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Heavy metal (elements)

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Samples of tungsten, a heavy metal. Shown are a 1 cm3 cube; and some rods with evaporated crystals; the foremost rod is prominently tarnished due to partial oxidation. The word tungsten comes from the Swedish tung sten, "heavy stone". With a density of 19.52 g/cm3, tungsten is about 70% heavier than lead (density 11.34).

Depending on the context, a heavy metal is usually regarded as a metal (or sometimes a metalloid) having a relatively high density, atomic weight or atomic number; they are also known for their generally insoluble sulfides, and are often assumed to be toxic. While some heavy metals are toxic, such as cadmium, mercury and lead, a number are essential nutrients in trace amounts. More specific definitions of a heavy metal have been proposed or published but none of these have obtained widespread acceptance. They are relatively scarce in the Earth's crust. Because of their heaviness and other specialised properties, heavy metals are useful in nearly all aspects of modern economic activity.

Definitions

Densities of metals and metalloids in the periodic table[n 1][n 2]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1  H He
2  Li Be B C N O F Ne
3  Na Mg Al Si P S Cl Ar
4  K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
5  Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
6  Cs Ba 1 asterisk Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
7  Fr Ra † Lr Rf Db Sg Bh Hs Mt Ds Rg Cn 113 Fl 115 Lv 117 118
 
1 asterisk La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb
† Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No
 
   < 3.5 g/cm3
  
   7 to 9.99
   3.5 to 4.99
  
   10 to 19.99
   5 to 6.99
  
   ≥ 20

There is no widely agreed criterion-based definition of a heavy metal. Different meanings may be attached by the term, depending on the context. In metallurgy, for example, a heavy metal may be defined on the basis of density,[5] whereas in physics the distinguishing criterion may be atomic number,[6] while a chemist may be more concerned with chemical behaviour.[7] In 2002 it was described as an effectively meaningless due to the use of so many different definitions in the previous 60 years.[8]

Quantitative criteria used to define heavy metals have included density, atomic weight and atomic number.[8][n 3] Density criteria range from above 3.5 g/cm3 to above 7 g/cm3. Atomic weight definitions start at greater than sodium (22.98) to greater than 40,[n 4] or 200 or more.[11] Atomic numbers of heavy metals are generally given as greater than 20; sometimes this is capped at 92 (uranium).[n 5] Density is the most commonly used criterion.[12] Metalloids meeting the applicable criteria are often counted as heavy metals, particularly in environmental chemistry.[8]

Criteria based on chemical behaviour or periodic table position are known or have been used. The United States Pharmacopeia includes a test for heavy metals which it describes as "metallic impurities that are colored by sulfide ion."[13][n 6] Hawkes, writing in 1997, and in the context of fifty years of experience with the term, said it referred to, "metals with insoluble sulfides and hydroxides, whose salts produce colored solutions in water, and whose complexes are usually colored". He suggested defining heavy metals as (in general) all of the metals in groups 3 to 16 that are in period 4 or greater, in other words, the transition metals and post-transition metals.[7][n 7] The lanthanides satisfy Hawkes' three-part description; the status of the actinides is not completely settled.[n 8][n 9]

In biochemistry, heavy metals are sometimes defined—on the basis of the Lewis acid (electronic pair acceptor) behaviour of their ions in aqueous solution—as class B and borderline metals.[36] In this scheme, class A metal ions prefer oxygen donors; class B ions prefer nitrogen or sulfur donors; and borderline or ambivalent ions show either class A or B characteristics, depending on the circumstances. Class A metals, which tend to have low electronegativity and form bonds with large ionic character, are the alkali and alkaline earths, aluminium, the group 3 metals, and the lanthanides and actinides. Class B metals, which tend to have higher electronegativity and form bonds with considerable covalent character, are mainly the heavier transition and post-transition metals. Borderline metals largely comprise the lighter transition and post-transition metals (plus arsenic and antimony). The distinction between the class A metals and the other two categories is sharp.[37][38] A frequently cited proposal[n 10] to use these classification categories instead of the more evocative[37] name heavy metal has not been widely adopted.[39]

Along with definitional looseness, the heavy metal status of some metals is occasionally challenged on the grounds that they are too light, or are involved in biological processes, or rarely constitute environmental hazards. Examples include scandium and titanium (too light);[8][40] vanadium to zinc (biological processes);[41] and rhodium, indium and osmium (too rare).[42]

Despite its questionable meaning, references to the term "heavy metal" appear regularly in scientific literature. A 2010 study found that it had been increasingly used and seemed to have become part of the language of science.[39] It is said to be an acceptable term, given its convenience and familiarity, as long as it is accompanied by a strict definition.[36] The counterparts to the heavy metals, the light metals, are alluded to by the The Minerals, Metals & Materials Society as including "aluminium, magnesium, beryllium, titanium, lithium, and other reactive metals."[43] The named metals have densities of 0.534 to 4.54 g/cm3.

Elements of atomic number 104 (rutherfordium) onwards are sometimes referred to as superheavy metals.[44] It remains to be seen if element 118, which is the heaviest element in the noble gas group, is in fact a metal. Predicted densities of elements 104–118 range from around 5 g/cm3 for element 118, to 41 g/cm3 for hassium (element 108);[2] the latter figure is 3.6 times that of lead (at 11.35 g/cm3).

Etymology and usage

The high densities of native metals such as copper, iron and gold may have been noticed in prehistory.[45] All other metals discovered from then until 1800 had relatively high densities. From 1809 onwards, light metals such as sodium, potassium and strontium were isolated. Their low densities challenged conventional wisdom and it was proposed to refer to them as metalloids (meaning "resembling in form or appearance").[46] This suggestion was unsuccessful and the new elements came to be recognised as metals.[47]

An early use of the term dates from 1817, when the German chemist Leopold Gmelin divided the elements into nonmetals, light metals and heavy metals.[48] Light metals had densities of 0.860–5.0 g/cm3; heavy metals 5.308–22.000.[49] The term later become associated with elements of high atomic weight or high atomic number.[8] It is sometimes used interchangeably with the term heavy element. For example, in discussing the history of nuclear chemistry, Magee[50] notes that the actinides were once thought to represent a new heavy element transition group whereas Seaborg and co-workers, "favoured ... a heavy metal rare-earth like series ...". In astronomy, however, a heavy element is any element heavier than hydrogen and helium.[51]

Toxicity

See also: Toxic heavy metal

Some heavy metals, especially chromium, arsenic, cadmium, mercury, lead and thallium are potentially hazardous due to their toxicity in combined or elemental forms.[n 11] Hexavalent chromium, for example, is highly toxic as is mercury vapour and many mercury compounds.[53] These six elements have a strong affinity for sulfur; in the human body they usually bind, via sulfhydryl groups (–SH), to enzymes responsible for controlling the speed of metabolic reactions. The resulting sulfur-metal bonds inhibit the proper functioning of the enzymes involved; human health deteriorates, sometimes fatally.[54] Other heavy metals noted for their potential toxicity include nickel, copper, zinc, selenium (a metalloid), silver, tin, and antimony.[55][n 12]

The more toxic heavy metals can cause environmental problems (and, subsequently, health issues) when they become concentrated as a result of industrial activities. Common sources of heavy metals in this context are mining and industrial wastes; vehicle emissions; lead-acid batteries; fertilisers; paints; treated woods; aging water supply infrastructure;[57] and microplastics floating in the world's oceans.[58] Recent examples of heavy metal contamination and health risks include the Bento Rodrigues dam disaster in Brazil,[59] and high levels of lead in drinking water supplied to the residents of Flint, Michigan, in north-east United States.[60]

Heavy metals essential for life (see next section) can be toxic if taken in excess; some of them have notably toxic forms. Vanadium pentoxide (V2O5) is carcinogenic in animals and, when inhaled, causes DNA damage.[61] The purple coloured permanganate ion MnO–
4 is toxic. Ingesting more than five grams of iron can be fatal. Cobalt, other than as a dietary salt, is a known animal carcinogen;[62] nickel carbonyl (Ni2(CO)4) is lethal at 30 parts per million.[63] Imbibing a gram or more of copper sulfate (Cu(SO4)2) can be fatal; survivors may be left with major organ damage. More than five milligrams of selenium is highly toxic, the recommended maximum daily intake being 0.45 milligrams.[64]

A few other non-essential heavy metals have one or more toxic forms. Fatalities have been recorded arising from the ingestion of germanium dietary supplements (~15 to 300 g in total consumed over a period of two months to three years).[61] The tetroxides of ruthenium (RuO4), and osmium (OsO4) are poisonous, but rarely encountered. Silver is extremely toxic to aquatic organisms.[65] Indium salts are toxic if more than few milligrams are ingested. Organometallic compounds of tin are toxic; antimony can kill; and two grams of sodium tellurate (Na2TeO4) can be lethal. Cisplatin (PtCl2(NH3)2), an important drug used to treat cancer, is a kidney and nerve poison.[61] Bismuth compounds can cause liver damage if taken in excess; uranium, radiation aside, is poisonous.[64]

Biological role

See also: Essential element

Trace amounts of some heavy metals, mostly in period 4, are required for certain biological processes. These are vanadium and manganese (enzyme regulation or activation); chromium (glucose utilisation); iron and copper (oxygen and electron transport); cobalt (complex syntheses and cell metabolism); nickel (cell growth); zinc (hydroxylation); arsenic (metabolic growth in some animals, and possibly humans) and selenium (antioxidant functioning and hormone production). There are not many essential heavy metals in periods 5 or 6. This is consistent with the incidence of essential trace elements tending to be related to their abundance (heavier elements tend to be less abundant).[66] In period 5, molybdenum is required for the catalysis of redox reactions; cadmium is used by some marine diatoms for the same purpose;[67] and tin may be required for growth in a few species.[64] In period 6, tungsten is required by some bacteria for metabolic processes.[38][64][68] A deficiency of any of these period 4–6 essential elements may increase susceptibility to heavy metal poisoning.[69] A few non-essential heavy metals have also been observed to have biological effects. Titanium (noting its status as a heavy metal is sometimes disputed) promotes growth in plants; gallium, germanium (a metalloid), indium and most lanthanides stimulate metabolism.[64]

Formation, abundance and occurrence

See also: Nucleosynthesis and Abundance of the chemical elements
 
Crustal abundance and main
[n 13][n 14]occurrence or source of heavy metals[n 13][n 14]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1  H He
2  Li Be B C N O F Ne
3  Na Mg lithophiles [n 15] Al Si P S Cl Ar
4  K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
5  Rb Sr Y Zr Nb Mo Ru Rh Pd Ag Cd In Sn Sb Te  I  Xe
6  Cs Ba 1 asterisk Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi
7  Ra † chalcophiles (Au is a siderophile; Sn is a lithophile) [n 16]
 
1 asterisk La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb
† Th Pa U
 
   Most abundant (56300 ppm by weight)
   Rare (0.01–0.99)
   Abundant (100–9999)
   Very rare (0.0001–0.0099)
   Uncommon (1–99)
   Least abundant (~0.000001)[n 17]

Heavy metals[n 18] up to the vicinity of iron are largely made by way of stellar nucleosynthesis. In this process, lighter elements from hydrogen to silicon undergo successive fusion reactions inside stars, resulting in the formation of heavier elements and the release of light and heat.[72]

Heavier heavy metals are not formed this way since fusion reactions involving such nuclei would consume rather than release energy. Rather, they are largely synthesised by neutron capture, with the two main modes of this repetitive capture being the s-process and the r-process. In the s-process ("s" stands for "slow"), singular captures are separated by years or decades, allowing the less stable nuclei to beta decay, while in the r-process, captures happen faster than nuclei can decay. Therefore, the s-process takes a more or less clear path: for example, stable cadmium-110 nuclei are successively bombarded by free neutrons inside a star until they form cadmium-115 nuclei which are unstable and decay to form indium-115 (which is nearly stable, with a half-life 30000 times the age of the universe). These nuclei capture neutrons and form indium-116, which is unstable, and decays to form tin-116, and so on.[72][73][n 19] In contrast, there is no such path in the r-process. While the s-process effectively stops at lead and bismuth, the r-process can go on to create even heavier elements such as thorium and uranium.

Stars lose most of their mass when it is ejected late in their stellar lifetimes, thereby increasing the abundance of elements heavier than helium in the interstellar medium. When gravitational attraction causes this matter to coalesce and collapse new stars and planets are formed.[75]

Heavy metals constitute an estimated 5% of the Earth's crust by weight, with iron comprising 95% of this quantity. Light metals (~20%) and non-metals (~75%) make up the other 95% of the crust.[70] Despite their overall scarcity, heavy metals can become concentrated in economically extractable quantities as a result of geological processes (such as mountain building or erosion).[76]

They are primarily found as lithophiles or chalcophiles. Lithophile (rock-loving) heavy metals are nearly all represented by the f-block and more reactive d-block elements. They have a strong affinity for oxygen and mostly exist as relatively low density silicate minerals.[77] Chalcophile (ore-loving) heavy metals are mainly the less reactive transition metal and post-transition metals. They are usually found in (insoluble) sulfide minerals. Being denser than the lithophiles, hence sinking lower into the crust at the time of its solidification, the chalcophiles tend to be less abundant than the lithophiles.[78]

Gold is a siderophile (iron-loving) element. It does not readily form compounds with either oxygen or sulfur.[79] As the noblest of metals, gold became concentrated in the Earth's core due its tendency to form high-density metallic alloys. Consequently, it is a relatively rare metal.[80] From a whole of Earth perspective, some other (less) noble heavy metals—molybdenum, rhenium, the platinum group metals, germanium and tin—are counted as siderophiles but all of these usually occur in the crust as chalcophiles, in small amounts.[71][n 20]

Uses

Several lead bricks each the size of small pillows, stacked up like lego bricks to form a fort-like structure
A lead castle built to shield a radioactive sample in a lab

Heavy metals pervade nearly all aspects of modern economic activity.[81] They find general uses in, for example, metalworking and plating, electronics, batteries, catalysis, paint and pigments, jewellery, fertilisers, pesticides and herbicides.[82]

Some uses of heavy metals, including in sport, mechanical engineering, military ordnance and nuclear science, take advantage of their relatively high densities.

In underwater diving, lead is used as a ballast; in handicap horse racing each horse must carry a specified lead weight, based on factors including past performance, so as to equalize the chances of competitors. In golf, tungsten, brass or copper inserts in fairway clubs and irons lower the centre of gravity of the club making it easier to get the ball into the air;[83] and golf balls with tungsten cores are claimed to have better flight characteristics.[84] In fly fishing, sinking fly lines have a PVC coating embedded with tungsten powder so as to achieve the required sink rate.[85] In track and field sport, steel balls used in the hammer throw and shot put events are filled with lead in order to attain the minimum weight required under international rules.[86] Tungsten was used in hammer throw balls at least up to 1980; the minimum size of the ball was increased in 1981 to eliminate the need for what was, at that time, an expensive metal (triple the cost of other hammers) not generally available in all countries.[87] Tungsten hammers were so dense that they penetrated too deeply into the turf.[88]

In mechanical engineering, heavy metals are used for balance weights on wheels and crankshafts,[89] gyroscopes and propellers,[90] and centrifugal clutches;[91] or as ballast in boats,[92] aeroplanes,[93] and motor vehicles,[94] in situations requiring maximum weight in minimum space (for example in watch movements).[93]

The higher the projectile density, the more effectively it can penetrate heavy armor plate ... Os, Ir, Pt, and Re ... are expensive ... U offers an appealing combination of high density, reasonable cost, and high fracture toughness.

AM Russell and KL Lee
Structure–property relations
in nonferrous metals (2005, p. 16)

In military ordnance, tungsten or uranium is used in armour plating[95] and armour piercing projectiles; and in nuclear weapons to increase efficiency (by reflecting neutrons and momentarily delaying the expansion of reacting materials).[96] In the 1970s, tantalum was found to be more effective than copper in shaped charge and explosively formed anti-armour weapons on account of its higher density, allowing greater force concentration, and better deformability.[97] Less toxic heavy metals, such as copper, tin, tungsten and bismuth, and probably manganese (and boron, a metalloid), have replaced lead and antimony in the bullets used by some armies and in some recreational shooting munitions.[98] Doubts have been raised about the green credentials of tungsten.[99][100]

In nuclear science, heavy metals are used for radiation shielding and to focus radiation beams in linear accelerators and radiotherapy applications.[101]

Niche uses of heavy metals with high atomic numbers occur in diagnostic imaging, electron microscopy, and nuclear science. In diagnostic imaging, heavy metals such as cobalt or tungsten make up the anode materials found in x-ray tubes.[102] In electron microscopy, heavy metals such as lead, gold, palladium, platinum, or uranium are used to make conductive coatings and to introduce electron density into biological specimens by staining, negative staining or shadowing.[103] In nuclear science, accelerated nuclei of heavy metals such as chromium, iron or zinc, are sometimes fired at other heavy metal targets to produce superheavy elements;[104] heavy metals are also employed as spallation targets for the production of neutrons[105] or radioisotopes such as astatine[106] (using lead, bismuth, thorium or uranium in the latter case).

Small translucent, pink-coloured crystals a bit like the colour of candy floss
Neodymium sulfate (Nd2(SO4)3), used to colour glassware[107]

Other references or instances of heavy metals occur in soap chemistry; glass making, ceramics and pyrotechnics; medicine; numismatics; and with respect to children's toys and low-cost jewellery. In soap chemistry, heavy metals form insoluble soaps that are used in lubricating greases, paint dryers, and fungicides (apart from lithium, the alkali metals and the ammonium ion form soluble soaps).[108] The colours of glass, ceramic glazes and pyrotechnics are produced by the inclusion of heavy metals (or their compounds) such as iron, nickel, copper, chromium, manganese, cobalt, gold, silver or neodymium. The biocidal effects of some heavy metals have been known since antiquity.[109] Platinum, osmium, copper, ruthenium and other heavy metals, including arsenic, are used in anti-cancer treatments, or have shown potential.[110] Antimony (anti-protozoal), bismuth (anti-ulcer), gold (anti-arthritic), and iron (anti-malarial) are also important in medicine.[111] Copper, zinc, silver, gold or mercury are used in antiseptic formulations;[112] small amounts of selected heavy metals are used to control algal growth in, for example, cooling towers.[113] In numismatics, of two dozen elements that have been used in the world's monetised coinage only two, carbon and aluminium, are not heavy metals.[114][n 21] Children's toys and low-cost jewellery may be made, to a significant degree, of heavy metals such as chromium, nickel, cadmium or lead.[116]

Notes

  1. ^ Selenium is commonly described as a metalloid in environmental science literature.[1]
  2. ^ Predicted densities have been used for At, Fr and elements 104–118.[2] Indicative densities were derived for Fm, Md, No and Lr based on their atomic weights, estimated metallic radii,[3] and predicted close-packed crystalline structures.[4]
  3. ^ More generally, any element having a high density, atomic weight or atomic number may be referred to as a heavy element.[9]
  4. ^ Excluding s- and f-block metals, hence starting with Sc[10]
  5. ^ Definitions based on atomic number have been criticised for including metals with low densities. For example, rubidium in group 1 has an atomic number of 37 but a density of only 1.532 g/cm3 which is below the threshold figure used by other authors.[8] The same problem may occur with atomic weight based definitions.
  6. ^ The test is not specific for any particular metals but is said to be capable of at least detecting Mo, Cu, Ag, Cd, Hg, Sn, Pb, As, Sb and Bi.[14] In any event, when the test uses hydrogen sulfide as the reagent it cannot detect Th, Ti, Zr, Nb, Ta or Cr.[15]
  7. ^ Transition and post-transition metals that do not usually form coloured complexes are Sc and Y in group 3;[16] Ag in group 11;[17] Zn and Cd in group 12;[16][18] and the metals of groups 13–16.[19]
  8. ^ Lanthanide (Ln) sulfides and hydroxides are insoluble;[20] the latter can be obtained from aqueous solutions of Ln salts as coloured gelatinous precipitates;[21] and Ln complexes have much the same colour as their aqua ions (the majority of which are coloured).[22] Actinide (An) sulfides may or may not be insoluble, depending on the author. Divalent uranium monosulfide is not attacked by boiling water.[23] Trivalent actinide ions behave similarly to the trivalent lanthanide ions hence the sulfides in question may be insoluble but this is not explicitly stated.[24] Tervalent An sulfides decompose[25] but Edelstein et al. say they are soluble[26] whereas Haynes says thorium(IV) sulfide is insoluble.[27] Early in the history of nuclear fission it had been noted that precipitation with hydrogen sulfide was a "remarkably" effective way of isolating and detecting transuranium elements in solution.[28] In a similar vein, Deschlag writes that the elements after uranium were expected to have insoluble sulfides by analogy with third row transition metals. But he goes on to note that the elements after actinium were found to have properties different from those of the transition metals and claims they do not form insoluble sulfides.[29] The An hydroxides are, however, insoluble[26] and can be precipitated from aqueous solutions of their salts.[30] Finally, many An complexes have "deep and vivid" colours.[31]
  9. ^ The heavier elements commonly to less commonly recognised as metalloids—Ge; As, Sb; Se, Te, Po; At—satisfy some of the three parts of Hawkes' definition. All of them have insoluble sulfides[30][32] but only Ge, Te and Po apparently have insoluble hydroxides.[33] All bar At can be obtained as coloured (sulfide) precipitates from aqueous solutions of their salts;[30] astatine is likewise precipitated from solution by hydrogen sulfide but, since visible quantities of At have never been synthesised, the colour of the precipitate is not known.[32][34] As p-block elements, their complexes are usually colourless.[35]
  10. ^ Google recorded 945 citations for the paper in question,[37] as at 19 April 2016.
  11. ^ The light metals beryllium (density 1.85 g/cm3 and aluminium (2.37) are sometimes considered to be heavy metals on account of their potential toxicity.[52]
  12. ^ Tungsten may be another such toxic heavy metal.[56]
  13. ^ Selenium is commonly described as a metalloid in environmental science literature
  14. ^ Abundances are from Lide;[70] occurrence types are from McQueen[71] and Emsley[64]
  15. ^ Iron and tin also occur as chalcophiles but are mined mainly as lithophiles
  16. ^ Cobalt, nickel and germanium also occur as lithophiles but are mined mainly as chalcophiles
  17. ^ Trace elements having an abundance much less than the one part per trillion of Ra and Pa (namely Tc, Pm, Po, At, Rn, Fr, Ac, Np, and Pu) are not shown
  18. ^ Here presumed to be those with a density of more than 5 g/cm3
  19. ^ In some cases, for example in the presence of high energy gamma rays or in a very high temperature hydrogen rich environment, the subject nuclei may experience neutron loss or proton gain resulting in the production of (comparatively rare) neutron deficient isotopes.[74]
  20. ^ Iron, cobalt, nickel, germanium and tin are also siderophiles from a whole of Earth perspective
  21. ^ Weller[115] classifies coinage metals as precious metals (e.g. silver, gold, platinum); heavy metals of very high durability (nickel); heavy metals of low durability (copper, iron, zinc, tin and lead); and light metals (aluminium).

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  8. ^ a b c d e f Duffus 2002
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  29. ^ Deschlag 2011, p. 226
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  66. ^ Valkovic 1990
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  92. ^ Moore & Ramamoorthy 1984, p. 102
  93. ^ a b National Materials Advisory Board 1973, p. 58
  94. ^ Livesey 2012, p. 57
  95. ^ Rockhoff 2012, p. 314
  96. ^ Morstein 2005, p. 129
  97. ^ Russell & Lee 2005, pp. 218–219
  98. ^ Lach et al. 2015; Di Maio 2016, p. 154
  99. ^ Preschel 2005
  100. ^ Guandalini et al. 2011
  101. ^ Scoullos et al. 2001, p. 315; Ariel, Barta & Brandon 1973, p. 126
  102. ^ Tisza 2001, p. 73
  103. ^ Chandler & Roberson 2009, p. 47; Ismail, Khulbe & Matsuura 2015, pp. 302, 367, 373
  104. ^ Ebbing & Gammon 2017, p. 695
  105. ^ Pan & Dai 2015, p. 69
  106. ^ Brown 1987, p. 48
  107. ^ McColm 1994, p. 215
  108. ^ Elliot 1946, p. 11; Warth 1956, p. 571
  109. ^ Weber & Rutula 2001, p. 415
  110. ^ Dunn 2009; Bonetti et al. 2009
  111. ^ Desoize 2004
  112. ^ Atlas 1986, p. 359; Lima et al. 2013
  113. ^ Volesky 1990, p. 174
  114. ^ Roe & Roe 1992
  115. ^ Weller 1976, p. 4
  116. ^ Guney & Zagury 2012; Cui et al. 2015

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