[2][3][4][5] This effect causes the radii of transition metals of group 5 and 6 to become unusually similar, as the expected increase in radius going down a period is nearly cancelled out by the f-block insertion, and has many other far ranging consequences in post-lanthanide elements.
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.
Thus the shielding effect is less able to counter the decrease in radius caused by increasing nuclear charge.
Melting points (in Kelvin) also increase consistently across these 12 lanthanides culminating in the value for the last being 161% of the first.
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).
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."
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.
It has been shown that lanthanide contraction plays a crucial role in determining the magnetic phase diagram of the heavy rare-earth elements,[9][10] i.e. those from Gadolinium onwards.
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.
[citation needed] 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.