Post-transition metal explained

The metallic elements in the periodic table located between the transition metals to their left and the chemically weak nonmetallic metalloids to their right have received many names in the literature, such as post-transition metals, poor metals, other metals, p-block metals and chemically weak metals. The most common name, post-transition metals, is generally used in this article.

Physically, these metals are soft (or brittle), have poor mechanical strength, and usually have melting points lower than those of the transition metals. Being close to the metal-nonmetal border, their crystalline structures tend to show covalent or directional bonding effects, having generally greater complexity or fewer nearest neighbours than other metallic elements.

Chemically, they are characterised—to varying degrees—by covalent bonding tendencies, acid-base amphoterism and the formation of anionic species such as aluminates, stannates, and bismuthates (in the case of aluminium, tin, and bismuth, respectively). They can also form Zintl phases (half-metallic compounds formed between highly electropositive metals and moderately electronegative metals or metalloids).

Applicable elements

The post-transition metals are located on the periodic table between the transition metals to their left and the chemically weak nonmetallic metalloids or nonmetals to their right. Generally included in this category are: the group 13–16 metals in periods 4–6 namely gallium, indium and thallium, tin and lead, bismuth, and polonium; and aluminium, a group 13 metal in period 3.

They can be seen at the bottom right in the accompanying plot of electronegativity values and melting points.

The boundaries of the category are not necessarily sharp as there is some overlapping of properties with adjacent categories (as occurs with classification schemes generally).^[1]

Some elements otherwise counted as transition metals are sometimes instead counted as post-transition metals namely the group 10 metal platinum; the group 11 coinage metals copper, silver and gold; and, more often, the group 12 metals zinc, cadmium and mercury.

Similarly, some elements otherwise counted as metalloids or nonmetals are sometimes instead counted as post-transition metals namely germanium, arsenic, selenium, antimony, tellurium, and polonium (of which germanium, arsenic, antimony, and tellurium are usually considered to be metalloids). Astatine, which is usually classified as a nonmetal or a metalloid, has been predicted to have a metallic crystalline structure. If so, it would be a post-transition metal.

Elements 112–118 (copernicium, nihonium, flerovium, moscovium, livermorium, tennessine, and oganesson) may be post-transition metals; insufficient quantities of them have been synthesized to allow sufficient investigation of their actual physical and chemical properties.

Rationale

The diminished metallic nature of the post-transition metals is largely attributable to the increase in nuclear charge going across the periodic table, from left to right.^[2] The increase in nuclear charge is partially offset by an increasing number of electrons but as these are spatially distributed each extra electron does not fully screen each successive increase in nuclear charge, and the latter therefore dominates.^[3] With some irregularities, atomic radii contract, ionisation energies increase,^[2] fewer electrons become available for metallic bonding,^[4] and "ions [become] smaller and more polarizing and more prone to covalency."^[5] This phenomenon is more evident in period 4–6 post-transition metals, due to inefficient screening of their nuclear charges by their d¹⁰ and (in the case of the period 6 metals) f¹⁴ electron configurations;^[6] the screening power of electrons decreases in the sequence s > p > d > f. The reductions in atomic size due to the interjection of the d- and f-blocks are referred to as, respectively, the 'scandide' or 'd-block contraction', and the 'lanthanide contraction'.^[7] Relativistic effects also "increase the binding energy", and hence ionisation energy, of the electrons in "the 6s shell in gold and mercury, and the 6p shell in subsequent elements of period 6."^[8]

Descriptive chemistry

Group 10

See main article: Platinum. Platinum is a moderately hard metal (MH 3.5) of low mechanical strength, with a close-packed face-centred cubic structure (BCN 12). Compared to other metals in this category, it has an unusually high melting point (2042 K v 1338 for gold). Platinum is more ductile than gold, silver or copper, thus being the most ductile of pure metals, but it is less malleable than gold. Like gold, platinum is a chalcophile element in terms of its occurrence in the Earth's crust, preferring to form covalent bonds with sulfur.^[9] It behaves like a transition metal in its preferred oxidation states of +2 and +4. There is very little evidence of the existence of simple metal ions in aqueous media;^[10] most platinum compounds are (covalent) coordination complexes.^[11] The oxide (PtO₂) is amphoteric, with acidic properties predominating; it can be fused with alkali hydroxides (MOH; M = Na, K) or calcium oxide (CaO) to give anionic platinates, such as red Na₂PtO₃ and green K₂PtO₃. The hydrated oxide can be dissolved in hydrochloric acid to give the hexachlormetallate(IV), H₂PtCl₆.^[12]

Like gold, which can form compounds containing the −1 auride ion, platinum can form compounds containing platinide ions, such as the Zintl phases BaPt, Ba₃Pt₂ and Ba₂Pt, being the first (unambiguous) transition metal to do so.^[13]

Darmstadtium should be similar to its lighter homologue platinum. It is expected to have a close-packed body-centered cubic structure. It should be a very dense metal, with a density of 26–27 g/cm³ surpassing all stable elements. Darmstadtium chemistry is expected to be dominated by the +2 and +4 oxidation states, similar to platinum. Darmstadtium(IV) oxide (DsO₂) should be amphoteric, and darmstadtium(II) oxide (DsO) basic, exactly analogous to platinum. There should also be a +6 oxidation state, similar to platinum. Darmstadtium should be a very noble metal: the standard reduction potential for the Ds²⁺/Ds couple is expected to be +1.7 V, more than the +1.52 V for the Au³⁺/Au couple.

Group 11

See main article: Group 11 element. The group 11 metals are typically categorised as transition metals given they can form ions with incomplete d-shells. Physically, they have the relatively low melting points and high electronegativity values associated with post-transition metals. "The filled d subshell and free s electron of Cu, Ag, and Au contribute to their high electrical and thermal conductivity. Transition metals to the left of group 11 experience interactions between s electrons and the partially filled d subshell that lower electron mobility."^[14] Chemically, the group 11 metals in their +1 valence states show similarities to other post-transition metals;^[15] they are occasionally classified as such.^[16]

Copper is a soft metal (MH 2.5–3.0)^[17] with low mechanical strength.^[18] It has a close-packed face-centred cubic structure (BCN 12).^[19] Copper behaves like a transition metal in its preferred oxidation state of +2. Stable compounds in which copper is in its less preferred oxidation state of +1 (Cu₂O, CuCl, CuBr, CuI and CuCN, for example) have significant covalent character.^[20] The oxide (CuO) is amphoteric, with predominating basic properties; it can be fused with alkali oxides (M₂O; M = Na, K) to give anionic oxycuprates (M₂CuO₂).^[21] Copper forms Zintl phases such as Li₇CuSi₂^[22] and M₃Cu₃Sb₄ (M = Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, or Er).^[23]

Silver is a soft metal (MH 2.5–3)^[24] with low mechanical strength.^[25] It has a close-packed face-centred cubic structure (BCN 12).^[26] The chemistry of silver is dominated by its +1 valence state in which it shows generally similar physical and chemical properties to compounds of thallium, a main group metal, in the same oxidation state.^[27] It tends to bond covalently in most of its compounds.^[28] The oxide (Ag₂O) is amphoteric, with basic properties predominating.^[29] Silver forms a series of oxoargentates (M₃AgO₂, M = Na, K, Rb).^[30] It is a constituent of Zintl phases such as Li₂AgM (M = Al, Ga, In, Tl, Si, Ge, Sn or Pb)^[31] and Yb₃Ag₂.^[32]

Gold is a soft metal (MH 2.5–3)^[33] that is easily deformed.^[34] It has a close-packed face-centred cubic structure (BCN 12).^[26] The chemistry of gold is dominated by its +3 valence state; all such compounds of gold feature covalent bonding,^[35] as do its stable +1 compounds.^[36] Gold oxide (Au₂O₃) is amphoteric, with acidic properties predominating; it forms anionic hydroxoaurates, where M = Na, K, ½Ba, Tl; and aurates such as NaAuO₂.^[37] Gold is a constituent of Zintl phases such as M₂AuBi (M = Li or Na);^[38] Li₂AuM (M = In, Tl, Ge, Pb, Sn)^[39] and Ca₅Au₄.^[32]

Roentgenium is expected to be similar to its lighter homologue gold in many ways. It is expected to have a close-packed body-centered cubic structure. It should be a very dense metal, with its density of 22–24 g/cm³ being around that of osmium and iridium, the densest stable elements. Roentgenium chemistry is expected to be dominated by the +3 valence state, similarly to gold, in which it should similarly behave as a transition metal. Roentgenium oxide (Rg₂O₃) should be amphoteric; stable compounds in the −1, +1, and +5 valence states should also exist, exactly analogous to gold. Roentgenium is similarly expected to be a very noble metal: the standard reduction potential for the Rg³⁺/Rg couple is expected to be +1.9 V, more than the +1.52 V for the Au³⁺/Au couple. The cation is expected to be the softest among the metal cations. Due to relativistic stabilisation of the 7s subshell, roentgenium is expected to have a full s-subshell and a partially filled d-subshell, instead of the free s-electron and full d-subshell of copper, silver, and gold.

Group 12

See main article: Group 12 element. On the group 12 metals (zinc, cadmium and mercury), Smith^[40] observed that, "Textbook writers have always found difficulty in dealing with these elements." There is an abrupt and significant reduction in physical metallic character from group 11 to group 12.^[41] Their chemistry is that of main group elements.^[42] A 2003 survey of chemistry books showed that they were treated as either transition metals or main group elements on about a 50/50 basis.^[43] The IUPAC Red Book notes that although the group 3−12 elements are commonly referred to as the transition elements, the group 12 elements are not always included.^[44] The group 12 elements do not satisfy the IUPAC Gold Book definition of a transition metal.^[45]

Zinc is a soft metal (MH 2.5) with poor mechanical properties.^[46] It has a crystalline structure (BCN 6+6) that is slightly distorted from the ideal. Many zinc compounds are markedly covalent in character.^[47] The oxide and hydroxide of zinc in its preferred oxidation state of +2, namely ZnO and Zn(OH)₂, are amphoteric;^[48] it forms anionic zincates in strongly basic solutions.^[49] Zinc forms Zintl phases such as LiZn, NaZn₁₃ and BaZn₁₃.^[50] Highly purified zinc, at room temperature, is ductile.^[51] It reacts with moist air to form a thin layer of carbonate that prevents further corrosion.^[52]

Cadmium is a soft, ductile metal (MH 2.0) that undergoes substantial deformation, under load, at room temperature.^[53] Like zinc, it has a crystalline structure (BCN 6+6) that is slightly distorted from the ideal. The halides of cadmium, with the exception of the fluoride, exhibit a substantially covalent nature.^[54] The oxides of cadmium in its preferred oxidation state of +2, namely CdO and Cd(OH)₂, are weakly amphoteric; it forms cadmates in strongly basic solutions.^[55] Cadmium forms Zintl phases such as LiCd, RbCd₁₃ and CsCd₁₃.^[50] When heated in air to a few hundred degrees, cadmium represents a toxicity hazard due to the release of cadmium vapour; when heated to its boiling point in air (just above 1000 K; 725 C; 1340 F; cf steel ~2700 K; 2425 C; 4400 F),^[56] the cadmium vapour oxidizes, 'with a reddish-yellow flame, dispersing as an aerosol of potentially lethal CdO particles.'^[53] Cadmium is otherwise stable in air and in water, at ambient conditions, protected by a layer of cadmium oxide.

Mercury is a liquid at room temperature. It has the weakest metallic bonding of all, as indicated by its bonding energy (61 kJ/mol) and melting point (−39 °C) which, together, are the lowest of all the metallic elements.^[57] Solid mercury (MH 1.5)^[58] has a distorted crystalline structure,^[59] with mixed metallic-covalent bonding,^[60] and a BCN of 6. "All of the [Group 12] metals, but especially mercury, tend to form covalent rather than ionic compounds."^[61] The oxide of mercury in its preferred oxidation state (HgO; +2) is weakly amphoteric, as is the congener sulfide HgS.^[62] It forms anionic thiomercurates (such as Na₂HgS₂ and BaHgS₃) in strongly basic solutions.^[63] It forms or is a part of Zintl phases such as NaHg and K₈In₁₀Hg.^[64] Mercury is a relatively inert metal, showing little oxide formation at room temperature.^[65]

Copernicium is expected to be a liquid at room temperature, although experiments have so far not succeeded in determining its boiling point with sufficient precision to prove this. Like its lighter congener mercury, many of its singular properties stem from its closed-shell d¹⁰s² electron configuration as well as strong relativistic effects. Its cohesive energy is even less than that of mercury and is likely only higher than that of flerovium. Solid copernicium is expected to crystallise in a close-packed body-centred cubic structure and have a density of about 14.7 g/cm³, decreasing to 14.0 g/cm³ on melting, which is similar to that of mercury (13.534 g/cm³). Copernicium chemistry is expected to be dominated by the +2 oxidation state, in which it would behave like a post-transition metal similar to mercury, although the relativistic stabilisation of the 7s orbitals means that this oxidation state involves giving up 6d rather than 7s electrons. A concurrent relativistic destabilisation of the 6d orbitals should allow higher oxidation states such as +3 and +4 with electronegative ligands, such as the halogens. A very high standard reduction potential of +2.1 V is expected for the Cn²⁺/Cn couple. In fact, bulk copernicium may even be an insulator with a band gap of 6.4±0.2 V, which would make it similar to the noble gases such as radon, though copernicium has previously been predicted to be a semiconductor or a noble metal instead. Copernicium oxide (CnO) is expected to be predominantly basic.

Group 13

See main article: Boron group.

Aluminium sometimes is^[66] or is not^[67] counted as a post-transition metal. It has a well shielded [Ne] noble gas core rather than the less well shielded [Ar]3d¹⁰, [Kr]4d¹⁰ or [Xe]4f¹⁴5d¹⁰ core of the post-transition metals. The small radius of the aluminium ion combined with its high charge make it a strongly polarizing species, prone to covalency.^[68]

Aluminium in pure form is a soft metal (MH 3.0) with low mechanical strength.^[69] It has a close-packed structure (BCN 12) showing some evidence of partially directional bonding.^[70] It has a low melting point and a high thermal conductivity. Its strength is halved at 200 °C, and for many of its alloys is minimal at 300 °C.^[71] The latter three properties of aluminium limit its use to situations where fire protection is not required,^[72] or necessitate the provision of increased fire protection.^[73] It bonds covalently in most of its compounds;^[74] has an amphoteric oxide; and can form anionic aluminates.^[49] Aluminium forms Zintl phases such as LiAl, Ca₃Al₂Sb₆, and SrAl₂.^[75] A thin protective layer of oxide confers a reasonable degree of corrosion resistance.^[76] It is susceptible to attack in low pH (<4) and high (> 8.5) pH conditions,^[77] a phenomenon that is generally more pronounced in the case of commercial purity aluminium and aluminium alloys.^[78] Given many of these properties and its proximity to the dividing line between metals and nonmetals, aluminium is occasionally classified as a metalloid. Despite its shortcomings, it has a good strength-to-weight ratio and excellent ductility; its mechanical strength can be improved considerably with the use of alloying additives; its very high thermal conductivity can be put to good use in heat sinks and heat exchangers;^[79] and it has a high electrical conductivity. At lower temperatures, aluminium increases its deformation strength (as do most materials) whilst maintaining ductility (as do face-centred cubic metals generally).^[80] Chemically, bulk aluminium is a strongly electropositive metal, with a high negative electrode potential.^[81]

Gallium is a soft, brittle metal (MH 1.5) that melts at only a few degrees above room temperature.^[82] It has an unusual crystalline structure featuring mixed metallic-covalent bonding and low symmetry^[82] (BCN 7 i.e. 1+2+2+2).^[83] It bonds covalently in most of its compounds,^[84] has an amphoteric oxide;^[85] and can form anionic gallates.^[49] Gallium forms Zintl phases such as Li₂Ga₇, K₃Ga₁₃ and YbGa₂.^[86] It is slowly oxidized in moist air at ambient conditions; a protective film of oxide prevents further corrosion.^[87]

Indium is a soft, highly ductile metal (MH 1.0) with a low tensile strength.^{[88] [89]} It has a partially distorted crystalline structure (BCN 4+8) associated with incompletely ionised atoms.^[90] The tendency of indium '...to form covalent compounds is one of the more important properties influencing its electrochemical behavior'.^[91] The oxides of indium in its preferred oxidation state of +3, namely In₂O₃ and In(OH)₃ are weakly amphoteric; it forms anionic indates in strongly basic solutions.^[92] Indium forms Zintl phases such as LiIn, Na₂In and Rb₂In₃.^[93] Indium does not oxidize in air at ambient conditions.^[89]

Thallium is a soft, reactive metal (MH 1.0), so much so that it has no structural uses.^[94] It has a close-packed crystalline structure (BCN 6+6) but an abnormally large interatomic distance that has been attributed to partial ionisation of the thallium atoms.^[95] Although compounds in the +1 (mostly ionic) oxidation state are the more numerous, thallium has an appreciable chemistry in the +3 (largely covalent) oxidation state, as seen in its chalcogenides and trihalides.^[96] It and aluminium are the only Group 13 elements to react with air at room temperature, slowly forming the amphoteric oxide Tl₂O₃.^{[97] [98]} It forms anionic thallates such as Tl₃TlO₃, Na₃Tl(OH)₆, NaTlO₂, and KTlO₂,^[98] and is present as the Tl⁻ thallide anion in the compound CsTl.^[99] Thallium forms Zintl phases, such as Na₂Tl, Na₂K₂₁Tl₁₉, CsTl and Sr₅Tl₃H.^[100]

Nihonium is expected to have a hexagonal close-packed crystalline structure, albeit based on extrapolation from those of the lighter group 13 elements: its density is expected to be around 16 g/cm³. A standard electrode potential of +0.6 V is predicted for the Nh⁺/Nh couple. The relativistic stabilisation of the 7s electrons is very high and hence nihonium should predominantly form the +1 oxidation state; nevertheless, as for copernicium, the +3 oxidation state should be reachable. Because of the shell closure at flerovium caused by spin-orbit coupling, nihonium is also one 7p electron short of a closed shell and would hence form a −1 oxidation state; in both the +1 and −1 oxidation states, nihonium should show more similarities to astatine than thallium. The Nh⁺ ion is expected to also have some similarities to the Ag⁺ ion, particularly in its propensity for complexation. Nihonium oxide (Nh₂O) is expected to be amphoteric.

Group 14

See main article: Carbon group.

Germanium is a hard (MH 6), very brittle semi-metallic element.^[101] It was originally thought to be a poorly conducting metal^[102] but has the electronic band structure of a semiconductor.^[103] Germanium is usually considered to be a metalloid rather than a metal.^[104] Like carbon (as diamond) and silicon, it has a covalent tetrahedral crystalline structure (BCN 4).^[105] Compounds in its preferred oxidation state of +4 are covalent.^[106] Germanium forms an amphoteric oxide, GeO₂^[107] and anionic germanates, such as Mg₂GeO₄. It forms Zintl phases such as LiGe, K₈Ge₄₄ and La₄Ge₃.^[108]

Tin is a soft, exceptionally^[109] weak metal (MH 1.5); a 1-cm thick rod will bend easily under mild finger pressure.^[109] It has an irregularly coordinated crystalline structure (BCN 4+2) associated with incompletely ionised atoms.^[90] All of the Group 14 elements form compounds in which they are in the +4, predominantly covalent, oxidation state; even in the +2 oxidation state tin generally forms covalent bonds.^[110] The oxides of tin in its preferred oxidation state of +2, namely SnO and Sn(OH)₂, are amphoteric;^[111] it forms stannites in strongly basic solutions.^[49] Below 13 °C (55.4 °F) tin changes its structure and becomes 'grey tin', which has the same structure as diamond, silicon and germanium (BCN 4). This transformation causes ordinary tin to crumble and disintegrate since, as well as being brittle, grey tin occupies more volume due to having a less efficient crystalline packing structure. Tin forms Zintl phases such as Na₄Sn, BaSn, K₈Sn₂₅ and Ca₃₁Sn₂₀.^[112] It has good corrosion resistance in air on account of forming a thin protective oxide layer. Pure tin has no structural uses.^[113] It is used in lead-free solders, and as a hardening agent in alloys of other metals, such as copper, lead, titanium and zinc.^[114]

Lead is a soft metal (MH 1.5, but hardens close to melting) which, in many cases,^[115] is unable to support its own weight.^[116] It has a close-packed structure (BCN 12) but an abnormally large inter-atomic distance that has been attributed to partial ionisation of the lead atoms.^{[95] [117]} It forms a semi-covalent dioxide PbO₂; a covalently bonded sulfide PbS; covalently bonded halides;^[118] and a range of covalently bonded organolead compounds such as the lead(II) mercaptan, lead tetra-acetate, and the once common, anti-knock additive, tetra-ethyl lead .^[119] The oxide of lead in its preferred oxidation state (PbO; +2) is amphoteric;^[120] it forms anionic plumbates in strongly basic solutions.^[49] Lead forms Zintl phases such as,, and .^[121] It has reasonable to good corrosion resistance; in moist air it forms a mixed gray coating of oxide, carbonate and sulfate that hinders further oxidation.^[122]

Flerovium is expected to be a liquid metal due to spin-orbit coupling "tearing" apart the 7p subshell, so that its 7s²7p_1/2² valence configuration forms a quasi-closed shell similar to those of mercury and copernicium. Solid flerovium should have a face-centered cubic structure and be a rather dense metal, with a density of around 14 g/cm³. Flerovium is expected to have a standard electrode potential of +0.9 V for the Fl²⁺/Fl couple. Flerovium oxide (FlO) is expected to be amphoteric, forming anionic flerovates in basic solutions.

Group 15

See main article: Pnictogen.

Arsenic is a moderately hard (MH 3.5) and brittle semi-metallic element. It is commonly regarded as a metalloid, or by some other authors as either a metal or a non-metal. It exhibits poor electrical conductivity which, like a metal, decreases with temperature. It has a relatively open and partially covalent crystalline structure (BCN 3+3). Arsenic forms covalent bonds with most other elements. The oxide in its preferred oxidation state (As₂O₃, +3) is amphoteric, as is the corresponding oxoacid in aqueous solution (H₃AsO₃) and congener sulfide (As₂S₃). Arsenic forms a series of anionic arsenates such as Na₃AsO₃ and PbHAsO₄, and Zintl phases such as Na₃As, Ca₂As and SrAs₃.

Antimony is a soft (MH 3.0) and brittle semi-metallic element. It is commonly regarded as a metalloid, or by some other authors as either a metal or a non-metal. It exhibits poor electrical conductivity which, like a metal, decreases with temperature. It has a relatively open and partially covalent crystalline structure (BCN 3+3). Antimony forms covalent bonds with most other elements. The oxide in its preferred oxidation state (Sb₂O₃, +3) is amphoteric. Antimony forms a series of anionic antimonites and antimonates such as NaSbO₂ and AlSbO₄, and Zintl phases such as K₅Sb₄, Sr₂Sb₃ and BaSb₃.

Bismuth is a soft metal (MH 2.5) that is too brittle for any structural use.^[123] It has an open-packed crystalline structure (BCN 3+3) with bonding that is intermediate between metallic and covalent.^[124] For a metal, it has exceptionally low electrical and thermal conductivity.^[125] Most of the ordinary compounds of bismuth are covalent in nature.^[126] The oxide, Bi₂O₃ is predominantly basic but will act as a weak acid in warm, very concentrated KOH.^[127] It can also be fused with potassium hydroxide in air, resulting in a brown mass of potassium bismuthate.^[128] The solution chemistry of bismuth is characterised by the formation of oxyanions;^[129] it forms anionic bismuthates in strongly basic solutions. Bismuth forms Zintl phases such as NaBi,^[130] Rb₇In₄Bi₆^[131] and Ba₁₁Cd₈Bi₁₄.^[132] Bailar et al.^[133] refer to bismuth as being, 'the least "metallic" metal in its physical properties' given its brittle nature (and possibly) 'the lowest electrical conductivity of all metals.'

Moscovium is expected to be a quite reactive metal. A standard reduction potential of −1.5 V for the Mc⁺/Mc couple is expected. This increased reactivity is consistent with the quasi-closed shell of flerovium and the beginning of a new series of elements with the filling of the loosely bound 7p_3/2 subshell, and is rather different from the relative nobility of bismuth. Like thallium, moscovium should have a common +1 oxidation state and a less common +3 oxidation state, although their relative stabilities may change depending on the complexing ligands or the degree of hydrolysis. Moscovium(I) oxide (Mc₂O) should be quite basic, like that of thallium, while moscovium(III) oxide (Mc₂O₃) should be amphoteric, like that of bismuth.

Group 16

See main article: Chalcogen. Selenium is a soft (MH 2.0) and brittle semi-metallic element. It is commonly regarded as a nonmetal, but is sometimes considered a metalloid or even a heavy metal. Selenium has a hexagonal polyatomic (CN 2) crystalline structure. It is a semiconductor with a band gap of 1.7 eV, and a photoconductor meaning its electrical conductivity increases a million-fold when illuminated. Selenium forms covalent bonds with most other elements, noting it can form ionic selenides with highly electropositive metals. The common oxide of selenium (SeO₃) is strongly acidic. Selenium forms a series of anionic selenites and selenates such as Na₂SeO₃, Na₂Se₂O₅, and Na₂SeO₄,^[134] as well as Zintl phases such as Cs₄Se₁₆.^[135]

Tellurium is a soft (MH 2.25) and brittle semi-metallic element. It is commonly regarded as a metalloid, or by some authors either as a metal or a non-metal. Tellurium has a polyatomic (CN 2) hexagonal crystalline structure. It is a semiconductor with a band gap of 0.32 to 0.38 eV. Tellurium forms covalent bonds with most other elements, noting it has an extensive organometallic chemistry and that many tellurides can be regarded as metallic alloys. The common oxide of tellurium (TeO₂) is amphoteric. Tellurium forms a series of anionic tellurites and tellurates such as Na₂TeO₃, Na₆TeO₆, and Rb₆Te₂O₉ (the last containing tetrahedral and trigonal bipyramidal anions),^[134] as well as Zintl phases such as NaTe₃.^[135]

Polonium is a radioactive, soft metal with a hardness similar to lead.^[136] It has a simple cubic crystalline structure characterised (as determined by electron density calculations) by partially directional bonding,^[137] and a BCN of 6. Such a structure ordinarily results in very low ductility and fracture resistance^[138] however polonium has been predicted to be a ductile metal.^[139] It forms a covalent hydride;^[140] its halides are covalent, volatile compounds, resembling those of tellurium.^[141] The oxide of polonium in its preferred oxidation state (PoO₂; +4) is predominantly basic, but amphoteric if dissolved in concentrated aqueous alkali, or fused with potassium hydroxide in air.^[142] The yellow polonate(IV) ion is known in aqueous solutions of low Cl^‒ concentration and high pH.^[143] Polonides such as Na₂Po, BePo, ZnPo, CdPo and HgPo feature Po²⁻ anions;^[144] except for HgPo these are some of the more stable of the polonium compounds.^[145]

Livermorium is expected to be less reactive than moscovium. The standard reduction potential of the Lv²⁺/Lv couple is expected to be around +0.1 V. It should be most stable in the +2 oxidation state; the 7p_3/2 electrons are expected to be so weakly bound that the first two ionisation potentials of livermorium should lie between those of the reactive alkaline earth metals magnesium and calcium. The +4 oxidation state should only be reachable with the most electronegative ligands. Livermorium(II) oxide (LvO) should be basic and livermorium(IV) oxide (LvO₂) should be amphoteric, analogous to polonium.

Group 17

See main article: Halogen.

Astatine is a radioactive element that has never been seen; a visible quantity would immediately be vaporised due to its intense radioactivity.^[146] It may be possible to prevent this with sufficient cooling.^[147] Astatine is commonly regarded as a nonmetal,^[148] less commonly as a metalloid^[149] and occasionally as a metal. Unlike its lighter congener iodine, evidence for diatomic astatine is sparse and inconclusive.^[150] In 2013, on the basis of relativistic modelling, astatine was predicted to be a monatomic metal, with a face-centered cubic crystalline structure.^[147] As such, astatine could be expected to have a metallic appearance; show metallic conductivity; and have excellent ductility, even at cryogenic temperatures.^[151] It could also be expected to show significant nonmetallic character, as is normally the case for metals in, or in the vicinity of, the p-block. Astatine oxyanions AtO⁻, and are known,^[152] oxyanion formation being a tendency of nonmetals.^[153] The hydroxide of astatine At(OH) is presumed to be amphoteric.^[154] Astatine forms covalent compounds with nonmetals,^[155] including hydrogen astatide HAt and carbon tetraastatide CAt₄.^[156] At⁻ anions have been reported to form astatides with silver, thallium, palladium and lead.^[157] Pruszyński et al. note that astatide ions should form strong complexes with soft metal cations such as Hg²⁺, Pd²⁺, Ag⁺ and Tl³⁺; they list the astatide formed with mercury as Hg(OH)At.^[158]

Tennessine, despite being in the halogen column of the periodic table, is expected to go even further towards metallicity than astatine due to its small electron affinity. The −1 state should not be important for tennessine and its major oxidation states should be +1 and +3, with +3 more stable: Ts³⁺ is expected to behave similarly to Au³⁺ in halide media. As such, tennessine oxide (Ts₂O₃) is expected to be amphoteric, similar to gold oxide and astatine(III) oxide.

Group 18

See main article: Oganesson. Oganesson is expected to be a very poor "noble gas" and may even be metallised by its large atomic radius and the weak binding of the easily removed 7p_3/2 electrons: certainly it is expected to be a quite reactive element that is solid at room temperature and has some similarities to tin, as one effect of the spin–orbit splitting of the 7p subshell is a "partial role reversal" of groups 14 and 18. Due to the immense polarisability of oganesson, it is expected that not only oganesson(II) fluoride but also oganesson(IV) fluoride should be predominantly ionic, involving the formation of Og²⁺ and Og⁴⁺ cations. Oganesson(II) oxide (OgO) and oganesson(IV) oxide (OgO₂) are both expected to be amphoteric, similar to the oxides of tin.

Aliases and related groupings

B-subgroup metals

Superficially, the B-subgroup metals are the metals in Groups IB to VIIB of the periodic table, corresponding to groups 11 to 17 using current IUPAC nomenclature. Practically, the group 11 metals (copper, silver and gold) are ordinarily regarded as transition metals (or sometimes as coinage metals, or noble metals) whereas the group 12 metals (zinc, cadmium, and mercury) may or may not be treated as B-subgroup metals depending on if the transition metals are taken to end at group 11 or group 12. The 'B' nomenclature (as in Groups IB, IIB, and so on) was superseded in 1988 but is still occasionally encountered in more recent literature.^[159]

The B-subgroup metals show nonmetallic properties; this is particularly apparent in moving from group 12 to group 16.^[160] Although the group 11 metals have normal close-packed metallic structures^[161] they show an overlap in chemical properties. In their +1 compounds (the stable state for silver; less so for copper)^[162] they are typical B-subgroup metals. In their +2 and +3 states their chemistry is typical of transition metal compounds.^[163]

Pseudo metals and hybrid metals

The B-subgroup metals can be subdivided into pseudo metals and hybrid metals. The pseudo metals (groups 12 and 13, including boron) are said to behave more like true metals (groups 1 to 11) than non-metals. The hybrid metals As, Sb, Bi, Te, Po, At — which other authors would call metalloids — partake about equally the properties of both. The pseudo metals can be considered related to the hybrid metals through the group 14 carbon column.^[164]

Base metals

Mingos^[165] writes that while the p-block metals are typical, that are not strongly reducing and that, as such, they are base metals requiring oxidizing acids to dissolve them.

Borderline metals

Parish^[166] writes that, 'as anticipated', the borderline metals of groups 13 and 14 have non-standard structures. Gallium, indium, thallium, germanium, and tin are specifically mentioned in this context. The group 12 metals are also noted as having slightly distorted structures; this has been interpreted as evidence of weak directional (i.e. covalent) bonding.

Chemically weak metals

Rayner-Canham and Overton^[167] use the term chemically weak metals to refer to the metals close to the metal-nonmetal borderline. These metals behave chemically more like the metalloids, particularly with respect to anionic species formation. The nine chemically weak metals identified by them are beryllium, magnesium, aluminium, gallium, tin, lead, antimony, bismuth, and polonium.

Frontier metals

Vernon^[168] uses the term "frontier metal" to refer to the class of chemically weak metals adjacent to the dividing line between metals. He notes that several of them "are further distinguished by a series of…knight's move relationships, formed between one element and the element one period down and two groups to its right."^[169] For example, copper(I) chemistry resembles indium(I) chemistry: "both ions are found mostly in solid-state compounds such as CuCl and InCl; the fluorides are unknown for both ions while the iodides are the most stable."^[169] The name frontier metal is adapted from Russell and Lee,^[170] who wrote that, "…bismuth and group 16 element polonium are generally considered to be metals, although they occupy 'frontier territory' on the periodic table, adjacent to the nonmetals."

Fusible metals

Cardarelli,^[171] writing in 2008, categorizes zinc, cadmium, mercury, gallium, indium, thallium, tin, lead, antimony and bismuth as fusible metals. Nearly 100 years earlier, Louis (1911)^[172] noted that fusible metals were alloys containing tin, cadmium, lead, and bismuth in various proportions, "the tin ranging from 10 to 20%."

Heavy metals (of low melting point)

Van Wert^[173] grouped the periodic table metals into a. the light metals; b. the heavy brittle metals of high melting point, c. the heavy ductile metals of high melting point; d. the heavy metals of low melting point (Zn, Cd, Hg; Ga, In, Tl; Ge, Sn; As, Sb, Bi; and Po), and e. the strong, electropositive metals. Britton, Abbatiello and Robins^[174] speak of 'the soft, low melting point, heavy metals in columns lIB, IlIA, IVA, and VA of the periodic table, namely Zn, Cd, Hg; Al, Ga, In, Tl; [Si], Ge, Sn, Pb; and Bi. The Sargent-Welch Chart of the Elements groups the metals into: light metals, the lanthanide series; the actinide series; heavy metals (brittle); heavy metals (ductile); and heavy metals (low melting point): Zn, Cd, Hg, [Cn]; Al, Ga, In, Tl; Ge, Sn, Pb, [Fl]; Sb, Bi; and Po.^[175]

Less typical metals

Habashi^[176] groups the elements into eight major categories: [1] typical metals (alkali metals, alkaline earth metals, and aluminium); [2] lanthanides (Ce–Lu); [3] actinides (Th–Lr); [4] transition metals (Sc, Y, La, Ac, groups 4–10); [5] less typical metals (groups 11–12, Ga, In, Tl, Sn and Pb); [6] metalloids (B, Si, Ge, As, Se, Sb, Te, Bi and Po); [7] covalent nonmetals (H, C, N, O, P, S and the halogens); and [8] monatomic nonmetals (that is, the noble gases).

Metametals

The metametals are zinc, cadmium, mercury, indium, thallium, tin and lead. They are ductile elements but, compared to their metallic periodic table neighbours to the left, have lower melting points, relatively low electrical and thermal conductivities, and show distortions from close-packed forms.^[177] Sometimes beryllium^[178] and gallium^[179] are included as metametals despite having low ductility.

Ordinary metals

Abrikosov^[180] distinguishes between ordinary metals, and transition metals where the inner shells are not filled. The ordinary metals have lower melting points and cohesive energies than those of the transition metals.^[181] Gray^[182] identifies as ordinary metals: aluminium, gallium, indium, thallium, nihonium, tin, lead, flerovium, bismuth, moscovium, and livermorium. He adds that, 'in reality most of the metals that people think of as ordinary are in fact transition metals...'.

Other metals

As noted, the metals falling between the transition metals and the metalloids on the periodic table are sometimes called other metals (see also, for example, Taylor et al.).^[183] 'Other' in this sense has the related meanings of, 'existing besides, or distinct from, that already mentioned'^[184] (that is, the alkali and alkaline earth metals, the lanthanides and actinides, and the transition metals); 'auxiliary'; 'ancillary, secondary'.^[185] According to Gray^[186] there should be a better name for these elements than 'other metals'.

p-block metals

The p-block metals are the metals in groups 13‒16 of the periodic table. Usually, this includes aluminium, gallium, indium and thallium; tin and lead; and bismuth. Germanium, antimony and polonium are sometimes also included, although the first two are commonly recognised as metalloids. The p-block metals tend to have structures that display low coordination numbers and directional bonding. Pronounced covalency is found in their compounds; the majority of their oxides are amphoteric.^[187]

Aluminium is an undisputed p-block element by group membership and its [Ne] 3s² 3p¹ electron configuration, but aluminium does not literally come after transition metals unlike p-block metals from period 4 and on. The epithet "post-transition" in reference to aluminium is a misnomer, and aluminium normally has no d electrons unlike all other p-block metals.

Peculiar metals

Slater^[188] divides the metals 'fairly definitely, though not perfectly sharply' into the ordinary metals and the peculiar metals, the latter of which verge on the nonmetals. The peculiar metals occur towards the ends of the rows of the periodic table and include 'approximately:' gallium, indium, and thallium; carbon, silicon '(both of which have some metallic properties, though we have previously treated them as nonmetals),' germanium and tin; arsenic, antimony, and bismuth; and selenium '(which is partly metallic)' and tellurium. The ordinary metals have centro-symmetrical crystalline structures whereas the peculiar metals have structures involving directional bonding. More recently, Joshua observed that the peculiar metals have mixed metallic-covalent bonding.^[189]

Poor metals

Farrell and Van Sicien^[190] use the term poor metal, for simplicity, 'to denote one with a significant covalent, or directional character.' Hill and Holman^[191] observe that, 'The term poor metals is not widely used, but it is a useful description for several metals including tin, lead and bismuth. These metals fall in a triangular block of the periodic table to the right of the transition metals. They are usually low in the activity (electrochemical) series and they have some resemblances to non-metals.' Reid et al. write that 'poor metals' is, '[A]n older term for metallic elements in Groups 13‒15 of the periodic table that are softer and have lower melting points than the metals traditionally used for tools.'^[192]

Post-transition metals

An early usage of this name is recorded by Deming, in 1940, in his well-known^[193] book Fundamental Chemistry.^[194] He treated the transition metals as finishing at group 10 (nickel, palladium and platinum). He referred to the ensuing elements in periods 4 to 6 of the periodic table (copper to germanium; silver to antimony; gold to polonium)—in view of their underlying d¹⁰ electronic configurations—as post-transition metals.

Semimetals

In modern use, the term 'semimetal' sometimes refers, loosely or explicitly, to metals with incomplete metallic character in crystalline structure, electrical conductivity or electronic structure. Examples include gallium,^[195] ytterbium,^[196] bismuth,^[197] mercury^[198] and neptunium.^[199] Metalloids, which are in-between elements that are neither metals nor nonmetals, are also sometimes instead called semimetals. The elements commonly recognised as metalloids are boron, silicon, germanium, arsenic, antimony and tellurium. In old chemistry, before the publication in 1789 of Lavoisier's 'revolutionary'^[200] Elementary Treatise on Chemistry,^[201] a semimetal was a metallic element with 'very imperfect ductility and malleability'^[202] such as zinc, mercury or bismuth.

Soft metals

Scott and Kanda^[203] refer to the metals in groups 11 to 15, plus platinum in group 10, as soft metals, excluding the very active metals, in groups 1−3. They note many important non-ferrous alloys are made from metals in this class, including sterling silver, brass (copper and zinc), and bronzes (copper with tin, manganese and nickel).

Transition metals

Historically, the transition metal series "includes those elements of the Periodic Table which 'bridge the gap' between the very electropositive alkali and allkaline earth metals and the electronegative non-metals of the groups: nitrogen-phosphorus, oxygen-sulfur, and the halogens."^[204] Cheronis, Parsons and Ronneberg^[205] wrote that, "The transition metals of low melting point form a block in the Periodic Table: those of Groups II 'b' [zinc, cadmium, mercury], III 'b' [aluminium, gallium, indium, thallium], and germanium, tin and lead in Group IV. These metals all have melting points below 425 °C."

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Further reading

• Lowrie RS & Campbell-Ferguson HJ 1971, Inorganic and physical chemistry, 2nd ed., chapter 25: The B-metals, Pergamon Press, Oxford, pp. 306–318
• Parish RV 1977, The metallic elements, chapter 9: The p-block metals, Longman, London, pp. 178–199
• Phillips CSG & Williams RJP 1966, Inorganic chemistry, vol. 2: Metals, Clarendon Press, Oxford, pp. 459–537
• Steele D 1966, The chemistry of the metallic elements, chapter 7: The later B-subgroup metals, Pergamon Press, Oxford, pp. 65–83

Notes and References

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2. [#Cox|Cox 2004, p.&nbsp;17]
3. [#Atkins2011|Atkins & de Paula 2011, p.&nbsp;352]
4. [#Greenwood2002|Greenwood & Earnshaw 1998, pp.&nbsp;222–3]
5. [#Steele|Steele 1966, p.&nbsp;193]
6. [#Johnson|Johnson 1970]
7. [#Huheey|Huheey & Huheey 1972, p.&nbsp;229]
8. [#Cox2004|Cox 2004, pp.&nbsp;20, 186, 188]
9. [#Reith|Reith & Shushter 2018, p. 115]
10. [#Loon|Van Loon & Barefoot 1991, p.&nbsp;52]
11. [#Pauling1988|Pauling 1988, p.&nbsp;695]
12. [#Lidin|Lidin 1996, p.&nbsp;347]
13. [#Karov|Karpov, Konuma & Jansen M 2006, p.&nbsp;839]
14. [#Russell2005|Russell & Lee 2005, p.&nbsp;302]
15. [#Steele|Steele 1966, p. 67]
16. [#Deming|Deming 1940, pp.&nbsp;705–7]
17. [#Cheemalapati|Cheemalapati, Keleher & Li 2008, p.&nbsp;226]
18. [#Liu|Liu & Pecht 2004, p.&nbsp;54]
19. [#Donohue|Donohue 1982, p.&nbsp;222]
20. [#Vanderah|Vanderah 1992, p.&nbsp;52]
21. [#Lidin|Lidin 1996, p.&nbsp;110]
22. [#Slabon|Slabon et al. 2012]
23. [#Larson|Larson et al. 2006, p.&nbsp;035111-2]
24. [#Schumann|Schumann 2008, p.&nbsp;52]
25. [#Braunović|Braunović 2014, p.&nbsp;244]
26. [#Donohue1982|Donohue 1982, p.&nbsp;222]
27. [#Banthorpe|Banthorpe, Gatforde & Hollebone 1968, p.&nbsp;61]
28. [#Steiner|Steiner & Campbell 1955, p.&nbsp;394]
29. [#Lidin|Lidin 1996, p.&nbsp;5]
30. [#Klassen|Klassen & Hoppe 1982]
31. [#Goodwin|Goodwin et al. 2005, p.&nbsp;341]
32. [#Köhler|Köhler & Whangbo 2008]
33. [#Arndt|Arndt & Ganino 2012, p.&nbsp;115]
34. [#Goffer|Goffer 2007, p.&nbsp;176]
35. [#Sidgwick1950|Sidgwick 1950, p.&nbsp;177]
36. [#Pauling1988|Pauling 1988, p.&nbsp;698]
37. [#Lidin|Lidin 1996, p.&nbsp;21–22]
38. [#Miller|Miller et al. 2011, p.&nbsp;150]
39. [#Fishcher|Fishcher-Bünher 2011, p.&nbsp;150]
40. [#Smith1990|Smith 1990, p.&nbsp;113]
41. [#Sorensen|Sorensen 1991, p.&nbsp;3]
42. [#KingRB1995|King 1995, pp.&nbsp; xiii, 273–288]
43. [#Jensen|Jensen 2003, p.&nbsp;952]
44. [#IUPAC2005|IUPAC 2005, p. 51]
45. [#Crichton|Crichton 2012, p.&nbsp;11]
46. [#Schweitzer|Schweitzer 2003, p.&nbsp;603]
47. [#Hutchinson|Hutchinson 1964, p.&nbsp;562]
48. [#Greenwood2002|Greenwood & Earnshaw 1998, p.&nbsp;1209]
49. [#Rayner2006|Rayner-Canham & Overton 2006, p.&nbsp;30]
50. [#Kneip|Kneip 1996, p.&nbsp;xxii]
51. [#Russell2005|Russell & Lee 2005, p.&nbsp;339]
52. [#Sequeira|Sequeira 2013, p.&nbsp;243]
53. [#Russell2005|Russell & Lee 2005, p.&nbsp;349]
54. [#Borsari|Borsari 2005, p.&nbsp;608]
55. [#Dirkse|Dirkse 1986, pp.&nbsp;287–288, 296]
56. [#Wanamaker|Wanamaker & Pennington 1921, p.&nbsp;56]
57. [#Rayner2006|Rayner-Canham 2006, p.&nbsp;570]
58. [#Poole|Poole 2004, p.&nbsp;821]
59. [#Mittemeijer|Mittemeijer 2010, p.&nbsp;138]
60. [#Russell2005|Russell & Lee 2005, pp.&nbsp;1–2; 354]
61. [#Rayner2006|Rayner-Canham 2006, p.&nbsp;567]
62. [#Moeller|Moeller 1952, pp. 859, 866]
63. [#Cooney|Cooney & Hall 1966, p.&nbsp;2179]
64. [#Deiseroth|Deiseroth 2008, pp.&nbsp;179‒180]
65. [#Russell2005|Russell & Lee 2005, p.&nbsp;354]
66. [#Whitten2014|Whitten et al. 2014, p.&nbsp;1045]
67. [#Cox2004|Cox 2004, p.&nbsp;186]
68. [#Kneen1972|Kneen, Rogers & Simpson 2004, p.&nbsp;370]
69. [#Gerard|Gerard & King 1968, p.&nbsp;16]
70. [#Russell2005|Russell & Lee 2005, pp.&nbsp;1–2; 359]
71. [#Lyons|Lyons 2004, p.&nbsp;170]
72. [#Cobb|Cobb 2009, p.&nbsp;323]
73. [#Polmear|Polemear 2006, p.&nbsp;184]
74. [#Cooper|Cooper 1968, p.&nbsp;25]
75. [#Kauzlarich|Kauzlarich 2005, pp.&nbsp;6009–10]
76. [#Dennis|Dennis & Such 1993, p.&nbsp;391]
77. [#Cramer|Cramer & Covino 2006, p.&nbsp;25]
78. [#Russell2005|Russell & Lee 2005, p.&nbsp;360]
79. [#Clegg|Clegg & Dovaston 2003, p.&nbsp;5/5]
80. [#Kent|Kent 1993, pp.&nbsp;13–14]
81. [#Steele1966|Steele 1966, p.&nbsp;60]
82. [#Russell2005|Russell & Lee 2005, p.&nbsp;387]
83. [#Driess|Driess 2004, p.&nbsp;151]
84. [#Walker|Walker, Enache & Newman 2013, p.&nbsp;38]
85. [#Atkins|Atkins et al. 2006, p.&nbsp;123]
86. [#Corbett|Corbett 1996, p.&nbsp;161]
87. [#Eranna|Eranna 2012, p.&nbsp;67]
88. [#Chandler|Chandler 1998, p.&nbsp;59]
89. [#Russell2005|Russell & Lee 2005, p.&nbsp;389]
90. [#Evans|Evans 1966, p.&nbsp;129–130]
91. [#Liang|Liang, King & White 1968, p. 288]
92. [#Busev|Busev 1962, p.&nbsp;33]
93. [#Kneip|Kneip 1996, p.&nbsp;xxii]
94. [#Russell2005|Russell & Lee 2005, p.&nbsp;390]
95. [#Wells|Wells 1985, p.&nbsp;1279–80]
96. [#Howe|Howe 1968a, p.&nbsp;709]
97. [#Chambers|Chambers & Holliday 1975, p.&nbsp;144]
98. [#Bashilova|Bashilova & Khomutova 1984, p.&nbsp;1546]
99. [#King&Schleyer|King & Schleyer 2004, p.&nbsp;19]
100. [#Corbett|Corbett 1996, p.&nbsp;153]
101. [#Wiberg2001|Wiberg, Holleman & Wiberg 2001, p.&nbsp;894]
102. [#Haller 2006|Haller 2006, p.&nbsp;3]
103. [#Russell2005|Russell & Lee 2005, p.&nbsp;399]
104. [#Ryan|Ryan 1968, p.&nbsp;65]
105. [#Wiberg2001|Wiberg, Holleman & Wiberg 2001, p.&nbsp;895]
106. [#Abd-El-Aziz|Abd-El-Aziz et al. 2003, p.&nbsp;200]
107. [#Cooper|Cooper 1968, pp.&nbsp;28–9]
108. [#Corbett|Corbett 1996, p.&nbsp;143]
109. [#Russell2005|Russell & Lee 2005, p.&nbsp;405]
110. [#Rayner2006|Rayner-Canham 2006, pp.&nbsp;306, 340]
111. [#Wiberg2001|Wiberg, Holleman & Wiberg 2001, p.&nbsp;247]
112. [#Corbett|Corbett 1996, p.&nbsp;143]
113. [#Russell2005|Russell & Lee 2005, pp.&nbsp;402, 405]
114. [#Russell2005|Russell & Lee 2005, p.&nbsp;402, 407]
115. [#Alhassan|Alhassan & Goodwin 2005, p.&nbsp;532]
116. [#Schweitzer|Schweitzer 2003, p.&nbsp;695]
117. [#Mackay|Mackay & Mackay 1989, p.&nbsp;86]
118. [#Hutchinson|Hutchinson 1959, p.&nbsp;455]
119. [#Durrant|Durrant & Durrant 1970, p.&nbsp;670]
120. [#Patnaik|Patnaik 2003, p.&nbsp;474]
121. [#Corbett|Corbett 1996, pp.&nbsp;143, 147]
122. [#Russell2005|Russell & Lee 2005, pp.&nbsp;411, 13]
123. [#Russell2005|Russell & Lee 2005, p.&nbsp;428]
124. [#Eagleson1994|Eagleson 1994, p.&nbsp;282]
125. [#Russell2005|Russell & Lee 2005, p.&nbsp;427]
126. [#Sidgwick|Sidgwick 1937, p.&nbsp;181]
127. [#Howe|Howe 1968, p.&nbsp;62]
128. [#Durrant|Durrant & Durrant 1970, p.&nbsp;790]
129. [#Wiberg2001|Wiberg, Holleman & Wiberg 2001, p.&nbsp;771]
130. [#Miller2002|Miller, Lee & Choe 2002, p.&nbsp;14]
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