Thermal Vibration Amplitude Research Articles

The combination of the classical dynamics simulation of a hot copper surface with the low-energy helium scattering simulated in the binary collision approximation

Abstract Since low energy ion scattering involves collision sequences with neighbouring atoms, it is sensitive to the surface properties. The present work emphasizes the relation between ion scattering and surface dynamics on an atomic scale. A hot surface is simulated by isothermal classical dynamics with a N-body potential known to reproduce the bulk elastic properties of copper at 0 K, as well as the full bulk phonon dispersion relations within the experimental error. Instantaneous surface configurations are then used to simulate the ion scattering with the MARLOWE program. The structure factor, the radial correlation function, the density function and the root mean square thermal vibration amplitudes, all characterizing the global order of a crystal, are defined locally and their temperature dependence is discussed in relation to properties of ion scattering, with particular emphasis on shadowing and blocking.

On the Pb thermal vibrations in PbHfO3 crystals

In PbHfO3 single crystals the amplitude of the thermal vibrations for Pb ions in the high-temperature Pm3m phase, calculated from the Debye-Waller factor, reached unexpectedly large values. The random displacements of Pb ions were assumed and the new thermal vibration amplitude, which is more reasonable from the crystal lattice dynamics point of view, was calculated. A possible displacive-type phase transition was observed in the vicinity of 400 degrees C.

Size dependent thermal vibrations and melting in nanocrystals

A simple model for the size-dependent amplitude of the atomic thermal vibrations of a nanocrystal is presented which leads to the development of a model for the size dependent melting temperature in nanocrystals on the basis of Lindemann's criterion. The two models are in terms of a directly measurable parameter for the corresponding bulk crystal, i.e., the ratio between the amplitude of thermal vibrations for surface atoms and that for interior ones. It is shown that the present model for the melting temperature offers not only a qualitative but even an excellent quantitative agreement with the experimentally observed size-dependent superheating, as well as melting point suppression in both the supported and embedded metallic and semiconductor nanocrystals.

Lattice-dynamical functions of solids at very high pressures

Abstract Vibrational spectra of face-centered cubical (f.c.c.) solids are investigated at the pressure region, where the quantum-statistical model for the electron energy is applicable. Phonon dispersion curves are obtained for different values of the specific volume. The integration of the phonon spectra over the Brillouin zone yields the zero-point vibrational energy, the Debye temperature, the Gruneisen coefficient, mean-square amplitude of zero-point and thermal vibration, the melting temperature. All quantities under consideration are calculated from the universal functions of the reduced volume, using the scaling relations for given atomic number 2.

Local atomic structure of relaxor ferroelectric solids studied by pulsed neutron scattering

Relaxor ferroelectrics, such as Pb(Mg1/3Nb2/3)O3 (PMN) or (Pb·88La ·12)(Zr·65Ti·35)O3 (PLZT), show diffuse ferroelectric transition which depends upon frequency of the a.c. field. In spite of their wide use in various applications details of their atomic structure and the mechanism of relaxor ferroelectric transition are not sufficiently understood. While their crystallographic structure is cubic perovskite, ABO3, their thermal factors (apparent amplitude of thermal vibration) is quite large, suggesting local displacive disorder due to heterovalent ion mixing. Electron microscopy suggests nano-scale structural as well as chemical inhomogeneity.We have studied the atomic structure of these solids by pulsed neutron scattering using the atomic pair-distribution analysis. The measurements were made at the Intense Pulsed Neutron Source (IPNS) of Argonne National Laboratory. Pulsed neutrons are produced by a pulsed proton beam accelerated to 750 MeV hitting a uranium target at a rate of 30 Hz. Even after moderation by a liquid methane moderator high flux of epithermal neutrons with energies ranging up to few eV’s remain.

Electron and positron channeling radiation from beryllium oxide.

We present experimental observations of planar and axial channeling radiation emitted by relativistic electrons and positrons traversing a BeO crystal. Values of thermal vibration amplitudes are obtained, and found to be in agreement with those obtained by other methods, namely, x-ray and neutron diffraction. The standard channeling-radiation theory matches correctly the observed radiation spectra when the particle is channeled along principal planes. Some of the planes with higher Miller indices give radiation spectra that can only be explained by the coupling of the particle wave function to neighboring axes or planes, or by population redistribution within the band.

Cation distributions, bonding and transport behavior in silver and copper fast-ion conductors with simple anion packings

The Ag + and Cu + halides and chalcogenides, the prototypes of cation-disordered fast-ion conductors, have structures based upon simple b.c.c., h.c.p., or f.c.c. anion arrays. The distribution of mobile cations among available interstices remained enigmatic until recently beacuse of disruptive phase transformations that hinder the preparation of single crystals, coupled with the small number of diffraction intensities available in powder patterns as a consequence of disorder and large thermal-vibration amplitudes. Single-crystal neutron diffraction techniques and the availability of a recent formalism for the description of scattering by anharmonically vibrating atoms have permitted precise description of the cation distribution in a number of structures. All display delocalized cations and strongly anharmonic thermal vibrations. The details of the cation distribution and transport process do not, however, depend solely on the geometry of the anion array, but are also influenced by the bonding characteristics and concentration of the mobile cations. Although Ag + and Cu + have the same ionic radii as Na + and Li + respectively, the structures, bond characteristics and transport properties of their halides and chalcogenides are quite distinct. A self-consistent field X α calculation of orbital interactions in α-AgI reveals significant covalent interaction between I 5p and Ag 4d and 5s. Two of the non-bonding interactions of Ag 4d and I 5p are anti-bonding for nearest anion neighbors, but bonding for second-nearest neighbors, a possible contribution to enhanced cation mobility.

Information on Grain Boundary Structure in Nanocrystalline Pd and Cr from Diffraction Studies

Comparisons of diffraction data from nanocrystalline and coarse-grained Pd samples indicate that grain boundaries in nanocrystalline Pd are reasonably ordered. Lattice parameter measurements show no significant grain boundary excess volume in nanocrystalline Pd, and therefore the reduced density typically observed in nanocrystalline Pd samples must be due to porosity. The lack of any significant change in both thermal expansion coefficients and average atomic vibrational amplitudes may indicate that rigid-body motions normal to grain boundaries in nanocrystalline Pd are severely constrained. Nanocrystalline Cr shows many similarities in behavior with nanocrystalline Pd, except that significantly more non-peak intensity is observed from a nanocrystalline Cr samples than from a coarse-grained Cr sample. Impurities may account for this behavior.

Thermal vibrational amplitudes of constituent atoms and mechanical stability in ZnxCd1-xTe and Hg1-yCdyTe.

Root-mean-square (rms) displacements of the constituent atoms in the ${\mathrm{Zn}}_{\mathit{x}}$${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Te (x=0,0.04,0.077,0.114,0.20,0.31) and ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$${\mathrm{Cd}}_{\mathit{y}}$Te (y=0,0.24,0.4,0.7) alloys are determined by ion channeling experiments combined with particle-induced x-ray emission and Rutherford backscattering. The experimental channeling angular scan data are interpreted by using a recently developed method, which uses a Monte Carlo simulation program of the channeling process, and includes a structural model for the ternary alloys based on extended x-ray-absorption fine-structure results on nearest-neighbor distances. Temperature-dependent measurements show that the experimentally deduced atomic displacements do not contain static contributions but they are rather due to the thermal vibrational amplitudes of the atoms.

The thermal properties of nanocrystalline Pd from 16 to 300 K

Abstract Quantitative X-ray diffraction measurements made over a temperature range 16–300K on a Pd sample of 8·3nm median grain size were compared with data acquired from a coarse-grained Pd reference sample. The larger Debye-Waller parameter of nanocrystalline Pd was found to be due to increased static displacements of atoms from their equilibrium sites compared with the static displacements in coarse-grained material. Consistent with this behaviour, the strain distribution determined from the width of intensity peaks was significantly broader in the nanocrystalline sample than in the coarse-grained sample. No grain-size-correlated differences in either thermal vibrational amplitude or lattice parameter were observed. In contradiction to previous reports of greatly increased thermal expansion coefficients in nanocrystalline metals, the change in lattice parameter of Pd from 16 to 300 K was observed to be independent of grain size. The results indicate that some regions of the nanocrystalline sample are in a state of compressive stress, while other regions are under a tensile stress. Comparisons with results for unconsolidated nanometre-sized powders indicate that the origin of the increased static displacements in nanocrystalline Pd may be due to the ultrafine powder production or subsequent consolidation processes, rather than being an inherent feature associated with a particular grain size.

Diffraction studies of the thermal properties of nanocrystalline Pd and Cr

Quantitative X-ray and neutron diffraction measurements were made on nanocrystalline and coarse-grained samples of Pd and Cr. For both materials, Debye-Waller parameter comparisons over a temperature range of approximately 20–300 K indicate that the nanocrystalline materials have increased static displacements of atoms from their equilibrium sites compared to coarse-grained material. No grain-size-correlated differences in thermal vibrational amplitude, lattice parameter, or thermal expansion coefficients were observed in either material. In contrast to earlier results on nanocrystalline Pd, significantly more non-peakintensity is observed from a nanocrystalline Cr sample than from a coarse-grained Cr sample. Impurities may account for the increased background intensity from nanocrystalline Cr. These results indicate that there is no significant grain boundary excess volume in nanocrystalline Pd, and therefore the reduced density typically observed in nanocrystalline Pd samples must be due to porosity.

Mössbauer effect in confined liquid molecules.

Results of experimental and theoretical studies on the $^{119}\mathrm{Sn}$ M\"ossbauer effect in ${\mathrm{SnCl}}_{4}$ molecules confined in porous glass are presented. A physical model, based on the assumption that diffusion is hindered in the pores, is developed. It is further assumed that the molecules in each pore form a harmonic lattice with fixed boundary conditions. The thermal-vibration amplitudes of the particles are calculated by using a normal-mode expansion satisfying fixed boundary conditions. It is rigorously shown that the transformation diagonalizes the Hamiltonian of the system, allowing subsequent use of standard calculational methods to derive expressions for the recoilless fraction and the second-order Doppler shift in restricted geometry. The result allows evaluation of these quantities for molecules at different sites in the lattice. Experiments were made with two Vycor-glass carriers at several temperatures below and above the 240-K freezing point of bulk ${\mathrm{SnCl}}_{4}$. The samples have average pore diameters of 40 and 36 \AA{}. M\"ossbauer data of confined ${\mathrm{SnCl}}_{4}$ reveal a resonance line shift corresponding to the solid-liquid transition. This change in isomer shift is attributed to volume expansion of ${\mathrm{SnCl}}_{4}$ at its melting point. The measured temperature dependence of the recoilless fraction of the confined ${\mathrm{SnCl}}_{4}$ molecules is explained by the theoretical model. With one adjustable parameter, the theory reproduces both the absolute level and the temperature slope of the experimental data for two spectral components corresponding to ${\mathrm{SnCl}}_{4}$ molecules at different locations in the pore.

Thermophysical properties of macromolecules in the block state

The macromolecules of linear polymers usually consist of regular helices. The paper presents the results of investigation of the concentration, thermal expansion coefficient and vibration amplitude of such helices at different temperatures. These parameters were determined from temperature dependences of the intensity, frequency and halfwidth of regular bands in IR and Raman spectra of polymers.

Simulation analysis of ion channeling spectra: thermal vibrational amplitude in Si

Abstract Energy spectra for 1 MeV He ions scattered by a Si single crystal over an angle of 58° were measured for incident directions along the 〈110〉 string and a number of directions 4° off the string: {100}, {110} and {111} planes as well as three non-channeling directions. The measurements were performed at a temperature of 164 K, under glancing-exit-angle conditions. The experimental spectra were reproduced by Monte Carlo simulation, and a x 2 analysis procedure was developed to determine the thermal vibrational amplitude in Si. Two ion-atom potentials used in the calculations (the ZBL potential and a Hartree-Fock potential) yielded essentially the same amplitude of 0.066(2) A. The corresponding Debye temperature of 490(15) K agrees well with recent determinations by other methods.

Can Thermal Vibration Amplitudes be Used as Indicators of Reaction Pathways? An Examination of [Nb, TaF7]2- Structures

Thermal vibrational amplitudes, determined from a single-crystal X-ray study of K2TaF7 at room temperature, show similar characteristics to the neutron values for isomorphous K2NbF7, exhibiting considerable variations in anisotropies for the different fluorine atoms. These variations can be rationalized by using a combination of electron pair repulsion theory and crystal packing considerations.

Proton-channeling investigation of La 2CuO 4

From a comparison of the experimental yields with the calculated ones is found that the oxygen sublattice is partly disordered (about 15–20% of the oxygen atoms displaced from the crystal sites in the LaCuO rows). The thermal vibrational amplitude of the oxygen atoms in the plane perpendicular to the OO rows is apparently less (0.07 Å) than derived from the Debye model (0.15 Å).

Structure and phases of the Au(001) surface: Absolute x-ray reflectivity

Specular and nonspecular absolute x-ray-reflectivity measurements have been performed on the Au(001) surface between T=300 and 1250 K. At all temperatures the surface-normal vibrational amplitudes are increased above the corresponding bulk thermal vibrational amplitude (Debye-Waller factor). Below T=1170 K, the surface is well described by an incommensurate, corrugated, hexagonal overlayer. The corrugation propagates several layers into the bulk. Above T=1170 K there is an abrupt decrease in the specular and nonspecular reflectivities, which we interpret in terms of surface disordering.

Thermal-vibrational amplitudes of silicon determined by channeling-radiation measurements.

We have observed radiation emitted by electrons channeled along the (110) and (100) planes of silicon for four different beam energies ranging from 16.9 to 54.5 MeV. Taking advantage of the great sensitivity of the positions of some of the spectral peaks to the vibrations of the Si nuclei, we have determined the vibrational amplitude at room temperature to be 0.0813\ifmmode\pm\else\textpm\fi{}0.0009 \AA{} for the (110) plane and 0.0789\ifmmode\pm\else\textpm\fi{}0.0007 \AA{} for the (100) plane. The values obtained from channeling-radiation measurements differ substantially from the value of 0.075 \AA{} obtained from x-ray-diffraction measurements, which fail to distinguish between vibrational amplitudes for different planes. For many crystals, electron-channeling-radiation measurements of thermal-vibrational amplitudes may prove to be more accurate than x-ray measurements.

Channeling simulation on YBa 2Cu 3O 7

We have performed computer simulations of 1.5 MeV He + channeling in YBa 2Cu 3O 7. Our results agree well with what can be expected from a simple extension of Lindhard's continuum model, taking into account the multicomponent nature of the material. We have extracted half-angle widths from our simulations, and found them compatible with most experimental data. More specifically, our simulations are consistent with the measurements and simulations of Meyer et al. [Nucl. Instr. and Meth. B35 (1988) 292] showing a dip curve of the signal from oxygen to be significantly narrower than those from all the other elements. We have also confirmed that the relationship between the half-angle width and the lattice vibration, as extrapolated by Sharma et al. [Phys. Rev. B38 (1988) 9287] from Barren's empirical formula for channeling in single-component crystals, is still largely valid. Thus. the anomaly in the temperature dependence of the half-angle for channeling in YBa 2Cu 3O 7 along the c-axis is reproduced when thermal vibration amplitudes, extracted from the measurements of Sharma et al., are employed as a temperature scale. Furthermore, we have investigated the effects of hypothetical changes in the lattice parameters, rearrangements of the positions of oxygen atoms in the unit cell. We have also explored the results of assuming different vibration amplitudes for different atoms in the unit cell.

Theoretical determination of the root mean square thermal vibration amplitudes of bulk and (110) surface atoms of InAs

We apply an analytical method, within the frame of an atomic interaction model, to calculate the bulk and (110) surface rms thermal vibration amplitudes, − 〈u 2〉 1 2 - in InAs. The calculated surface enhancement factor S is compared with experiment and the role of long-range Coulomb interactions is discussed.