ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 38

a substantial increase in the atomic volume. The relatively weak bind-
ing of the 4 f states in the divalent rare earths is clearly apparent in
the experiments of Lang et al. (1981), who used X-ray photoemission to
measure the energies required to transfer a 4 f electron to the Fermi level,
throughout the whole series. By inverse photoemission (Bremsstrahlung
Isochromat Spectroscopy) they were similarly able to deduce the energies
required to move an electron from the Fermi level to the unoccupied 4 f
states. Combining the two experiments, the Coulomb correlation energy
required to transfer an electron from an occupied level on another site
could be deduced. These energies were later calculated by Min et al.
(1986a) using a supercell method, in which rare earth ions with different
f occupancies are considered as distinct species, and the agreement with
experiment was generally very satisfactory.
For close-packed structures, the atomic volume is almost indepen-
dent of the structure, but there are small differences in the electronic
contribution to the cohesive energy, which manifest themselves in the
common structural sequence hcp

fcc in the
rare earths, as the atomic number is reduced or the pressure is increased.
Duthie and Pettifor (1977) proposed that the d -electron occupancy,

→ dhcp → Sm-structure →

Fig. 1.15. The occupation numbers of the 5 d states for the trivalent
lanthanides, at the observed equilibrium atomic volumes, after Skriver
(1983). For Ce, the 4 f electrons are included in the energy bands. The
experimentally observed crystal structures are labelled by h, s, d, and
f, for hcp, Sm-structure, dhcp, and fcc, respectively. The empirical d -
occupation numbers which separate the different structures are indicated
by the lines on the right.