The structure factor for liquid nitrogen and liquid oxygen from neutron scattering studies

The structure factor, S(Q), has been measured for liquid nitrogen at 77 K and liquid oxygen at 84 K by neutron diffraction over a range of momentum transfer, Q, from 0·3 to 7·3 Å^-1. In the case of oxygen a correction for magnetic scattering has been included.

The liquid structure factor for nitrogen compares well with that obtained from X-ray diffraction measurements but there are significant discrepancies in the case of oxygen. These may be partially attributed to uncertainty in the form factor for paramagnetic scattering.

The data have been analysed in terms of several different models for the orientational correlation between neighbouring molecules. The results are particularly sensitive to uncertainties in the absolute normalization of the data, the inter-nuclear distance for the molecular structure and Placzek corrections; the effect of these errors is considered in detail. It is shown that some form of orientation correlation must exist but its precise nature could not be obtained from the present data.     

Structural studies of tetrachloride liquids

The differential cross-sections for neutron scattering from liquid carbon tetrachloride have been measured with the TSS instrument at the Harwell Electron Linac. Data were taken at seven different scattering angles for a wavelength range of 0·2–3·5 Å. The observed diffraction patterns at high momentum transfer (> 8–30 Å^-1) have been analysed in terms of the molecular form factor f ₁(Q). It was found that the oscillation amplitudes could be satisfactorily described only by introducing an energy-dependent term into the Debye-Waller factors of the form factor. The f ₁(Q) data were fitted with a four-parameter function for measurements at scattering angles of 150°, 90° and 58°. The carbon-chlorine bond length parameter was accurately defined in all cases and had a mean value of 1·766 ± 0·002 Å. The inclusion of an anharmonicity constant in the form factor gave an improved χ²-fit to the data with an increased value of 1·770 ± 0·002 Å for the bond length. The results are in excellent agreement with other measurements and show the importance of pulsed neutron techniques for molecular structure studies of disordered materials.     

Neutron diffraction studies of liquid carbon suboxide

The structure factor S _m(Q) for liquid carbon suboxide has been determined for a Q-value range of 0·4 to 60 Å^-1 by neutron diffraction measurements using a steady-state (reactor) and a pulsed (linac) neutron source. The bond lengths of the molecule have been determined from the data and give good agreement with the results of electron diffraction measurements on the vapour phase after application of a molecular recoil correction term. The quasi-linear nature of the molecule is confirmed but the shape of the form factor indicates that large amplitude bending motion probably occurs in the liquid phase.

Oscillations in the intermolecular pair correlation function are observed to have a regular periodicity extending to 12 Å but details of orientational effects cannot be established from a single diffraction measurement.     

The structure factor for liquid bromine by neutron diffraction

Thermal neutrons from steady-state (reactor) and pulsed (linac) neutron facilities have been used to study the structure factor for liquid bromine at 20°C, covering a wide range of values (0·6-35 Å^-1) of the momentum transfer (?Q). The diffraction pattern at high Q-values (>10 Å^-1) gives information on the structural properties of the individual molecules but detailed interpretation is complicated by the vibrational motion which causes a systematic variation in the periodic oscillations of the molecular form-factor. An internuclear distance (bond length) of 2·28 ± 0·01 Å is found to be suitable for data at lower Q-values and has been used in the analysis of the liquid structure. The results show that some form of orientational correlation between molecules must be present and the nuclear (atom) pair correlation function is split into two peaks for the coordination shell corresponding to nearest-neighbour molecules. The results are compared with other studies of liquid bromine and similar neutron experiments for liquid nitrogen and liquid oxygen.     

The correlation of molecular orientation in liquid water by neutron and X-ray scattering

The neutron diffraction structure factor for heavy water at 22°c has been measured for momentum transfers, ?Q, up to a Q of 13 å ^-1. The results have been interpreted by abstracting the molecular structure effects as far as possible and using models for the correlation of orientation of pairs of molecules ranging from completely uncorrelated orientation to that for adjacent molecules in ice I. Neither these nor any of the popular models for the structure of water, nor a non-hydrogen bonded model, fit the neutron diffraction data over the whole range of Q. Nevertheless, information about the molecular-centres structure factor is obtained, especially for Q up to about 3 å ^-1.

The method of analysis is generalized and applied to x-ray diffraction data and in particular to x-ray data for liquid water. It is shown that this method of analysis has some advantages over the conventional one. The effect of correlation of molecular orientation is less than that of molecular structure on x-ray scattering by water and rather more extensive information is obtained for the molecular-centres structure factor than from neutron data—if the conventional assumption of atomic electron clouds is accepted.

A comparison of the x-ray and neutron scattering data for liquid heavy water shows that the two sets of data are reasonably consistent for any of the usual models for water, except for the region of Q between 3 and 5 å ^-1. The molecular-centres structure factor of water has a weak double humped first maximum with peaks at 2·0 å ^-1 and 2·9å ^-1, probably followed by a damped oscillation. This contrasts with atomic liquids but is similar to that found in liquid carbon tetrachloride. The structure of liquid water is not, therefore, necessarily unique or unusual.     

The structure factor for liquid nitrogen and liquid oxygen by neutron scattering

The structure factor S(Q) has been measured for liquid nitrogen at 77 K by neutron diffraction at four wavelengths. The effects of Placzek corrections on the self [1, 2] and interference [3] components of the observed differential scattering cross-sections at 0·35, 0·7, 0·84 and 1·06 Å [4] have been investigated. Effective molecular masses and internuclear bond lengths have been obtained by fitting a modified Placzek model to the observed data. It is concluded that after correction the different structure factors agree satisfactorily within the statistical errors of the measurements and the internuclear bond length is close to that measured in the gas phase.     

Die β-Zerfallsenergie der Technetiumisotope Tc103, Tc104 und Tc105

Molybdenum fission products from Uranium were rapidly separated using a sublimation technique. Their Technetium daughters could be separated from the Molybdenum sample by a second sublimation. The decay of Tc¹⁰³, Tc¹⁰⁴ and Tc¹⁰⁵ was investigated using scintillation counters and coincidence methods. Tc¹⁰³ decays by the emission of twoβ-groups at energies of 2·0 Mev and 2·2 Mev followed byγ-lines of 135 kev, 215 kev and 350 kev. According to a proposed decay-scheme Tc¹⁰³ decays with aQ-value of 2·35±0·10 Mev into Ru¹⁰³. Tc¹⁰⁵ emits aβ-group of about 3·4 Mev maximum energy followed by a 110 kevγ-transition. TheQ-value of the Tc¹⁰⁵ decay was estimated to be 3·4±0·2 Mev. Fromβ?γ- andγ?γ-coincidence spectra of Tc¹⁰⁴ fourβ?γ-γ-cascades could be identified, which populate excited states of 0·36 Mev, 0·89 Mev, 2·5 Mev, 3·5 Mev and 4·05 Mev in Ru¹⁰⁴. TheQ-value of the Tc¹⁰⁴ decay was found to be 5·85±0·10 Mev. TheQ-values and spin assignements of the groundstates of Tc¹⁰³ and Tc¹⁰⁵ are discussed in a more detailedβ-decay systematic.     

Electron spin relaxation in solutions of manganese (II) ions

Measurements of the neutron scattering static structure factor S(Q) are reported for orthobaric liquid fluorine at 77K for an incident wavelength of 1·2Å. The observed S(Q) and the atom-atom correlation function are discussed and compared with those of other halogens and oxygen. From the d(r) pair distribution function it is shown that liquid fluorine has a coordination number of first neighbours more similar to liquid oxygen than halogens. The number of atoms in the first and second coordination shell is in good agreement with a close-packed arrangement of atoms.     

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.     

Reactive scattering of alkali dimers: chemi-ionization

Measurements of total cross sections Q_i for chemi-ionization in scattering of a K₂ dimer beam by a range of halogen containing molecules, at translational energies E ～ 7–11 kcal mol^-1, are reported. Substantial cross sections, Q_i ～ 2–10 Ų are exhibited by the halogen molecules Br₂, ICl, IBr, I₂. Distinctly lower values Q_i ～ 0·1–0.2 Ų are exhibited by BrCN and the mercuric and stannic halides, HgX₂, SnX₄. The results show a close correlation with the chemi-ionization exoergicities, particularly for formation of a K⁺,X^- ion pair. These chemi-ionization data and results from previous reactive scattering studies are compared, in order to estimate relative reaction yields for different reaction paths. The reaction dynamics for K₂ with halogen molecules and cyanohalides are rationalized in terms of the electronic structure of the potential surface, where the orientation of the K₂ dimer plays a crucial role.     

Optical and Zeeman studies of the first excited singlet state of zinc porphin in a single crystal of n-octane: Evidence for Jahn-Teller instability

The absorption and fluorescence spectra of Zn porphin in an n-octane single crystal at 4·2 K are reported in the region between 17 400 and 18 500 cm^-1. A strong peak appears in both spectra at 17 961 cm^-1 and is assigned to the origin of one component (|x, 0>) of the nearly degenerate Q-band. In absorption a second strong line occurs at a frequency δ = 109 cm^-1 above the first; a corresponding line is almost totally absent in the emission spectrum at 4·2 K, but it appears as a hot band of appreciable intensity when the temperature is raised to 80 K. This feature is assigned to the origin of the other component (|y, 0>) of the Q-band. The lifting of the degeneracy of the Q-band is interpreted as a crystal field splitting of the Jahn-Teller unstable ¹ E_u state.

The Zeeman effect is investigated for the 0–0 transition of the phosphorescence spectrum and the |x, 0> and |y, 0> components of the Q-band absorption spectrum. From the phosphorescence experiment it is concluded that the great majority of the ZnP guests are oriented in the host with an angle of about 25° between the out-of-plane molecular axes and the crystal a-axis. The analysis of the Zeeman effect in absorption (H//crystal a-axis) is complicated by the Jahn-Teller instability which causes two additional unknowns to appear in the problem: the frequency ν and the nuclear displacement parameter α of the active mode. When not making an assumption about these parameters one can only derive a lower limit for the matrix element of the orbital angular momentum between the two electronic components: Λ > 4·6. If is identified with the low-frequency mode of 180 cm^-1 appearing in the absorption spectrum, then it follows that Λ = 6·1 ± 0·6 with α = 1·4 ± 0·1.     

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.     

Ground-state constants A 0 and DK 0 of 12CH3I from perturbation-allowed transitions

The upper levels of the bands v ₅ and v ₃ + v ₆ of CH₃I are coupled through a Fermi and an l(2, -1) resonance. This gives rise to perturbation-allowed transitions. Altogether, more than 200 such lines corresponding to three different K-value pairs have been observed between 1320 cm^-1 and 1520 cm^-1. By fixing the sextic constant H^K ₀ equal to zero, the following values were obtained: A ₀ = 5·173931(2) cm^-1 and D^K ₀ = 87·36(6) × 10^-6 cm^-1. The possible values of H^K ₀ and their effects on the results are discussed.     

Thermal conductivity of nitrogen in the temperature range 350–2500 K

The thermal conductivity of nitrogen is determined in a conductivity column instrument in the temperature range of 338 to 2518 K with an estimated uncertainty of about ± 1·5 per cent. The experimental data points are correlated by a cubic polynomial in temperature, viz. k(T)/(mW m^-1 K^-1) = 12·18 + 0·05224(T/K) - 0·6482 × 10^-6(T/K)² - 0·2765 × 10^-9(T/K)³. These conductivity values determined from heat transfer data taken in the continuum regime are found to be in fair agreement with the values obtained from similar data referring to low pressure range.

The present results are compared with the conductivity determinations of other workers and with the predictions of various theories developed for polyatomic gases. It is pointed out that a reliable calculation of thermal conductivity over an extended temperature range is impossible at the present time due to the absence of a large variety of experimental molecular data needed for such an effort. Average values of the vibrational energy diffusion coefficient, D _vib, are computed from the present k(T) data.     

A partial analysis of rotational structure in the 2710 Å system of p-fluorotoluene

The region of the 0-0 band of the 2710 Å system of p-fluorotoluene has been photographed at high resolution.

The rotational contour of the 0-0 band has been interpreted using two approximations in computed contours: (i) treating the molecule as a symmetric top with free internal rotation, and (ii) treating it as a rigid asymmetric top. The first approximation has enabled an estimate of AT' to be made where AT is the rotational constant of the methyl group about the top axis: the second approximation resulted in valves of AF', B' and C', where AF is the A rotational constant of the ring, although to a rather lower accuracy than has been the case in other substituted benzenes.

Interpretation of the rotational constants shows that in the excited state the methyl group has closed up a little: two extreme interpretations of the constant AT' result in either a decrease in the HCH angles of 1·2±0·7° or a decrease in the C-H bond-lengths of 0·009 ± 0·005 Å. The values of AF', B' and C' indicate that the C-CH₃ bond contracts by about 0·03 Å. This suggests a considerable increase in hyperconjugation in the excited state of p-fluorotoluene compared to the ground state.

The 0-0 band was found to be a type B band implying a polarization of the electronic transition moment along the short in-plane axis. The origin of the band was found to be at 36 859·6±0·3 cm^-1.     

High resolution absorption and magnetic circular dichroism of spin-forbidden ligand field transitions in Cs3CoBr5

The axial absorption spectrum of Cs₃CoBr₅ has been recorded from 3100 to 6500 Å at 4·2 K with a spectral bandpass of 0·1 Å and the magnetic circular dichroism spectrum at 4·2 K and 47·5 kG over the same wavelength range with a spectral bandpass of 1 Å. The electronic origins of the spinorbit and tetragonal field components of most of the doublet ligand field states are definitively located and assigned. In a number of instances it has also proved possible to determine whether the doublet gains its intensity from the 3/2 U′ or 5/2 U′ spin-orbit component of ⁴ T ₁, and arguments are also presented to show that the higher energy doublets derive the greater part of their intensity from the lowest ⁴ T ₁ charge transfer state and not the ⁴ T ₁(P) ligand field state. The vibronic sidebands accompanying the doublet transitions are also assigned to internal modes of CoBr₄ ^2- and to lattice modes. In a number of the transitions non-totally symmetric modes are excited with greater intensity than totally symmetric.     

ΔT-window neutron spectrometer

A high resolution neutron spectrometer making use of a ΔT-window filter for the analyser and time-of-flight technique for analysing incident neutron energy has been designed. The spectrometer will provide a continuously variable energy resolution ΔE from 40–50μeV at ∼ 5230μeV. The range of energy transfer allowed is −1450μeV to +2950μeV and the range of wavevector transferQ allowed is 0·82–3·06 ?⁻¹. Depending on the resolution used, the counting rates are expected to vary from 28–60 × 10³ counts/hr if one assumes 10% isotropic elastic scattering from the sample.     

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.     

Zeeman spectroscopy of the 4 Eu → 2 B 1g phosphorescence of copper porphin in an n-alkane single crystal

The phosphorescence spectrum of the metastable ⁴ E_u state of copper porphin in single crystals of n-octane (C₈) and n-decane (C₁₀) has been studied between 2·3 and 35 K, with and without a magnetic field B. The crystal field splitting between the orbital components observed at 35 K is δ = 30·3 ± 0·3 (C₈), 13·8 ± 0·2 cm^-1 (C₁₀). From the Zeeman shifts we derive the effective orbital angular momentum Λ′ = 0·8 ± 0·2 (C₁₀), the spin-orbit coupling parameter |Z′| = 1·5 ± 1·0 cm^-1 (C₁₀), the spin-spin dipolar interaction parameters D = -0·1 ± 0·2 cm^-1 (C₈, C₁₀) and |E| = 0·31 ± 0·03 cm^-1 (C₈, C₁₀), and the g-factors g _∥ = 2·14 ± 0·04 (C₈, C₁₀) and g _⊥ = 2·00 ± 0·03 (C₈, C₁₀).     

Photoelectron spectra of halides

High resolution photoelectron spectra, obtained with He I (584 Å) resonance radiation, are reported for ClF, ClF₃, BrF₃ and BrF (partial spectrum). In some cases Ne I (736–744 Å) radiation has also been used. Spinorbit and vibrational fine structure is resolved for the ground ²II states of ClF⁺ and BrF⁺; values obtained for ClF⁺ and ζ = 630 cm^-1, v′ = 870 cm^-1, and for BrF⁺ ζ = 2600 cm^-1, v′ = 750 cm^-1. From the vibrational envelope of the X ²∏ states, a bond length change of δr _e (-)0·10 Å for ClF⁺ and BrF⁺ is estimated. Ab initio SCF-MO calculations for ClF and ClF₃ are used to aid in the interpretation of the spectra via Koopmans' theorem. A considerable amount of charge delocalization in the trifluorides is inferred from the photoelectron spectra, and this is borne out by the calculations.