Thermal Vibration Amplitude Research Articles

Thermal vibration amplitude of surface atoms measured by specialized low-energy ion scattering spectroscopy: TiC(111)

The thermal vibration amplitude of Ti atoms in the top layer of the TiC(111) surface has been measured by a specialized technique in low-energy ion scattering spectroscopy. The root-meansquare amplitude of the surface Ti atoms is ∼0.076 Å along the surface normal at room temperature.

The structure of the hollandite type phase of synroc b in the temperature range 20–1060°c

The crystal structure of the hollandite type phase Ba 1.17Ti 5.04Al 2.10O 16 has been determined by neutron diffraction powder methods in the temperature range 20–1060°C. The lattice parameters, the positional parameters and the anisotropic thermal parameters of each atom have been determined at seven temperatures. The principal results are: 1. (1) the thermal expansion coefficients are almost isotropic, α a = (10.40 ± 0.25) × 10 −6 , α c = (11.17 ± 0.35) × 10 −6 ; 2. (2) the fractional atomic coordinates do not change in this temperature range; 3. (3) the Debye temperature is (581 ± 15) K; and 4. (4) the amplitude of thermal vibration of the barium atoms is anomalously high at all temperatures.

Simple variational approach to the thermal properties of ionic crystals

The thermal properties of ionic crystals are analysed using the variational principle of classical statistical mechanics. The Einstein and Debye pictures of the lattice vibrations are adopted as trial Hamiltonians. No explicit calculation of the lattice spectrum is needed. The variational result for the thermal expansion in the Einstein picture is identical to that recently derived by Narayan and Ramaseshan by a physically motivated thermal force picture. The agreement with experimental values in the alkali halide family of crystals is surprisingly good, the root mean square error being about 14%. The parameters in the interionic potential used are obtained from the lattice spacings and compressibilities of the crystals and not from anharmonic properties. The Debye picture gives about equally good results for the thermal expansion, but better results for the thermal vibration amplitudes of the ions. It differs from the Einstein picture in incorporating correlated vibrations of atoms and in having an explicit Coulomb contribution to the thermal properties. It is suggested that the theory given in this paper has a useful role to play in studies of thermal expansion and phase stability for large families of ionic crystals when combined with semi-empirical theories.

Ion channeling in natural diamond. II. Critical angles

In this paper the critical angles for ions channeling in diamond single crystals are presented and considered. Careful attention was paid to experimental precautions to ensure reliable results. In diamond the thermal vibration amplitude is much less than the Thomas-Fermi screening distance even at ordinary temperatures, and this crystal can be expected to furnish a stringent test of theoretical critical-angle expressions which depend on the ratio of these two quantities. Data were taken for different axes and planes, for different ions and ion energies, and for different crystal temperatures. It is shown that most of the diamond data are in fact well represented by the established semiempirical expressions due to Barrett and can also be predicted accurately by the procedure of Varelas and Sizmann. This provides fresh confirmation of the continuum model for channeling and of some of the physical considerations underlying these theoretical approaches. The areas of disagreement serve to highlight important second-order effects of crystal geometry and can be understood within the terms of current theory.

Structure study of oxygen-adsorbed Ni(111) surface by high energy ion scattering

Surface atomic structures of clean, oxygen-adsorbed, and oxidized (111) nickel have been studied quantitatively by using MeV ion scattering in combination with AES and MEED. We show that; the clean (111) nickel surface has the bulk-like structure with reconstruction or relaxation less than 0.02 Å, the surface thermal vibration amplitude is enhanced by ~20% compared to the bulk value, adsorbed oxygen results in surface lattice expansion by ~0.15 Å which is closely correlated to the p(2 × 2) or (√3 × √3) R30° superstructure, and oxidation at room temperature saturates at a stage which incorporates ~ 3 monolayers of nickel in a stoichiometric amorphous film of NiO whereas at temperatures higher than ~200° C thicker oxide films are produced. Our study indicates that each oxygen atom adsorbed on the Ni(111) surface interacts with and relaxes three nearest neighbor nickel atoms, and after saturation of the relaxation, oxidation of three monolayers takes place abruptly after which the oxide layer on the surface apparently blocks further reaction.

The charge density in imidazole by X-ray diffraction at 103 and 293 K

The static charge density has been determined for imidazole, based on X-ray (Mo Ka) intensity data [1892 reflections with F o > 6ty(F) and sin 0/2 4o(F) and sin 0/2 < 0.8 A -1 at 293 K]. Full-matrix least-squares refinements were carried out using Stewart's rigid pseudoatom model. Fixed neutron values were assumed for the nuclear positional parameters, and for selected thermal parameters (Utj for H atoms and third-order Cjk I values for all atoms). The model gave a satisfactory fit to the X-ray data in terms of 150 variables which included population parameters for multipole expansions of the charge density as far as octapole terms for C and N atoms and quadrupoles for H atoms. Although ring-atom mean-square thermal vibrational amplitudes are considerably different at the two temperatures (U ~ 0.06 A 2 at 293 K; U ~ 0.02 A 2 at 103 K), the derived static charge distributions are in good agreement. This is attributed to the importance of the octapole deformation density for the imidazole-ring atoms. The charge density is consistent with a simple electrostatic theory for the strong NH...N hydrogen bond. It is also found that the approximate 2mm symmetry in the molecular geometry extends to the charge distribution, and that there are similarities with

Structure study of oxygen-adsorbed Ni(111) surface by high energy ion scattering

Abstract Surface atomic structures of clean, oxygen-adsorbed, and oxidized (111) nickel have been studied quantitatively by using MeV ion scattering in combination with AES and MEED. We show that; the clean (111) nickel surface has the bulk-like structure with reconstruction or relaxation less than 0.02 A, the surface thermal vibration amplitude is enhanced by ~20% compared to the bulk value, adsorbed oxygen results in surface lattice expansion by ~0.15 A which is closely correlated to the p(2 × 2) or (√3 × √3) R30° superstructure, and oxidation at room temperature saturates at a stage which incorporates ~ 3 monolayers of nickel in a stoichiometric amorphous film of NiO whereas at temperatures higher than ~200° C thicker oxide films are produced. Our study indicates that each oxygen atom adsorbed on the Ni(111) surface interacts with and relaxes three nearest neighbor nickel atoms, and after saturation of the relaxation, oxidation of three monolayers takes place abruptly after which the oxide layer on the surface apparently blocks further reaction.

Study of ionic conductors by X-ray and neutron diffraction

Thermally excited ions can move through the crystal lattice in fast ionic conductors. Therefore the potential has to be shallow along the diffusion path of these mobile ions. Their thermal vibrations are characterized by large amplitudes, at least in the directions of their diffusion paths. Diffraction experiments allow an exact determination of the thermal vibrational amplitudes and thereby the determination of an effective atomic potential. These potentials can be used to construct the potential along the diffusion path of the mobile ions and to estimate their activation energy. This is shown for the Li conductor Li3N and the high temperature phases of the Ag conductors AgI, Ag3SI and Ag2S.

Radiation damage in the non-metal sublattices of V 3Ge and V 3Si single crystals

Channeling measurements on V 3Ge and V 3Si single crystals, which have been irradiated with He-ions, revealed a considerable narrowing of the angular yield curves for the B-atom sublattices. Analysing the data with a computer simulation, the best agreement with the experiment was achieved by adding a static contribution to the thermal vibration amplitudes. After irradiation with He-fluences, which cause a saturation in the degradation of the superconducting transition temperature in the V 3Ge and V 3Si films, it was concluded that the average static displacement amplitude was 0.006 nm for the Ge-atoms and 0.01 nm for the Si-atoms.

An X – Ray Study of the p-n-Alkoxycinnamic Acids. Part III.1

Abstract The effect upon molecular packing of increasing chain length in a homologous series of mesogens has been examined in the case of the p-n-alkoxycinnamic acids by determination of the crystal structures of the four nematogenic acids having two, four, six, and eight carbon atoms in the alkyl chain. The chains have the all-trans extended conformation, and the molecules exist in the crystal as planar hydrogen-bonded dimers. The dimers are arranged in end-to end fashion in parallel rows. Similar side-to-side packing of pairs of dimmers is found in each crystal structure giving a good fit between adjacent aromatic cores, but the amplitudes of thermal vibration of the chain carbon atoms increase markedly with increasing chain length, indicating a low packing efficiency for these moieties.

Ion channeling and dechanneling in natural diamonds

Precise measurements are reported of critical channeling angles and minimum yields for light ions backscattered from good-quality natural diamond crystals under various conditions of temperature and energy. A comparison with the theoretical predictions of Barrett and others reveals excellent agreement, despite the fact that diamond represents an extreme case (the ratio of the thermal vibration amplitude at ordinary temperatures to the Thomas-Fermi screening distance is unusually small). The minimum yield as a function of depth is found to scale with energy according to the electronic stopping power. Theoretical calculations based on the diffusion model with initial transverse energy distributions calculated from a multistring continuum model give good agreement with experiment.

Potential Functions of Ions in Cubic BaTiO3

Integrated intensities of X-ray Bragg reflections (Ag-K α radiation) from barium titanate single crystal were measured as a function of temperature above the Curie point of 131.2°C. The harmonic and fourth order anharmonic potential parameters for constituent ions were estimated from the thermal vibration amplitude of each ion. Potential parameters are: α(Ba)=1.018 ×10 -11 erg A -2 , α(Ti)=0.730 ×10 -11 erg A -2 , α(O)=0.265 ×10 -11 erg A -2 , α'(O)=0.999 ×10 -11 erg A -2 , γ(Ba)=0.055 ×10 -11 erg A -4 , γ(Ti)=0.679 ×10 -11 erg A -4 , γ(O)=-0.400 ×10 -11 erg A -4 , γ'(O)=2.99 ×10 -11 erg A -4 ; and the Gruneisen constant is 1.22. These values are consistent with suggestions presented in previous neutron diffraction studies by Y. Yamada et al. and J. Harada et al.

Ion scattering by atomic chains on a solid surface

Abstract The computer simulations of ion scattering by some rarefied infinite atomic chains and some broken chains, consisting of a finite number of atoms, taking into account correlated thermal vibrations and two types of interaction potential were carried out. It was shown, that the increase both of the interatomic distances and the amplitude of thermal vibration and also the potential cut-off, results in an increase of the size of loops in the energy-versus-scattering angle diagram, that explains the scattering in the observed directions, shadowed in case of ideal chain. The calculations allow the establishment of the correlation between the type of surface defect and the shape of the energy spectra.

Relaxation effects and thermal vibrations in a Pt(111) surface measured by medium energy ion scattering

Medium energy ion scattering, in conjunction with channeling and blocking has been applied to search for differences in the planar spacing of the first two layers of a Pt(111) crystal surface as compared to the spacing in the bulk. We find a small expansion of 1.5 ± 1%. The measurements have yielded a value for the transverse rms thermal vibration amplitude of a surface atom relative to its neighbour along the [001] direction and likewise for the [110] axis. The results are giving evidence for an enhanced amplitude for the surface atom perpendicular to the surface. A strong blocking effect has been observed along the [110] axis, which may be due to correlation effects, although the role of surface defects cannot be ruled out.

Two-atom model for the calculation of surface blocking in medium and high energy ion scattering

A two-atom blocking model has been developed to analyze surface blocking patterns recently obtained in medium energy ion scattering experiments. In the model the mean square thermal vibration amplitude of a surface atom can be used as a fitting parameter in comparison with experimental results. Anisotropic surface vibrations have been taken into account by assuming a non-spherical Gaussian probability distribution for the thermal displacement of the surface atom. In addition, some analytical expressions have been derived for the effective nuber of target atoms contributing to the yield of ions backscattered into a blocking direction.

Piezoelectric langbeinite-type K2Cd2(SO4)3 structure at four temperatures below and one above the 432°K ferroelastic–paraelastic transition

K2Cd2(SO4)3 is orthorhombic below 432°K, with space group P212121, and cubic above with space group P213. A structural study has been completed at 298, 351, 390.5, 417.5, and 443.5°K based, respectively, on 3383, 1377, 1803, 1724, and 1022 symmetry-independent structure factors. Measurement of integrated intensities was made using a CAD-4 diffractometer with Nb-filtered MoKα radiation. An air-flow microfurnace with temperature controller provided a thermal stability better than ±1°. The a, b, c lattice constants in the orthorhombic phase are 10.2084(8), 10.2813(8), 10.1684(8) Å at 298°K; 10.2239(8), 10.2897(8), 10.1821(8) Å at 351°K; 10.2386(8), 10.2951(8), 10.1981(8) Å at 390.5°K; and 10.2501(10), 10.2972(8),10.2132(9) Å at 417.5°K. In the cubic phase, a=10.2704(10) Å at 443.5°K. The model previously obtained at room temperature [J. Chem. Phys. 67, 2146(1977)] was refined by the method of least squares using the new sets of measurements. The final agreement factors are R=0.028 (298°K), 0.032(351°K), 0.026(390.5°K), 0.037(417.5°K), and 0.026(443.5°K). Normal probability plot analysis shows the furnace does not introduce new systematic error in the Fmeas. The amplitudes of thermal vibration for the oxygen atoms increase gradually between 298 and 417.5°K and sharply between 417.5 and 443.5°K. The metal atom vibrations have smaller increases. The metal ions undergo displacements averaging 0.16 Å at the transition, with displacements in the orthorhombic phase averaging 0.05 Å over a 120°K interval. The sulfur atom displacements are comparable, with simultaneous rotations of the SO2−4 tetrahedra. Two K–O contacts are broken and one is made in the K1+ coordination polyhedra at the phase transition. The Cd–O coordination polyhedra remain unchanged.

Surface studies of W(100) by MeV He scattering

The backscattered energy spectrum of a beam of MeV ions incident along a major axial direction of a single crystal displays a high energy peak which represents the interaction of the beam with the surface region of the solid. Measurements under U.H.V. conditions, on well characterized surfaces, yield information on the thermal vibration amplitude, relaxation and reconstruction of the first monolayer(s) of the solid; this information is not easily obtainable by standard surface physics techniques. Such studies are of importance in the field of catalysis and semiconductors as well as the fundamental understanding of surfaces. An U.H.V. system for surface analysis studies couple to a 3.75 MeV Van de Graaff accelerator shall be described. Measurements of the surface peak intensity for W(100) are presented and shown to be in good agreement with theoretical models of the scattering process. The interpretation of such measurements in terms of surface physics parameters will be discussed.

Determination of thermal vibration amplitudes in graphite using integrated X-ray intensities corrected for thermal diffuse scattering

Vibrational amplitudes in graphite are determined using the temperature dependent intensity diminution of the (002)-, (004)-, (110)- and (112)-reflections between room-temperature and 1900°C. Besides Lorentz polarization and atomic scattering factors the integrated intensities were corrected for thermal diffuse scattering (TDS). For this reason a modified Debye-model has been established to calculate the TDS in powder diagrams of layer structures.

Thermal vibration amplitudes of TlCl between 296 and 534 K

AbstractThe thermal motion parameters, B, of the Tl+ and Cl― ions of TICI are determined by X‐ray diffraction from powder samples between 296 and 534 K. The B‐values increase linearly with temperature from BTI = 3.39 Å2 and BCI = 2.09 Å2 at 296 K to BTI = 5.68 Å2 and BCI = 3.38 Å at 483 K. This corresponds to a constant Debye temperature of ΘM = 95 K. The results suggest strong second‐neighbour interactions and a mutual cancelation of the anharmonic effects.

The relationship between crystal ionicity and some physical properties of the alkali halides

Abstract In the alkali halides a linear dependence is found between the values of crystal ionicity, spectroscopically determined, and crystal properties such as interatomic distances, potential energy and amplitudes of atomic vibration. Such a correlation appears to allow a quantitative prediction of coefficients of thermal expansion and amplitudes of thermal vibrations of the atoms.