Bulk modulus lanthanides

Softening of zone boundary LO phonons in the NaCl structure and also of the bulk modulus are the striking effects caused by the electron-phonon interaction due to volume modulations of the lanthanide ion by the phonons as calculated by Bennemann and Avignon (1979), Ghatak and Bennemann (1979) and Cantrell and Stevens (1984). One expects a strong scattering intensity from those deformations which also describe the phonon anomaly. 

The bulk modulus may be obtained from the calculated equation of state by differentiation. This quantity is more difficult to calculate accurately than is the equilibrium volume, both because it involves the difference in two calculated numbers and it is sensitive to the volume at which it is calculated. The calculated volumes of the transition metals (Andersen et al. 1985) are usually a little lower than those measured (LDA tends to overbond), and bulk moduli evaluated at the calculated volumes tend to be higher. The bulk moduli of the lanthanide metals calculated by Skriver (1983b) for the fee structure at the calculated equilibrium radii, are shown in fig. 28. The observed slow increase across the series, broken only by the low values for the divalent metals, is reproduced well, although the calculated bulk moduli are typically 30% too high. 

Pu. However, the bulk modulus is extremely volume dependent, and if it is evaluated at the experimentally observed equilibrium radius - which deviates from the calculated values for Np and Pu - it drops from U to Pu, as shown in fig. 29. In the heavy actinides, i.e. beyond americium, the atomic volume has increased considerably, due to the localization of the 5f states, and hence the bulk moduli attain low values - typical of those found in the lanthanide series. 

Isothermal bulk modulus K (GPa) and its pressure derivative Kg for intermetallic compounds of the lanthanides and actinides, as determined from high-pressure X-ray diffraction study. Errors as indicated in the original publications (n.d. not determined.)... 

Isothermal bulk moduli, (GPa), and pressure derivatives Kg determined from high-pressure X-ray diffraction, for the lanthanide (Ln) pnictides and chalcogenides of the B1 structure type. For each compound the table lists, from top to bottom the bulk modulus, in GPa, the pressure derivative, and references. Errors as indicated in the original publications. (x means compound unknown, - studied under pressure, but no compressibility data known, -l- compound exists, but no HPXRD study known and constr. ... 

Isothermal bulk modulus (GPa) and its pressure derivative K for ambient pressure phases of lanthanide and actinide compounds of the Fe2As and PbFCl structure types. 

A bulk modulus of 50 5 GPa was derived for the dhcp form of californium metal, which compares favorably with the bulk moduli for many of the lanthanide metals but is significantly lower than the moduli of thorium to plutonium metals. In recent studies of californium metal under pressures up to 48 GPa, it was found that the metal transforms into an a-uranium orthorhombic-type structure which corresponds to the onset of 5f-electron participation in the metallic bonding [79]. 

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