Quasi-elastic neutron scattering of benzene in Na-mordenite

The rotational and translational dynamics of benzene adsorbed in Na-mordenite have been studied by incoherent quasi-elastic neutron scattering. The measurements were performed at two benzene coverages at 300, 400 and 450 K. The observed quasi-elastic broadenings are described by a uniaxial rotational model about the six-fold axis of benzene. The mean time between successive jumps, at 300 K, is τ=1.45 × 10^?12 s at low coverage and 2.05×10^?12 s at high coverage. The correlation times follow an Arrhenius law with E_A=4.51 kJ mol^?1, at both coverages. The translational diffusion coefficient has been measured at 300 K and was found to be 0.67 × 10^?6 cm²s^?1.     

Diffusivity of a two-dimensional lattice fluid: CH4 adsorbed on MgO(100)

The diffusive motions of a 0.8 layer of CH₄ adsorbed on MgO(100) are measured at 72, 88 and 97 K by quasi-elastic neutron scattering. It is shown that at 72 K the methane film is solid and its molecules perform an isotropic rotational motion. At 88 and 97 K, the adsorbed layer is in a two-dimensional fluid state in which the molecules jump between equidistant (4.21 Å) lattice sites of the MgO surface. The mean residence time has been determined ( ∼ 1 × 10 ⁻¹⁰ s at 88 K and ∼ 4 × 10⁻¹¹ s at 97 K). The corresponding translational diffusion coefficients are ∼ 5 × 10⁻⁶ cm² s⁻¹ at 88 K and 12 × 10⁻⁶ cm² s⁻¹ at 97 K. The diffusivity of this lattice fluid is compared to that of the same molecules adsorbed on graphite (0001) previously reported. The reduced mobility observed in the case of CH₄/MgO(100) is related to the important depth of the potential wells on the MgO(100) surface.     

Neutron scattering study of NH4+ Motion in NH4+ β-alumina

Incoherent inelastic neutron scattering has been used to study the motion of NH₄⁺ ions in NH₄⁺ β-alumina. The results establish that jump reorientation of NH₄⁺ ions is rapid compared to translational diffusion: The data are consistent with thermally activated jumps between equivalent NH₄⁺ orientations with a proton jump frequency of $\text{~1.0 × 10}{}^{12}\text{sec}$ at room temperature.The data are inconsistent with either free rotation or unrestricted rotational diffusion. The residence time between translational diffusion jumps is >6 × 10^?11 sec at temperatures less than 473°K.     

An N.M.R. study of molecular motion in solid trimethylaminegallane

Continuous wave and pulsed ¹H N.M.R. data have been obtained for solid H₃GaN(CH₃)₃ over the temperature range 63–300 K. A theoretical expression for the relaxation behaviour of a methyl group in a trimethylamine moeity undergoing various motions has been obtained to aid analysis of the data. We find the activation energy to rotation of the -GaH₃ group to be 3·6 ± 0·3 kJ/mole (0·86 ± 0·07 kcal/mole), and to a different motion in the molecule to be 21 ± 2 kJ/mole (5·0 ± 0·5 kcal/mole). In the continuous wave spectra effects due to motion of the -CH₃ groups and the whole -NMe₃ moeity may be distinguished.     

The special features of the ground state in CeAl3

The temperature (3–60 K) and transferred momentum (0.3–2.3 Å^?1) dependences of the intensity of quasi-elastic magnetic neutron scattering were studied for the polycrystalline heavy-fermion CeAl₃ compound to elucidate the special features of its ground state. Transferred momentum variations caused oscillations of the intensity of quasi-elastic magnetic neutron scattering, which was evidence of magnetic correlations in the f-electron subsystem occurring in a fairly wide temperature range.     

Study of jump models for the diffusion of hydrogen in NbH0.02 by means of the quasielastic scattering of slow neutrons

The quasielastic scattering of slow neutrons in a NbH_0.02 single crystal has been measured for a wavevector transfer Q between 0.5 ≤ |Q| ≤ 2.5 Å^?1 at 293, 431 and 581 K for several sample orientations. The data have been analysed in terms of several jump models for the diffusion of hydrogen by comparing the spectral lineshape with the incoherent scattering law S_inc(Q, ω) of the models. The model of jumps to nearest-neighbor sites becomes progressively worse with increasing temperature. The discrepancy cannot be remedied by taking into account jumps to the second-neighbor sites. On the other hand the measured spectral lineshape can be well reproduced in the whole |Q| range by a double-jump model and a two-state model. For comparison, the method of fitting one Lorentzian to theory and experiment has also been used.     

Pressure broadening of UF6 by argon

Pressure broadening of the R(6) manifold in ν₃ of UF₆ at 628.32 cm^?1 has been measured at pressures of 0–30 torr of Ar in a long-path cell at 199 ± 1 K. We obtain a pressure-broadening coefficient of 9.0 ± 1.5 MHz/torr (FWHM), which corresponds to 7.3 ± 1.2 MHz/torr at 300 K. The UF₆-Ar optical collision diameter is 7.4 ± 0.6 Å; this is larger than the hard-sphere kinetic theory collision diameter of 5.2 Å obtained from the diffusion coefficient and implies rapid rotational relaxation.     

Molecular motion in supercooled glycerol

Quasi-elastic Rayleigh scattering of 14·4 keV photons has been measured on supercooled liquid glycerol at -30°C and 0°C by employing the Mössbauer effect. Total scattered intensity, quasi-elastically scattered intensity I _q and energy width of I _q(k, ω) have been determined for k=0·6 to 4·2 Å^-1. The molecular motion is modelled as: random-walk diffusional motions for the centre-of-mass translation and for the orientation of independent rigid molecules, plus fast-bounded translational jitter (vibration). The model parameters are evaluated. The temperature dependence of the translational diffusion constant corresponds to an activation energy of 12 kcal/mol. Comparison is made especially with N.M.R. results for rotational motion. The effect of orientational jitter (libration) is considered and its possible influence on nuclear magnetic relaxation is pointed out.     

The properties of some derivative autocorrelation functions computed with the atom-atom potential

High-resolution quasi-elastic neutron-scattering measurements have been made on two nematogens: DMBCA with a nematic range 108 to 119°C, and 5CB and a tail-deuteriated sample (D5CB), having a nematic range 22·6 to 35·1°C.

Results on 5CB in the crystal phase at ～18°C showed no significant quasielastic broadening, which means that any random motions of the alkyl chain are slower than about 5 × 10⁹ rad s^-1. Measurements were made at a single temperature in the nematic phases on specimens aligned in a magnetic field of 0·25T; for DMBCA with scattering vector Q⊥n (n is the nematic director) and for 5CB and D5CB with Q⊥n and Q∥n and also on the isotropic liquid phase of D5CB at 45°C. Analysis of the coherent scattering from nematic D5CB at Q = 1·2 Å^-1 and 25°C gave an order parameter <P ₂>=0·55, close to the simple mean field value for this temperature. The coherent scattering from DMBCA is too weak to allow this experiment to be performed.

The most remarkable qualitative feature of the results is the close similarity of the scattering law S(Q, ω) for D5CB (and 5CB) with Q⊥n and Q∥n. Analysis of the results in all cases was made using values for the translational diffusion constants measured previously. Corrections for multiple scattering are shown to be important and a single simple model has been devised which fits the line shapes of all the results for D5CB in nematic (Q⊥n and Q∥n) and isotropic liquid phases and DMBCA. The model involves uniaxial rotational diffusion about the long molecular axis m coupled to a displacement along the rotation axis giving a net rotation in a plane whose normal makes an angle ∝ relative to the direction m. Values for the rotational diffusion constant D _rd ns^-1 are as follows: D5CB, 25°C, 6 (∝ ～ 50°); 45°C, 10. DMBCA, 112°C, 16, (all ±10–15 per cent).

The results for D5CB and 5CB are so similar that no additional detailed model fitting was attempted for the fully hydrogenous sample and it is concluded that while the motion of the alkyl tails is freer, the time scale of the motions is not more than about a factor of 2 faster than that of the molecular cores.     

Molekularstrahlmessungen von Stoßquerschnitten für Übergänge zwischen definierten Rotationszuständen zwei-atomiger Moleküle

Inelastic collision cross sections for transitions between specified rotational states designated by (J, M) have been measured in a molecular beam apparatus. With an electrostatic four pole field molecules in a specified rotational state are separated out of a molecular beam and focussed into a gas filled scattering chamber. Molecules which have been scattered by less than 1/2° are then collected in a second four pole field, located directly behind the scattering chamber, and are analyzed for their rotational state. From a comparison of the measured pressure dependence with calculated curves a determination of inelastic collision cross sections for specified quantum jumps is possible. Measured inelastic scattering cross sections for the transitions (2,0→3,0) are reported for the gases He, Ne, Ar, Kr, CH₄, SF₆, H₂, O₂, Air, N₂O, H₂O, CF₂Cl₂. The values range between about 5 and 100 Ų in the order indicated. The scattering gases NH₃ und ND₃ yielded larger cross sections of about 600 Ų and, in addition, the transitions (3,0)→(2,0),(1,0)→(2,0), (2,0)→(1,0) and (3,0)→(1,0) were observed. Total cross sections for the same gases were also measured with the apparatus.     

Amorphous germanium II. Structural properties

The coherent X-ray scattering for momentum transfer, k, between 0·025 and 15·0 Å^?1 has been measured for a series of sputtered amorphous Ge films prepared at various substrate temperatures, T _s, between 0 and 350°C. Differences in the radial distribution function (RDF) of films of different T _s have been determined by an accurate differential scattering technique. The small angle scattering (SAS) of the films is less than 100 electron units for k < 1 Å^?1. From a combination of SAS, RDF and scanning electron microscope studies, it is concluded that an observed increase in film density with increasing T _s occurs through a reduction in the number of voids about 7 Å or less in diameter. No variation of bond length with T _s is found. With increasing T _s, there is an increase in first and second-neighbour coordination and a reduction in bond angle distortion.

The rate of change of coordination, C, with density, ρ₀, is found to be d ln C/d ln ρ₀ = 0·6±0·2. Using a new, general theory of the dependence of the RDF on the dihedral angle distribution, P(θ), it is shown that with increasing T _s there is an increased probability of dihedral angles corresponding to the staggered configuration. For all films, the experimental RDF between r = 4·5 and 6·2 Å agrees with a nearly random P(θ) distribution. Comparison of experimental RDF's of crystalline and amorphous Ge indicates the static distortion of the first-neighbour bond length has a standard deviation of only about 0·04 Å.     

Conformational interconversion in the monovalent ions of 1,2,3,6,7,8-hexahydropyrene II

The E.P.R. spectra of the monovalent positive and negative ions of 1,2,3,6,7,8-hexahydropyrene reveal an alternating line broadening, caused by the non-synchronized motion of the two aliphatic bridges in the molecule. When this motion is described by the modified Bloch equations, using a four-sites jump model, spectra are obtained which agree quite well with the experimental ones.

The potential barrier for the conformational interconversion can be calculated from the temperature dependence of the lifetime of each configuration and is found to be 10·0±0·4 kcal mole^-1 for the radical anion and 3·5±0·4 kcal mole^-1 for the radical cation. The inversion rate at 0°C equals 2·8 × 10⁶ s^-1 for the anion and 4·2 × 10⁶s^-1 for the cation.     

Neutron quasi-elastic scattering of n-triacosane

A neutron quasi-elastic investigation on a well-orientated chain axis crystal of n-triacosane has been undertaken using the twin rotor spectrometer on the Pluto reactor at Harwell with an incident neutron wavelength of 2·64 Å. Data taken in the plastic phase show considerable quasi-elastic broadening, both perpendicular and parallel to the chain axis. Good agreement with experiment is obtained using a continuous rotation diffusion model with translational diffusion. On cooling below the plastic phase transition, slight quasi-elastic broadening isalso seen in both configurations.     

A neutron-diffraction study of liquid acetonitrile

Neutron-diffraction studies on liquid acetonitrile CD₃C¹⁵N at 20°C were carried out at neutron wavelengths of 0·5 Å and 0·7 Å. The data were corrected for background, absorption, multiple scattering and inelastic effects (Placzek correction) and then were normalized to absolute differential cross section by comparison with vanadium standard. The absolute coherent distinct differential cross section was separated into intermolecular and intramolecular contributions. From the latter the molecular structure in the liquid was determined.     

Quasi-elastic scattering due to fast oxygen diffuson in yttria stabilized zirconia

Evidence for fast oxygen diffusion at high temperatures in single crystal ZrO₂ containing 12 mol % Y₂O₃ is presented from quasi-elastic light scattering data. Lattice vacancies are responsible for the enhanced ionic diffusion and the structural disorder. In the temperature range investigated we estimate the barrier activation energy for the jumping of oxygen vacancies to be 0.25 eV. At 1500°K the jump time is ～ 4 × 10^?12 sec., the diffusion constant is ～ 3.26 × 10^?5 cm²/sec. and the conductivity is ～ 0.24 (Ωcm)^?1.     

The structure of the water molecule in liquid water

The slow neutron scattering measurements of Walford, Clarke and Dore for liquid heavy water at 21°C for incident neutron wavelengths of 0·694 Å and 0·347 Å [7] have been reinterpreted using a sophisticated correction for recoil and detector effects [10] for the molecular contribution to the scattering cross-section. For momentum transfer greater than 6 Å^-1 the liquid structure contribution is negligible and a very good agreement between theory and experiment is obtained. It is concluded that the intramolecular oxygen nucleus-deuteron distance is 0·98₃±0·00₈ Å, and that the deuteron-deuteron distance is 1·55±0·02 Å. This molecular structure is nearer to that of the molecule in the vapour than that in ice I for the conventional interpretation for ice I. It is concluded that there is an environmental effect on the molecular internuclear distances at most of order 0·01 Å for the molecule in the orthobaric liquid near the triple point.     

A nuclear magnetic resonance study of molecular motion in solid diethylamine and in diethylamine clathrate deuterate

The proton magnetic resonance second moment and spin-lattice relaxation data are reported for the two solids namely pure diethylamine and diethylamine clathrate deuterate, over the temperature range 77 K to 270 K. The results indicate that in both materials the only motion which occurs at a rate great enough to affect the N.M.R. observables is methyl group reorientation and for such motion activation energies of (2·9₀±0·02) kcal mole^-1 and (2·3₄±0·02) kcal mole^-1 are obtained for pure diethylamine, and the deuterate, respectively. The strength of the dipolar interaction in the deuterate as estimated from both the second moment and the maximum in the temperature dependence of nuclear relaxation rate is consistent with a carbon-proton distance of 1·10 Å and a large degree of chemical exchange of the amine protons with the deuterons of D₂O.     

Oscillator strengths from line absorption in a high-temperature furnace—II. The (0,0) band of the B2σ+—X2σ+ transition in CN*

Quantitative high-resolution absorption spectroscopy was applied to the (0,0) violet band of CN. The CN radical was prepared in a furnace at 1421°K containing pure cyanogen gas. Since the calculated CN concentration is dependent on the controversial CN heat of formation, only the relationship, f_υ = 6·84 X 10^-3exp (0·354δ), where f_υ is the excess over the initially assumed ΔH⁰_f(CN) = 100·8 kcal/mole, could be directly determined in this study with an estimated error in f_υ of ±20%. For δ = 0, our f_υ is a factor of 4·8 smaller than an average value of 0·033±0· derived from other measurements. If this latter value of f_υ is assumed, our relationship yields ΔH⁰_f(CN) = 105·3±1· kcal/mole or D₀(CN) = 7·66±0·05 eV. The rotational temperature and line widths for this band were also measured.     

Infra-red spectrum,structure and properties of the N2-Ar van der Waals molecule

The first spectroscopic observation of bound N₂-Ar van der Waals molecules has been achieved with a cryogenic long path cell maintained at 87 K. The infra-red spectrum exhibits prominent fine structure near the N₂ stretching frequency which is assigned to hindered internal rotation of N₂ within the weakly bound complex. An analysis of this fine structure yields a T-shaped equilibrium geometry in which the N₂ bond axis is perpendicular to the N₂-Ar van der Waals bond axis. The observed spectrum is shown to be consistent with an internal rotational barrier of 20 cm^-1 (57 cal/mole). Approximately 20 per cent of the bound species are trapped by this rotational barrier and acquire a locked semi-rigid structure. The remaining 80 per cent have ill-defined geometry and undergo hindered internal rotation. The rotational envelope of an infra-red fundamental is analysed to give an estimate of the N₂-Ar bond length as 3·9 Å.     

Chromium tracer diffusion in NiO crystals

Diffusion of ⁵¹Cr in NiO single crystals in air has been studied by the tracer-sectioning technique. In the temperature range 1192–1642°C, the diffusion coefficient can be expressed by the Arrhenius expression D=D_oexp(-Q/RT), with D_o=(8·6±1·2)×10^?3 cm²/sec and Q=67·4±1·1 kcal/mole. The use of a high specific-activity tracer and a special configuration for the diffusion anneal prevented the self-dopling effect found by Seltzer and the evaporation of chromium from the sample surface. The present results, in conjunction with published results on nickel self-diffusion in NiO and interdiffusion in the NiO?Cr₂O₃ system, are used to determine a chromium ion-vacancy binding energy of about 5 kcal/mole in pure NiO.