Erbium
Encyclopedia
Erbium is a chemical 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...

 in the lanthanide
Lanthanide
The lanthanide or lanthanoid series comprises the fifteen metallic chemical elements with atomic numbers 57 through 71, from lanthanum through lutetium...

 series, with the symbol Er and atomic number
Atomic number
In chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...

 68. A silvery-white solid metal when artificially isolated, natural erbium is always found in chemical combination with other elements on Earth. As such, it is a rare earth element
Rare earth element
As defined by IUPAC, rare earth elements or rare earth metals are a set of seventeen chemical elements in the periodic table, specifically the fifteen lanthanides plus scandium and yttrium...

 which is associated with several other rare elements in the mineral
Mineral
A mineral is a naturally occurring solid chemical substance formed through biogeochemical processes, having characteristic chemical composition, highly ordered atomic structure, and specific physical properties. By comparison, a rock is an aggregate of minerals and/or mineraloids and does not...

 gadolinite
Gadolinite
Gadolinite, sometimes also known as Ytterbite, is a silicate mineral which consists principally of the silicates of cerium, lanthanum, neodymium, yttrium, beryllium, and iron with the formula 2FeBe2Si2O10...

 from Ytterby
Ytterby
Ytterby is a village on the Swedish island of Resarö, in Vaxholm Municipality in the Stockholm archipelago.The name of the village means "outer village", implying that its location is its most noteworthy feature....

 in Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....

.

Erbium's principal uses involve its pink-colored Er3+ ions, which have optical fluorescent properties particularly useful in certain laser applications. Erbium-doped glasses or crystals can be used as optical amplification media, where erbium (III) ions are optically pumped at around 980 nm or 1480 nm and then radiate light at 1530 nm in stimulated emission. This process results in an unusually mechanically simple laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

 optical amplifier
Optical amplifier
An optical amplifier is a device that amplifies an optical signal directly, without the need to first convert it to an electrical signal. An optical amplifier may be thought of as a laser without an optical cavity, or one in which feedback from the cavity is suppressed...

 for signals transmitted by fiber optics. The 1550 nm wavelength is especially important for optical communications because standard single mode optical fibers have minimal loss at this particular wavelength. In addition to optical fiber lasers, a large variety of medical applications (i.e. dermatology, dentistry) utilize erbium ion's 2940 nm emission (see Er:YAG laser
Er:YAG laser
Er:YAG lasers are solid-state lasers whose lasing medium is erbium-doped yttrium aluminium garnet . Er:YAG lasers typically emit light with a wavelength of 2940 nm, which is infrared light. Unlike Nd:YAG lasers, the output of an Er:YAG laser is strongly absorbed by water because of atomic resonances...

), which is highly absorbed in water in tissues, making its effect very superficial. Such shallow tissue deposition of laser energy is helpful in laser surgery
Laser surgery
Laser surgery is surgery using a laser to cut tissue instead of a scalpel. Examples include the use of a laser scalpel in otherwise conventional surgery, and soft tissue laser surgery, in which the laser beam vaporizes soft tissue with high water content...

, and for the efficient production of steam for laser enamel ablation in certain types of laser dentistry.

Physical properties

A trivalent
Valence (chemistry)
In chemistry, valence, also known as valency or valence number, is a measure of the number of bonds formed by an atom of a given element. "Valence" can be defined as the number of valence bonds...

 element, pure erbium metal
Metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...

 is malleable (or easily shaped), soft yet stable in air, and does not oxidize as quickly as some other rare-earth metals. Its salt
Salt
In chemistry, salts are ionic compounds that result from the neutralization reaction of an acid and a base. They are composed of cations and anions so that the product is electrically neutral...

s are rose-colored, and the element has characteristic sharp absorption spectra bands in visible light, ultraviolet
Ultraviolet
Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...

, and near infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

. Otherwise it looks much like the other rare earths. Its sesquioxide
Sesquioxide
A sesquioxide is an oxide containing three atoms of oxygen with two atoms of another element. For example, aluminium oxide is a sesquioxide.Many sesquioxides contain the metal in the +3 oxidation state and the oxide ion, e.g., Al2O3, La2O3...

 is called erbia. Erbium's properties are to a degree dictated by the kind and amount of impurities present. Erbium does not play any known biological role, but is thought to be able to stimulate metabolism
Metabolism
Metabolism is the set of chemical reactions that happen in the cells of living organisms to sustain life. These processes allow organisms to grow and reproduce, maintain their structures, and respond to their environments. Metabolism is usually divided into two categories...

.

Erbium is ferromagnetic below 19 K, antiferromagnetic between 19 and 80 K and paramagnetic above 80 K.

Erbium can form propeller-shaped atomic clusters Er3N, where the distance between the erbium atoms is 0.35 nm. Those clusters can be isolated by encapsulating them into fullerene
Fullerene
A fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, or tube. Spherical fullerenes are also called buckyballs, and they resemble the balls used in association football. Cylindrical ones are called carbon nanotubes or buckytubes...

 molecules, as confirmed by transmission electron microscopy
Transmission electron microscopy
Transmission electron microscopy is a microscopy technique whereby a beam of electrons is transmitted through an ultra thin specimen, interacting with the specimen as it passes through...

.

Chemical properties

Erbium metal tarnishes slowly in air and burns readily to form erbium(III) oxide
Erbium(III) oxide
Erbium oxide, a pink solid, is a compound of erbium sometimes used as a colouring for glasses and a dopant for optical fibres and optical amplifiers...

:
4 Er + 3 O2 → 2 Er2O3


Erbium is quite electropositive and reacts slowly with cold water and quite quickly with hot water to form erbium hydroxide:
2 Er (s) + 6 H2O (l) → 2 Er(OH)3 (aq) + 3 H2 (g)


Erbium metal reacts with all the halogens:
2 Er (s) + 3 F2 (g) → 2 ErF3 (s) [pink]
2 Er (s) + 3 Cl2 (g) → 2 ErCl3 (s) [violet]
2 Er (s) + 3 Br2 (g) → 2 ErBr3 (s) [violet]
2 Er (s) + 3 I2 (g) → 2 ErI3 (s) [violet]


Erbium dissolves readily in dilute sulfuric acid
Sulfuric acid
Sulfuric acid is a strong mineral acid with the molecular formula . Its historical name is oil of vitriol. Pure sulfuric acid is a highly corrosive, colorless, viscous liquid. The salts of sulfuric acid are called sulfates...

 to form solutions containing hydrated Er(III) ions, which exist as yellow [Er(OH2)9]3+ hydration complexes:
2 Er (s) + 3 H2SO4 (aq) → 2 Er3+ (aq) + 3 (aq) + 3 H2 (g)

Isotopes

Naturally occurring erbium is composed of 6 stable 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, , , , , , and with being the most abundant (33.503% natural abundance
Natural abundance
In chemistry, natural abundance refers to the abundance of isotopes of a chemical element as naturally found on a planet. The relative atomic mass of these isotopes is the atomic weight listed for the element in the periodic table...

). 29 radioisotopes have been characterized, with the most stable being with a half-life
Half-life
Half-life, abbreviated t½, is the period of time it takes for the amount of a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms , but it may apply to any quantity which follows a set-rate decay.The original term, dating to...

 of , with a half-life of , with a half-life of , with a half-life of , and with a half-life of . All of the remaining radioactive isotopes have half-lives that are less than , and the majority of these have half-lives that are less than 4 minutes. This element also has 13 meta states, with the most stable being with a half-life of .

The isotopes of erbium range in atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...

 from to . The primary decay mode before the most abundant stable isotope, , is electron capture
Electron capture
Electron capture is a process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino...

, and the primary mode after is beta decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

. The primary decay product
Decay product
In nuclear physics, a decay product is the remaining nuclide left over from radioactive decay. Radioactive decay often involves a sequence of steps...

s before are element 67 (holmium
Holmium
Holmium is a chemical element with the symbol Ho and atomic number 67. Part of the lanthanide series, holmium is a rare earth element. Its oxide was first isolated from rare earth ores in 1878 and the element was named after the city of Stockholm....

) isotopes, and the primary products after are element 69 (thulium
Thulium
Thulium is a chemical element that has the symbol Tm and atomic number 69. Thulium is the second least abundant of the lanthanides . It is an easily workable metal with a bright silvery-gray luster...

) isotopes.

History

Erbium (for Ytterby
Ytterby
Ytterby is a village on the Swedish island of Resarö, in Vaxholm Municipality in the Stockholm archipelago.The name of the village means "outer village", implying that its location is its most noteworthy feature....

, a village in Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....

) was discovered by Carl Gustaf Mosander
Carl Gustaf Mosander
Carl Gustaf Mosander was a Swedish chemist. He discovered the elements lanthanum, erbium and terbium....

 in 1843. Mosander separated "yttria" from the mineral gadolinite
Gadolinite
Gadolinite, sometimes also known as Ytterbite, is a silicate mineral which consists principally of the silicates of cerium, lanthanum, neodymium, yttrium, beryllium, and iron with the formula 2FeBe2Si2O10...

 into three fractions which he called yttria, erbia, and terbia. He named the new element after the village of Ytterby where large concentrations of yttria and erbium are located. Erbia and terbia, however, were confused at this time. After 1860, terbia was renamed erbia and after 1877 what had been known as erbia was renamed terbia. Fairly pure Er2O
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...

3 was independently isolated in 1905 by Georges Urbain
Georges Urbain
Georges Urbain - French chemist, professor of Sorbonne. He studied at the elite École supérieure de physique et de chimie industrielles de la ville de Paris . He discovered the element Lutetium in 1907.-References:...

 and Charles James. Reasonably pure metal wasn't produced until 1934 when Klemm and Bommer reduced the anhydrous
Anhydrous
As a general term, a substance is said to be anhydrous if it contains no water. The way of achieving the anhydrous form differs from one substance to another...

 chloride
Chloride
The chloride ion is formed when the element chlorine, a halogen, picks up one electron to form an anion Cl−. The salts of hydrochloric acid HCl contain chloride ions and can also be called chlorides. The chloride ion, and its salts such as sodium chloride, are very soluble in water...

 with potassium
Potassium
Potassium is the chemical element with the symbol K and atomic number 19. Elemental potassium is a soft silvery-white alkali metal that oxidizes rapidly in air and is very reactive with water, generating sufficient heat to ignite the hydrogen emitted in the reaction.Potassium and sodium are...

 vapor. It was only in the 1990s that the price for Chinese-derived erbium oxide became low enough for erbium to be considered for use as a colorant in art glass.

Occurrence

The concentration of erbium in the Earth crust is about 2.8 mg/kg and in the sea water 0.9 ng/L. This concentration is enough to make erbium about 45th in elemental abundance in the Earth's crust
Abundance of elements in Earth's crust
The table shows the abundance of elements in Earth's crust. Numbers show percentage or parts per million in mass; 10,000 ppm = 1%.Note that numbers are estimates, and they will vary depending on source and method of estimation. Order of magnitude of data can roughly be relied upon.The table shows...

.

Like other rare earths, this element is never found as a free element in nature but is found bound in monazite
Monazite
Monazite is a reddish-brown phosphate mineral containing rare earth metals. It occurs usually in small isolated crystals. There are actually at least four different kinds of monazite, depending on relative elemental composition of the mineral:...

  sand ores. It has historically been very difficult and expensive to separate rare earths from each other in their ores but ion-exchange production techniques developed in the late 20th century have greatly brought down the cost of production of all rare-earth metals and their chemical compound
Chemical compound
A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...

s.

The principal commercial sources of erbium are from the minerals xenotime
Xenotime
Xenotime is a rare earth phosphate mineral, whose major component is yttrium orthophosphate . It forms a solid solution series with chernovite- and therefore may contain trace impurities of arsenic, as well as silicon dioxide and calcium...

 and euxenite
Euxenite
Euxenite or euxenite- is a brownish black mineral with a metallic luster.-Chemistry:It contains calcium, niobium, tantalum, cerium, titanium, yttrium, and typically uranium and thorium, with some other metals. The chemical formula is: 2O6...

, and most recently, the ion adsorption clays of southern China; in consequence, China has now become the principal global supplier of this element. In the high-yttrium versions of these ore concentrates, yttrium is about two-thirds of the total by weight, and erbia is about 4-5%. When the concentrate is dissolved in acid, the erbia liberates enough erbium ion to impart a distinct and characteristic pink color to the solution. This color behavior is similar to what Mosander and the other early workers in the lanthanides would have seen in their extracts from the gadolinite minerals of Ytterby.

Production

Crushed minerals are attacked by hydrochloric or sulfuric acid
Sulfuric acid
Sulfuric acid is a strong mineral acid with the molecular formula . Its historical name is oil of vitriol. Pure sulfuric acid is a highly corrosive, colorless, viscous liquid. The salts of sulfuric acid are called sulfates...

 that transforms insoluble rare-earth oxides into soluble chlorides or sulfates. The acidic filtrates are partially neutralized with caustic soda (sodium hydroxide) to pH 3-4. Thorium
Thorium
Thorium is a natural radioactive chemical element with the symbol Th and atomic number 90. It was discovered in 1828 and named after Thor, the Norse god of thunder....

 precipitates out of solution as hydroxide and is removed. After that the solution is treated with ammonium oxalate
Ammonium oxalate
Ammonium oxalate, C2H8N2O4, is an oxalate salt with ammonia. It is a constituent of some types of kidney stone. Found also in guano....

 to convert rare earths into their insoluble oxalate
Oxalate
Oxalate , is the dianion with formula C2O42− also written 22−. Either name is often used for derivatives, such as disodium oxalate, 2C2O42−, or an ester of oxalic acid Oxalate (IUPAC: ethanedioate), is the dianion with formula C2O42− also written (COO)22−. Either...

s. The oxalates are converted to oxides by annealing. The oxides are dissolved in nitric acid
Nitric acid
Nitric acid , also known as aqua fortis and spirit of nitre, is a highly corrosive and toxic strong acid.Colorless when pure, older samples tend to acquire a yellow cast due to the accumulation of oxides of nitrogen. If the solution contains more than 86% nitric acid, it is referred to as fuming...

 that excludes one of the main components, cerium
Cerium
Cerium is a chemical element with the symbol Ce and atomic number 58. It is a soft, silvery, ductile metal which easily oxidizes in air. Cerium was named after the dwarf planet . Cerium is the most abundant of the rare earth elements, making up about 0.0046% of the Earth's crust by weight...

, whose oxide is insoluble in HNO3. The solution is treated with magnesium nitrate
Magnesium nitrate
Magnesium nitrate is a hygroscopic salt with the formula Mg2. In air, it quickly forms the hexahydrate with the formula Mg2·6H2O . It is very soluble in both water and ethanol.-Uses:...

 to produce a crystallized mixture of double salt
Double salt
Double salts are salts containing more than one cation or anion. They form when more than one salt is dissolved in a liquid and when together they crystallize in a regular pattern. A well-known double salt is alum containing two cations and a sulfate anion...

s of rare-earth metals. The salts are separated by ion exchange
Ion exchange
Ion exchange is an exchange of ions between two electrolytes or between an electrolyte solution and a complex. In most cases the term is used to denote the processes of purification, separation, and decontamination of aqueous and other ion-containing solutions with solid polymeric or mineralic 'ion...

. In this process, rare-earth ions are sorbed onto suitable ion-exchange resin by exchange with hydrogen, ammonium or cupric ions present in the resin. The rare earth ions are then selectively washed out by suitable complexing agent. Erbium metal is obtained from its oxide or salts by heating with calcium
Calcium
Calcium is the chemical element with the symbol Ca and atomic number 20. It has an atomic mass of 40.078 amu. Calcium is a soft gray alkaline earth metal, and is the fifth-most-abundant element by mass in the Earth's crust...

 at 1450 °C under argon atmosphere.

Applications

Erbium's everyday uses are varied. It is commonly used as a photographic filter, and because of its resilience it is useful as a metallurgical additive. Other uses:
  • Used in nuclear
    Nuclear power
    Nuclear power is the use of sustained nuclear fission to generate heat and electricity. Nuclear power plants provide about 6% of the world's energy and 13–14% of the world's electricity, with the U.S., France, and Japan together accounting for about 50% of nuclear generated electricity...

     technology in neutron-absorbing control rod
    Control rod
    A control rod is a rod made of chemical elements capable of absorbing many neutrons without fissioning themselves. They are used in nuclear reactors to control the rate of fission of uranium and plutonium...

    s.
  • When added to vanadium
    Vanadium
    Vanadium is a chemical element with the symbol V and atomic number 23. It is a hard, silvery gray, ductile and malleable transition metal. The formation of an oxide layer stabilizes the metal against oxidation. The element is found only in chemically combined form in nature...

     as an alloy
    Alloy
    An alloy is a mixture or metallic solid solution composed of two or more elements. Complete solid solution alloys give single solid phase microstructure, while partial solutions give two or more phases that may or may not be homogeneous in distribution, depending on thermal history...

    , erbium lowers hardness and improves workability.
  • Erbium oxide has a pink color, and is sometimes used as a colorant for glass
    Glass
    Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

    , cubic zirconia
    Cubic zirconia
    Cubic zirconia is the cubic crystalline form of zirconium dioxide . The synthesized material is hard, optically flawless and usually colorless, but may be made in a variety of different colors. It should not be confused with zircon, which is a zirconium silicate...

     and porcelain
    Porcelain
    Porcelain is a ceramic material made by heating raw materials, generally including clay in the form of kaolin, in a kiln to temperatures between and...

    . The glass is then often used in sunglasses
    Sunglasses
    Sunglasses or sun glasses are a form of protective eyewear designed primarily to prevent bright sunlight and high-energy visible light from damaging or discomforting the eyes. They can sometimes also function as a visual aid, as variously termed spectacles or glasses exist, featuring lenses that...

     and cheap jewelry.
  • Erbium-doped optical silica-glass fibers are the active element in erbium-doped fiber amplifiers (EDFAs), which are widely used in optical communications. The same fibers can be used to create fiber lasers. Co-doping of optical fiber with Er and Yb is used in high-power Er/Yb fiber lasers, which gradually replace CO2 lasers for metal welding and cutting applications. Erbium can also be used in erbium-doped waveguide amplifiers.
  • An erbium-nickel
    Nickel
    Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...

     alloy Er3Ni has an unusually high specific heat capacity at liquid-helium temperatures and is used in cryocoolers; a mixture of 65% Er3Co
    Cobalt
    Cobalt is a chemical element with symbol Co and atomic number 27. It is found naturally only in chemically combined form. The free element, produced by reductive smelting, is a hard, lustrous, silver-gray metal....

     and 35% Er0.9Yb
    Ytterbium
    Ytterbium is a chemical element with the symbol Yb and atomic number 70. A soft silvery metallic element, ytterbium is a rare earth element of the lanthanide series and is found in the minerals gadolinite, monazite, and xenotime. The element is sometimes associated with yttrium or other related...

    0.1Ni by volume improves the specific heat capacity even more.
  • A large variety of medical applications (i.e. dermatology, dentistry) utilize erbium ion's 2940 nm emission (see Er:YAG laser
    Er:YAG laser
    Er:YAG lasers are solid-state lasers whose lasing medium is erbium-doped yttrium aluminium garnet . Er:YAG lasers typically emit light with a wavelength of 2940 nm, which is infrared light. Unlike Nd:YAG lasers, the output of an Er:YAG laser is strongly absorbed by water because of atomic resonances...

    ), which is highly absorbed in water (absorption coefficient
    Attenuation coefficient
    The attenuation coefficient is a quantity that characterizes how easily a material or medium can be penetrated by a beam of light, sound, particles, or other energy or matter. A large attenuation coefficient means that the beam is quickly "attenuated" as it passes through the medium, and a small...

     about 12000/cm). Such shallow tissue deposition of laser energy is necessary for laser surgery, and the efficient production of steam for laser enamel ablation in dentistry.

Precautions

As with the other lanthanides, erbium compounds are of low to moderate toxicity
Toxicity
Toxicity is the degree to which a substance can damage a living or non-living organisms. Toxicity can refer to the effect on a whole organism, such as an animal, bacterium, or plant, as well as the effect on a substructure of the organism, such as a cell or an organ , such as the liver...

, although their toxicity has not been investigated in detail. Metallic erbium in dust form presents a fire and explosion hazard.

Popular culture

In Carl Sagan's novel "Contact"
Contact (novel)
Contact is a science fiction novel written by Carl Sagan and published in 1985. It deals with the theme of contact between humanity and a more technologically advanced, extraterrestrial life form. It ranked No. 7 on the 1985 U.S. bestseller list....

, a machine is constructed from a blueprint received through a extraterrestrial radio transmission. An important (and unexplained) component of the machine are dowels constructed out of erbium.

See also

Erbium compounds
  • Terbium
    Terbium
    Terbium is a chemical element with the symbol Tb and atomic number 65. It is a silvery-white rare earth metal that is malleable, ductile and soft enough to be cut with a knife...

  • Ytterbium
    Ytterbium
    Ytterbium is a chemical element with the symbol Yb and atomic number 70. A soft silvery metallic element, ytterbium is a rare earth element of the lanthanide series and is found in the minerals gadolinite, monazite, and xenotime. The element is sometimes associated with yttrium or other related...

  • Yttrium
    Yttrium
    Yttrium is a chemical element with symbol Y and atomic number 39. It is a silvery-metallic transition metal chemically similar to the lanthanides and it has often been classified as a "rare earth element". Yttrium is almost always found combined with the lanthanides in rare earth minerals and is...


Further reading

  • Guide to the Elements – Revised Edition, Albert Stwertka, (Oxford University Press; 1998) ISBN 0-19-508083-1

External links

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
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