Geochemistry
Encyclopedia
The field of geochemistry involves study of the chemical
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

 composition of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

 and other planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

s, chemical processes and reactions that govern the composition of rock
Rock (geology)
In geology, rock or stone is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock. In general rocks are of three types, namely, igneous, sedimentary, and metamorphic...

s, water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

, and soil
Soil
Soil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...

s, and the cycles of matter and energy that transport the Earth's chemical components in time and space, and their interaction with the hydrosphere
Hydrosphere
A hydrosphere in physical geography describes the combined mass of water found on, under, and over the surface of a planet....

 and the atmosphere
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...

.

Some subsets of geochemistry are:
  1. Isotope geochemistry
    Isotope geochemistry
    Isotope geochemistry is an aspect of geology based upon study of the relative and absolute concentrations of the elements and their isotopes in the Earth. Variations in the abundance of these isotopes, typically measured with an isotope ratio mass spectrometer or an accelerator mass spectrometer,...

    :Determination of the relative and absolute concentrations of the element
    Chemical element
    A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

    s and their isotope
    Isotope
    Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

    s in the earth and on earth's surface.
  2. Examination of the distribution and movements of elements in different parts of the earth (crust, mantle, hydrosphere etc.) and in minerals with the goal to determine the underlying system of distribution and movement.
  3. Cosmochemistry
    Cosmochemistry
    Cosmochemistry or chemical cosmology is the study of the chemical composition of matter in the universe and the processes that led to those compositions. This is done primarily through the study of the chemical composition of meteorites and other physical samples...

    : Analysis of the distribution of elements and their isotopes in the cosmos
    Universe
    The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

    .
  4. Biogeochemistry
    Biogeochemistry
    Biogeochemistry is the scientific discipline that involves the study of the chemical, physical, geological, and biological processes and reactions that govern the composition of the natural environment...

    : Field of study focusing on the effect of life on the chemistry of the earth.
  5. Organic geochemistry
    Organic geochemistry
    Organic geochemistry is the study of the impacts and processes that organisms have had on the Earth. The study of organic geochemistry is usually traced to the work of Alfred E. Treibs, "the father of organic geochemistry." Treibs first isolated metalloporphyrins from petroleum. This discovery...

    : A study of the role of processes and compounds that are derived from living or once-living organisms.
  6. Aqueous geochemistry: Understanding the role of various elements in watersheds, including copper
    Copper
    Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

    , sulfur
    Sulfur
    Sulfur or sulphur is the chemical element with atomic number 16. In the periodic table it is represented by the symbol S. It is an abundant, multivalent non-metal. Under normal conditions, sulfur atoms form cyclic octatomic molecules with chemical formula S8. Elemental sulfur is a bright yellow...

    , mercury
    Mercury (element)
    Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...

    , and how elemental fluxes are exchanged through atmospheric-terrestrial-aquatic interactions.
  7. Regional, environmental and exploration geochemistry
    Regional, environmental and exploration geochemistry
    Regional geochemistry is the study of the spatial variation in the chemical composition of materials at the surface of the Earth, on a scale of tens to thousands of kilometres...

    : Applications to environmental, hydrological and mineral exploration studies.


Victor Goldschmidt
Victor Goldschmidt
Victor Moritz Goldschmidt was a mineralogist considered to be the founder of modern geochemistry and crystal chemistry, developer of the Goldschmidt Classification of elements.-Early life & career:Goldschmidt was born in Zürich...

 is considered by most to be the father of modern geochemistry and the ideas of the subject were formed by him in a series of publications from 1922 under the title ‘Geochemische Verteilungsgesetze der Elemente’ (geochemical laws of distribution of the elements).

Chemical characteristics

The more common rock constituents are nearly all oxides; chlorides, sulfides and fluorides are the only important exceptions to this and their total amount in any rock is usually much less than 1%. F. W. Clarke
Frank Wigglesworth Clarke
Frank Wigglesworth Clarke of Boston, Massachusetts, and Washington, D.C. was an American scientist and chemist. Sometimes known as the "Father of Geochemistry," Clarke is credited with determining the composition of the Earth's crust...

 has calculated that a little more than 47% of the Earth's crust consists of oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

. It occurs principally in combination as oxides, of which the chief are silica, alumina, iron oxide
Iron oxide
Iron oxides are chemical compounds composed of iron and oxygen. All together, there are sixteen known iron oxides and oxyhydroxides.Iron oxides and oxide-hydroxides are widespread in nature, play an important role in many geological and biological processes, and are widely utilized by humans, e.g.,...

s, and various carbonate
Carbonate
In chemistry, a carbonate is a salt of carbonic acid, characterized by the presence of the carbonate ion, . The name may also mean an ester of carbonic acid, an organic compound containing the carbonate group C2....

s (calcium carbonate
Calcium carbonate
Calcium carbonate is a chemical compound with the formula CaCO3. It is a common substance found in rocks in all parts of the world, and is the main component of shells of marine organisms, snails, coal balls, pearls, and eggshells. Calcium carbonate is the active ingredient in agricultural lime,...

, magnesium carbonate
Magnesium carbonate
Magnesium carbonate, MgCO3, is a white solid that occurs in nature as a mineral. Several hydrated and basic forms of magnesium carbonate also exist as minerals...

, sodium carbonate
Sodium carbonate
Sodium carbonate , Na2CO3 is a sodium salt of carbonic acid. It most commonly occurs as a crystalline heptahydrate, which readily effloresces to form a white powder, the monohydrate. Sodium carbonate is domestically well-known for its everyday use as a water softener. It can be extracted from the...

, and potassium carbonate
Potassium carbonate
Potassium carbonate is a white salt, soluble in water , which forms a strongly alkaline solution. It can be made as the product of potassium hydroxide's absorbent reaction with carbon dioxide. It is deliquescent, often appearing a damp or wet solid...

). The silica functions principally as an acid, forming silicates, and all the commonest minerals of igneous rocks are of this nature. From a computation based on 1672 analyses of numerous kinds of rocks Clarke arrived at the following as the average percentage composition: SiO2=59.71, Al2O3=15.41, Fe2O3=2.63, FeO=3.52, MgO=4.36, CaO=4.90, Na2O=3.55, K2O=2.80, H2O=1.52, TiO2=0.60, P2O5=0.22, total 99.22%). All the other constituents occur only in very small quantities, usually much less than 1%.

These oxides combine in a haphazard way. For example, potash
Potash
Potash is the common name for various mined and manufactured salts that contain potassium in water-soluble form. In some rare cases, potash can be formed with traces of organic materials such as plant remains, and this was the major historical source for it before the industrial era...

 (potassium carbonate) and soda (sodium carbonate
Sodium carbonate
Sodium carbonate , Na2CO3 is a sodium salt of carbonic acid. It most commonly occurs as a crystalline heptahydrate, which readily effloresces to form a white powder, the monohydrate. Sodium carbonate is domestically well-known for its everyday use as a water softener. It can be extracted from the...

) combine to produce feldspar
Feldspar
Feldspars are a group of rock-forming tectosilicate minerals which make up as much as 60% of the Earth's crust....

s. In some cases they may take other forms, such as nepheline
Nepheline
Nepheline, also called nephelite , is a feldspathoid: a silica-undersaturated aluminosilicate, Na3KAl4Si4O16, that occurs in intrusive and volcanic rocks with low silica, and in their associated pegmatites...

, leucite
Leucite
Leucite is a rock-forming mineral composed of potassium and aluminium tectosilicate K[AlSi2O6]. Crystals have the form of cubic icositetrahedra but, as first observed by Sir David Brewster in 1821, they are not optically isotropic, and are therefore pseudo-cubic. Goniometric measurements made by...

, and muscovite
Muscovite
Muscovite is a phyllosilicate mineral of aluminium and potassium with formula KAl22, or 236. It has a highly-perfect basal cleavage yielding remarkably-thin laminæ which are often highly elastic...

, but in the great majority of instances they are found as feldspar. Phosphoric acid
Phosphoric acid
Phosphoric acid, also known as orthophosphoric acid or phosphoric acid, is a mineral acid having the chemical formula H3PO4. Orthophosphoric acid molecules can combine with themselves to form a variety of compounds which are also referred to as phosphoric acids, but in a more general way...

 with lime (calcium carbonate) forms apatite
Apatite
Apatite is a group of phosphate minerals, usually referring to hydroxylapatite, fluorapatite, chlorapatite and bromapatite, named for high concentrations of OH−, F−, Cl− or Br− ions, respectively, in the crystal...

. Titanium dioxide
Titanium dioxide
Titanium dioxide, also known as titanium oxide or titania, is the naturally occurring oxide of titanium, chemical formula . When used as a pigment, it is called titanium white, Pigment White 6, or CI 77891. Generally it comes in two different forms, rutile and anatase. It has a wide range of...

 with ferrous oxide gives rise to ilmenite
Ilmenite
Ilmenite is a weakly magnetic titanium-iron oxide mineral which is iron-black or steel-gray. It is a crystalline iron titanium oxide . It crystallizes in the trigonal system, and it has the same crystal structure as corundum and hematite....

. Part of the lime forms lime feldspar. Magnesium carbonate and iron oxides with silica crystallize as olivine
Olivine
The mineral olivine is a magnesium iron silicate with the formula 2SiO4. It is a common mineral in the Earth's subsurface but weathers quickly on the surface....

 or enstatite
Enstatite
Enstatite is the magnesium endmember of the pyroxene silicate mineral series enstatite - ferrosilite . The magnesium rich members of the solid solution series are common rock-forming minerals found in igneous and metamorphic rocks...

, or with alumina and lime form the complex ferro-magnesian silicates of which the pyroxene
Pyroxene
The pyroxenes are a group of important rock-forming inosilicate minerals found in many igneous and metamorphic rocks. They share a common structure consisting of single chains of silica tetrahedra and they crystallize in the monoclinic and orthorhombic systems...

s, amphibole
Amphibole
Amphibole is the name of an important group of generally dark-colored rock-forming inosilicate minerals, composed of double chain tetrahedra, linked at the vertices and generally containing ions of iron and/or magnesium in their structures.-Mineralogy:...

s, and biotite
Biotite
Biotite is a common phyllosilicate mineral within the mica group, with the approximate chemical formula . More generally, it refers to the dark mica series, primarily a solid-solution series between the iron-endmember annite, and the magnesium-endmember phlogopite; more aluminous endmembers...

s are the chief. Any excess of silica above what is required to neutralize the bases will separate out as quartz
Quartz
Quartz is the second-most-abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2. There are many different varieties of quartz,...

; excess of alumina crystallizes as corundum
Corundum
Corundum is a crystalline form of aluminium oxide with traces of iron, titanium and chromium. It is a rock-forming mineral. It is one of the naturally clear transparent materials, but can have different colors when impurities are present. Transparent specimens are used as gems, called ruby if red...

. These must be regarded only as general tendencies. It is possible, by rock analysis, to say approximately what minerals the rock contains, but there are numerous exceptions to any rule.

Mineral constitution

Hence we may say that except in acid or siliceous rocks containing 66% of silica and over, quartz will not be abundant. In basic rocks (containing 20% of silica or less) it is rare and accidental. If magnesia and iron be above the average while silica is low, olivine may be expected; where silica is present in greater quantity over ferro-magnesian minerals, such as augite, hornblende, enstatite or biotite, occur rather than olivine. Unless potash is high and silica relatively low, leucite will not be present, for leucite does not occur with free quartz. Nepheline, likewise, is usually found in rocks with much soda and comparatively little silica. With high alkalis, soda-bearing pyroxenes and amphiboles may be present. The lower the percentage of silica and the alkalis, the greater is the prevalence of calcium feldspar as contracted with soda or potash feldspar. Clarke has calculated the relative abundance of the principal rock-forming minerals with the following results: apatite=0.6, titanium minerals=1.5, quartz=12.0, feldspars=59.5, biotite=3.8, hornblende and pyroxene=16.8, total=94.2%. This, however, can only be a rough approximation.

The other determining factor, namely the physical conditions attending consolidation, plays on the whole a smaller part, yet is by no means negligible, as a few instances will prove. Certain minerals are practically confined to deep-seated intrusive rocks, e.g., microcline, muscovite, diallage. Leucite is very rare in plutonic masses; many minerals have special peculiarities in microscopic character according to whether they crystallized in depth or near the surface, e.g., hypersthene, orthoclase, quartz. There are some curious instances of rocks having the same chemical composition, but consisting of entirely different minerals, e.g., the hornblendite of Gran, in Norway, which contains only hornblende, has the same composition as some of the camptonites of the same locality that contain feldspar and hornblende of a different variety. In this connection we may repeat what has been said above about the corrosion of porphyritic minerals in igneous rocks. In rhyolites and trachytes, early crystals of hornblende and biotite may be found in great numbers partially converted into augite and magnetite. Hornblende and biotite were stable under the pressures and other conditions below the surface, but unstable at higher levels. In the ground-mass of these rocks, augite is almost universally present. But the plutonic representatives of the same magma, granite and syenite contain biotite and hornblende far more commonly than augite.

Acid, intermediate and basic igneous rocks

Those rocks that contain the most silica, and on crystallizing yield free quartz, form a group generally designated the "acid" rocks. Those again that contain least silica and most magnesia and iron, so that quartz is absent while olivine
Olivine
The mineral olivine is a magnesium iron silicate with the formula 2SiO4. It is a common mineral in the Earth's subsurface but weathers quickly on the surface....

 is usually abundant, form the "basic" group. The "intermediate" rocks include those characterized by the general absence of both quartz and olivine. An important subdivision of these contains a very high percentage of alkalis, especially soda, and consequently has minerals such as nepheline
Nepheline
Nepheline, also called nephelite , is a feldspathoid: a silica-undersaturated aluminosilicate, Na3KAl4Si4O16, that occurs in intrusive and volcanic rocks with low silica, and in their associated pegmatites...

 and leucite
Leucite
Leucite is a rock-forming mineral composed of potassium and aluminium tectosilicate K[AlSi2O6]. Crystals have the form of cubic icositetrahedra but, as first observed by Sir David Brewster in 1821, they are not optically isotropic, and are therefore pseudo-cubic. Goniometric measurements made by...

 not common in other rocks. It is often separated from the others as the "alkali" or "soda" rocks, and there is a corresponding series of basic rocks. Lastly a small sub-group rich in olivine and without feldspar has been called the "ultrabasic" rocks. They have very low percentages of silica but much iron and magnesia.

Except these last, practically all rocks contain felspars or feldspathoid minerals. In the acid rocks the common feldspars are orthoclase, perthite, microcline, and oligoclase—all having much silica and alkalis. In the basic rocks labradorite, anorthite and bytownite prevail, being rich in lime and poor in silica, potash and soda. Augite is the commonest ferro-magnesian of the basic rocks, but biotite and hornblende are on the whole more frequent in the acid.
Commonest Minerals Acid Intermediate Mafic Ultramafic
Quartz
Orthoclase (and Oligoclase), Mica, Hornblende, Augite
Little or no Quartz:
Orthoclase hornblende, Augite, Biotite
Little or no Quartz:
Plagioclase Hornblende, Augite, Biotite
No Quartz
Plagioclase Augite, Olivine
No Felspar
Augite, Hornblende, Olivine
Plutonic or Abyssal type Granite
Granite
Granite is a common and widely occurring type of intrusive, felsic, igneous rock. Granite usually has a medium- to coarse-grained texture. Occasionally some individual crystals are larger than the groundmass, in which case the texture is known as porphyritic. A granitic rock with a porphyritic...

 
Syenite
Syenite
Syenite is a coarse-grained intrusive igneous rock of the same general composition as granite but with the quartz either absent or present in relatively small amounts Syenite is a coarse-grained intrusive igneous rock of the same general composition as granite but with the quartz either absent or...

 
Diorite
Diorite
Diorite is a grey to dark grey intermediate intrusive igneous rock composed principally of plagioclase feldspar , biotite, hornblende, and/or pyroxene. It may contain small amounts of quartz, microcline and olivine. Zircon, apatite, sphene, magnetite, ilmenite and sulfides occur as accessory...

 
Gabbro
Gabbro
Gabbro refers to a large group of dark, coarse-grained, intrusive mafic igneous rocks chemically equivalent to basalt. The rocks are plutonic, formed when molten magma is trapped beneath the Earth's surface and cools into a crystalline mass....

 
Peridotite
Peridotite
A peridotite is a dense, coarse-grained igneous rock, consisting mostly of the minerals olivine and pyroxene. Peridotite is ultramafic, as the rock contains less than 45% silica. It is high in magnesium, reflecting the high proportions of magnesium-rich olivine, with appreciable iron...

Intrusive or Hypabyssal type Quartz-porphyry
Quartz-porphyry
Quartz-porphyry, in petrology, is the name given to a group of hemi-crystalline acid rocks containing porphyritic crystals of quartz in a fine-grained matrix, usually of micro-crystalline or felsitic structure...

 
Orthoclase-porphyry  Porphyrite Dolerite  Picrite
Lavas or Effusive type Rhyolite
Rhyolite
This page is about a volcanic rock. For the ghost town see Rhyolite, Nevada, and for the satellite system, see Rhyolite/Aquacade.Rhyolite is an igneous, volcanic rock, of felsic composition . It may have any texture from glassy to aphanitic to porphyritic...

, Obsidian
Obsidian
Obsidian is a naturally occurring volcanic glass formed as an extrusive igneous rock.It is produced when felsic lava extruded from a volcano cools rapidly with minimum crystal growth...

 
Trachyte
Trachyte
Trachyte is an igneous volcanic rock with an aphanitic to porphyritic texture. The mineral assemblage consists of essential alkali feldspar; relatively minor plagioclase and quartz or a feldspathoid such as nepheline may also be present....

 
Andesite
Andesite
Andesite is an extrusive igneous, volcanic rock, of intermediate composition, with aphanitic to porphyritic texture. In a general sense, it is the intermediate type between basalt and dacite. The mineral assemblage is typically dominated by plagioclase plus pyroxene and/or hornblende. Magnetite,...

 
Basalt
Basalt
Basalt is a common extrusive volcanic rock. It is usually grey to black and fine-grained due to rapid cooling of lava at the surface of a planet. It may be porphyritic containing larger crystals in a fine matrix, or vesicular, or frothy scoria. Unweathered basalt is black or grey...

 
Limburgite
Limburgite
In petrology, limburgite is a dark-colored volcanic rock resembling basalt in appearance, but containing normally no feldspar. The name is taken from Limburg, Germany, where they occur in the well-known rock of the Kaiserstuhl. They consist essentially of olivine and augite with a brownish glassy...



Rocks that contain leucite or nepheline, either partly or wholly replacing felspar, are not included in this table. They are essentially of intermediate or of basic character. We might in consequence regard them as varieties of syenite, diorite, gabbro, etc., in which feldspathoid minerals occur, and indeed there are many transitions between syenites of ordinary type and nepheline — or leucite — syenite, and between gabbro or dolerite and theralite or essexite. But, as many minerals develop in these "alkali" rocks that are uncommon elsewhere, it is convenient in a purely formal classification like that outlined here to treat the whole assemblage as a distinct series.
Nepheline and Leucite-bearing Rocks
Commonest Minerals Alkali Feldspar, Nepheline or Leucite, Augite, Hornblend, Biotite Soda Lime Feldspar, Nepheline or Leucite, Augite, Hornblende (Olivine) Nepheline or Leucite, Augite, Hornblende, Olivine
Plutonic type Nepheline-syenite, Leucite-syenite, Nepheline-porphyry Essexite and Theralite Ijolite and Missourite
Effusive type or Lavas Phonolite, Leucitophyre Tephrite and Basanite Nepheline-basalt, Leucite-basalt


This classification is based essentially on the mineralogical constitution of the igneous rocks. Any chemical distinctions between the different groups, though implied, are relegated to a subordinate position. It is admittedly artificial by it has grown up with the grown of the science and is still adopted as the basis on which more minute subdivisions are erected. The subdivisions are by no means of equal value. The syenites, for example, and the peridotites, are far less important than the granites, diorites and gabbros. Moreover, the effusive andesites do not always correspond to the plutonic diorites but partly also to the gabbros. As the different kinds of rock, regarded as aggregates of minerals, pass gradually into one another, transitional types are very common and are often so important as to receive special names. The quartz-syenites and nordmarkites may be interposed between granite and syenite, the tonalites and adamellites between granite and diorite, the monzoaites between syenite and diorite, norites and hyperites between diorite and gabbro, and so on.

See also

  • Important publications in geochemistry
  • Petrology
    Petrology
    Petrology is the branch of geology that studies rocks, and the conditions in which rocks form....

  • Tephrochronology
    Tephrochronology
    250px|thumb|right|Tephra horizons in south-central [[Iceland]]. The thick and light coloured layer at the height of the [[volcanologists]] hands is [[rhyolitic]] [[tephra]] from [[Hekla]]....


Further reading

  • Holland, H.D., & Turekian, K.K. (2004). Treatise on Geochemistry. 9 Volumes. Elsevier
  • Marshall, C., & Fairbridge, R. (2006). Encyclopedia of Geochemistry. ISBN 1-4020-4496-8. Berlin: Springer.
  • Bernard Gunn: The Geochemistry of Igneous Rocks
  • Gunter Faure
    Gunter Faure
    Gunter Faure is a leading geochemist who currently holds the position of Professor Emeritus in the School of Earth Science of Ohio State University. He obtained his PhD from the Massachusetts Institute of Technology in 1961....

     (1986). Principles of Isotope Geology, John Wiley & Sons
    John Wiley & Sons
    John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing and markets its products to professionals and consumers, students and instructors in higher education, and researchers and practitioners in scientific, technical, medical, and...

    . ISBN 0-471-86412-9
  • H.R. Rollinson (1993), Using Geochemical Data: evaluation, presentation, interpretation (Longman
    Longman
    Longman was a publishing company founded in London, England in 1724. It is now an imprint of Pearson Education.-Beginnings:The Longman company was founded by Thomas Longman , the son of Ezekiel Longman , a gentleman of Bristol. Thomas was apprenticed in 1716 to John Osborn, a London bookseller, and...

    ). ISBN 978-0582067011
  • W.M. White: Geochemistry (Free Download)
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK