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The dispute on the composition of group 3 of the periodic table concerns whether the elements under scandium (Sc) and yttrium (Y) in the periodic table should be lanthanum (La) and actinium (Ac), or lutetium (Lu) and lawrencium (Lr). Some compromises between the two can also be found.

The dispute grew out of the problems that Dmitri Mendeleev had with inserting the rare earth elements, and has been discussed in the literature for over a century. It arises because of differing viewpoints on the importance and interpretation of electronic and physicochemical considerations.

As variation in the literature on this issue can puzzle students and instructors, IUPAC began a project in 2015 to make a decision on the composition of group 3. In 2021, this project issued a provisional report. This report took the position that the matter was one of convention rather than objectively resolvable, and supported Sc-Y-Lu-Lr as group 3 based on three desiderata: (1) retaining the order of increasing atomic number throughout the table; (2) avoiding any split blocks; and (3) ensuring that the widths of the blocks are 2, 6, 10, and 14, conforming with the quantum mechanical bases of the periodic table.

Early history

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From 1871 onward, Dmitri Mendeleev attempted to fit the rare earths into his periodic table as analogues of other known elements. He found this difficult as they did not show the valences that his classification expected. Lanthanum and cerium, whose maximal valences were 3 and 4, could be accommodated in groups III and IV; didymium seemed to be the next element, and he recognised that it would be important to show that it can have valence 5. Bohuslav Brauner spent decades attempting to show this, but was unsuccessful; moreover, in 1885 Carl Auer von Welsbach found that didymium was not an element at all, but a mixture of praseodymium and neodymium. After 25 years of fruitless labour, Brauner came to the conclusion that the maximum valence of the rare earths is 3 or 4.[1] As such, in 1902, Brauner advocated a classification in which all rare earths would be placed in group IV. He named this the asteroid hypothesis, as all the rare earths would then share one place in the periodic system, just as there is an asteroid belt between Mars and Jupiter rather than one planet. Other authors agreed with having the rare earths share a box, though they disagreed over whether they should be placed in group IV, group III, across both, or even across groups II through IV together. This is the origin of the Sc-Y-*-** form sometimes used as a compromise.[1]

However, with the advent of Niels Bohr's theory of the atom in 1912, alternatives began to emerge where the rare earths were viewed as belonging to their own groups in the periodic system, unrelated to any others. This is consistent with quantum mechanics, where they are the first f-block elements, and it became the preferred way to show the rare earths in the 20th century. Some early tables following this approach were drawn by Henry Bassett (1892), Julius Thomsen (1895), and Alfred Werner (1905). Werner's table is the first modern long-form table: it isolates La–Yb as the rare earth elements and draws them between groups II and III. Lutetium (then appearing as a blank space as it had not yet been discovered) is treated as a transition metal, below scandium and yttrium. Bassett and Werner mark the first appearances of group 3 as Sc-Y-Lu-Lr (though Lu and Lr were not yet discovered then).[1] Though they both treated the known actinides as analogues of the rare earths, it was not until Glenn T. Seaborg synthesised more transuranium elements in the 1940s that the actinide concept became standard.[1]

By the 1940s, tables based on electronic configurations and the idea of the differentiating electron started to be adopted, often showing the Sc-Y-La-Ac composition of group 3 – though the electronic configurations that they had been based on were not always accurate according to modern knowledge.[2] Particularly influential was the Sc-Y-La-Ac table published by the Sargent-Welch company, which increased the popularity of this form.[3]

From the 1940s onwards, physicists and chemists began publishing on the composition of group 3. Most authors who published arguments supported Sc-Y-Lu-Lr,[4] but authors of textbooks tended to retain Sc-Y-La-Ac.[5] Over the years, the prevalence of Sc-Y-La-Ac in textbooks decreased; by the 2010s, it had lost its majority, but still retained a plurality over Sc-Y-*-** and Sc-Y-Lu-Lr.[6]

Physical and chemical considerations

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In the early 20th century, the separation of the rare earths was primarily achieved by repeated precipitation or crystallization. The first separation achieved by these methods was into two main groups: the cerium group and the yttrium group. The reason for this division arose from the difference in solubility of rare-earth double sulfates with sodium and potassium. The sodium double sulfates of the cerium group are poorly soluble, while those of the yttrium group are very soluble.[7] Sc, Y, and Lu appear in the yttrium group, while La and Ac appear in the cerium group.[2] This is also true for the occurrence of Sc, Y, Lu (yttrium group) and La (cerium group) in minerals.[1] Thus La and Ac differ chemically from Sc, Y, and Lu and some chemists have used this as an argument for group 3 as Sc-Y-Lu-Lr.[2]

 

In the 1960s and 1970s, physicists amassed evidence based on properties where Sc, Y, Lu behave the same way, but La behaves differently. In 1982, Jensen quoted some cases of this in an influential article in the Journal of Chemical Education: the metallic crystal structure at room temperature; the structure of the oxides; the structure of the chlorides; a d-block like structure for the conduction band; and the presence or absence of superconductivity. This was used to argue for Sc-Y-Lu-Lr.[2] All the arguments focused on La vs Lu, because no data was available for highly radioactive Ac and Lr.[4]

In 1985, Norman E. Holden gave a presentation at the 33rd IUPAC General Assembly in Lyon, France. He noted that density trends in the transition metals favoured Lu in group 3 rather than La. Referring to some physical properties for Sc, Y, La, and Lu (crystal structure of the metals and oxides, melting points, shear modulus, Young's modulus, and coefficient of thermal expansion) where La differs from Sc, Y, and Lu, he argued that Sc-Y-Lu-Lr should replace Sc-Y-La-Ac.[8]

Jensen also noted that if trends are plotted for atomic radius, sum of the first two ionisation energies, melting points, and Allred-Rochow electronegativity, Sc-Y-Lu is consistently a better match for the trends down the other groups of the d-block (Ti-Zr-Hf, V-Nb-Ta, etc.) than Sc-Y-La.[2] Eric Scerri has nonetheless criticised his case on the grounds of selectivity, as if one sums the first three ionisation energies, Sc-Y-La matches the typical d-block trend better for this property than Sc-Y-Lu. Scerri thus argues that cases based on specific physical or chemical data cannot be conclusive on this problem.[5]

In a 2015 update to his 1982 article, Jensen added some more recent findings in support of Sc-Y-Lu-Lr: values of the force constant for Lu2 (matching the d-block trend better than La2), trends in relativistic corrections to the size of the 6s shell (where there is a clear difference between La–Yb and Lu–Ir), bonding in the dimers of Sc, Y, La, and Lu with aluminium (where the La dimer has a different chemical bond from those of Sc, Y, and Lu), enthalpy of vaporisation of the lanthanides and actinides (where Lu and Lr do not fit the trend of La–Yb and Ac–No), and enthalpy of adsorption for the actinides (where the value for Lr matches that expected from predictions of the following d-block elements Rf and Db, not f-block or p-block elements).[4] In 2017, he added that Sc-Y-La-Ac would make Lu and Lr not fit trends in ionisation energy in the f-block, but that Sc-Y-Lu-Lr would make them fit the trends of the d-block (noting however that values for the d-block elements beyond Lr were either calculations or approximations).[9]

Chistyakov, a Soviet chemist, argued for Sc-Y-Lu on the grounds of the secondary periodicity trend, where a zig-zag or alternating trend in properties appears when one descends a group of elements. He noted that Sc-Y-Lu exhibits secondary periodicity for example in atomic radii, just like Ti-Zr-Hf and other d-block groups, whereas Sc-Y-La does not. On this basis he supported Sc-Y-Lu.[5]

Some authors have argued for all fifteen lanthanides to be placed below yttrium, which is a reversion to Brauner's asteroid hypothesis.[1] The reasoning is that it clarifies the similarity and continuity of properties across the entire set of lanthanides from La to Lu.[1][10] However, this intermingles the f- and d-blocks.[1] Moreover, an f-subshell has a maximum occupancy of 14 electrons and hence the f-block should only be 14 elements long. Jensen criticises this as "chemical nonsense" and an "antiquated interpretation", as this puts the f-block elements all into group 3, while many of them can achieve an oxidation state higher than +3.[11]

Electronic considerations

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Atomic electron configurations

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The electron configurations of the relevant atoms are as follows: scandium [Ar]3d14s2, yttrium [Kr]4d15s2, lanthanum [Xe]5d16s2, lutetium [Xe]4f145d16s2, actinium [Rn]6d17s2, and lawrencium [Rn]5f147s27p1. The symbol in square brackets denotes the preceding noble gas core, and the superscripts denote subshell occupancy. For example, [Xe]4f145d16s2 for lutetium indicates fourteen electrons in the 4f subshell, one in the 5d, and two in the 6s, all above a core matching the configuration of the preceding noble gas xenon. (The electron configuration of Lr was not determined till fairly recently, so in many early papers discussing the dispute, it was thought to be [Rn]5f146d17s2 like lutetium.)[2] The maximal occupancies of s, p, d, and f subshells respectively (the four types) are 2, 6, 10, and 14.[12]

Most of the lanthanides were originally thought to have the configuration [Xe]4fx5d16s2.[13] The tables from the 1940s that first introduced Sc-Y-La-Ac did so on the basis of the differentiating electron from the previous element. Barium has configuration [Xe]6s2, so lanthanum [Xe]5d16s2 (adding a 5d electron) was taken as the first d-block element of the sixth period. Still in period 6, it was thought that ytterbium had the configuration [Xe]4f135d16s2, so lutetium [Xe]4f145d16s2 added the last f-electron and was regarded as the last f-block element. However, already in 1937 it had been experimentally determined that ytterbium's true configuration is [Xe]4f146s2, so lutetium [Xe]4f145d16s2 in fact adds a d-electron to the preceding element. Therefore, differentiating electrons would make La and Lu equally valid candidates for the position below scandium and yttrium.[2]

As more experimental data came in, it emerged that most of the lanthanides have a configuration [Xe]4fx6s2, with no d electron. Eleven of the fifteen lanthanides have no d electron; only four do (La, Ce, Gd, and Lu). As for the actinides, eight have a [Rn]5fx7s2 configuration with no d electron; five have one (Ac, Pa, U, Np, and Cm); and one has two (Th);[2] Lr [Rn]5f147s27p1 with its p electron is a one-of-a-kind anomaly. In particular, the filling of the 4f subshell spans only thirteen elements (Ce–Yb), which means that both Sc-Y-La-Ac and Sc-Y-Lu-Lr encounter a problem as quantum mechanics suggests that since there are fourteen spaces in the 4f subshell, there should be fourteen 4f elements.[14] Because the majority of the lanthanides and actinides have the fxs2 configuration, it has been argued that this is the ideal configuration, and that the exceptional fxd1s2 configurations (including those for La and Ac) are an anomaly: this argument would support Sc-Y-Lu-Lr.[2]

Since neither La nor Ac actually has an f-electron as a single atom, some authors have argued that they cannot be f-elements, especially because they form the only paired anomaly where all elements in a group do not have the correct outer electrons for their block. This would support Sc-Y-La-Ac.[15][16] However, others have pointed out that thorium [Rn]6d27s2 has no f-electron either, but was accepted since Seaborg as part of the f-block without controversy; thus they considered it an inconsistency to allow thorium to be an f-block element, but not lanthanum and actinium.[2] Jensen has also noted that there are other cases where the majority of the elements in a group are anomalies (e.g. group 11, where all the stable elements are d10s1 instead of the expected d9s2). When lawrencium's correct configuration was measured, it led to further discussion. Laurence Lavelle argued that its [Rn]5f147s27p1 anomalous configuration prohibited it from being a d-block element and suggested that it was an analogue of thallium ([Xe]4f145d106s26p1) in the p-block. But since he simultaneously argued that lawrencium should remain in the f-block, Jensen's rebuttal accused him of inconsistency.[17]

It has also been argued that the configurations of La and Ac are closer to Sc and Y, because Sc, Y, La, and Ac do not have a filled f14 subshell above the noble gas core, whereas Lu and Lr do. However, Jensen argues that this is misleading, as all nine other d-block elements of period 6 add such a f14 subshell. For example, in group 4 the configurations are Ti [Ar]3d24s2, Zr [Kr]4d25s2, and Hf [Xe]4f145d26s2. Thus, in his opinion the analogy instead favours Sc-Y-Lu-Lr.[2]

Lev Landau and Evgeny Lifshitz wrote in their Course of Theoretical Physics that since "the 4f shell is complete in lutetium", it was incorrect to place Lu as a rare-earth, and that it should therefore be a transition metal;[18] this argument was repeated by Holden in his 1985 presentation to IUPAC.[8]

Other electronic considerations

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It has sometimes been argued that atomic configurations in the gas-phase are not very relevant. Some authors have argued that the periodic table is based on ideal rather than real configurations, pointing to other elements for evidence: there are many anomalies in the d-block, but they have not been used to question the placements of those elements.[17] Chemists generally agree that the elements ending the d-block in periods 4 through 6 are zinc ([Ar]3d104s2), cadmium ([Kr]4d105s2), and mercury ([Xe]4f145d106s2), even though the d-orbitals are actually fully occupied earlier, at copper ([Ar]3d104s1), palladium ([Kr]4d10), and gold ([Xe]4f145d106s1).[1] The ideal configurations fxs2 always can exist as excited states for La–Yb and Ac–No even when they are not the real ground-state configurations (e.g. for La and Ac),[14] but they cannot for Lu and Lr. This has been used to support Sc-Y-Lu-Lr.[9]

The Aufbau principle states that:

  1. Electron subshells fill in order of increasing n + ℓ.
  2. If two electron subshells are available with the same value of n + ℓ, then the one with the smaller n fills first.

It is typically used to determine ideal electron configurations, and is correct for all but 20 elements, which suggests that those twenty are simply exceptions to a general rule. According to the Aufbau principle, all the subshells will n + ℓ values up to 6 have been filled at barium. For the next n + ℓ value, 7, the subshells available are 4f, 5d, 6p, and 7s. As 4f has the lowest value of n (4), the Aufbau principle states that it should fill first (from La to Yb), before the 5d subshell fills (n = 5) from Lu to Hg. Hence the Aufbau principle supports Sc-Y-Lu-Lr.[1]

The Aufbau principle has been criticised, as while it predicts that 4s fills before 3d in the transition metals, the 4s electrons in fact ionise first. This is unexpected as if the 3d electrons were the last to fill in, they would be expected to be the first to be ionised out. W. H. Eugen Schwarz has suggested abandoning the Aufbau principle altogether, because its predicted filling order only matches the ionisation order in the s-block. Scerri however disagrees, as the Aufbau principle still successfully lists the differentiating electron in all but 20 cases.[19]

Jensen notes that La and Ac have low-lying f-orbitals that do not behave like the high-up ones in the hydrogen atom, whereas Lu and Lr do not.[17] In other words, in hydrogen through barium, the 4f orbitals are far enough from the nucleus that when analysing them, one can approximate the core and remaining electrons as a point charge; starting from lanthanum, this ceases to be the case, with lanthanum showing 4f levels more similar to those of the following rare earths. This has been used to support Sc-Y-Lu-Lr.[20]

Ground-state gas-phase configurations are for isolated atoms. However, chemistry considers bonding atoms in compounds, which often show different configurations.[21] Moreover, there are multiple excited states for each configuration and in some cases they can overlap (e.g. nickel or terbium). The lowest states for each configuration can be separated by very little energy, making which configuration happens to be the ground state chemically quite irrelevant.[22] Schwarz contends that it is the dominant electron configuration of atoms in chemical environments, and not free gaseous atoms in a vacuum, that can rationalise qualitative chemical behaviour;[23] in his view, gas-phase ground state electron configurations are only important for a few specialised topics, such as atom–molecular gas-phase reactions.[23] Christian K. Jørgensen noted that the relationship between chemistry and gas-phase ground-state configuration is "not simple", with the example that helium (1s2) matches the alkaline earth metals by configuration, but the noble gases by chemistry.[4]

Schwarz considers that La/Ac and Lu/Lr are all d-block elements, and duplicates Sc and Y over each pair, because in his opinion none of them have '"active" f valence electrons'.[24] However, not all authors agree with Schwarz's opinion on the activity of f valence electrons. Jørgensen considered the amount of 4f valence involvement for lanthanum to be approximately equal to the amount of 5f valence involvement for thorium,[22] and that Lu "can most conveniently be considered as the first member of the 5d series".[25] Jørgensen noted that the 4f element ions Pr3+ through Yb3+ show characteristic narrow bands with their positions almost completely independent on the ligands, but the following 5d elements (along with the 3d and 4d elements) behave significantly differently; while both types of elements show electron-transfer bands, ligand field theory becomes important for the d elements.[22]

 
Melting points of group 1-4 metals, from Gschneidner, K. A. (2016). Systematics. Handbook on the Physics and Chemistry of Rare Earths, 1–18. doi:10.1016/bs.hpcre.2016.07.001 "Pseudo-La" refers to a hypothetical La without 4f electrons; the real melting point values for La and Lu are also plotted.

Some physicists contend that La has a 4f valence contribution that is lacking in Sc, Y, and Lu, on the grounds that it would explain some of the aforementioned properties where La differs from Sc, Y, and Lu. For instance, while Sc, Y, and Lu crystallise in the hcp crystal structure, La crystallises in the dhcp crystal structure. Jörg Wittig argued that this difference is due to a 4f valence band for La that is absent from Lu. In support of his hypothesis, he points to the fact that the grounds that the dhcp structure is only otherwise seen in f-block elements, and that the pressure-temperature phase diagram of lanthanum is isomorphic to those of Pr and Nd, which are uncontroversially f-block. Wittig argued that a 4f valence band may similarly be responsible for low-temperature superconductivity of La, which Sc, Y, and Lu do not exhibit. As the critical temperature for superconductivity of Lu matches the d-block trends well, he argued that Sc-Y-Lu-Lr was the proper placement.[26] Karl Gschneidner noted that a "pseudo-La" without 4f involvement should have a higher melting point than it actually does, and argued that 4f valence bands were responsible.[27]

Other properties

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If elements are to be placed in order of increasing atomic number, then a Sc-Y-La-Ac table requires a split in the d-block. Lanthanum appears as the first d-block element, but then fourteen f-block elements intervene (Ce to Lu), before the d-block finishes with Hf through Hg. No such thing is necessary in a Sc-Y-Lu-Lr table. A split d-block has widely been considered undesirable,[14][28] although a few authors have defended it based on the atomic configurations of La and Ac.[29] In particular, Eric Scerri considers it to be an ad hoc move that for justification requires an independent argument, that "is especially not available to authors ... who maintain that the d-block perfectly reflects the filling of five d orbitals by ten outer electrons. Why should there be a break only between the first and second of these electron-filling processes?"[28]

Scerri has noted that Y, Lu, and Lr form an atomic number triad (71 is the average of 39 and 103), whereas Y, La, and Ac do not.[5] Michael Laing has responded noting that Sc, Y, La form an atomic number triad (39 is the average of 21 and 57) while Sc, Y, Lu do not. However, Scerri argued back that the situations are different, because La/Lu and Ac/Lr lie inside periods of equal length, whereas Y and La/Lu do not.[30]

IUPAC

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In 1988, IUPAC published a report on the numbering of groups in the periodic table that also touched on the group 3 problem. It wrote:

According to the electron configurations of the elements, the scandium group consists of the elements

Sc, Y, Lu, Lr.

This was pointed out as early as 1959 by L.D. Landau (ref. 20) and later by other authors (ref. 13, 14, 20 to 25). Most periodic tables in textbooks and classrooms, however, list Sc, Y, La, and Ac as elements of the scandium group and designate the elements Ce to Lu and Th to Lr as lanthanides and actinides, respectively. The historical background for this arrangement is given in a paper by W.B. Jensen (ref. 21). Based upon their electronic configurations and their chemical and physical properties, the elements La to Yb and Ac to No should be inserted between barium and lutetium and between radium and lawrencium or for practical reasons be listed at the bottom of the table.

Despite this, it also stated that the forthcoming IUPAC Red Book (a collection of nomenclature rules for inorganic chemistry) would use a compromise,[31] which turned out to be the Sc-Y-*-** form. The 1990 Red Book displayed the periodic table in three formats, 8-column (based on Mendeleev's original), 18-column, and 32-column; the first two showed Sc-Y-*-** in group 3, but the third showed Sc-Y-Lu-Lr as group 3.[32] In 2005, the 8-column and 32-column forms were dropped from the IUPAC Red Book, leaving only the compromise version in 18-column format.[33]

Since then, the so-called IUPAC periodic table has shown Sc-Y-*-**[34] (though IUPAC has not approved any specific form of the periodic table),[35] though the IUPAC newsmagazine Chemistry International has published two articles by Scerri arguing for Sc-Y-Lu-Lr.[36][19][12] In the 2012 article, Scerri claims that arguments based on chemical, physical, or electronic properties are "not completely categorical". He argues instead that if the periodic table is presented in 32-column format, then Sc-Y-Lu-Lr is "the natural choice", because Sc-Y-La-Ac either disrupts the atomic number sequence or splits the d-block. He dismisses the split d-block as "a very asymmetrical possibility", and although he notes that it appears in textbooks and articles, he argues that "does not render it any more legitimate".[36] In the 2019 article, he reiterates the point about the atomic number sequence, and recommends that group 3 should be Sc-Y-Lu-Lr and that La should "formally" start the f-block even though it does not have an f-electron. He points out that this is analogous to the situation expected for the future g-block, starting at around element 121: this would only be a "formal beginning", because only at about element 125 is the first actual g-electron expected.[19]

In 2015 IUPAC began a project to form a view as to whether either lanthanum and actinium or lutetium and lawrencium should appear in group 3, chaired by Scerri and including Jensen and Lavelle. It considered the question to be "of considerable importance" for chemists, physicists, and students, noting that the variation in published periodic tables on this point typically puzzled students and instructors.[6]

A provisional report appeared from the project in 2021.[12] It concluded that the group 3 dispute cannot be decided by any objective means and that that made it more important for IUPAC to decide it as a matter of convention. The report noted the following points:[12]

  • Sc-Y-La-Ac requires a very unevenly split d-block, while Sc-Y-Lu-Lr does not. While both forms "seem to be equally plausible" in the 18-column form, this is because the d-block split is masked by that form; it is much more obvious in the 32-column form.
  • Sc-Y-*-** makes the f-block rows appear with 15 elements, breaking the connection with orbital capacity as the quantum mechanical bases of the periodic table require (as an f-subshell can hold at most 14 elements).
  • Only Sc-Y-Lu-Lr avoids a split d-block and retains 14-element f-block rows.
  • Assigning electron configurations to atoms, as well as assigning elements to blocks, is an approximation. For example, all forms under consideration assign Th to the f-block even though its atom does not have any f-electrons.
  • The Sc-Y-*-** table was stated to have been "designed by practitioners of specialized branch of relativistic quantum mechanics concerned with the properties of super-heavy elements". While such considerations may support grouping together 15 elements rather than 14 as the f-block, it is "interest-dependence" and should not "be imposed on the majority of users of the periodic table".
  • Quantum mechanics explain the periodic table, as proven by "historical developments", though they do not provide a "full and exact reduction".

As such, the report concluded that "perhaps a compromise could be reached on" Sc-Y-Lu-Lr, based on the following three stated desiderata:[12]

First, it displays all the elements in order of increasing atomic number. Secondly, it avoids splitting the d-block into two highly uneven portions, and thirdly, it depicts all the blocks of the periodic table in accordance with the underlying quantum mechanical account of the periodic table which calls for 2, 6, 10 and 14 orbitals to occur in the extra-nuclear electron-shells.

References

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  1. ^ a b c d e f g h i j Thyssen, P.; Binnemans, K. (2011). Gschneidner, K. A. Jr.; Bünzli, J-C.G; Vecharsky, Bünzli (eds.). Accommodation of the Rare Earths in the Periodic Table: A Historical Analysis. Vol. 41. Amsterdam: Elsevier. pp. 1–94. doi:10.1016/B978-0-444-53590-0.00001-7. ISBN 978-0-444-53590-0. {{cite book}}: |journal= ignored (help)
  2. ^ a b c d e f g h i j k William B. Jensen (1982). "The Positions of Lanthanum (Actinium) and Lutetium (Lawrencium) in the Periodic Table". J. Chem. Educ. 59 (8): 634–636. Bibcode:1982JChEd..59..634J. doi:10.1021/ed059p634.
  3. ^ Matthias
  4. ^ a b c d Jensen, William B. (2015). "The positions of lanthanum (actinium) and lutetium (lawrencium) in the periodic table: an update". Foundations of Chemistry. 17: 23–31. doi:10.1007/s10698-015-9216-1. S2CID 98624395. Archived from the original on 30 January 2021. Retrieved 28 January 2021.
  5. ^ a b c d Scerri, pp. 392−401, 413
  6. ^ a b "The constitution of group 3 of the periodic table". IUPAC. 2015. Archived from the original on 5 July 2016. Retrieved 30 July 2016.
  7. ^ B. Smith Hopkins: "Chemistry of the rarer elements", D. C. Heath & Company, 1923.
  8. ^ a b Holden, Norman E. (1985). "Status of the Lanthanides and Actinides in the Periodic Table" (PDF). iaea.org. Retrieved 8 November 2022.
  9. ^ a b http://web.archive.org/web/20201222124218/http://www.che.uc.edu/jensen/W.%20B.%20Jensen/Reprints/251.%20Lawrencium.pdf
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  11. ^ https://pubs.acs.org/doi/pdf/10.1021/ed085p1491.2
  12. ^ a b c d e Scerri, Eric (18 January 2021). "Provisional Report on Discussions on Group 3 of the Periodic Table" (PDF). Chemistry International. 43 (1): 31–34. doi:10.1515/ci-2021-0115. S2CID 231694898. Archived (PDF) from the original on 13 April 2021. Retrieved 9 April 2021.
  13. ^ Luder
  14. ^ a b c Johnson, David (1984). The Periodic Law (PDF). London: Educational Techniques Group, Royal Society of Chemistry. p. 54. ISBN 0-85186-428-7.
  15. ^ Dash
  16. ^ Lavelle
  17. ^ a b c Jensen, William B. (2009). "Misapplying the Periodic Law" (PDF). Journal of Chemical Education. 86 (10): 1186. Bibcode:2009JChEd..86.1186J. doi:10.1021/ed086p1186. Retrieved 16 May 2020.
  18. ^ L. D. Landau, E. M. Lifshitz (1958). Quantum Mechanics: Non-Relativistic Theory. Vol. 3 (1st ed.). Pergamon Press. pp. 256–7.
  19. ^ a b c Scerri, Eric (2019). "Looking Backwards and Forwards at the Development of the Periodic Table". Chemistry International. 41 (1): 16–20. doi:10.1515/ci-2019-0104. Retrieved 8 November 2022.
  20. ^ Hamilton, David C. (1965). "Position of Lanthanum in the Periodic Table". American Journal of Physics. 33: 637–640. doi:10.1119/1.1972042.
  21. ^ Scerri, Eric (2016). "The Changing Views of a Philosopher of Chemistry on the Question of Reduction". In Scerri, Eric; Fisher, Grant (eds.). Essays in the Philosophy of Chemistry. Oxford University Press.
  22. ^ a b c Jørgensen, Christian K. (1988). "Influence of rare earths on chemical understanding and classification". Handbook on the Physics and Chemistry of Rare Earths. Vol. 11. pp. 197–292. doi:10.1016/S0168-1273(88)11007-6. ISBN 9780444870803.
  23. ^ a b Schwarz, W. H. Eugen (2010). "The Full Story of the Electron Configurations of the Transition Elements". Journal of Chemical Education. 87 (4): 444–8. Bibcode:2010JChEd..87..444S. doi:10.1021/ed8001286.
  24. ^ https://pubs.acs.org/doi/pdf/10.1021/ed800124m
  25. ^ doi:10.1002/anie.197300121
  26. ^ Wittig, Jörg (1973). "The pressure variable in solid state physics: What about 4f-band superconductors?". In H. J. Queisser (ed.). Festkörper Probleme: Plenary Lectures of the Divisions Semiconductor Physics, Surface Physics, Low Temperature Physics, High Polymers, Thermodynamics and Statistical Mechanics, of the German Physical Society, Münster, March 19–24, 1973. Berlin, Heidelberg: Springer. pp. 375–396. doi:10.1007/BFb0108579. ISBN 978-3-528-08019-8.
  27. ^ Gschneidner Jr., K. A. (December 1971). "On the nature of 4ƒ bonding in the lanthanide elements and their compounds". Journal of the Less Common Metals. 25 (4): 405–422. doi:10.1016/0022-5088(71)90184-6.
  28. ^ a b Scerri, Eric (2009). "Which Elements Belong in Group 3?". Journal of Chemical Education. 86 (10): 1188. Bibcode:2009JChEd..86.1188S. doi:10.1021/ed086p1188.
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  35. ^ Leigh, G. Jeffery (2009). "Periodic Tables and IUPAC". Chemistry International. 31 (1): 4–6. doi:10.1515/ci.2009.31.1.4. Retrieved 8 November 2022.
  36. ^ a b Scerri, Eric (2012). "Mendeleev's Periodic Table Is Finally Completed and What To Do about Group 3?". Chemistry International. 34 (4): 28–31. doi:10.1515/ci.2012.34.4.28. Retrieved 8 November 2022.
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