Lustre or luster is the way light interacts with the surface of a crystal, rock, or mineral. The word traces its origins back to the latin lux, meaning light, a range of terms are used to describe lustre, such as earthy, metallic and silky. Similarly, the term refers to a glassy lustre. A list of terms is given below. Lustre varies over a continuum, and so there are no rigid boundaries between the different types of lustre. The terms are frequently combined to describe types of lustre. Some minerals exhibit unusual optical phenomena, such as asterism or chatoyancy, a list of such phenomena is given below. Adamantine minerals possess a superlative lustre, which is most notably seen in diamond, such minerals are transparent or translucent, and have a high refractive index. Minerals with an adamantine lustre are uncommon, with examples being cerussite. Minerals with a degree of lustre are referred to as subadamantine, with some examples being garnet. Dull minerals exhibit little to no lustre, due to coarse granulations which scatter light in all directions, a distinction is sometimes drawn between dull minerals and earthy minerals, with the latter being coarser, and having even less lustre.
Greasy minerals resemble fat or grease, a greasy lustre often occurs in minerals containing a great abundance of microscopic inclusions, with examples including opal and cordierite. Many minerals with a greasy lustre feel greasy to the touch, metallic minerals have the lustre of polished metal, and with ideal surfaces will work as a reflective surface. Examples include galena and magnetite, pearly minerals consist of thin transparent co-planar sheets. Light reflecting from these layers give them a lustre reminiscent of pearls, such minerals possess perfect cleavage, with examples including muscovite and stilbite. Resinous minerals have the appearance of resin, chewing gum or plastic, a principal example is amber, which is a form of fossilized resin. Silky minerals have an arrangement of extremely fine fibres, giving them a lustre reminiscent of silk. Examples include asbestos and the satin spar variety of gypsum, a fibrous lustre is similar, but has a coarser texture
Lead is a chemical element with atomic number 82 and symbol Pb. When freshly cut, it is bluish-white, it tarnishes to a dull gray upon exposure to air and it is a soft and heavy metal with a density exceeding that of most common materials. Lead has the second-highest atomic number of the stable elements. Lead is a relatively unreactive post-transition metal and its weak metallic character is illustrated by its amphoteric nature and tendency to form covalent bonds. Compounds of lead are found in the +2 oxidation state. Exceptions are mostly limited to organolead compounds, like the lighter members of the group, lead exhibits a tendency to bond to itself, it can form chains and polyhedral structures. Lead is easily extracted from its ores and was known to people in Western Asia. A principal ore of lead, often bears silver, Lead production declined after the fall of Rome and did not reach comparable levels again until the Industrial Revolution. Nowadays, global production of lead is about ten million tonnes annually, Lead has several properties that make it useful, high density, low melting point and relative inertness to oxidation.
In the late 19th century, lead was recognized as poisonous, Lead is a neurotoxin that accumulates in soft tissues and bones, damaging the nervous system and causing brain disorders and, in mammals, blood disorders. A lead atom has 82 electrons, arranged in a configuration of 4f145d106s26p2. The combined first and second ionization energies—the total energy required to remove the two 6p electrons—is close to that of tin, leads upper neighbor in group 14. This is unusual since ionization energies generally fall going down a group as an elements outer electrons become more distant from the nucleus, the similarity is caused by the lanthanide contraction—the decrease in element radii from lanthanum to lutetium, and the relatively small radii of the elements after hafnium. The contraction is due to shielding of the nucleus by the lanthanide 4f electrons. The combined first four ionization energies of lead exceed those of tin, for this reason lead, unlike tin, mostly forms compounds in which it has an oxidation state of +2, rather than +4.
Relativistic effects, which become particularly prominent at the bottom of the periodic table, as a result, the 6s electrons of lead become reluctant to participate in bonding, a phenomenon called the inert pair effect. A related outcome is that the distance between nearest atoms in crystalline lead is unusually long, the lighter group 14 elements form stable or metastable allotropes having the tetrahedrally coordinated and covalently bonded diamond cubic structure. The energy levels of their outer s- and p-orbitals are close enough to allow mixing into four hybrid sp3 orbitals
El Paso County, Colorado
El Paso County is one of the 64 counties of the U. S. state of Colorado. The 2014 Census recorded a population of 663,519 for El Paso County, the Census Bureaus 2014 estimate indicates it is the second most populous county in Colorado, after the City and County of Denver. The county seat is Colorado Springs, the second most populous city in Colorado, El Paso County is included in the Colorado Springs, CO Metropolitan Statistical Area. El Paso County is located in Colorados 5th congressional district, the Democratic Party won El Paso County four additional times prior, and the Populist Party won in 1892, with General James B. Together with state funding for COSMIX and the I-25 interchange with Highway 16, in 2010 and 2014 the county voted pro-marijuana. In July 1858, gold was discovered along the South Platte River in Arapahoe County and this discovery precipitated the Pikes Peak Gold Rush. Many residents of the region felt disconnected from the remote territorial governments of Kansas and Nebraska.
The following month, the Jefferson Territorial Legislature organized 12 counties for the new territory including El Paso County, El Paso County was named for the Spanish language name for Ute Pass north of Pikes Peak. Colorado City served as the county seat of El Paso County, the Jefferson Territory never received federal sanction, but on February 28,1861, U. S. President James Buchanan signed an act organizing the Territory of Colorado. El Paso County was one of the original 17 counties created by the Colorado legislature on November 1,1861, part of its western territory was broken off to create Teller County in 1899. Originally based in Old Colorado City, El Paso Countys county seat was moved to Colorado Springs in 1873. According to the U. S. Census Bureau, the county has an area of 2,130 square miles. Douglas County - north Elbert County - northeast Lincoln County - east Crowley County - southeast Pueblo County - south Fremont County - west Teller County - west Interstate 25 U. S. Highway 24 U. S, the population density was 243 people per square mile.
There were 202,428 housing units at a density of 95 per square mile. The racial makeup of the county was 81. 19% White,6. 51% Black or African American,0. 91% Native American,2. 53% Asian,0. 24% Pacific Islander,4. 70% from other races, and 3. 91% from two or more races. 11. 30% of the population were Hispanic or Latino of any race,23. 90% of all households were made up of individuals and 6. 10% had someone living alone who was 65 years of age or older. The average household size was 2.61 and the family size was 3.11. In the county, the population was out with 27. 60% under the age of 18,10. 50% from 18 to 24,32. 50% from 25 to 44,20. 70% from 45 to 64
A gemstone is a piece of mineral crystal which, in cut and polished form, is used to make jewelry or other adornments. However, certain rocks or organic materials that are not minerals are used for jewelry and are therefore often considered to be gemstones as well. Most gemstones are hard, but some soft minerals are used in jewelry because of their luster or other properties that have aesthetic value. Rarity is another characteristic that lends value to a gemstone, apart from jewelry, from earliest antiquity engraved gems and hardstone carvings, such as cups, were major luxury art forms. A gem maker is called a lapidary or gemcutter, a worker is a diamantaire. The carvings of Carl Fabergé are significant works in this tradition, the traditional classification in the West, which goes back to the ancient Greeks, begins with a distinction between precious and semi-precious, similar distinctions are made in other cultures. In modern usage the precious stones are diamond, sapphire, other stones are classified by their color and hardness.
Another unscientific term for semi-precious gemstones used in art history and archaeology is hardstone, in modern times gemstones are identified by gemologists, who describe gems and their characteristics using technical terminology specific to the field of gemology. The first characteristic a gemologist uses to identify a gemstone is its chemical composition, for example, diamonds are made of carbon and rubies of aluminium oxide. Next, many gems are crystals which are classified by their crystal system such as cubic or trigonal or monoclinic, another term used is habit, the form the gem is usually found in. For example, which have a crystal system, are often found as octahedrons. Gemstones are classified into different groups and varieties, for example, ruby is the red variety of the species corundum, while any other color of corundum is considered sapphire. Other examples are the Emerald, red beryl, goshenite and morganite, gems are characterized in terms of refractive index, specific gravity, cleavage and luster.
They may exhibit pleochroism or double refraction and they may have luminescence and a distinctive absorption spectrum. Material or flaws within a stone may be present as inclusions, gemstones may be classified in terms of their water. This is a grading of the gems luster, transparency. Very transparent gems are considered first water, while second or third water gems are those of a lesser transparency, there is no universally accepted grading system for gemstones. Diamonds are graded using a system developed by the Gemological Institute of America in the early 1950s, all gemstones were graded using the naked eye
Forty-eight of the fifty states and the federal district are contiguous and located in North America between Canada and Mexico. The state of Alaska is in the northwest corner of North America, bordered by Canada to the east, the state of Hawaii is an archipelago in the mid-Pacific Ocean. The U. S. territories are scattered about the Pacific Ocean, the geography and wildlife of the country are extremely diverse. At 3.8 million square miles and with over 324 million people, the United States is the worlds third- or fourth-largest country by area, third-largest by land area. It is one of the worlds most ethnically diverse and multicultural nations, paleo-Indians migrated from Asia to the North American mainland at least 15,000 years ago. European colonization began in the 16th century, the United States emerged from 13 British colonies along the East Coast. Numerous disputes between Great Britain and the following the Seven Years War led to the American Revolution. On July 4,1776, during the course of the American Revolutionary War, the war ended in 1783 with recognition of the independence of the United States by Great Britain, representing the first successful war of independence against a European power.
The current constitution was adopted in 1788, after the Articles of Confederation, the first ten amendments, collectively named the Bill of Rights, were ratified in 1791 and designed to guarantee many fundamental civil liberties. During the second half of the 19th century, the American Civil War led to the end of slavery in the country. By the end of century, the United States extended into the Pacific Ocean. The Spanish–American War and World War I confirmed the status as a global military power. The end of the Cold War and the dissolution of the Soviet Union in 1991 left the United States as the sole superpower. The U. S. is a member of the United Nations, World Bank, International Monetary Fund, Organization of American States. The United States is a developed country, with the worlds largest economy by nominal GDP. It ranks highly in several measures of performance, including average wage, human development, per capita GDP. While the U. S. economy is considered post-industrial, characterized by the dominance of services and knowledge economy, the United States is a prominent political and cultural force internationally, and a leader in scientific research and technological innovations.
In 1507, the German cartographer Martin Waldseemüller produced a map on which he named the lands of the Western Hemisphere America after the Italian explorer and cartographer Amerigo Vespucci
Copper is a chemical element with symbol Cu and atomic number 29. It is a soft and ductile metal with high thermal and electrical conductivity. A freshly exposed surface of copper has a reddish-orange color. Copper is one of the few metals that occur in nature in directly usable metallic form as opposed to needing extraction from an ore and this led to very early human use, from c.8000 BC. Copper used in buildings, usually for roofing, oxidizes to form a green verdigris, Copper is sometimes used in decorative art, both in its elemental metal form and in compounds as pigments. Copper compounds are used as agents and wood preservatives. Copper is essential to all living organisms as a trace dietary mineral because it is a key constituent of the enzyme complex cytochrome c oxidase. In molluscs and crustaceans, copper is a constituent of the blood pigment hemocyanin, replaced by the hemoglobin in fish. In humans, copper is found mainly in the liver, the adult body contains between 1.4 and 2.1 mg of copper per kilogram of body weight.
The filled d-shells in these elements contribute little to interatomic interactions, unlike metals with incomplete d-shells, metallic bonds in copper are lacking a covalent character and are relatively weak. This observation explains the low hardness and high ductility of single crystals of copper, at the macroscopic scale, introduction of extended defects to the crystal lattice, such as grain boundaries, hinders flow of the material under applied stress, thereby increasing its hardness. For this reason, copper is supplied in a fine-grained polycrystalline form. The softness of copper partly explains its high conductivity and high thermal conductivity. The maximum permissible current density of copper in open air is approximately 3. 1×106 A/m2 of cross-sectional area, Copper is one of a few metallic elements with a natural color other than gray or silver. Pure copper is orange-red and acquires a reddish tarnish when exposed to air, as with other metals, if copper is put in contact with another metal, galvanic corrosion will occur. A green layer of verdigris can often be seen on old structures, such as the roofing of many older buildings.
Copper tarnishes when exposed to sulfur compounds, with which it reacts to form various copper sulfides. There are 29 isotopes of copper, 63Cu and 65Cu are stable, with 63Cu comprising approximately 69% of naturally occurring copper, both have a spin of 3⁄2
In the field of mineralogy, fracture is the texture and shape of a rocks surface formed when a mineral is fractured. Minerals often have a highly distinctive fracture, making it a feature used in their identification. Fracture differs from cleavage in that the latter involves clean splitting along the planes of the minerals crystal structure. All minerals exhibit fracture, but when very strong cleavage is present, conchoidal fracture breakage that resembles the concentric ripples of a mussel shell. It often occurs in amorphous or fine-grained minerals such as flint, opal or obsidian, subconchoidal fracture is similar to conchoidal fracture, but with less significant curvature. Earthy fracture is reminiscent of freshly broken soil and it is frequently seen in relatively soft, loosely bound minerals, such as limonite and aluminite. Hackly fracture is jagged and not even and it occurs when metals are torn, and so is often encountered in native metals such as copper and silver. Splintery fracture comprises sharp elongated points and it is particularly seen in fibrous minerals such as chrysotile, but may occur in non-fibrous minerals such as kyanite.
Uneven fracture is a surface or one with random irregularities. It occurs in a range of minerals including arsenopyrite and magnetite. Rudolf Duda and Lubos Rejl, Minerals of the World http, //www. galleries. com/minerals/property/fracture. htm
Feldspars are a group of rock-forming tectosilicate minerals that make up about 40% of the Earths continental crust. Feldspars crystallize from magma as veins in both intrusive and extrusive rocks and are present in many types of metamorphic rock. Rock formed almost entirely of plagioclase feldspar is known as anorthosite. Feldspars are found in types of sedimentary rocks. The name feldspar derives from the German Feldspat, a compound of the words Feld and Spat, the change from Spat to -spar was influenced by the English word spar, a synonym for mineral. Feldspathic refers to materials that contain feldspar, the alternate spelling, has largely fallen out of use. This group of minerals consists of tectosilicates, solid solutions between albite and anorthite are called plagioclase, or more properly plagioclase feldspar. Only limited solid solution occurs between K-feldspar and anorthite, and in the two solid solutions, immiscibility occurs at temperatures common in the crust of the earth. Albite is considered both a plagioclase and alkali feldspar, the alkali feldspars are as follows, orthoclase —KAlSi3O8 sanidine —AlSi3O8 microcline —KAlSi3O8 anorthoclase —AlSi3O8 Sanidine is stable at the highest temperatures, and microcline at the lowest.
Perthite is a texture in alkali feldspar, due to exsolution of contrasting alkali feldspar compositions during cooling of an intermediate composition. The perthitic textures in the alkali feldspars of many granites can be seen with the naked eye, microperthitic textures in crystals are visible using a light microscope, whereas cryptoperthitic textures can be seen only with an electron microscope. Barium feldspars are considered alkali feldspars, barium feldspars form as the result of the substitution of barium for potassium in the mineral structure. The barium feldspars are monoclinic and include the following, celsian—BaAl2Si2O8 hyalophane—4O8 The plagioclase feldspars are triclinic, the immiscibility gaps in the plagioclase solid solutions are complex compared to the gap in the alkali feldspars. The play of colours visible in some feldspar of labradorite composition is due to very fine-grained exsolution lamellae, chemical weathering of feldspars results in the formation of clay minerals.
About 20 million tonnes of feldspar were produced in 2010, mostly by three countries, Italy and China, Feldspar is a common raw material used in glassmaking, and to some extent as a filler and extender in paint and rubber. In glassmaking, alumina from feldspar improves product hardness, durability, in ceramics, the alkalis in feldspar act as a flux, lowering the melting temperature of a mixture. Fluxes melt at a stage in the firing process, forming a glassy matrix that bonds the other components of the system together. In the US, about 66% of feldspar is consumed in glassmaking, including glass containers and other uses, such as fillers, accounted for the remainder
Pikes Peak is the highest summit of the southern Front Range of the Rocky Mountains, in North America. The ultra-prominent 14, 115-foot fourteener is located in Pike National Forest,12.0 miles west by south of downtown Colorado Springs, the mountain is named in honor of American explorer Zebulon Pike, who was unable to reach the summit. The summit is higher than any point in the United States east of its longitude, Pikes Peak is one of Colorados 53 fourteeners, mountains more than 14,000 feet above sea level. The mountain rises 8,000 ft above downtown Colorado Springs, Pikes Peak is a designated National Historic Landmark. Tava or “sun, ” is the Ute word that was given by these first people to the mountain that we now call Pikes Peak, the band of Ute people who called the Pikes Peak region their home were the Tabeguache, meaning the People of Sun Mountain. The Ute people first arrived in Colorado about 500 A. D. although their traditions say they were created on Pikes Peak, in the 1800s, when the Arapaho people arrived in Colorado, they knew the mountain as Heey-otoyoo’ meaning Long Mountain.
Early Spanish explorers named the mountain El Capitán meaning The Leader, American explorer Zebulon Pike named the mountain Highest Peak in 1806, and the mountain was commonly known as Pikes Highest Peak. American explorer Stephen Harriman Long named the mountain James Peak in honor of Edwin James who climbed to the summit in 1820, the mountain was renamed Pikes Peak in honor of Pike. The name was simplified to Pikes Peak by the United States Board on Geographic Names in 1890, Pikes Peak is composed of a characteristic pink granite called Pikes Peak granite. The color is due to an amount of potassium feldspar. Through the process of uplifting, the hardened rock pushed through the Earths crust and created a dome-like mountain, years of erosion and weathering removed the soil and rock leaving the exposed mountain. Soils on Pikes Peak are classified as Cirque Land above timberline, the first Europeans to discover Pikes Peak were the Spanish in the 1700s. The first American sighting is credited to members of the Pike expedition.
After a failed attempt to climb to the top in November 1806, Pike wrote in his journal. here we found the snow middle deep, the thermometer which stood at 9° above 0 at the foot of the mountain, here fell to 4° below 0. The first European-American to climb the peak came 14 years after Pike, Edwin James, a young student who had just graduated from Middlebury College in Vermont, signed on as the relief botanist for Stephen Harriman Longs expedition after the first botanist had died. The expedition explored the South Platte River up as far as present-day Denver, turned south and two other men left the expedition, camped on the plains, and climbed the peak in two days, encountering little difficulty. Along the way, James was the first to describe the blue columbine, Gold was discovered in the area of present-day Denver in 1858, and newspapers referred to the gold-mining area as Pikes Peak. Pikes Peak or Bust became the slogan of the Colorado Gold Rush and this was more due to Pikes Peaks visibility to gold seekers traveling west across the plains than any actual significant gold find anywhere near Pikes Peak
Virginia is a state located in the Mid-Atlantic region of the United States, as well as in the historic Southeast. The geography and climate of the Commonwealth are shaped by the Blue Ridge Mountains and the Chesapeake Bay, the capital of the Commonwealth is Richmond, Virginia Beach is the most populous city, and Fairfax County is the most populous political subdivision. The Commonwealths estimated population as of 2014 is over 8.3 million, the areas history begins with several indigenous groups, including the Powhatan. In 1607 the London Company established the Colony of Virginia as the first permanent New World English colony, slave labor and the land acquired from displaced Native American tribes each played a significant role in the colonys early politics and plantation economy. Although the Commonwealth was under one-party rule for nearly a century following Reconstruction, the Virginia General Assembly is the oldest continuous law-making body in the New World. The state government was ranked most effective by the Pew Center on the States in both 2005 and 2008 and it is unique in how it treats cities and counties equally, manages local roads, and prohibits its governors from serving consecutive terms.
Virginias economy changed from agricultural to industrial during the 1960s and 1970s. Virginia has an area of 42,774.2 square miles, including 3,180.13 square miles of water. Virginias boundary with Maryland and Washington, D. C. extends to the mark of the south shore of the Potomac River. The southern border is defined as the 36° 30′ parallel north, the border with Tennessee was not settled until 1893, when their dispute was brought to the U. S. Supreme Court. The Chesapeake Bay separates the portion of the Commonwealth from the two-county peninsula of Virginias Eastern Shore. The bay was formed from the river valleys of the Susquehanna River. Many of Virginias rivers flow into the Chesapeake Bay, including the Potomac, Rappahannock and James, the Tidewater is a coastal plain between the Atlantic coast and the fall line. It includes the Eastern Shore and major estuaries of Chesapeake Bay, the Piedmont is a series of sedimentary and igneous rock-based foothills east of the mountains which were formed in the Mesozoic era.
The region, known for its clay soil, includes the Southwest Mountains around Charlottesville. The Blue Ridge Mountains are a province of the Appalachian Mountains with the highest points in the state. The Ridge and Valley region is west of the mountains and includes the Great Appalachian Valley, the region is carbonate rock based and includes Massanutten Mountain. The Cumberland Plateau and the Cumberland Mountains are in the southwest corner of Virginia, in this region, rivers flow northwest, with a dendritic drainage system, into the Ohio River basin
Miass is a city in Chelyabinsk Oblast, located 96 kilometers west of Chelyabinsk, on the eastern slope of the Southern Ural Mountains, on the bank of the Miass River. Miass name is taken from the Bashkirs, the inhabitants of these places. It was founded in 1773 as a copper mining factory, during the 19th century, the development was driven by the discovery of the richest gold deposits in the Urals. Average annual extraction of gold from the Miass region was about 640 kilograms, in the mid-19th century, the volume of gold mining went down, and the development of Miass slowed. Town status was granted to Miass in 1923, in 1941, an automobile factory was built. As a municipal division, the City of Miass is incorporated as Miassky Urban Okrug, currently Miass is a major machinery center. The truck manufacturer UralAZ is one of its most important factories, a total of 260 businesses operate in Miass. UralAZ produces multiaxle-axle, full-drive trucks of high cross-country passability and exports 8% of the trucks, UralAZ was included in the rating of 200 biggest Russian companies in 2000 in volume of sales, and employs 105,000 people.
It was established in 1942, when the ZiS factory was evacuated from Moscow during World War II The Makeyev Rocket Design Bureau creates Submarine-launched ballistic missile, in 1955, it was moved from Zlatoust, where it was established at 1947, to Miass. The old part of the city comprises 19th-century wooden houses with balconies, jambs. The house of the gold mines administrator, has been preserved, lake Turgoyak is located near Miass and is a popular tourist location, with crystal clear water. Miass has a rich mineralogical museum, as it is close to the Ilmensky Mineral conservation area, to the East of Miass is the Ilmenskyy Zapovednik, a large protected forest. Not far into the forest, trails lead to fresh-water springs, Постановление №161 от25 мая2006 г. «Об утверждении перечня муниципальных образований Челябинской области и населённых пунктов, входящих в их состав», Постановления №2255 от23 октября2014 г. «О внесении изменений в перечень муниципальных образований Челябинской области и населённых пунктов, Вступил в силу со дня официального опубликования.
Опубликован, Южноуральская панорама, №111–112,14 июня2006 г, official website of Miass Unofficial website of Miass
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 often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress and 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. A mathematical description of wave propagation in a birefringent medium is presented below, following is a qualitative explanation of the phenomenon. Thus rotating the material around this axis does not change its optical behavior and this special direction is known as the optic axis of the material. Light whose polarization is perpendicular to the 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, and this is called an ordinary ray.
The magnitude of the difference is quantified by the birefringence, Δ n = n e − n o, the propagation of the ordinary ray is simply described by no as if there were no birefringence involved. However the extraordinary ray, as its name suggests, propagates unlike any wave in an optical material. Its refraction at a surface can be using the effective refractive index. However it is in fact an inhomogeneous wave whose power flow is not exactly in the direction of the wave vector and this causes an additional shift in that beam, even 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 ray, to rotate slightly around that of the ordinary ray. When the light propagates either along or orthogonal to the optic axis, 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, for instance, a quarter-wave plate is commonly used to create circular polarization from a linearly polarized source.
The case of so-called biaxial crystals is substantially more complex and 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 around which a rotation leaves the optical properties invariant, for this reason, birefringent materials with three distinct refractive indices are called biaxial