Volume 46, Issue 4, 15 February 1967

Measurements of Electron Impact Excitation Cross Sections of Laser States of Argon(II)
View Description Hide DescriptionCross sections for the excitation of the upper laser levels 4p ^{2} D _{5/2}, ^{2} D _{3/2}, ^{2} P _{3/2}, and ^{2} S _{1/2} of Ar (II) by electron impact with ground‐state neutral atoms have been found by measuring the incoherent light produced by a triode‐type structure filled with argon to pressures near 0.1 torr. Peak values in the vicinity of 5×10^{−19} cm^{2} are found. By operating the same structure in an argon‐ion laser cavity, an increase in coherent output is measured. The amount of the increase in output may be used in conjunction with the measured upper‐state cross section to estimate the cross section for electron excitation of the lower laser levels.

Theory of Collision‐Broadened Ion Cyclotron Resonance Spectra
View Description Hide DescriptionA formalism for calculating collision‐broadened ion cyclotron resonance spectra is developed in detail. The Boltzmann transport equation describing the time variation of the arbitrary function of ion velocity X (v) is extended to include resonant charge transfer. Then with X (v) =v and X (v) =v ^{2}, equations describing, respectively, the velocity and energy of an average particle are developed. The solution of these equations is used to obtain the power absorption of the ions from the observing radio‐frequency electric field.
The effects of collisions are treated in terms of specific ion—molecule interactions. The equations of motion for a mixture of ions, A and B, are coupled by the collision term which accounts for the charge‐transfer process A^{+}+B⇄A+B^{+}. As numerical examples the collision frequencies are evaluated for the rare gases and used to calculate absorption spectra for Ar^{+} in Ar and mixtures of He and Ne isotopes. The formalism permits the straightforward examination of the effects of electric‐field strength, pressure, and temperature on the line shapes.

Glass Transition in o‐Terphenyl
View Description Hide DescriptionVolumetric and thermal measurements on its undercooled liquid indicate that o‐terphenyl undergoes a glass transition in the vicinity of −30°C. This glass temperature is about 60°C higher than that predicted by correlations applicable to simple molecular glass formers. The viscosity of the undercooled liquid was measured over the temperature range 20° to −16°C. These data and the higher‐temperature data of other investigators are described approximately (between 250° and −16°C) by the equationThe apparent activation energy for viscous flow increases from about ¼ of the heat of vaporization ΔH_{v} at the highest part to about 5 ΔH_{v} at the lowest part of the temperature range. The rates of volume relaxation in the vicinity of the glass transitiontemperature were measured. Each relaxation isotherm could be described with a single time constant over volume changes ranging up to 0.2%. In a cylindrical dilatometer, with a large length‐to‐diameter ratio, the relaxation rates apparently were limited by a flow process reflecting the adhesion of terphenyl to the dilatometer walls. Approximate values of the shear viscosity were inferred from a model for this process. Apparently, the homogeneous nucleation frequency of crystals in amorphous o‐terphenyl does not reach a measurable level. The undercooling dependence of the rate of advance of the crystallization front was measured.

Quantum‐Mechanical Kinetic Theory of Loaded Spheres. II. The Classical Limit
View Description Hide DescriptionIn a previous paper, the quantum‐mechanical scattering amplitudes and collision cross sections of loaded spheres were obtained as power series in δ/σ, where σ is the diameter of the sphere and δ is the amount by which the center of mass is displaced from the geometrical center, and the coefficients of the zero, first, and second powers of δ/σ were evaluated explicitly. These results are used to obtain the classical limit of the relaxation time and the coefficients of shear viscosity,thermal conductivity, and diffusion. The results are found to agree with results obtained by purely classical methods.

Optical Spectra of Orientationally Disordered Crystals. I. Theory for Translational Lattice Vibrations
View Description Hide DescriptionThere is a class of crystals in which the molecules are arranged on or near regular positions in space, but are irregularly oriented. The irregular orientation of the molecules frequently perturbs only slightly the translational lattice vibrations of the crystal, that would be perfectly periodic if the irregular orientation were absent. For a first approximation, then, the crystal can be considered to have mechanically regular vibrations. In particular, any normal vibration can be described in terms of a wave vector k that is the wave vector of the dominant Fourier component of the vibration. The irregular orientation of the molecules will cause the dipole‐moment change due to a displacement of a particular molecule to depend in magnitude and direction upon its own orientation and upon the orientation of its neighbors. The crystal is thus in a sense electrically irregular.
The theory of the optical spectra due to the translational lattice vibrations of these mechanically regular, electrically irregular crystals is discussed assuming that the translational and rotational vibrations are not coupled. All the vibrations are active in both infrared and Raman spectra, and to a first approximation, for a crystal with only one nearest‐neighbor central interaction, the intensity of absorption or of Raman scattering by any particular normal vibration of the crystal that is active only because of the irregularity of the orientations (there may, of course, be vibrations that are active in the absence of electrical irregularity) is proportional to the square of its frequency. For more realistic models, the relationship is more complicated. The optical spectra of these crystals provides, therefore, information about the spectrum of lattice vibrations. In particular, features in the optical spectrum probably arise mainly from features in the vibrational spectrum, and it may be possible to identify corresponding features.
In addition, these crystals are intermediate between perfect crystals, which are mechanically and electrically regular, and vitreous solids, which are mechanically and electrically irregular. The study of their spectra should therefore provide an approach to understanding the spectra of vitreous phases.

Optical Spectra of Orientationally Disordered Crystals. II. Infrared Spectrum of Ice Ih and Ice Ic from 360 to 50 cm^{−1}
View Description Hide DescriptionThe far‐infrared spectra in the range 360–50 cm^{−1} of ice Ih and ice Ic made from H_{2}O and from D_{2}O, and of vitreous ice made made from H_{2}O have been investigated. The spectra are due to essentially purely translational vibrations, and have been interpreted using the theory of the spectra of orientationally disordered phases developed in the preceding paper. There are peaks at 229.2 and 164 cm^{−1} that are due (in ice Ic) to maxima in the density of vibrational states due to the transverse optic and longitudinal acoustic vibrations, respectively, and a shoulder at 190 cm^{−1} due to the maximum in the longitudinal optic vibrations. There is also a peak just below 50 cm^{−1} in the spectrum of optical density divided by the square of the frequency that is due to the maximum in the transverse acoustic vibrations. Corresponding assignments are proposed for ice Ih. The Raman spectrum can in principle yield similar information, and agrees with the infrared spectrum in so far as the measurements can be compared.
Some of the observed frequencies can be fitted reasonably well with a simple nearest‐neighbor bond‐stretching and angle‐bending potential field, but there is absorption at sufficiently high frequencies to indicate that long‐range forces are important in determining the translational lattice vibrations of ice. The effects of temperature and of deuterium substitution on the spectrum are discussed.

Electron Spin Resonance and Optical Absorption Studies of Cr^{3+} in a Phosphate Glass
View Description Hide DescriptionOptical absorption and electron spin resonance(ESR)spectra of a chromium‐doped phosphate glass have been studied as a function of Cr_{2}O_{3} concentration. While the optical spectrum appears to be independent of chromium‐ion density, the ESR spectrum exhibits a pronounced concentration dependence. The spectra have been attributed to a combination of isolated, octahedrally coordinated Cr^{3+} and antiferromagnetically coupled pairs of Cr^{3+} ions which are individually sixfold coordinated. The measured value of the crystal‐field parameter Δ is 14 500 cm^{−1}. The ESR data are analyzed within the framework of the spin‐Hamiltonian formalism. In the case of the isolated Cr^{3+} it is estimated that the axial field parameter  D  lies in the range 0.15 to 0.5 cm^{−1}. The assumption of a relatively strong isotropic exchange interaction is adequate to describe the gross features of the Cr^{3+} pair spectrum. Speculative models for the glass structure in the neighborhood of an isolated Cr^{3+} ion and a Cr^{3+} pair are presented.

Deuteron Magnetic Resonance and Proton Relaxation Times in Ferroelectric Ammonium Sulfate
View Description Hide DescriptionThe deuteron nuclear magnetic resonance of single crystals of (ND_{4})_{2}SO_{4} has been studied from 77° to 300°K and particularly in the region of the first‐order ferroelectric phase transition at 223°K. At high temperatures four closely spaced pairs of lines (10‐G max separation) are observed, which shift abruptly as the crystal is cooled through the transition temperature (T_{c} ). These lines are assigned to the two inequivalent ND_{4} ^{+} ions (I and II) in a unit cell, which are slightly distorted from the tetrahedral configuration and rapidly reorienting so as to average the quadrupolar splitting to a small value. At 130°K only two pairs of closely spaced lines are observed due to ND_{4} ^{+} (II); at 77°K eight pairs of widely spaced (400‐G max separation) lines are observed corresponding to ND_{4} ^{+} (I). In the transition to the ferroelectric phase the principal coordinate system of the electric‐field gradient (EFG) tensor rotates by about 30° for each ion with little change in the coupling constants or asymmetry parameters. The spontaneous polarization produced by the distorted ions has been calculated from the observed EFG tensors and is in reasonable agreement with the experimental value.
Proton spin—lattice relaxation times (T _{1}) and protonrelaxation times along the rf field (T _{1ρ}) have been measured for polycrystalline (NH_{4})_{2}SO_{4}. T _{1} versus temperature (T) has two minima, and may be interpreted as due to the two inequivalent NH_{4} ^{+} tetrahedra reorienting at different frequencies and coupled to each other via dipole—dipole interaction. Correlation times τ_{ c } at various temperatures have been obtained for the two inequivalent NH_{4} ions from the T _{1} and T _{1ρ} measurements; above T_{c} and below 170°K, logτ_{ c } is a linear function of T ^{−1}, with normal values of pre‐exponential factors. The activation energies change only slightly at the transition, in agreement with recent neutron inelastic scattering data. τ_{ c } is, however, anomalously short immediately below T_{c} due to the volume contraction of the crystal. Correlation times have also been estimated from deuteron resonance linewidths and proton second moments. The results are consistent with those derived from the protonT _{1} and T _{1ρ} data.
An order—disorder mechanism is proposed for the phase transition in which NH_{4} ^{+} tetrahedra are disordered with respect to the crystal ab plane. A first‐order transition is described by the molecular field approximation for a sufficiently strong dependence of the interaction parameter on the spontaneous polarization.

First‐Order Ferroelectric Transition in (NH_{4})_{2}SO_{4}
View Description Hide DescriptionA modified molecular‐field approximation is presented in which a dependence of the interaction parameters on the number of misoriented ion pairs is explicitly included. The usual second‐order phase transition becomes first order for a sufficiently strong dependence of the interaction parameters on the number of misoriented pairs. Values of the parameters for a simple lattice necessary to account for the transition in (NH_{4})_{2}SO_{4} are given. A qualitative explanation of the dependence of the crystal volume on temperature is proposed based on the hydrogen‐bond structure of (NH_{4})_{2}SO_{4}.

Relaxation of a Gas of Harmonic Oscillators
View Description Hide DescriptionThe temporal evolution of the vibrational distribution function for a gas of harmonic oscillators undergoing binary collisions, in which they can exchange vibrational quanta among themselves as well as transfer energy between the vibrational and translational degrees of freedom, is determined exactly. The solution, given in terms of a generating function, involves only a double integral and is valid for transition probabilities due to an interaction potential linear in the oscillator coordinate. The relaxation toward ``local equilibrium'' of the vibrational distribution is found to be at least twice as fast as the relaxation of the average vibrational energy to the final equilibrium value. The solution is valid for an arbitrary initial vibrational distribution and for arbitrary ``dilution'' of the oscillators by inert collision partners.

Effects of Chemical Reactions on the Bimolecular Rate Constant
View Description Hide DescriptionThe dependence of the bimolecular rate constant on the reaction rate, degree of anisotropic scattering, mass ratio, and other parameters is investigated by considering the Boltzmann equation for a dilute homogeneous reacting gas. For highly anisotropicelastic scattering, a differential form of the Boltzmann equation is derived and a solution obtained, which yields an analytical expression for the rate constant. It is found that the correction to the standard reaction‐rate formula is significant for highly anisotropic scattering, small mass ratios, and large reaction cross sections.

Adsorption and Occlusion of Gases by the Low‐Temperature Forms of Ice
View Description Hide DescriptionWater vapor condensed on a surface at −196°C in the presence of O_{2}, N_{2}, Ar, or CH_{4}, forms a condensate which, on warming, evolves gas in three temperature ranges. The rate of gas evolution first goes through a maximum between −196° and −125°C probably from release of adsorbed gas due to decrease in surface area of the amorphous ice. A second peak in the gas evolution rate appears in the same temperature range as the formation of cubic ice between −120° and −110°C. The remainder of the occluded gas comes out between −70° and −40° (at 15° rise/min) where cubic ice transforms to the hexagonal form. Nitrogen adsorption isotherms indicate surface areas as high as 241 m^{2}/g for amorphous ice prepared at −196°C, and annealing measurements suggest areas as high as 500 m^{2}/g for lower‐temperature preparations. Water—oxygen mixtures subjected to a microwavedischarge, then condensed at −196° and allowed to warm, evolve as much as 97% of the product oxygen between −70° and −40°C.

Radiative Recombination of Chlorine Atoms in Shock Waves
View Description Hide DescriptionThe equilibrium emission behind shock waves in Cl_{2}–Ar mixtures has been measured as a function of temperature, wavelength, and atom concentration. The emission spectrum has been recorded at 2200°K and the absolute rate of emission has been measured in two regions of the visible spectrum. The emission is found to behave in adequate accordance with a theory based on calculation of the equilibrium concentrations of molecules in excited states. However, it is necessary that the radiative lifetime of the ^{3}Π_{0+ u } state be considerably shorter than previously thought. It appears to be a few microseconds, i.e., of the same order as the ^{1}Π_{1u }.

Rate of Dissociation of Chlorine in Shock Waves
View Description Hide DescriptionEmission of light from the radiative recombination of chlorine atoms has been used to measure the rate of dissociation of molecular chlorine behind shock waves in 1:5 Cl_{2}:Ar mixtures between 1735° and 2582°K. Assuming second‐order kinetics for the dissociation, —d[Cl_{2}]/dt=k_{d} [Cl_{2}][M], the rate constants k_{d} are adequately expressed by the equationover the indicated temperature range.

Thermodynamic and Conformational Properties of Polystyrene. II. Intrinsic Viscosity Studies on Dilute Solutions of Linear Polystyrenes
View Description Hide DescriptionThe results of an extensive study of the intrinsic viscosity [η] of a series of linear, homogeneous (anionically prepared) polystyrenes (1.9<10^{−4} M<440) over a wide temperature interval (10°<T<110°C) in decalin and toluene are described. The data are discussed in relation to the interaction parameter in which the constants B _{0}, Θ, and 〈s ^{2}〉_{0}/M have been determined from thermodynamic studies reported in Part I of this series. It is found that [η]/[η]_{0} is not a single‐valued function of z except for M>∼10^{6}. Above this molecular weight the dependence of [η]/[η]_{0} on z is satisfactorily predicted by recent calculations of Fixman; [η]/[η]_{0} is not linear in z contrary to other recent suggestions. The failure of the data on lower molecular weight polymers to be a single‐valued function of z is discussed in terms of partial draining effects.

fd and f ^{13} d Configurations in a Crystal Field, and the Spectrum of Yb^{++} in Cubic Crystals
View Description Hide DescriptionThe energy levels of the configurations fd and f ^{13} d in cubic crystal fields have been calculated as a function of the f‐ and d‐electron crystal‐field parameters. The results are used to explain the spectrum of Yb^{++} in SrCl_{2}. Both the calculated energies and calculated intensities agree well with experiment.

Debye—Waller Factors of Copper and Gold
View Description Hide DescriptionThe temperature variation of the Debye—Waller exponents for copper and gold are calculated using the electron gas model for the lattice dynamics of metals propounded by one of us earlier. The results of the calculation are compared with available x‐ray measurements. Good agreement with the experimental data is obtained for gold, but not in the case of copper.

Spectroscopic and Electrical Properties of Polymeric Donor—Acceptor Complexes
View Description Hide DescriptionThe spectroscopic and electrical properties of poly (p‐dimethylaminostyrene) complexes with a variety of electron acceptors have been measured. Weak electron acceptors yield charge‐transfer complexes, whereas strong electron acceptors are partially converted into radical anions. As may be concluded from measurements of the Seebeck coefficient, charge transport is caused by electrons. The electrical conductivity of the complexes is critically dependent on acceptor concentration and is attributed to hopping processes between radical anions and neutral acceptor molecules.

Irreversibility in Finite Quantum‐Statistical‐Mechanical Systems
View Description Hide DescriptionIt is shown that the usual proofs of the quasiperiodicity of isolated, finite quantum‐statistical systems, previously thought to be general proofs, are in reality based on the special case of a discrete array. Quasiperiodicity is demonstrated for the analogous special case (the discrete distribution) in classical statistical mechanics. The density‐operator formalism is set up for the case of a continuous array. The question of the possibly irreversible behavior of isolated, finite quantum‐statistical systems with continuous arrays is investigated. An argument is given indicating that such systems generally behave irreversibly. The situations in classical and quantum statistics then appear to be entirely analogous, since it is well known that isolated, finite classical‐statistical systems may, in the case of a continuous distribution (the analog of a continuous quantum‐statistical array), behave irreversibly.

Isotope Effects in the Diffusion and Solubility of Hydrogen in Nickel
View Description Hide DescriptionThe solubility and diffusivity of hydrogen and deuterium in a single crystal of nickel have been measured in the range 490°—690°K. The theory of isotope effects has been developed in the harmonic approximation. It is shown that the experimental results can be quantitatively accounted for in terms of the derived expressions. The theory is tested by calculation of the pre‐exponential factor for diffusion (D _{0}) using only the data for the relative diffusivities of hydrogen and deuterium. The calculated value is in excellent agreement with experiment if it is assumed that direct jumps of hydrogen from one octahedral site to another are involved.