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Volume 62, Issue 3, 01 February 1975

Pyroelectric Nd(IO_{3})_{3}⋅H_{2}O. Crystal structure of the transition‐metal iodates. II
View Description Hide DescriptionNeodymium iodate monohydrate, Nd(IO_{3})_{3}⋅H_{2}O, crystallizes in the monoclinic system with space group P2_{1} and two formulas in the unit cell. The pyroelectric coefficient at room temperature is about 2.2×10^{−5} cm^{−2}/°K. The lattice constants at 298°K are a = 10.2012±0.0013, b = 6.70530±0.00004, c = 7.3538±0.0009 Å, and β = 113.11±0.02° (λ CuKα_{1} = 1.540562 Å). A total of 8060 reflections were measured within a reciprocal hemisphere having (sin ϑ)/λ ? 1.02 Å^{−1}, using PEXRAD. The crystal structure was solved by the interpretation of Patterson and Fourier series and refined by the method of least squares using 2603 independent F _{meas}, with final agreement factor R = 0.058. The three independent IO_{3} ^{−} ions share oxygen atoms to form a three−dimensional framework of corner−sharing polyhedra. Two iodine atoms are coordinated by seven and the third by six oxygen atoms. All iodine polyhedra have three short I−O distances averaging about 1.81 Å, and longer I−O distances ranging to 3.3 Å. The water molecule links all three independent iodate groups together. Nd^{3+} occupies a distorted bicapped trigonal prism with average Nd−O distance of 2.45 Å . The piezoelectric coefficient d _{22} is strong and readily detected.

Dielectric constant of compressed solid methane at low temperature
View Description Hide DescriptionMeasurements of the static dielectric constant and the derived Clausius−Mossotti (CM) values for the solid phases of methane at densities ranging to 20% above the triple point density are reported. The dielectric constant data for 60<T<260 K and 0.52<ρ0.60 g/cm^{3} may be fitted within experimental error to ε_{ s }(ρ,T) = 0.7293±0.0006 − (3.2±0.3) × (10^{−5}) T + (2.066±0.008) ρ and the CM data to CM (ρ,T) = 6.497±0.022 − (1.76±0.16) × (10^{−4}) T + (0.061±0.04) ρ. Within experimental error, the CM function is constant across the fluid−solid transition at T = 157.2 K and is independent of density in the solid phase. These data are discussed in terms of a model based on the dielectric behavior of octupole−induced dipoles. The low temperature solid−solid P−Tphase diagram is mapped using dielectric anomalies at the transitions and calculated pressures. The existence of a fourth, or δ, phase is demonstrated by a dielectric anomaly that is suggestive of ferro− or antiferroelectric behavior.

Decay of an emitting dipole between two parallel mirrors
View Description Hide DescriptionA classical treatment is presented for the modification of the emission rate of an atom between two parallel mirrors. For the case of two perfectly reflecting mirrors, the results are identical with previous treatments of this problem using a quantum mechanical approach. The purely classical treatment has the advantage of being able to treat nonperfectly reflecting mirrors.

Theorems on chemical network stability
View Description Hide DescriptionThe stability of steady states of a chemical reaction system is considered within a diagrammatic formulation of the problem. The system’s stability depends upon the kinds of cycles that can be constructed from a set of arrows. The following theorems are proven. (1) A chemical network has no unstable steady states if the set of cycles which can be constructed contains only certain 2−cycles or is empty; (2) an m−cycle, which passes through a reactant whole self−vertex is exactly cancelled by autocatalysis destabilizes the network in certain restrictive circumstances; and (3) a 3−cycle as in (2) destabilizes the network under broader circumstances. The restrictive circumstances of the second theorem do not appear to be capable of being broadened in general because of complexities that can be understood within the full diagrammatic formulation of the problem.

Elastic continuum theory cutoffs and order in nematics and solids
View Description Hide DescriptionThermal disorder in liquid crystal molecular orientation and thermal displacement of atoms in monatomic crystals can be described with analogous elastic continuum theories having short wavelength cutoffs. Half the short wavelength cutoff that gives the observed displacement is remarkably close to 1.8 times the cube root of the atomic volume in monatomic crystals. Half the short wavelength cutoff that gives the observed order parameter in PAA is also about 1.8 times the cube root of the molecular volume. Some data give a number about twice as large for MBBA. This large cutoff may be due to a large error in measured order parameter, or it may suggest that MBBA molecules tend to form groups in the nematic phase.

Adsorption of ^{4}He on graphitized carbon in the submonolayer region between 2 and 15°K
View Description Hide DescriptionThe adsorption of ^{4}He on graphitized carbon (Spheron 6) was studied at submonolayer coverages between 2 and 15°K. Heat capacities, heats of adsorption(measured calorimetrically), and equilibrium pressures are reported. The data indicate that adsorbed helium remains localized up to at least 15°K. A phase transition is observed at temperatures above 9°K for the 22.26 cm^{3} STP/g adsorbent coverage. Frequencies of three−dimensional asymmetric localized harmonic oscillators which can reproduce the experimental results are given. Excited levels are heavily populated at the temperatures of measurement. The zero point energy of adsorbed helium is approximately 200 J/mole. Another change in the state of adsorbed helium takes place below 7°K to the lowest temperature attained, 2°K. The rate of this change in the state of adsorbed helium follows first order kinetics. It is suggested that this process involves the ’’falling’’ of the adatoms from higher to lower levels as the temperature is lowered. The residual entropies are calculated for two coverages. The residual entropy is attributed to the distribution of helium atoms over the localized surface sites.

Molecular dynamics of octane in a gas liquid solution
View Description Hide DescriptionA gas/liquid solution was formed by applying up to 70 (MPa) of argon to n−octane. The molecular dynamics of octane in the solution were measured by NMR relaxation techniques. A relatively insoluble gas, helium, was also applied so that the effect of pressure could be contrasted with the effect of solution. The transport properties of octane compressed by argon possessed two distinguishing features. First, the behavior of its diffusion constant indicated that the viscosity of the fluid decreased with pressure as more argon dissolved into the liquid. Second, the pressure depencence of octane’s over−all rotational correlation time was much less than the estimated pressure dependence of the solution’s viscosity. This latter feature could be explained by a microviscosity theory which takes into account the effect of solvent size on the coupling between molecular rotation and viscosity.

Density of methoxybenzylidene butylaniline about the isotropic–nematic phase transition
View Description Hide DescriptionWe have measured the density and determined the coefficient of expansion of MBBA about its isotropic−nematic transition temperature using a Mettler/Paar density meter. Our results show essential agreement with those of Press and Arrott using a buoyancy method. The small difference (<0.3°C) between the actual transition temperature and the virtual critical temperature differs from that determined by light scattering studies which yield values of about 1°C. Further examination on the nature of the virtual critical temperature is suggested.

Short−range order fluctuations in the isotropic phase of a liquid crystal MBBA
View Description Hide DescriptionWe have measured the polarized (I _{∥}) and the depolarized (I _{⊥}) scattered light intensities by fluctuations of the orientational order parameter as a function of two scattering angles over a range of temperatures close to and above the isotropic−nematic phase transition of p a r a−methoxybenzylidine p a r a−n−butylaniline (MBBA). The coherence length χ was found to diverge as ε^{−0.50±0.01}, in essential agreement with the last results of Stinson and Litster and the theoretical predictions of de Gennes, where ε = (T − T _{ c }*)/T _{ c }* and T _{ c }* is a pseudocritical temperature slightly below T _{ p }. We have also measured the temperature dependence of the extinction coefficient of MBBA using the 632.8 nm wavelength of He−Ne laser light and observed that (limKμ0) 1/I _{∥} or _{⊥} after attenuation correction diverges as ε^{γ} with γ = 0.85±0.05 which differs from γ = 1 as reported by previous studies. K represents the magnitude of the momentum transfer vector.

Shock tube study of the thermal decomposition of O_{3} from 1000 to 3000°K
View Description Hide DescriptionMeasurements have been made of the thermal decomposition of O_{3} behind incident shock waves. Both uv absorption and Schumann−Runge emission measurements were made in separate experiments to follow the O_{3} and O−atom concentrations, respectively. The high temperature data are interpreted to indicate a departure from the Arrhenius form for the rate constant of the unimolecular reaction O_{3} + M ? O + O_{2} + M. The rate constant for this reaction is measured to be approximately a factor of 2 smaller at 3000°K than predicted by the Arrhenius fit to the low temperature data (200°K ? T ⩽ 900°K).

Ultrasound propagation in NH_{3}–H_{2}O mixtures
View Description Hide DescriptionData on the sound velocity and absorption in liquid mixtures of NH_{3} and H_{2}O are presented. The sound velocity at 10 MHz was measured as a function of concentration and temperature. The absorption was measured as a function of frequency (between 10 and 85 MHz), concentration, and temperature. The results indicate that the NH_{3}−H_{2}O system behaves ultrasonically like mixtures of associated liquids with a relaxation due to the electrolytic nature of NH_{3}.

Some observations on the continuum emission from NO_{2}
View Description Hide DescriptionThe fluorescencespectrum of NO_{2} produced by laser excitation in the visible region consists of a discrete banded structure superimposed on what appears to be a continuum. Previous experiments have implied that the intensity of continuum emission increases relative to that of the discrete emission as the pressure is raised, and that therefore the continuum emission is produced by some collision mechanism. In this paper we describe some magnetic quenching experiments which indicate that the continuum/discrete ratio is pressure independent. We also describe experiments which indicate that the continuum emission lifetime is longer than the discrete emission lifetime, and this allows a reinterpretation of previous observations which is not in conflict with the conclusion based on our magnetic quenching data. These observations suggest that either the continuum emission originates in the isolated molecule, or else, that the cross section for any bimolecular process is extremely large.

Comprehensive optical and collision data for radiation action. I. H_{2}
View Description Hide DescriptionWe apply a multistep program of Platzman to construct a complete set of inelastic cross sections for electron scattering at all incident energies. The initial step constructs a complete spectrum of optical oscillator strengths from photoabsorption and other optical data subjected to the constraint of sum rules. Measured cross sections for nonionizing collisions are then adjusted to fit Bethe’s formula. Experimental differential ionization cross sections are analyzed by a new method of Kim’s. The resulting set of all inelastic cross sections is subjected to the Inokuti−Kim−Platzman sum rule. The value of W, the mean energy per ion pair, is calculated from the adopted cross sections and compared with experiment, taking into account dissociation and recombination processes.

Comprehensive optical and collision data for radiation action. II. Ar
View Description Hide DescriptionWe present a complete set of optical oscillator strengths and electron impact cross sections for argon gas. The cross sections were obtained utilizing a semiempirical method of Platzman which stresses the close relationship between photoabsorption and fast electron−atom collisions. The data evaluation was done by analyzing a great variety of experimental measurements of various nature and piecing them together on the basis of theory, with the constraints of sum rules. The mean energy per ion pair, W, calculated from adopted cross sections allowing for inner shell contributions is 26.9 eV. This value is expected to exceed the measured value of 26.4 eV, which is reduced by the contribution of collateral ionization.

Vacuum ultraviolet absorption spectra of the bromomethanes
View Description Hide DescriptionThe vapor phase vacuum ultraviolet absorption spectra of methyl bromide, methylene bromide, bromoform, and carbon tetrabromide are reported for the region 40 000−90 000 cm^{−1} (250−110 nm). Many of the Rydberg and intravalent absorptions of the bromine electrons in the nonbonding p orbitals, which are perpendicular to the C−Br bonding axes, and the σ*←σ (C−Br) absorptions of the compounds have been assigned. A correlation of the molecular Rydberg series of methyl bromide to series in krypton, which has made possible the assignment of the 4d and 4fRydberg absorptions, is presented. Expanded vibrational progressions of the first n s and n pRydberg transitions of methylbromide are presented. The analysis of these progressions indicates that transitions to the 5s and 5pRydberg orbitals bring about a Jahn−Teller distortion of the molecule. Three n sRydberg series of methylene bromide were assigned which converge on the ionization potentials of 10.629±0.010, 10.839±0.010, and 11.261±0.010 eV. The states formed upon ionization are assigned as the b _{2}, b _{1}, and a _{1}, respectively, as the n s transitions of the a _{2} combination of bromine p orbitals are forbidden in C _{2v } symmetry. Other absorptions of methylene bromide, as well as the majority of the first n s, n p, and n d molecular Rydberg assignments of bromoform and carbon tetrabromide were made using the term values of the bands with respect to the ionization potentials of the molecules. It was found that the averaged n s term values of the bromomethanes vary slightly through the series, while the n p term values were increased in methylene bromide and bromoform. In each spectrum the assignment of the σ*←σ (C−Br) bands was made based on an empirically derived relation.

Evaporation and condensation for general gas–liquid surface scattering
View Description Hide DescriptionThe Onsager matrix for the liquid−vapor phase change of a monatomic gas in the presence of a Knudsen layer is calculated for a general gas surface sscattering law. The linearized Boltzmann equation is solved by the variational technique. The driving forces are the macroscopic pressure and temperature jumps. The calculated phenomenological coefficients show the influence of the reflection probability of the molecules on the surface and satisfy Onsager’s symmetry relation and the inequalities which follow from the fact that the entropy production rate in nonequilibrium is positive definite. In particular, the influence of the evaporation coefficient and the thermal accomodation coefficient is given. Simpler expressions are given for a generalized Maxwellian boundary condition.

Multiconfiguration self‐consistent‐field calculation of the dipole moment function and potential curve of NO(X ^{2}Π)
View Description Hide DescriptionThe electronic dipole moment function, potential energy curve, and other one−electron properties of the ^{2}Π ground state of NO have been calculated from R = 1.6 to R = 3.4 bohr by the optimized valence configurations (OVC) multiconfiguration self−consistent−field method. At internuclear separations only 0.6−0.7 bohr larger than R _{ e }, the ground statewavefunction is found to exhibit a nearly equal mixing of electronic configurations corresponding to the X ^{2}Π and B ^{2}Π states of NO. This behavior and its manifestations in the OVC framework are discussed in detail. The theoretical OVC−MCSCF dipole curve is shown to be consistent with available experimental data in that (1) its first derivative near R _{ e } of 1.10 D/bohr is in excellent agreement with that deduced from observed infrared intensities, and (2) the v = 0 dipole expectation value obtained from the computed moment function and accurate vibrational wavefunctions is −0.139 D (N^{−}O^{+}), which is within 0.02 D of the Stark effectmicrowave result of ±0.158 D. A comparison of the calculated potential curve with an accurate RKR potential for NO (X ^{2}Π) indicates relative congruency to within 0.06 eV over the full range of inernuclear separations spanning the turning points of the v = 25 vibrational level. Comparisons with previous theoretical treatments of this molecule are also presented.

Total x‐ray scattering by H_{2}
View Description Hide DescriptionFrom the Waller−Hartreee theory, the total x−ray scattering of H_{2} has been calculated with the first 10 natural orbitals of Davidson and Jones. Vibrational averaging has not been included. The calculated intensities differ by as much as 5% from a similar calculation with the Davidson and Jones SCF orbital. The accuracy of the calculations is demonstrated by agreement of 〈r _{12} ^{−1}〉 from Tavard’s sum rule with 〈r _{12} ^{−1}〉 values given by Davidson and Jones. The coherent intensities from the first 10 natural orbitals are in close agreement with the SCF results. By correcting the calculated inelastic scattered intensities for relativistic effects, the total scattering intensities from the correlated wavefunction are in excellent agreement with the experimental values of Wollan. Corresponding SCF values are significantly different. The results for molecular hydrogen encourage us to suggest more accurate gas phase measurements of total x−ray scattering by other diatomic molecules in order to determine the two electron expectation 〈r _{12} ^{−1}〉.

Spin–lattice relaxation in cross relaxed systems: Anisole
View Description Hide DescriptionSpin−lattice relaxation has been monitored as a function of temperature in liquid anisole and its partially deuterated analogues C_{6}D_{5}OCH_{3} and C_{6}H_{5}OCD_{3}, as pure liquids and in solution in C_{6}D_{5}OCD_{3}. Conventional pulse and Fourier transform techniques have been used. The high resolution spectrum of C_{6}H_{5}OCH_{3} was found to contain three groups of lines, one associated with the methyl protons, one associated with the meta phenyl protons, and one associated with the ortho and para phenyl protons. The two groups of aromatic lines were found to have, within experimental error, identical spin−lattice relaxation times and activation energies. The contribution of intermolecular interactions to the relaxation mechanism was found to decrease with increasing temperature and was ? 36% for T ? 312°K. A method is discussed for determining the cross relaxation rate between the differently relaxing methyl and phenyl spins. This method utilizes average T _{1} values for C_{6}H_{5}OCH_{3}, C_{6}D_{5}OCH_{3}, and C_{6}H_{5}OCD_{3} and yields for anisole a positive cross relaxation rate as a function of temperature. The cross relaxation is found to proceed primarily by intramolecular interactions which cause methyl and phenyl spins to flip in the same sense. Correlation times for over−all molecular tumbling are calculated and compared to results from dielectric relaxation experiments. The comparison indicates that the over−all molecular tumbling may be near to the limit of large diffusive steps discussed by Ivanov [Sov. Phys.−JETP 18, 1041 (1964)]. A correlation time for the threefold methyl reorientation is also calculated. Activation energies were found for the species C_{6}H_{5}OCH_{3}, C_{6}D_{5}OCH_{3}, and C_{6}H_{5}OCD_{3} to be 2.77±0.08, 2.78±0.23, and 3.32±0.26 kcal/mole, respectively.

Group theoretic prediction of configuration mixing effects due to Coulomb repulsions in atoms with applications to doubly‐excited spectra
View Description Hide DescriptionA group theoretical method which predicts Coulomb repulsion mixing coefficients of doubly−excited atomic states is presented. Good agreement with calculated mixings in helium is found. Two new quantum numbers and three rules classify and predict the energy level orderings. The exact mathematical construction of 1/r _{12} in the group theoretical configuration−mixed basis is given. It leads naturally to a formulation of the corresponding many−electron problem of configurational mixings.