Nottingham Trent University ILL/ESRF Summer School Programme Lattice Dynamics studies of UO 2 using IXS Myron Huzan Supervisor: Luigi Paolasini Summer School Coordinators: Paul Steffens Patrick Bruno Laurence Tellier 4th September 2017 - 29th September 2017 1 ILL/ESRF Summer School Programme
Contents 1 Introduction 3 1.1 Uranium Dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Inelastic X-Ray Scattering 4 2.1 Lattice Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 ID28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Data Analysis 6 3.1 Transverse Acoustic Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Multi-Peak Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 Conclusions 11 5 Acknowledgements 11 2 ILL/ESRF Summer School Programme
1 Introduction 1.1 Uranium Dioxide The most common use for Uranium Dioxide (UO 2 ) is as fuel in control rods, and since the 1960s extensive research of the lattice dynamics have been undertaken due to the observed unique elec- tronic and magnetic properties of the material [1]. There exist numerous competing and coinciding structural and magnetic phenomena, of which the main processes will be discussed in this introduction. A magnetic transition temperature, T N , was first discovered to exist in antiferromagnetic materials by Louis N´ eel in 1934 [2] and is now know as the N´ eel Temperature . This transition occurs when the thermal energy of the sample is great enough to overcome the macroscopic magnetic domain ordering. UO 2 transition temperature exists at 30.7K below which the material orders from paramagnetic to anti-ferromagnetic, Figure 1, 2 [3]. Figure 1: Paramagnetic FCC Fluorite structure Figure 2: Anti-Ferromagnetic ordering above T N The simplest anti-ferromagnetic structuring exists as collinear 1- k , in which planes of magnetic mo- ments are parallel with respect to each other. This ordering can extend to 2 dimensions (e.g. x-y) producing a non-collinear 2- k ordering and even, as exists in UO 2 , a 3-dimensional anti-ferromagnetic ordering, Triple-K magnetic ordering [4]. Below T N this phenomenon adds additional complexi- ties in the understanding of the material. Figure 3: Representation of multiple ordering within anti-ferromagnetic structures. In addition to the 3- k magnetic ordering there exists a 3- k structural ordering of the atoms below T N due to the Jahn-Teller Effect [5]. This spontaneous structural reordering of the atoms occurs to reduce the energy and symmetry of the material by removing any degeneracy in the molecule. 3 ILL/ESRF Summer School Programme
Symmetrically across the molecule two O 2 − atoms along the � 111 � plane move δ =0.014˚ A [3] closer to each U 4+ atoms, however still keeping the same symmetry and volume as the initial unit cell. Uranium Dioxide possesses additional material properties which are responsible for its unique struc- tural and magnetic properties; however, of primary interest of this investigation is the proposed quadrupolar waves [6]. Quadrupole moments exist within the atoms of UO 2 due to an asymmetri- cal distribution of charge within the nucleus resulting in nuclear spin, I > 1 2 . The propagation of these waves are theorised to travel due to distortion of the atoms, and it is this phenomenon Inelastic X-Ray Scattering (IXS) hopes to probe. 2 Inelastic X-Ray Scattering IXS probes the motion of the electronic cloud of a nucleus, and the 92 electrons present in uranium greatly masks the scattering contribution of the 8 electrons from oxygen atoms. Therefore, IXS will predominantly provide structural information about the uranium atoms. Comparatively, Inelastic Neutron Scattering (INS) probes the nuclear motion of the atoms, and the nuclear scattering cross-section of uranium and oxygen is significantly more comparable and provides separation between the two atom sites. Additionally, INS polarisation analysis provides magnetic or- dering information within the material, which is unable to be probed with IXS. However, comparison of IXS and INS can distinctly prove if excited modes are magnetic or vibrational. For comparison of IXS and INS, an adiabatic approximation is considered, which assumes that the electrons of each atom travel with the nuclei. This approximation is particularly valid for hard X-Rays since scattering occurs between core electrons. X-Ray focussing is achieved by Beryllium compound refractive lenses to produce a minimum incident spot size of 20x10 µ m 2 (H x V) on the ID28 beamline. This focusing is significantly smaller than anything feasible on INS beamlines, and as a consequence, the smaller sample environments enable diamond anvil cells to investigate pressures in excess of 100GPa and experiments undertaken with smaller, single crystal samples. Currently, 3 rd generation synchrotrons provide a significantly increased Brilliance, (Eqn. 1) to any neutron spallation or reactor sources, and with the further upgrades of ESRF and 4 th generation synchrotrons the flux is substantially higher with X-Rays. However, both IXS and INS provide very complimentary methods of investigating the lattice dynamics of materials and within this report results from both techniques will be compared and discussed for UO 2 . Photons/sec B = (1) [ mrad 2 ] × [ mm 2 ] × [0 . 1% BW ] 2.1 Lattice Dynamics Phonons are the propagation of vibrational energy within the crystal due to oscillations of atoms. There exist three modes of vibration, one longitudinal and two transverse. However, due to the exper- imental configuration, only 1 of the transverse phonon excitations should be excited since the reciprocal space being investigated was such that the reduced momentum transfer, q, is nearly perpendicular to the reciprocal lattice vector G hkl . Additionally, since there exist two atoms within the unit cell, Uranium and Oxygen, there will exist an acoustic and optic phonon branch due to the in-phase and 4 ILL/ESRF Summer School Programme
out-of-phase vibrational motions respectively. Magnons are quantised spin waves travelling through the crystal due to disturbances of the electron’s spin. X-Rays do not possess a magnetic moment, therefore cannot directly probe the magnetic struc- ture in the form of spin waves. However, there do exist additional X-Ray techniques such as X-Ray Magnetic Circular Dichroism (XMCD) which provides magnetic ordering from X-Rays. Disruption to quadrupole moments within uranium will distort the oxygen cage in which surrounds it. This distortion is proposed to propagate through the sample in the form of a quadrupolar wave and is hoped to be probed directly with IXS. Simulations calculated using a mean-field random phase approximation from Cacuiffo [7], present energy modes of Phonons, Magnons and Quadrupolar excitations neglecting all coupling interactions, Figure 4 a). However, complications of these modes are increased due to the couplings between the modes causing avoided crossings within the dispersion curves Figure 4 b). These branches of the simulation are what INS and IXS hope to validate or disprove to further develop the current theoretical model of UO 2 . Figure 4: Intensity map of the theory of dispersion curves for UO 2 as modelled by Caciuffo a) Independent branches of non-interacting modes b) Interacting modes creating avoided crossings, yellow arrows. 2.2 ID28 X-Rays generated by guiding electrons from the synchrotron beam through undulators are directed towards the respective beamlines. Collimation and pre-monochromators reduce the bandwidth of the X-Ray spectrum before incidence onto the main backscattering monochromator. Silicon is chosen as the monochromator and selection of the high-order Bragg reflection enables control over the X-Ray flux, Energy Resolution and Energy. Bragg reflection (999) was selected for investigation of UO 2 which provided an X-Ray energy of 17.794KeV and energy resolution of 3meV [8]. Selection of the 5 ILL/ESRF Summer School Programme
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