Periodic Table, The: Past, Present, And Future
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Chapter 11
Isodiagonality
Diagonal relationships in the Periodic Table were recognized by both Mendeléev and Newlands. More appropriately called isodiagonal relationships, the same three examples of lithium with magnesium; beryllium with aluminum; and boron with silicon; are commonly quoted. Here these three pairs of elements are discussed in detail, together with evidence of isodiagonal linkages elsewhere in the Periodic Table.
Though the vertical groups and horizontal periods are emphasized as being the key relationships in the Periodic Table (see Chapters 7 and 8), chemistry historian Ihde has noted that both Mendeléev and Newlands had reported the diagonal similarities of lithium with magnesium; beryllium with aluminum; and boron with silicon; as early as 1860 [1].
Isodiagonality
It was in 1937 that French explored the diagonal relationship in detail. In fact, he considered diagonality to extend further down the Periodic Table [2]:
In chemical behavior, bismuth bears a much greater resemblance to silicon and boron than to nitrogen.
This diagram, from French’s article, was probably the first to illustrate the diagonal linkages (Figure 11.1).
Figure 11.1 French’s diagram of the isodiagonal linkages (from Ref. [2]).
Figure 11.2 The first three Periods of French’s slanting periodic table to illustrate group and diagonal linkages (adapted from Ref. [2] — note “A” was the former symbol for argon).
French was concerned that diagonality not be overemphasized, adding:
… silicon for instance, resembles neither carbon nor boron in chemical properties but might be said to lie between the two.
Thus, French suggested that the best mode of display of the “cross relationships” might be that shown in his “warped” Periodic Table in the following (Figure 11.2).
More recently, Rich proposed the term isodiagonal for species related on an upper-left to lower-right diagonal [3]. He subsequently authored a version of the Periodic Table to specifically emphasize isodiagonalities (Figure 11.3) [4].
Here the following definition of isodiagonal will be used:
An isodiagonal relationship is identified by similarity in chemical properties between an element and that to the lower right of it in the periodic table.
Isodiagonality is, in some ways, a general attribute of the properties of the chemical elements. For example, Edwards and Sienko commented that the metal–nonmetal divide forms an “almost diagonal demarcation” [5]. Similarly, the elements often considered to be semimetals fall on a roughly diagonal boundary between the metals and nonmetals, see Chapter 5 [6].
Figure 11.3 Rich’s version of the periodic table to emphasize isodiagonal relationships (from Ref. [4]).
A related phenomenon, the change in bonding type across Periods, similarly lies upon a diagonal [7]. The pattern is usually for a change from ionic (to the left) to small-molecule covalent (to the right) with a species that can be assigned as possessing network covalent bonding at the transition point. As was shown in Chapter 7, for 2nd Period and 3rd Period oxides, this intermediate bond type occurs with B2O3 and SiO2. For fluorides, the transition is displaced left by one group so that it occurs with BeF2 and AlF3, and similarly for hydrides with (BeH2)x and (AlH3)x.
Explanations for Isodiagonality
Cartledge, in 1928, was the first to suggest a possible explanation for isodiagonality [8]. He proposed that the phenomenon could be explained in terms of ionic potential, Z/r, what is now more commonly known as charge–radius ratio. The ionic potential was recalculated by Hanusa using Shannon–Prewitt ionic radii and these values correlated well with isodiagonal links for some pairs, but not others [9]. As an example, the ionic potential for Be2+ of 74 nm−1 is very close to the value of 77 nm−1 for Al3+. However, there is no match in the values for the pair of Li+ (17 nm−1) and Mg2+ (35 nm−1). The same ratio, but called polarizing power, was qualitatively used to explain isodiagonality by Puddephatt and Monaghan [10].
Lee provided a variety of explanations [11]. He first proposed polarizing power, then suggested radius similarities for the Li+–Mg2+ link; and charge per unit area to explain the Be2+–Al3+ link; but commented that electronegativity similarities was another possible explanation. Finally, in the context of the Be2+–Al3+ link, Lee stated:
Just as was the case with lithium and magnesium, the similarity in atomic and ionic sizes is the main factor underlying this relationship.
King also favored electronegativity as an explanation [12]. Housecroft and Sharpe, by contrast, proposed that isodiagonality could be explained in terms of similarities in ionic radius [13]. However, this contradicted Hanusa’s conclusions, as ion radius and ionic potential are reciprocal relationships.
Rayner-Canham and Overton found that charge density is a useful parameter for predicting ionic versus covalent behavior in simple binary compounds and that it could also account for the diagonal Li+–Mg2+ and Be2+–Al3+ links [1
4]. This term, charge density, dates back to at least the 1960s [15]. It is defined as:
The charge density of a real or hypothetical ion is defined as the ion charge divided by the ion volume.
In order to obtain numbers in meaningful units and, at the same time, avoid the need for enormous exponents, Rayner-Canham and Overton utilized the electron charge in Coulombs and the ionic radius in millimeters. Thus, for each real or theoretical ion, the integer ion charge was multiplied by the electron charge and divided by 4/3π times the ion volume to give values in C⋅mm−3.
Unfortunately, some sources confuse charge density with charge–radius ratio. For example, Rogers stated that charge density was defined as “charge on a metal cation over its ionic radius” [16]. This parameter is, in fact, correctly named charge–radius ratio.
Despite this confusion, Rogers provides one of the more comprehensive discussions of isodiagonality. He correlated the parameters of ionic radius, charge–radius ratio, and electronegativity for the Li–Mg, Be–Al, and B–Si pairs:
There appear to be three principal factors why these pairs — take beryllium and aluminum as a representative example — have so much chemistry in common. One factor is ionic size; the others are charge density (or charge-radius-ratio, Z/r) and electronegativity. … The two metal ions, then, will similarly polarize the X atom in an M−X bond and give rise to a similar additional covalent character on that basis.
He added the caveats:
First, keep in mind that group relationships (for example, between beryllium and magnesium) are still the dominant factor. … Second, the ions … particularly the highly charged B3+, C4+, and Si4+ really do not exist as such. … Nevertheless, even with these warnings, the diagonal relationship remains a good organizing principle.
Table 11.1 shows some of the parameters for these eight ions. The ionic radii in pm (Shannon–Prewitt), both for 4- and 6-coordination are from Ref. [17]; charge–radius ratio values are calculated from the Shannon–Prewitt ion radius values for 6-coordination (in nm−1); charge density values are from Ref. [14] (in C⋅mm−3); and Allred–Rochow electronegativity values are from Ref. [18].
It is difficult to attribute any one parameter as a ubiquitous explanation for all isodiagonal resemblances. This is not surprising, considering the Li–Mg pair are predominantly ionic in behavior while B–Si are totally covalent in their properties. In the following sections, individual pairs of elements will be compared and contrasted in terms of possible isodiagonal relationships.
Table 11.1 Parameter values for the early 2nd Period and 3rd Period elements
Isodiagonality of Lithium and Magnesium
Though lithium and magnesium are often taken as the prototypical isodiagonal pair, it more highlights the 2nd Period Anomaly: that the 2nd Period elements are uniquely different to the lower members of their group (see Chapter 7). As we see in the following, there are indeed specific similarities between lithium and magnesium, though on the basis of free energies of formation of compounds, Hanusa found a closer resemblance of lithium with calcium [9]. On the other hand, Greenwood and Earnshaw contended that magnesium is atypical of Group 2 (though beryllium is even more so) and that lithium does match well and uniquely with magnesium [19].
General Resemblance of Lithium to Group 2 Elements
First, there are resemblances between lithium and the Group 2 elements as a whole:
•Lithium does not form an isolatable hydrogen carbonate whereas solid hydrogen carbonate salts can be obtained for the other Group 1 metals. Solid hydrogen carbonates cannot be isolated for the Group 2 metals.
•Lithium salts tend to be hydrated (often as a trihydrate) whereas the salts of the other Group 1 elements tend to be anhydrous. Many Group 2 metal salts are hydrated.
•Three lithium salts — carbonate, phosphate, and fluoride — have very low solubility unlike the salts of the other Group 1 metals. These anions form insoluble salts with the Group 2 metals.
•Lithium is the only Group 1 metal to form a nitride, Li3N. The Group 2 metals all form nitrides.
All four of these properties can be attributed to the significant difference in ionic radius between the large “typical” Group 1 metals and the significantly smaller lithium ion (Table 11.1). For example, it is only the larger low-charge-density cations that can stabilize the large low-charge anions, such as hydrogen carbonate, in a crystal lattice. Lithium ion, being more the size of a Group 2 metal, cannot. Instead, formation of the higher lattice energy carbonate compound will be energetically preferred. The opposite argument can be used with the formation of ionic nitrides (and carbides, see in the following): that only a small higher charge-density cation can stabilize the high-charge anion.
Specific Resemblance of Lithium to Magnesium
The best examples of resemblance specifically between the chemistry of lithium and that of magnesium are
•The only tricarbides(4–), C34−, of the Group 1 and 2 elements are Li4C3 and Mg2C3.
•Many lithium salts exhibit a high degree of covalency in their bonding as do those of magnesium.
•Lithium forms organometallic compounds similar to those of magnesium.
•Lithium is believed to occupy the same receptor site as magnesium in the treatment of bipolar disorder [20].
As with the nitrides, the formation of tricarbides can be interpreted in terms of stabilization by higher charge-density cations. The covalent behavior can also be explained as a result of lithium and magnesium being higher charge-density cations than the other members of their respective group.
Mackinnon [21] has pointed out that some other claimed evidence for the diagonality of these two elements is fallacious. For example, heating lithium nitrate gives lithium nitrite and oxygen gas (like the other Group 1 elements), not lithium oxide, nitrogen dioxide, and oxygen (like the Group 2 elements), contrary to some sources.
Does Li–Mg Isodiagonality Extend to Scandium? . . . and Beyond?
Though diagonality has traditionally been considered a unique property of the early elements of the 2nd Period and 3rd Period, there have been suggestions that diagonality extends into subsequent periods (as will be discussed in the following). The first complete diagonal series is shown in Figure 11.4.
Figure 11.4 The first diagonal series.
As an example of isodiagonality extension, scandium, too, forms an insoluble fluoride, carbonate, and phosphate. Uniquely, scandium is the only other metal to form a carbide containing the tricarbide(4−) ion, though the compound, Sc3C4, also contains carbide(4−) and dicarbide(2−) ions within the same lattice structure. Also, in one of the few ores of scandium, jervisite, the same lattice site is occupied by scandium and magnesium: (Na,Ca,Fe(II)) (Sc,Mg,Fe(II))Si2O6.
Scandium, in turn, has a resemblance to zirconium and thence to tantalum. For example, scandium forms [Sc6Cl12]3– clusters, while zirconium and tantalum (and also niobium) form related [M6Cl12] cluster species.
Isodiagonality of Beryllium and Aluminum
The second pair to be examined here, that of beryllium and aluminum, has more common features unique to the diagonality. It is of relevance that, in the topological study of the chemical elements by Restrepo et al. [22], beryllium and aluminum were the only pair for which isodiagonal similarities exceed Group resemblances. This pair is the only diagonality example mentioned by House [23]. In addition to the other evidence that is widely cited, he refers to the two ions being particularly toxic — perhaps indicating a common biochemical bonding site.
Beryllium has a specific similarity to aluminum (and, to gallium) in terms of its aqueous (ionic) chemistry. Feinstein commented upon the similarities between the two elements in the context of analysis procedures. One example he gave was [24]:
… the spectrophotometric method for beryllium or aluminum using the ammonium salt of aurin tricarboxylic acid.
The similarity is particularly apparent when the Pourbaix (Eh–pH) diagrams [25] of the respective elements are compared (Table 11.2). The lower coord
ination number of the beryllium cation in acid solution may be explained as Be2+ being physically too small to accommodate six surrounding water molecules at a bonding distance.
In terms of compounds, there are several similarities:
•Beryllium and aluminum form carbides containing the carbide(4–), C4– ion, both Be2C and Al4C3 reacting with water to producing methane.
Table 11.2 A comparison of aqueous beryllium and aluminum species
•They form dimeric chlorides containing pairs of chlorine bridging atoms: ClBeCl2BeCl and Cl2AlCl2AlCl2.
•The two elements form methyl organometallics, Be(CH3)2 and Al(CH3)3, with bridging CH3 groups. Both compounds are spontaneously flammable in air and are explosively hydrolyzed by water.
Does Be–Al Isodiagonality Extend to Germanium? . . . or to Titanium?
Roesky [26] has suggested that the diagonal relationship in this series continues to germanium. This proposal came as a result of his work on organometallic compounds of aluminum and attempts to synthesize germanium analogs.
However, Habashi [27] has pointed out that the chemistry of the aluminum ion more resembles that of the Group 3 elements rather than that of the lower members of Group 13 (see Chapter 9). Following from this proposal, the next member of the diagonal series should be considered as titanium. Titanium, like aluminum, is a low-density metal that reacts with the oxygen in air to form a tenacious protective layer of oxide to prevent further corrosion. One example of chemical similarities is that, for both aluminum and titanium, the fluorides are hexacoordinate species while the other halides are low-melting tetrahedrally coordinated species, such as Al2Cl6 and TiCl4, which are hydrolyzed by water. The second complete diagonal series is shown in Figure 11.5.