Monoclinic crystal system
In crystallography, the monoclinic crystal system is one of the 7 crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system, they form a rectangular prism with a parallelogram as its base. Hence two vectors are perpendicular, while the third vector meets the other two at an angle other than 90°. There is only one monoclinic Bravais lattice in two dimensions: the oblique lattice. Two monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic lattices. In the monoclinic system there is a used second choice of crystal axes that results in a unit cell with the shape of an oblique rhombic prism. In this axis setting, the primitive and base-centered lattices swap in centering type; the table below organizes the space groups of the monoclinic crystal system by crystal class. It lists the International Tables for Crystallography space group numbers, followed by the crystal class name, its point group in Schoenflies notation, Hermann–Mauguin notation, orbifold notation, Coxeter notation, type descriptors, mineral examples, the notation for the space groups.
Sphenoidal is monoclinic hemimorphic. The three monoclinic hemimorphic space groups are as follows: a prism with as cross-section wallpaper group p2 ditto with screw axes instead of axes ditto with screw axes as well as axes, parallel, in between; the four monoclinic hemihedral space groups include those with pure reflection at the base of the prism and halfway those with glide planes instead of pure reflection planes. Crystal structure Crystallography Crystal Hurlbut, Cornelius S.. Manual of Mineralogy. Pp. 69–73. ISBN 0-471-80580-7. Hahn, Theo, ed.. International Tables for Crystallography, Volume A: Space Group Symmetry. A. Berlin, New York: Springer-Verlag. Doi:10.1107/97809553602060000100. ISBN 978-0-7923-6590-7
Gemology or gemmology is the science dealing with natural and artificial gemstone materials. It is considered a branch of mineralogy; some jewelers are academically trained are qualified to identify and evaluate gems. Rudimentary education in gemology for jewelers and gemologists began in the nineteenth century, but the first qualifications were instigated after the National Association of Goldsmiths of Great Britain set up a Gemmological Committee for this purpose in 1908; this committee matured into the Gemmological Association of Great Britain, now an educational charity and accredited awarding body with its courses taught worldwide. The first US graduate of Gem-A's Diploma Course, in 1929, was Robert Shipley, who established both the Gemological Institute of America and the American Gem Society. There are now several professional schools and associations of gemologists and certification programs around the world; the first gemological laboratory serving the jewelry trade was established in London in 1925, prompted by the influx of the newly developed "cultured pearl" and advances in the synthesis of rubies and sapphires.
There are now numerous gem laboratories around the world requiring more advanced equipment and experience to identify the new challenges - such as treatments to gems, new synthetics, other new materials. It is difficult to obtain an expert judgement from a neutral laboratory. Analysis and estimation in the gemstone trade have to take place on site. Professional gemologists and gemstone buyers use mobile laboratories, which pool all necessary instruments in a travel case; such so-called travel labs have their own current supply, which makes them independent from infrastructure. They are suitable for gemological expeditions. Gemstones are categorized based on their crystal structure, specific gravity, refractive index, other optical properties, such as pleochroism; the physical property of "hardness" is defined by the non-linear Mohs scale of mineral hardness. Gemologists study these factors while appraising cut and polished gemstones. Gemological microscopic study of the internal structure is used to determine whether a gem is synthetic or natural by revealing natural fluid inclusions or melted exogenous crystals that are evidence of heat treatment to enhance color.
The spectroscopic analysis of cut gemstones allows a gemologist to understand the atomic structure and identify its origin, a major factor in valuing a gemstone. For example, a ruby from Burma will have definite internal and optical activity variance from a Thai ruby; when the gemstones are in a rough state, the gemologist studies the external structure. The stone is identified by its color, refractive index, optical character, specific gravity, examination of internal characteristics under magnification. Gemologists use a variety of tools and equipment which allow for the accurate tests to be performed in order to identify a gemstone by its specific characteristics and properties; these include: Corrected 10× loupe Microscope Refractometer Polarising filter Magnifying eyepiece Contact liquid for RI up to 1.81 Polariscope Optic figure sphere Dichroscope Spectroscope Penlight Tweezers Stone cloth Color filter Immersion cell Ultraviolet lamp Gem identification is a process of elimination. Gemstones of similar color undergo non-destructive optical testing until there is only one possible identity.
Any single test is indicative, only. For example, the specific gravity of ruby is 4.00, glass is 3.15–4.20, cubic zirconia is 5.6–5.9. So one can tell the difference between cubic zirconia and the other two. And, as with all occurring materials, no two gems are identical; the geological environment they are created in influences the overall process so that although the basics can be identified, the presence of chemical "impurities" and substitutions along with structural imperfections create "individuals". One test to determine the gem's identity is to measure the refraction of light in the gem; every material has a critical angle. This can be measured and thus used to determine the gem's identity; this is measured using a refractometer, although it is possible to measure it using a microscope. Specific gravity known as relative density, varies depending upon the chemical composition and crystal structure type. Heavy liquids with a known specific gravity are used to test loose gemstones. Specific gravity is measured by comparing the weight of the gem in air with the weight of the gem suspended in water.
This method uses a similar principle to how a prism works to separate white light into its component colors. A gemological spectroscope is employed to analyze the selective absorption of light in the gem material; when light passes from one medium to another, it bends. Blue light bends more than red light. How much the light bends will vary depending on the gem material. Coloring agents or chromophores show bands in the spectroscope and indicate which element is responsible for the gem's color. Inclusions can help gemologists to determine whether or not a gemstone is natural, synthetic or treated. Institutes and laboratories American Gem Society - AGS Asian Institute of Gemological Sciences - AIGS Canadian Gemmological Association - CGA Canadian Institute of Gemmology - CIG European Gemological Laboratory - EGL Gemmological Association of Australia - GAA Gemmological Association of Great Britain - Gem-A Gemological Institute of America - GIA Gübelin
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent; the birefringence is quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are birefringent, as are plastics under mechanical stress. Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking different paths; this effect was first described by the Danish scientist Rasmus Bartholin in 1669, who observed it in calcite, a crystal having one of the strongest birefringences. However it was not until the 19th century that Augustin-Jean Fresnel described the phenomenon in terms of polarization, understanding light as a wave with field components in transverse polarizations. A mathematical description of wave propagation in a birefringent medium is presented below.
Following is a qualitative explanation of the phenomenon. The simplest type of birefringence is described as uniaxial, meaning that there is a single direction governing the optical anisotropy whereas all directions perpendicular to it are optically equivalent, thus rotating the material around this axis does not change its optical behavior. This special direction is known as the optic axis of the material. Light propagating parallel to the optic axis is governed by a refractive index no. Light whose polarization is in the direction of the optic axis sees an optical index ne. For any ray direction there is a linear polarization direction perpendicular to the optic axis, this is called an ordinary ray. However, for ray directions not parallel to the optic axis, the polarization direction perpendicular to the ordinary ray's polarization will be in the direction of the optic axis, this is called an extraordinary ray. I.e. when unpolarized light enters an uniaxial birefringent material it is split into two beams travelling different directions.
The ordinary ray will always experience a refractive index of no, whereas the refractive index of the extraordinary ray will be in between no and ne, depending on the ray direction as described by the index ellipsoid. The magnitude of the difference is quantified by the birefringence: Δ n = n e − n o; the propagation of the ordinary ray is described by no as if there were no birefringence involved. However the extraordinary ray, as its name suggests, propagates unlike any wave in a homogenous optical material, its refraction at a surface can be understood using the effective refractive index. However it is in fact an inhomogeneous wave whose power flow is not in the direction of the wave vector; this causes an additional shift in that beam when launched at normal incidence, as is popularly observed using a crystal of calcite as photographed above. Rotating the calcite crystal will cause one of the two images, that of the extraordinary ray, to rotate around that of the ordinary ray, which remains fixed.
When the light propagates either along or orthogonal to the optic axis, such a lateral shift does not occur. In the first case, both polarizations see the same effective refractive index, so there is no extraordinary ray. In the second case the extraordinary ray propagates at a different phase velocity but is not an inhomogeneous wave. A crystal with its optic axis in this orientation, parallel to the optical surface, may be used to create a waveplate, in which there is no distortion of the image but an intentional modification of the state of polarization of the incident wave. For instance, a quarter-wave plate is used to create circular polarization from a linearly polarized source; the case of so-called biaxial crystals is more complex. These are characterized by three refractive indices corresponding to three principal axes of the crystal. For most ray directions, both polarizations would be classified as extraordinary rays but with different effective refractive indices. Being extraordinary waves, the direction of power flow is not identical to the direction of the wave vector in either case.
The two refractive indices can be determined using the index ellipsoids for given directions of the polarization. Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution but is described by three unequal principle refractive indices nα, nβ and nγ, thus there is no axis. Although there is no axis of symmetry, there are two optical axes or binormals which are defined as directions along which light may propagate without birefringence, i.e. directions along which the wavelength is independent of polarization. For this reason, birefringent materials with three distinct refractive indices are called biaxial. Additionally, there are two distinct axes known as optical ray axes or biradials along which the group velocity of the light is independent of polarization; when an arbitrary beam of light strikes the surface of a b
Peridot is gem-quality olivine and a silicate mineral with the formula of 2SiO4. As peridot is a magnesium-rich variety of olivine, the formula approaches Mg2SiO4; the origin of the name peridot is uncertain. The Oxford English Dictionary suggests an alteration of Anglo–Norman pedoretés, a kind of opal, rather than the Arabic word faridat, meaning "gem"; the Middle English Dictionary's entry on peridot includes several variations: peridod, peritot and pilidod – other variants substitute y for the is seen here. The earliest use in England is in the register of the St Albans Abbey, in Latin, its translation in 1705 is the first use of "peridot" in English, it records that on his death in 1245, Bishop John bequeathed various items, including peridot, to the Abbey. Peridot is one of the few gemstones; the intensity and tint of the green, depends on the percentage of iron in the crystal structure, so the color of individual peridot gems can vary from yellow, to olive, to brownish-green. In rare cases, peridot may have a medium-dark toned, pure green with no secondary yellow hue or brown mask.
Olivine, of which peridot is a type, is a common mineral in mafic and ultramafic rocks found in lava and in peridotite xenoliths of the mantle, which lava carries to the surface. Peridots can be found in meteorites. Peridots can be differentiated by composition. A peridot formed as a result of volcanic activity tends to contain higher concentrations of lithium and zinc than those found in meteorites. Olivine is an abundant mineral, but gem-quality peridot is rather rare due to its chemical instability on Earth's surface. Olivine is found as small grains and tends to exist in a weathered state, unsuitable for decorative use. Large crystals of forsterite, the variety most used to cut peridot gems, are rare. In the ancient world, mining of peridot, called topazios on St. John's Island in the Red Sea began about 300 B. C; the principal source of peridot olivine today is the San Carlos Apache Indian Reservation in Arizona. It is mined at another location in Arizona, in Arkansas, Hawaii and New Mexico at Kilbourne Hole, in the US.
Peridot crystals have been collected from some pallasite meteorites. Peridot is sometimes mistaken for other green gems. Notable gemologist George Frederick Kunz discussed the confusion between emeralds and peridots in many church treasures, notably the "Three Magi" treasure in the Dom of Cologne, Germany; the largest cut peridot olivine is a 310 carat specimen in the Smithsonian Museum in Washington, D. C. Peridot olivine is the birthstone for the month of August. Peridot is a major character on the Cartoon Network show Steven Universe. Peridot is a character on the Japanese anime show Jewelpet, she is depicted as a papillon dog. USGS peridot data Emporia Edu Florida State University – Peridot
Danburite is a calcium boron silicate mineral with a chemical formula of CaB22. It has a Mohs hardness of 7 to 7.5 and a specific gravity of 3.0. The mineral has an orthorhombic crystal form, it is colourless, like quartz, but can be either pale yellow or yellowish-brown. It occurs in contact metamorphic rocks; the Dana classification of minerals categorizes danburite as a sorosilicate, while the Strunz classification scheme lists it as a tectosilicate. Its crystal symmetry and form are similar to topaz; the clarity and strong dispersion of danburite make it valuable as cut stones for jewelry. It is named for Danbury, United States, where it was first discovered in 1839 by Charles Upham Shephard
Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, 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, as well as their utilization. Early writing on mineralogy on gemstones, comes from ancient Babylonia, the ancient Greco-Roman world and medieval China, Sanskrit texts from ancient India and the ancient Islamic World. Books on the subject included the Naturalis Historia of Pliny the Elder, which not only described many different minerals but explained many of their properties, Kitab al Jawahir by Persian scientist Al-Biruni; 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. This was generalized and established experimentally by Jean-Baptiste L. Romé de l'Islee in 1783. René Just Haüy, the "father of modern crystallography", showed that crystals are periodic and established that the orientations of crystal faces can be expressed in terms of rational numbers, as encoded in the Miller indices. In 1814, Jöns Jacob Berzelius introduced a classification of minerals based on their chemistry rather than their crystal structure. William Nicol developed the Nicol prism, which polarizes light, in 1827–1828 while studying fossilized wood. James D. Dana published his first edition of A System of Mineralogy in 1837, in a edition introduced a chemical classification, still the standard. X-ray diffraction was demonstrated by Max von Laue in 1912, developed into a tool for analyzing the crystal structure of minerals by the father/son team of William Henry Bragg and William Lawrence Bragg.
More driven by advances in experimental technique and available computational power, the latter of which has enabled accurate atomic-scale simulations of the behaviour of crystals, the science has branched out to consider more general problems in the fields of inorganic chemistry and solid-state physics. It, retains a focus on the crystal structures encountered in rock-forming minerals. In particular, the field has made great advances in the understanding of the relationship between the atomic-scale structure of minerals and their function. To this end, in their focus on the connection between atomic-scale phenomena and macroscopic properties, the mineral sciences display more of an overlap with materials science than any other discipline. An initial step in identifying a mineral is to examine its physical properties, many of which can be measured on a hand sample; these can be classified into density. Hardness is determined by comparison with other minerals. In the Mohs scale, a standard set of minerals are numbered in order of increasing hardness from 1 to 10.
A harder mineral will scratch a softer, so an unknown mineral can be placed in this scale by which minerals it scratches and which scratch it. A few minerals such as calcite and kyanite have a hardness that depends on direction. Hardness can be measured on an absolute scale using a sclerometer. Tenacity refers to the way a mineral behaves when it is broken, bent or torn. A mineral can be brittle, sectile, flexible or elastic. An important influence on tenacity is the type of chemical bond. Of the other measures of mechanical cohesion, cleavage is the tendency to break along certain crystallographic planes, it is described by the orientation of the plane in crystallographic nomenclature. Parting is the tendency to break along planes of weakness due to twinning or exsolution. Where these two kinds of break do not occur, fracture is a less orderly form that may be conchoidal, splintery, hackly, or uneven. If the mineral is well crystallized, it will have a distinctive crystal habit that reflects the crystal structure or internal arrangement of atoms.
It is affected by crystal defects and twinning. Many crystals are polymorphic, having more than
A crystal or crystalline solid is a solid material whose constituents are arranged in a ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations; the scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification; the word crystal derives from the Ancient Greek word κρύσταλλος, meaning both "ice" and "rock crystal", from κρύος, "icy cold, frost". Examples of large crystals include snowflakes and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Examples of polycrystals include most metals, rocks and ice. A third category of solids is amorphous solids, where the atoms have no periodic structure whatsoever.
Examples of amorphous solids include glass and many plastics. Despite the name, lead crystal, crystal glass, related products are not crystals, but rather types of glass, i.e. amorphous solids. Crystals are used in pseudoscientific practices such as crystal therapy, along with gemstones, are sometimes associated with spellwork in Wiccan beliefs and related religious movements; the scientific definition of a "crystal" is based on the microscopic arrangement of atoms inside it, called the crystal structure. A crystal is a solid where the atoms form a periodic arrangement.. Not all solids are crystals. For example, when liquid water starts freezing, the phase change begins with small ice crystals that grow until they fuse, forming a polycrystalline structure. In the final block of ice, each of the small crystals is a true crystal with a periodic arrangement of atoms, but the whole polycrystal does not have a periodic arrangement of atoms, because the periodic pattern is broken at the grain boundaries.
Most macroscopic inorganic solids are polycrystalline, including all metals, ice, etc. Solids that are neither crystalline nor polycrystalline, such as glass, are called amorphous solids called glassy, vitreous, or noncrystalline; these have no periodic order microscopically. There are distinct differences between crystalline solids and amorphous solids: most notably, the process of forming a glass does not release the latent heat of fusion, but forming a crystal does. A crystal structure is characterized by its unit cell, a small imaginary box containing one or more atoms in a specific spatial arrangement; the unit cells are stacked in three-dimensional space to form the crystal. The symmetry of a crystal is constrained by the requirement that the unit cells stack with no gaps. There are 219 possible crystal symmetries, called crystallographic space groups; these are grouped into 7 crystal systems, such as hexagonal crystal system. Crystals are recognized by their shape, consisting of flat faces with sharp angles.
These shape characteristics are not necessary for a crystal—a crystal is scientifically defined by its microscopic atomic arrangement, not its macroscopic shape—but the characteristic macroscopic shape is present and easy to see. Euhedral crystals are those with well-formed flat faces. Anhedral crystals do not because the crystal is one grain in a polycrystalline solid; the flat faces of a euhedral crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal: they are planes of low Miller index. This occurs; as a crystal grows, new atoms attach to the rougher and less stable parts of the surface, but less to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. One of the oldest techniques in the science of crystallography consists of measuring the three-dimensional orientations of the faces of a crystal, using them to infer the underlying crystal symmetry.
A crystal's habit is its visible external shape. This is determined by the crystal structure, the specific crystal chemistry and bonding, the conditions under which the crystal formed. By volume and weight, the largest concentrations of crystals in the Earth are part of its solid bedrock. Crystals found in rocks range in size from a fraction of a millimetre to several centimetres across, although exceptionally large crystals are found; as of 1999, the world's largest known occurring crystal is a crystal of beryl from Malakialina, Madagascar, 18 m long and 3.5 m in diameter, weighing 380,000 kg. Some crystals have formed by magmatic and metamorphic processes, giving origin to large masses of crystalline rock; the vast majority of igneous rocks are formed from molten magma and the degree of crystallization depends on the conditions under which they solidified. Such rocks as granite, which have cooled slowly and under great pressures, have crystallized.