5f bandwidth

A formalism similar to that presented for actinide metals has been developed for the ground state properties of binary compounds by Andersen et al. leading to a general form of equation of state (see Chap. F). However, this analysis of bonding contributions must draw from detailed results of band calculations more heavily than for the metals case (where the explanation of the qualitative behaviour of ground state properties vs. atomic number needed only the hypothesis of a constant 5f-bandwidth and its volume dependence as predicted by the general theory). In fact, the bond is more complicated ... 

Within the actinide series Pu is the most intriguing element. On the basis of the Hubbard model, and taking into account an unhybridized bandwidth Wf (due only to f-f overlapping), the Un/Wf ratio is 0.7 for U and 3 for Pu in fact, one would have expected already for Pu a 5 f electron localization, since Uh > Wf. However, a hybridization of 5 f with (6d7s) states broadens the 5f bandwidth and delays the Mott-like transition (see Chap. A) from Pu to Am This influences many properties of Pu metaf . ... 

Fig. 18. The f bandwidth, Wf, evaluated as a funcion of atomic volume and atomic radius, S. The solid circles indicate the 5f bandwidths calculated at the experimental equilibrium atomic radii, while the open circles indicate the bandwidths obtained at the calculated (non-spin-polarized) equilibrium atomic radii.

It has been suggested by Brooks (1983) that the deviations from theory observed in Np and Pu may in part be explained by the relativistic volume effect (sect. 3.8). If there is a preferential occupation of the j = f band, there is a 7 = contribution to the pressure in eq. (54), which, in the limit where the spin-orbit interaction is much larger than the 5f bandwidth, vanishes for Mf = 6, i.e. between Pu and Am. It turns out that this limit is not realized in any of the metals Np, Pu or Am, but the effect is sufficiently large to cause deviations from Pauli theory. Even with spin-orbit interaction included, the calculated radii of Np and Pu are too low compared with experiments. The remaining deviation may be due to correlation effects not included in our one-electron scheme. Both Np and Pu are known to be nearly magnetic (Brodsky 1978), which indicates strong f correlations. An additional reason for the discrepancies might be found in the crystal structures. 

The region F is specified by its boimdary 5F. Besides lines, adequate elements to describe the boundary of a F-region are circles, hyperbolas, and ellipses. Lines parallel to the imaginary axis restrict the settling time, circles the bandwidth. Circles can be used to limit the bandwidth, or - in its inverted version - to guarantee a minimal bandwidth. 

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