Volume 31, Issue 4, 01 October 1959

Infrared Absorption Spectrum of Lithium Hydroxide
View Description Hide DescriptionThe polarized infrared absorptionspectrum of crystalline lithium hydroxide in the region between 2500 cm^{—1} and 8000 cm^{—1} has been obtained with a grating spectrometer. The spectrum consists in part of a strong band at 3678 cm^{—1} polarized parallel to the c axis and bracketed in a nearly symmetric manner by five pairs of side bands polarized perpendicular to the c axis and by two pairs of side bands polarized parallel to the c axis. In addition an isolated band at 7172 cm^{—1} is observed polarized parallel to the c axis. Changes in the spectrum as the sample temperature is increased from room temperature to 400°C are described.
The hydrogen positions in lithium hydroxide have been deduced. It is shown, using the factor group selection rules as a guide, that the spectrum can be explained as consisting of an infrared active OH stretching fundamental surrounded by binary combinations of lattice fundamentals with the infrared and Raman OH fundamentals. The band at 7172 cm^{—1} is assigned as the binary combination of the two OH fundamentals. The vibrational modes of the crystal belonging to irreducible representations of the factor group have been constructed to within a good approximation. Tentative assignments of deduced lattice frequencies to constructed modes are presented. The present explanation of the lithium hydroxide spectrum is contrasted with the rotation‐vibration explanation of Hexter.

Near Infrared Spectra of Crystalline Alkali Hydroxides
View Description Hide DescriptionThe technique of melting alkali hydroxides between alkali halide plates has been used to obtain the near infrared absorption spectra of LiOH, LiOD, NaOH, NaOD, KOH, and KOD. Complicated combination band structure is observed in NaOH similar to that observed previously in LiOH, Ca(OH)_{2} and Mg(OH)_{2}. The deuterated spectra of LiOH and NaOH indicate that both translational and librational (or rotational) modes couple to the fundamental OH^{—} ion vibrations. Fundamental frequencies of 3611±4 cm^{—1} and 2654±2 cm^{—1} are observed for KOH and KOD, respectively. Reactions of the alkali hydroxides with certain alkali halides are observed.

Microwave Spectrum, Internal Barrier, Structure, Conformation, and Dipole Moment of Acetyl Fluoride
View Description Hide DescriptionThe microwave spectra of eight isotopic species of acetyl fluoride are reported. Interaction of internal and over‐all rotation splits the rotational lines into doublets. From the doublet separations of CH_{3}COF the height of the threefold (sinusoidal) barrier to internal rotation was calculated to be 1041 cal/mole. Splittings in the spectra of C^{13}H_{3}COF, CH_{3}CO^{18}F, and CD_{3}COF gave barriers of 1041, 1055, and 1031 cal/mole, respectively.
With the assumption of a symmetrical methyl group, the following structural parameters were determined from the observed rotational constants:If the requirement of methyl group symmetry is dropped, the best fit to all the data is obtained with the following methyl group parameters:The observed rotational constants of CH_{2}DCOF and CHD_{2}COF were found to require the H(in‐plane)‐F trans‐equilibrium conformation.
From Stark effect measurements on CH_{3}COF and CH_{3}CO^{18}F the dipole moment was calculated to be 2.96 D. The dipole moment makes an angle of 9°30′ with the C–C bond axis and is directed toward the oxygen atom.

Microwave Spectrum of Acetyl Cyanide
View Description Hide DescriptionThe microwave spectra of eight isotopic species of acetyl cyanide have been investigated in the region 8000 to 34 000 Mc. The hindered internal rotation of the methyl group splits some of the rotational lines into doublets. Analysis of these splittings for four isotopic species gives a barrier to internal rotation of 1270±30 cal/mole.
From the rotational constants of CH_{3}COCN, C^{13}H_{3}COCN, CH_{3}COC^{13}N, CH_{3}CO^{18}CN, CD_{3}COCN, and CD_{3}C^{13}OCN the following structural parameters were determined:A study of CH_{2}DCOCN and CHD_{2}COCN shows that in its equilibrium configuration, the acetyl cyanide molecule has a methyl hydrogen opposite the oxygen atom.
A dipole moment of 3.45D was obtained from Stark effect measurements.

Equilibrium in the Exchange of Hydrogen between Arsine and Water
View Description Hide DescriptionThe equilibrium constant for the reaction AsH_{2}D(g)+H_{2}O(l)⇌AsH_{3}(g)+HDO(l) has been measured at 25.4° and found to be 1.89±0.02, corresponding to a value in the gas phase of 1.77±0.02. With the known vibrational spectra of AsH_{3} and AsH_{3}—d _{3} the gas phase equilibrium constant was calculated at 25.4°, K _{2}=0.777e ^{258/T }=1.84.

H_{3} Activated Complex and the Rate of Reaction of Hydrogen Atoms with Hydrogen Molecules
View Description Hide DescriptionThe method recently proposed by Sato for determining potential energy surfaces is compared with the semiempirical method of Eyring and co‐workers. The two methods are found to be equally empirical. The potential energy surface for the H_{3} complex has been constructed with the Sato method to give an activation energy which agrees with the experimental value. The H_{3} complex is found to be linear and symmetrical, with a bond length of 0.93 A and vibrational frequencies of 2108, 877, and 1918i cm^{—1}. Anharmonicity constants for the real frequencies make a negligible contribution to the zero‐point energy. A large contribution to the H+H_{2}reaction from tunneling through the potential barrier is predicted, contrary to experimental data. However, at 1000°K, the calculated pre‐exponential factor and ratios of rate constants for isotopic species are in reasonably good agreement with experimental values.

High Frequency Factors in Unimolecular Reactions
View Description Hide DescriptionThe high frequency factors which are associated with certain unimolecular reactions are discussed in terms of an extended Kassel‐type model, in which the critical energy is localized in more than one oscillator.

On an Approximate Theory of Transport in Dense Media
View Description Hide DescriptionA new approximate theory of transport is presented which starts from the general statistical mechanical theory of heat flux and the stress tensor and uses three principal approximations. These are (a) the expansion of the gradient of the pair interaction potential between molecules at time t+s about the gradient at time t and the neglect of all terms higher than the second, (b) the use of a local equilibrium distribution function in pair‐space, and (c) the approximation of the pair diffusiontensor as the direct sum of singlet diffusiontensors. The intermolecular force contributions to the shear viscosity, bulk viscosity, and thermal conductivity are related to equilibrium properties of the fluid and, respectively, to other coefficients of the set of transport coefficients. Absolute calculations for liquid argon are within a factor of two of experiment. A semiempirical calculation suggested by the theory and using the observed diffusion coefficient is in exact agreement with experiment. The validity of the three approximations is discussed.

Color Centers in KI:T1 X‐Rayed at Low Temperatures
View Description Hide DescriptionThe optical properties of the phosphor KI:Tl have been studied after x‐raying at 5 or 78°K. The interactions among the several simultaneously produced centers have been studied by following and correlating changes in luminescent intensity and optical absorptionspectra as the crystal is warmed, and an explanation of these effects is offered in terms of retrapping and recombination. Perturbation bands due to the modification of the energy levels of the luminescent center as a result of the interaction with a color center are observed. The major centers produced in the more heavily doped crystals by brief irradiation at low temperatures do not involve vacancies and are identified as an electron center associated with Tl, I_{2} ^{—}, and V centers near Tl^{+}. The optical absorptionspectrum of I_{2} ^{—} consists of bands at 404 and 800 mμ. (The absorption of Br_{2} ^{—} in KBr:Tl incidentally has also been identified.) On the basis of certain similarities in luminescence properties, essentially similar effects are proposed for ultraviolet as for x‐ray excitation.

Lengths of CC ``Single'' Bonds and Radii of Hybrid Orbitals of Carbon
View Description Hide DescriptionThe variation in the CC σ‐bond length in hydrocarbons and related compounds has been ascribed primarily to the variation in the covalent radius of the carbon atom with hybridization, resonance effects being considered to be of little importance in the ground states of these molecules. Values for the radii of the hybrid orbitals of carbon have been assigned, and they have been shown to reproduce satisfactorily the lengths of the CC σ bonds in a variety of compounds, both aliphatic and aromatic.

Apparent Activation Energy and Frequency Factor for a Process Involving Competing Mechanisms
View Description Hide DescriptionIf a process involves competing mechanisms, each of which individually obeys Arrhenius' equation, the dependence of the combined rate on temperature is in general not of this type. However, apparent activation energies and frequency factors can be measured. In this paper, several sets of mechanisms distributed with respect to activation energy are considered and the apparent activation energies and frequency factors are calculated in terms of the parameters of the distributions. The results for a two‐peak distribution, a flat distribution, and a truncated exponential distribution are given analytically and graphically. A simple approximate method is described for determining the apparent activation energy in some cases. Some remarks are made about the ``compensation effect.''

Growth Mechanism of Copper Whiskers by Hydrogen Reduction of Cuprous Iodide
View Description Hide DescriptionA study has been made of the growth of copperwhiskers by hydrogen reduction of cuprous iodide. Alternative mechanisms have been proposed involving, respectively, vapor phase reduction and reduction at the whisker tip. A necessary consequence of the vapor phase reduction mechanism is the presence of a highly supersaturated copper vapor. It is shown that the vapor phase is not highly supersaturated in copper vapor and that reduction must occur heterogeneously. It is further shown that the reduction process occurs only at the tip and is most simply accounted for by assuming reduction at the step associated with an axial dislocation.

Low‐Temperature Heat Capacity of Azurite
View Description Hide DescriptionThe heat capacity of azurite,Cu_{3}(CO_{3})_{2}(OH)_{2}, has been measured in the temperature range of 1.7–3.6°K. The characteristic λ‐type heat capacity anomaly associated with the antiferromagnetic‐paramagnetic transition in the crystal has been observed, the Néel point being 1.84°K. The entropy change associated with this transition has been found to be 1.17 cal/deg mole and agrees fairly well with the theoretical value of 1.38 cal/deg mole calculated from R ln (2S+1). The contribution to this entropy change above the Néel temperature was approximately 35%, which indicates a comparatively slow diminution of the short‐range ordering of the Cu^{++} spins.

Paramagnetic Resonance of F Centers in Potassium Iodide
View Description Hide DescriptionThe electron‐spin resonance of F centers in potassium iodide is observed at 293°K, 77°K, and 4°K. Additively‐colored crystals of several concentrations and x‐rayed crystals show the same resonance with g = 1.970 and a width of 213 gauss at maximum slope. The saturation of the absorption is measured. The resonances of F centers in potassium halides are compared.

Microwave Spectrum and Internal Rotation of 1‐Chloro‐2‐Butyne
View Description Hide DescriptionThe microwave spectrum of CH_{3}C≡CCH_{2}Cl has been investigated in the region from 20–30 kMc. The existence of nearly free internal rotation gives rise to regions of very dense absorption. Transitions of the type ΔJ = 1, ΔK = 0 have been identified for the ground torsional state (m = 0). The ground state spectrum is that of an effective rigid rotor with the rotational constants modified by the internal rotation. Values for the effective rotational constants are 17 631, 1490.55, 1385.06 Mc for the Cl^{35} species; and 17 329, 1459.76, 1357.26 Mc for the Cl^{37} species. These rotational constants permit an upper bound of 100 cal/mole to be established for the barrier to internal rotation. A structural analysis indicates that the CCl bond is longer than in CH_{3}Cl.

Abnormal Excitation of OH in H_{2}/O_{2}/N_{2} Flames
View Description Hide DescriptionThe emission from the first four vibrational levels of OH^{2}Σ^{+} and the concentrations of ground state OH^{2}II have been measured in a series of rich H_{2}/O_{2}/N_{2}flames held on flat porous burners as a function of distance from the burner. The intensity of emission of each of the bands is proportional to the cube of the concentration of ground state OH, but the constant of proportionality depends on the band and the flame conditions. This dependence, as well as absolute intensity measurements, establish the fact that the radiation is nonthermal.
The dependence of the emission intensity on an integral power of OH strongly indicates that the excited OH is formed as a result of one or more of a set of possible radical recombination reactions. It is shown that in general it is not possible to obtain a unique determination of the excitation mechanism for any band. The only exception to this is that definite evidence for the preassociation reaction, O+H→OH^{2}Σ, v=2, has been obtained. The vibrational distributions of excited OH are shown to be consistent with ``temperatures'' from 3000°K to 5000°K (compared with maximum flame gas temperatures of 1600°K), which is probably to be expected from a reaction with the exothermicity of H+OH+OH→H_{2}+OH^{*}. It is concluded from this and from the general behavior of the data, that this last reaction is most likely responsible for the nonthermal emission of all the bands, with the exception of that specifically known to be due to the preassociation reaction.

Force Parameters for Some Nonpolar Molecules on the Exp 6–8 Model
View Description Hide DescriptionForce parameters for the Buckingham‐Corner (exp 6–8) potential have been calculated for Kr, Xe, and C_{2}H_{4}. For Kr and Xe, crystal data and second virial data have been used. Crystal data could not be used for C_{2}H_{4}. For these substances the exp 6–8 potential has been compared with the other potential forms. It has been observed that the second virial coefficient is not sensitive enough to show the relative importance of the contributions of the r ^{—6} and r ^{—8} terms to the London attractive potential.

Equation of State and Thermodynamic Properties of Gases at High Temperatures. I. Diatomic Molecules
View Description Hide DescriptionMethods for evaluating the thermodynamic properties of assemblies of chemically reacting unionized atoms are discussed. The desirability of using the virial coefficients at high temperatures instead of the customary use of the molecular partition functions with anharmonicity corrections is emphasized. The most realistic three‐parameter diatomic potential energy function that is available at present, i.e., the Rydberg potential, is selected for the evaluation of the classical second virial coefficient. B(T), T(dB/dT) and T ^{2}(d ^{2} B/dT ^{2}) are obtained as linear combinations involving the five functions:[k= —1, 0, 1, 2, and 3, and θ=(U_{e}/kT)] with only the coefficients that multiply A_{k} depending on b′. A_{k} is tabulated for 0.05≤θ≤10. A simple expression for estimating the quantum correction to B(T) is given. The inclusion of the contribution of the higher diatomic electronic states to B(T) is considered. The treatment is applied to sodium (including the ^{3}Σ repulsive state), and B(T) and thermodynamic properties calculated at two temperatures by several methods are compared.

LCAO Wave Functions for Hydrogen Fluoride with Hartree‐Fock Atomic Orbitals
View Description Hide DescriptionAccurate Hartree‐Fock fluorine functions and an exponential Slater 1s hydrogen orbital have been used as basis functions in a conventional SCF LCAO—MO treatment of the HF molecule at five internuclear distances. Comparison with Hartree‐Fock calculations for the isoelectronic F^{—} and Ne systems gives a qualitative indication that a rather close approximation to the true molecular Hartree‐Fock solution for HF has been achieved. Configuration interaction has been included with the restriction that the 1σ orbital remains filled. Molecular energies, dipole moments, and other molecular quantities are evaluated and compared with experimental results and with other theoretical work.

Method for the Analysis of Multicomponent Exponential Decay Curves
View Description Hide DescriptionA frequently encountered problem in many branches of science involves the resolution of experimental data into a sum of independent exponential curves of the formin order to estimate the physically significant parameters N_{i} and λ_{ i }. Such problems arise, for example, in the analysis of multicomponent radioactive decay curves, and in the study of the dielectric properties of certain compounds. This paper is concerned with the numerical evaluation of a mathematical approach to the problem. The approach is based on the inversion of the Laplace integral equation by a method of Fourier transforms. The results of the analysis appear in the form of a frequency spectrum. Each true peak in the spectrum indicates a component, the abscissa value at the center of the peak is the decay constant λ_{ i }, while the height of the peak is directly proportional to N_{i} /λ_{ i }. Results obtained on an IBM 650 computer indicate that the method may possess certain advantages over previous methods of analysis.