Volume 39, Issue 11, 01 December 1963

Temperature Dependences of Nuclear‐Transfer and Spin‐Relaxation Phenomena of Water Adsorbed on Silica Gel
View Description Hide DescriptionNMR relaxation‐time measurements have been made from 193° to 374°K on the protons in a sample of ¾ statistical monolayer of water adsorbed on silicagel.Protons in two different environmental states were observed. Proton transfers occur between these two environmental states. For the first time, the T _{2} value for the longer T _{2} state has been observed without shortening by nuclear transfers. This longer T _{2} value increases with temperature in accordance with an activation energy of approximately 7 kcal/mole. The weighted average T _{1} value has a similar temperature dependence in the range 225° to 270°K. The data were analyzed in detail by use of previously developed theory. Near room temperature, the activation energy for proton transfer is 4.9 kcal/mole, and the average lifetime of a proton in a given state is a few milliseconds. The protons in both states experience very rapid motion; one of the states has an additional slow motion.

Molecular Motion and the Moment Analysis of Molecular Spectra in Condensed Phases. I. Dipole‐Allowed Spectra
View Description Hide DescriptionMolecular absorption and emission spectra (of a vibrational transition or of a single vibrational component of an electronic transition) are analyzed in terms of moments of their intensity distributions. The results are valid for an arbirtary intermolecular potential energy. The first‐moment formula allows one to identify, in an experimental spectrum, the shifted band origin. The second moment is found to have additive contributions from dynamical terms and from fluctuations in the environmental frequency shift. The dynamical terms depend on the average molecular rotational kinetic energy, the principal moments of inertia of the molecule, and the direction of the transition moment relative to the principal axes of inertia. In the classical limit, the average rotational kinetic energy is determined by the temperature, and the dynamical terms of the second moment are then independent of the intermolecular potential energy. If general, the measurement of a second moment gives an upper limit to the average rotational kinetic energy. If the shift fluctuation effect is small, the second moment measures the rotational kinetic energy. The third and higher moments depend on averages of angular derivatives of the intermolecular potential energy, as well as on the rotational kinetic energy and shift‐fluctuation‐type terms found in the second moment. For example, one of the contributions to the fourth moment of a linear molecule is the mean squared torque on the molecule.

Valence‐Bond Theory of Resonance: Aniline, Phenol, and Fluorobenzene
View Description Hide DescriptionA perturbation‐type valence‐bond theory is developed for the computation of pi‐orbital charge distributions in substituted benzenes. Application is made to aniline, phenol, and fluorobenzene, employing for comparison approximate charge distributions derived from protonchemical shift measurements. An important finding is that the previously employed approximation of including only single‐electron transfers between adjacent atoms is not valid. The inclusion of second‐order transfer interactions permits one to compute charge distributions which agree well with the experimental data. However, one must employ empirical integral parameters which are slightly different from the estimated values. Detracting from the theory is the fact that the computations apparently place too much charge on the carbon atom adjacent to the substituent.

Some Topics in the Theory of Fluids
View Description Hide DescriptionIt is shown how certain thermodynamic functions, and also the radial distribution function, can be expressed in terms of the potential energy distribution in a fluid. A miscellany of results is derived from this unified point of view. (i) With g(r) the radial distribution function and Φ(r) the pair potential, it is shown that g exp (Φ/kT) may be written as a Fourier integral, or as a power series in r ^{2} the terms of which alternate in sign. (ii) A potential‐energy distribution which is independent of the temperature implies an equation of state which is a generalization of a number of well‐known approximations. (iii) The grand partition function of the one‐dimensional lattice gas is obtained from thermodynamic arguments without evaluating a sum over states. (iv) If in a two‐dimensional honeycomb (three‐coordinates) lattice gas f_{r} (r=0, 1, 2, 3) is the fraction of all the empty sites which at equilibrium are neighbored by exactly r filled sites, then at the critical density the values of all four of the f's as functions of temperature follow from previously known properties of this system; in particular, at the critical point,f _{0} = 3/8+5√3/24, f _{1} = 1/8+√3/24, f _{2} = 1/8—√3/24, f _{3} = 3/8–5√3/24.

Field Desorption of Carbon Monoxide from Tungsten
View Description Hide DescriptionThe field desorption of CO from tungsten has been investigated at three coverage intervals, corresponding to heats of adsorption of 0.7, 1.90, and 3.30 eV, respectively. Potential‐energy curves of adsorption have been obtained for these cases which seem to correspond to different binding states of CO on tungsten.Polarization corrections have relatively little effect on the shape of the curves but do shift them outward by small amounts. General agreement with the theory of field desorption proposed previously seems to hold and could be confirmed, in particular, for the energetics of desorption and for adsorbatetunneling. The discrepancy between the calculated values of the pre‐exponential terms of the desorption rate constant and the very low values found experimentally at low temperature in this and other cases seems to have no simple explanation and is blamed on entropy effects. The general reasonableness of the potential curves and that of the CO–W spacings obtained indicates that the ion—metal interaction can be expressed by an image potential to distances of the order of 2 Å.

Morphological Development of Aluminum Oxide Crystals Grown by Vapor Deposition
View Description Hide DescriptionThe growth of aluminum oxide crystals by vapor‐phase chemical reaction has been studied at an elevated temperature. The growth process was observed microscopically in progress. The results are of particular interest since they pertain to the growth of an anisotropiccrystal structure. The course of morphological development was consistent with crystal growththeory.

Growth of Anthracene Whiskers by Vapor Deposition
View Description Hide DescriptionAnthracenewhiskers were observed to grow at low supersaturations consistent with the screw dislocation mechanism of whiskergrowth.Whiskers were observed to grow coherently from a larger crystal in a few crystallographic directions. The simultaneous growth of whiskers in the habit plane and normal to the habit plane, for example, requires a regenerative axial growthdefect. A screw dislocation appears to be the only line defect with the required properties.

ESR Study of Free Radicals Produced in Irradiated Cyclopentadiene and Cyclohexene: The Cyclopentadienyl and Cyclohexenyl Radicals
View Description Hide DescriptionThe ESR spectra of irradiated cyclopentadiene and cyclohexene were measured at various temperatures. The spectra showed motional narrowing on raising temperature and the free radicals were identified from analysis of the narrowed spectra. Cyclopentadiene showed a well‐resolved sextet spectrum of 5.6‐G splitting, which was assigned to the cyclopentadienyl radical. Cyclohexene gave a spectrum consisting at least of 26 lines, which can be reasonably attributed to the cyclohexenyl radical by assuming appropriate hyperfine constants.

Optical Spectra of Exchange Coupled Mn^{++} Ion Pairs in ZnS:MnS
View Description Hide DescriptionThe optical spectra of several ZnS:MnS (1 to 10 mole%) mixed crystals were obtained at temperatures from 4.2° to 300°K. A concentration dependence was found which proved that certain bands were due to pairs of Mn^{++} ions in nearest‐neighbor cation sites. Temperature—dependent absorption bands were found which were interpreted to give an interionic exchange integral in the ground state of —9 cm^{—1} in the spin—spin Hamiltonian H = —2JS _{1}·S _{2}. This agrees with the value obtained from the analysis of the susceptibility of pure MnS. The narrow bands due to transitions to the ^{4} A _{1}, ^{4} E(G) states were shown to fit an isotropic spin—spin coupling law with J = +6 cm^{—1} for each state. The inversion of sign from the ground state is not fully understood. The selection rules for the transitions do not follow those for the total spin (ΔS = 0).

Millimeter Wave Spectroscopy of Unstable Molecular Species. I. Carbon Monosulfide
View Description Hide DescriptionThe carbon monosulfide species CS^{32} and CS^{34} are investigated with a millimeter wave spectrometer designed for the study of short‐lived molecules in the frequency range from 60 000 to 300 000 Mc/sec. Spectroscopic constants obtained are:The spectrometer is described. Its sensitivity has been estimated to be the order of 10^{—5} to 10^{—6} cm^{—1}.

P—R Maxima Separations in Unresolved Parallel Bands of Symmetric‐ and Slightly Asymmetric‐Top Molecules
View Description Hide DescriptionThe formulas derived by Gerhard and Dennison for calculating P and R branch separations in parallel type vibration—rotation bands have been applied to 50 symmetric and slightly asymmetric molecules. If consideration is restricted to those fundamental bands that are not obviously overlapped or perturbed by interaction with other bands the average difference between observed and calculated separations is found to be ±5% with only seven differences exceeding ±10%.

Electron Spin Resonance Studies of Irradiated Glasses Containing Boron
View Description Hide DescriptionElectron spin resonance(ESR)spectra have been observed for various types of alkali borate and borosilicate glasses which were exposed to γ‐ray or thermal neutron irradiations. The irradiated alkali borate glasses (Li_{2}O–B_{2}O_{3}, Na_{2}O–B_{2}O_{3}, K_{2}O–B_{2}O_{3}, Rb_{2}O–B_{2}O_{3}, and Cs_{2}O–B_{2}O_{3}) containing less than 25 mole % alkali oxide exhibit spectra consisting of five peaks in the resonance absorption curve at an operating microwave frequency in the vicinity of 9.2 kMc/sec. The same five‐line resonance has also been observed in the irradiatedborosilicate glasses (Corning 7070, 7740, and 7720). Investigations of the irradiatedglasses by means of a K‐band ESR spectrometer operating at approximately 23.3 kMc/sec have yielded spectra which are partially resolved into six lines. Alkali borate glasses isotopically enriched with B^{10} display a 10‐line resonance at the X‐band frequency when irradiated with γ rays or neutrons. It is concluded that the five‐ and six‐line resonances arise from an axially symmetric hyperfine interaction of a hole with a B^{11} nucleus, while the 10‐line structure arises from such a hyperfine interaction with a B^{10} nucleus. The atom containing this B^{11} or B^{10} nucleus is believed to be in a BO_{4} tetrahedral configuration in the glass structure.

Elastic Constants of Ammonium Chloride near the Lambda Point
View Description Hide DescriptionThe adiabatic elastic constants of single‐crystal ammonium chloride have been measured as functions of sound frequency from 5 to 55 Mc/sec, and as functions of temperature from ∼150° to 300°K by an ultrasonic pulse technique. The values of the constants at 300°K are c _{11} = 3.70, c _{44} = 0.86, (c _{11}—c _{12})/2 = 1.41 in units of 10^{11} dyn cm^{—2}. Special emphasis was given to the region around 243°K, the critical temperature for the order—disorder transition. The results are discussed in terms of the phenomenological thermodynamic theory of Pippard.

Crystal Structure of Cerium Magnesium Nitrate Hydrate
View Description Hide DescriptionAccording to single‐crystal x‐ray diffraction data, crystals of Ce_{2}Mg_{3}(NO_{3})_{12}·24H_{2}O are rhombohedral, space group R . The hexagonal cell with a = 11.004±0.006, c = 34.592±0.012 Å contains three formula units. Atomic parameters were refined by least squares, and interatomic distances were corrected for thermal motion. The average N–O bond distance in nitrate is 1.26 Å. The Ce atoms, on the threefold axis at z = ±0.2497, are each surrounded by 12 oxygen atoms at an average distance of 2.64 Å. These oxygen atoms, belonging to six nitrate ions, are at the corners of a somewhat irregular icosahedron. The Mg atoms are of two kinds, located, respectively, at the origin and on the threefold axis at z = ±0.4279. Each Mg atom is surrounded by six water molecules with the oxygen atoms at the corners of an octahedron with an average Mg–O distance of 2.07 Å. One‐fourth of the water molecules are not coordinated to cations. Evidence for the hydrogen atom positions from the diffraction data indicates that six of the eight independent hydrogen atoms are involved in normal hydrogen bonds.

Study of Moderately Rapid Chemical Exchange Reactions by Means of Nuclear Magnetic Double Resonance
View Description Hide DescriptionA nuclear magnetic double‐resonance method for the determination of chemical exchange rates has been developed. The method is applicable to systems in which a nuclear spin is reversibly transferred between two nonequivalent sites, A and B. The lifetime (τ_{ A }) and spin—lattice relaxation time (T _{1A }) in Site A are obtained through the study of the decay to a new equilibrium value of Signal A upon the sudden saturation of Signal B. The converse experiment permits the determination of τ_{ B } and T _{1B }. A number of data for cross checks are furthermore obtained through the study of the recovery of the signals upon the release of various combinations of saturating rf fields.
A simple theory based on the Bloch equations as modified by McConnell to incorporate the effects of chemical exchange is given. Experimental results on the hydroxyl proton exchange in the system salicylaldehyde and 2‐hydroxyacetophenone are well described by this simple theory.
The present method, which can readily be extended to systems with several sites, offers a complement to the Gutowsky—Saika single‐resonance method and is particularly suited to the study of exchange rates slower than those accessible by the single‐resonance method.

Sound Dispersion in Substituted Methane—Inert Gas Mixtures
View Description Hide DescriptionBinary halomethane—noble gas mixtures were examined ultrasonically. The methanes used were CF_{4}, CHF_{3}, and CCl_{2}F_{2} and the noble gases were Ar, Ne, and He. Results obtained show that the reciprocal relaxation times for these mixtures vary linearly with the concentration. Also, Ar—X collisions are less effective, He—X collisions are much more effective, and Ne—X collisions differ little from X—X collisions in vibrational energy transfer. X represents the dispersive gas. Theoretical values of Z _{10} ^{AB}, the mean collision lifetime of an A molecule in an otherwise pure gas of B molecules, were calculated according to the Schwartz, Slawsky, and Herzfeld theory.Intermolecular potentials appropriate for the treatment of the data were examined, and it was found that the Lennard‐Jones 6:12 potential was appropriate for the noble gases, and the 7:28 form was appropriate for the halomethanes.

Infrared Spectra of the Germyl Halides
View Description Hide DescriptionThe infrared spectra of GeH_{3}F, GeH_{3}Cl, GeH_{3}Br, GeH_{3}I, and their fully deuterated analogs have been measured. All the fundamental vibrations have been observed and assigned. Normal coordinate treatments based on both simple valence and Urey—Bradley force fields have been performed. For germyl fluoride, unusually large frequency shifts have been observed to accompany the phase transition from gas to solid.

Antiferromagnetic and Crystal Structure of Lithium Cupric Chloride Dihydrate
View Description Hide DescriptionA neutron‐diffraction study of LiCuCl_{3}·2H_{2}O in the temperature range 1.4°—5.1°K, together with a magnetic susceptibility study in the range 1.4°—300°K, has determined its magnetic and crystal structure. The crystal contains linear Li–Cu–Cu–Li, planar Li_{2}Cu_{2}Cl_{6} groups. Each cation is at the center of a distorted octahedron, of composition LiCl_{3}O_{3} and CuCl_{5}O: the four octahedra share Cl–Cl edges. The most important distances in this complex are Cu–Cl at 2.25, 2.34, and 2.96 Å; Cu–O at 2.56 Å; Li–O at 2.04 and 2.18 Å; Li–Cl at 2.44 and 2.97 Å; Li–Cu at 3.34 Å; and Cu–Cu at 3.47 Å. The ``nonbridging'' Cl atoms in the Li_{2}Cu_{2}Cl_{6} group form OH···Cl bonds of 3.17 and 3.26 Å to other complexes in the crystal. The spins (S = ½) on the Cu^{2+} within each complex are antiparallel and lie on the 3.47‐Å Cu–Cu internuclear line. The spin‐density maximum is displaced 0.15 Å from the nearest neighbor Cu^{2+} of opposite spin. The neutron‐scattering data indicates d _{ x 2—y 2 } to be the ground‐state orbital. Above a critical fieldH_{c} = 9kOe, spin flopping similar to that in CuCl_{2}·2H_{2}O takes place.

Approximate Expression for the Tunneling Correction
View Description Hide DescriptionBy using an approximate method, the tunneling‐correction factor for the unsymmetrical Eckart potential function and its temperature dependence are formulated in forms which are capable of simple numerical calculations. The method is designed to evaluate the integral which includes a violently changing exponent. The result is compared with Johnston's results obtained by electronic computation; the agreement is good in chemically interesting cases.

On the Hydrogen—Bromine Reaction Rate in a Nonsteady State
View Description Hide DescriptionThe deviations of atom concentrations and over‐all rate from steady‐state conditions for the H_{2}–Br_{2}reaction are evaluated as functions of the extent of reaction in a temperature range 1000°—1600°K. Both the concentration and rate deviations are serious at 1400°—1600°K. The major source of the nonsteady state deviation in rate is the reactionk _{5}[H][Br_{2}] and the regenerating cycle proceeds in nonsteady state except at the later stage of the reaction. A previously obtained result that two atom concentration deviations ε_{1} and ε_{2} are nearly identical is equivalent to the condition that the rate of change of the H‐atom concentration vanishes. At elevated temperatures, analysis of the atom concentration deviations alone does not give sufficient information for the evaluation of the steady‐state hypothesis; the over‐all rate deviation must be obtained to answer the question of steady‐state validity.