Thermal vibrations and α → β polymorphic transformation in lanthanum

Abstract

Neutron diffraction was used to determine temperature dependence of the Debye-Waller factor and thermal atomic displacements for two polymorphic modifications of lanthanum, namely, α-La with a double hcp (dhcp) crystal structure and β-La with an fcc crystal structure. No substantial changes in the mean-square thermal atomic displacements were shown to occur; the Debye temperatures of the two polymorphic modifications, α-La and β-La, are equal to 135 and 130 K, respectively. However, the relative (with respect to the lattice parameters) displacements along the axes change substantially. The transition from the anisotropic hexagonal modification to the isotropic cubic modification leads to a decrease in the maximum thermal atomic displacements and a weakening of their temperature dependence because of their redistribution over the crystallographic axes. Upon the α → β transformation, the volume decreases and the anharmonicity increases as demonstrated by a twofold increase in the volumetric thermal expansion coefficient. An analysis of literature data available for the polymorphic transformations shows that the enhancement in the anharmonicity is related to an increase in the specific volume in the course of transition from the low-temperature to the high-temperature modification. The explanation of this phenomenon is suggested.