Volume 29, Issue 3, 01 September 1958

Vibrational Spectrum and Structure of Metal‐Cyanide Complexes in the Solid State. IV. K_{3}Cu(CN)_{4}
View Description Hide DescriptionThe polarized infrared spectrum of single crystals of K_{3}Cu(CN)_{4} has been observed. The fundamental frequencies of Cu(CN)_{4} ^{—3} under point group T_{d} have been assigned as 2094, 288, 324, 63, 2079, 364, 306, 74, and 250 cm^{—1}. From these frequencies, valence force symmetry force constants were calculated. Both the CN and CuC stretching force constants were found to be quite low (16.2 and 1.3 md/A, respectively). The CuC force constant, along with Badger's rule, gives a CuC distance of 2.05 A, somewhat shorter than the single bond distance of 2.12 A, predicted from the tetrahedral radii.

Volumes of Activation for Diffusion in Solids
View Description Hide DescriptionActivation volumes for the following simple models of lattice defects are calculated: (a) simple vacancy in a monatomic lattice, (b) simple vacancy with elastictheory of relaxation, (c) Schottky defect in an ionic crystal with dielectric theory of relaxation, (d) surface tension model of a vacancy in a metal, (e) elastic sphere model of an interstitial atom, and (f) strain energy theory of defect motion. The calculations are compared with experimental measurements. The comparison is satisfactory in many cases. In particular, it is observed that most of the data can be represented by the equation ΔV=4βΔH (β=compressibility, ΔH=activation energy), and that an equation of this type can be derived from several of the models. This equation can be used with a result of Lawson's to derive Zener's expression for the activation entropy of diffusion.

Absolute Infrared Intensities of the Fundamental Vibrations of NF_{3}
View Description Hide DescriptionThe absolute infrared intensities of the fundamental vibrations of NF_{3} have been measured. The results have been interpreted in terms of the N–F bond moment (μ), its derivative , and the unshared pair moment on the N atom (μ_{u.p.}). The bond moment obtained from the A _{1} bending mode is found to be in the vicinity of 1 D. μ_{u.p.} is in the vicinity of either 1.2 D or 1.7 D depending upon the sign assumed for the molecular dipole moment. The bond moment calculated from the E mode is quite sensitive to the potential function. Since this function is not known with high accuracy, one is not able to determine whether the bond moments from the two different symmetry species are in agreement.
There is a striking difference in the values of from the two symmetry species with (A _{1}) in the range of 1.5 to 2 D/A and (E) in the vicinity of 4.5 D/A. A qualitative explanation for this difference is offered.

Potential Function of NF_{3}
View Description Hide DescriptionAn approximate potential function has been determined for NF_{3} by using the four fundamental frequencies, the experimentally determined rotational distortion constant D_{J}, and physical arguments based on the absolute intensity results. Use has also been made of an argument proposed by Polo and Wilson based on a comparison of NF_{3} with the isoelectronic molecule CF_{3}H.
The rotational distortion constants have been calculated as a function of the force field using the method of Kivelson and Wilson. Explicit formulas are given for the change in moment of inertia with symmetry coordinate for an XY_{3}(C_{3v }) type molecule.
Using the approximate potential function, values of the valence type force constants and the rotational distortion constant D_{K} have been calculated.

Vibrational Spectra of the Crystalline Methyl Halides
View Description Hide DescriptionThe infrared spectra of the crystalline methyl halides, CH_{3}Cl, CH_{3}Br, and CH_{3}I, at 80°K are reported. Information on gas‐solid frequency shifts, band splittings due to site symmetry and intermolecular coupling, librational frequencies, and relative intensities of band components is summarized and compared.
Relative intensities of band components are not in agreement with the predictions of the ``oriented gas'' model. Most other observations are consistent with the assumption of isomorphism between the crystal structures of the three compounds, but the data are not sufficient to prove the isomorphism.

Improved Simple Analytical Wave Functions for Atoms
View Description Hide DescriptionApproximate wave functions for the ground states of He, Be, Ne, and Na^{+} are constructed which are antisymmetrized products of single Slater orbitals of nonintegral principal quantum numbers, , and variable orbital exponents, . Best values for the several parameters n and ζ are determined by the variational method, and the corresponding energies are computed. Significant improvements over the usual integral‐n approximations are found; for Na^{+} there is obtained an energy — 161.44 a.u., compared with the integral‐n result — 160.94 a.u. and the Hartree‐Fock value — 161.88 a.u. The ground states of the two‐electron ions H^{—} through NaX are similarly treated, and the diamagnetic susceptibilities of He, Be, Ne, and Na^{+} are computed theoretically and compared with observed and other theoretical values.

Statistical Thermodynamics of Polymer Solutions. I. Theory of the Second Virial Coefficient for a Homogeneous Solute
View Description Hide DescriptionAn approximate theory of the second virial coefficient A _{2} for a system of identical random flight polymer chains of n steps, of average length b, is developed on the basis of a treatment by Zimm in power series form which, though formally exact, is not rapidly enough convergent to be practically useful. By introducing, as an approximation, a spherically symmetrical distribution of the chain segments of two interacting molecules averaged relative to the locus of an initial intersegmental contact, it becomes possible to sum the series, the terms of which relate to molecular configurations with progressively greater numbers of simultaneous contacts. The result, a double integral, is evaluated numerically; but the simple relationin which and β is the mutually excluded volume for a pair of segments, differs from the integral by less than one percent for all positive values of the parameter ψ. The analytical form of this equation is justified in terms of the theory.
Virial coefficients calculated from the theory with parameters derived from intrinsic viscosity measurements agree fairly well with the observed dependence on solute molecular weight for two systems in good solvents, but the magnitudes obtained are too small. If, however, the parameters of the theory are considered arbitrary, correspondence with experiment, to within errors of measurement, can be achieved.

Electron Capture Processes in the Hydrogen Halides
View Description Hide DescriptionThe formation of negative ions by resonance capture processes of the type XY+e=X+Y^{—}, has been studied for the hydrogen halides. A monoenergetic electron source has been used and it has been possible to determine the true shape of the resonance capture peaks in these cases. It has been found that the negative ions appear at energies which are in agreement with recent values for the dissociation energies of the H—X bonds, and the electron affinities of the halogen atoms.

Gaseous Detonations. XI. Double Waves
View Description Hide DescriptionPhotographic studies of detonations of benzene‐oxygen mixtures with the slit and rotating drum camera arrangement have shown under well defined conditions the occurrence of a sharp luminous front receding at a constant rate (ca 73m/sec) from the detonation wave front. The same phenomenon has been observed in several other hydrocarbon‐oxygen mixtures but not in mixtures of hydrogen and oxygen. Measurements of gas densities by the method of x‐ray absorption gave confirmatory evidence that the secondary fronts are shock waves in the domain of the rarefaction wave. A qualitative theory of the secondary wave is developed by analogy with the steady supersonic gas flow through convergent‐divergent nozzles. It is concluded that the secondary wave is due to entropy increase in the rarefaction wave, caused by a spontaneous reaction. Detonation velocity measurements of benzene‐oxygen mixtures and thermodynamic velocity calculations show indeed that thermodynamic equilibrium is not attained in the C‐J state of the detonation wave, but the nature of the lagging chemical reaction cannot be established.

Infrared Emissivity of NO in High‐Temperature Air
View Description Hide DescriptionThe emissivity treatment developed by Mayer has been modified herein for specific application to rotation‐vibration spectra. In order to obtain the oscillator strengths requisite to such a calculation, an earlier developed calculation of the vibrational matrix elements of NO has been utilized. The emissivity of an equilibrium distribution of NO in high‐temperature air has been calculated for one layer thickness and several values of temperature and pressure. This emissivity calculation has been programed on the IBM 704 electronic data processing machine.

Negative Ion Formation and Electric Breakdown in Some Halogenated Gases
View Description Hide DescriptionUtilizing a conventional electron gun and mass spectrometer, the formation of negative ions at low electron energies have been investigated for a number of halogen containing gases used in electric breakdown studies. The SF_{6} ^{—} peak is used as an energy calibration for establishing the appearance potential and the energy width over which capture occurs for the individual gases. It is found that the relative areas of the negative ion curves can be correlated with the electric strength of the gases. The results suggest that the formation of SF_{5} ^{—} rather than SF_{6} ^{—} may be the important process in providing the relatively high electric breakdown value for SF_{6}. Electron attachment associated with SF_{6} and CCl_{4} is found to be an extremely sensitive function of the gas temperature. The gases investigated include CCl_{4}, CCl_{3}F, CCl_{2}F_{2}, CClF_{3}, CF_{4}, CF_{3}SF_{5}, SeF_{6}, C_{2}F_{3}Cl, CHCl_{2}F, CF_{2}Cl–CF_{2}Cl, and ClO_{3}F.

Morse Potentials for Excited States of Diatomic Molecules
View Description Hide DescriptionA model is presented, according to which the nuclear potential functions of the various electronic states of a diatomic molecule form a one‐parameter family of Morse functions. The variable parameter represents the fraction of the valence electrons which are in antibonding orbitals. By using the properties of the ground state to determine the Morse constants, a relation between ω_{ e } and r_{e} of the various electronic states is obtained. This relation reproduces the observed data rather accurately. Somewhat cruder predictions of vibrational anharmonicity, ω_{ e }χ_{ e }, and of dissociation energies are also obtained. Properties of molecular ions and of bonds in polyatomic molecules are also obtained from the model. The measure of bond strength obtained from the model is similar to that deduced from electron configurations in the usual way.

Electroconvectional Heat Transfer in Gases
View Description Hide DescriptionElectroconvectional heat transfers have been measured in gaseous N_{2}, CO_{2}, NH_{3}, SO_{2}, and CCl_{3}F. The results are interpreted and correlated according to the theories of Kronig and of Senftleben and Bültmann. The theoretical predictions of Senftleben and Bültmann concerning the dependence of the electroconvectional heat transfer on the pressure of the gas and the magnitude of the electric field are found to fit the experimental results.

Number of Single, Double, and Triple Clusters in a System Containing Two Types of Atoms
View Description Hide DescriptionA set of graphs are presented from which one can read directly the probability that, in a lattice containing two types of atoms A and B randomly distributed over the lattice sites, a type A atom will be in a cluster of one, two, or three A atoms. Results are presented as a function of concentration for simple cubic, body‐centered cubic, face‐centered cubic, and hexagonal close‐packed lattices.

Theory of Diffusion near Walls
View Description Hide DescriptionA model previously proposed for momentum transport in fluids, in which momentum and energy are carried by dipole density waves centered on the molecule of interest, is here applied to a calculation of the hindering effect of a wall on diffusion. Consideration is given to both specular and diffuse reflection of the density waves by the wall. The ratio γ of the diffusion constant at a distance l from the wall to the bulk fluid diffusion constant is calculated for diffusion parallel to the wall (γ_{ x }), and perpendicular to the wall (γ_{ z }). For the diffuse reflection case and l _{0} is estimated as where η is the shear viscosity,m _{0} the molecular mass, and ν the mass density of solvent;l _{0} may be as large as several hundred angstroms for simple liquids at room temperature.

Additivity Rules for the Estimation of Molecular Properties. Thermodynamic Properties
View Description Hide DescriptionA general limiting law is proposed which can be used to systematize the various laws of additivity of molecular properties. This can be stated as follows: ``If φ is a molecular property, then for the disproportionation reaction: RNR+SNS⇄2RNS, Δφ→0 as the separation between R and S becomes large compared to their dimensions.
It is shown that the zero‐order approximation is equivalent to the law of additivity of atomic properties, the first‐order approximation to the law of additivity of bondproperties, the second‐order approximation to the law of additivity of group properties, and so forth. It is shown that for C_{p} and S° (ideal gases), the additivity of atomic properties works to about ±2 cal/mole‐°K, while the additivity of bondproperties is usually good to about ±1 cal/mole‐°K. The latter also estimates ΔH_{f} ° to about ±3 kcal/mole. The group additivity relation is generally obeyed to within ±0.5 cal/mole‐°K for C_{p} and S° and about ±0.6 kcal/mole for ΔH_{f} °. Tables are presented for each of the partial properties at 25°C.
The agreements found for the various additivity rules is examined from a molecular point of view and certain extensions and limitations indicated. The application and utility of the rules in estimation of thermodynamic properties is discussed.
The estimation of bonddissociation energies is possible with the additivity rules as are the thermodynamic properties of free radicals. An application of the rules to species NR_{2} and NS_{2} show that R and S may be ordered according to their general bond‐weakening or bond‐strengthening properties. For systems where N is C_{2}H_{4} it is shown that the first and second bonddissociation energies for RC_{2}H_{4}R is very likely a constant = 59.5 kcal, the excitation energy of C_{2}H_{4}.

Size Effect in Heterogeneous Nucleation
View Description Hide DescriptionAssuming a spherical nucleating particle, the effect of particle size and surface properties upon nucleation efficiency is investigated. A general result is derived which is then applied to the condensation,sublimation, and freezing of water on foreign nuclei. The size effect is found to become important in the range 100–1000 A of particle radius. For particles larger than this, nucleation efficiency is substantially independent of size, while for smaller particles the efficiency is very greatly reduced.

Microwave Studies of the Structure of Cyclopropyl Derivatives
View Description Hide DescriptionThe microwave spectra of cyclopropyl chloride and cyclopropyl cyanide have been studied and rotational constants for the Cl^{35} and Cl^{37} molecules of the chloride and for the normal molecule and two deuterated species of the cyanide have been determined. The two deuterated species are the cis and trans forms of
For C_{3}H_{5}Cl^{35}, A = 16 625±145 Mc, B = 3905.4±0.3 Mc, and C = 3622.5±0.3 Mc. For C_{3}H_{5}Cl^{37}, A = 16085±415, B = 3810.4±0.5 Mc, and C = 3540.8±0.5 Mc. The following structure fits the rotational constants within the experimental errors: dC–C = 1.5131 A, dC–Cl = 1.7780 A, dC–H = 1.105 A, ≰HCH = 114°36′, ≰HCCl = 120°52.9′.
For C_{3}H_{5}CN, A = 15 917 Mc, B = 3465.06 Mc, and C = 3286.22 Mc. For cis C_{3}H_{4}DCN, A = 14 543 Mc, B = 3419.34 Mc, and C = 3229.15 Mc. For trans C_{3}H_{4}DCN, A = 15 367 Mc, B = 3358.79 Mc, and C = 3161.26 Mc.
The following structure fits the rotational constantsB and C to an average of 1.5 Mc: dC–C_{(ring)} = 1.5131 A, dC–C_{(CN)} = 1.4679 A, dC–H = 1.112 A, dC≡N = 1.1574 A, ≰H–C–H = 115°35′, and
Analysis of the quadrupole structure in C_{3}H_{5}Cl shows that eqQ along the C–Cl bond axis is —71.7 Mc for Cl^{35}, indicating 23% ionic character. The asymmetry η = 0.156 for Cl^{35} indicates a double bond character of 4%.

Mean Amplitudes of Vibration in Allene and Allene‐d _{4} Molecules. I
View Description Hide DescriptionObserved fundamentals for allene and allene‐d _{4} are used for performing a normal coordinate analysis. Eight alternative sets of 13 force constants from the harmonic potential energy function are evaluated numerically. The normal coordinates for allene and allene‐d _{4} are determined. Analytical expressions for all the seven types of interatomic distance displacements are given. For each of these types, both in allene and allene‐d _{4}, the standard deviations (here called mean amplitudes of vibration) are calculated. The obtained values at four temperatures, T = 0, 273, 298, and 323 °K, are reported.

Vibrational Energy Exchange between Diatomic Molecules and a Surface
View Description Hide DescriptionThe problem of the steady‐state vibrational energy distribution of diatomic molecules that temporarily reside on a surface during exposure to a molecular beam is examined according to the rate equations proposed by Klemperer and Herschbach. It is shown that it is possible to obtain explicitly the steady‐state vibrational energy distribution for different vibrational energy distributions in the incident beam and that the vibrational energy accommodation coefficient suitably defined is of a very simple form.