Volume 37, Issue 8, 15 October 1962

Mechanism for the Chloride‐Catalyzed Thermal Decomposition of Ammonium Nitrate
View Description Hide DescriptionA kinetic study of the thermal decomposition of NH_{4}NO_{3} in the presence of NaCl has been carried out using the differential kinetic technique previously described. The rate law for N_{2} evolution is of the form k _{1}(NH_{4} ^{+})+k _{2}(NH_{4} ^{+}) (Cl^{—})^{½}. A radical mechanism is proposed in which the role of chloride is catalytic, being oxidized by NO_{2} ^{+} to Cl atoms which are reduced back by NH_{4} ^{+} and NH_{3}. These hydrogen abstraction reactions leave NH_{3} ^{+} and NH_{2}, respectively, in reaction cages in which subsequent radical recombinations yield nitramide and nitrosamine as precursors for N_{2}O and N_{2}. Parallel Cl atom recombinations give Cl_{2}, part of which escapes by volatilization, the rest reacting with NH_{3} to provide a second source of N_{2}.

Spin‐Orbit Matrices of the d ^{5} Configuration
View Description Hide DescriptionThe spin‐orbit matrices of the d ^{5} configuration have been calculated in a strong‐cubic‐field scheme using the methods of Tanabe and Kamimura. The matrices were checked by comparing their eigenvalues with the spin‐orbit matrix elements in a j—j coupling scheme.

Stable Steady State and the Thermokinetic Potential
View Description Hide DescriptionThe mathematical postulate of Carathéodory for the existence of the entropy function is shown to be a direct consequence of the physical postulate of the existence of a stable equilibrium state for any given set of state variables. Similarly, the existence of thermokinetic potential is shown to be a direct consequence of the physical postulate of the existence of a stable steady state for any given set of nonequilibrium state variables.

Symmetry Properties of the Asymmetric‐Rotator Centrifugal‐Distortion Constants
View Description Hide DescriptionThe symmetry properties of the first‐order centrifugal‐distortion Hamiltonian for the asymmetric rotator have been studied. The number of independent distortion constants needed to interpret centrifugal‐distortion effects in microwave and infrared spectra of asymmetric top molecules is determined for the asymmetric‐rotator point groups and a number of relationships existing between these constants is given.

Growth Rates of Potassium Crystal from the Vapor Phase
View Description Hide DescriptionMeasurements of the growth rate of potassium (110) faces, for low vapor supersaturations σ between 3.1 and 0.11 (the lowest value studied) have given unit condensation coefficients for all supersaturations. This result is in agreement with the theory of Burton, Cabrera, and Frank and gives the values βC _{0} = 1, σ_{1}≤0.046 for potassium. No evidence of two‐dimensional surfacenucleation was found. Careful attention to the reduction of impurities, through the use of ultra‐high vacuum techniques, was shown to be necessary in studying this system. Results of earlier work by Hock and Neumann on potassium can be well described by an application of the Cabrera—Vermilyea theory of impurity effects, with an effective partial pressure of active gases of 0.8×10^{—11} mm Hg. In the present experiments this value is less than 1.4×10^{—13} mm Hg. The unit condensation coefficients are shown to be in disagreement with a theoretical prediction of Hirth and Pound.

Vapor‐Phase Growth Kinetics of Potassium Whiskers by Field Emission
View Description Hide DescriptionUsing the method originated by Gomer, we have studied the growth kinetics of potassiumwhiskers, as they grow from the vapor phase in an electron field emission tube. To the best of our knowledge, this represents the first use of an alkali metal as a field emitter.
The results for potassiumwhiskers show some features similar to those previously found for mercury, and some new features. The former include positive exponential growth, and the attainment of terminal lengths. New features include the absence, usually, of symmetric emission patterns, a very low activation energy for surface self‐diffusion, the fact that the whiskers cannot be pulled off but instead appear to shorten gradually if the field is raised, and finally, an interesting sensitivity of the growth processes to illumination of the whiskers with visible light.

Reaction of Methyl‐d _{3} Radicals with Isobutane, Isobutane‐2‐d, and Propane
View Description Hide DescriptionThe relative rates of abstraction by CD_{3} radicals of primary, secondary, and tertiary H atoms have been measured. Using a standard rate constant for abstraction of D from acetone‐d _{6}, the following rate constants are obtained:Isotope effects obtained are, for secondary H and D in propaneand for tertiary H and D in isobutaneThese isotope effects are within experimental error of that given by the general expression for the deuterium isotope effect previously proposedand are in excellent correspondence with the theoretical treatment of Johnston and Rapp.

Direct‐Product Representation of Wavefunctions
View Description Hide DescriptionA direct‐product representation for N particle wavefunctions is introduced through a coefficient matrix C_{p}. Density matrices and the natural p states are redefined in terms of C_{p}. The projection‐operator formalism is used to derive an eigenvalue equation for the natural p states. A generalization of the exact self‐consistent field equations is derived from the concept of natural group functions.

``Improved'' Free Volume Theory of Liquids. III. Approximate Theory of Molecular Correlations in Liquids
View Description Hide DescriptionAn approximate theory of molecular correlations in liquids is presented in an effort to improve the free volume theory of Dahler and Hirschfelder. Two approximations are studied, one suggested by Taylor and the other corresponding to the ``cell‐cluster'' expansion scheme of de Boer. The formalism is based entirely upon the self‐consistent field theory of Paper II except that the cell distribution functions are replaced by Gaussian error functions in order to facilitate numerical computation and to make the problem more tractable. The results ``suggest'' quantitative improvements over those obtained in II and illustrate that the treatment of correlative effects is practical from a numerical standpoint. Extensive tables of compressibility factor, configurational energy, and configurational entropy are given. Graphical comparisons between our results and those of other theories and experiments are presented.

Fourth Virial Coefficient for a Square‐Mound‐Potential Gas
View Description Hide DescriptionThe fourth virial coefficient D is derived for a gas composed of particles interacting according to the square‐mound potential ψ(r) defined by the conditions ψ(r) = ε>0 for 0≤r≤1 and ψ(r) = 0 for r>1, where ε is a constant and the particle diameter is the unit of length. The calculations are based on the Born—Green—Yvon equation and the modified form of the original Kirkwood superposition approximation, viz., g ^{(3)}(r, s, t) = g ^{(2}(r)g ^{(2)}(s)g ^{(2)}( t)(1+X _{1} n), where g ^{(3)} and g ^{(2)} are, respectively, the triplet and pair distributions, n is the particle number density, and (r, s, t) are the triplet particle separation distances. X _{1} is chosen in order to ensure consistence between the values of D calculated from the virial theorem and from fluctuation theory. If z≡1—exp(—ε/kT), where T is the gas temperature, and the function X _{1} is assumed to be a function of z alone then it is found thatwhere b is four times a particle volume. This leads to a single consistent value of D, written D^{M}, Numerical values are given, and the formulas are discussed.

Isotopic Hydrogen‐Ion—Molecule Reactions
View Description Hide DescriptionThe reactions of isotopic hydrogen‐molecule ions with isotopic hydrogen molecules have been investigated using a mass spectrometerion source as the reaction chamber. No significant differences were detected in a study of the velocity distributions of the product and reactant ions. Rate constants for the formation of H_{3} ^{+}, D_{3} ^{+}, and H_{2}D^{+}+D_{2}H^{+} were obtained from the reactions of H_{2} ^{+}–H_{2}, D_{2} ^{+}—D_{2}, and HD^{+}—HD, respectively, which were in excellent agreement with theory. Isotopic fractionation was observed in the production of H_{2}D^{+} and D_{2}H^{+} from mixtures of H_{2} and D_{2}, HD and H_{2}, HD and D_{2}. The isotope effects are qualitatively consistent with a more rapid formation of lower zero‐point energy intermediates.

Diffusion of Krypton‐85 in Dense Gases
View Description Hide DescriptionWith two high‐pressure quasi‐stationary diffusion cells, one depending upon ionization current measurement and the other scintillation detection of radioactive tracer activity, Fick's law diffusivities were determined for the diffusion of tracer amounts of krypton‐85 in dense gases of krypton, argon, nitrogen, helium, carbon dioxide, and ethylene for isotherms about room temperature and densities to 15 mole/liter. In order to obtain absolute diffusivities, the cross‐sectional area to length ratio of a primary standard porous plug consisting of a bundle of glass capillaries was precisely determined by weight‐of‐mercury and resistance‐of‐mercury calibrations. Stirring in the end chambers of the ionization cell was found to increase the determined diffusivity of krypton‐85 in argon at 35°C by as much as 4.5% at a density of 12 mole/liter. The density—diffusivity product increases with density in the lower density region below about five moles per liter for all the isotherms. Extrapolations of the experimental data to low densities yield diffusivities which are in good agreement with low‐pressure results by other investigators and Chapman—Enskog dilute‐gas‐theory predictions. Krypton self‐diffusion coefficients calculated according to the real‐gas modified Enskog theory with PVT properties, agree remarkably well with the experimental data over the density range investigated. The binary diffusivities of krypton‐85 in dense base gases of argon, nitrogen, and ethylene are best predicted by the real‐gas modified Enskog theory with PVT properties evaluated at a base‐gas reduced temperature corresponding to the temperature of the system reduced by the mixed interaction potential temperature. In terms of precision of results and technological ease of operation the ionization cell proved to be superior to the scintillation cell.

Frequency Counting in Lattice Dynamics
View Description Hide DescriptionA method for determining the frequency distribution of crystal lattices on the basis of Born—von Kárman theory is proposed. This is a full account of the previous work, and a generalization to the case of three‐dimensional crystal lattices is described.
The procedure for obtaining the frequency distribution involves the following stages:
(1) One must solve the secular equation for determining the squared circular frequency ω^{2} along the edges of an appropriate part of the first Brillouin zone in the reciprocal lattice in the same manner as did Houston.
(2) One must find, in addition, a few important contours of constant frequency on the surface of the zone as accurately as possible.
(3) On the basis of (1) and (2), one can calculate or trace the desired contours of constant frequency on the surfaces by the proposed interpolation scheme [Eq. (1) or Eq. (2)].
(4) The contours of constant frequency in the inner planes can be calculated or traced by the proposed interpolation scheme described in Sec. IV.
(5) The volume V(ω^{2}) enclosed by the surface of constant frequency means the number of modes of vibrations whose frequencies are less than ω^{2}, and its magnitude may be computed by the proposed numerical or mechanical mean of integration described in Sec. V.
(6) V(ω^{2}) thus calculated is fitted in an analytical form, and at this time the results of van Hove's analysis for singularities may be taken into account to obtain the actual shape of frequency distribution in the vicinity of singularities. A differentiation of V(ω^{2}) with respect to ω^{2} yields the frequency distribution.
Applications to the two‐dimensional and three‐dimensional simple cubic lattices are made, and an excellent agreement with the exact frequency distributions calculated by Montroll and Rosenstock is obtained. The present method is thought to be far easier to handle than the conventional ones.

Mass Spectrometric Studies of Metastable Nitrogen Atoms and Molecules in Active Nitrogen
View Description Hide DescriptionMetastable nitrogen atoms and molecules produced by electrical discharges in N_{2} and He–N_{2} mixtures have been studied by mass spectrometry. N(^{2} D) and N(^{2} P) atoms in addition to ground‐state N(^{4} S) atoms were clearly identified in the products observed about 1 msec after leaving the discharge. The concentration of metastables was much higher for a discharge in a He–N_{2} mixture than for a discharge in pure N_{2}. Assuming that the ionization cross sections for the atoms at corresponding excess energies were equal, the relative concentrations were: N(^{4} S) = 1.00, N(^{2} D) = 0.17, and N(^{2} P) = 0.06 for the He–N_{2} discharge; and N(^{4} S) = 1.00, N(^{2} D) = 0.0068, and N(^{2} P) = 0.0025 for the pure‐N_{2} discharge. Metastable N_{2} molecules with excitation energies of up to several eV were also observed. Ionization processes involving the metastable molecules are discussed. To explain the experimentally obtained N_{2}ionization curves, it was found necessary to assume that, in addition to vibrationally excited ground‐state molecules, an appreciable concentration of N_{2} molecules in various vibrational levels of the metastable A ^{3}Σ_{ u } ^{+} state were present. Metastable N atoms are very easily deactivated by wall collisions. Metastable molecules survive for longer times, indicating that they are less readily destroyed by wall collisions.

Influence of Vibrations on Molecular Structure Determinations. I. General Formulation of Vibration—Rotation Interactions
View Description Hide DescriptionThe structure of a polyatomic molecule derived from observed spectroscopic moments of inertia differs appreciably from both the equilibrium structure and the zero‐point average structure. A perturbation expansion of the moments of inertia is derived here in a form which allows the vibrational displacements to be referred to any fixed configuration of the atoms as origin. A method for evaluating the expansion coefficients is given which proceeds ``atom by atom.'' Linear WXYZ, branched WXYZ, and symmetric WXY_{3} molecules are treated in detail.
Empirical data show that the anharmonicity of the vibrations gives rise to the most important of the corrections required to obtain the equilibrium structure. Except for a few molecules, the anharmonicity is not accurately known. It is shown, however, that to a practical approximation the anharmonic contributions are completely absorbed in displacing the average configuration from the equilibrium one. Therefore the moments of inertia for the zero‐point average configuration of a molecule can be derived from the observed effective moments by applying corrections which depend only upon the harmonic part of the vibrational potential.

Influence of Vibrations on Molecular Structure Determinations. II. Average Structures Derived from Spectroscopic Data
View Description Hide DescriptionFormulas are given which enable structural parameters for the average molecular configuration in the ground vibrational state to be calculated for some simple types of molecules. The data required are the observed effective moments of inertia and harmonic force constants. No knowledge of anharmonic constants is necessary. The average structural parameters have a well‐defined physical meaning and are directly comparable with diffraction results. Polyatomic molecules for which explicit calculations are given are CO_{2}, CS_{2}, H_{2}O, SO_{2}, O_{3}, NO_{2}, CH_{4}, HCN, and C_{2}H_{2}. It is found that the average bond lengths involving H are usually 0.003–0.005 Å longer than the corresponding D bond. For bonds involving heavier elements isotopic differences are smaller but nonetheless significant. Implications of the results for the general problem of structural determination are discussed.

Rare‐Gas Sensitized Radiolysis of Propane
View Description Hide DescriptionThe radiolysis of mixtures of C_{3}H_{8} and nitric oxide containing excess amounts of the rare gases Xe, Kr, Ar, and He, and of equimolar amounts of C_{3}H_{8}–C_{3}D_{8} in the same mixtures has been investigated. The product yields are compared with those expected assuming that the primary process leading to decomposition of the hydrocarbon is charge exchange with the appropriate noble gas, followed by ion—molecule reactions of the hydride‐transfer type. The experiments with deuterated propane demonstrate the formation of ethane and acetylene in bimolecular processes, and the production of methane, ethylene, and propylene chiefly by unimolecular decomposition. If it is assumed that neutralization of propyl ions results in the formation of ethylene and propylene as molecular products, the observations are consistent with the reaction sequence charge transfer, ion—molecule reactions, and neutralization leading to the production of unscavengeable species.

Dielectric Relaxation in Associated Liquids
View Description Hide DescriptionThe dielectric properties of the associated liquids butanediol 1,3, 2‐methyl pentanediol 2,4, glycerol, and hexanetriol 1,2,6 have been measured over the temperature range —20° to +10°C, and over a frequency range of 0.01 to 1200 Mc/sec. Dielectric relaxation times and their distributions have been determined and indicate the following: (a) All four liquids exhibit an asymmetric distribution of relaxation times of the Davidson—Cole form. (b) With the exception of hexanetriol 1,2,6, the distribution of relaxation times becomes narrower with increasing temperature. It is proposed that groups (regions of appreciable order) exist in these liquids, and that dielectric orientation is closely related to the structural breakup of these groups, this breakup being a necessary condition for dipole reorientation. It is further proposed that the structural breakup is a cooperative process which does not proceed exponentially, therefore giving rise to a nonexponential decay of dielectric polarization. This concept offers an explanation for the observed distribution of relaxation times. The temperature dependence of the width of the distribution is explained by assuming that the group‐size decreases with increasing temperature, and that as the groups become smaller, the structural‐decay process becomes more exponential.

Field Desorption of Barium from Tungsten
View Description Hide DescriptionThe field desorption of Ba has been studied over a range of fields and coverages in an attempt to determine the mechanism of desorption and the charge of the desorbing species. It was found that adsorption seems to be polar but not ionic and that desorption of Ba^{++} occurs under our conditions. If this interpretation is correct α≅60 Å^{3} for the polarizability of adsorbed Ba results, close to the value for the free atom. The accessible field‐temperature range is restricted by the onset of field‐dependent surface diffusion, which was also investigated. It was found that positive fields have more effect on the activation energyE_{d} and pre‐exponential term of the diffusion coefficient than negative ones. While a ½ αF ^{2} dependence of E_{d} is compatible with the limited data obtained for negative fields, no simple behavior was found for positive ones, E_{d} going through a minimum of 0, accompanied by a drastic reduction in pre‐exponential term. A tentative explanation in terms of a compensation effect is advanced.
Values for the zero field heat of adsorption were obtained over a wide coverage interval and agree well with those of Moore and Allison where overlap occurs.

Field Desorption of Cesium from Tungsten
View Description Hide DescriptionThe field desorption of Cs from tungsten has been investigated at low coverage. The results can best be explained on the basis of a polar groundstate and suggest that an adiabatic transition is involved in the desorption process. On this basis the polarizability of adsorbed Cs is found to be close to that of the free atom. The results are very similar to those obtained with Ba.