THE LANTHANIDE CONTRACTION
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BODIE E. DOUGLAS The University of Pittsburgh, Pittsburgh, Pennsylvania
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transition series and can probably be attributed t o differences in structure and in the number of valence electrons available for bonding. There is an appreciable increase in the atomic radii of europium and ytterbium in comparison to the preceding elements while no increase is observed for the corresponding trivalent ions. The size increase in the case of the free metals is attributed to the presence of dipositive ions giving only two valence electrons for metallic bonding instead of the three usually encountered for lanthanide metals. The structures of these two metals also differ from the hexagonal, closely packed structure encountered for most of the lanthanide metals.' Europium and ytterbium might be expected to give only two valence electrons because of the stability of half-filled and filled f orbitals which would be achieved in these instances. Compounds of europium(I1) and ytterbium(I1) are well characterized. The decrease in size within a period is not always consistent, hut there are some regularities which are significant. The decrease in size within a period is greatest between the alkali and alkaline earth metals and less for the other representative elements. The differences in size become smaller toward the ends of the periods. The size decrease is small within the transition series, again becoming smaller toward the ends of t,he series. The smallest decrease to be found in any series of more than a few elements is to be found in the inner transition series. Thus, the decrease in size is most pronounced as s electrons are added to a shell, and becomes progressively smaller for p, d, and j electrons. This is the order of decreasing "penetration" of the respective orbits. Although the contraction from one element to the next in the lanthanide series is very small, the effects are very pronounced since it extends through 15 elements in the same family of the periodic table. As a direct result of the lanthanide contraction the atomic radius of hafnium is slightly smaller than the radius of zirconium. The lanthanide contraction continues t o affect the sine and properties of the elements beyond hafnium, but to a diminishing extent for each successive element. Another very striking result of the lanthanide contraction is the fact that yttrium is intermediate in size between dysprosium and holmium and is difficult to separate from these elements. However, the nuRare Earth Elements and Their Compounds," John Wiley & clear charge has to be increased by nine units before Sons, Ino., New York, 1947,p. 53. 2 MOELLER, T.,!'Inorgamo Chemistry," John Wiley & Sons, the size of one of the lanthanides is reduced t o approxi-
consequences of the change in size in the lanthanide series are well known and the discussions of the effects of the lanthanide contraction in most reference sources are quite adequate. However, the discussions of the nature and magnitude of the lanthanide coutraction itself and its relationship to size changes in the periodic table as a whole are usually misleading to the student. The contraction is commonly explained simply as the result of increased nuclear charge' or as the result of increased nuclear charge without compensation for it through alteration of the outer arrangement of electron^.^ While such statements are not in error, the fist does not indicate the magnitude of the contractiou and the second misleads the student through the implication that the contraction would be smaller if the outer arrangement of electrons were altered. The contraction in the lanthanide series is smaller than that encountered in any extended group of elements in any period of the periodic table, with the exception of the actinide series, where the contraction would be expected to be comparable. Graduate students in my own classes have been asked t o study the information available and then write a discussion of the lanthanide contract,ion in their own words. This has usually resulted in statemeuts which were not merely misleading, but erroneous. With only two exceptions the sizes of atoms3 increase with increasing atomic number within a family, since a new shell is added for each succeeding period. I n a given period the size of the atoms generally decreases with increasing nuclear charge, since no new shells are introduced. The inert gas atoms appear to he striking exceptions t o the general shrinkage within a period. The atomic radius of each of the inert gases is considerably larger than that of the preceding halogen. The increase in size is sometimes attributed to the mutual repulsion of electrons in a closed shell, but the atomic radii of the inert gases are really nonhonded van der Waals radidii. If compared to the van der Waals radii for the other nonmetals there is a regular decrease through the period including the inert gases. There are a few other instances of small increases in size through a period. Most of these occur for metals at the ends of the transition series or just following the I YOST, D. M., H . RUSSELL, JR., A N D C. S. GARNER, "The
Inc., New York, 1952, p. 146. 4 H~~CKE UT., L , ' ' S t ~ u ~ t u ~Chemistry al of Inorganic ComThe atomic, ionic, covalent, and van der Wads radii referred to in the following discussion are those summarized from various pounds," translated by L. H. Long, Elnevier Publishing Co., Inc., New York, 1950, p. 214. sources by Moeller; see Ref. 2, Chap. 5. 598
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mately that of yttrium. If we compare scandium and yttrium, the size difference is much greater than that between yttrium and lanthanum. I n spite of the great,erdifference in size between scandium and yttrium, only two unit,s need be added to the nuclear charge of yttrium to give an atom (Nb) considerably smaller than scandium if the electrons added are d instead of f electrons. The pronounced contraction in a transition series causes the only other instance of a decrease in size with increasing atomic number in a family. The covalent radius of gallium is slightly smaller than that of
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aluminum although there are only ten elements between ralcium and gallium, representing the filling of the Sd orbitals. The size change in the lanthanide series is very small, but the differences i n chemical properties, although slight, are enhanced by the relatively high charge on the ions. For the same size difference the differences in chemical properties are greater for tripositive ions than for ions of lower charge. The relative differences can be seen by comparing values of ionic potentials (charge/size) for the same size differenre hut different charges.
