X-Ray Diffraction Study of Correlated Electron System at Low Temperatures

Abstract

By using an ultra-low temperature X-ray diffractometer, we studied low temperature phase transitions of several materials. These phase transitions are classified into a ferro quadrupole ordered phase, that is, Jahn–Teller distortion (TmVO $$_4$$ , ZnCr $$_2$$ O $$_4$$ ), an antiferro quadrupole ordered phase (CeB $$_6$$ , PrPb $$_3$$ ), and a superconducrivity (MgB $$_2$$ ). We also investigated unknown phases, such as the low temperature phase in PrPtBi and the 4th phase in Ce $$_{0.7}$$ La $$_{0.3}$$ B $$_6$$ . Our low temperature X-ray measurement gives rise to a fruitful information about the phase transition. Not only a whole profile of the reflection peaks, which can be analyzed by the Rietveld method, we also made the precise measurement of the temperature dependence of the integrated intensity of the reflection peak, the full width at half maximum, and the lattice spacing for some fixed reflections. The temperature dependence of the integrated intensity (I.I.) can be expressed by the Debye–Waller expression. At low temperatures, the change of the phonon frequency can be obtained from the I.I. through the Debye–Waller factor. In MgB $$_2$$ we observed the hardening of the phonon and the softening of phonon above and below the superconducting transition temperature, respsctively. This result suggests the relevant mechanisim of superconductivity in MgB $$_2$$ is the electron–phonon interaction. From the precise measurement of the lattice constant, we found the negative thermal expansion at low temperatures in many correlated electron system. This negative thermal expansion can be explained by the Fermi liquid theory by Misawa.