Lattice and spin dynamics ofγ-Ce

Inelastic-neutron-scattering techniques have been used to study the lattice dynamics and magnetic scattering of fcc $\gamma$-Ce. The phonon dispersion curves at room temperature were determined along the [100], [110], [111], and [$0\xi 1$] symmetry directions. Comparison of the measured dispersion curves with those of Th show that the spectrum of $\gamma$-Ce is in general softer than one would expect by taking into account the differences in mass, interatomic spacing, and melting temperatures of these elements. This relative softening of the phonon frequencies is more pronounced for the phonon branches whose slopes in the elastic limit involve the elastic constants $c_{11}$ and $c_{12}$ which determine the bulk modulus of the element. Thus it seems that premonitory effects of the $\gamma \to \alpha$ transition are present in the room-temperature dispersion curves of $\gamma$-Ce. The elastic constants and lattice specific heat were evaluated by a standard Born—von Kármán analysis. We find that the values of $c_{11}$ and $c_{44}$ are comparable, which is extraordinary for an fcc metal. As a result the shear moduli $c_{44}$ and $\frac{1}{2}(c_{11}-c_{12})$ differ by almost a factor of 3 which implies large anisotropy with regard to the propagation of elastic waves. Constant-$Q$ scans performed at reciprocal-lattice points, where the one-phonon contribution to the scattering vanishes, show unambiguously that there is no well-defined low-energy crystal-field excitation in $\gamma$-Ce. The magnetic scattering follows quite well the $4f$ magnetic form factor of ${\mathrm{Ce}}^{3+}$. Assuming a relaxational form for the imaginary part of the generalized susceptibility, the spin relaxation energy $\hslash \Gamma$ is found to be approximately 4 THz.