Mohs scale of mineral hardness
The Mohs scale of mineral hardness is a qualitative ordinal scale characterizing scratch resistance of various minerals through the ability of harder material to scratch softer material. Created in 1812 by German geologist and mineralogist Friedrich Mohs, it is one of several definitions of hardness in materials science, some of which are more quantitative; the method of comparing hardness by observing which minerals can scratch others is of great antiquity, having been mentioned by Theophrastus in his treatise On Stones, c. 300 BC, followed by Pliny the Elder in his Naturalis Historia, c. 77 AD. While facilitating the identification of minerals in the field, the Mohs scale does not show how well hard materials perform in an industrial setting. Despite its lack of precision, the Mohs scale is relevant for field geologists, who use the scale to identify minerals using scratch kits; the Mohs scale hardness of minerals can be found in reference sheets. Mohs hardness is useful in milling, it allows assessment of.
The scale is used at electronic manufacturers for testing the resilience of flat panel display components. The Mohs scale of mineral hardness is based on the ability of one natural sample of mineral to scratch another mineral visibly; the samples of matter used by Mohs are all different minerals. Minerals are chemically pure solids found in nature. Rocks are made up of one or more minerals; as the hardest known occurring substance when the scale was designed, diamonds are at the top of the scale. The hardness of a material is measured against the scale by finding the hardest material that the given material can scratch, or the softest material that can scratch the given material. For example, if some material is scratched by apatite but not by fluorite, its hardness on the Mohs scale would fall between 4 and 5. "Scratching" a material for the purposes of the Mohs scale means creating non-elastic dislocations visible to the naked eye. Materials that are lower on the Mohs scale can create microscopic, non-elastic dislocations on materials that have a higher Mohs number.
While these microscopic dislocations are permanent and sometimes detrimental to the harder material's structural integrity, they are not considered "scratches" for the determination of a Mohs scale number. The Mohs scale is a purely ordinal scale. For example, corundum is twice as hard as topaz; the table below shows the comparison with the absolute hardness measured by a sclerometer, with pictorial examples. On the Mohs scale, a streak plate has a hardness of 7.0. Using these ordinary materials of known hardness can be a simple way to approximate the position of a mineral on the scale; the table below incorporates additional substances that may fall between levels: Comparison between hardness and hardness: Mohs hardness of elements is taken from G. V. Samsonov in Handbook of the physicochemical properties of the elements, IFI-Plenum, New York, USA, 1968. Cordua, William S. "The Hardness of Minerals and Rocks". Lapidary Digest, c. 1990
Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate. The Mohs scale of mineral hardness, based on scratch hardness comparison, defines value 3 as "calcite". Other polymorphs of calcium carbonate are the minerals vaterite. Aragonite will change to calcite over timescales of days or less at temperatures exceeding 300 °C, vaterite is less stable. Calcite is derived from the German Calcit, a term coined in the 19th century from the Latin word for lime, calx with the suffix -ite used to name minerals, it is thus etymologically related to chalk. When applied by archaeologists and stone trade professionals, the term alabaster is used not just as in geology and mineralogy, where it is reserved for a variety of gypsum. In publications, two different sets of Miller indices are used to describe directions in calcite crystals - the hexagonal system with three indices h, k, l and the rhombohedral system with four indices h, k, l, i. To add to the complications, there are two definitions of unit cell for calcite.
One, an older "morphological" unit cell, was inferred by measuring angles between faces of crystals and looking for the smallest numbers that fit. A "structural" unit cell was determined using X-ray crystallography; the morphological unit cell has approximate dimensions a = 10 Å and c = 8.5 Å, while for the structural unit cell they are a = 5 Å and c = 17 Å. For the same orientation, c must be multiplied by 4 to convert from morphological to structural units; as an example, the cleavage is given as "perfect on " in morphological coordinates and "perfect on " in structural units. Twinning and crystal forms are always given in morphological units. Over 800 forms of calcite crystals have been identified. Most common are scalenohedra, with faces in the hexagonal directions or directions. Habits include acute to tabular forms, prisms, or various scalenohedra. Calcite exhibits several twinning types adding to the variety of observed forms, it may occur as fibrous, lamellar, or compact. A fibrous, efflorescent form is known as lublinite.
Cleavage is in three directions parallel to the rhombohedron form. Its fracture is difficult to obtain. Scalenohedral faces are chiral and come in pairs with mirror-image symmetry. Rhombohedral faces are achiral, it has a defining Mohs hardness of 3, a specific gravity of 2.71, its luster is vitreous in crystallized varieties. Color is white or none, though shades of gray, orange, green, violet, brown, or black can occur when the mineral is charged with impurities. Calcite is transparent to opaque and may show phosphorescence or fluorescence. A transparent variety called. Acute scalenohedral crystals are sometimes referred to as "dogtooth spar" while the rhombohedral form is sometimes referred to as "nailhead spar". Single calcite crystals display; this strong birefringence causes objects viewed through a clear piece of calcite to appear doubled. The birefringent effect was first described by the Danish scientist Rasmus Bartholin in 1669. At a wavelength of ≈590 nm calcite has ordinary and extraordinary refractive indices of 1.658 and 1.486, respectively.
Between 190 and 1700 nm, the ordinary refractive index varies between 1.9 and 1.5, while the extraordinary refractive index varies between 1.6 and 1.4. Calcite, like most carbonates, will dissolve with most forms of acid. Calcite can be either dissolved by groundwater or precipitated by groundwater, depending on several factors including the water temperature, pH, dissolved ion concentrations. Although calcite is insoluble in cold water, acidity can cause dissolution of calcite and release of carbon dioxide gas. Ambient carbon dioxide, due to its acidity, has a slight solubilizing effect on calcite. Calcite exhibits an unusual characteristic called retrograde solubility in which it becomes less soluble in water as the temperature increases; when conditions are right for precipitation, calcite forms mineral coatings that cement the existing rock grains together or it can fill fractures. When conditions are right for dissolution, the removal of calcite can increase the porosity and permeability of the rock, if it continues for a long period of time may result in the formation of caves.
On a landscape scale, continued dissolution of calcium carbonate-rich rocks can lead to the expansion and eventual collapse of cave systems, resulting in various forms of karst topography. Ancient Egyptians carved many items out of calcite, relating it to their goddess Bast, whose name contributed to the term alabaster because of the close association. Many other cultures have used the material for similar carved applications. High-grade optical calcite was used in World War II for gun sights in bomb sights and anti-aircraft weaponry. Experiments have been conducted to use calcite for a cloak of invisibility. Microbiologically precipitated calcite has a wide range of applications, such as soil remediation, soil stabilization and concrete repair. Calcite, obtained from an 80 kg sample of Carrara marble, is used as the IAEA-603 isotopic standard in mass spectrometry for the calibration of δ18O and δ13C. Calcite is a common constituent
Marble is a metamorphic rock composed of recrystallized carbonate minerals, most calcite or dolomite. Marble is not foliated, although there are exceptions. In geology, the term "marble" refers to metamorphosed limestone, but its use in stonemasonry more broadly encompasses unmetamorphosed limestone. Marble is used for sculpture and as a building material; the word "marble" derives from the Ancient Greek μάρμαρον, from μάρμαρος, "crystalline rock, shining stone" from the verb μαρμαίρω, "to flash, gleam". This stem is the ancestor of the English word "marmoreal", meaning "marble-like." While the English term "marble" resembles the French marbre, most other European languages, more resemble the original Ancient Greek. Marble is a rock resulting from metamorphism of sedimentary carbonate rocks, most limestone or dolomite rock. Metamorphism causes variable recrystallization of the original carbonate mineral grains; the resulting marble rock is composed of an interlocking mosaic of carbonate crystals.
Primary sedimentary textures and structures of the original carbonate rock have been modified or destroyed. Pure white marble is the result of metamorphism of a pure limestone or dolomite protolith; the characteristic swirls and veins of many colored marble varieties are due to various mineral impurities such as clay, sand, iron oxides, or chert which were present as grains or layers in the limestone. Green coloration is due to serpentine resulting from magnesium-rich limestone or dolostone with silica impurities; these various impurities have been mobilized and recrystallized by the intense pressure and heat of the metamorphism. Examples of notable marble varieties and locations: White marble has been prized for its use in sculptures since classical times; this preference has to do with its softness, which made it easier to carve, relative isotropy and homogeneity, a relative resistance to shattering. The low index of refraction of calcite allows light to penetrate several millimeters into the stone before being scattered out, resulting in the characteristic waxy look which gives "life" to marble sculptures of any kind, why many sculptors preferred and still prefer marble for sculpting.
Construction marble is a stone, composed of calcite, dolomite or serpentine, capable of taking a polish. More in construction the dimension stone trade, the term "marble" is used for any crystalline calcitic rock useful as building stone. For example, Tennessee marble is a dense granular fossiliferous gray to pink to maroon Ordovician limestone, that geologists call the Holston Formation. Ashgabat, the capital city of Turkmenistan, was recorded in the 2013 Guinness Book of Records as having the world's highest concentration of white marble buildings. According to the United States Geological Survey, U. S. domestic marble production in 2006 was 46,400 tons valued at about $18.1 million, compared to 72,300 tons valued at $18.9 million in 2005. Crushed marble production in 2006 was 11.8 million tons valued at $116 million, of which 6.5 million tons was finely ground calcium carbonate and the rest was construction aggregate. For comparison, 2005 crushed marble production was 7.76 million tons valued at $58.7 million, of which 4.8 million tons was finely ground calcium carbonate and the rest was construction aggregate.
U. S. dimension marble demand is about 1.3 million tons. The DSAN World Demand for Marble Index has shown a growth of 12% annually for the 2000–2006 period, compared to 10.5% annually for the 2000–2005 period. The largest dimension marble application is tile. In 1998, marble production was dominated by 4 countries that accounted for half of world production of marble and decorative stone. Italy and China were the world leaders, each representing 16% of world production, while Spain and India produced 9% and 8%, respectively. Italy is the world leader in marble export, with 20% share in global marble production, followed by China with 16%, India with 10%, Spain with 6%, Portugal with 5%. Dust produced by cutting marble could cause lung disease but more research needs to be carried out on whether dust filters and other safety products reduce this risk; the Occupational Safety and Health Administration has set the legal limit for marble exposure in the workplace as 15 mg/m3 total exposure and 5 mg/m3 respiratory exposure over an 8-hour workday.
The National Institute for Occupational Safety and Health has set a recommended exposure limit of 10 mg/m3 total exposure and 5 mg/m3 respiratory exposure over an 8-hour workday. Acids damage marble, because the calcium carbonate in marble reacts with them, releasing carbon dioxide: CaCO3 + 2H+ → Ca2+ + CO2 + H2O Thus, vinegar or other acidic solutions should never be used on marble. Outdoor marble statues, gravestones, or other marble structures are damaged by acid rain; the haloalkaliphilic methylotrophic bacterium Methylophaga murata was isolated from deteriorating marble in the Kremlin. Bacterial and fungal degradation was detected in four samples of marble from Milan cathedral; as the favorite medium for Greek and Roman sculptors and architects, marble has become a cultural symbol of tradition and refined taste. Its varied and colorful patterns make i
Apatite is a group of phosphate minerals referring to hydroxylapatite and chlorapatite, with high concentrations of OH−, F− and Cl− ions in the crystal. The formula of the admixture of the three most common endmembers is written as Ca1062, the crystal unit cell formulae of the individual minerals are written as Ca1062, Ca106F2 and Ca106Cl2; the mineral was named apatite by the German geologist Abraham Gottlob Werner in 1786, although the specific mineral he had described was reclassified as fluorapatite in 1860 by the German mineralogist Karl Friedrich August Rammelsberg. Apatite is mistaken for other minerals; this tendency is reflected in the mineral's name, derived from the Greek word απατείν, which means to deceive or to be misleading. Apatite is one of a few minerals used by biological micro-environmental systems. Apatite is the defining mineral for 5 on the Mohs scale. Hydroxyapatite known as hydroxylapatite, is the major component of tooth enamel and bone mineral. A rare form of apatite in which most of the OH groups are absent and containing many carbonate and acid phosphate substitutions is a large component of bone material.
Fluorapatite is more resistant to acid attack. Fluoridated water allows exchange in the teeth of fluoride ions for hydroxyl groups in apatite. Toothpaste contains a source of fluoride anions. Too much fluoride results in dental fluorosis and/or skeletal fluorosis. Fission tracks in apatite are used to determine the thermal histories of orogenic belts and of sediments in sedimentary basins. /He dating of apatite is well established from noble gas diffusion studies for use in determining thermal histories and other, less typical applications such as paleo-wildfire dating. Phosphorite is a phosphate-rich sedimentary rock, that contains between 18% and 40% P2O5; the apatite in phosphorite is present. The primary use of apatite is in the manufacture of fertilizer – it is a source of phosphorus, it is used as a gemstone. Green and blue varieties, in finely divided form, are pigments with excellent covering power. During digestion of apatite with sulfuric acid to make phosphoric acid, hydrogen fluoride is produced as a byproduct from any fluorapatite content.
This byproduct is a minor industrial source of hydrofluoric acid. Fluoro-chloro apatite forms the basis of the now obsolete Halophosphor fluorescent tube phosphor system. Dopant elements of manganese and antimony, at less than one mole-percent, in place of the calcium and phosphorus impart the fluorescence, adjustment of the fluorine-to-chlorine ratio adjusts the shade of white produced; this system has been entirely replaced by the Tri-Phosphor system. In the United States, apatite-derived fertilizers are used to supplement the nutrition of many agricultural crops by providing a valuable source of phosphate. Apatites are a proposed host material for storage of nuclear waste, along with other phosphates. Apatite is infrequently used as a gemstone. Transparent stones of clean color have been faceted, chatoyant specimens have been cabochon-cut. Chatoyant stones are known as cat's-eye apatite, transparent green stones are known as asparagus stone, blue stones have been called moroxite. If crystals of rutile have grown in the crystal of apatite, in the right light the cut stone displays a cat's-eye effect.
Major sources for gem apatite are Brazil and Mexico. Other sources include Canada, Czech Republic, India, Mozambique, South Africa, Sri Lanka, the United States. Apatite is found to contain significant amounts of rare-earth elements and can be used as an ore for those metals; this is preferable to traditional rare-earth ores such as monazite, as apatite is not radioactive and does not pose an environmental hazard in mine tailings. However, apatite contains uranium and its radioactive decay-chain nuclides. Apatite is an ore mineral at the Hoidas Lake rare-earth project; the standard enthalpies of formation in the crystalline state of hydroxyapatite, chlorapatite and a preliminary value for bromapatite, have been determined by reaction-solution calorimetry. Speculations on the existence of a possible fifth member of the calcium apatites family, have been drawn from energetic considerations. Structural and thermodynamic properties of crystal hexagonal calcium apatites, Ca1062, have been investigated using an all-atom Born-Huggins-Mayer potential by a molecular dynamics technique.
The accuracy of the model at room temperature and atmospheric pressure was checked against crystal structural data, with maximum deviations of c. 4% for the haloapatites and 8% for hydroxyapatite. High-pressure simulation runs, in the range 0.5-75 kbar, were performed in order to estimate the isothermal compressibility coefficient of those compounds. The deformation of the compressed solids is always elastically anisotropic, with BrAp exhibiting a markedly different behavior from those displayed by HOAp and ClAp. High-pressure p-V data were fitted to the Parsafar-Mason equation of state with an accuracy better than 1%; the monoclinic solid phases Ca1062 and the molten hydroxyapatite compound have been studied by molecular dynamics. Moon rocks collected by astronauts during the Apollo program contain traces of apatite. Re-analysis of these samples in 2010 revealed water trapped in the mineral as hydrox
Silicate minerals are rock-forming minerals made up of silicate groups. They are the largest and most important class of minerals and make up 90 percent of the Earth's crust. In mineralogy, silica SiO2 is considered a silicate mineral. Silica is found in nature as the mineral quartz, its polymorphs. On Earth, a wide variety of silicate minerals occur in an wider range of combinations as a result of the processes that have been forming and re-working the crust for billions of years; these processes include partial melting, fractionation, metamorphism and diagenesis. Living organisms contribute to this geologic cycle. For example, a type of plankton known as diatoms construct their exoskeletons from silica extracted from seawater; the tests of dead diatoms are a major constituent of deep ocean sediment, of diatomaceous earth. A silicate mineral is an ionic compound whose anions consist predominantly of silicon and oxygen atoms. In most minerals in the Earth's crust, each silicon atom is the center of an ideal tetrahedron, whose corners are four oxygen atoms covalently bound to it.
Two adjacent tetrahedra may share a vertex, meaning that the oxygen atom is a bridge connecting the two silicon atoms. An unpaired vertex represents an ionized oxygen atom, covalently bound to a single silicon atom, that contributes one unit of negative charge to the anion; some silicon centers may be replaced by atoms of other elements, still bound to the four corner oxygen corners. If the substituted atom is not tetravalent, it contributes extra charge to the anion, which requires extra cations. For example, in the mineral orthoclase n, the anion is a tridimensional network of tetrahedra in which all oxygen corners are shared. If all tetrahedra had silicon centers, the anion would be just neutral silica n. Replacement of one every four silicon atoms by an aluminum atom results in the anion n, whose charge is neutralized by the potassium cations K+. In mineralogy, silicate minerals are classified into seven major groups according to the structure of their silicate anion: Note that tectosilicates can only have additional cations if some of the silicon is replaced by an atom of lower valence such as aluminium.
Al for Si substitution is common. Nesosilicates, or orthosilicates, have the orthosilicate ion, which constitute isolated 4− tetrahedra that are connected only by interstitial cations; the Nickel–Strunz classification is 09. A –examples include: Phenakite group Phenakite – Be2SiO4 Willemite – Zn2SiO4 Olivine group Forsterite – Mg2SiO4 Fayalite – Fe2SiO4 Tephroite – Mn2SiO4 Garnet group Pyrope – Mg3Al23 Almandine – Fe3Al23 Spessartine – Mn3Al23 Grossular – Ca3Al23 Andradite – Ca3Fe23 Uvarovite – Ca3Cr23 Hydrogrossular – Ca3Al2Si2O83−m4m Zircon group Zircon – ZrSiO4 Thorite – SiO4 Hafnon – SiO4 Al2SiO5 group Andalusite – Al2SiO5 Kyanite – Al2SiO5 Sillimanite – Al2SiO5 Dumortierite – Al6.5–7BO333 Topaz – Al2SiO42 Staurolite – Fe2Al942 Humite group – 732Norbergite – Mg32 Chondrodite – Mg522 Humite – Mg732 Clinohumite – Mg942 Datolite – CaBSiO4 Titanite – CaTiSiO5 Chloritoid – 2Al4Si2O104 Mullite – Al6Si2O13 Sorosilicates have isolated pyrosilicate anions Si2O6−7, consisting of double tetrahedra with a shared oxygen vertex—a silicon:oxygen ratio of 2:7.
The Nickel–Strunz classification is 09. B. Examples include: Hemimorphite – Zn42·H2O Lawsonite – CaAl22·H2O Axinite – 3Al2 Ilvaite – CaFeII2FeIIIO Epidote group Epidote – Ca23O Zoisite – Ca2Al3O Tanzanite – Ca2Al3O Clinozoisite – Ca2Al3O Allanite – CaAl2O Dollaseite- – CaCeMg2AlSi3O11F Vesuvianite – Ca102Al4524 Cyclosilicates, or ring silicates, have three or more tetrahedra linked in a ring; the general formula is 2x−, where one or more silicon atoms can be replaced by other 4-coordinated atom. The silicon:oxygen ratio is 1:3. Double rings have the formula 2x−; the Nickel–Strunz classification is 09. C. Possible ring sizes include: Some example minerals are: 3-member single ring Benitoite – BaTi 4-member single ring Papagoite – CaCuAlSi2O63. 6-member single ring Beryl – Be3Al2 Bazzite – Be3Sc2 Sugilite – KNa22Li3Si12O30 Tourmaline – 3−634 Pezzottaite – CsAl2Si6O18 Osumilite – 2312O30 Cordierite – 2Al4Si5O18 Sekaninaite – 2Al4Si5O18 9-member single ring Eudialyte – Na15Ca63Zr3SiO3222 6-member double ring Milarite – K2Ca4Al2Be4H2ONote that the ring in axinite contains two B and four Si tetrahedra and is distorted compared to the other 6-member ring cyclosilicates.
Inosilicates, or chain silicates, have interlocking chains of silicate tetrahedra with either SiO3, 1:3 ratio, for single chains or Si4O11, 4:11 ratio, for double chains. The Nickel–Strunz classification is 09. D – examples include: Pyroxene group Enstatite – orthoferrosilite series Enstatite – MgSiO3 Ferrosilite – FeSiO3 Pigeonite – Ca0.251.75Si2O6 Diopside – hedenbergite series Diopside – CaMgSi2O6 Hedenbergite – CaFeSi2O6 Augite – 2O6 Sodium pyroxene series Jadeite – NaAlSi2O6 Aegirine (or ac
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
Norway the Kingdom of Norway, is a Nordic country in Northern Europe whose territory comprises the western and northernmost portion of the Scandinavian Peninsula. The Antarctic Peter I Island and the sub-Antarctic Bouvet Island are dependent territories and thus not considered part of the kingdom. Norway lays claim to a section of Antarctica known as Queen Maud Land. Norway has a total area of 385,207 square kilometres and a population of 5,312,300; the country shares a long eastern border with Sweden. Norway is bordered by Finland and Russia to the north-east, the Skagerrak strait to the south, with Denmark on the other side. Norway has an extensive coastline, facing the Barents Sea. Harald V of the House of Glücksburg is the current King of Norway. Erna Solberg has been prime minister since 2013. A unitary sovereign state with a constitutional monarchy, Norway divides state power between the parliament, the cabinet and the supreme court, as determined by the 1814 constitution; the kingdom was established in 872 as a merger of a large number of petty kingdoms and has existed continuously for 1,147 years.
From 1537 to 1814, Norway was a part of the Kingdom of Denmark-Norway, from 1814 to 1905, it was in a personal union with the Kingdom of Sweden. Norway was neutral during the First World War. Norway remained neutral until April 1940 when the country was invaded and occupied by Germany until the end of Second World War. Norway has both administrative and political subdivisions on two levels: counties and municipalities; the Sámi people have a certain amount of self-determination and influence over traditional territories through the Sámi Parliament and the Finnmark Act. Norway maintains close ties with both the United States. Norway is a founding member of the United Nations, NATO, the European Free Trade Association, the Council of Europe, the Antarctic Treaty, the Nordic Council. Norway maintains the Nordic welfare model with universal health care and a comprehensive social security system, its values are rooted in egalitarian ideals; the Norwegian state has large ownership positions in key industrial sectors, having extensive reserves of petroleum, natural gas, lumber and fresh water.
The petroleum industry accounts for around a quarter of the country's gross domestic product. On a per-capita basis, Norway is the world's largest producer of oil and natural gas outside of the Middle East; the country has the fourth-highest per capita income in the world on the World IMF lists. On the CIA's GDP per capita list which includes autonomous territories and regions, Norway ranks as number eleven, it has the world's largest sovereign wealth fund, with a value of US$1 trillion. Norway has had the highest Human Development Index ranking in the world since 2009, a position held between 2001 and 2006, it had the highest inequality-adjusted ranking until 2018 when Iceland moved to the top of the list. Norway ranked first on the World Happiness Report for 2017 and ranks first on the OECD Better Life Index, the Index of Public Integrity, the Democracy Index. Norway has one of the lowest crime rates in the world. Norway has two official names: Norge in Noreg in Nynorsk; the English name Norway comes from the Old English word Norþweg mentioned in 880, meaning "northern way" or "way leading to the north", how the Anglo-Saxons referred to the coastline of Atlantic Norway similar to scientific consensus about the origin of the Norwegian language name.
The Anglo-Saxons of Britain referred to the kingdom of Norway in 880 as Norðmanna land. There is some disagreement about whether the native name of Norway had the same etymology as the English form. According to the traditional dominant view, the first component was norðr, a cognate of English north, so the full name was Norðr vegr, "the way northwards", referring to the sailing route along the Norwegian coast, contrasting with suðrvegar "southern way" for, austrvegr "eastern way" for the Baltic. In the translation of Orosius for Alfred, the name is Norðweg, while in younger Old English sources the ð is gone. In the 10th century many Norsemen settled in Northern France, according to the sagas, in the area, called Normandy from norðmann, although not a Norwegian possession. In France normanni or northmanni referred to people of Sweden or Denmark; until around 1800 inhabitants of Western Norway where referred to as nordmenn while inhabitants of Eastern Norway where referred to as austmenn. According to another theory, the first component was a word nór, meaning "narrow" or "northern", referring to the inner-archipelago sailing route through the land.
The interpretation as "northern", as reflected in the English and Latin forms of the name, would have been due to folk etymology. This latter view originated with philologist Niels Halvorsen Trønnes in 1847; the form Nore is still used in placenames such as the village of Nore and lake Norefjorden in Buskerud county, still has the same meaning. Among other arguments in favour of the theor