(than either adjacent element) for melting points (lower by >10<43%), Vickers hardness (lower by >32<82%), and densities (lower by >26<33%, when exclude Ce, where the density increases by 10% vs lanthanum). The lower densities for europium and ytterbium (than their adjacent lanthanides) are associated with larger atomic volumes at 148% and 128% of the average volume for the typical 12 lanthanides (i.e., 28.979, 25.067, and 19.629 cm3/mol, respectively).

Because the atomic volume of Yb is 21% more than that of Ce, it is understandable that the density for Ce (the 2nd lanthanide) is 98% of that of ytterbium (the 14th lanthanide) when there is a 24% increase in atomic weight for the latter, and the melting point for Ce (1068 K) is nearly the same as the 1097 K for ytterbium and the 1099 K for europium. These 3 elements are the only lanthanides with melting points below the lowest for the other twelve, which is 1193 K for lanthanum. Because europium has a half-filled 4f subshell, this may account for its atypical values when compared with the data for 12 of the lanthanides. Lutetium is the hardest and densest lanthanide and has the highest melting point at 1925 K, which is the year that Goldschmidt published the terminology "Die Lanthaniden-Kontraktion."

Unlike the m. p. data for the lanthanides (where the values increase consistently when the 2nd, 7th & 14th are excluded), the b. p. temperatures show a repeated pattern at 162% and 165% for the 8th lanthanide relative to the 6th and the 15th relative to the 13th (which ignores the atypical 7th and 14th). The 8th and 15th are among the four lanthanides with one electron in the 5d shell (where the others are the 1st and 2nd) and the b. p. values for these four are +/- 2.6% about 3642 K. See the post-lanthanides section for more comments on the 5d-shell electrons. There is also a repeated b. p. pattern at 66% and 71% for the 6th and 13th lanthanides (relative to the preceding elements) that differ by one electron in the 4f shell, i.e., 5 to 6 and 12 to 13.

Magnetism of the lanthanides

It has been shown that lanthanide contraction plays a crucial role in determining the magnetic phase diagram of the heavy rare-earth elements, i.e. those from Gadolinium onwards.

Influence on the post-lanthanides

The lanthanide contraction causes the transition metals in periods 5 and 6 that are in the same group to have near-identical atomic and ionic radii. This makes their separation by chemical means very difficult.

The elements following the lanthanides in the periodic table are influenced by the lanthanide contraction. When the first three post-lanthanide elements (Hf, Ta, and W) are combined with the 12 lanthanides, the Pearson correlation coefficient increases from 0.982 to 0.997. On average for the 12 lanthanides, the melting point (on the Kelvin scale) = 1.92x the density (in g/cm^3) while the three elements following the lanthanides have similar values at 188x, 197x, and 192x before the densities continue to increase but the melting points decrease for the next 2 elements followed by both properties decreasing (at different rates) for the next 8 elements. Hafnium is rather unique because not only do density and m. p. temperature change proportionally (relative to lutetium, the last lanthanide) at 135% and 130% but also the b. p. temperature at 133%. The elements with 2, 3, & 4 electrons in the 5d shell (post-lanthanides Hf, Ta, W) have increasing b. p. values such that the b. p. value for W (wolfram, aka tungsten) is 169% of that for the element with one 5d electron (Lu). The high melting point and two other properties of tungsten originates from strong covalent bonds formed between tungsten atoms by the 5d electrons. The elements with 5 to 10 electrons in the 5d shell (Re to Hg) have progressively lower b. p. values such that the element with ten 5d electrons (Hg) has a b. p. value at 52% of tungsten's (with four 5d electrons).

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. For example, the atomic radius of the metal zirconium, Zr (a period-5 transition element), is 155 pm (empirical value) and that of hafnium, Hf (the corresponding period-6 element), is 159 pm. The ionic radius of Zr⁴⁺ is 84 pm and that of Hf⁴⁺ is 83 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 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. 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.