Amplitude Of Atomic Displacements Research Articles

Capturing interference variations of atomic motion in vibrational modes by non-resonant Raman images

Non-resonant Raman imaging associated with vibrational modes provides an optical means to structure and function characterisation for a single molecule, where the interference between atomic motions in a vibrational mode plays an important role. Taking the [18]annulene as a proof-of-the-concept molecule, we present here a comprehensive study on the dependence of non-resonant Raman images on interference variations involving the phase and amplitude of atomic displacements in vibrational modes. Calculations demonstrate that constructive and destructive phase interferences contribute to the characteristic merging and repulsion of Raman patterns, respectively, which should be attributed to the same/opposite signs of Raman polarisability. In addition, the imaging characteristic by constructive and destructive interferences become more significant with the increase of plasmonic size. Moreover, Raman images are highly sensitive to the subtle variations of interference induced by molecular symmetry and element substitution, highlighting the importance of amplitude variations of interference in modes for Raman images to monitor molecular structure changes. Our findings propose the capability of Raman images toward capturing interference variations in modes, serving as good references for Raman imaging to characterise various molecules and their corresponding structure changes by analysing interference effects in vibrational modes.

Plane and plane-radial discrete breathers in fcc metals

Discrete breather (DB) is a time-periodic, spatially localized vibrational mode in a perfect nonlinear lattice. In this study, two new types of DBs are reported in fcc metals (Al, Cu and Ni), based on the molecular dynamics simulations using standard embedded atom method interatomic potentials. All calculations are performed at a zero temperature in a three-dimensional computational cell with the use of periodic boundary conditions. A plane DB is excited in a single (111) atomic plane by displacing the atoms from their equilibrium lattice sites according to a specific pattern corresponding to a delocalized vibrational mode in a two-dimensional triangular lattice. This plane DB is delocalized in two dimensions and localized in one dimension, normal to the excited (111) plane. It is shown that in all studied metals the plane DBs have maximal lifetimes of 17–22 ps in the range of initial amplitudes of 0.15–0.30 Å. Herewith the studied mode demonstrates a hard type of nonlinearity, i.e. its frequency increases with amplitude. The second new type of DB is the plane-radial DB obtained by imposing a radial localizing function on the plane DB. This disk-type DB is localized in all three dimensions. The time evolution of the atomic displacement amplitudes and the kinetic energy are studied. The DBs of this type can exist for 9 and 4 ps in Cu and Ni, respectively, and then they decay by dissipating their vibrational energy onto neighboring atoms. The long-lived plane-radial DB in Al is not found.

Features of the Crystal Structure of Tm1–xYbxB12 Dodecaborides near a Quantum Critical Point and at a Metal–Insulator Transition

The magnetic phase diagram of Tm1–xYbxB12 antiferromagnets is determined from the specific heat measurements performed at low and ultralow temperatures (0.07–10 K). Precise experimental studies of the features of the crystal structure at room temperature suggest that a metal−insulator transition occurring in Tm1–xYbxB12 with the growth of x is accompanied by a significant (by a factor of 2–6) increase in the amplitude of atomic displacements in the boron and rare-earth sublattices. There is also a signature of an instability arising in the electron configuration of ytterbium ions at this transition. At room temperature, near the quantum critical point at xc ≈ 0.25, anomalies in the structural characteristics of dodecaborides under study are observed.

Pressure-induced bcc to hcp transition in Fe: Magnetism-driven structure transformation

The pressure induced bcc to hcp transition in Fe has been investigated via ab initio electronic structure calculations. It is found by the disordered local moment (DLM) calculations that the temperature induced spin fluctuations result in the decrease of the energy of Burgers type lattice distortions and softening of the transverse $N$-point $T{A}_{1}$ phonon mode with $[\overline{1}10]$ polarization. As a consequence, spin disorder in an system leads to the increase of the amplitude of atomic displacements. On the other hand, the exchange coupling parameters obtained in our calculations strongly decrease at large amplitude of lattice distortions. This results in a mutual interrelation of structural and magnetic degrees of freedom leading to the instability of the bcc structure under pressure at finite temperature.

Distinctive features of thermal expansion of niobium diselenide

The characteristic features of thermal expansion of bulk samples of niobium diselenide have been determined experimentally and analyzed theoretically. The manifestation of the so-called membrane effect in this compound due to the significant difference in the temperature dependences of the mean-square amplitudes of atomic displacements in the parallel and perpendicular directions toward the layers has been investigated.

Protein Dynamics and Stability: The Distribution of Atomic Fluctuations in Thermophilic and Mesophilic Dihydrofolate Reductase Derived Using Elastic Incoherent Neutron Scattering

The temperature dependence of the dynamics of mesophilic and thermophilic dihydrofolate reductase is examined using elastic incoherent neutron scattering. It is demonstrated that the distribution of atomic displacement amplitudes can be derived from the elastic scattering data by assuming a (Weibull) functional form that resembles distributions seen in molecular dynamics simulations. The thermophilic enzyme has a significantly broader distribution than its mesophilic counterpart. Furthermore, although the rate of increase with temperature of the atomic mean-square displacements extracted from the dynamic structure factor is found to be comparable for both enzymes, the amplitudes are found to be slightly larger for the thermophilic enzyme. Therefore, these results imply that the thermophilic enzyme is the more flexible of the two.

Optical, Magnetic and Structural Properties of the Spin‐Crossover Complex [Fe(btr)2(NCS)2]·H2O in the Light‐Induced and Thermally Quenched Metastable States

Abstract[Fe(btr)2(NCS)2]·H2O [btr = 4,4′‐bis(1,2,4‐triazole)] is thearchetype of highly cooperative and low‐dimensional spin‐crossover complexes, which exhibit low‐spin (LS) to high‐spin (HS) light‐induced conversion at very low temperature. The structural reorganizations related to the light‐induced and thermally induced LS–HS transitions were characterized by single‐crystal X‐ray diffraction below the relaxation temperature (T = 15 K < TLIESST) and at 130 K within the thermal hysteresis loop. We show that the LIESST and thermal spin transitions lead to the same structural variations, namely an elongation of the Fe–N bonds by 0.18 Å (Fe–NNCS) and 0.20 Å (Fe–Nbtr), on going from LS to HS, together with a reorientation of the NCS group by nearly 13°. The atomic displacement amplitudes, derived from the crystal structures, indicate lattice vibration modes of larger amplitudes and correlatively lower vibration frequencies in the HS state. The deformation of the crystal lattice as a function of temperature and laser excitation was quantitatively analyzed in terms of the HS and LS thermal‐expansion (αHS and αLS) and spin‐transition spontaneous‐strain (ϵ) tensors. The eigendirections and eigenvalues of the α and ϵ tensors correlate well with the weak and strong interactions in the solid and are responsible for the high cooperativity and low‐dimensional behaviour. Magnetic and spectroscopic measurements were performed in all the different spin states and related to the structural findings. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)

Effects of milling, doping and cycling of NaAlH 4 studied by vibrational spectroscopy and X-ray diffraction

The effects of milling and doping NaAlH 4 with TiCl 3, TiF 3 and Ti(OBu n ) 4, and of cycling doped NaAlH 4 have been investigated by infrared (IR) and Raman spectroscopy and X-ray powder diffraction. Milling and doping produce similar effects. Both decrease the crystal domain size (∼900 Å for milled and ∼700 Å for doped, as compared to ∼1600 Å for unmilled and undoped NaAlH 4) and increase anisotropic strain (by a factor >2.5, mainly along c). They also influence structure parameters such as the axial ratio c/ a, cell volume and atomic displacement amplitudes. They show IR line shifts by ∼15 cm −1 to higher frequencies for the Al–H asymmetric stretching mode ν 3, and by ∼20 cm −1 to lower frequencies for one part of the H–Al–H asymmetric bending mode ν 4, thus suggesting structural changes in the local environment of the [AlH 4] − units. The broad ν 3 bands become sharpened which suggests a more homogeneous local environment of the [AlH 4] − units, and there appears a new vibration at 710 cm −1. The Raman data show no such effects. Cycling leads to an increase in domain size (1200–1600 Å), IR line shifts similar to doped samples (except for TiF 3: downward shift by ∼10 cm −1) and a general broadening of the ν 3 mode that depend on the nature of the dopants. These observations support the idea that some Ti diffusion and substitution into the alanate lattice does occur, in particular during cycling, and that this provides the mechanism through which Ti-doping enhances kinetics during re-crystallisation.

Ab initio Determination of Total-Energy Surfaces for Distortions of Ferroelectric Perovskite Oxides

We established a new ab initio structure optimization technique of determining the valley line on a total-energy surface accurately for the zone-center distortions of ferroelectric perovskite oxides, and applied this technique to the analysis of barium titanate (BaTiO3), lead titanate (PbTiO3), and lead zirconate (PbZrO3). The proposed technique is an improvement over King-Smith and Vanderbilt's scheme [Phys. Rev. B 49 (1994) 5828] of evaluating total energy as a function of the amplitude of atomic displacements. The results of numerical calculations show that total energy can be expressed as a fourth-order function of the amplitude of atomic displacements in BaTiO3 but not in PbTiO3 and PbZrO3. These results will provide some hints about the reason Pb(ZrxTi1-x)O3(PZT) has a large piezoelectric response. These results are due to the fact that our structure optimization technique automatically takes account of the higher-order coupling between atomic displacements and strains, and not only the atomic displacements of the Γ15 soft mode but also that of the hard modes.

Motion and disorder in crystal structure analysis: measuring and distinguishing them.

Dynamic processes in crystalline solids are reflected in the atomic displacement amplitudes determined, together with the atomic coordinates, by crystal structure analysis. The interpretation of such amplitudes poses two severe problems: (a) The relative phases of the atomic displacements are lost; and (b) the amplitudes may reflect disorder in the structure and systematic error in the diffraction experiment in addition to motion, but the three contributions cannot be separated on the basis of measurements at a single temperature. Several approximate ways to solve these problems, e.g. rigid-body and segmented-rigid-body analysis, are reviewed together with their limitations. A more recent approach that represents a significant advance with respect to both difficulties is also described: Crystal structures are determined over a range of temperatures; the mean square amplitude quantities are interpreted by taking explicit account of their temperature dependence, i.e. by exploiting the difference in behavior of a microscopic oscillator in the low-temperature, quantum regime and in the high-temperature, classical regime. A distinction between low-frequency and high-frequency motion, disorder, and systematic error becomes possible with this model; this is illustrated with the help of case studies.

Distortion of atoms around the neutral vacancy in a Si crystal

The single-particle electronic structure of a neutral lattice vacancy in a Si crystal is treated theoretically within the 16-atom supercell using the conventional tight-binding approximation. The physical mechanism leading to a spontaneous symmetric and tetragonal displacement of atoms surrounding a vacancy is discussed in detail. The elastic response of the lattice is calculated using the Keating valence force model applied to the cluster contained 441 atoms. The directions and amplitudes of atomic displacements are strongly symmetry-dependent. The amplitudes decrease with the distance R from the vacancy, approximately, as R-2, independently of the distortion symmetry. The influence of the vacancy defects on the lattice parameter is considered and estimated.

Peculiarities of phonon spectra and lattice heat capacity in Ir aned Rh

A simple pseudopotential model is proposed, which allows the phonon spectra and temperature dependence of the lattice heat capacity of Ir and Rh be described with a high enough accuracy. A careful comparison of the calculated and experimental values of the lattice heat capacity is carried out, with the procedure of the identification of the phonon contribution to the heat capacity and determination of the characteristics (momenta) of the phonon density of states from the experimental values of the total heat capacity of metal at a constant pressure being described in detail. The results of the theoretical calculations explain, in particular, such peculiar feature of Ir and Rh, unusual for cubic metals, as a sharp (more than by a factor of 1.5) decrease in the effective Debye temperature with increasing termperature. The temperature dependence of the mean square amplitude of atomic displacements in Ir and Rh has been calculated. Basing on the band calculations the manifestation of the Kohn singularities in the phonon spectra of Ir are discussed.

The Correlation Between Diffusion Behaviour and Phonon Softening in BCC Metals

AbstractA new approach is proposed to explain the wide spread of self diffusion behaviour and the curvature of the Arrhenius plots in bcc metals by typical diffusion‐relevant low‐energy phonon modes. In bcc transition metals the activation enthalpy and the energy of the LA 2/3 (111) phonon mode decrease systematically with decreasing d‐electron concentration, while the diffusivity and the degree of curvature increase. The migration enthalpy HM is related to the frequency of this mode, i.e. to the amplitude of atomic displacements in the 〈111〉 nearest neighbour jump direction. On the basis of experimental results a good correlation between the square of this phonon frequency and the activation enthalpy is obtained. The curvatures of the Arrhenius plots are explained by a decrease of HM with decreasing temperature due to the temperature dependence of the soft T1A 1/2 〈110〉 mode, which causes a “breathing” motion of the saddle point atoms. Thus the model of phonon‐assisted diffusion jumps via monovacancies yields a uniform explanation for the main features of diffusion in bcc metals.

Multiple Scattering of Axially Channeled Particles by Thermal Vibrations and Electrons

AbstractWithin the framework of the classical small‐angle scattering theory a microscopic description of positively charged particle behaviour during axial channeling in a crystal is given. Assuming that statistical equilibrium in a transverse plane is established, the differential Fokker‐Planck‐type equation is obtained from the detailed‐balance relation. The coefficients of this equation are determined by the atomic scattering potential and distribution function of scatterers and are studied at various relations between the amplitude of the thermal atom vibrations and their screening radius. It is shown that for relatively small depths (high transverse energies) the processes of direct particle knocking‐out of a channel are predominant. At low transverse energies the scattering particle behaviour is determined by nuclear and electron diffusion processes. In this case, if the distance of closest approach of the particle to a chain exceeds considerably the amplitudes of atomic displacements, the corresponding coefficients are analogous to those obtained earlier.

Phenylalanine transfer RNA: molecular dynamics simulation.

Yeast phenylalanine transfer RNA was subjected to a 12-picosecond molecular dynamics simulation. The principal features of the x-ray crystallographic analysis are reproduced, and the amplitudes of atomic displacements appear to be determined by the degree of exposure of the atoms. An analysis of the hydrogen bonds shows a correlation between the average length of a bond and the fluctuation in that length and reveals a rocking motion of bases in Watson-Crick guanine X cytosine base pairs. The in-plane motions of the bases are generally of larger amplitude than the out-of-plane motions, and there are correlations in the motions of adjacent bases.

The Critical Voltage Effect in High-Voltage Electron Microscopy

In addition to revealing the internal microstructures of materials, the high-voltage electron microscope can also be used to characterize “invisible” features such as electron scattering, site occupancy, and atomic displacement amplitudes on a quantitative basis. The physical basis of the unique “critical voltage effect” is the occurrence of destructive interference between current waves within the specimen at a particular accelerating voltage. Potential applications to studies of random and ordered alloy solid solutions largely depend on the magnitude of the size disparity between solute and solvent atoms.

Raman scattering by polaritons

In crystals lacking a center of inversion, polaritons participate in first order (one polariton) Raman scattering via electric-dipole excitation- and electric field-induced changes in the electric susceptibility. The electric-dipole oscillation and the electric field amplitudes of polaritons can be obtained, simply and directly, from the expression for the energy density of electromagnetic radiation in a dispersive dielectric medium and the relation between the electric-dipole oscillation and electric field amplitudes, which is obtained from the equations of motion. The magnitudes of the macroscopic electric field and the atomic displacement amplitudes of coupled plasmon-LO phonon modes are shown to be the same as the corresponding quantities of the coupled photon-TO phonon polariton modes having the same frequency.