8
THE LANTHANIDE CONTRACTION AS A TEACHING AID' R. N. KELLER University of Michigan, Ann Arbor, Michigan
ATBEST only a minute fraction of the enormous bulk of recorded chemical facts can be grasped and retained by any individual. Perhaps because of this limitation, a natural tendency among chemists has been to search for means of organizing and classifyingthese facts. One of the most popular devices for this purpose is the periodic table. The remarkable success of this table stems from the fact that it emphasizes the interplay of two fundamental properties of the atoms-size and electronic structure. The qualitative similarities of the elements in the familiar "families" or groups of the periodic table result predominantly from similarities in the outermost electronic stmctures of their atoms, while the variations within a family arise mainly from differences in the sizes of the atoms. In comparing properties of ions, an additional important factor-the charge-must be considered. Qualitative similarities
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in chemical properties may be anticipated, then, among atoms when their sizes and outermost electronic structures are similar, and among ions when their sizes, outermost electronic structures, and charges are similar. We shall examine in some detail the variations in properties accompanying variations in atomic and ionic sizes, particularly in that porhion of the periodic table in which the lanthanide rare earths occur. ATOMIC VOLUMES
A favorite method for graphically depicting the variations in size of the atoms of the elements involves plotting atomic volume as a function of atomic number. In this way the familiar atomic volume curve (Figure 1). is obtained. The term "atomic volume" is ordinarily understood to mean the volume in cubic centimeters occupied by one gram atomic weight of the element in the solid state. It is calculated from the formula,
at the 118th Meeting of the American Chemical Sarietv in Chicago, Illinois, Eeptemher 4, 1950.
F i g 1.
Atomic Volume Cur..
312
Atomic volume =
atomic weight density
THE PERIODIC T A B L E O F THE ELEMENTS
*
LANTHANIDE RARE EARTHS
L*
ACTINIDE RARE EARTHS
58
59
60
90
91
92
61
62
63
64
65
66
67
68
69
70
71
Ce Pr Nd Prn Sm EU Gd T b Dy HO Er Tm Yb LU 93
94
95
96
97
96
Th Pa U Np Pu Am Crn Bk Cf
Inasmuch as all gram atomic weights contain the same number of atoms, atomic volumes can be used as qualitative guides to the relative volumes of the individual atoms. An atomic volume curve is at best, however, only an approximation (1). In calculating atomic volumes no allowances are ordinarily made for differences in crystal structures of the solids, variations of the atomic volumes with temperature, differences in atomic aggregation of the elements in the solid state, etc.% Notwithstanding the above inherent deficiencies, the atomic volume curve bears a number of interesting features ($), some of which are cited beloa. 4 Data for the curve in Figure 1 were obtained from the literature or calculated from the best available values for densities. Dotted lines a n used where no values are available as s t Tc and Pm. No values for hydrogen and helium are platted. Calculations of atomic volumes for the rare earths from densities and atomic weights give abnarmdly luge values for Eu and Yb. Since there are no corresponding irregularities in ionic radii a t these points for the tripositive ions of the ntre earths, t h e n is some question as to whether the atomic volumes for Eu and Yb are meaningful as guides to relative atomic sizes. These values m y be merely reflecting the fact that Eu and Yh crystallize in the cubic system as distinct from all the other rare earth metals which crystallize in the hexagonal system (3). Because of this uncertainty and in order not to detract fram the more important over-all trend within the family, the value8 for Eu and Yb are omitted irom the curve.
(1) The periodic relationship between atomic volume and atomic number is strikingly shown. (2) The alkali metals, with extraordinarily large volumes, occupy the maximum points of the curves while elements near the middle of both the short and long periods of the ordinary periodic table (Figure 2) have relatively small volumes and occupy the troughs of the U-shaped curves. (3) The gaseous, volatile, or easily fusible elements lie a t the peaks or on the rising portions of the U-shaped curves, whereas the nonvolatile or difficultly fusible elements lie either in the troughs or on the descending portions of the curves. (4) In atomic volume, as in most other properties, there appears to be less variation from element to element among the transition metals (Sc to Cu, Y to Ag, and La, Hf to Au) than there is between elements outside these groups. (5) The addition of one s electron on top of an inert gas structure results in a marked increase in volume (alkali metals). (6) The addition of a second s electron, however, results in a marked decrease in volume (alkaline earth metals). (7) The filling of a p subshell in the long periods results in a steady increase in atomic volume (cf. Cu to Kr,
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Ag to Xe, and Au to Rn). Except for a slight irregularity in the first period, the same general tendency appears in both short periods. (8) Filling a d subshell (transition elements) results in general in a decrease in volume until the subshell is filled or almost filled. (9) Filling an f suhshell (rare earths) likewise results in a decrease in atomic volume. The above facts and trends are significant in interpreting, correlating, and predicting properties of the elements. Unfortunately, it is not. easy to transfer the information contained in the curve as drawn in Figure 1 to a family or group basis. To be sure, elements of a given family occupy approximately correspondmg positions on the curves and a decided trend can be readily followed. For example, it is quite apparent from Figure 1 that the atomic volumes or sizes of the atoms of the alkali family increase from lithium to cesium. However, it is much less obvious as to what has happened in the case of vanadium, niobium, and tantalum. In Figure 3 the atomic volumes for the three long periods are plotted in such a manner that the familiar families or groups of the periodic table are preserved, with one obvious difference--that most of them are inverted. The individual values for the rare earth elements are omitted but the range in atomic volumes covered by the entire family is indicated between lanthanum and hafnium. It is clear, when the data are plotted in this fashion, that the decrease in atomic volume of the rare earths results in the elements of the third long period being practically superimposed upon those of the second, starting with the elements zirconium and hafnium and continuing as far as silver and gold. The diminution in volume which begins with lanthanum and continues through the rare earths has become known as the "lanthanide contraction" (2, 7, 8, 9). This contraction appears to be related to the fact that the successive electrons which are being added from cerium to lutetium are not added to a new external shell, well shielded from the nucleus, but to an inner shell which previously had been only partially filled. Thus, with an ever-increasing charge on the nucleus from 58 to 71 but with no compensating increase in the distance from the nucleus of the entering electrons, the whole electronic system shrinks.' This same phenomenon is evidently occurring also in the building UD of the transition elements (see Firmres 1 and 3)- The dotted line in Figure 3 represents a hypothetical atomic volume curve for the elements of the third long period on the assumption that no rare earths intervene beween lanthanum and hafnium and the general shape of the curve approximates that of the other long periods. If this were the actual situation, a more or less uniform variation in properties should he expected between any two successive members of a eiven familv. However.
-
An analogous effect hss been reported recently (10) in the actinide series of rare earths from Ac (atomic number 89) t o Am (atomic number 95).
as a result of the lanthanide contraction it will not be surprising to find irregularities or actual reversals of trends within a post-rare-earth family between the elements of the second and third long periods. Tables 1, 2, 3, and 4 give the trends for several properties of blocks of elements, some of which precede and some of which follow the rare earths in the periodic table. TRENDS IN PROPERTIES
In Tahle 1 a section of the long form of the periodic Tahle (Figure 2) is reproduced with the values for the atomic volumes of the elements indicated. Between lanthanum and hafnium, of course, the fourteen rare TABLE 1 Atomic Volumes (cc. per gram atom)
Ba 39
La 22.6
Hf -14
Ta 10.9
W 9.5
earth elements are omitted. ks already indicated graphically in Figure 3, the atomic volumes of the elements in the first two columns of Table 1 increase going downward. This trend is interrupted in the next column a t zirconium and hafnium, whose atomic volumes are practically identical within experimental error, and may be actually reversed a t niobium and tantalum. At any rate, it is clear that the atomic volumes of niobium and tantalum and of molybdenum and wolfram are quite similar. Tahle 2 includes the same group of elements as in Table 1and lists the values for their respective densities (11, 18). The most striking feature of this table is the extraordinarily large values for hafnium, tantalum, and wolfram-that is, for those elements following the rare earths. This is to be expected, of course, in view of the close similarity in atomic volumes of these elements TABLE 2 Densities (s.per cc.)
Ba. 3.5
La
Hf
6.1
12.8
Ta 16.6
W 19.3
and those directly above them. From the formula for atomic volume it follows that if two elements have similar values for their atomic volumes the one with the greater atomic weight must also have the greater density. The difference in atomic weights between zirconium and hafnium, for instance, is approximately 87 yet they have almost identical atomic volumes. In Tahle 3 approximate values are given for the apparent ionic radii (13, 14, 15, 16) of the ions of these same elements for the highest charge characteristic of their respective groups. Again, the effect of the lan-
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315
thanide contraction on the trends in ionic sizes is obvi-
TABLE 3 Ionic Radii (Angstrom units)
OUS.
Selected families of elements, some preceding and some following the rare earths, are listed in Table 4 along with the values for their first ionization potentials (11). The table reveals that the maximum value for this property is reached with the first member of the families preceding the rare earths whereas for families not too far removed from the rare earths the exact reverse appears to be the case.
Cs+z l,o s,+r
1.1 Ba+' 1.3
So+= 0.8 Y+a 1.0
La+" 1.2
Tit4 0.65 Zr+*
0.8 Hf +' (0.8)
Cr* 0.5 Mo+' 0.62
V+6
0.6 Nb +s 0.7 Ta+& 0.72
W +'
0.65
ferences. It would not seem at all unreasonable to postulate, for example, that aa the result of this omission CHEMICAL CONSEQUENCES the atomic volume of hafnium should be larger than that A number of the outstanding chemical consequences of lanthanum and much larger than that of zirconium. of the lanthanide contraction can now be summarized. That this is not the case has already been pointed out in Nonuniform and Reversed Trends in Post-Rare- connection with Table 1. i n the event of either a "lanthanide contraction" or a Earth Families. In an examination of the properties of the elements in the preceding tables, it is not surprising "lanthanide expansion," the trends in properties of that decided differences apTABLE 4 pear between the elements ' on either side of the rare First Ionization Potentials (electron volts) earths. Dropping out 14 Ca Sc As Gs. Ge Cr Fe Ni Cu Zn elements between lantha- 4.32 6.09 6.7 6.74 7.83 7.61 7.68 9.36 5.97 8.09 10.5 num andhafniumcanhardly ~b sr Y Mo RU ~d Ag Cd In Sn Sb pass unnoticed. What is 4.16 5.67 6.5 7.2 (7.7) 8.3 7.54 8.96 5.76 7.30 8.35 TI Pb Bi somewhat surprising, is the B& La W 0s Pt Au Hg 3.87 5.19 5.59 8.1 8.7 8.88 9.19 10.38 6.07 7.38 7.25 specific nature of these dif-
5
I Atomic Number Units (arbitrary scale) Fi-e
3.
Atomic Volume C u m Showing Qrovp Rdationship. among tha Long P d o d UemenU
316
families containing an element following the rare earths are likely to he markedly different from the trends for those families all members of which precede the rare earths. This is clearly indicated for the atomic volumes in Tahle 1, densities of the solid elements in Table 2, and ionic radii of similarly charged ions in Tahle 3. Ionization potentials are related to the tightness with which outermost electrons are held by atoms and are therefore important chemically. The first ionization potential refers to the energy necessary to remove the most loosely bound electron from the gaseous atom. There is, of course, no chemical equivalent of this reaction hut nonetheless the energy involved is significant in interpreting properties of atoms. For the families preceding the rare earths the usual trend is decreasing ionization potential with increasing atomic numher (Tahle 4). This is one of the factors which, for example, is responsible for the increase in chemical activity and basicity (4, 18) of these elements going downward in the families. Unfortunately, reliable values for ionization potentials are not available for all the elements of families following the rare earths. From the data of Tahle 4, less well-defined trends seem the rule among these elements, yet at the same time unexpectedly large values are uniformly indicated for those elements in the third long period which follow the rare earths. Indeed, these values exceed even those for the first members of the respective families. This is one of the reasons, for example, why gold is the most noble of the copper group elements instead of the most active. The enhanced values for the ionization potentials for the elements of the third long period may be qualitatively associated with the fact that the atomic sizes of the corresponding elements in the second and third long periods are approximately the same (Figure 3) whereas the nuclear charges of the latter are very much greater (Figure 2). This effect seems to be clearly marked as far removed from the rare earths as the gallium-indiumthallium family of elements. Lead, in the next family, has a value greater than tin but less than germanium, the first member of the family. In the arsenic-antimony-bismuth family, the "normal" trend returns. Decreasing Basicity of the Rare Earths with Increasing Atomic Number. The usual trend among atoms which are electronically similar is an increase in basicity (4, 18) with an increase in atomic number. For example, cesium is more basic than lithium and iodine is more basic than fluorine. This trend results because with increasing atomic number there is normally an increase in atomic or ionic size. However, in the rare earth series this trend is completely reversed, lanthanum being t,hemost basic instead of the least as might he supposed. In fact, La(OH)d appears to he one of the strongest hydroxides of any.trivalent metal. Due30 the regular decrease in ionic size from La+S (-1.2 A,) to L U + ~(-1.0 A,), an increase in atomic number among these elements is accompanied by a uniform decrease in basicity (.5). The slight difference in basicity between successive rare earth elements is the basis for a numher of procedures for separating t,hem (6, $0).
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Chemical Resemblance oj Hajnium to Zirconium. It is a remarkable fact that zirconium and hafnium, differing in atomic weight by 87 units, are so alike chemically that their separation has taxed the ingenuity of analytical chemists for years ($9). This unexpected likeness becomes understandable when the role of the lanthanide contraction is considered (93). Chemical reactions of atoms and ions depend to only a slight degree on their masses hut to a high degree on their electronic make-up and charge. Zirconium and hafnium, which are in the same group in the periodic table, have similar external electronic configurations and, due to the lanthanide contraction, their atoms and tetrapositive ions are almost identical in size. Thus, the conditions which favor similarity have been conferred accidentally upon these two elements to a degree not found between any other pair in one family but in different periods of the periodic table. Similarities between Other Pairs oj Elements. Pronounced similarities between the corresponding elements of the second and third long periods of the periodic table are in no wise limited to zirconium and hafnium. The effect of the lanthanide contraction is projected well beyond these elements, so much so in fact that it is common practice among textbook writers and teachers to consider niobium and tantalum in Group V and molybdenum and wolfram in Group V1 as "natural" pairs. Presumably the same relationship should exist between technetium and rhenium. The striking resemblances of ruthenium to osmium. rhodium to iridium, and palladium to platinum are undoubtedly associated with this same phenomenon. The horizontal or series relationships in the transition elements appear to reach their culmination in the triads of Group VIII. As a result of the combined effect of the similarities in a horizontal direction among the Group VIII elements and the similarities in a perpendicular direction arising as a result of the lanthanide contraction, these six so-called platinum metals are usually treated as one group of closely related elements. The similarity of iron, cobalt, and nickel to the corresponding elements in the second long period is distinctly less than that hetween the latter elements and their analogues in the third long period. While silver and gold resemble one another more than either resembles copper, in general the effect of the lanthanide contraction on the properties of the elements beyond the transition elements is less tangible. There is some evidence, however, that this phenomenon may be exerting a subtle influence on the properties of elements as far removed as francium ($4). Rare-Earthlike Properties of Seandium and Yttrium. Scandium and yttrium are not, in the strict sense, rare earths yet these elements occur in a number of rare earth minerals and both, notably yttrium, go along with the rare earths in many analytical procedures. In fact, one of the common groups into which the rare earths are frequently divided for convenience is known as the yttrium-group (6). An insight into this apparent anomaly can be obtained by reference to Figure 3.
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317
The diminution in atomic volume of the rare earths LITERATURE CITED with increasing atomic number is such that the atomic (1) EPIIRAIM,F. "A Textbook of Inorganic Chemistry,"Sth ed., volume of yttrium is reached near holmium, as indicated Interscience Publishers, Inc., New York, 1948, p. 33. (2) Ibid., pp. 435-7. by the dotted line drawn through the value for yttrium. D.M., H. RUSSELL,Jr., m~ C. S. GARNEB,"The However, the smaller volume of scandium is not quite (3) YOST, Flare-earth Elements and Their Compounds," John Wiley attained even by the heaviest rare earth. The com& Sons, Inc., New York, 1947,p. 52. bination of effects among these elements results in the (4) Ibid., p. 57. (5) Ibid., p. 58. following interesting order of decreasing ionic size for the tri-positive ions and decreasing basicity for the GOLDSCHMIDT, V. IM., Z. Elekt7-ochern., 34, 453-63 (1928); group (19, 25): La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Trans. Faraday Soe., 25, 25343 (1929). Y, Ho, Er, Tm, Yb, Lu, Sc. In view of this it is perVON HEVESY,G., "Die Seltenen Erden vom Standpunkte haps less surprising to find yttrium concentrating with des Atombauees," Julius Springer, Berlin, 1927, pp. 22, 27; Z. anorg. allgem. Chern., 147, 217-32 (1925). holmium, and scandium concentrating with the heaviest CLARK, C. H. D., "The Electronic Structure and Properties rare earths during many fractionation procedures inof Matter," John Wiley & Sans, Inc., New York, 1934,pp. volving these elements (21). This latter fact is difficult 169-70. t,o explain on any other basis inasmuch as scandium, ZACHARIASEN, W. H., Chem. Eng. N e w , 28, 1563 (1950). LANGE,N. A,, "Handbook of Chemistry," 7th ed., Hand the lightest of the Group Ill transition elements, rebook Publishers, Inc., Smdusky, Ohio, 1949, pp. 118-23. sembles not the rare earths nearest to it in atomic Ibid., pp. 116-7. weight but rather those ~vhoseatomic weights are most HODGMAN, C. D. (Ed.), "Handbook of Chemistry and remote. Physics," 31st ed., Chemical Rubber Publishing Co., DU. 1711-3. Cleveland. Ohio. 1949.... CONCLUSION The chemical implications of the decreasing atomic volume and decreasing ionic size which occur in the lanthanide series of rare earth elements have been adequat,ely discussed in original journal articles but the potentialities of this phenomenon as a teaching device appear t.o have been largely overlooked by most textbook writers and teachers. Presented in this paper is a modified form of the atomic volume curve which illustrates graphically the effect of the so-called lanthanide contraction. Also a number of the chemical consequences of this effect are discussed. The author believes that many of the seeming anomalies of the periodic table become explicable when considered in the light of the factors which cont,ribute to similarities or dissimilarities in chemical properties among the elements.
(14) rbid., pp. 2680-2. L., "The Nature of the Chemical Bond," 2nd ed. (15) PAULING, Cornell University Press, Ithaci~,N. Y., 1940,p., 346. (16) RICE,0. K., "Electronic Structure and Chemical Bmding," McGraw-Hill Co.. Inc., New York. 1940, 0.220. (17) Ibid... u. . 96. j18) MOELLER, T., AND H. E. KREMERS, Chern. Rw., 37,98 (l!I&). (19) Ibid., p. 102. (20) HOPKINS,B. S., "Chapters in the Chemistry of the Less Familiar Elements," Stipes Publishing Co., Champaign, Ill., 1938, Chap. 6,pp. 11, 13. (21) Ibid., p. 18. (22) VON HEVESY,G., "D&EElement Hafnium," Julius Springer, Berlin. 1927,. u. . 42. (23) Ibid., p. 45. (24) FINKELNBURG, W.,Z.Naturjorsch., 2a, 16-20(1947); Chenc. Abstracts, 41,6785f (1947). (25) VON HEVESY,G., "Chemical Analysis by X-rays and Its Amlications." MrGrm-Hill Book Co.. Ine.. Nea York.
