Orientation Averaging Research Articles

Effects of Reorientation in Vibrational Sum-Frequency Spectroscopy

Vibrational sum-frequency spectroscopy (VSFS) has become a widely used tool for studying molecules at interfaces. While VSFS data are often interpreted in terms of static structure, Wei and Shen demonstrated that orientational dynamics that occur on the time scale of vibrational dephasing can influence the strength of the VSFS signal (Wei, X.; Shen, Y. R. Phys. Rev. Lett. 2001, 86, 4799). In this report, we consider the orientational averages relevant to VSFS under different polarization conditions in terms of the infrared transition dipole and the Raman tensor when the infrared and Raman transitions are simultaneous and when they are separated by a delay that is greater than the orientational correlation time. We examine specific cases of orientational averaging that apply to commonly studied functional groups. This analysis makes possible the identification of the circumstances under which reorientation should be taken into account when using VSFS to determine molecular orientation at interfaces.

On the effective number of tracked trajectories in normal human vision

Z. W. Pylyshyn and R. W. Storm (1988) have shown that human observers can accurately track four to five items at a time. However, when a threshold paradigm is used, observers are unable to track more than a single trajectory accurately (S. P. Tripathy & B. T. Barrett, 2004). This difference between the two studies is examined systematically using substantially suprathreshold stimuli. The stimuli consisted of one (Experiment 1) or more (Experiments 2 and 3) bilinear target trajectories embedded among several linear distractor trajectories. The target trajectories deviated clockwise (CW) or counterclockwise (CCW) (by 19 degrees, 38 degrees, or 76 degrees in Experiments 1 and 2 and by 19 degrees, 38 degrees, or 57 degrees in Experiment 3), and observers reported the direction of deviation. From the percentage of correct responses, the "effective" number of tracked trajectories was estimated for each experimental condition. The total number of trajectories in the stimulus and the number of deviating trajectories had only a small effect on the effective number of tracked trajectories; the effective number tracked was primarily influenced by the angle of deviation of the targets and ranged from four to five trajectories for a +/-76 degrees deviation to only one to two trajectories for a +/-19 degrees deviation, regardless of whether the different magnitudes of deviation were blocked (Experiment 2) or interleaved (Experiment 3). Simple hypotheses based on "averaging of orientations," "preallocation of resources," or pop-out, crowding, or masking of the target trajectories are unlikely to explain the relationship between the effective number tracked and the angle of deviation of the target trajectories. This study reconciles the difference between the studies cited above in terms of the number of trajectories that can be tracked at a time.

Optimization of Algorithms for Ion Mobility Calculations

Ion mobility spectrometry (IMS) is increasingly employed to probe the structures of gas-phase ions, particularly those of proteins and other biological macromolecules. This process involves comparing measured mobilities to those computed for potential geometries, which requires evaluation of orientationally averaged cross sections using some approximate treatment of ion-buffer gas collisions. Two common models are the projection approximation (PA) and exact hard-spheres scattering (EHSS) that represent ions as collections of hard spheres. Though calculations for large ions and/or conformer ensembles take significant time, no algorithmic optimization had been explored. Previous EHSS programs were dominated by ion rotation operations that allow orientational averaging. We have developed two new algorithms for PA and EHSS calculations: one simplifies those operations and greatly reduces their number, and the other disposes of them altogether by propagating trajectories from a random origin. The new algorithms were tested for a representative set of seven ion geometries including diverse sizes and shapes. While the best choice depends on the geometry in a nonobvious way, the difference between the two codes is generally modest. Both are much more efficient than the existing software, for example faster than the widely used Mobcal (implementing EHSS) approximately 10-30-fold.

First-principles calculation of nuclear resonance vibrational spectra

We present a ‘first-principles’ methodology for the calculation of the parameters that are required for the simulation of nuclear resonance vibrational spectra (NRVS) of molecular systems. Formulae are given for the intensities of vibrational transitions corresponding to the so-called single- and double-phonon contributions to the NRVS signal. The method is also valid for those vibrations that are not in the high-frequency/low-temperature limit. We have rigorously treated the issue of orientational averaging of the Lamb–Mossbauer factor and the effect of the neglect of its anisotropy on the calculated NRVS pattern. Normal mode composition factors are determined in a compact form as appropriate components of an orthogonal matrix that diagonalizes the Hessian matrix. The method is illustrated by simulating the NRVS spectra and the partial vibrational density of states of [FeO(H2O)5]2+ on the basis of vibrational frequencies and normal mode composition factors obtained from density functional theory (DFT) calculations.

Ventral extra-striate cortical areas are required for optimal orientation averaging

We examined the ability of a previously well-studied patient with visual agnosia to compute the average orientation of elements in visual displays. In a structural MRI study, we show that the lesion is likely to involve a variety of ventral extra-striate areas, including V2, V3 and V4; however, the lesion does not extend dorsally. Subsequently we show that some ability to compute average orientation is spared, though there are limitations on the ability to scale the averaging process as a function of the numbers of elements. The results suggest that some aspects of orientation averaging can be accomplished in spared regions of V1 but flexible averaging requires ventral extra-striate cortex.

Domain Switching Under Cyclic Mechanical Loading in Lead Zirconate Titanate

The domain‐switching behavior of lead zirconate titanate (PZT) during mechanical cyclic loading between 10 and 150 MPa was investigated by in situ time‐of‐flight neutron diffraction. The domain‐switching behavior was represented by a change of the pole density distribution during cycling. With increasing number of cycles, domain switching becomes saturated, correlating with a decrease in the rate of remnant strain accumulation in the stress–strain curve. Moreover, a relationship was demonstrated between the macroscopic strain and that developed from ferroelastic domain switching. The contribution of ferroelastic strain to the macroscopic strain was calculated from an orientation average of the domain switching distributions and the c/a ratio. The results show that nearly 80% of macroscopic strain arises from ferroelastic domain switching during mechanical cyclic loading.

Efficient orientational averaging by the extension of Lebedev grids via regularized octahedral symmetry expansion

Gaussian spherical quadrature methods in the guise of the Lebedev sampling grids are highly efficient for some orientational (“powder”) averaging problems in solid state NMR. However, their applicability is currently restricted, as the sets of orientations are derived analytically and because they are not well adapted to simulate the broad peakshapes encountered, for example, in the NMR on static powders or on half-integer quadrupolar spins subject to second order quadrupolar interactions under magic-angle spinning conditions. We remedy these problems by (i) introducing the recursive procedure regularized octahedral symmetry expansion (ROSE), to which any existing Lebedev set may be subjected. Each recursive step gives a 9-fold enlarged set of orientations. (ii) We demonstrate that ROSE-expanded grids, in conjunction with spectral interpolation, is well suited for calculating broad peakshapes. These advances combine into the apparently most efficient general-purpose two-angle orientational averaging technique proposed to date for solid state NMR applications.

Elasticity of composites with irregularly oriented shape-anisotropic filler particles

A variant of determining the elastic characteristics of composites containing irregularly oriented shape-anisotropic filler particles of two types (short fibers and thin platelets) is considered. The effective elastic constants of the composites are calculated by using the method of orientational averaging of elastic characteristics of isolated transversely isotropic structural elements reinforced with unidirectionally oriented short fibers or coplanarly arranged thin platelets. The superposition of elastic properties of the irregularly oriented structural elements, with account of their orientational distribution in the composite material, is accepted. The calculation results are compared with experimental data for the effective elastic moduli of polymeric composites reinforced with short glass fibers and of polymeric nanocomposites containing the platelet-type particles of organically modified montmorillonite.

Stiffness and strength of flax fiber/polymer matrix composites

AbstractFlax fiber composites with thermoset and thermoplastic polymer matrices have been manufactured and tested for stiffness and strength under uniaxial tension. Flax/polypropylene and flax/maleic anhydride grafted polypropylene composites are produced from compound obtained by coextrusion of granulated polypropylene and flax fibers, while flax fiber mat/vinylester and modified acrylic resin composites are manufactured by resin transfer molding. The applicability of rule‐of‐mixtures and orientational averaging based models, developed for short fiber composites, to flax reinforced polymers is considered. POLYM. COMPOS. 27:221–229, 2006. © 2006 Society of Plastics Engineers

Infrared actuation in aligned polymer-nanotube composites

Rubber composites containing multiwalled carbon nanotubes have been irradiated with near-infrared light to study their reversible photomechanical actuation response. We demonstrate that the actuation is reproducible across differing polymer systems. The response is directly related to the degree of uniaxial alignment of the nanotubes in the matrix, contracting the samples along the alignment axis. The actuation stroke depends on the specific polymer being tested; however, the general response is universal for all composites tested. We conduct a detailed study of tube alignment induced by stress and propose a model for the reversible actuation behavior based on the orientational averaging of the local response. The single phenomenological parameter of this model describes the response of an individual tube to adsorption of low-energy photons; its experimentally determined value may suggest some ideas about such a response.

Rotational averaging and optimization of laser-induced population transfer in molecules

The dynamics of a molecule subject to a short laser pulse is investigated, with focus on the averaging over initial rotational states and on the optimization of laser parameters for the efficient population transfer between vibrational and electronic states. A relation is established between final-state populations obtained with a fixed orientation and those based on a full treatment of the rotational degrees of freedom. In the short-pulse approximation, rotational averaging amounts to integrating the fixed molecule results over all orientations. The theory is applied to a variety of model systems and verified with numerical calculations using Gaussian pulses. We calculate target state populations with three procedures, optimizing the laser pulse for a fixed orientation without orientational averaging, averaging without changing the laser parameters, and reoptimizing the parameters after averaging. The analysis of the two-level system provides a reference for the order of magnitude of the effects of averaging. The three-level system brings out the relevant role of the geometry of polarization vectors and transition dipoles. The multiphoton excitation of a Morse oscillator shows the importance of taking into account the dependence of resonance frequencies on the laser intensity. Within a proton transfer model we discuss the results obtained with and without chirping and we show that "optimizing after averaging" can be as effective as choosing a more refined pulse shape.

A micromechanics-based Cosserat-type model for dense particulate solids

A two-dimensional continuum theory is presented for cohesionless granular media consisting of identical rigid disks. While the normal deformation of contacting particles is constrained, the tangential frictional contact is modelled by a line spring with a constant stiffness. To describe the static frictional system transmitting couples at contacts, a Cosserat-type continuum including rotational degrees of freedom is appropriate. Contrary to the classical elastic medium, movement of particles within a granular system in response to applied loads can give rise to localisations of force chains and large voids. In addition to relative displacement and rotation, a director governing the direction of interparticle forces and a phase field delineating density variation, are therefore introduced. Total work done involving these two order parameters for a particle is attained on an orientation average. Based on the formulation of free energy, a concentration- and anisotropy-dependent formulation for static quantities (stress and couple stress) in the rate form is derived in light of the principles of thermodynamics. It is consistent with the requirement of observer independence and material symmetry. The governing equations for two order parameters are derived, in which void concentration and stress anisotropy are related to relative displacement and rotation. As an example, the proposed model is applied to the hardening regime of deformation of a dense particle assembly with initial perfect lattice under simple shear. It is demonstrated that in the presence of dilatancy and director variation, there exists a linear relation between the shear stress and strain, in coincidence with experimental observations.

Intermolecular interactions in a radiation field via the method of induced moments

Molecular quantum electrodynamics is employed to calculate a generalized formula for the energy shift between a pair of molecules that have electric polarizability of arbitrary multipole order and are in the presence of an intense electromagnetic field. In contrast to a previous calculation of the dipole-dipole contribution, which required fourth-order time-dependent perturbation theory for its evaluation, the present approach involves calculating the interaction between the multipole moments induced at each center by the incident beam and the resonant multipole-multipole coupling tensor together with the average value of the spatial correlation function of the displacement field for an $N$-photon state. The theory developed applies to the situation where the molecular pair is held fixed relative to the direction of propagation of the radiation field or is allowed to be completely randomly oriented. Explicit results are obtained for dipole-quadrupole and quadrupole-quadrupole polarizable molecules. For oriented systems the energy shift for linear and circular polarizations is examined for incident radiation propagating in directions parallel and perpendicular to the intermolecular join, and the asymptotic behavior is obtained at the limits of short and large separation distance. After performing a pair orientation average, the energy shift in the near zone is found to exhibit an ${R}^{\ensuremath{-}1}$ power-law behavior with separation distance, while the far zone has a modulated ${R}^{\ensuremath{-}2}$ dependence in all of the cases considered. None of the energy shifts obtained display discriminatory characteristics, with respect to either the handedness of the incident beam or the individual species.

Extreme Poisson's ratios and related elastic crystal properties

With the aim of understanding anisotropic crystals that possess a negative Poisson's ratio and to lay a foundation for investigating molecular mechanisms, we discuss the definition of the ratio and establish conditions on the compliance that govern its sign. We derive results on orientation averaging that are useful in the context of anisotropy and helpful in the investigation of isotropic polycrystals. We discuss α -cristobalite, a polymorph of silicon dioxide that possesses interesting negative ratio properties in single crystals and hypothetical polycrystals. In this connection, we draw attention to the transverse compliance as an alternative and simpler metric for gaging the ratio and for orientation averaging. For α -cristobalite, we arrive at new results for the directions that yield the most negative Poisson's ratio. This result should be of value in divining the underlying molecular mechanism that explains the negative values of Poisson's ratio in α -cristobalite, a crystal of tetragonal symmetry that possesses six independent elastic constants.

Porous irregular aggregates of sub-micron sized grains to reproduce cometary dust light scattering observations

The present study intends to interpret some of the characteristic features of the light scattered by cometary dust, such as phase angle and wavelength dependence of its polarization, through simulations using Ballistic Cluster-Cluster Aggregation (BCCA) or Ballistic Particle-Cluster Aggregation (BPCA) aggregates of up to 128 sub-micron sized grains (spherical and spheroidal with a possible size distribution) of various composition (silicates, organics, silicates core with organics mantle). The dependence of the linear polarization with the size parameter is shown to depend highly on the size and composition of the constitutive grains. Internal interactions induced by shape or orientation averaging of the grains may lessen this dependence, leading to results comparable to those observed on cometary dust for fluffy aggregates of grains with a size parameter in the 1.3–1.8 range. A size distribution of realistically shaped particles (aggregates of spheroids and larger spheroids) following a power law size distribution with a power index of - 3 , the smallest grains radius by 0.03– 0.2 μ m and the largest spheroids effective radius by 20 μ m , gives a very good fit to the Hale-Bopp observed phase curves. The best silicates–organics ratio ranges from about 50–75% organics and 25–50% silicates in volume considering the eventual presence of core-mantle grains.

Interpretation of Unusual Absorption Bandwidths and Resonance Raman Intensities in Excited State Mixed Valence

Excited state mixed valence (ESMV) occurs in molecules in which the ground state has a symmetrical charge distribution but the excited state possesses two or more interchangeably equivalent sites that have different formal oxidation states. Although mixed valence excited states are relatively common in both organic and inorganic molecules, their properties have only recently been explored, primarily because their spectroscopic features are usually overlapped or obscured by other transitions in the molecule. The mixed valence excited state absorption bands of 2,3-di-p-anisyl-2,3-diazabicyclo[2.2.2]octane radical cation are well-separated from others in the absorption spectrum and are particularly well-suited for detailed analysis using the ESMV model. Excited state coupling splits the absorption band into two components. The lower energy component is broader and more intense than the higher energy component. The absorption bandwidths are caused by progressions in totally symmetric modes, and the difference in bandwidths is caused by the coordinate dependence of the excited state coupling. The Raman intensities obtained in resonance with the high and low energy components differ significantly from those expected based on the oscillator strengths of the bands. This unexpected observation is a result of the excited state coupling and is explained by both the averaging of the transition dipole moment orientation over all angles for the two types of spectroscopies and the coordinate-dependent coupling. The absorption spectrum is fit using a coupled two-state model in which both symmetric and asymmetric coordinates are included. The physical meaning of the observed resonance Raman intensity trends is discussed along with the origin of the coordinate-dependent coupling. The well-separated mixed valence excited state spectroscopic components enable detailed electronic and resonance Raman data to be obtained from which the model can be more fully developed and tested.

Determination of a mean orientation in electron backscatter diffraction measurements

The average orientation of an electron backscatter diffraction (EBSD) map is calculated by the quaternion method and is compared with nonlinear solving by the Hill Climbing and Barton-Dawson methods. An automated EBSD system acquires orientations on a regular grid of pixels based on indexation of Kikuchi patterns and the orientation is described by one of the crystal symmetry-related equivalents. In order to calculate the quaternion average, it is necessary to make a cloud for a set of pixels in a grain. A cloud consists of the representative orientations with small misorientation between each and every pair of points. The position criterion says that two adjacent pixels have a smaller misorientation than with all others. With this, the proper equivalent orientation, or representative orientation for the cloud, can be selected from among all the crystal symmetry-related equivalents. The orientation average is the quaternion summation divided by its norm. The instant average or cumulative average is useful for dealing with polycrystalline grains or orientation discontinuity and is also useful for selection of the proper orientation of EBSD map with large scattering. The quaternion, Hill Climbing, and Barton-Dawson nonlinear methods are tested with a Gaussian distribution around the ideal texture component, Brass {110}〈112〉. The accuracy of the three results is similar but the nonlinear methods are associated with longer computation times than the quaternion method. The quaternion method is adapted for characterization of a partially-recrystallized interstitial-free (IF) steel and randomly distributed Brass, S, and cube texture components according to several different orientation spreads.

Heme Axial Methionine Fluxion in Pseudomonas aeruginosa Asn64Gln Cytochrome c551

Heme axial methionine ligands in ferricytochromes c552 from Hydrogenobacter thermophilus (HT) and Nitrosomonas europaea, both members of the cyt c8 family, display fluxional behavior. The ligand motion, proposed to be inversion at sulfur, results in an unusually small range of hyperfine shifts for heme substituents in these proteins. Herein, heme axial Met fluxion is induced in a structurally homologous cytochrome c551 from Pseudomonas aeruginosa (PA) by substituting heme pocket residue Asn64 with Gln. The mutant, PA-N64Q, displays a highly compressed range of heme substituent hyperfine shifts, temperature-dependent heme methyl resonance line broadening, low rhombic magnetic anisotropy, and a magnetic axes orientation consistent with Met orientational averaging. Analysis of NMR properties of PA-N64Q demonstrates that the heme pocket of the mutant resembles that of HT. This result confirms the importance of peripheral interactions and, in particular, residue 64 in determining axial Met orientation and heme electronic structure in proteins in the cyt c8 family.

Micromechanics of inelastic composites with misaligned inclusions: Numerical treatment of orientation

This paper is concerned with the micromechanics of multi-phase fiber- or inclusion-reinforced inelastic composites with a special emphasis on the numerical treatment of misaligned orientation. Mean-field homogenization of these composites involves volume and orientation averaging. The latter usually needs average orientation measures known as the second- and fourth-rank orientation tensors a and A, respectively. Usually the only orientation data available is a and a first issue is to reconstruct A using closure approximations. We propose a new weighted regularization method which deals with orientations which are strictly neither 1D, 2D nor 3D and ensures a smooth transition between the 3 cases. A second issue is that there are situations where the inclusions’ orientation distribution function (ODF) is needed for homogenization but is unavailable. The ODF is recovered using a and A and numerically computed at a number of discrete orientations. A third issue is the actual computation of orientation averaging integrals. An efficient algorithm approximates the integrals with sums over a finite number of orientations. Orientation and volume averaging concepts are applied to the mean-field homogenization of two classes of multi-phase composites: linear thermo-elastic and rate-independent inelastic. In the latter case, an incremental formulation is proposed which enables the simulation of unloading, cyclic and otherwise non-proportional loadings. Implicit time-discretization and consistent tangent operators are employed. The procedures and the corresponding algorithms were implemented in the [DIGIMAT version 1.4, 2004. Linear and nonlinear multi-scale material modeling software, e-Xstream engineering SA (http://www.e-Xstream.com), Louvain-la-Neuve, Belgium.] software and several numerical simulations show their accuracy and efficiency.

Calculation of the Parent hcp Grain Orientation from Inherited Variants in the hcp to t and in the hcp to cc Phase Transformations Application to the α-γ Transformation in TiAl-Based Alloys

The orientations of the inherited tetragonal (resp. cubic) variants are calculated from the parent hcp orientation in the case of a strict orientation relation. The numbering of the variants is proposed, as well as the misorientations between them. Conversely, a method for calculating the parent hcp orientation from a sufficient number of inherited variants is proposed. It is based on orientation correlating and orientation averaging, and it is particularly useful when the inherited variants are not exactly related to the parent orientation by a strict orientation relation or when the orientations of the inherited volumes slightly vary at different locations of the variant. The method is illustrated by considering the a to g phase transformation taking place in TiAl-based alloys