Lanthanide contraction

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The lanthanide contraction is the greater-than-expected decrease in ionic radii of the elements in the lanthanide series from atomic number 57, lanthanum, to 71, lutetium, which results in smaller than otherwise expected ionic radii for the subsequent elements starting with 72, hafnium.[1][2][3] The term was coined by the Norwegian geochemist Victor Goldschmidt in his series "Geochemische Verteilungsgesetze der Elemente".[4]

Element La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
Atomic electron configuration
(all begin with [Xe])
5d16s2 4f15d16s2 4f36s2 4f46s2 4f56s2 4f66s2 4f76s2 4f75d16s2 4f96s2 4f106s2 4f116s2 4f126s2 4f136s2 4f146s2 4f145d16s2
Ln3+ electron configuration 4f0 4f1 4f2 4f3 4f4 4f5 4f6 4f7 4f8 4f9 4f10 4f11 4f12 4f13


Ln3+ radius (pm) (6-coordinate) 103 102 99 98.3 97 95.8 94.7 93.8 92.3 91.2 90.1 89 88 86.8 86.1


The effect results from poor shielding of nuclear charge (nuclear attractive force on electrons) by 4f electrons; the 6s electrons are drawn towards the nucleus, thus resulting in a smaller atomic radius.

In single-electron atoms, the average separation of an electron from the nucleus is determined by the subshell it belongs to, and decreases with increasing charge on the nucleus; this in turn leads to a decrease in atomic radius. In multi-electron atoms, the decrease in radius brought about by an increase in nuclear charge is partially offset by increasing electrostatic repulsion among electrons. In particular, a "shielding effect" operates: i.e., as electrons are added in outer shells, electrons already present shield the outer electrons from nuclear charge, making them experience a lower effective charge on the nucleus. The shielding effect exerted by the inner electrons decreases in the order s > p > d > f. Usually, as a particular subshell is filled in a period, atomic radius decreases. This effect is particularly pronounced in the case of lanthanides, as the 4f subshell which is filled across these elements is not very effective at shielding the outer shell (n=5 and n=6) electrons. Thus the shielding effect is less able to counter the decrease in radius caused by increasing nuclear charge. This leads to "lanthanide contraction". The ionic radius drops from 103 pm for lanthanum(III) to 86.1 pm for lutetium(III).

About 10% of the lanthanide contraction has been attributed to relativistic effects.[5]


The results of the increased attraction of the outer shell electrons across the lanthanide period may be divided into effects on the lanthanide series itself including the decrease in ionic radii, and influences on the following or post-lanthanide elements.

Properties of the lanthanides[edit]

The ionic radii of the lanthanides decrease from 103 pm (La3+) to 86 pm (Lu3+) in the lanthanide series.

Across the lanthanide series, electrons are added to the 4f shell. This first f shell is inside the full 5s and 5p shells (as well as the 6s shell in the neutral atom); the 4f shell is well-localized near the atomic nucleus and has little effect on chemical bonding. The decrease in atomic and ionic radii does affect their chemistry, however. Without the lanthanide contraction, a chemical separation of lanthanides would be extremely difficult. However, this contraction makes the chemical separation of period 5 and period 6 transition metals of the same group rather difficult.

There is a general trend of increasing Vickers hardness, Brinell hardness, density and melting point from lanthanum to lutetium (with europium and ytterbium being the most notable exceptions; in the metallic state, they are divalent rather than trivalent). Lutetium is the hardest and densest lanthanide and has the highest melting point.

Element Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium
Vickers hardness (MPa) 491 270 400 343 ? 412 167 570 863 540 481 589 520 206 1160
Brinell hardness (MPa) 363 412 481 265 ? 441 ? ? 677 500 746 814 471 343 893
Density (g/cm.3) 6.162 6.770 6.77 7.01 7.26 7.52 5.264 7.90 8.23 8.540 8.79 9.066 9.32 6.90 9.841
Melting point (K) 1193 1068 1208 1297 1315 1345 1099 1585 1629 1680 1734 1802 1818 1097 1925
Atomic radius (pm) 187 181.8 182 181 183 180 180 180 177 178 176 176 176 176 174

Influence on the post-lanthanides[edit]

The elements following the lanthanides in the periodic table are influenced by the lanthanide contraction. The radii of the period-6 transition metals are smaller than would be expected if there were no lanthanides, and are in fact very similar to the radii of the period-5 transition metals, since the effect of the additional electron shell is almost entirely offset by the lanthanide contraction.[2]

For example, the atomic radius of the metal zirconium, Zr, (a period-5 transition element) is 159 pm and that of hafnium, Hf, (the corresponding period-6 element) is 156 pm. The ionic radius of Zr4+ is 79 pm and that of Hf4+ is 78 pm. The radii are very similar even though the number of electrons increases from 40 to 72 and the atomic mass increases from 91.22 to 178.49 g/mol. The increase in mass and the unchanged radii lead to a steep increase in density from 6.51 to 13.35 g/cm3.

Zirconium and hafnium therefore have very similar chemical behaviour, having closely similar radii and electron configurations. Radius-dependent properties such as lattice energies, solvation energies, and stability constants of complexes are also similar.[1] Because of this similarity hafnium is found only in association with zirconium, which is much more abundant, and was discovered as a separate element 134 years later (in 1923) than zirconium (discovered in 1789). Titanium, on the other hand, is in the same group but differs enough from those two metals that it is seldom found with them.

See also[edit]


  1. ^ a b Housecroft, C. E.; Sharpe, A. G. (2004). Inorganic Chemistry (2nd ed.). Prentice Hall. pp. 536, 649, 743. ISBN 978-0130399137. 
  2. ^ a b Cotton, F. Albert; Wilkinson, Geoffrey (1988), Advanced Inorganic Chemistry (5th ed.), New York: Wiley-Interscience, pp. 776, 955, ISBN 0-471-84997-9 
  3. ^ Jolly, William L. Modern Inorganic Chemistry, McGraw-Hill 1984, p. 22
  4. ^ Goldschmidt, Victor M. "Geochemische Verteilungsgesetze der Elemente", Part V "Isomorphie und Polymorphie der Sesquioxyde. Die Lanthaniden-Kontraktion und ihre Konsequenzen", Oslo, 1925
  5. ^ Pekka Pyykko (1988). "Relativistic effects in structural chemistry". Chem. Rev. 88 (3): 563–594. doi:10.1021/cr00085a006. 

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