Kinks and d-waves from phonons: The intermediate coupling story

I present results from an approach that extends the Eliashberg theory by systematic expansion in the vertex function; an essential extension at large phonon frequencies, even for weak coupling. In order to deal with computationally expensive double sums over momenta, a dynamical cluster approximation (DCA) approach is used to incorporate momentum dependence into the Eliashberg equations. First, I consider the effects of introducing partial momentum dependence on the standard Eliashberg theory using a quasi-local approximation; which I use to demonstrate that it is essential to include corrections beyond the standard theory when investigating d-wave states. Using the extended theory with vertex corrections, I compute electron and phonon spectral functions. A kink in the electronic dispersion is found in the normal state along the major symmetry directions, similar to that found in photo-emission from cuprates. The phonon spectral function shows that for weak coupling Wλ<ω₀, the dispersion for phonons has weak momentum dependence, with consequences for the theory of optical phonon mediated d-wave superconductivity, which is shown to be 2nd order in λ. In particular, examination of the order parameter vs. filling shows that vertex corrections lead to d-wave superconductivity mediated via simple optical phonons. I map out the order parameters in detail, showing that there is significant induced anisotropy in the superconducting pairing in quasi-2D systems.     

Lattice dynamics of cubic SrZrO3

Using density functional perturbation theory, the optical dielectric constant, Born effective charges and phonon dispersion curves of cubic SrZrO₃ have been calculated. The obtained dispersion curves show a soft phonon branch spreading from R to M points of the cubic Brillouin zone. An analysis based on the symmetry relationships indicates that the experimentally observed low-symmetry phases of SrZrO₃ can be considered as results of the soft mode condensation at R and M points.     

Ab initio study of phonons in the rutile structure of TiO2

The local-density approximation is used to find the phonon dispersion relations, total and partial phonon density of states for TiO₂ crystal of rutile structure. For that the Hellmann-Feynman forces were computed and direct method applied. Some thermodynamic quantities are also presented. Calculated results are analyzed and compared with the experimental neutron scattering and optic data. Good agreement has been achieved. A giant LO/TO splitting is observed for A_2u and E_u modes.     

Collective dynamics of supercritical water

Inelastic X-ray scattering experiments on sub- and supercritical water were performed to investigate collective dynamics of this unique solvent. Analysis within a generalized Langevin formalism shows that the positive dispersion of the sound velocity, as compared to the hydrodynamic value, first decreases (1.0<ρ<0.8 g cm⁻³) at all measured momentum transfers (1.3-10.7 nm⁻¹), and then increases (0.7<ρ<0.26 g cm⁻³) again only at higher momentum transfers. We suggest the initial decrease is due to approaching the percolation limit in the number of hydrogen bonds, and the subsequent increase is due to the formation of rigid dimers in sub- and supercritical water.     

The effect of doping LiMn2O4 spinel on its use as a cathode in Li-ion batteries: neutron diffraction and electrochemical studies

A series of compounds Li_1+yMn_2−xM′_xO₄ (x≤0.1;y≤0.02), have been synthesised by doping the parent LiMn₂O₄ spinel with various metal ions of variable oxidation state. Powder neutron diffraction data has been collected on these samples alongside a series of electrochemical experiments in order to elucidate the relationship between structure on the performance of these systems as Li batteries. Doping the LiMn₂O₄ spinel with a small amount of metal ions has a remarkable effect on the electrochemical properties. Whereas the capacity of the spinels doped with trivalent ions is much greater, the cycling fading properties are much enhanced with using divalent ions as dopants. The underlying reasons for this are discussed, and it is suggested that the occupancy of the tetrahedral site with divalent ions to form a more compact structure offers an improved structural stability to support greater Li insertion/extraction, but which ultimately prevents the free movement of Li also sited on the tetrahedral site of the lattice.     

Inelastic X-ray scattering investigations of lattice dynamics in SmFeAsO1−xFysuperconductors

We report measurements of the phonon density of states as probed with inelastic X-ray scattering in SmFeAsO_1−xF_y powders. An unexpected strong renormalization of phonon branches around 23 meV is observed as fluorine is substituted for oxygen. Phonon dispersion measurements on SmFeAsO_1−xF_y single crystals allow us to identify the 21 meV A_1g in-phase (Sm,As) and the 26 meV B_1g (Fe,O) modes to be responsible for this renormalization, and may reveal unusual electron-phonon coupling through the spin channel in iron-based superconductors.     

Ab initio calculations of the stability and lattice dynamics of the MgSiO3 post-perovskite

Using the first-principles computations we have calculated phonon-dispersion relations and the phonon density of states for perovskite and post-perovskite phases of MgSiO₃. From them using the quasiharmonic approximation we have estimated the free energies, bulk modulus and volume expansion coefficients of both structures at various pressures and temperatures. Our calculations indicate that the thermal expansivity of MgSiO₃ changes very little across the phase transition. We have determined the P-T coexisting line of perovskite and post-perovskite phases.     

Optical phonon modes and structure of ZnGa2Se4 and ZnGa2S4

We present the infrared and Raman study of the optical phonon modes of the defective compounds ZnGa₂Se₄ and ZnGa₂S₄. Most of the compounds have been found to crystallize in the thiogallate structure (defect chalcopyrite) with space group where all cations and vacancies are ordered. For some Zinc compounds a partially disordered cationic sublattice with various degrees of cation and vacancy statistical distribution, which lead to the higher symmetry (defect stannite), has been reported. For ZnGa₂Se₄ we have found three modes of A symmetry, showing Raman activity only. In addition, we have observed each five modes of B and E symmetry, showing infrared as well as Raman activity. The number of modes and their symmetry assignment, based on polarized measurements, clearly indicate space group for the investigated crystals of ZnGa₂Se₄.Regarding ZnGa₂S₄ we have found three modes exclusively showing Raman activity (2A⊕1B₁), and only eight modes showing infrared as well as Raman activity (3B₂⊕5E). The assignment of the modes has been derived by analyzing the spectral positions of the vibrational modes in comparison to a number of compounds. From the number and symmetry assignment of the optical phonon modes we confirm that ZnGa₂S₄ most likely crystallizes in space group .     

Tight-Binding study of Boron structures

We have performed Linearized Augmented Plane Wave (LAPW) calculations for five crystal structures (alpha, dhcp, sc, fcc, bcc) of Boron which we then fitted to a non-orthogonal tight-binding model following the Naval Research Laboratory Tight-Binding (NRL-TB) method. The predictions of the NRL-TB approach for complicated Boron structures such as R105 (or β-rhombohedral) and T190 are in agreement with recent first‐principles calculations. Fully utilizing the computational speed of the NRL-TB method we calculated the energy differences of various structures, including those containing vacancies using supercells with up to 5000 atoms.     

The stability of Na-doped Bi2(NbCr)O7−x pyrochlores: The non-existence of “(BiNa)(NbCr)O6”

We show that the pyrochlore described as “(BiNa)(NbCr)O₆” is in fact a non-stoichiometric pyrochlore with an approximate composition of (Bi_1.33Na_0.67)(Nb_1.33Cr_0.67)O_7−x. Refinement of this structure using constant wavelength powder neutron diffraction data reveals the presence of vacancies in the anion sites coupled with displacive disorder of the Bi and Na cations. This is necessary to achieve a satisfactory bonding arrangement for both the Bi and Na cations that occupy the pyrochlore A-type sites. Attempts to prepare other pyrochlores in the series Bi_2−xNa_x(NbCr)O₆ were unsuccessful and it appears that the pyrochlore is only stable only over a very narrow composition range. The structure of the pure Bi pyrochlore Bi₂(NbCr)O₇ is also described.     

Structural studies of rhodium doped Sr2RuO4

The influence of Rh doping on the structure of Sr₂RuO₄ has been investigated using neutron powder diffraction methods. The metallic Ru rich compounds adopt a regular K₂NiF₄-type structure, space group I4/mmm, with Ru-O-Ru bond angles of 180°. The structures of the nonmetallic Rh rich compounds crystallise in space group I4/acd and are characterised by tilting of the MO₆ octahedra reducing the Ru-O-Ru angle to about 160°. Irrespective of Rh content the MO₆ polyhedra are not regular octahedra but are elongated along the c direction. The temperature dependence of the structure of Sr₂Ru_0.9Rh_0.1O₄ was investigated and revealed this elongation to be weakly temperature dependent.     

Influence of vapor transport equilibration on Raman spectra of Er:LiNbO3 crystals

Raman spectra of as-grown and vapor transport equilibration (VTE) treated Er:LiNbO₃ crystals, which have different cut orientations (X-cut and Z-cut), different Er-doping levels (Er:(0.2, 0.4 and 2.0 mol%)LiNbO₃) and different VTE durations (80, 120, 150 and 180 h), were recorded at room temperature in the wavenumber range 50-1000 cm⁻¹ by using backward scattering geometry. The spectra were attributed on the basis of their spectral features and the previous experimental work and the most recent theoretical progress in lattice dynamics on pure LiNbO₃. In comparison with the pure crystal the most remarkable effect of Er-doping on the Raman spectrum is observed for the E(TO₉) mode. It does not appear at 610 cm⁻¹ as the pure crystal, but locates at 633 cm⁻¹. In addition, the doping also results in the lowering of the Raman phonon frequency, the broadening of the Raman linewidth and the changes of the relative Raman intensity of some peaks. The VTE treatment results in the narrowing of the linewidth, the recovery of the lowered phonon frequency and the further changes of relative Raman intensity. The narrowing of Raman linewidth indicates that the VTE processing has brought these crystals closer to stoichiometric composition. The VTE treatment has induced the formation of a precipitate ErNbO₄ in the high-doped Er(2.0%):LiNbO₃ crystals whether X- or Z-cut. For these precipitated crystals, besides above linewidth and phonon frequency features, they also display more significant Raman intensity changes compared with those not precipitated crystals. In addition, a slight mixing between A₁(TO) and E(TO) spectra is also observed for these precipitated crystals. Above doping and VTE effects on Raman spectra were quantitatively or qualitatively correlated with the characteristics of the crystal structure and phonon vibrational system.     

CO2 motion in carbon dioxide deuterohydrate determined by applying maximum entropy method to neutron powder diffraction data

Crystal structures of carbon dioxide deuterohydrate were studied by neutron powder diffraction at temperatures from 10 to 200 K. Maps of scattering length density distribution were obtained using a maximum entropy method (MEM), which clarified the motion of CO₂ molecules in the hydrate. In small cages, the carbon atom of the CO₂ molecule is at the center of the cage, and the oxygen atoms of CO₂ revolve freely around the carbon atom. In large cages, the carbon atom also is at the center of the cage, but the oxygen atoms tend to revolve around the carbon atom along the plane parallel to the hexagonal facets of the cage.     

Powder-neutron diffraction studies of geometric isotope and hydrogen-bonding effects in β-CrOOH

Powder-neutron diffraction studies have been done on β-CrOOH and β-CrOOD to confirm whether or not the reported exceptionally large geometric isotope effect is real, and also to study hydrogen-bonding effects in β-CrOOH compared to the prototype CrO₂. The R(O?O) distance in the H-compound at room temperature is confirmed to be 2.472(3) Å, but in the D-compound it is significantly shorter, 2.518(3) Å, than in the earlier work. The resulting magnitude of the geometric isotope effect, 0.046(4) Å, is thus not as exceptionally large as earlier reported, but is still within the maximum range. Structural comparison with CrO₂ clarified the hydrogen-bonding effect in β-CrOOH: the formation of hydrogen bonds brings CrO₆ closer to a regular octahedron.     

Heat-induced charge transfer in cobalt iron cyanide

The heating of Co(2+) ferricyanide above 80 °C induces an inner charge transfer from Co(2+) towards Fe(III) to form the mixed valence system Co(2+)Co(III) ferri- ferro-cyanide. This charge transfer takes place preserving the material framework and forming a solid solution of the initial and final species. The cell edge of the cubic cell (Fm-3m) of this solid solution follows a regular variation with the material composition. This mixed valence system was characterized using X-ray diffraction, infrared, thermo-gravimetric, Mössbauer and magnetic measurements. Its formation is easily detected by the appearance of an intermediate ν(CN) absorption band in the infrared spectra at around 2120 cm⁻¹, 40 cm⁻¹ below and above the observed frequency for this vibration in Co(2+) ferri- and ferro-cyanide, respectively.     

Raman spectra of samarium-fullerene intercalation compounds

Samarium-fullerene intercalation compounds of nominal composition Sm_xC₆₀ (x=1,2,…,6) have been synthesized by a solid-state reaction method. We obtain a Sm_2.75C₆₀ superconducting phase with orthogonal structure and a Sm₆C₆₀ phase with body-centered cubic structure. The broadening and weakening of Raman peaks of the Sm_xC₆₀ compounds are due to the distortion of C₆₀ and electron-phonon interaction. The Raman measurements reveal that the distortion of C₆₀ decrease in Sm_xC₆₀ (x=3,4,5) exposed to air, although the fulleride solids have transformed into an amorphous state. The Raman results also show that the distortion of C₆₀ is still very large in the Sm₆C₆₀ exposed to air, or the C₆₀ molecules have been destroyed and become some amorphous carbide.     

A high temperature powder neutron diffraction structural study of the apatite-type oxide ion conductor, La9.67Si6O26.5

High-resolution neutron powder diffraction studies of the oxide ion conductor La_9.67Si₆O_26.5 are reported for temperatures ranging between 25 and 900 °C. The best fit to the data was obtained for space group P6₃ and there was no evidence for any change in symmetry over the temperature range studied. Interstitial oxide ions are identified lying in sites similar to those predicted by previous computer modelling studies, and in agreement with structural studies on related materials. Furthermore, occupancy of these sites is enhanced by Frenkel-type disorder from neighbouring positions. The results thus add further weight to the interpretation that, in these apatite-type systems, the silicate substructure is important for the accommodation of interstitial oxide ions and their migration.     

Mixed valence states in cobalt iron cyanide

Cobalt iron cyanide with both Co and Fe in mixed valence states were prepared and characterized. In this mixed valence system the cobalt atom is found both as high spin Co(2+) and low spin Co(III) while iron always appears in low spin state to form two solid solutions: Co(2+)Co(III) hexacyanoferrates (II,III), and Co(2+)Co(III) hexacyanoferrate (II). Such solid solutions have the following formula units: (Co²⁺)_x(Co^III)_1−xK[(Fe^II)_1−x(Fe^III)_x(CN)₆]·H₂O and (Co²⁺)_1.5x(Co^III)_1−xK[Fe^II(CN)₆]·yH₂O (0?x?1, 1?y?14). Compounds within these two series were characterized from Infrared, Mössbauer, X-ray diffraction and thermo-gravimetric data, and magnetic measurements at low temperature. A model for their crystal structure is proposed and the structure for a representative composition refined from XRD powder patterns using the Rietveld method. A simple and reproducible procedure to prepare these solid solutions is provided. Within hexacyanoferrates, such mixed valence states system in both metal centres shows unique features, which are discussed from the obtained data.     

Investigation of the vibrational properties of cubic yttria-stabilized zirconia: A combined experimental and theoretical study

A combined experimental and theoretical investigation into the vibrational properties of cubic 8–9 mol% yttria-stabilized zirconia (YSZ) is presented. Measurements of acoustic phonon dispersion curves have been obtained from inelastic neutron scattering investigations using a triple axis spectrometer, as well as calculations of the vibrational density-of-states (vDOS) using density-functional theory. The present measurements agree closely with, and extend, previously published results. The phonons become broader and decrease in intensity as the Brillouin zone boundary is approached, particularly in the Γ–Δ–X direction. Interestingly, there is evidence of a previously unreported low energy phonon band (8–9 meV) in the Γ–Σ–X direction, which could possibly be related to the stabilization (by yttria doping) of the imaginary mode of cubic ZrO₂ about the X-point. Compared to pure cubic ZrO₂, the vDOS of YSZ are broader and extend to higher frequency. Furthermore, the prominent Zr-related feature in the vDOS of c-ZrO₂ at ≈14 meV is shifted to higher energy in the vDOS of YSZ. This behavior is consistent with the measured dispersion bands (first acoustic branch in the Γ–X direction, about the X-point) of YSZ which is higher in energy by a similar amount relative to that of c-ZrO₂, thus providing support for the structural model considered.