Actinide bulk modulus

The Cohesive Energy and the Bulk Modulus of Light Actinides in Friedel s 101... 

The trends in several ground state properties of transition metals have been shown in Figs. 2, 3 and 15 of Chap. A and Fig. 7 of Chap. C. The parabolic trend in the atomic volume for the 3-6 periods of the periodic table plus the actinides is shown in Fig. 3 of Chap. A. We note that the trend for the actinides is regular only as far as plutonium and that it is also broken by several 3 d metals, all of which are magnetic. Similar anomalies for the actinides would probably be found in Fig. 15 of Chap. A - the bulk modulus - and Fig. 7 of Chap. C - the cohesive energy if more measurements had been made for the heavy actinides. 

Fig. 36. Bulk modulus of various RBCj, and ABCjj compound (A = actinide) plotted as a function of QIV (2 is the valence of the R or A ion and V the unit cell volume) as given by Mock and Giintherodt (1985).

Comparison of the nonrelativistic and scalar-relativistic results for fee Au reveals the large impact that relativity has on the lattice constant (6%) and bulk modulus (57%) [542]. The most important quaUtative change in the band structure of fee Au is the more than 2-eV lowering of the s-band relative to the bottom of d-bands. In addition, the overall width of the d-bands is increased by more than 15% due to a relativistic delocaUzation of the d- states. The spin-orbit coupling included LGGTO DFT-GGA calculations were made for fluorite structure actinide oxides MO2 (M=Th,U,Pu) and their clean and hydroxylated surfaces, [556], magnetic ordering in fee Pn [557] and bulk properties of fee Pb [558]. 

We have already mentioned above that PuTe is the actinide counterpart of SmTc. Thus, we can take the experimental volume-pressure relation of SmTe (Jayaraman 1979) and differentiate it to obtain the bulk moduli. This curve is shown in a relative pressure scale (normalized with respect to the fcc-bcc transition pressure) in fig. 131. In the same figure wc plot the bulk moduli of PuTe (Dabos-Seignon et al. 1990) also obtained by differentiating the volume—pressure experiment. It is obvious that the PuTe curve now falls exactly on the SmTe curve. The zero pressure bulk modulus of PuTe is now with 370 kbar... 

The total pressure also has a parabolic variation with atomic number, which, according to eq. (48), may be attributed to the increasing filling of the bonding 5f states. If the bulk modulus were independent of atomic number and volume, the atomic volumes (radii) could be obtained directly from the total-pressure curve. Although the bulk modulus does depend upon atomic number and volume, it is still correct to conclude that the parabolic trend observed in the atomic volumes of the light actinides, Th-Pu, is determined mainly by the properties of the 5f electrons. 

The bulk moduli of the actinides, calculated by Skriver and co-workers (Brooks et al. 1984), are shown in fig. 29. The rise from a low value in Fr to the maximum in U is caused initially by the sp and later also the d electrons, which become trapped between the rapidly decreasing atomic volume and their slowly contracting cores. If the atomic volume continued to decrease with atomic number as much as the calculated volume (fig. 27), the bulk modulus would rise to a value of approximately 2 Mbar in... 

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. 

The bulk modulus of ThBeij is practically the same as that of the corresponding uranium compound, with only a minor difference in the pressure derivatives. The value of 108 GPa compares to the bulk moduli for beryllium, 126GPa (Landolt-Bornstein 1967), for uranium, 147 GPa (Benedict 1987), and for thorium, 58 GPa (Bellussi et al. 1981). It is noteworthy that the large difference in bulk modulus between thorium and uranium is not reflected in the bulk moduli of their MBejj compounds. This seems to show that the compression of these compounds is to a large extent determined by the skeleton of beryllium atoms, into which a relatively small number of actinide atoms is imbedded. 

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 Ko (GPa) and pressure derivatives K for the actinide carbides, pnictides, and chalcogenides AnX (An = Th, U, Np, Pu). For each compound the table lists, from top to bottom the bulk modulus, the pressure derivative, and references. Errors as indicated in the original publications. (-1-means compound exists. but no HPXRD study known and constr. constrained.)... 

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. 

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