Incorporating anisotropic electronic structure in crystallographic determination of complex metals: iron and plutonium

Abstract

Anisotropic electronic structure is incorporated in crystallographic determination of the structure of ferromagnetic Fe, δ-Pu and a Pu–3.7 at% Ga alloy. This is achieved by using anisotropic aspects of the inter-atomic bonds as a motif in combination with the high-symmetry cubic lattice. In the case of Fe, it is shown that ferromagnetic ordering reduces the symmetry of the structure from body centred cubic to body centred tetragonal with an associated effect on elasticity. Thus, the ferromagnetic α- and paramagnetic β-phase are separate and unique phases that should both be addressed on the Fe phase diagrams. In the case of Pu, first-principles density-functional theory calculations are used to show that the bond strengths between the 12 nearest neighbours in δ-plutonium vary greatly. Employing the calculated bond strengths as a motif in crystallographic determination yields a structure with the monoclinic space group Cm for δ-Pu rather than face-centred cubic . The reduced space group for δ-Pu illuminates why it is the only metal with a monoclinic ground state, why lattice distortions of the metal are viable and has implications for the behaviour of the material as it ages due to self-irradiation. Results for a Pu–3.7 at% Ga alloy show that the nearest neighbour bond strengths around a Ga atom are more uniform – a result that explains why Ga stabilizes face-centred cubic δ-Pu. This paper illustrates how an expansion of classical crystallography, which accounts for anisotropic electronic and magnetic structure, can explain complex materials in a novel way.

Acknowledgements

This paper is dedicated to Hub Aaronson, a fiery friend and colleague who we will all miss and who will surely enjoy the stir that our thesis will create. This work was performed under the auspices of the US Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

Notes

†The symbol m′ represents a mirror plane combined with time inversion. For example, see 28.

†We have attempted detection of extra reflections using electron diffraction in a transmission electron microscope (TEM). However, high thermal diffuse scattering, large amounts of double diffraction due to the high atomic number, and omnipresent surface oxidation have precluded the ability to do this. For these reasons, X-ray diffraction of large, single-grain samples performed at low temperatures will be the appropriate experiment.