Volume 45, Issue 8, 15 October 1966

Phase Diagrams of Sodium Nitrite and Potassium Nitrite to 40 kbar
View Description Hide DescriptionThe phase diagrams of NaNO_{2} and KNO_{2} were determined to 40 kbar. The NaNO_{2}phase diagram consists of five solid phases and the liquid. The ferroelectricCurie point (the III—II phase transition) and the Néel point (the I—II transition) were detected by differential thermal analysis (DTA) and determined to 40 kbar. The results are in good agreement with the work of Gesi and his co‐workers to 10 kbar. Points on the III—IV boundary were determined by the volume‐discontinuity method. The transition manifests itself as a break in the slope of the compression curve of NaNO_{2} and seems to be a second‐order transition. The transition pressures are lower than those estimated previously. The melting curve increases with pressure. A new high‐pressure solid‐phase, NaNO_{2} V, wad discovered. The I—V phase boundary branches off the melting curve at the liquid—I—V triple point at 9.8 kbar and 343°C.
The KNO_{2}phase diagram consists of six solid phases and the liquid. The I—II and IV—V phase boundaries, determined by DTA, rise very slowly with pressure. The II—IV, I—IV, and I—V boundaries were determined by the volume‐discontinuity method with application of piston rotation. Two new high‐pressure phases, KNO_{2} V and KNO_{2} VI, were discovered. The melting curve of KNO_{2} exhibits a maximum at 7.0 kbar and 466°C, meets the I—V boundary at a triple point at 15.2 kbar and 413°C, and then increases steeply with pressure.

Energy Levels of Er^{3+} and Pr^{3+} in Hexagonal LaBr_{3}
View Description Hide DescriptionThe spectra of Er^{3+} in LaBr_{3} are similar to, but not the same as, those of Er^{3+} in LaCl_{3}. The Stark splittings of the Y and Z groups are used to determine the crystalline‐field parameters for LaBr_{3}, which are B _{2} ^{0}=117, B _{4} ^{0}=−39.6, B _{6} ^{0}=−19.2, and B _{6} ^{6}=212 cm^{−1}. These are significantly different from those of LaCl_{3}. The centers of gravity of the excited Stark groups are higher in LaCl_{3} than in LaBr_{3}, and this shift increases with increasing wavenumber. Spectra and energy levels of Pr^{3+} in LaBr_{3} are also given.

On the Multiplicity of the Phosphorescent State of Organic Molecules
View Description Hide DescriptionThe value of the ``multiplicity'' g_{u} for use in the equation is discussed and shown to lie in the range 1 ≤g_{u} ≤∞. The value best suited to most organic compounds at 77°K is shown to be g_{u} =3. The number of emitting triplet components is shown to be readily derivable for large classes of compounds and to correlate with experiment. The effects of magnetic‐field strength on triplet component energies, on phosphorescence lifetime, on phosphorescencepolarization, and on g_{u} are calculated and shown to produce large effects in the specific case of naphthalene‐d _{8}.

Resonances in Inelastic Electron Scattering from H_{2}
View Description Hide DescriptionResonance structure in the electron scattering from H_{2} has been observed in two inelastic channels corresponding to excitation to the first and second vibration levels of H_{2}(X ^{1}Σ_{ g } ^{+}). An overlapping of resonances due to at least two H_{2} ^{−} states lying between 11 and 13 eV is apparent. The structure in the inelastic channels is compared to the observed resonance structure in the transmission channel. The resonances are found to affect the inelastic channels more strongly than the transmission channel. The excitation function for direct vibrational excitation to the v=1 level was measured near threshold and found to increase approximately linearly in this region.

Crystal Structure of the Transition‐Metal Molybdates and Tungstates. II. Diamagnetic Sc_{2}(WO_{4})_{3}
View Description Hide DescriptionSc_{2}(WO_{4})_{3}, diamagnetic above 30°K, crystallizes in the orthorhombic system, Space Group Pnca, with lattice constantsa=9.596±0.004, b=13.330±0.003, and c=9.512±0.004 Å at 298°K. The complete x‐ray scattering pattern within a reciprocal lattice hemisphere of radius (sinθ)/λ=1.02 Å^{−1} was measured with PEXRAD. The crystal structure was solved by use of three‐dimen sional Patterson and Fourier series and refined by the method of least squares, using 1731 independent structure factors. The final agreement factor R is 0.0622. Scandium atoms occupy slightly distorted octahedra, with average Sc–O=2.063 Å and Sc–O distances ranging from 2.026±0.015 to 2.124±0.010 Å. Two crystallographically independent W atoms are surrounded by somewhat distorted tetrahedra: the W–O distances vary from 1.695±0.009 to 1.829±0.016 Å, the average being 1.761 Å. The thermal vibrations are significantly anisotropic. Sc_{2}(WO_{4})_{3} forms the structure type for 23 trivalent metal tungstates and molybdates, including the nine smaller rare‐earth tungstates. The larger rare‐earth tungstates, crystallizing in the Eu_{2}(WO_{4})_{3}structure type, have 8 coordination about the rare‐earth ion; the smaller have 6 coordination. A simple correlation is found between the variation in radius ratio due to the lanthanide contraction and the change in coordination.

Upper Limits to Electric‐Field‐Induced Nuclear Magnetic Dipole—Dipole Couplings in Polar Liquids
View Description Hide DescriptionThe alignment of polar molecules in liquids by an external electric field is investigated by pulsed nuclear magnetic resonance methods. Sensitive rotating‐frame techniques are described for the detection of the expected induced nuclear magnetic dipole—dipole coupling. In no case could an induced coupling be detected. The upper experimental limits for the induced couplings disagree with the predictions of the Lorentz localfield model. For nitrobenzene and p‐nitrotoluene, disagreement is also obtained with the Onsager local‐field model by a reduction of almost an order of magnitude in the expected size of the effect. The negative results for these two compounds are indicative of strong local antiparallel ordering of the molecular electric dipoles. The induced coupling in p‐nitrotoluene, reported by Buckingham and McLauchlan using standard NMR methods, is found to be absent in this investigation, which employs a measuring technique more sensitive by at least one order of magnitude.

Shear‐Rate Dependence of the Intrinsic Viscosity of Flexible Linear Macromolecules
View Description Hide DescriptionShear‐rate dependence of the intrinsic viscosity has been studied on polystyrene in four different solvents by using a Zimm—Crothers rotational viscometer and Ubbelohde viscometers. The former viscometer was employed particularly for measuring zero‐shear intrinsic viscosity [η]_{0}. The results are summarized in terms of the [η]/[η]_{0} versus generalized rate of shear β=([η]_{0}η_{ s } M/RT)G, where η_{ s } is the solventviscosity,M the solute molecular weight, G the rate of shear, and others have usual significance. It has been found that, (i) at the values of β below 0.1, [η] is practically independent of rate of shear (or shear stress); (ii) the non‐Newtonian effect does exist even in θ conditions; and (iii) at the values of β below 2, the [η]/[η]_{0}‐vs‐β curves of the systems with different molecular weights and in different solvents give a single composite curve, which fairly well resembles to the curve of a prolate ellipsoid with the axial ratio p=3.

Flash Photolysis of Matrix‐Isolated Cyanogen Azide in Solid Nitrogen
View Description Hide DescriptionFlash photolysis combined with matrix‐isolation spectroscopy has been employed to investigate the decomposition of a cyanogen azide—nitrogen solid at 20.4°K. Two primary processes have been observed leading to the formation of NCN radicals either in an electronically excited ^{1}Δ_{ g } level or in the ^{3}Σ_{ g } ^{−}ground state. The first‐order decay of NCN (^{1}Δ_{ g }) has been studied and the mean lifetime in the solid found to be approximately 500 μsec.

Semiempirical Molecular Orbital Calculations. II. The Nonbonding Orbital, the Electronic Spectrum, and the Spin—Orbit Coupling in X_{2}CO Molecules
View Description Hide DescriptionPhosphorescence lifetimes have been calculated for the T _{1}→S _{0}(π^{*}→n) transition in formaldehyde and some of its halogen substituents. The wavefunctions used were obtained by a charge self‐consistent Wolfsberg—Helmholz method. The so‐called n orbital on the oxygen atom is mixed with carbon and halogen p orbitals to a considerable extent. As a consequence, one‐center terms on the halogens have to be considered in the evaluation of spin—orbit coupling matrix elements. The results indicate a considerable internal heavy‐atom effect on the (π^{*}→n) phosphorescence lifetimes of formaldehyde derivatives. The available experimental evidence agrees with this conclusion.

^{13}C Spin—Rotation Interaction and Magnetic Shielding at the Carbon and Oxygen Nuclei in Formaldehyde
View Description Hide DescriptionA large‐sized L‐band microwave absorbtion cell was used to observe the ^{13}C spin—rotation interaction in formaldehyde. The results yield . By making sign assumptions, the paramagnetic shielding at ^{13}C is estimated to be σ^{ p }=−215×10^{−6} compared to σ^{ p }=−730×10^{−6} at the oxygen nucleus.
Hybrid orbitals and the symmetric orthogonalization method are used to compute 10 one‐electron properties in formaldehyde to compare with the LCAO SCF results. The hybrid orbitals chosen yield slightly better agreement with experiment than the SCF functions. However, the minimal basis set used here and in the SCF functions does not allow enough flexibility to fit all of the observables within the experimental error. Reasonable values of the carbon and oxygen diamagnetic shielding are chosen on the basis of the calculations and are combined with the ^{13}C spin—rotation constants in this paper and the ^{17}O spin—rotation constants in a previous work to yield the absolute shielding at the carbon and oxygen nuclei in formaldehyde. The values for the total magnetic shielding in formaldehyde are σ(carbon)=125×10^{−6} and σ(oxygen)=−268×10^{−6}.
The ^{17}O–^{12}C spectrum in the literature is reinterpreted to yield the ^{17}O spin—rotation interaction in that molecule. Our interpretation for ^{17}O–^{12}C yields χ_{ aa }=4.43±0.10 Mc/sec and M_{bb} =29±10 kc/sec. The ^{17}O spin—rotation information is combined with a recent calculation of the oxygen diamagnetic shielding in CO to yield the absolute shielding at the oxygen nucleus which is σ_{Av}=−14×10^{−6}.

Calculation of One‐Electron Properties for the Formaldehyde Molecule with the LCAO MO SCF Function of Foster and Boys
View Description Hide DescriptionUsing the approximate molecular orbital wavefunction of Foster and Boys, we have calculated the expectation values of 12 one‐electron operators: diamagnetic susceptibility, dipole moment,protondiamagnetic shielding, electric‐field‐gradient tensor components at the oxygen and deuteron nuclei, and forces at the oxygen, carbon, and hydrogen nuclei. Several methods for evaluating the molecular integrals for these various one‐electron operators were employed. Since the one‐electron operators sample the electronic distribution differently in various regions of the molecule, the calculation of these molecular properties should provide a critical test of the accuracy of the predicted charge distribution. Some of the results are in fairly good agreement with experiment, but many are off by a factor of 2 or more.

Microwave Absorption and Molecular Structure in Liquids. LXVII. The Dielectric Behavior of Mixtures of Two Polar Components
View Description Hide DescriptionDielectric constants and losses have been measured at wavelengths of 575 m, 10.1 cm, 3.22 cm, 1.22 cm and 2.2 mm for eight binary mixtures of benzophenone, 2‐chloronaphthalene, 4‐iodobiphenyl, tetrahydrofuran, chloroform, and pyridine. Three of these mixtures have also been measured in dilute benzene solutions. The dielectric data for each mixture have been analyzed in terms of two superimposed Debye regions. In each case there is evidence of two distinct relaxation times corresponding to the two polar components. The effect of weak hydrogen bonding between benzophenone and chloroform has been found in their binary mixtures, but in ternary mixtures with benzene the relaxation of one polar component is independent of the other. The relaxation times in the binary mixtures are closely related to the relaxation times of the pure components.

Morphology of Ice Dendrites
View Description Hide DescriptionThe morphology of ice crystals produced in supercooled aqueous solutions is described. A freely growingice dendrite in distilled water propagates in the direction and has the shape of a very thin flat sheet. The first examples of dendrites which grow in an irrational crystallographic direction, best described as , have been produced in aqueous solutions. The value of Z has been found to vary between 0 and 0.35, depending upon amount of supercooling, the solute, and solute concentration. Growth of ice upon a substrate is of a very complex nature with numerous grain boundaries and a varying orientation relative to the substrate.

Growth Rate of Ice Dendrites in Aqueous Solutions
View Description Hide DescriptionThe free‐growth rate and substrate growth rates of ice dendrites in aqueous solutions as a function of supercooling Δ_{ T } and solute concentration are presented. The free‐growth rate ν in distilled water was found to be ν=0.228(Δ_{ T })^{2.39} mm/sec. In distilled water having 2° to 4°C supercooling, growth upon a substrate was as much as an order of magnitude faster. Solutes in a concentration on the order of 0.01 moles/liter produced a slight increase in the free‐growth rate, while at greater concentration the growth rate decreased.

On the Activation Energies of Diffusion
View Description Hide DescriptionThe self‐diffusional activation energies of liquid ethane have been calculated. In accordance with Dienes' suggestions, the effective activation energy depends nonlinearly upon the temperature. The Gibbs free‐energy change is found to be a strong function of temperature going through a pronounced maximum in the close vicinity of the critical point.

Statistical Thermodynamics of Polymer Solutions. V. Interactions between Geometrically Dissimilar Polymer Chains in a Poor Solvent
View Description Hide DescriptionBy the standard perturbation technique of Zimm, the second virial coefficient A _{2} is calculated in the ``double‐contact'' approximation for mixtures of two polymers in a single solvent. The two solute molecules are alike chemically, but they differ in size (molecular weight) and/or geometry (in the sense of straight‐chain, branched, or closed‐ring architecture). From investigation of a number of pairs of species, some tentative generalizations emerge on limiting behavior for A _{2} small but positive, i.e., near, but above, the theta temperature. If the two polymer molecules have exactly the same structure and differ only in size (e.g., two straight chains of different molecular weight, two ring molecules of different weight), the virial coefficient, as measured by either osmotic pressure or light scattering, is always a monotone function of the proportions of the two components in the mixed solute; but when the models are different, there can exist a range of relative molecular weights of the two solutes within which A _{2} passes through a maximum as a function of composition. A minimum is never found.

Interaction of Oxygen with Hot Tungsten
View Description Hide DescriptionThe reaction of oxygen at a polycrystallinetungstensurface has been studied over a temperature range from 1300° to 2450°K and for oxygen pressures from ∼10^{−5} to ∼10^{−8} torr. A mass spectrometer was used to measure the oxygen pressure. In determining absolute pressures care was taken to avoid errors which may arise due to spurious currents in a Bayard—Alpert ion gauge. The efficiency of removal of carbon impurity from tungsten, by heating in oxygen, was determined. After obtaining a low carbon content, the rates of removal of oxygen at the tungstensurface were determined as a function of temperature. At temperatures below ∼2000°K evaporation of oxides of tungsten occurs at predictable rates. At higher temperatures atomic oxygen is produced and the observed rate of removal of oxygen is strongly influenced by the specific surfaces present in the entire system. For example, a silversurface efficiently reacts with oxygen atoms, without apparent saturation, to give a large apparent increase in the pumping speed at a tungstensurface enclosed in a glass system.

Use of Hellmann—Feynman and Hypervirial Theorems to Obtain Anharmonic Vibration—Rotation Expectation Values and Their Application to Gas Diffraction
View Description Hide DescriptionA recursion relation for the moments of the probability function for a one‐dimensional anharmonic oscillator are derived by using a hypervirial relation. In addition it is shown that the first few moments of the probability function can be easily obtained by use of Hellmann—Feynman, virial, and Ehrenfest's theorems if the vibrational—rotational energy is known as a function of the anharmonic force constants. Expressions for the first four moments of a potential function containing cubic and quartic anharmonic terms are given by use of Dunham's expression for the vibrational energy. The application of anharmonic moments in gas electron diffraction is considered in detail.

Electron Spin Resonance of Met‐Myoglobin: Field Dependence of g⊥^{eff}
View Description Hide DescriptionThe spin Hamiltonian for high‐spin Fe^{3+} in single crystals of met‐myoglobin has the form . In view of the large value of D the only ESR signal that can be observed is the transition from the m_{s} =—½ to m_{s} =+½ states. The resonance condition for the ground doublet is described by g ^{eff}βH=hν. When the magnetic field is applied along the z axis g∥^{eff}=g∥ and when the magnetic field is applied perpendicular to the z axis . Through measurement of g⊥^{eff} and g∥^{eff} at 13 and 35 Gc/sec the spin‐Hamiltonian parameters were found to be g∥=2.002±0.001, g⊥=1.985±0.002, and 2D=8.76±1.2, cm^{−1}.
These results are interpreted by replacing the pure 3dwavefunctions from which the (3d)^{5} electronic configuration of Fe^{3+} is usually formed by covalent molecular orbitals which are only part 3d. The values for g∥, g⊥, and D can be explained in terms of a single low‐lying pure antibonding state of ^{4} A _{2} symmetry 2000 cm^{−1} above the ^{6} A _{1}ground state and coupled to it by the spin—orbit interaction. Numerical agreement between theory and experiment requires molecular orbits which have an average 3d character of only 68%. These highly covalent orbitals are in very good agreement with the theoretical results of Zerner and Gouterman.

Geometry of Molecules. II. Diborane and Ethane
View Description Hide DescriptionThe diborane molecule has been investigated in its equilibrium D _{2h } geometry, in the D _{3d } (ethane) structure, and three intermediate configurations. Charge‐contour diagrams show that the electron distribution between the boron nuclei is considerably less concentrated than in the boron—bridge‐hydrogen bonds. Calculations for ethane in both equilibrium and bridged‐hydrogen configurations show that the carbonp functions of C_{2}H_{6} play a much greater role in molecular binding than those of boron in B_{2}H_{6} and this fact explains their different geometry.