ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 36

the pressure while the d and f states provide the binding, through their
negative, attractive partial pressure. This difference is essentially due to
thefactthatthe s and p wavefunctions have a positive curvature at the
atomic sphere, over the energy range of the corresponding bands, as illus-
trated in Fig. 1.5, while the d and f functions have a negative curvature.
Consequently, a decrease in volume causes an increase in the logarithmic
derivative for the former and a decrease for the latter, and since D l ( E )
is a decreasing function of energy, the s and p bands must rise and the d
and f bands fall in order to maintain the boundary condition. Equation
(1.3.25) then immediately accounts for the signs of the corresponding
partial pressures. The attractive f pressure for α -Ce is substantial; if
it is removed, the lattice expands to a volume greater than that of γ -
Ce. The partial pressures at a constant atomic volume for the trivalent
rare earths are shown in Fig. 1.13. As may be seen, it is primarily the
decrease in the s and p pressures, which has its origin in the incompletely
Fig. 1.13. The partial 6 s ,6 p ,and5 d pressures for the trivalent rare
earths, calculated for a common atomic volume close to the equilibrium
value for Gd, after Skriver (1983). It is the decrease in the s and p
pressures which gives rise to the lanthanide contraction.