Lanthanide contraction

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The lanthanide contraction is the greater-than-expected decrease in atomic radii/ionic radii of the elements in the lanthanide series from atomic number 57, lanthanum, to 71, lutetium, which results in smaller than otherwise expected atomic radii/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" (Geochemical distribution laws of the elements).[4]

Element Atomic electron
(all begin with [Xe])
Ln3+ electron
Ln3+ radius (pm)
La 5d16s2 4f0 103
Ce 4f15d16s2 4f1 102
Pr 4f36s2 4f2 99
Nd 4f46s2 4f3 98.3
Pm 4f56s2 4f4 97
Sm 4f66s2 4f5 95.8
Eu 4f76s2 4f6 94.7
Gd 4f75d16s2 4f7 93.8
Tb 4f96s2 4f8 92.3
Dy 4f106s2 4f9 91.2
Ho 4f116s2 4f10 90.1
Er 4f126s2 4f11 89
Tm 4f136s2 4f12 88
Yb 4f146s2 4f13 86.8
Lu 4f145d16s2 4f14 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, the 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, as 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 Vickers
Lanthanum 491 363 6.162 1193 187
Cerium 270 412 6.770 1068 181.8
Praseodymium 400 481 6.77 1208 182
Neodymium 343 265 7.01 1297 181
Promethium ? ? 7.26 1315 183
Samarium 412 441 7.52 1345 180
Europium 167 ? 5.264 1099 180
Gadolinium 570 ? 7.90 1585 180
Terbium 863 677 8.23 1629 177
Dysprosium 540 500 8.540 1680 178
Holmium 481 746 8.79 1734 176
Erbium 589 814 9.066 1802 176
Thulium 520 471 9.32 1818 176
Ytterbium 206 343 6.90 1097 176
Lutetium 1160 893 9.841 1925 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 155 pm[6] (empirical value) and that of hafnium, Hf (the corresponding period-6 element), is 159 pm.[7] The ionic radius of Zr4+ is 84 pm and that of Hf4+ is 83 pm.[8] 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 behavior, 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. This also meant that hafnium was discovered as a separate element in 1923, 134 years after zirconium was 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 978-0-13-039913-7.
  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.
  6. ^ "Zirconium | Zr (Element) - PubChem".
  7. ^ "Hafnium".
  8. ^ Nielsen, Ralph H.; Updated by Staff (2013-04-19), "Hafnium and Hafnium Compounds", in John Wiley & Sons, Inc. (ed.), Kirk-Othmer Encyclopedia of Chemical Technology, Hoboken, NJ, USA: John Wiley & Sons, Inc., pp. 0801061414090512.a01.pub3, doi:10.1002/0471238961.0801061414090512.a01.pub3, ISBN 978-0-471-23896-6, retrieved 2022-11-25
  9. ^ "Lanthanide Contraction - Chemistry LibreTexts".

External links[edit]