Elasticity, lattice dynamics, and thermal expansion for uranium and U–6Nb alloy (elastic moduli) are calculated from density functional theory that is extended to include orbital polarization (DFT+OP). Introducing 12.5 at.% of niobium, substitutionally, in uranium softens all the cii elastic moduli, resulting in a significantly softer shear modulus (G). Combined with a nearly invariant bulk modulus (B), the quotient B/G increases dramatically for U–6Nb, suggesting a more ductile material. Lattice dynamics from a harmonic model coupled with a DFT+OP electronic structure is applied for α uranium, and the obtained phonon density of states compares well with inelastic neutron-scattering measurements. The Debye temperature associated with the lattice dynamics falls within the range of experimentally observed Debye temperatures and it also validates our quasi-harmonic (QH) phonon model. The QH Debye–Grüneisen phonon method is combined with a DFT+OP electronic structure and used to explore the anisotropic thermal expansion in α uranium. The anomalous negative thermal expansion (contraction) of the b lattice parameter of the α-phase orthorhombic cell is relatively well reproduced from a free-energy model consisting of QH-phonon and DFT+OP electronic structure contributions.
Lattice dynamics and negative thermal expansion in the framework compound
ZnNi(CN)4
with two-dimensional and three-dimensional local environments
