Plane Of Reciprocal Space Research Articles

Formation mechanism of co-axial grain boundaries in a Mg alloy

Due to the insufficient slip systems in hexagonal close-packed structure, twinning is frequently activated to support stable plastic deformation of Mg alloy. In this work, we found four typical twin-like interfaces with misorientations of 102°, 109°, 142° and 149°, respectively, which had not only a shared [11 2 ¯ 0] zone axis of neighboring grains, but also overlapped diffraction spots similar to twins. However, high-resolution transmission electron microscope (HRTEM) analysis revealed that the interfaces in real space deviated from the supposed twinning planes in reciprocal space, i.e. their overlapped diffraction spots. We clarified that the incoherent interfaces were co-axial grain boundaries (CGBs). Additionally, a special angle of θ , close to 90°, between the interface and one side of basal plane, was frequently formed in CGBs. We proposed that interaction of multiple twinning contributes to the formation of CGBs, and the θ is formed due to alternative tensile and compression twinning under a uniaxial loading.

Layered Topological Crystalline Insulators.

Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a three-dimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the interlayer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) (μ1,μ2) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as a PbSe (001) monolayer/h-BN heterostructure and can be tuned by mechanical strain. Our results shed light on the role of the MCNs on inequivalent mirror-symmetric planes in reciprocal space and open new possibilities for finding new topological materials.

States of hydrogen and deuterium in chemically charged high purity aluminum

In the present study, the deuterium distribution through the specimen thickness during charging and aging at various temperatures was characterized using the secondary ion mass spectrometry (SIMS) method. The advantages of this method are that the actual concentration–depth profiles are obtained from hydrogen (H) introduced during the growth, storage and melting environments (in single crystal or polycrystalline) of aluminum. Separately, the deuterium (D) concentration–depth profiles introduced from chemical processes or interactions with water during the experimental test processes, obtained by charging was characterized. Analysis of the pores, voids and bubbles related to hydrogen and deuterium was performed by small and wide X-ray scattering (SAXS and WAXS) and by high magnification transmission and scanning electron microscopy (TEM and SEM). Large (some micrometers in diameter) to very small (nanometers in diameter) sizes in the distribution and variability in the density of the voids/bubbles were found. The internal and surface bubbles and dense distributions of voids near dislocations related to the hydrogen distribution were studied. Moreover, the hydrogen–vacancy interactions related to microstructure changes must be taken into account in the process of characterizing the state of hydrogen in aluminum. An interpretation of the two dimensional anisotropic iso-intensities obtained by SAXS for octants voids was coded to obtain iso-intensity in the [1 1 0] plane in reciprocal space.

High-energy X-ray diffuse scattering

Diffuse X-ray scattering has been an important tool for understanding the atomic structure of binary systems for more than 50 years. The majority of studies have used laboratory-based sources providing 8 keV photons or synchrotron radiation with similar energies. Diffuse scattering is weak, with the scattering volume determined by the X-ray absorption length. In the case of 8 keV photons, this is not significantly different from the typical extinction length for Bragg scattering. If, however, one goes to energies of the order of 100 keV the scattering volume for the diffuse scattering increases up to three orders of magnitude while the extinction length increases by only one order of magnitude. This leads to a gain of two orders of magnitude in the relative intensity of the diffuse scattering compared with the Bragg peaks. This gain, combined with the possibility of recording the intensity from an entire plane in reciprocal space using a two-dimensional X-ray detector, permits time-resolved diffuse scattering studies in many systems. On the other hand, diffraction features that are usually neglected, such as multiple scattering, come into play. Four types of multiple scattering phenomena are discussed, and the manner in which they appear in high-energy diffraction experiments is considered.

Revisiting static and dynamic spin-ice correlations inHo2Ti2O7with neutron scattering

Elastic and inelastic neutron-scattering studies have been carried out on the pyrochlore magnet ${\text{Ho}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$. Measurements in zero applied magnetic field show that the disordered spin-ice ground state of ${\text{Ho}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ is characterized by a pattern of rectangular diffuse elastic scattering within the [HHL] plane of reciprocal space, which closely resembles the zone-boundary scattering seen in its sister compound ${\text{Dy}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$. Well-defined peaks in the zone-boundary scattering develop only within the spin-ice ground state below $\ensuremath{\sim}2\text{ }\text{K}$. In contrast, the overall diffuse-scattering pattern evolves on a much higher-temperature scale of $\ensuremath{\sim}17\text{ }\text{K}$. The diffuse scattering at small wave vectors below [001] is found to vanish on going to $\mathbf{Q}=0$, an explicit signature of expectations for dipolar spin ice. Very high energy-resolution inelastic measurements reveal that the spin-ice ground state below $\ensuremath{\sim}2\text{ }\text{K}$ is also characterized by a transition from dynamic to static spin correlations on the time scale of ${10}^{\ensuremath{-}9}\text{ }\text{s}$. Measurements in a magnetic field applied along the $[1\overline{1}0]$ direction in zero-field-cooled conditions show that the system can be broken up into orthogonal sets of polarized $\ensuremath{\alpha}$ chains along $[1\overline{1}0]$ and quasi-one-dimensional $\ensuremath{\beta}$ chains along [110]. Three-dimensional correlations between $\ensuremath{\beta}$ chains are shown to be very sensitive to the precise alignment of the $[1\overline{1}0]$ externally applied magnetic field.

Diffuse scattering from large-angle, thermally induced, orientational disorder in molecular crystals

Large-angle rotational motion (libration) characteristic of molecular solids has not been properly included in many scattering calculations because of the need to develop scattering theory through small-angle approximations. A simple but effective approach to calculating the influence of large-angle librations on the thermal disorder scattering given by molecular solids is to treat the molecules as independent librators, each in a harmonic potential well, using the mathematics appropriate for large-angle rotations. The resulting probability distribution for angular misorientations is Gaussian and this distribution can be used to smear the molecular form factor, enabling the librational influence on the scattering to be calculated. It is shown how to apply this direct approach quite generally and by way of examples the technique is used with the molecular solids sulfur hexafluoride (SF(6)), adamantane (C(10)H(16)) and buckminsterfullerene (C(60)). For these materials, the molecular Fourier transform (i.e. the molecular form factor) have been calculated in selected planes in reciprocal space, followed by the separate effects of librational and translational smearing. It is found that the librational smearing produces a large effect on the form factor, particularly at larger scattering vectors, that is not sensitive to approximations in the argument. Additionally, the Debye-Waller effect of vibrational motion is included in the calculations, showing quantitatively the decreasing influence of vibrations on the scattering with increasing scattering vector. Both effects illustrate with pedagogic clarity how different processes modify the basic molecular scattering.

Magnetic and atomic short-range order in Cu-richCu-Mn

Elastic diffuse neutron scattering from $\text{Cu}\text{\ensuremath{-}}17\phantom{\rule{0.3em}{0ex}}\text{at.}%$ Mn was measured within three planes of reciprocal space, at room temperature and at $11\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ (far above and below the spin-glass temperature of $71\phantom{\rule{0.3em}{0ex}}\mathrm{K}$) to determine the atomic and magnetic short-range order parameters. Using two samples with frozen-in states of thermal equilibrium of 483 and $553\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, respectively, the antiferromagnetic character of the spin glass was found to be robust against changes in the degree of atomic order while the ferromagnetic character is rapidly reduced with lower atomic order. This confirms conclusions of ab initio calculations by Ling et al. [J. Phys.: Condens. Matter 6, 6001 (1994)].

Linear Framework Defects in Zeolite Mordenite

Framework defect correlations are identified in zeolite mordenite that explain both X-ray powder diffraction anomalies and diffuse intensity features in previously reported electron diffraction data. The c/2 displacement of linear “chains” of framework material parallel to the main [001] channel are shown to selectively suppress and broaden the l = 2n + 1 Bragg reflections, thereby linking these framework defects to observed trends in a number of diffracted intensity ratios. At the same time, these defects are shown to produce thin sheets of diffuse scattering that are restricted to the l = 2n + 1 planes of reciprocal space, features that have been reported in electron diffraction studies of mordenite. An empirical relationship between the defect concentration and the framework aluminum content is also established.

Neutron scattering studies of the cooperative paramagnet pyrochloreTb2Ti2O7

We have carried out extensive neutron-scattering studies on the pyrochlore antiferromagnet ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ in both polycrystalline and single-crystal form. This insulating material belongs to a family of rare-earth titanate pyrochlores, ${R}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7},$ whose magnetic rare-earth ions reside on a network of corner sharing tetrahedra. Such a local geometry is known to give rise to geometrical frustration in the presence of antiferromagnetic interactions. Earlier studies have shown ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ to be an Ising system with large moments constrained to point along local [1, 1, 1] directions; that is, into and out of the tetrahedra. It displays a cooperative paramagnetic or spin liquid state at low temperatures, with neither long-range N\'eel order nor spin glass ordering at temperatures as low as 0.07 K. Our elastic neutron-scattering measurements show that very short-range correlations develop below \ensuremath{\sim}100 K. At 4 K a checkerboard pattern of diffuse magnetic scattering within the [h,h,l] plane in reciprocal space is observed, consistent with spin correlations over near neighbors only. Inelastic scattering measurements on both powder and single-crystal samples show three bands of magnetic excitations. At temperatures above \ensuremath{\sim}20 K, these bands are dispersionless, but at low temperature an appreciable softening in the lowest band of excitations occurs at those wave vectors which characterize the development of the very short-range magnetic order, qualitatively consistent with theoretical expectations derived from the single-mode approximation.

Correlated Simultaneous Phason Jumps in an Icosahedral Al-Mn-Pd Quasicrystal

A triple-axis neutron-scattering experiment has been performed on a large single-grain sample of an icosahedral Al-Mn-Pd quasicrystal. The scattering plane in reciprocal space was a binary plane of the quasicrystal. The intensities of the quasielastic signals collected were compared with model calculations assuming isolated single-particle jumps along two-, three-, and fivefold axes of the quasicrystal. The agreement turned out to be unsatisfactory. We were able to explain the experimental data only by assuming the existence of correlated simultaneous jumps of several atoms.

A neutron diffraction study of the superionic transition in with x = 0.06

We have investigated the high-temperature superionic transition of the anion-excess fluorite with x = 0.06 using both monochromatic and time-of-flight Laue single-crystal neutron diffraction. The measured Bragg intensities indicate that the cuboctahedral defect clusters found at ambient temperature start to break up into smaller fragments even below the superionic transition temperature, . Information concerning the local defect configuration at T = 1173 K has been provided by modelling the measured distribution of the coherent elastic diffuse scattering within the plane of reciprocal space. The high-temperature defects are of the `Willis' type and strongly resemble the short-lived Frenkel clusters found in the pure fluorites such as above .

On the minimum number of beams needed to distinguish enantiomorphs in X-ray and electron diffraction

The minimum strategy for distinguishing enantiomorphs by dynamical diffraction is determined. It is found that, in the absence of anomalous dispersion, it is possible to determine the absolute hand of an enantiomorphic crystal by three-beam dynamical X-ray or electron diffraction in a general orientation only if a fourth noncoplanar reciprocal-lattice point can be identified. Three-beam dynamical diffraction alone is unable to distinguish enantiomorphic forms. Identification is possible using four or more dynamical beams, in general, unless all relevant structure factors lie on a plane in reciprocal space passing through the origin. Supporting computations are given.

A simplified multidimensional search used for crystal structure solution of pCpGpCpGpCpG with two duplexes pre asymmetric unit.

A simplified multidimensional search was applied to determine the structure of deoxyhexamer CGCGCG in the crystal form belonging to the space group C222(1) (a = 45.6 A, b = 37.3 A, c = 70.3 A). This crystal form contains two Z-DNA duplexes per asymmetric unit in a similar orientation. The search consists of several main steps. As a first step, the analysis of packing modes is carried out and constraints for the position of duplexes in asymmetric unit are formulated. In order to choose true packing mode duplexes are represented as cylinders of a constant density and global search is carried out. Only reflections belonging to the plane in reciprocal space perpendicular to DNA axis were used in the calculations. An analytical representation of diffraction from a hollow cylinder is given which allows further refinement of corresponding parameters. During the global search the value of a linear correlation coefficient is estimated for each solution to pick up the best one. At the second step the "more local" search is carried out. The DNA model of a certain conformation (in our case Z-DNA) is taken and several parameters are being varied. These are: a) rotations of the independent duplexes around their axes (only two rotational parameters for two duplexes in our example) and b) a few positional parameters for which there is no corresponding constraint in the packing mode tested. In our case we had to vary only x1 and y2, where subindex corresponds to molecule number. The last stage concerned is quite similar to the multidimensional search realised in program ULTIMA. The only difference that the number of variable parameters is less in our search. This number for the case under consideration was 4 instead of 12 that would be necessary in a conventional multidimensional search.

Evaluation of 3D small-angle scattering from non-spherical particles in single crystals

Three-dimensional small-angle scattering is discussed as a tool for investigation of anisometric particles in single-crystalline alloys. The measurement and evaluation methods take advantage of the well defined orientation relation between the precipitates and the matrix in alloys. The determination of shape, size and orientation of precipitates from the scattering in several planes of reciprocal space is discussed for the example of ellipsoids and plates. Shape and orientation of ellipsoids with small aspect ratio can be determined by deviations of the scattering intensity from spherical symmetry in certain planes of reciprocal space. Particle size is obtained from one-dimensional slices along certain directions. The small-angle scattering of plate-like particles with large aspect ratio is concentrated along radial streaks in reciprocal space. Slices along and across these streaks allow the determination of the plate thickness as well as size and aspect ratio of the plate surface. In addition, the evaluation of such `off-center' slices provides a resolution enhancement of almost one order of magnitude compared to the conventional Guinier method applied to spherically averaged data.

Diffuse scattering in La-Sm-Sr-Cu-O

Abstract Diffuse scattering, reflecting structural disorder in La1.8-x Sm x Sr0.2CuO z , have been investigated by means of electron diffraction. In the T∗-structure, in addition to the fundamental spots due to the T∗-structure there exists cylindrical-shape diffuse scattering due to static displacements of the apical oxygen atoms in the CuO5 pyramids. On the other hand, both thermal diffuse scattering and superlattice spots have been found in diffraction patterns obtained from the T-structure. The thermal diffuse scattering is distributed on the {100}∗ planes of reciprocal space. In addition, the superlattice spots appear in a range of 0.3 ∗ directions. On the basis of the extinction rule for the superlattice spots, the crystal system of the T-structure for 0.3 < x< 0.6 is concluded to be orthorhombic while the system for 0 < x< 0.3 is tetragonal.

Misfit Layer Compounds Based on Double Layers MX and Sandwiches TX2 (M=Sn, Pb, Sb, Bi, Ln; T=Ti, V, Cr, Nb, Ta; X=S, Se)

Misfit layer compounds have a composite structure with two interpenetrating subsystems, an MX and an TX2 or (TX2)2 subsystem. Several structure types occur, the main difference coming from the different type of coordination of transition metal T by X atoms of the TX2 sandwiches. All structures show the presence of a common (b*, c*) plane in reciprocal space which comes from space fitting and from the interaction between the two subsystems. A classification of structures can be given based on the symmetries of the two subsystems. Since the diffraction pattern of the composite crystal is given by four reciprocal vectors, the symmetry can be described in (3+1)D superspace. The composition, which is generally non-stoichiometric, is determined by the ratio of the unit cell volumes of the two sublattices; the temperature dependence of the composition is governed by the thermal expansion. The physical properties are discussed in relation with chemical bonding. The electrical resistivity for compounds with NbX2, TaX2 or TiX2 sandwiches is metallic, the inplane resistivity being about 10-4 smaller than the resistivity along c. Hall effect and thermopower seem to indicate that the conduction takes place within the sandwich layers. For compounds with M=Sn, Pb, Sb, Bi, the intralayer M-X distances are shorter than the interlayer distances indicating a weak interaction; Hall effect and photoelectron spectroscopy indicate no or hardly any electron transfer from MX to TX2 for such compounds. The interaction between layers LnX and TX2 is strong; intra- and interlayer Ln-X distances are about equal and correspond to those for Ln3+; the magnetic properties also point to Ln3+. Hall effect and thermopower are in a greement with electron transfer and conduction in the TX2 sandwiches. Photoelectron spectroscopy confirms that Ln is trivalent; indications for charge transfer are less clear. Reflection spectra in the range 2000–20,000 cm-1 are in agreement with charge transfer.

The defect structure of anion-excess (Ca 1− xY x)F 2+ x with x = 0.06

The defect structure of the anion-excess fluorite (Ca 1− x Y x )F 2+ x with x = 0.06 has been investigated using single-crystal neutron diffraction. Least-squares refinement of the measured Bragg intensities has been performed considering four positions for the disordered anions within the Fm 3m unit cell: in 48 i sites at ( 1 2, u, u ) with u = 0.39; in 32 f sites at ( w, w, w) with w = 0.38; in 32 f sites at ( v, v, v) with v = 0.27, and in the empty cube center 4 b sites at ( 1 2 , 1 2 , 1 2 ) . The results indicate that only the ( 1 2 , u, u) and ( v, v, v) sites are significantly occupied. Information concerning the local defect configuration has been provided by least-squares refinement of the measured distribution of coherent elastic diffuse scattering within the (1 10) plane of reciprocal space. The best agreement with both Bragg diffraction and diffuse scattering data is obtained by adopting a model of randomly distributed cuboctahedral anion polyhedra, of the type observed in ordered anion-excess fluorite superlattices.

Observation of the thermal diffuse scattering in La2-xMxCuO4 (M=Sr,Ba).

Thermal diffuse scattering of ${\mathrm{La}}_{2\ensuremath{-}x}{M}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ ($M=\mathrm{S}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{B}\mathrm{a}$) is examined by means of electron diffraction, both at room temperature and liquid-nitrogen temperature. The diffraction patterns show nonradial diffuse streaks which correspond to thermal diffuse scattering distributed on ${{100}}_{t}$ and ${{114}}_{t}$ planes in reciprocal space. In addition, strong diffuse scattering along the ${[114]}_{t}$ and ${[11\overline{4}]}_{t}$ directions around fundamental spots is also observed in the orthorhombic phase.

Diffuse x-ray scattering and the structure of oxide layers on real GaAs(111) surfaces

The possibility of using diffuse X-ray scattering for obtaining information about the structure of native oxide layers on real semiconductor surfaces was demonstrated. Equi-intensity contours of the diffuse X-ray scattering in the ( hhl) plane of reciprocal space in GaAs suggest a model of oriented crystalline oxide particles on the Ga(111) face. Ordering is produced by the mechanical-chemical polishing of the GaAs surface. Diffuse streaks in the [111] direction are interpreted as being due to a two-dimensional effect in the scattering phenomenon and are consistent with a thickness of 20±3 Å for the oxide layer.

Acoustic phonon instabilities and structural phase transitions

Structural phase transitions are considered in which the order parameter is a homogeneous deformation of the crystal. The fluctuations at these transitions are the acoustic modes, and it is shown that an effective Hamiltonian may be constructed describing the homogeneous deformations and their fluctuations. There are three cases which result, those in which there are no fluctuations with wavelengths less than the crystal dimensions, those in which the acoustic modes have strongly temperature-dependent velocities for wave vectors on particular lines of reciprocal space, and those for which the velocities are temperature dependent for wave vectors within planes in reciprocal space. In many cases, the transitions are expected to be first order because of the presence of cubic invariants in the effective Hamiltonian. In those which may be continuous, the behavior is shown by use of renormalization-group theory to be that of classical Landau theory, with the possibility of logarithmic corrections in one particular instance. Unfortunately, we are unaware of any examples of this case, but in the other cases, the results are in accord with experimental results.