Volume 49, Issue 4, 15 August 1968

Isotope Exchange Rates. V. The Homogeneous Reaction between H_{2}S and D_{2}
View Description Hide DescriptionSingle‐pulse shock‐tube data were obtained for the homogeneous isotopic exchange reaction between deuterium and hydrogen sulfide, highly diluted in argon, over the temperature range 1260–1590°K. Three sets of experiments were performed independently in two laboratories. H_{2}S/D_{2} ratios were varied over the range 4/1–1/4, at total reaction densities from 6 × 10^{−6} to 5 × 10^{−5} moles/cm^{3}. The agreement among the three sets of data is generally good. An average activation energy of 52 ± 3 kcal/mole was deduced from them. All three sets of data may be fitted by a second‐order power rate expression which is first order in D_{2} and roughly order with respect to H_{2}S and to Ar. These data support a mechanism, suggested previously for similar isotopic exchange reactions, in which metathesis reactions during collisions between H_{2}S and D_{2} occur with significant probability only when the deuterium molecule contains at least a critical amount of vibrational energy. The rate‐limiting process is the maintainance of an adequate population in the 4th and 5th vibrational levels of deuterium. The relative efficiencies for excitation of deuterium by collisions with the various species present, as determined from the kinetics data, are in reasonable agreement with values determined directly from vibrational relaxation studies.

Molecular Dynamics. VI. Free‐Path Distributions and Collision Rates for Hard‐Sphere and Square‐Well Molecules
View Description Hide DescriptionFree‐path distributions and collision rates for systems of hard‐sphere and square‐well molecules are computed and compared to simple models. Mean free paths for solids and dense fluids are found to be within 2% of those predicted by dividing the kinetic‐theory mean free path by the relative probability of two molecules in contact. These mean free paths are much smaller than a mean intermolecular spacing or even the diameter of a free volume. For hard‐sphere and hard‐disk fluids, free‐path distributions are found to be monotone decreasing, nearly exponential, and when scaled by the mean free path, nearly density independent for all fluid densities. This density independence precludes any essential difference in transport mechanisms between dilute and dense fluids based on independent free paths. Scaled free‐path distributions for hard‐sphere and hard‐disk solids are found to agree with those of their fluid counterparts except for long free paths where the smaller free‐path distribution for solids reflects their increased molecular localization. The free‐volume theory and its simple extensions are shown to be qualitatively inconsistent with the shape of observed free‐path distributions in solids. For fluids of square‐well molecules, the rate of hard‐core collisions is found to be insensitive to the presence of the square well, and so is the free‐path distribution as well as selected values of the pair‐distribution function. These features are in good agreement with the van der Waals hypothesis, which neglects soft collisions. For dense liquids, hard‐core collisions are in the majority, invalidating the hypothesis that soft‐core collisions cause a Brownian motion between successive hard‐core collisions.

Studies with the Mössbauer Effect of the Formation of Xenon Bromides in Beta Decay
View Description Hide DescriptionThe reaction has been observed for a pure sample of the potassium salt by use of the Mössbauer effect of the 39.48‐keV gamma ray of ^{129}Xe. With the assumption of bonding, the quadrupole splitting leads to a value of 0.41 electron transferred to each Br. This is to be compared with 0.52 to each Cl in XeCl_{2} and 0.72 to each F in XeF_{2}. An impure KIBr_{2} source shows a qualitatively different velocity spectrum—either due to a distribution of unknown xenon halides or to a molecular rearrangement observed in the act of occurring. If the latter is correct, the linewidth gives a mean life for the rearrangement. A source of CsIBr_{2} gives a broad singlet spectrum with no trace of XeBr_{2}. The line represents either atomic xenon or a cubic rearrangement product such as XeBr_{6} ^{4−} or XeBr_{4} ^{2−}. Evidence from data on recoilless fraction and isomer shifts somewhat favors atomic xenon as the product but is not completely conclusive.

Dynamics of Krypton Atoms in Clathrate by the Mössbauer Technique
View Description Hide DescriptionThe temperature dependence of the mean‐square displacement of the Kr guest atoms in the hydroquinone–Kr clathrates has been studied by the Mössbauer effect. The results show that at all temperatures the observed is about twice as large as can be accounted for by the “rattling” frequency observed in the far infrared. This implies that low lattice frequencies contribute substantially to the motion of the Kr atoms and therefore the system cannot be described solely in terms of the van der Waals “particle‐in‐a‐box” model.

Valence Excited States of NH and CH and Theoretical Transition Probabilities
View Description Hide DescriptionThe electronic structure of the four lowest excited states of NH and CH was studied by means of single‐configuration SCF calculations. The calculation located the singlet system of NH with respect to the triplet and predicted the location of the experimentally unknown state of CH. A number of one‐electron molecular properties was computed. The calculated electric dipole moments agreed well with experiment. The parameters for the hyperfine splitting of the ground state of CH was also calculated. The oscillator strengths computed for a number of transitions in NH and CH were shown to have order of magnitude accuracy only. The same situation is expected to hold in the calculation of oscillator strengths for other molecular systems with SCF wavefunctions.

Effects of X‐ and Γ‐Ray Radiation on the Thermal Decomposition of Solid Orthorhombic Ammonium Perchlorate. I. Experimental and Results
View Description Hide DescriptionThe thermal decomposition kinetics of unirradiated, x‐ray and gamma‐ray irradiated orthorhombic ammonium perchlorate have been determined in the temperature range of 193°–238°C. Both millimeter size and powdered crystals were used. When all of the decomposition gases are allowed to collect, the pressure vs time curves consist of the following stages: First, an induction stage with a puff or burst superimposed on it; second, an acceleratory stage followed by a third, or decay, stage. When only the noncondensable gases, i.e., gases not condensed in a trap at −23°C or lower, are allowed to accumulate, the puff or burst, but not the induction period, is eliminated. Irradiation prior to decomposition reduces the induction period and increases the acceleratory period decomposition rate. Both of these effects increase as the dose is increased. If the decomposition is interrupted before the decay period, the sample irradiated with a fixed gamma‐ray dose, and the decomposition resumed, the following changes occur in the pressure vs time curves. First, the decomposition proceeds along the curve for unirradiated material but only for a constant period of time equivalent to the induction period for irradiated material. Second, at the end of this period, the decomposition rate abruptly increases to the approximate value obtained for irradiated material. The subsequent decay stage is similar to that observed with irradiated crystals. In addition to the kinetic studies the decomposition gases were analyzed with a mass spectrometer and preliminary measurements made on the low‐temperature thermoluminescence of gamma‐ray irradiated material.

Effects of X‐ and Γ‐Ray Radiation on the Thermal Decomposition of Solid Orthorhombic Ammonium Perchlorate. II. Kinetics and Discussion
View Description Hide DescriptionThe experimental data obtained by thermally decomposing unirradiated and irradiated orthorhombic ammonium perchlorate in the temperature range 193°–238°C has been carefully analyzed. Most of this data consists of pressure vs time curves of the total evolved gas or that not trapped at −95°C or lower, obtained with powders and millimeter‐size crystals. All of these curves can be described by the Avrami–Erofeyev equation. The increase in the acceleratory period rate, which is induced by, and is proportional to, x‐ or γ‐ray irradiation prior to decomposition, can be attributed to the introduction of additional decomposition sites, an increase in the rate that each nucleus grows, or a combination of these. Independent microscopic examination of partially decomposed crystals also indicates that irradiation has increased the concentration of decomposition nuclei. In addition, the curve analysis shows that irradiation has increased the rate that potential decomposition sites are converted to active sites. The same activation energy, 28.4 ± 2.5 kcal mole^{−1}, was obtained for both the acceleratory and decay periods from irradiated and unirradiated crystals. Irradiation also increases the duration of the acceleratory period, shortens the decay period, and reduces the induction period. In fact, the induction period for irradiated NH_{4}ClO_{4} can be described by the relation log (dose). Taken together, these observations suggest that the same processes occur in both unirradiated and irradiated ammonium perchlorate, but the rate constants are increased by prior irradiation.

General Internal Motion of Molecules, Classical and Quantum‐Mechanical Hamiltonian
View Description Hide DescriptionThe dynamics and the Hamiltonian of a general asymmetric‐top molecule undergoing almost arbitrary deformations are discussed. s vector notations are used for translational, rotational, and internal‐velocity coordinates. The kinetic energy is formulated by generalizing the G‐matrix technique known from the theory of molecular vibrations. A geometrical definition of the rotational coordinates referring to the instantaneous principal axis system is compared with a dynamical definition involving the over‐all angular momentum. States of general internal motion are associated by definition with zero linear momentum and zero over‐all angular momentum.

Magnetic Characteristics of Europium–Aluminum Intermetallics
View Description Hide DescriptionBulk magnetic characteristics of EuAl_{2} and EuAl_{4} are reported for temperatures ranging from 4°–300°K and for field strengths up to 20 kOe. To evaluate the influence of electron concentration on the magnetic interactions a series of Eu_{x}La_{1−x}Al_{2} alloys, with ranging from 0.1 to 0.8, was studied over the same interval of temperature and field strength. Between 50° and 300°K all samples exhibited Curie–Weiss behavior with an effective moment characteristic of dipositive europium. EuAl_{4}, EuAl_{2}, and Eu_{0.8}La_{0.2}Al_{2} become antiferromagnetic below 20°K, two types of antiferromagnetic order being indicated for the latter two intermetallics. Increasing the electron concentration by replacing Eu with tripositive La alters the interaction from predominantly antiferromagnetic to predominantly ferromagnetic as the electron concentration approaches 9. The change in sign of the interaction occurs at about 8.4 electrons per magnetic atom. Eu_{0.1}La_{0,9}Al_{2} and Eu_{0,2}La_{0.8}Al_{2} are ferromagnetic at 4°K with Eu moments of about per formula unit. Eigenvalues of the spin–Hamiltonian are obtained for Eu^{++} in a site of tetragonal symmetry and used to interpret the saturation moments observed for the ferromagnetic ternaries and the deviations from Curie–Weiss behavior for EuAl_{2} and the (Eu, La)Al_{2} alloys. The bulk magnetic properties can be quite successfully accounted for on the basis of an over‐all (Zeeman‐like) splitting of 480°K.

Electron Attachment to Halogenated Aliphatic Hydrocarbons
View Description Hide DescriptionMean attachment cross sections as a function of mean electron energy are reported and discussed for 22 halogenated aliphatic hydrocarbons.

Crystallite Orientation Distribution in Biaxially Oriented Polyethylene
View Description Hide DescriptionThe procedure of Roe for describing the crystallite orientation in polycrystalline samples having general texture is tested using two samples of biaxially drawn polyethylene. An automated four‐circle diffractometer was used to obtain 12 pole figures (4332 fixed points) for the film having stretching ratios 3.0 × 2.0, and 13 pole figures (4693 fixed points) for the film having stretching ratios 1.7 × 1.6. The selection of measurement geometry, procedures for data reduction and correction, and methods for computer calculation of the crystallite orientation distribution are described. While the best representation of the crystallite orientation distribution was obtained from the series of generalized associated Legendre polynomials by retaining terms through , the characteristic features of the distribution are already evident when the series is truncated at . Thus, for materials belonging to the orthorhombic crystal class, as few as four or five pole figures suffice to determine the principal features of the crystallite distribution in biaxially oriented samples. The crystallographic axis is found to be normal to the film plane in both samples examined. The axes are nearly randomly arranged in the film plane for the sample having stretching ratios 1.7 × 1.6, while the 3.0 × 2.0 sample exhibits a combination of this texture and that previously observed for uniaxially drawn polyethylene.

Quantum Corrections for the Second Gas‐Surface Virial Coefficient
View Description Hide DescriptionThe quantum corrections for the second gas–surface virial coefficient are derived and applied to the experimental data for H_{2}, D_{2}, CH_{4}, and CD_{4} in the external field provided by a uniform graphite surface. These corrections cause quite sizable differences in the interaction energies and areas obtained for the hydrogen pair, but the differences are, of course, small in the case of the methanes.Quantum effects have been measured in dilute adsorption systems and found to be of considerable importance. Theoretically, Yaris and Sams have developed the second gas–surface virial coefficient from the Wigner–Kirkwood expansion to order and examined three different models for the gas–surface interaction potential, using the data of Constabaris et al. Due to a misprint in the term of Uhlenbeck and Beth, which has been carried through in the calculations of Yaris and Sams, we have recalculated the quantum corrected and fitted it to the data mentioned above.

Absorption Spectra of Erbium Tricyclopentadienide at Liquid‐Helium Temperature
View Description Hide DescriptionThe absorption spectra of Er(C_{5}H_{5})_{3} in 2‐methyl tetrahydrofuran have been studied at room temperature, liquid‐nitrogen, and liquid‐helium temperature. Hypersensitive line groups have been found at ∼19 000 and ∼26 000 cm^{−1}. Large splittings of levels have also been observed. A correlation between hypersensitivity and large second‐degree terms of the crystalline potential is suggested. Although some line groups in Er(C_{5}H_{5})_{3} showed unusually large splittings, no drastic changes in the usual energy‐level pattern for were found in this volatile, organometallic compound of erbium.

Effect of Localized Lattice Vibration on the Matrix Spectra of Diatomic Molecules
View Description Hide DescriptionThe effect of the interaction between the localized lattice vibrations and the rotational motion of a diatomic molecule trapped in rare‐gas matrices on their matrix spectra is investigated theoretically. This results from the dependence of the crystalline field on the intermolecular separation. The instantaneous interaction between the molecule–rare‐gas atom is expanded in powers of the displacements of the lattice points from their equilibrium positions, and then this is averaged over all the neighboring atoms. The resulting self‐energy of the molecule is then treated as a perturbation to calculate the displacement of the rotational levels. Expressions for the resulting shifts in the frequencies of the rotational transitions are given and this has been calculated in some typical cases to demonstrate the importance of this coupling between the localized lattice vibrations and the rotational motion of the molecule in the matrix.

Flux and Speed Distributions of Molecular Beams after Scattering by Metal Surfaces
View Description Hide DescriptionHigh‐intensity, nearly monoenergetic, nozzle‐type molecular beams together with a sensitive time‐of‐flight detection system have been employed to study the scattering of argon and nitrogen from polycrystallinenickel and stainless‐steel surfaces. The apparatus has allowed the precise measurement of essentially complete flux and speed distributions of the particles reflected in the plane of the incident beam and the target normal. Incident energy (0.065–0.24 eV), surface temperature (300°–1000°K), angle of incidence, and angle of reflection have been varied. At room temperature, prior to any heat treatment in the apparatus, these unpolished targets exhibit essentially the classical diffuse scatteringpattern with almost complete thermal accommodation. With the Nisurfaces tested, outgassing and annealing at approximately 900°K resulted in highly lobular scattered flux patterns for target temperatures between 550° and 950°K. These patterns are accompanied by a marked angular variation of the reflected‐particle speed distribution, which differs the more from the fully accommodated Maxwellian distribution the farther the angle of scattering is from the surface normal. These lobular flux patterns are in qualitative agreement with the predictions of the so‐called “hand‐cube” model, but for the scattered particles the angular variation of the mean speed is smaller, and the angular variation of the relative spread in kinetic energies is greater, than predicted. Stainless steel exhibits similar but less pronounced scattering lobes accompanied by somewhat subdued angular variations of the speed distributions.

Proton NMR Relaxation Effects. Cross‐Relaxation Processes in Pure Liquids
View Description Hide DescriptionSpin–lattice relaxation in a liquid containing protons in two different molecular environments can proceed by three different routes. There is a route to relaxation associated with each of the environments resulting from interactions between protons within that same environment. The third route to relaxation results from interaction between protons in different environments and is called cross relaxation. In such a system, the total spin–lattice relaxation decay determined by pulsed NMR will be the sum of two exponentials. Three relaxation rate constants are derived from such data. When cross relaxation arises entirely from dipole–dipole interaction in the extreme narrowing limit, these rate constants may be associated with the three routes to relaxation. (The cross‐relaxation rate can always be identified, regardless of the mechanism.) To illustrate such relaxation behavior and the methods for obtaining three independent relaxation rates, 1‐phenylpropyne was studied as a function of temperature.

Bimolecular Ionization of the Triplet State of Aromatic Hydrocarbons in Solution
View Description Hide DescriptionThe production of free ionic carriers due to bimolecular triplet encounters of anthracene, naphthalene, phenanthrene, and pyrene in solvents methyltetrahydrofuran (MTHF), tetrahydrofuran (THF), benzonitrile (C_{6}H_{5}CN), and acetonitrile (CH_{3}CN), whose dielectric constants fell between 6.2 and 36.7, was verified. The probability of producing free carriers per triplet–triplet collision from phenanthrene was found to be 1.9 × 10^{−4}, 1.9 × 10^{−3}, and 0.41 in MTHF, THF, and CH_{3}CN, respectively. The probability of free carrier production in fluid THF was found to be 1.4 × 10^{−2}, 1.3 × 10^{−2}, and less than 10^{−4}, respectively, for triplets of anthracene, pyrene, the tetracene. The significance of escape of carriers from a Coulomb well was delineated and shown to be of maximal concern for media whose dielectric constant was less than 15. Similarly, carrier escape was shown to be primarily responsible for the lack of observed photocurrents from these aromatic hydrocarbons in n‐hexane and cyclohexane.

Microwave Spectrum of Cyclopropyl Bromide
View Description Hide DescriptionThe microwave spectra of four isotopic species of cyclopropyl bromide, namely C_{3}H_{5} ^{79}Br, C_{3}H_{5} ^{81}Br, C_{3}H_{4}D^{79}Br, and C_{3}H_{4}D^{81}Br have been analyzed in the frequency region of 19 000–31 000 Mc/sec. The rotational constants obtained are as follows (given in megacycles per second): Two structures compatible with these data have been obtained for this molecule. Structure I was calculated by assuming for the hydrogen parameters values obtained for cyclopropyl chloride, whereas Structure II was derived with the assumption that all and the ∠H–C–H's are bisected by the ring. The analysis of the hyperfine structures of the spectra gives the following quadrupole coupling constants. For C_{3}H_{5} ^{79}Br ; C_{3}H_{5} ^{81}Br ; C_{3}H_{4}D^{79}Br ; C_{3}H_{4}D^{81}Br . The ionicity of the bond was estimated to approximately 22%.

Electrolysis of SiO_{2} on Silicon
View Description Hide DescriptionThe application of an external voltage across a layer of SiO_{2} on silicon causes a reduction in the thickness of the oxide layer by electrolysis when the applied voltage exceeds the theoretical cell voltage of the cell O_{2}, Pt/SiO_{2}/Si and the electric field is oriented such that the silicon–silicon dioxide interface is negative with respect to the oxide–gas interface. A measurement of the stopping voltage reveals that four equivalents are involved in the reaction, thus indicating that O^{=} ions or some similarly charged defect could be involved in the electrolysis. Further evidence shows that the transport of uncharged oxygen species is negligible during the electrolysis of SiO_{2}.

Analytical Treatment of Excluded Volume. III. Alternative Calculations of the Contacts Density in Chains
View Description Hide DescriptionThe excluded volume effect is expressed in terms of certain probabilities for segment contacts in the real chain, the derivation following a method recently described by Fujita et al. It is then assumed that these probabilities can be calculated from the Gaussian expressions for an “equivalent ideal chain.” On this basis an integral equation is derived for , the asymptotic result being . While Fixman's theory [A], the author's previous theory [B], and the present theory [C] express the segment contacts in different ways, they have the common property of preserving the chain connectedness and of assuming contacts probability to be Gaussian. Dissimilar results are reached with the three theories and the reasons for the discrepancy are examined. It appears that the results obtained with the present theory [C], similar to [A] but in contradistinction to [B], do not agree with the original assumption of the contacts probability being Gaussian.