Fig. 2 | Nature Communications

Fig. 2

From: Coulomb spin liquid in anion-disordered pyrochlore Tb2Hf2O7

Fig. 2

Crystallographic characterization of Tb2Hf2O7 from powder samples. ac Final Rietveld plots of the joint refinement of high-resolution synchrotron X-ray a, b and neutron c powder diffraction data. The X-ray patterns were recorded using incident wavelengths of a 1.65304 Å (i.e., about 10 eV lower than the L3 X-ray absorption edge of Tb, which provides a significant contribution of the anomalous terms to the X-ray scattering factor of Tb) and b 0.49599 Å (an energy that minimizes the absorption). The neutron pattern c was measured with a wavelength 1.155 Å on a large angular range detector, which yields an excellent sensitivity to the thermal displacement factors in general and to the occupancy factors of the different oxygen sites in particular. Arrows indicate some of the satellite reflections originating from the pyrochlore superstructure relative to a defective fluorite phase due to both the disorder-free long-range order of Tb(16d) and Hf(16c) cations, and to the partially disordered long-range order of oxygen atoms in 8b sites and oxygen vacancies in 8a sites. d, e show the pyrochlore superstructure reflections (311) and (553) from the data of a, c respectively, compared to calculations for various densities of antisite cation disorder (d the percentage indicates the fraction of Tb cations occupying the Hf site and vice versa) and anion Frenkel disorder (e the percentage indicates the fraction of vacancies on the 48 f position). f Defects as they appear in a difference Fourier map plotted in fractional coordinates x of the crystallographic directions of the cubic unit cell. The map is obtained from the high-resolution neutron powder diffraction data in the case of a refinement to a perfect pyrochlore model (i.e., without oxygen Frenkel pair defects). Additional scattering density is clearly observed around the 8a position (0.125, 0.125, 0.125), i.e., at crystallographic positions that are normally vacant in pyrochlore materials

Back to article page