physical property of allowing light to pass through the material without being scattered. On a macroscopic scale, the photons can be said to follow Snell's Law. Translucency is a superset of transparency: it allows light to pass through, but does not follow Snell's law. In other words, a translucent medium allows the transport of light while a transparent medium not only allows the transport of light but allows for image formation. Transparent materials appear clear, with the overall appearance of one color, or any combination leading up to a brilliant spectrum of every color; the opposite property of translucency is opacity. When light encounters a material, it can interact with it in several different ways; these interactions depend on the nature of the material. Photons interact with an object by some combination of reflection and transmission; some materials, such as plate glass and clean water, transmit much of the light that falls on them and reflect little of it.
Many liquids and aqueous solutions are transparent. Absence of structural defects and molecular structure of most liquids are responsible for excellent optical transmission. Materials which do not transmit light are called opaque. Many such substances have a chemical composition which includes what are referred to as absorption centers. Many substances are selective in their absorption of white light frequencies, they absorb certain portions of the visible spectrum while reflecting others. The frequencies of the spectrum which are not absorbed are either reflected or transmitted for our physical observation; this is. The attenuation of light of all frequencies and wavelengths is due to the combined mechanisms of absorption and scattering. Transparency can provide perfect camouflage for animals able to achieve it; this is easier in turbid seawater than in good illumination. Many marine animals such as jellyfish are transparent. With regard to the absorption of light, primary material considerations include: At the electronic level, absorption in the ultraviolet and visible portions of the spectrum depends on whether the electron orbitals are spaced such that they can absorb a quantum of light of a specific frequency, does not violate selection rules.
For example, in most glasses, electrons have no available energy levels above them in range of that associated with visible light, or if they do, they violate selection rules, meaning there is no appreciable absorption in pure glasses, making them ideal transparent materials for windows in buildings. At the atomic or molecular level, physical absorption in the infrared portion of the spectrum depends on the frequencies of atomic or molecular vibrations or chemical bonds, on selection rules. Nitrogen and oxygen are not greenhouse gases because there is no absorption, but because there is no molecular dipole moment. With regard to the scattering of light, the most critical factor is the length scale of any or all of these structural features relative to the wavelength of the light being scattered. Primary material considerations include: Crystalline structure: whether or not the atoms or molecules exhibit the'long-range order' evidenced in crystalline solids. Glassy structure: scattering centers include fluctuations in density or composition.
Microstructure: scattering centers include internal surfaces such as grain boundaries, crystallographic defects and microscopic pores. Organic materials: scattering centers include fiber and cell structures and boundaries. Diffuse reflection - Generally, when light strikes the surface of a solid material, it bounces off in all directions due to multiple reflections by the microscopic irregularities inside the material, by its surface, if it is rough. Diffuse reflection is characterized by omni-directional reflection angles. Most of the objects visible to the naked eye are identified via diffuse reflection. Another term used for this type of reflection is "light scattering". Light scattering from the surfaces of objects is our primary mechanism of physical observation. Light scattering in liquids and solids depends on the wavelength of the light being scattered. Limits to spatial scales of visibility therefore arise, depending on the frequency of the light wave and the physical dimension of the scattering center.
Visible light has a wavelength scale on the order of a half a micrometer. Scattering centers as small. Optical transparency in polycrystalline materials is limited by the amount of light, scattered by their microstructural features. Light scattering depends on the wavelength of the light. Limits to spatial scales of visibility therefore arise, depending on the frequency of the light wave and the physical dimension of the scattering center. For example, since visible light has a wavelength scale on the order of a micrometer, scattering centers will have dimensions on a similar spatial scale. Primary scattering centers in polycrystalline materi
In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as n = c v, where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. The refractive index determines how much the path of light is bent, or refracted, when entering a material; this is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are the angles of incidence and refraction of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices determine the amount of light, reflected when reaching the interface, as well as the critical angle for total internal reflection and Brewster's angle; the refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.
This implies that vacuum has a refractive index of 1, that the frequency of the wave is not affected by the refractive index. As a result, the energy of the photon, therefore the perceived color of the refracted light to a human eye which depends on photon energy, is not affected by the refraction or the refractive index of the medium. While the refractive index affects wavelength, it depends on photon frequency and energy so the resulting difference in the bending angle causes white light to split into its constituent colors; this is called dispersion. It can be observed in prisms and rainbows, chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index; the imaginary part handles the attenuation, while the real part accounts for refraction. The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves, it can be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, a reference medium other than vacuum must be chosen.
The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, the phase velocity v of light in the medium, n = c v. The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves; the definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used. Air at a standardized pressure and temperature has been common as a reference medium. Thomas Young was the person who first used, invented, the name "index of refraction", in 1807. At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers; the ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396".
Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9". Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1. Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols: n, m, µ; the symbol n prevailed. For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table; these values are measured at the yellow doublet D-line of sodium, with a wavelength of 589 nanometers, as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. All solids and liquids have refractive indices above 1.3, with aerogel as the clear exception. Aerogel is a low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76.
For infrared light refractive indices can be higher. Germanium is transparent in the wavelength region from 2 to 14 µm and has a refractive index of about 4. A type of new materials, called topological insulator, was found holding higher refractive index of up to 6 in near to mid infrared frequency range. Moreover, topological insulator material are transparent; these excellent properties make them a type of significant materials for infrared optics. According to the theory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be lower than 1; the refractive index measures the phase velocity of light. The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, thereby give a refractive index below 1; this can occur close to resonance frequencies, for absorbing media, in plasmas, for X-rays. In the X-ray regime the refractive indices are
Specific gravity is the ratio of the density of a substance to the density of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance; the reference substance for liquids is nearly always water at its densest. Nonetheless, the temperature and pressure must be specified for the reference. Pressure is nearly always 1 atm. Temperatures for both sample and reference vary from industry to industry. In British beer brewing, the practice for specific gravity as specified above is to multiply it by 1,000. Specific gravity is used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, antifreeze coolants, sugar solutions and acids. Being a ratio of densities, specific gravity is a dimensionless quantity; the reason for the specific gravity being dimensionless is to provide a global consistency between the U. S. and Metric Systems, since various units for density may be used such as pounds per cubic feet or grams per cubic centimeter, etc.
Specific gravity varies with pressure. Substances with a specific gravity of 1 are neutrally buoyant in water; those with SG greater than 1 are denser than water and will, disregarding surface tension effects, sink in it. Those with an SG less than 1 will float on it. In scientific work, the relationship of mass to volume is expressed directly in terms of the density of the substance under study, it is in industry where specific gravity finds wide application for historical reasons. True specific gravity can be expressed mathematically as: S G true = ρ sample ρ H 2 O where ρsample is the density of the sample and ρH2O is the density of water; the apparent specific gravity is the ratio of the weights of equal volumes of sample and water in air: S G apparent = W A, sample W A, H 2 O where WA,sample represents the weight of the sample measured in air and WA,H2O the weight of water measured in air. It can be shown that true specific gravity can be computed from different properties: S G true = ρ sample ρ H 2 O = m sample V m H 2 O V = m sample m H 2 O g g = W V, sample W V, H 2 O where g is the local acceleration due to gravity, V is the volume of the sample and of water, ρsample is the density of the sample, ρH2O is the density of water and WV represents a weight obtained in vacuum.
The density of water varies with pressure as does the density of the sample. So it is necessary to specify the temperatures and pressures at which the densities or weights were determined, it is nearly always the case. But as specific gravity refers to incompressible aqueous solutions or other incompressible substances, variations in density caused by pressure are neglected at least where apparent specific gravity is being measured. For true specific gravity calculations, air pressure must be considered. Temperatures are specified by the notation, with Ts representing the temperature at which the sample's density was determined and Tr the temperature at which the reference density is specified. For example, SG would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, we note that, while SGH2O = 1.000000, it is the case that SGH2O = 0.998203⁄0.999840 = 0.998363. Here, temperature is being specified using the current ITS-90 scale and the densities used here and in the rest of this article are based on that scale.
On the previous IPTS-68 scale, the densities at 20 °C and 4 °C are 0.9982071 and 0.9999720 respective
In the field of mineralogy, fracture is the texture and shape of a rock's surface formed when a mineral is fractured. Minerals have a distinctive fracture, making it a principal feature used in their identification. Fracture differs from cleavage in that the latter involves clean splitting along the cleavage planes of the mineral's crystal structure, as opposed to more general breakage. All minerals exhibit fracture, but when strong cleavage is present, it can be difficult to see. Conchoidal fracture breakage that resembles the concentric ripples of a mussel shell, it occurs in amorphous or fine-grained minerals such as flint, opal or obsidian, but may occur in crystalline minerals such as quartz. Subconchoidal fracture is similar to with less significant curvature. Earthy fracture is reminiscent of freshly broken soil, it is seen in soft, loosely bound minerals, such as limonite and aluminite. Hackly fracture is jagged and not even, it occurs when metals are torn, so is encountered in native metals such as copper and silver.
Splintery fracture comprises sharp elongated points. It is seen in fibrous minerals such as chrysotile, but may occur in non-fibrous minerals such as kyanite. Uneven fracture is a rough one with random irregularities, it occurs in a wide range of minerals including arsenopyrite and magnetite. Rudolf Duda and Lubos Rejl: Minerals of the World http://www.galleries.com/minerals/property/fracture.htm