Brass

For other uses, see Brass (disambiguation).
Brass astrolabe
Brass lectern with an eagle. Attributed to Aert van Tricht, Limburg (Netherlands), c. 1500.

Brass is a metal alloy made of copper and zinc; the proportions of zinc and copper can be varied to create a range of brasses with varying properties.[1] It is a substitutional alloy: atoms of the two constituents may replace each other within the same crystal structure.

By comparison, bronze is principally an alloy of copper and tin.[2] However, bronze and brass may also include small proportions of a range of other elements including arsenic, phosphorus, aluminium, manganese, and silicon. The term is also applied to a variety of brasses, and the distinction is largely historical.[3] Modern practice in museums and archaeology increasingly avoids both terms for historical objects in favour of the all-embracing "copper alloy".[4]

Brass is used for decoration for its bright gold-like appearance; for applications where low friction is required such as locks, gears, bearings, doorknobs, ammunition casings and valves; for plumbing and electrical applications; and extensively in brass musical instruments such as horns and bells where a combination of high workability (historically with hand tools) and durability is desired. It is also used in zippers. Brass is often used in situations in which it is important that sparks not be struck, such as in fittings and tools used near flammable or explosive materials.[5]

Properties

Microstructure of rolled and annealed brass (400X magnification)

Brass has higher malleability than bronze or zinc. The relatively low melting point of brass (900 to 940 °C, 1652 to 1724 °F, depending on composition) and its flow characteristics make it a relatively easy material to cast. By varying the proportions of copper and zinc, the properties of the brass can be changed, allowing hard and soft brasses. The density of brass is 8.4 to 8.73 g/cm³ (approximately .303 lb/cubic inch).[6]

Today, almost 90% of all brass alloys are recycled.[7] Because brass is not ferromagnetic, it can be separated from ferrous scrap by passing the scrap near a powerful magnet. Brass scrap is collected and transported to the foundry where it is melted and recast into billets. Billets are heated and extruded into the desired form and size. The general softness of brass means that it can often be machined without the use of cutting fluid, though there are exceptions to this.[8]

Aluminium makes brass stronger and more corrosion-resistant. Aluminium also causes a highly beneficial hard layer of aluminium oxide (Al2O3) to be formed on the surface that is thin, transparent and self-healing. Tin has a similar effect and finds its use especially in seawater applications (naval brasses). Combinations of iron, aluminium, silicon and manganese make brass wear and tear resistant.[9]

Lead content

To enhance the machinability of brass, lead is often added in concentrations of around 2%. Since lead has a lower melting point than the other constituents of the brass, it tends to migrate towards the grain boundaries in the form of globules as it cools from casting. The pattern the globules form on the surface of the brass increases the available lead surface area which in turn affects the degree of leaching. In addition, cutting operations can smear the lead globules over the surface. These effects can lead to significant lead leaching from brasses of comparatively low lead content.[10]

Silicon is an alternative to lead; however, when silicon is used in a brass alloy, the scrap must never be mixed with leaded brass scrap because of contamination and safety problems.[11]

In October 1999 the California State Attorney General sued 13 key manufacturers and distributors over lead content. In laboratory tests, state researchers found the average brass key, new or old, exceeded the California Proposition 65 limits by an average factor of 19, assuming handling twice a day.[12] In April 2001 manufacturers agreed to reduce lead content to 1.5%, or face a requirement to warn consumers about lead content. Keys plated with other metals are not affected by the settlement, and may continue to use brass alloys with higher percentage of lead content.[13][14]

Also in California, lead-free materials must be used for "each component that comes into contact with the wetted surface of pipes and pipe fittings, plumbing fittings and fixtures." On January 1, 2010, the maximum amount of lead in "lead-free brass" in California was reduced from 4% to 0.25% lead. The common practice of using pipes for electrical grounding is discouraged, as it accelerates lead corrosion.[15][16]

Corrosion-resistant brass for harsh environments

Brass sampling cock with stainless steel handle

The so-called dezincification resistant (DZR or DR) brasses, sometimes referred to as CR (corrosion resistant) brasses, are used where there is a large corrosion risk and where normal brasses do not meet the standards. Applications with high water temperatures, chlorides present, or deviating water qualities (soft water) play a role. DZR-brass is excellent in water boiler systems. This brass alloy must be produced with great care, with special attention placed on a balanced composition and proper production temperatures and parameters to avoid long-term failures.

Use in musical instruments

A collection of brass instruments

The high malleability and workability, relatively good resistance to corrosion, and traditionally attributed acoustic properties of brass, have made it the usual metal of choice for construction of musical instruments whose acoustic resonators consist of long, relatively narrow tubing, often folded or coiled for compactness; silver and its alloys, and even gold, have been used for the same reasons, but brass is the most economical choice. Collectively known as brass instruments, these include the trombone, tuba, trumpet, cornet, baritone horn, euphonium, tenor horn, and French horn, and many other "horns", many in variously-sized families, such as the saxhorns. Other wind instruments may be constructed of brass or other metals, and indeed most modern student-model flutes and piccolos are made of some variety of brass, usually a cupronickel alloy similar to Nickel Silver/German Silver. Clarinets, especially low clarinets such as the contrabass and subcontrabass, are commonly made of metal to avoid the problems associated with obtaining sufficiently large billets of the dense, fine-grained tropical woods traditionally preferred for smaller woodwinds. For the same reason, some low clarinets, bassoons and contrabassoons feature a hybrid construction, with long, straight sections of wood, and curved joints, neck, and/or bell of metal.The use of metal also avoids the risks of exposing wooden instruments to changes in temperature or humidity, which can cause sudden cracking. Even though the saxophones and sarrusaphones are classified as woodwind instruments, they are normally made of brass for similar reasons, and because their wide, conical bores and thin-walled bodies are more easily and efficiently made by forming sheet metal than by machining wood.

The keywork of most modern woodwinds, including wooden-bodied instruments, is also usually made of an alloy such as Nickel Silver/German Silver. Such alloys are stiffer and more durable than the brass used to construct the instrument bodies, but still workable with simple hand tools -- a boon to quick repairs. The mouthpieces of both brass instruments and, less commonly, woodwind instruments are often made of brass, among other metals, as well.

Next to the brass instruments, the most notable use of brass in music is in various percussion instruments, most notably cymbals, gongs, and orchestral (tubular) bells (large "church" bells are normally made of bronze). Small handbells and "jingle bells" are also commonly made of brass.

The harmonica is a free reed aerophone, also often made from brass. In organ pipes of the reed family, brass strips (called tongues) are used as the reeds, which beat against the shallot (or beat "through" the shallot in the case of a "free" reed). Although not part of the brass section, snare drums are also sometimes made of brass. Some parts on electric guitars are also made from brass, especially inertia blocks on tremolo systems for its tonal properties, and for string nuts and saddles for both tonal properties and its low friction.

Germicidal and antimicrobial applications

The bactericidal properties of brass have been observed for centuries, particularly in marine environments where it prevents biofouling. It is the copper in brass that makes brass germicidal. Depending upon the type and concentration of pathogens and the medium they are in, brass kills these microorganisms within a few minutes to hours of contact.[17][18][19]

A large number of independent studies[17][18][19][20][21][22][23] confirm this antimicrobial effect, even against antibiotic-resistant bacteria such as MRSA and VRSA. The mechanisms of antimicrobial action by copper and its alloys, including brass, are a subject of intense and ongoing investigation.[18][24][25]

Research is being conducted at this time to determine whether brass, copper, and other copper alloys can help to reduce cross contamination in public facilities and reduce the incidence of nosocomial infections (hospital-acquired infections) in healthcare facilities.

Season cracking

Cracking in brass caused by ammonia attack

Brass is susceptible to stress corrosion cracking, especially from ammonia or substances containing or releasing ammonia. The problem is sometimes known as season cracking after it was first discovered in brass cartridges used for rifle ammunition during the 1920s in the British Indian Army. The problem was caused by high residual stresses from cold forming of the cases during manufacture, together with chemical attack from traces of ammonia in the atmosphere. The cartridges were stored in stables and the ammonia concentration rose during the hot summer months, thus initiating brittle cracks. The problem was resolved by annealing the cases, and storing the cartridges elsewhere.

Brass types

Class Copper (%) Zinc (%) Notes
Alpha brasses > 65 < 35 Alpha brasses are malleable, can be worked cold, and are used in pressing, forging, or similar applications. They contain only one phase, with face-centered cubic crystal structure. With their high proportion of copper, these brasses have a more golden hue than others
Alpha-beta brasses 55–65 35–45 Also called duplex brasses, these are suited for hot working. They contain both α and β' phases; the β'-phase is body-centered cubic and is harder and stronger than α. Alpha-beta brasses are usually worked hot. The higher proportion of zinc means these brasses are brighter than alpha brasses.
Beta brasses 50–55 45–50 Beta brasses can only be worked hot, and are harder, stronger, and suitable for casting. The high zinc-low copper content means these are some of the brightest and least-golden of the common brasses.
Gamma brasses 61–67 33–39 There are also Ag-Zn and Au-Zn gamma brasses, Ag 30–50%, Au 41%.[26]
White brass < 50 > 50 These are too brittle for general use. The term may also refer to certain types of nickel silver alloys as well as Cu-Zn-Sn alloys with high proportions (typically 40%+) of tin and/or zinc, as well as predominantly zinc casting alloys with copper additives. These have virtually no yellow coloring at all, and instead have a much more silvery appearance.

Brass alloys
Alloy name Copper (%) Zinc (%) Tin (%) Lead (%) Other Notes
Abyssinian gold 90 10
Admiralty brass 69 30 1 Tin inhibits loss of zinc in many environments.
Aich's alloy 60.66 36.58 1.02 1.74 iron Designed for use in marine service owing to its corrosion resistance, hardness and toughness. A characteristic application is to the protection of ships' bottoms, but more modern methods of cathodic protection have rendered its use less common. Its appearance resembles that of gold.[27]
Aluminum brass 77.5 20.5 2% aluminum Aluminum improves corrosion resistance. It is used for heat exchanger and condenser tubes.[28]
Arsenical brass arsenic, frequently aluminum Used for boiler fireboxes.
Cartridge brass (C260) 70 30 ≤ 0.07 [29] Good cold working properties. Used for ammunition cases, plumbing, and hardware.
Common brass 63 37 Also called rivet brass. Cheap and standard for cold working.
DZR brass arsenic Dezincification resistant brass with a small percentage of arsenic.
Delta metal 55 41-43 1-3% iron with the balance consisting of various other metals. The proportions used make the material harder and suitable for valves and bearings.
Free machining brass (C360) 61.5 35.5 3 0.35% iron Also called 360 or C360 brass. High machinability. Lead content 2.5%–3.7% [29]
Gilding metal 95 5 Softest type of brass commonly available. Gilding metal is typically used for ammunition bullet "jackets", e.g., full metal jacket bullets. Almost red in color.
High brass 65 35 Has a high tensile strength and is used for springs, screws, and rivets.
Leaded brass >0 An alpha-beta brass with an addition of lead for improved machinability.
Lead-free brass < 0.25 Defined by California Assembly Bill AB 1953 contains "not more than 0.25 percent lead content".[15] Prior upper limit was 4%.
Low brass 80 20 Light golden color, very ductile; used for flexible metal hoses and metal bellows.
Manganese brass 70 29 1.3% manganese Most notably used in making golden dollar coins in the United States.[30]
Muntz metal 60 40 traces of iron Used as a lining on boats.
Naval brass 59 40 1 Similar to admiralty brass.
Nickel brass 70 24.5 5.5% nickel Used to make pound coins in the pound sterling currency. Also the main constituent of the bi-metallic One Euro coin and the centre part of the Two Euro coin.
Nordic gold 89 5 1 5% aluminium Used in 10, 20, and 50 cents euro coins.
Prince's metal 75 25 A type of alpha brass. Due to its yellow color, it is used as an imitation of gold.[31] Also called Prince Rupert's metal, the alloy was named after Prince Rupert of the Rhine.
Red brass, Rose brass (C230) 85 5 5 5 Both an American term for the copper-zinc-tin alloy known as gunmetal, and an alloy which is considered both a brass and a bronze.[32][33] Red brass is also an alternative name for copper alloy C23000, which is composed of 14–16% zinc, a minimum 0.05% iron and minimum 0.07% lead content,[29] and the remainder copper.[34] It may also refer to ounce metal, another copper-zinc-tin alloy.
Rich low brass, Tombac 5–20 Often used in jewelry applications.
Silicon tombac 80 16 4% silicon Used as an alternative for investment casted steel parts.
Tonval brass >0 Also called CW617N or CZ122 or OT58. It is not recommended for seawater use, being susceptible to dezincification.[35][36]
Yellow brass 67 33 An American term for 33% zinc brass.

History

Although forms of brass have been in use since prehistory,[37] its true nature as a copper-zinc alloy was not understood until the post medieval period because the zinc vapor which reacted with copper to make brass was not recognised as a metal.[38] The King James Bible makes many references to "brass".[39] The Shakespearean English form of the word 'brass' can mean any bronze alloy, or copper, rather than the strict modern definition of brass. The earliest brasses may have been natural alloys made by smelting zinc-rich copper ores.[40] By the Roman period brass was being deliberately produced from metallic copper and zinc minerals using the cementation process and variations on this method continued until the mid-19th century.[41] It was eventually replaced by speltering, the direct alloying of copper and zinc metal which was introduced to Europe in the 16th century.[40]

Early copper zinc alloys

In West Asia and the Eastern Mediterranean early copper zinc alloys are now known in small numbers from a number of third millennium BC sites in the Aegean, Iraq, the United Arab Emirates, Kalmykia, Turkmenistan and Georgia and from 2nd Millennium BC sites in West India, Uzbekistan, Iran, Syria, Iraq and Palestine.[42] However, isolated examples of copper-zinc alloys are known in China from as early as the 5th Millennium BC.[43]

The compositions of these early "brass" objects are highly variable and most have zinc contents of between 5% and 15% wt which is lower than in brass produced by cementation.[44] These may be "natural alloys" manufactured by smelting zinc rich copper ores in redox conditions. Many have similar tin contents to contemporary bronze artefacts and it is possible that some copper-zinc alloys were accidental and perhaps not even distinguished from copper.[44] However the large number of copper-zinc alloys now known suggests that at least some were deliberately manufactured and many have zinc contents of more than 12% wt which would have resulted in a distinctive golden color.[44][45]

By the 8th–7th century BC Assyrian cuneiform tablets mention the exploitation of the "copper of the mountains" and this may refer to "natural" brass.[46] "Oreikhalkon" (mountain copper),[47] the Ancient Greek translation of this term, was later adapted to the Latin aurichalcum meaning "golden copper" which became the standard term for brass.[48] In the 4th century BC Plato knew orichalkos as rare and nearly as valuable as gold[49] and Pliny describes how aurichalcum had come from Cypriot ore deposits which had been exhausted by the 1st century AD.[50] X-ray fluorescence analysis of 39 orichalcum ingots recovered from a 2,600-year-old shipwreck off Sicily found them to be an alloy made with 75–80 percent copper, 15–20 percent zinc and small percentages of nickel, lead and iron.[51][52]

Brass making in the Roman World

7th-century Persian ewer in brass with copper inlay

During the later part of first millennium BC the use of brass spread across a wide geographical area from Britain[53] and Spain[54] in the west to Iran, and India in the east.[55] This seems to have been encouraged by exports and influence from the Middle East and eastern Mediterranean where deliberate production of brass from metallic copper and zinc ores had been introduced.[56] The 4th century BC writer Theopompus, quoted by Strabo, describes how heating earth from Andeira in Turkey produced "droplets of false silver", probably metallic zinc, which could be used to turn copper into oreichalkos.[57] In the 1st century BC the Greek Dioscorides seems to have recognised a link between zinc minerals and brass describing how Cadmia (zinc oxide) was found on the walls of furnaces used to heat either zinc ore or copper and explaining that it can then be used to make brass.[58]

By the first century BC brass was available in sufficient supply to use as coinage in Phrygia and Bithynia,[59] and after the Augustan currency reform of 23 BC it was also used to make Roman dupondii and sestertii.[60] The uniform use of brass for coinage and military equipment across the Roman world may indicate a degree of state involvement in the industry,[61][62] and brass even seems to have been deliberately boycotted by Jewish communities in Palestine because of its association with Roman authority.[63]

Brass was produced by the cementation process where copper and zinc ore are heated together until zinc vapor is produced which reacts with the copper. There is good archaeological evidence for this process and crucibles used to produce brass by cementation have been found on Roman period sites including Xanten[64] and Nidda[65] in Germany, Lyon in France[66] and at a number of sites in Britain.[67] They vary in size from tiny acorn sized to large amphorae like vessels but all have elevated levels of zinc on the interior and are lidded.[66] They show no signs of slag or metal prills suggesting that zinc minerals were heated to produce zinc vapor which reacted with metallic copper in a solid state reaction. The fabric of these crucibles is porous, probably designed to prevent a buildup of pressure, and many have small holes in the lids which may be designed to release pressure[66] or to add additional zinc minerals near the end of the process. Dioscorides mentioned that zinc minerals were used for both the working and finishing of brass, perhaps suggesting secondary additions.[68]

Brass made during the early Roman period seems to have varied between 20% to 28% wt zinc.[69] The high content of zinc in coinage and brass objects declined after the first century AD and it has been suggested that this reflects zinc loss during recycling and thus an interruption in the production of new brass.[70] However it is now thought this was probably a deliberate change in composition[71] and overall the use of brass increases over this period making up around 40% of all copper alloys used in the Roman world by the 4th century AD.[72]

Brass making in the medieval period

Little is known about the production of brass during the centuries immediately after the collapse of the Roman Empire. Disruption in the trade of tin for bronze from Western Europe may have contributed to the increasing popularity of brass in the east and by the 6th–7th centuries AD over 90% of copper alloy artefacts from Egypt were made of brass.[73] However other alloys such as low tin bronze were also used and they vary depending on local cultural attitudes, the purpose of the metal and access to zinc, especially between the Islamic and Byzantine world.[74] Conversely the use of true brass seems to have declined in Western Europe during this period in favour of gunmetals and other mixed alloys[75] but by about 1000 brass artefacts are found in Scandinavian graves in Scotland,[76] brass was being used in the manufacture of coins in Northumbria[77] and there is archaeological and historical evidence for the production of brass in Germany[78] and The Low Countries,[79] areas rich in calamine ore.

These places would remain important centres of brass making throughout the medieval period,[80] especially Dinant. Brass objects are still collectively known as dinanterie in French. The baptismal font at St Bartholomew's Church, Liège in modern Belgium (before 1117) is an outstanding masterpiece of Romanesque brass casting, though also often described as bronze. The metal of the early 12th-century Gloucester Candlestick is unusual even by medieval standards in being a mixture of copper, zinc, tin, lead, nickel, iron, antimony and arsenic with an unusually large amount of silver, ranging from 22.5% in the base to 5.76% in the pan below the candle. The proportions of this mixture may suggest that the candlestick was made from a hoard of old coins, probably Late Roman.[81] Latten is a term for decorative borders and similar objects cut from sheet metal, whether of brass or bronze. Aquamaniles were typically made in brass in both the European and Islamic worlds.

Brass aquamanile from Lower Saxony, Germany, c. 1250

The cementation process continued to be used but literary sources from both Europe and the Islamic world seem to describe variants of a higher temperature liquid process which took place in open-topped crucibles.[82] Islamic cementation seems to have used zinc oxide known as tutiya or tutty rather than zinc ores for brass-making, resulting in a metal with lower iron impurities.[83] A number of Islamic writers and the 13th century Italian Marco Polo describe how this was obtained by sublimation from zinc ores and condensed onto clay or iron bars, archaeological examples of which have been identified at Kush in Iran.[84] It could then be used for brass making or medicinal purposes. In 10th century Yemen al-Hamdani described how spreading al-iglimiya, probably zinc oxide, onto the surface of molten copper produced tutiya vapor which then reacted with the metal.[85] The 13th century Iranian writer al-Kashani describes a more complex process whereby tutiya was mixed with raisins and gently roasted before being added to the surface of the molten metal. A temporary lid was added at this point presumably to minimise the escape of zinc vapor.[86]

In Europe a similar liquid process in open-topped crucibles took place which was probably less efficient than the Roman process and the use of the term tutty by Albertus Magnus in the 13th century suggests influence from Islamic technology.[87] The 12th century German monk Theophilus described how preheated crucibles were one sixth filled with powdered calamine and charcoal then topped up with copper and charcoal before being melted, stirred then filled again. The final product was cast, then again melted with calamine. It has been suggested that this second melting may have taken place at a lower temperature to allow more zinc to be absorbed.[88] Albertus Magnus noted that the "power" of both calamine and tutty could evaporate and described how the addition of powdered glass could create a film to bind it to the metal.[89] German brass making crucibles are known from Dortmund dating to the 10th century AD and from Soest and Schwerte in Westphalia dating to around the 13th century confirm Theophilus' account, as they are open-topped, although ceramic discs from Soest may have served as loose lids which may have been used to reduce zinc evaporation, and have slag on the interior resulting from a liquid process.[90]

Brass in Africa

12th century "Bronze Head from Ife", actually of "heavily leaded zinc-brass"

Some of the most famous objects in African art are the lost wax castings of West Africa, mostly from what is now Nigeria, produced first by the Kingdom of Ife and then the Benin Empire. Though normally described as "bronzes", the Benin Bronze plaques, now mostly in the British Museum and other Western collections, and the large portrait heads such as the Ife Head of "heavily leaded zinc-brass" and the Bronze Head of Queen Idia, both also British Museum, are better described as brass, though of variable compositions.[91] Work in brass or bronze continued to be important in Benin art and other West African traditions such as Akan goldweights, where the metal was regarded as a more valuable material than in Europe.

Brass making in Renaissance and post-medieval Europe

The Renaissance saw important changes to both the theory and practice of brassmaking in Europe. By the 15th century there is evidence for the renewed use of lidded cementation crucibles at Zwickau in Germany.[92] These large crucibles were capable of producing c.20 kg of brass.[93] There are traces of slag and pieces of metal on the interior. Their irregular composition suggesting that this was a lower temperature not entirely liquid process.[94] The crucible lids had small holes which were blocked with clay plugs near the end of the process presumably to maximise zinc absorption in the final stages.[95] Triangular crucibles were then used to melt the brass for casting.[96]

16th-century technical writers such as Biringuccio, Ercker and Agricola described a variety of cementation brass making techniques and came closer to understanding the true nature of the process noting that copper became heavier as it changed to brass and that it became more golden as additional calamine was added.[97] Zinc metal was also becoming more commonplace By 1513 metallic zinc ingots from India and China were arriving in London and pellets of zinc condensed in furnace flues at the Rammelsberg in Germany were exploited for cementation brass making from around 1550.[98]

Eventually it was discovered that metallic zinc could be alloyed with copper to make brass; a process known as speltering[99] and by 1657 the German chemist Johann Glauber had recognised that calamine was "nothing else but unmeltable zinc" and that zinc was a "half ripe metal."[100] However some earlier high zinc, low iron brasses such as the 1530 Wightman brass memorial plaque from England may have been made by alloying copper with zinc and include traces of cadmium similar those found in some zinc ingots from China.[99]

However the cementation process was not abandoned and as late as the early 19th century there are descriptions of solid-state cementation in a domed furnace at around 900–950 °C and lasting up to 10 hours.[101] The European brass industry continued to flourish into the post medieval period buoyed by innovations such as the 16th century introduction of water powered hammers for the production of battery wares.[102] By 1559 the Germany city of Aachen alone was capable of producing 300,000 cwt of brass per year.[102] After several false starts during the 16th and 17th centuries the brass industry was also established in England taking advantage of abundant supplies of cheap copper smelted in the new coal fired reverberatory furnace.[103] In 1723 Bristol brass maker Nehemiah Champion patented the use of granulated copper, produced by pouring molten metal into cold water.[104] This increased the surface area of the copper helping it react and zinc contents of up to 33% wt were reported using this new technique.[105]

In 1738 Nehemiah's son William Champion patented a technique for the first industrial scale distillation of metallic zinc known as distillation per descencum or "the English process."[106][107] This local zinc was used in speltering and allowed greater control over the zinc content of brass and the production of high-zinc copper alloys which would have been difficult or impossible to produce using cementation, for use in expensive objects such as scientific instruments, clocks, brass buttons and costume jewellery.[108] However Champion continued to use the cheaper calamine cementation method to produce lower-zinc brass[108] and the archaeological remains of bee-hive shaped cementation furnaces have been identified at his works at Warmley.[109] By the mid-to-late 18th century developments in cheaper zinc distillation such as John-Jaques Dony's horizontal furnaces in Belgium and the reduction of tariffs on zinc[110] as well as demand for corrosion-resistant high zinc alloys increased the popularity of speltering and as a result cementation was largely abandoned by the mid-19th century.[111]

See also

Wikimedia Commons has media related to Brass.

References

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Bibliography

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