Thermal vibrations and polymorphic β → γ transition in cerium

Abstract

Method of neutron diffraction was used to determine the temperature dependence of the Debye-Waller factor and the related thermal atomic displacements for two polymorphic modifications of cerium, namely, for β-Ce with a double hexagonal closed-packed (dhcp) structure and for γ-Ce with a face-centered cubic (fcc) structure. It has been shown that the phase transition does not lead to substantial changes in the root-mean-square thermal atomic displacements and that the Debye temperatures of the two modifications are close: 131 K for β-Ce and 127 K for γ-Ce. However, the relative (with respect to the lattice parameters) displacements along the axes change considerably. The transition from the anisotropic hexagonal to the isotropic cubic modification leads, because of a redistribution of thermal atomic displacements along the crystallographic axes, to a decrease in the maximum values of these quantities and to a weakening of their temperature dependence. It has also been shown that a change in the thermal atomic vibrations and in the vibrational contribution to the entropy of the polymorphic transformations is connected with the sign of the volume effect of the transformation (stronger upon a positive effect and weaker, upon a negative one). The reasons for this behavior are discussed.