We have from first principles calculated the elastic constants (${\mathit{C}}_{11}$, ${\mathit{C}}_{12}$, and ${\mathit{C}}_{44}$) of all nonmagnetic cubic d transition metals, and obtained good agreement with experimental data. We show that the trend exhibited by the tetragonal shear constant in the transition metals can be simply understood. In particular, we show that .ul4 the trend of the tetragonal shear constant, C’, of cubic transition metals and alloys is determined by the energy difference between the fcc and bcc structures of a given system, which in turn is determined by band filling. This finding is in turn due to the result that these systems have a Bains path with similar shape, and our ‘‘canonical’’ Bains path illustrates this behavior. The trend of C’ is further studied by including selected alloys (thereby obtaining a finer tuning of band-filling effects). The scaling of C’ with the bcc-fcc energy difference is found to hold also for the studied alloys (roughly), and the calculated C’ is found to agree well with available experimental data.

Ab initio electronic-structure calculations, based on density-functional theory and a full-potential linear-muffin-tin-orbital method, have been used to predict crystal-structure phase stabilities, elastic constants, and Brillouin-zone-boundary phonons for iron under compression. Total energies for five crystal structures, bcc, fcc, bct, hcp, and dhcp, have been calculated over a wide volume range. In agreement with experiment and previous theoretical calculations, a magnetic bcc ground state is obtained at ambient pressure and a nonmagnetic hcp ground state is found at high pressure, with a predicted bcc → hcp phase transition at about 10 GPa. Also in agreement with very recent diamond-anvil-cell experiments, a metastable dhcp phase is found at high pressure, which remains magnetic and consequently accessible at high temperature up to about 50 GPa. In addition, the bcc structure becomes mechanically unstable at pressures above 2 Mbar (200 GPa) and a metastable, but still magnetic, bct phase ($\frac{c}{a}\simeq 0.875$) develops. For high-pressure nonmagnetic iron, fcc and hcp elastic constants and fcc phonon frequencies have been calculated to above 4 Mbar. These quantities rise smoothly with pressure, but an increasing tendency towards elastic anisotropy as a function of compression is observed, and this has important implications for the solid inner-core of the earth. The fcc elastic-constant and phonon data have also been used in combination with generalized pseudopotential theory to develop manybody interatomic potentials, from which high-temperature thermodynamic properties and melting can be obtained. In this paper, these potentials have been used to calculate full fcc and hcp phonon spectra and corresponding Debye temperatures as a function of compression.

Total energies for the six known polymorphs of plutonium metal have been calculated within spin and orbital polarized density-functional theory as a function of lattice constant. Theoretical equilibrium volumes and bulk moduli correspond well with experimental data and the calculated total energies are consistent with the known phase diagram of Pu. It is shown that a preference for the formation of magnetic moments, increasing through the $\alpha \to \beta \to \gamma$ phases, explains their position in the ambient pressure phase diagram and their anomalous variation of atomic density. A simple model is presented that establishes a relationship between atomic density, crystal symmetry, and magnetic moments which is universally valid for all Pu phases.

First-principles theory, based on the density-functional approach, is used to study the crystal structures of Ce and the light actinides (Th-Pu) at low temperatures as a function of hydrostatic pressure. Calculated ground-state properties, such as crystal structure, atomic volume and bulk modulus, are shown to be very well described within this theory. We present the following pressureinduced phase transitions: Ce, fcc -> bct -> hcp; Th, fcc -> bct -> hcp; Pa, bct -> alphaU bct -> hcp; U, alpha-U -> bct -> bcc; Np, alpha-Np -> beta-Np -> bcc; Pu, alpha-Pu -> alphaNp -> beta-Np -> bcc. We explain the occurrence of low-symmetry (complex) structures in these metals as a consequence of a symmetry-breaking mechanism that shows similarities to a Peierls distortion. The ultimate high-pressure phases are well accounted for in a canonical model for the f bands for these metals.

We present a comparison between calculations based upon the local-density approximation (LDA) and the generalized- gradient approximation (GGA) of the ground-state properties of the f-electron metals Ce, Th, Pa, U, Np, and Pu in their α phase. For α-Ce, Th, Pa, U, and Np the calculations have been performed for the observed crystal structures. Studies for the hypothetical fcc crystal structure have also been done for Pa, U, Np, and Pu. Equilibrium volumes and bulk moduli for these f-electron metals have been calculated for both the LDA and GGA formulation of the exchange-correlation energy functional in the full-potential implementation of the linear-muffin-tin-orbital method. The equilibrium volumes, which generally are too low in LDA calculations, are improved considerably by the gradient correction for these elements. Similarly the bulk moduli are decreased substantially when LDA is replaced by GGA and thereby they come closer to the experimentally observed values.