Thermal Vibration Amplitude Research Articles

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

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

Model-calculations of the nearly linear temperature-dependent densities of rare gas crystals

The nearly linear temperature-density ( T-p) dependence of crystalline rare gases is described by an idealized model. The semiclassical Planck-Sommerfeld method applied to the sum of Lennard-Jones interactions indicates at low T an increase of the separations of intermolecular vibration levels with the quantum number ν. Estimations of the thermal vibration amplitudes for the Boltzmann population of these levels and a step by step calculation with increasing T indicate T-dependent level separations and agree with the T-constancy of p at low temperatures and with the linear p- T relation at higher temperatures. The calculated intermolecular levels indicate a region of a near-continuum of quantized oscillator frequencies similar to Debye's theory and Planck's black body radiation.

Reorientation of CCl3 group in tricoordinated carbon atom (According to NQR data)

By means of the temperature dependence of the spectral and relaxation parameters of chlorine-35 nuclei, a study has been made of the reorientation of the trichloromethyl group in crystalline CCi3CON-HCH2Ci. The reorientationai mobility of the CCi 3 group bonded with a tricoordinated carbon atom has been examined as a whole; and the magnitude of the corresponding potential barrier is judged, a barrier which, for crystalline compounds, is within the limits of 3.5-12 kcai/moie according to the data obtained in a number of studies. it had been noted previously that the reorientational mobility of the trichloromethyi group is governed to a considerable degree by the coordination of the central atom to which it is bonded [i]. in this article we will examine the intracrystai mobility of this atomic group in the case in which it is attached to a tricoordinated carbon atom. To this end, we applied 3SCi nuclear quadrupoie resonance (NQR) in a study of the compound CCi~CON-HCH2Ci at temperatures from 77 K to the melting point (352 K) and compared the data with the results obtained in analogous studies reported in the literature. in Figs. i and 2 we show the temperature dependences of the resonance frequency v and time T I of quadrupoie spin-lattice relaxation of 35Ci nuclei in crystalline CCi3CONFHCH2CI (the experimental procedure and the treatment of the results from the measurements were the same as in [2]). The 35Ci NQR frequencies at 77 K have the following values (in MHz): 39.988, 39.683, and 39.289 (CCi 3 group), and 34.768 (CH2Ci group); these values decrease with increasing temperature as a consequence of the increase in amplitude of molecular thermal iibrationai vibrations, in the crystal, these vibrations are also the source of a mechanism of nuclear quadrupoie spin-lattice relaxation, termed the iibration mechanism (the corresponding rate of relaxation varies with temperature in accordance with a power law aT n [3]). From the temperature dependences v(T) and Ti(T) that have been reported, it can be seen that, apart from molecular iibrations, there is reorientationai motion of the CCI~ group in solid CCiaCONHCH2Ci , which is manifested upon heating the crystal in the disappearance of the resonance signals of this group at about 240 K (i.e., more than i00 ~ below the melting point of the sample), and, prior to this disappearance, an exponential decrease in the time T i. Both of these phenomena are due to the exponential increase in the rate of CCi a reorientation with increasing temperature (following the Arrhenius law). On the whole, the temperature behavior of spin--lattice relaxation of 3sCl nuclei of the CCI a group is described by an additive expression that takes into account the independent action of the libration and reorientation mechanism [3]:

Calculation of temperature dependence of interbase breathing motion of a guanine-cytosine DNA double helix with adenine-thymine insert.

The modified self-consistent phonon approximation is generalized to calculate the critical temperature of a DNA double helix with block inserts of different base pair sequences. An iterative method based entirely on the Green's function is developed to compute efficiently the self-consistent anharmonic force constants and thermal mean-squared vibrational amplitudes in hydrogen bonds. The calculation is carried out for a long guanine-cytosine (G-C) type helix with an insert of d(A${)}_{4}$-d(T${)}_{4}$. The melting-associated behavior is predicted to initiate in major groove bonds in the inserted adenine-thymine (A-T) base pairs at 349 K. This temperature is above the mean-field melting temperature of poly(dA)-poly(dT) due to stabilization of the A-T bonds by the G-C helix and below the mean-field melting temperature of poly(dG)-poly(dC), where dA refers to repeating ade- nine bases on one strand and dT the repeating thymine bases on the other strand.

An investigation of the Si(111)−(√3 × √3)R30°−Ag surface by Li + impact collision ion scattering spectroscopy

The Si(111)−(√3 × √3)R30°−Ag surface has been investigated using the technique of Li + impact collision ion scattering spectroscopy. Typical LEED √3 domain sizes were estimated to be on the order of 150 Å for a 1 ML coverage of Ag, with the √3 structure persisting for coverages of Ag up to 35 ML. Silver islanding was found to influence the appearance of the 5 keV Li + ICISS angular scans even for 1 ML coverages of Ag deposited at 480°C. A detailed structural analysis of the Si(111)−√3−Ag surface (0.25 ML deposition) involved the comparison of 5 keV Li + ICISS experimental data along the [11 2 ], [ 1 10] and [2 bar3 1] azimuths with computer simulations of the scattered ion intensities based on previously proposed models for the √3 surface. Nine structurally different models were tested, and only the missing-top-layer (MTL) and the honeycomb-chained-trimer (HCT) models were found to be consistent with all the experimental results. An estimate of 0.4 Å for the maximum downward vertical displacement of the Ag atoms with resect to the surface Si atoms in the MTL model is made. The effects of increased thermal vibrational amplitude in the simulation of SiAg shadowing effects is also discussed. The interpretations of previous noble gas ICISS results are shown to be inconsistent with the present alkali metal ICISS study of the √3 surface.

Planar channeling in superlattices. III. Potential and parameter dependence of catastrophic dechanneling.

Catastrophic planar dechanneling in strained-layer superlattices provides for a critical evaluation of fundamental-particle channeling phenomena, as well as a method of strain assessment. Using continuum-model theory, the equation of projectile motion is solved numerically. The depth and angular dependences of catastrophic dechanneling are examined as a function of the parameters: incident energy and angle, superlattice strain, crystal potential, and the minimum impact parameter for channeling. The catastrophic dechanneling increases with the strain-induced tilt angle \ensuremath{\Delta}\ensuremath{\psi} and contains well-defined structures in the angular and depth dependences. These features are particularly sensitive to strain for the region \ensuremath{\Delta}\ensuremath{\psi}\ensuremath{\sim}0.1 to 1.0 times the critical angle for channeling. Also, there is a range of energies (\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}10%) about the resonant value for which good catastrophic dechanneling behavior is retained. Using the thermally averaged Doyle-Turner potential and data from a ${\mathrm{GaAs}}_{\mathit{x}}$${\mathrm{P}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$/GaP superlattice, we obtain a minimum impact parameter for planar channeling of 1.3 times the Thomas-Fermi screening length. When scaled by thermal vibrational amplitude, this value (2.3${\mathit{u}}_{1}$, where ${\mathit{u}}_{1}$ is the one-dimensional amplitude) is consistent with recent computer-simulation results for the steering of particles by single-crystal planes.

Numerical convergence of dynamical calculations of reflection high-energy electron diffraction intensities

Numerical convergence of multi-slice dynamical calculations of reflection high-energy electron diffraction (RHEED) intensities for numbers of slices, atomic layers and beams is reported for a Ag(001) surface. Criterions of the convergence for numbers of slices and atomic layers are delivered by a thermal vibration amplitude of atoms and an electron absorption coefficient, respectively. From comparison of the curves of 11-beam calculation for the zeroth Laue zone and those of 61-beam calculation with higher order Laue zones, it is revealed that low-order RHEED intensities obtained by the 11-beam calculation are not significantly different from those of the 61-beam calculation. Therefore, calculated RHEED intensities for the zeroth Laue zone spots are obtained well by dynamical calculation with a beam set in only the zeroth Laue zone. Effects of the Debye-Waller factor on RHEED intensities of higher order Laue zones are also discussed.

Interfacial stiffening of Cu, Ni, and Ag thin films on the Ru(0001) surface.

We have studied the vibrational behavior of overlayer films of Cu, Ni, and Ag grown on the Ru(0001) surface as a function of film thickness. Specifically, we have measured the thermal mean-square vibrational amplitude, through a Debye-Waller analysis of low-energy electron diffraction, for films having thicknesses ranging between 1 and 10 monolayers. The analysis indicates that the strong interfacial interaction, which gives rise to a pseudomorphic structure for 1 monolayer Cu and Ni films, also results in a reduction in the overlayer vibrational amplitude (i.e., the films are stiffened by the interaction). In addition, we find that this interfacial stiffening is long ranged and requires overlayer-film thicknesses in excess of about 10 monolayers to heal to bulklike values. In contrast, Ag is found not to grow pseudomorphically at the 1-monolayer level, and the vibrational behavior shows a lesser degree of stiffening and a much more rapid healing to bulklike values. These findings are discussed in terms of the instrumental aspects of the Debye-Waller analysis, and in terms of the I-V character of the diffraction process, and are contrasted with similar studies of the structural and electronic properties of film growth for these overlayer systems.

Segregation at the Pt0.5Ni0.5(111) surface studied by medium-energy ion scattering.

Medium-energy ion scattering combined with shadowing and blocking is used to study the Pt-Ni alloy surface. By applying three scattering geometries in which different numbers of atomic layers are visible to the incoming ion beam, the compositions and relaxations of the first three layers of the crystal are accurately determined. An oscillating segregation profile is found in which (75\ifmmode\pm\else\textpm\fi{}2)% Pt is present in the first layer, (27\ifmmode\pm\else\textpm\fi{}3)% Pt in the second layer, and (53\ifmmode\pm\else\textpm\fi{}5)% Pt in the third layer. The relaxations of the first and second interlayer distances amount to (-2.0\ifmmode\pm\else\textpm\fi{}0.5)% and (-2.0\ifmmode\pm\else\textpm\fi{}0.5)%. An enhancement of the thermal vibration amplitudes in the first three layers is found. The results support those obtained by other methods and agree with theoretical calculations.

Asymmetry in channeling spectra for the 〈110〉 angular scan in GaP

Backscattering spectra for 2-MeV He ions incident on single-crystal GaP at small angles to the 〈110〉 axis, parallel to the {110} plane, have been studied. For symmetric tilts 0.6° ≤ |θ|≤ 2°, pronounced asymmetry in a complex structure of the spectra is observed. The spectra normalized to the random yield have been reproduced by a Monte Carlo simulation. Thermal vibration amplitudes found previously for the 〈100〉 axis have been used. The effects of beam angular divergence and ion-atom potential are studied in detail. Consequences for lattice location applications are discussed.

Anomalous ion-channeling behavior across the superconducting transition in high-Tc materials

Axial channeling scans with minimum RBS yields of ≤ 2% were obtained for 1.5 MeV 4He ions incident along the c-axis in YBa2Cu3O7−δ and ErBa2Cu3O7−δ single crystals. Large variations in the FWHM of the (001) channeling dip were observed fo temperatures between 30 and 300 K. An abrupt, ∼ 8% increase was measured as the temperature was lowered through the superconducting transition (Tc); the relative increase across Tc. in the width of the axial dip was even larger for angles of i less than the critical angle. A simple analytical procedure for polyatomic materials yields isotropic, average thermal vibrational amplitudes that agree well with considerably less precise neutron powder diffraction results on sintered samples. The individual contribution to the angular channeling dip from the row of Er and Ba atoms parallel to the c-axis can be isolated in the RBS scans of the Er compound. This separation reveals normal (Debye-type) behavior for atoms in the ErBa row, demonstrating that the anomalous changes are due solely to atomic displacements in the CuO row. The large magnitude ( ∼ 30% in Debye temperature) of the change found for the CuO row at Tc suggests that the atomic displacements in this row become highly correlated in the superconducting state. New measurements using X-ray and resonance backscattering yields are presented which considerably improve the experimental statistics, and which also permit more direct identification of the contributions from the individual atomic species to the observed channeling phenomena. These new results confirm that Cu and O are responsible for the observed anomalous temperature dependence. Finally, X-ray studies using specimens with different O stoichiometries reveal that the anomalous change in the FWHM shifts in temperature in direct proportion to the change in Tc.

Conformational calculation of the conditions of internal rotation and torsional vibrations of cyclic groups in poly(4,4′-oxydiphenylene)pyromellitimide

For PI on the basis of pyromellitic acid dianhydride and 4,4′-diaminodiphenyl ether, the potential surface for the motion of cyclic chain fragments was calculated in the atom-atom approximation. The amplitudes of thermal vibrations and energy barriers to rotation of pyromellitimide and phenylene rings were calculated for a defect-free crystalline lattice and for defective fragments resulting from point defects and from local density fluctuations in the polymer. Types of motions of cyclic fragments which can be manifested as local relaxation processes are proposed.

Synthesis, Structure, and Ionic Conductivity of K3NdSi6O15

AbstractA structure earlier reported for K3NdSi6O15 suggests the possibility for fast—ion conduction by virtue of K+ ions which not only reside in connected channels, but which also display very large thermal vibration amplitudes. No properties of the phase had heretofore been examined. Crystals up to 2mm inlength have been synthesized under a variety of hydrothermal conditions. Refinement of the structure with single crystal x-ray data to a residual of 8.3% confirms the composition and structure of our crystals and reveals a very high thermal vibration amplitude along c for K+ ions which reside in interconnected [001] channels.A reversible phase transformation has been discovered at 180ºC with a heat of transformation of 4J/g. Preliminary measurements of the conductivity of the high temperature phase yield a preexponential factor of 3.4/cm and an activation energy of 0.61ev along [001], indicating that this compound is not a particularly good fast—ion conductor.

Lattice site location of Te in GaAs

Abstract The lattice site of donor Te atoms in GaAs was studied by the channeling technique in order to determine the position of the nonsubstitutional fraction. Single crystals of pure GaAs with a (100) orientation were implanted with 220 keV Te ions to a dose of 3 × 1014 cm−2. After rapid thermal annealing (820°C, 15 s) angular scans through three major axial directions were measured with 3.9 MeV He+ ions. A strong asymmetry, observed in 〈110〉 scans along a (211) plane, is discussed and quantitatively explained by Monte Carlo simulations. Analysis of the data for Te, by comparison with computer simulations, shows that practically all Te atoms are close to As sites, with an average displacement of 0.32 ± 0.04 A . A clear separation in a substitutional fraction and a nonsubstitutional fraction at a unique site is not evident. The best overall fit for the Ga + As RBS spectra was obtained for thermal vibration amplitudes corresponding to a Debye temperature of 260 ± 10 K.

Studies of surface atomic structure of Al(l00) by MeV ion scattering

An UHV system specially designed for studying surface and interface atomic structure by MeV ion scattering and channeling is described. The vacuum in the UHV chamber is 1 × 10 −10 Torr. The chamber is equipped with an ion gun used for sample cleaning, a translatable four-grid LEED-Auger system used for characterization of the crystal surface, and a three-dimensional goniometer. The crystal preparation and cleaning procedure of Al(100) are presented. The surface peak intensity of Al(100)-〈100〉 and Al(100)-〈110〉 has been measured by MeV ion channeling and scattering. The measured surface peak intensity was compared with that of a Monte Carlo simulation. The experimental results indicate that the thermal vibration amplitude of Al(100) surface atoms is 1.2–1.3 times that of bulk atoms. The relaxation of the first layer for Al(100) is less than −0.05 Å.

Surface studies of AIIIB

Backscattering-energy spectra were measured for 2-MeV He ions channeled in 〈100〉 GaP, GaAs, and InP single crystals with natural oxide surface layers. The analysis of the experimental spectra was performed by the Monte Carlo simulation. The simulation program is based on the binary-collision model. The influence of the surrounding atoms and the energy loss of the channeled particles were taken into account. Also, different types of the ion-atom potential were tested. The simulated channeling spectra were calculated with respect to the random yield which makes it possible to fit experimental spectra without any normalization. Based on the simulation program, the thickness of the surface oxide layer, thermal vibration amplitudes of crystal atoms, and random stopping power of incident ions were determined. The values obtained were compared with the previously published theoretical and experimental data.

Ion-channeling analysis for epitaxial YBa 2Cu 3O x superconducting thin films by laser deposition

Rutherford backscattering/channeling has been applied to study structures of as-deposited epitaxial YBa 2Cu 3O x thin films prepared on {100}SrTiO 3 by laser deposition. The epitaxial growth has been proved by a planar channeling experiment and transmission electron microscopy. An axial angular yield profile for barium along the c-axis has ideal characters of compensating shoulders and of a flat region at the bottom of the channeling dip. The thermal vibration amplitude, which has been determined from a half-angle of the axial angular yield profile by using Gemmell's channeling model for polyatomic crystals, is compared to those from diffraction experiments.

Crystal structure of form II of cholesteryl palmitelaidate at 295 K.

Form II for cholesteryl palmitelaidate (trans-9-hexadecenoate) (C43H74O2) is monoclinic P2(1) with a = 12.745(3), b = 9.006(2), c = 18.153(4) A, beta = 96.63 (2) degrees, Z = 2. The X-ray crystal structure of form II has been determined from 2506 reflections of which 2126 gave (F greater than 2 sigma). The data up to sin theta/lambda = 0.44A-1 (Dmin = 1.14 A) were measured with CuK alpha radiation from a sealed tube. These were supplemented up to sin theta/lambda = 0.52 A-1 (Dmin = 0.96 A) by measurements on the same crystal using a rotating anode X-ray source. The electron density was diffuse in the ester chain and the atoms of the cholesteryl tail were found to be disordered. The tail and the chain atoms were refined by restrained least squares methods to give R = 0.087 and Rw = 0.10 for reflections with F greater than 2 sigma. Crystal forms I and II represent two standard structure types already characterized for fatty acid esters of cholesterol. In form II, the ester chain is almost fully extended as is also the case for one of the two independent molecules (A) in form I. In form II, the chains pack loosely together for most of their length. M.s. amplitudes of thermal vibration for the chain C-atoms are almost uniform along the entire chain (approximately 0.25 A2 at 295 K). In form I, the proximal part of the A chain is surrounded by rigid cholesteryl groups. In this region, C-atom m.s. amplitudes are much reduced (approximately 0.10 A2) but they increase to about 0.5 A2 at the distal end of the chain where packing is very loose.

Crystal Structures of BaBiO3-x at High Temperatures

High-temperature crystal structures of BaBiO3-x (x=0∼0.2) were studied by in-situ neutron and X-ray powder diffraction techniques using controlled oxygen pressures. Rietveld profile analysis of the neutron data from BaBiO3 at 900 K has revealed that the structure is cubic with large anisotropic thermal vibration amplitudes of the O ions perpendicular to the Bi–O bonds. For oxygen-deficient BaBiO3-x, both the neutron and X-ray data showed that the system is not a single phase. The X-ray data from BaBiO2.99 at 1010 K indicated a two-phase system comprising a cubic perovskite and a tetragonal structure with a doubled cell. Profile analyses gave refined cell parameters of a=6.293 and c=9.054 Å for the tetragonal phase. In more reduced BaBiO2.8 at 1075 K this tetragonal structure was replaced by another pseudotetragonal structure with a slightly expanded cell.

Thermal stability of a supersaturated solution of hafnium in aluminium

A number of single crystals of aluminium were implanted with 110 keV hafnium ions to doses of 2 × 10 14 – 2 × 10 15 cm −2, corresponding to a maximum local concentration of about 0.13 –1.3 at.%, which is far above the solubility limit. A small dose of radioactive 181Hf atoms was co-implanted. The samples were studied by means of Rutherford backscattering spectrometry-channelling and perturbed angular correlations (PACs) . Both channelling and PAC measurements show that all hafnium atoms in the asimplanted samples occupy substitutional sites in a damage-free close environment. The r.m.s. thermal vibration amplitude of the hafnium atoms was determined from a comparison of measured and simulated channelling dips. The temperature dependence of this amplitude strongly deviates from the prediction of a simple Debye model. PAC measurements on the samples with 2 × 10 15 Hf atoms cm −2 showed that precipitation in the implanted layer starts during annealing at 380 °C. The precipitates grow during prolonged annealing at 420 °C. After annealing at 535 °C, most hafnium atoms are diffused to the surface. At the same time a strong, well-defined quadrupole interaction was observed by PAC, which may be attributed to oxygen association of hafnium atoms at the interface between aluminium and the thin surface layer of Al 2O 3. In channelling, precipitate formation shows up as a very slight narrowing of the channelling dips, which means that the precipitates are coherent.