Tetragonal Axis Research Articles

Ab initio and shell model studies of structural, thermoelastic and vibrational properties of SnO2 under pressure

The pressure dependences of the structural, thermoelastic and vibrational properties of SnO2 in its rutile phase are studied, as well as the pressure-induced transition to a CaCl2-type phase. These studies have been performed by means of ab initio (AI) density functional theory calculations using the localized basis code SIESTA. The results are employed to develop a shell model (SM) for application in future studies of nanostructured SnO2. A good agreement of the SM results for the pressure dependences of the above properties with the ones obtained from present and previous AI calculations as well as from experiments is achieved. The transition is characterized by a rotation of the Sn-centered oxygen octahedra around the tetragonal axis through the Sn. This rotation breaks the tetragonal symmetry of the lattice and an orthorhombic distortion appears above the critical pressure Pc. A zone-center phonon of B1g symmetry in the rutile phase involves such rotation and softens on approaching Pc. It becomes an Ag mode which stabilizes with increasing pressure in the CaCl2 phase. This behavior, together with the softening of the shear modulus (C11−C12)/2 related to the orthorhombic distortion, allows a precise determination of a value for Pc. An additional determination is provided by the splitting of the basal plane lattice parameters. Both the AI and the experimentally observed softening of the B1g mode are incomplete, indicating a small discontinuity at the transition. However, all results show continuous changes in volume and lattice parameters, indicating a second-order transition. All these results indicate that there should be sufficient confidence for the future employment of the shell model.

Investigations of g-factor for Ti3+, V4+ and Cr5+ in anatase

The g-factor formulas for d(1) ions in anatase are deduced from the Jahn-Teller effect and contributions of the charge transfer levels. The tetragonal distortions R∥-R⊥ (where R∥ and R⊥ denote the metal-ligand distances parallel with and perpendicular to the tetragonal axis) for Ti(3+), V(4+) and Cr(5+) in anatase are studied to calculate the g-factors and the calculations are in good agreement with the experimental values. The distortions are much larger than the corresponding values in the pure crystal. The contributions of the charge transfer levels to g factors increase with the increasing valence state. It must be taken into account in the precise calculations of g factors for the high valence state d(1) ions in crystals.

Spin excitations and electron paramagnetic resonance in two-layer antiferromagnetic system Y1-xYbxBa2Cu3O6+y

An experimental and theoretical study of the EPR spectrum of Y0.98Yb0.02Ba2Cu3O6.1 is reported. A strong anisotropy of the EPR linewidth is revealed for the parallel and perpendicular orientations of the external magnetic field relative to the tetragonal symmetry axis. This anisotropy is related to the indirect spin-spin interaction between the ytterbium ions via antiferromagnetic spin-waves. The explicit expressions for the coupling of ytterbium ions with the spin waves and the corresponding indirect spin-spin interactions are derived. An estimate of the exchange coupling between the ytterbium and copper ions is found from the comparison of the theory with the experiment.

Paramagnetic hole centres in natural zircon and zircon colouration

Paramagnetic defect centres and their relation to variable types of colouration were studied for eleven natural zircon crystals from three localities in North Carolina (USA), Massif Central (France), and Ural Mountains (Russia) using electron paramagnetic resonance (EPR) and optical absorption spectroscopy. The presence of tetragonal centres of trivalent rare-earth elements (REE 3+ ) and niobium (Nb 4+ ) irrespective of the colouration type and also in colourless grains suggests that these defects are not directly related to any specific zircon colouration. In contrast, the occurrence of two hole centres in crystals from North Carolina and the Massif Central correlates with the formation of specific broad bands in the absorption spectra. The appearance of pink colouration corresponds to the occurrence of a hole located at an oxygen nearest to Y 3+ on zirconium site. This defect displays a single line at g = 2.006 in the EPR spectra for external magnetic field orientations parallel to the tetragonal crystal axis c . The related broad band in the optical absorption spectra peaks at 340–350 nm and its low-energy wing extends into the visible range. Reddish colour results from an intense broad absorption feature around 510–515 nm caused by a hole located at an oxygen next nearest to Y 3+ substituting for Zr 4+ . A single line at g = 2.011 related to this “red” hole centre is observed in the EPR spectra in magnetic field orientation parallel c . The nature of the two paramagnetic centres was verified by their angular dependencies. Reddish-brownish and orange colour of zircon may appear for certain intensity relations between the two absorption bands with possible additional influence from charge transfer bands caused by Tb 4+ centres. Yellowish-brownish colouration of zircon from the Ural Mountains is essentially different in nature. Several other paramagnetic defects with spin S = 1/2 were found in zircon from this locality besides the “red” hole centre, Tb 4+ , and REE 3+ defects. There is a characteristic set of four bands in the optical absorption spectra. Additional heating and irradiation experiments are necessary for a correct assignment of paramagnetic defects to specific colour centres in this case.

Field-induced spin exciton doublet splitting indx2−y2-waveCeMIn5(M=Rh,Ir,Co)heavy-electron superconductors

We investigate the spin-exciton modes in the superconducting d_{x^2-y^2} state of CeMIn_5 heavy fermion compounds found at the antiferromagnetic wave vector by inelastic neutron scattering. We present a theoretical model that explains the field dependence for both field directions. We show that the recently observed splitting of the spin exciton doublet in CeCoIn_5 into two non-degenerate modes for in-plane field appears naturally in this model. This is due to the spin anisotropy of g- factors and quasiparticle interactions which lead to different resonant conditions for the dynamic susceptibility components. We predict that the splitting of the spin resonance doublet becomes strongly nonlinear for larger fields when the energy of both split components decreases. For field along the tetragonal axis no splitting but only a broadening of the resonance is found in agreement with experiment.

Magnetic Studies of Ternary Germanides U3Co4Ge7 and U3Co2Ge7 with Strong Uniaxial Anisotropy

U 3 Co 4 Ge 7 and U 3 Co 2 Ge 7 have been prepared as single crystals by the solution growth method from tin flux and studied by X-ray diffraction, magnetic, transport, and specific-heat measurements; ab initio electronic-structure calculations have also been performed to study magnetism theoretically. U 3 Co 4 Ge 7 has a tetragonal structure ( I 4/ m m m ), while U 3 Co 2 Ge 7 crystallizes in en orthorhombic structure ( C m m m ), which appears to be a distortion of a tetragonal structure. All measurements document ferromagnetism in U 3 Co 4 Ge 7 below T C = 21 K with a strong magnetocrystalline anisotropy. The c -axis has a strong ferromagnetic contribution to magnetization and was found to be the easy-magnetization direction. U 3 Co 2 Ge 7 orders magnetically below 40 K; the magnetic structure is sensitive to the ratio a / c ≈1, e.g., the deviation from the tetragonal axis.

In‐Operando Neutron Diffraction Studies of Transition Metal Hydrogen Storage Materials

Neutron diffraction studies of hydrogen absorption and desorption (non-isotopically enriched) in the metal hydride Ti25Cr50V20Mo5Hx, reveal the origin of the reduction in capacity exhibited by this material on cycling. The sequestered hydrogen is principally located in the octahedral and tetrahedral interstitial sites in the basal plane, while local diffusion along the unique tetragonal axis appears to be preferred.

Chemically ordered MnPt ultrathin films on Pt(001) substrate: Growth, atomic structure, and magnetic properties

Ultrathin MnPt films have been grown on Pt(001) single crystals by alternate deposition of Mn and Pt and studied in situ by grazing incidence x-ray diffraction. The growth mode and chemical order strongly depend on the deposition conditions. At room temperature, a 3D growth mode for Pt leads to a disordered and rough MnPt film. After annealing at 770 K, chemical order develops with the tetragonal axis oriented in the surface plane. At 570 K, Pt grows in a quasi layer-by-layer mode. For all depositions, and even after annealing, Mn remains essentially at the surface with negligible diffusion into bulk. As a consequence, the film deposited at 570 K is chemically ordered, with the tetragonal axis oriented mainly perpendicular to the surface. Coupled to ferromagnetic layers with in-plane (out-of-plane) anisotropy, these ultrathin ($\ensuremath{\approx}$3 nm) MnPt films exhibit exchange bias properties and enhanced coercivity at low temperature.

First-principles cluster variation calculations of tetragonal-cubic transition in ZrO2

Abstract It is attempted to extend the basic idea of continuous displacement cluster variation method (CDCVM) to the study of a displacive phase transition . As a preliminary study, we focus on cubic to tetragonal transition in ZrO 2 in which oxygen atoms on the cubic lattice are displaced alternatively in the opposite direction (upward and downward) along the tetragonal axis. Within the CDCVM, displaced atoms are regarded as different atomic species, and two distinguished atoms, A -oxygen (upward shifting) and B -oxygen (downward shifting), are introduced in the description of the free energy. FLAPW electronic structure total energy calculations are performed to extract effective interaction energies among displaced oxygen atoms, and by combing them with CDCVM, the transition temperature is calculated from the first-principles.

Determination of the magnetostrictive atomic environments in FeCoB alloys

The atomic environments of Fe and Co involved in the magnetostriction effect in FeCoB alloys have been identified by differential extended x-ray fine structure (DiffEXAFS) spectroscopy. The study, done in amorphous and polycrystalline FeCoB films, demonstrates that the alloys are heterogeneous and that boron plays a crucial role in the origin of their magnetostrictive properties. The analysis of DiffEXAFS in the polycrystalline and amorphous alloys indicates that boron activates magnetostriction when entering as an impurity into octahedral interstitial sites of the Fe bcc lattice, causing its tetragonal distortion. Magnetostriction would be explained then by the relative change in volume when the tetragonal axis of the site is reoriented under an externally applied magnetic field. The experiment demonstrates the extreme sensitivity of DiffEXAFS to characterize magnetostrictive environments that are undetectable in their related EXAFS spectra.

Molybdenum Disilicide - Diffusion, Defects, Diffusion Correlation, and Creep

Molybdenum disilicide (MoSi2) is an interesting material for high-temperature applications. It has a high melting temperature, good thermal and electrical conductivity and an excellent oxidation resistance. For many years the primary use of MoSi2has been in heating elements, which can be used for temperatures up to 1800°C. Since the 1990s the potential of MoSi2as a high-temperature structural material has been recognized as well. Its brittleness at lower temperatures and a poor creep resistance above 1200°C have hindered its use as in load-bearing parts. These disadvantages may be offset at least partly by using it together with a second material in a composite or an alloy. Projected applications of MoSi2-based materials include, e.g. stationary hot section components in gas turbine engines and glow plugs in diesel engines. For future research and development directions of MoSi2-based composites diffusion is a crucial property because creep is closely connected with diffusion. This paper is devoted to the basic diffusion and defect properties of MoSi2. Data of Si and Mo as well as Ge diffusion from the Münster laboratory for both principal directions are briefly summarized. For all three kinds of atoms diffusion perpendicular to the tetragonal axis is faster than parallel to it. The diffusivities of Mo in both directions are many orders of magnitude slower than those of Si and Ge. The huge asymmetry between Mo and Si (or Ge) diffusion suggests that atomic motion of each constituent is restricted to its own sublattice. Positron annihilation studies on MoSi2from the Stuttgart laboratory are reviewed as well. They show that formation of thermal vacancies occurs primarily on the Si sublattice but cannot exclude vacancy formation on the Mo sublattice at higher temperatures. Correlation factors for Si and Mo diffusion via sublattice vacancies in the respective sublattices of MoSi2have been calculated recently mainly by Monte Carlo simulation techniques and are also briefly described. Diffusion, in particular self-diffusion, is discussed in connection with literature data on high-temperature creep, which is diffusion-controlled. Grain-size effects of creep have been reported and can be attributed to Nabarro-Herring and Coble creep. Power-law creep is attributed to diffusion-controlled dislocation creep. Some details are, however, not completely understood, presumably due to a lack of theoretical concepts for creep in uniaxial, stochiometric compounds and due to missing information on grain-boundary diffusion.

Effects of Cu Underlayer on the Growth and Magnetic Properties of FePt Thin Films on MgO (001) Substrate

During ordering process of face centered tegragonal (fct) L1(0) phase of the FePt alloy, there exist three growth variants of axes (001) from original disordered fcc structured phase. When FePt film was directly deposited on the MgO (001) substrate, the variant perpendicular to the film plane grew, resulting in a low out-of-plane coercivity of 1.3 kOe. By using Cu underlayer, two variants lying in the film plane got same chance to grow, which caused an in-plane perpendicular alignment of the tetragonal axes of FePt L1(0) phases. The crystallographic relationship between Cu and FePt layers is Cu (100)<100>//fct FePt (100)<100>. A high in-plane coercivity of 4.6 kOe was obtained due to the high density of micro-defects (mcro-twins, anti-phase boundaries, etc.) in the film plane. This work demonstrated a way of selecting the growth variants of ordering process to adjust the magnetic properties of the ordered FePt thin films.

Ferroelectric Instability and Dimensionality in Bi-Layered Perovskites and Thin Films

The dielectric and thermal properties of Bi (bismuth)-layered perovskite SrBi2Ta2O9(SBT) are discussed in comparison with ferroelectric thin BaTiO3films. Although these two perovskites exhibit quite a different nature, the dielectric properties of BaTiO3thin film are similar to those in bulk SBT. The dielectric properties and pseudo-two-dimensional structure between SBT and thin film suggest that the bulk layered ferroelectric SBT is a good model of ultra-thin ferroelectric film with two perovskite layers, free from any misfit lattice strain with substrate and surface charge at the interface with electrodes. Based on the mechanism of ferroelectric phase transition of SBT, it seems plausible that the ferroelectric interaction is still prominent but shows a crossover from ferroelectric to antiferroelectric interaction in perovskite ultra-thin films along the tetragonal axis.

Superionic Conductivity and Specific Effects Induced by γ-Radiation in Nanofibrous TlGaTe2 Crystals

Temperature dependences of electrical conductivity (T), switching effect, THz spectra and permittivity e(T) of onedimensional (1D) TlGaTe2 single crystals are investigated. The superionic conductivity observed at temperatures above 305 K is related to diffusion of Tl+ ions via vacancies in the thallium sublattice between   2 2 3 Te Ga nanochains. A relaxation character of dielectric anomalies suggests the existence of electric charges weakly bound to the crystal lattice. Upon the transition to the superionic state, relaxors in the TlGaTe2 crystals are Tl+ dipoles ((   2 2 3 Te Ga ) nanochains) that arise due to melting of the thallium sublattice and hops of Tl+ ions from one localized state to another. The effect of a fieldinduced transition of the TlGaTe2 crystal to the superionic state is detected. The temperature dependences of σ(T) and currentvoltage characteristics subjected to various doses of γradiation in both geometries of the experiment, along nanochains parallel to the tetragonal axis of the crystal σ) and perpendicular to these nanochains, are studied. It is shown that the dependence σ(T) measured in the ohmic region of the current-voltage characteristic is the shape typical of the hopping mechanism. The current-voltage characteristics in the region of a more abrupt increase in the current are also studied and explained in the context of the Pool-Frenkel thermal-field effect. It is shown that anisotropy of electrical conductivity changes under the effect of irradiation, which brings about translational ordering of nanochains. Terahertz time-domain spectroscopy reveals absorption lines at approximately 0.2 THz that may be attributed to the libration oscillations of the nanofibers in the superionic phase.

Structural changes that occur upon photolysis of the Fe(II)a3–CO complex in the cytochrome ba3-oxidase of Thermus thermophilus: A combined X-ray crystallographic and infrared spectral study demonstrates CO binding to CuB

The purpose of the work was to provide a crystallographic demonstration of the venerable idea that CO photolyzed from ferrous heme-a3 moves to the nearby cuprous ion in the cytochrome c oxidases. Crystal structures of CO-bound cytochrome ba3-oxidase from Thermus thermophilus, determined at ~2.8–3.2Å resolution, reveal a Fe–C distance of ~2.0Å, a Cu–O distance of 2.4Å and a Fe–C–O angle of ~126°. Upon photodissociation at 100K, X-ray structures indicate loss of Fea3–CO and appearance of CuB–CO having a Cu–C distance of ~1.9Å and an O–Fe distance of ~2.3Å. Absolute FTIR spectra recorded from single crystals of reduced ba3–CO that had not been exposed to X-ray radiation, showed several peaks around 1975cm−1; after photolysis at 100K, the absolute FTIR spectra also showed a significant peak at 2050cm−1. Analysis of the ‘light’ minus ‘dark’ difference spectra showed four very sharp CO stretching bands at 1970cm−1, 1977cm−1, 1981cm−1, and 1985cm−1, previously assigned to the Fea3–CO complex, and a significantly broader CO stretching band centered at ~2050cm−1, previously assigned to the CO stretching frequency of CuB bound CO. As expected for light propagating along the tetragonal axis of the P43212 space group, the single crystal spectra exhibit negligible dichroism. Absolute FTIR spectrometry of a CO-laden ba3 crystal, exposed to an amount of X-ray radiation required to obtain structural data sets before FTIR characterization, showed a significant signal due to photogenerated CO2 at 2337cm−1 and one from traces of CO at 2133cm−1; while bands associated with CO bound to either Fea3 or to CuB in “light” minus “dark” FTIR difference spectra shifted and broadened in response to X-ray exposure. In spite of considerable radiation damage to the crystals, both X-ray analysis at 2.8 and 3.2Å and FTIR spectra support the long-held position that photolysis of Fea3–CO in cytochrome c oxidases leads to significant trapping of the CO on the CuB atom; Fea3 and CuB ligation, at the resolutions reported here, are otherwise unaltered. This article is part of a Special Issue entitled: Respiratory Oxidases.

Structure and energetics of 180° domain walls in PbTiO3 by density functional theory

Density functional theory at the level of the local density approximation withthe projector augmented wave method is used to determine the structure of180° domain walls intetragonal ferroelectric PbTiO3. In agreement with previous studies, it is found that PbO-centered {100} walls have lower energies thanTiO2-centered {100} walls, leading to a Peierls potential barrier for wall motion along⟨010⟩ of ∼ 36 mJ m − 2. In addition to the Ising-like polarization along the tetragonal axis, it is found thatnear the domain wall, there is a small polarization in the wall-normal directionaway from the domain wall. These Néel-like contributions to the domain wall areanalyzed in terms of the Landau–Ginzburg–Devonshire phenomenological theoryfor ferroelectrics. Similar characteristics are found for {110} domain walls, whereOO-centered walls are energetically more favorable than the PbTiO-centered walls.

Calculation of carrier-concentration-dependent effective mass in Nb-doped anatase crystals of TiO2

The calculated optical effective masses of electrons, both orthogonal and parallel to the tetragonal axis of the crystal, are reported as a function of carrier concentration in Nb-doped anatase. The calculation is based on the band structure, obtained by density functional theory in the generalized gradient approximation or by using the HSE06 screened hybrid functional. The anisotropy of the crystal and the nonparabolicity of the bands both have been taken into account. It has been found that in the concentration range relevant for transparent conductive oxide applications, the effective mass is determined by several branches of the conduction band, leading to a complicated dependence on the carrier concentration. The form of the function obtained with HSE06 is in line with experiment. The strong anisotropy in the effective mass is confirmed, and very large values are predicted along the tetragonal axis for high carrier concentrations.

Theoretical studies of the spin Hamiltonian parameters and the local structures for the tetragonal Cu 2+ centers in the LKB glasses

The spin Hamiltonian parameters ( g factors g ∥, g ⊥ and the hyperfine structure constants A ∥, A ⊥) for the Cu 2+ centers in the lithium potassium borate (LKB) glasses xLi 2O·(30 − x)·K 2O·70B 2O 3 (0 ≤ x ≤ 25) were theoretically studied using the high-order perturbation formulas of these parameters for a 3d 9 ion in a tetragonally elongated octahedron. The [CuO 6] 10− clusters in the LKB glasses are found to suffer the relative elongations of about 3% along the tetragonal axis due to the Jahn–Teller effect. The concentration dependences of the g factors are illustrated by the approximately linear decrease of the cubic field parameter Dq as well as the increases of the covalency factor N and the relative elongation ratio ρ due to the slight expansion of the cell volume or bond lengths with increasing the Li 2O concentration x. Meanwhile, the slow non-linear increases of the hyperfine structure constants are described as the rough exponential increase of the core polarization constant κ with x due to the increase of the tetragonality of the systems. The theoretical spin Hamiltonian parameters and their concentration dependences show good agreement with the experimental data. To evaluate validity and applicability of the present theoretical model and formulas, the EPR results of the Cu 2+ centers in similar lithium sodium borate (LNB) xLi 2O·(30 − x)·Na 2O·70B 2O 3 (5 ≤ x ≤ 25 mol%) glasses are also analyzed and compared with those in the LKB systems using the uniform model and formulas.

Magnetic vortex lattice in HgBa2CuO4+δobserved by small-angle neutron scattering

We report the direct observation of the magnetic vortex lattice in the model high-temperature superconductor HgBa${}_{2}$CuO${}_{4+\ensuremath{\delta}}$. Using small-angle neutron scattering on high-quality crystals, we observe two equal domains of undistorted triangular vortex lattices well aligned with the tetragonal crystallographic axes. The signal decreases rapidly with increasing magnetic field and vanishes above $0.4$ T, which we attribute to a crossover from a three-dimensional to a two-dimensional vortex system, similar to previous results for the more anisotropic compound Bi${}_{2.15}$Sr${}_{1.95}$CaCu${}_{2}$O${}_{8+\ensuremath{\delta}}$. Our result indicates that a triangular vortex lattice (with or without distortion) at low magnetic fields is a generic property of cuprates with critical temperatures above $80$ K.

Atomic-scale modeling of nanostructure formation in Fe–Ga alloys with giant magnetostriction: Cascade ordering and decomposition

The Fe–Ga body-centered cubic (bcc) alloys within the 15–20 at.% Ga composition range have abnormally high magnetostriction. There is growing evidence that this effect is associated with the magnetic field-induced flip of tetragonal axes of nanoparticles of the ordered phase formed in this range. We studied structural transformations within this composition range at 550 °C by using computer modeling of the atomic-scale ordering and clustering in the atomic density field approximation. It is shown that the initial stage of equilibration of the compositionally homogeneous bcc solid solution with 19 at.% Ga results in bcc → B2 congruent ordering followed by a precipitation of Ga-rich B2 particles, which eventually transform to particles of the DO 3 phase. At the composition 21 at.% Ga, the congruently ordered B2 phase undergoes further B2 → DO 3 congruent ordering, which is followed by decomposition into an equilibrium mixture of the bcc and DO 3 phases. An important result is that the phase transformations at 0.15 < c < 0.19 produce nanoparticles of transient B2 phase. We assume that the nanoprecipitates of the transient B2 phase undergo a diffusionless cubic → tetragonal transformation, forming the L1 0 phase during cooling to the room temperature, and that this involves a magnetic field-induced flipping of tetragonality of these nanoprecipitates which may be responsible for the giant magnetostriction.