Strong atomic displacements around nitrogen in tantalum determined by energy-dispersive x-ray diffraction

The nitrogen induced attenuation of Bragg reflections (static Debye-Waller Factor) of tantalum single crystals containing nitrogen has been measured by energy-dispersive x-ray diffraction. N has been dissolved in Ta up to a concentration ofc=3.3% N/Ta. From a detailed study of the concentration andK dependence (K=scattering vector) of the static Debye-Waller Factor exponent 2L we conclude:i) 2L increases linearly with the nitrogen content forc1.8% N/Ta,ii) The displacements of the atomic shells due to N on the octahedral sites areu ₁=0.45 (5) Å,u ₂=(–)0.11 (2) Å.u ₃=0.25 (2) Å,iii) The thermal vibrations of those atoms close to N are changed, due to the strong static displacements that they experience. The unusual strong and extended displacements around N in Ta are in contradiction to calculations where two-force models have been used. We propose arguments that displacements are responsible for the specific site chosen by hydrogen atoms when they are trapped by nitrogen in Ta.     

The structure of the glass phase of Rb1−x(ND4)xD2PO4

X-ray scattering techniques have been used to study the diffuse scattering from a single crystal of Rb_1–x(ND₄)_xD₂PO₄ withx=0.65. This system has a structural glass phase at low temperatures resulting from the competing ferroelectric interactions of RbD₂PO₄ and antiferroelectric interactions of (ND₄)D₂PO₄. The diffuse scattering shows a broad peak with a maximum occurring at a wavevector of about 0.3a ^*, and the intensity of these peaks is surprisingly different for wavevectorsq on opposite sides of the Bragg reflections. A model of the D bonding is developed which suggests that the diffuse scattering arises from the interaction between ferroelectric displacements alongc, ferroelectric displacements alongb, and transverse acoustic modes polarized alongb andc. The model accounts for the incommensurate wavevector and, qualitatively, for the intensity of the diffuse scattering around different Bragg reflections. The temperature dependence of the scattering is also measured.     

X-ray determination of mean Debye-Waller factors and Debye temperatures of the K x Rb(1−x)Br mixed crystal system

The integrated intensities of Bragg reflections have been measured for mixed crystals in the K _x Rb_(1−x)Br system with an x-ray powder diffractometer. From the intensities, the mean Debye-Waller factors are determined. The Debye-Waller factors are corrected for static contribution and Debye temperature values are determined for the entire composition range. The x-ray Debye temperatures follow the Kopp-Neumann equation closely.     

Polarization analysis in soft X‐ray diffraction to study magnetic and orbital ordering

An experimental approach to the analysis of charge, magnetic and orbital ordering in 3d transition‐metal oxides is presented. The technique combines two important components: azimuthal rotations around the Bragg wavevector and polarization analysis of the Bragg intensities in the range 500–900 eV. The polarization analysis is performed using graded multilayers, which are translated and rotated in the vacuum chamber. It is shown why these two components are important to determine the origin of the Bragg scattered signals and how they allow us to separate the different contributions. Examples are given for the oxygen K and the Mn, Co, Ni and Cu L_2,3‐edges, and the advantages and drawbacks of this experimental technique are discussed.     

Electron transport and anisotropy of the upper critical magnetic field in Ba<Subscript>0.68</Subscript>K<Subscript>0.32</Subscript>Fe<Subscript>2</Subscript>As<Subscript>2</Subscript> single crystals

Early work on the iron-arsenide compounds supported the view, that a reduced dimensionality might be a necessary prerequisite for high-T _c superconductivity. Later, however, it was found that the zero-temperature upper critical magnetic field, H _c2(0), for the 122 iron pnictides is in fact rather isotropic. Here, we report measurements of the temperature dependence of the electrical resistivity, ρ(T), in Ba_0.5K_0.5Fe₂As₂ and Ba_0.68K_0.32Fe₂As₂ single crystals in zero magnetic field and in Ba_0.68K_0.32Fe₂As₂ in static and pulsed magnetic fields up to 60 T. We find that the resistivity of both compounds in zero field is well described by an exponential term due to inter-sheet umklapp electron-phonon scattering between light electrons around the M point to heavy hole sheets at the Γ point in reciprocal space. From our data, we construct an H-T phase diagram for the inter-plane (H | c) and in-plane (H | ab) directions for Ba_0.68K_0.32Fe₂As₂. Contrary to published data for 122 underdoped FeAs compounds, we find that H _c2(T) is in fact anisotropic in optimally doped samples down to low temperatures. The anisotropy parameter, γ = H _c2 ^ab /H _c2 ^c , is about 2.2 at T _c . For both field orientations we find a concave curvature of the H _c2 lines with decreasing anisotropy and saturation towards lower temperature. Taking into account Pauli spin paramagnetism, we perfectly can describe H _c2 and its anisotropy.     

Attenuation of phonon scattering intensities by point defects

The cross section of the coherent, inelastic neutron scattering is characteristically decreased in the presence of defect-induced lattice distortions. This effect is in analogy to the attenuation of Bragg intensities due to a static Debye-Waller factor. The integrated scattering intensities from transversal acoustic (TA-) phonons of the system NbN_0.014 have been measured and are shown to be attenuated with respect to the scattering intensities from the phonons of a pure Nb crystal. We discuss the obtained results through comparison with various model calculations.     

Structural deformations of the cubic lattice of the Zn1 ? x Fe x Se (x = 0.001) crystal

The structural state of a Zn_{1 ? x} Fe _x Se (x = 0.001) crystal has been studied using thermal neutron diffraction. The diffraction patterns of the cubic crystal have been found to contain diffuse scattering regions concentrated in the vicinity of the strong Bragg reflections. It has been shown that the diffuse scattering effects are due to local transverse displacements of the crystal lattice atoms, and these displacements are induced by iron ions that demonstrate the static Jahn-Teller effect of the tetragonal type in the ZnSe compound.     

Static displacements of atoms near isotopic impurities and residual resistivity

The question of the residual resistivity of chemically pure metals which are mixtures of atoms of different isotopes is discussed. The question of the static displacements appearing near isotopic impurities due to differences in the zero-point vibrations is analyzed in a microscopic approach. It is shown that such static displacements have a significant influence on the residual resistivity ρr. Their contribution to ρr is far greater than the contribution due to differences in the dynamic elastic electron scattering amplitudes. Zh. éksp. Teor. Fiz. 114, 2153–2165 (December 1998)     

Deep impurity-center ionization by far-infrared radiation

An analysis is made of the ionization of deep impurity centers by high-intensity far-infrared and submillimeter-wavelength radiation, with photon energies tens of times lower than the impurity ionization energy. Within a broad range of intensities and wavelengths, terahertz electric fields of the exciting radiation act as a dc field. Under these conditions, deep-center ionization can be described as multiphonon-assisted tunneling, in which carrier emission is accompanied by defect tunneling in configuration space and electron tunneling in the electric field. The field dependence of the ionization probability permits one to determine the defect tunneling times and the character of the defect adiabatic potentials. The ionization probability deviates from the field dependence e(E) ∝ exp(E ²/E _c ² ) (where E is the wave field, and E _c is a characteristic field) corresponding to multiphonon-assisted tunneling ionization in relatively low fields, where the defects are ionized through the Poole-Frenkel effect, and in very strong fields, where the ionization is produced by direct tunneling without thermal activation. The effects resulting from the high radiation frequency are considered and it is shown that, at low temperatures, they become dominant. Fiz. Tverd. Tela (St. Petersburg) 39, 1905–1932 (November 1997)     

Determination of static displacements around non-metal vacancies in NbN1−c and TiC1−c by channeling

The results of channeling experiments, which have been performed on B1-NbN_1?c-single crystals with 0.07 ? c ? 0.18 and on a B1-TiC_0.9-single crystal in order to get information on lattice distortions due to non-metal vacancies, are presented. Angular yield curves were measured at temperatures of 295, 78 and 5 K. Monte-Carlo calculations with a defect model of mean static displacements of all metal atoms were used to analyze the experimental data. Static displacements for the Nb-atoms of 0.14 ± 0.02 Å and for the Ti-atoms of 0.04 ± 0.01 Å have been determined. The results on the Nb- and the Ti-displacements were in good agreement with results obtained by neutron diffraction experiments on B1-NbN_1?c powder samples and by diffuse neutron scattering experiments on B1-TiC- crystals, respectively.     

Influence of crystal defects on the irreversibility line of YBa2Cu3O7-x single crystals

High quality flux grown and defect enriched peritectically grown YBa₂Cu₃O_7–x single crystals have been investigated by an ac-susceptibility technique. This method allows to determine an irreversibility line from the temperature and field dependence of the peaked imaginary part of the susceptibility, which is due to magnetic losses. For magnetic fieldsH _ac perpendicular to thec-axis of the crystal, the irreversibility line of the defect enriched crystal shows a shift to higher field values as compared to the perfect crystal, a sign that crystal defects like Y₂BaCuO₅(211)-precipitates and microcracks act as strong pinning centers. ForH _ac parallel to thec-axis no clear evidence for a stronger pinning is found. From these results we conclude that different pinning mechanisms are dominating at different field orientations.     

Spatial topology of local nano scale inhomogeneity of crystal structure Zn<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Fe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se (<Emphasis Type="Italic">x</Emphasis> = 0.001)

The method of thermal neutron diffraction is used to study a structural state of crystal Zn_{1 − x} Fe _x Se (x = 0.001) obtained in the sphalerite modification. It was found that the diffractive pictures of a cubic crystal contain the regions of diffuse scattering in the vicinity of Bragg reflections of an initial crystal lattice. It was shown that the diffuse scattering effects were caused by the local transverse displacements of atoms in a crystal lattice induced by Fe²⁺ ions. It is concluded that a static tetragonal-type Jahn-Teller effect exists in a ZnSe alloy doped by magnetoactive iron ions.     

Nuclear magnetic resonance of 55Mn in the antiferromagnet CsMnBr3 in a variable longitudinal magnetic field

The spectrum and intensities of NMR lines are investigated experimentally and theoretically for excitation by an alternating magnetic field h‖ parallel to a static field H in the quasi-one-dimensional, six-sublattice antiferromagnet CsMnBr₃. According to theory, two new NMR lines, which are not excited by a transverse magnetic field h _⊥, are observed near the phase transition from triangular to collinear structure (H=H _c ) [JETP 86, 197 (1998)]. Zh. éksp. Teor. Fiz. 115, 2228–2241 (June 1999)     

Rayleigh scattering of Mössbauer radiation on a myoglobin single crystal

The RSMR technique was used to determine the fraction of radiation which is scattered elastically and inelastically, respectively, into Bragg reflections of a metmyoglobin single crystal. From this measurement 〈x² _1c〉=0.027±0.008 A² has been determined which is due to long range correlated motions in analogy to acoustic and optic modes in solids.     

Magnetism in a UNi2/3Rh1/3Al single crystal

We report a magnetization, magnetostriction, electrical resistivity, specific heat and neutron scattering study of a UNi_2/3Rh_1/3Al single crystal, a solid solution of an antiferromagnet UNiAl and a ferromagnet URhAl. The huge uniaxial magnetic anisotropy confining the principal magnetic response to the c axis in the parent compounds persists also for the solid solution. The magnetization curve at 1.6 K has a pronounced S shape with an inflection at 12 T. The temperature dependence of magnetic susceptibility exhibits a maximum around 10 K and is magnetic history dependent at lower temperatures where the resistivity increases linearly with decreasing temperature. The low-temperature ρ(T) anomaly is removed in a magnetic field applied along c, which yields a large negative magnetoresistance amounting to m46 zin 14T (at 2 K). The C/T values exhibit a minimum around 12 K and below 8 K they become nearly constant (about 250 mJ mol^?1 K^?2), which is strongly affected by magnetic fields. Neutron scattering data confirm a non-magnetic ground state of UNi_2/3Rh_1/3Al. The bulk properties at low temperatures are tentatively attributed to the freezing of U magnetic moments with antiferromagnetic correlations. The additional intensities detected on top of nuclear reflections in neutron diffraction in a magnetic field applied along c are found to be proportional to the field-induced magnetization, which reflects field-induced ferromagnetic coupling of U magnetic moments. This scenario is corroborated also by finding low-temperature magnetostriction data that also scale with the square of magnetization.     

The role of nucleon recoil in low-energy antikaon-deuteron scattering

The effect of the nucleon recoil for the antikaon-deuteron scattering is investigated in the framework of the effective field theory. In particular, we concentrate on the calculation of the nucleon recoil effect for the double-scattering process. It is shown that the leading correction to the static term that emerges at order x^1/2 \xi^{{1/2}}_{} with x \xi = M _K/m _N vanishes due to a complete cancellation of individually large contributions. The resulting recoil effect in this process is found to be of the order of 10-15% as compared to the static term. We also briefly discuss the application of the method in the calculations of the multiple-scattering diagrams.     

Vortex lattice transitions in YNi2B2C

We have performed extensive small-angle neutron scattering (SANS) diffraction studies of the vortex lattice in single crystal YNi₂B₂C for B‖c. High-resolution SANS, combined with a field-oscillation vortex lattice preparation technique, allows us to separate Bragg scattered intensities from two orthogonal domains and accurately determine the unit cell angle, β. The data suggest that upon increasing field there is a finite transition width where both low- and high-field distorted hexagonal vortex lattice phases, mutually rotated by 45°, coexist. The smooth variation of diffracted intensity from each phase through the transition corresponds to a redistribution of populations between the two types of domains.     

Effect of atomic vibrations in XANES: polarization‐dependent damping of the fine structure at the Cu K‐edge of (creat)2CuCl4

Polarization‐dependent damping of the fine structure in the Cu K‐edge spectrum of creatinium tetrachlorocuprate [(creat)₂CuCl₄] in the X‐ray absorption near‐edge structure (XANES) region is shown to be due to atomic vibrations. These vibrations can be separated into two groups, depending on whether the respective atoms belong to the same molecular block; individual molecular blocks can be treated as semi‐rigid entities while the mutual positions of these blocks are subject to large mean relative displacements. The effect of vibrations can be efficiently included in XANES calculations by using the same formula as for static systems but with a modified free‐electron propagator which accounts for fluctuations in interatomic distances.     

X-ray diffraction studies on dilute solid solution of NaCl with Ag impurities

Abstract

X-ray investigations of Bragg scattering measurements have been carried out on the dilute solid solutions of Ag _x Na_1?x Cl for x = 0.03 and 0.10. The integrated intensities are measured on spherical single crystals, using a home-built manual X-ray diffractometer. The analysis of experimental data indicates an enhancement of Debye-Waller factor in this system. The size effect distortion factors evaluated are compared with the calculated values on the basis of different theoretical models and the results are discussed. The measured cell constant and density data indicate the existence of vacancies in these crystals.     

Negative Poisson coefficient of fractal structures

On the basis of a fractal model the macroscopic elastic properties of an inhomogeneous medium with random structure have been determined. It is shown that if the ratio of the bulk moduli of the phases K ₂/K ₁→0, then the percolation threshold p _c the Poisson coefficient is equal to 0.2. A study of the behavior of a two-phase medium with negative Poisson coefficient is carried out. Fiz. Tverd. Tela (St. Petersburg) 41, 2147–2153 (December 1999)