Volume 25, Issue 6, 01 December 1956

High‐Temperature Thermodynamic Properties of Uranium Dioxide
View Description Hide DescriptionEffusion measurements have been carried out with uranium dioxide over a temperature range from 1600° to 2800°K and a pressure range from 10^{—8} to 6 mm. Four different isotopic compositions, three different effusion cells and two different apparatuses were used. The results are concordant and demonstrate that the oxide vaporizes congruently in this range. The cubic (fluorite)lattice parameter of the congruently vaporizing composition, UO_{2.00}, is 5.4588±0.0002kX.‡ All higher oxides will yield UO_{2.00} when heated above 1300°C in a vacuum of 10^{—6} mm Hg. A least‐squares analysis of the data yields for the total volatility, calculated as the dioxide, the equation,and reveals a pronounced positive curvature at the higher temperatures. It is doubtful that this curvature arises from a deviation of the flow rate from that predicted by kinetic theory, and hence it must be caused by two vaporization processes. The volatility of a uranium and uranium dioxide mixture shows that no gaseous suboxides are important. The principal vapor species at the lower temperatures (1600–2000°K) is undoubtedly UO_{2} for which the vapor pressure is given byThe heat and entropy of sublimation are 137.1±1.7 kcal/mole and 36.4±0.9 eu at 1800°K and 159.6 kcal/mole and 49.4 eu at 298°K. The heat of sublimation at absolute zero is estimated to be 160 kcal/mole with an estimated uncertainty of 5 kcal/mole. This value leads to 14.4 ev for the dissociation energy for gaseous UO_{2}. The positive curvature cannot be caused by solid monoxide or gaseous UO_{3} on the basis of existing thermodynamic data. It is postulated that the curvature is caused by a dimer U_{2}O_{4}(g) which becomes important at the high temperatures. Its vapor pressure is represented byThe heat and entropy of dissociation of the dimer are 88.9 kcal/mole and 16.6 eu at 2450°K. Crude absolute entropy calculations indicate this entropy change to be reasonable.

Modified Atomic Orbital Method. II. The Electronic Structure of the Oxygen Molecule
View Description Hide DescriptionA modified form of the nonempirical atomic orbital method, shown previously to be considerably successful in calculating the electronic energy levels of the ethylene molecule, is now applied to the computation of the lower excited π‐electron levels of the oxygen molecule. The results of the calculation are again satisfactory in that they are almost as good as those obtained by the semiempirical methods of Moffitt and of Fumi and Parr.

Color Centers and Luminescence in Single Crystals of Lanthanum Trichloride Containing Dipositive Europium
View Description Hide DescriptionThe edge of the fundamental absorption band in pure LaCl_{3} is at about 2250 A. There is no change in the absorptionspectrum of pure LaCl_{3} in the range 2250 to 25 000 A on exposure at room temperature to 10^{7}r of gamma rays from a Co^{60} source. The crystals do not luminesce after such treatment.
In contradistinction, LaCl_{3} containing small amounts of europium exhibits a blue luminescence and thermoluminescence when exposed to ultraviolet or gamma radiation. The luminescent properties are profoundly influenced by long continued gamma irradiation. In addition, color centers are formed which absorb visible radiation.
Chemical as well as paramagnetic resonance experiments show that all of these effects are due to the presence in the LaCl_{3} lattice of dispositive europium. There are at least three different color centers giving rise to three overlapping absorption bands which decay thermally with different rates. The maxima of the absorption bands are at 8000, 6500, and 5500 A. Studies with polarized light show that the color center transitions are all electric dipole in nature and are highly anisotropic. The most intense band has been tentatively identified with an F‐center‐like s→p transition.
Experiments on the thermal decay of the color bands and the glow curve of the crystal indicate that an intimate relationship exists between the color center and the luminescence phenomena.
It is suggested that when these crystals are irradiated, dipositive europium loses an electron to become tripositive, the electron being captured by an anion vacancy to form a color center. On thermal freeing of the electron, return to the ground state is accompanied by the emission of visible radiation.

Electronic Spectrum and Structure of Azulene
View Description Hide DescriptionA previously given theoretical method is applied to the azulene molecule. π‐electron energies, transtion moments, dipole moments, charge distributions, and bond orders are calculated for the ground state and for the lower singlet and triplet excited states.
The same detailed procedure which had previously given good results for the polyacenes is used here. Configuration interaction is included for all singly excited configurations. Two parallel calculations, one starting with conventional Hückel MOs and the other with perimeter MOs, are carried through.
Hückel MOs lead to numerical results in good agreement with available experimental spectral data. In this connection some previous assignments are confirmed and some new ones are proposed. For the π‐electron dipole moment for the ground state, one calculates 1.88 D with Hückel MOs and 3.36 D with perimeter MOs; the experimental value is 1 D.
One may conclude that the present procedure gives results in substantial agreement with experiment provided that good MOs, e.g., Hückel MOs, are employed. For computation of excited state energies it is essential to include interaction among nearly degenerate configurations. More extensive configuration interaction, however, appears to improve the transition energies and especially the transition moments and dipole moments.

Theory of Rotational‐Vibrational Interaction in Polyatomic Molecules
View Description Hide DescriptionGroup theoretical considerations show that an eigenfunction of the Schroedinger equation for a polyatomic molecule may be written as a sum of products of representation coefficients of the group of three‐dimensional rotations and functions which depend only upon the relative configuration of the atoms and hence only upon the normal coordinates. A perturbation solution of the Schroedinger equation is described which is based on zero‐order wave functions which are consistent with this group theoretical result. All of the angular momentum operators appearing in the wave equation are shown to be recursion operators in the representation coefficients. Subsequent utilization of the orthogonality of the representation coefficients then leads to a set of coupled differential equations for the functions which depend only on the normal coordinates. This set of coupled differential equations is a generalization of the matrix equations for the rotational motion of a rigid body.
The functions of the normal coordinates are then expanded as sums of products of Hermite functions of the individual normal coordinates. Use of the orthogonality relations of the Hermite functions then yields a set of equations for the expansion coefficients. The eigenvalues of the associated matrix are then, of course, the exact rotational‐vibrational energy levels of the polyatomic molecule. These energy levels are obtained approximately by a diagonalization in the rotational quantum numbers followed by a perturbation technique in which the coupling between vibrational levels is assumed to be small (except in the case of degeneracy). The lowest approximation to the energy levels contains terms which may be interpreted as due to coupling effects which in previous solutions appear only in higher order approximations.

Crystal Structure of Barium and Europium at 293, 78, and 5°K
View Description Hide DescriptionReasons are reviewed for suspecting that it may be possible to induce phase transformations in barium and europium. X‐ray diffraction patterns at 78°K and 5°K, however, revealed no transformation from the normal body‐centered cubic structure; there was none, also, after cold work at 5°K. The lattice constants at 5°K are 4.551±0.003 A for europium, 5.000±0.002 A for barium.

Modification of the Vector Model to Include a First‐Order Nonorthogonality Correction
View Description Hide DescriptionWhen the vector model is used to describe chemical bonding it appears that the orbitals participating in bond formation are required to be orthogonal. The success of the model on an empirical basis is puzzling because chemical bonding will not occur without overlap. In the present work the many‐electron functions, consisting of products of appropriately overlapping ordinary atomic orbitals, are orthogonalized. The characteristic simple form of the model is then retained provided that the exchange integral is replaced by a corrected exchange integral called a bond integral. The success of the model becomes less puzzling because this integral is usually evaluated empirically. The nature of the bond integral is examined in the framework of the Heitler‐London treatment of the hydrogen molecule.

Infrared Spectrum and Structure of Perchlorylfluoride
View Description Hide DescriptionThe infrared spectrum of gaseous perchlorylfluoride, ClO_{3}F, has been obtained over the range 3–43 μ. A satisfactory assignment has been achieved on the basis of a C _{3v } model in which the four peripheral atoms are each bonded to the central chlorine. The a _{1} fundamentals occur at 1061, 715, and 549 cm^{—1}; the e fundamentals are found at 1315, 589, and 405 cm^{—1}. The stability of the C _{3v } structure for ClO_{3}F is discussed with reference to ClO_{4} ^{—} and related molecules.

Infrared Spectrum of Hydrogen Sulfide
View Description Hide DescriptionThe absorption of hydrogen sulfide has been investigated in the 8 μ region under high resolution. The absorption has been analyzed as a B‐type band and assigned as the (n _{1},n _{2},n _{3})=(0,1,0) band. The resulting inertial constants agree well with those predicted from previously analyzed bands. The best values of the constants for this band are, v _{0}=1182.68 cm^{—1}, A=10.724, B=9.211, C=4.670. The knowledge of this band center, together with previously determined frequencies, enable the evaluation of the constants in the quadratic expression for the vibrational energy. A second‐order resonance was found which arises from the near coincidence of the frequencies v _{1} and v _{3}.

Hydrogen as a Donor in Zinc Oxide
View Description Hide DescriptionHydrogen is found to diffuse into and increase the conductivity of single ZnO crystals. The diffusion rates have been obtained, as well as the temperature and pressure dependencies of the quantity of hydrogen in the crystal. This quantity is found to be influenced by the electrons already in the crystal. It is thought likely that hydroxyl groups are formed from the hydrogen and oxide ions. The donor center has an ionization energy of 0.04 ev.

Importance of Doubly Excited Configurations in the Interpretation of Electronic Spectra
View Description Hide DescriptionAn investigation has been carried out to determine the importance of doubly excited configurations in calculating the energies of the electronic states of an aromatic hydrocarbon. It is found that the calculated low energy states of benzene are largely unaffected by consideration of doubly excited states, except for the appearance of an E _{2g } state with energy comparable to that of the E _{1u } states. In addition, inductive and mesomeric shifts in the lowest energy (α) transition have been calculated for all the distinct positions of substitution in benzene, in terms of two parameters which depend on the substituent. It is seen that the inclusion of doubly excited states in the calculation is necessary in order to predict these effects reliably.

Delta‐Function Model. I. Electronic Energies of Hydrogen‐Like Atoms and Diatomic Molecules
View Description Hide DescriptionThe electron in a one‐electron atom or diatomic molecule is considered to move in one dimension on a line through the nuclei. The potential energy is taken as zero except at the nuclei where it goes to minus infinity as negative delta functions. The exact solution is easily obtained with the wave function accurately expressible as a linear combination of atomic orbitals. In contrast to the free electron model this method handles heteronuclear molecules, does not arbitrarily limit the coordinate, and can predict ionization energies.

Delta‐Potential Function Model. II. Aromatic Hydrocarbons
View Description Hide DescriptionThe pi electrons are considered as following a one‐dimensional network through the molecule as in the free electron model. The potential energy is taken as zero everywhere except at each pi‐carbon nucleus where it goes to minus infinity as a negative delta function. By a procedure of linear combination of atomic orbitals, suitably defined, exact solutions of the Schrödinger equation are easily obtained. Negative one‐electron energy levels, of which there may be as many as there are pi‐carbon nuclei, are interpreted as bound states, with energy zero or positive as ionized states.
This model stands between the free electron model on the one hand and the LCAO molecular orbital model on the other. It goes beyond the former in that it can predict not only excitation energies and resonance energies, but also ionization potentials. It surpasses the latter in that exact solutions are obtainable. Numerical results are qualitatively of the right order of magnitude after adjustment of the strength of the delta function which is the one and only variable parameter.

Application of Probability Theory to Explosive‐Ignition Phenomena
View Description Hide DescriptionThe problem of explosive ignition concerns itself both with the probability of occurrence of local energy fluctuations and with the transition of these disturbances into a combustion or detonation wave. The former concept does not appear to have been comprehensively discussed; a treatment of this process is presented here for the case of fluctuations due to frictional forces.
The theory is applied to several cases of impact ignition, both with and without grit particles and it is found to be in good agreement with experiment. Information is obtained through application of the theory concerning the nature and location of the local disturbances responsible for ignition.

Isothermal Calorimeter and the Heat of Mixing of Iso‐Octane‐Perfluoroheptane Solutions
View Description Hide DescriptionAn isothermal calorimeter for measuring heats of mixing of binary solutions has been designed. The instrument utilizes twin calorimeters to eliminate troublesome corrections and a pair of differential thermistors for controlling the electrical circuit. There is no vapor space and the rate of mixing is controlled so that the heat absorbed is automatically compensated and the maximum temperature change is of the order of 0.001° to 0.002°C. This is accomplished by a differential bridge.
The heats of mixing of perfluoroheptane and isooctane were measured and the results compared with the values calculated from vapor pressuremeasurements.

Infrared Investigation of Acetic Acid and Acetic Acid‐d Vapors and a Vibrational Assignment for the Monomeric Acids
View Description Hide DescriptionThe infrared spectra of acetic acid and acetic acid‐d, as vapors at 150°C, have been obtained from 2–25μ and an assignment of the fundamental vibrational frequencies made for the monomeric acids, with the exception of the two low lying type A″ torsional frequencies. Infrared spectra of the two acids, in the vapor phase, have also been obtained over the 5–15μ region at 25°, 65°, 105°, and 150° and the effect of temperature on some of the frequencies discussed.

Pure Rotational Spectra of CO, NO, and N_{2}O between 100 and 600 Microns
View Description Hide DescriptionThe pure rotational absorption lines of carbon monoxide (CO) for J = 3 to J = 23, of nitrous oxide (N_{2}O) for J = 19 to J = 40, and of nitric oxide (NO) for J = 5½ to J = 24½ have been observed for the first time. The possibility of using lines of CO and N_{2}O for calibrating a far infrared spectrograph is considered. The pure rotational absorptionspectrum of NO yields rotational constants of the molecule in the ground state.

Properties of a Cadmium Sulfide Photorectifier
View Description Hide DescriptionMeasurements on a CdS photorectifier show it to have a high resistance in both the forward and reverse directions in the dark. Under illumination considerable conductivity in the forward direction is observed. Light to dark current ratios of 10^{6} have been observed. The spectral response of the cell shows two peaks, one at the absorption cutoff the other at 5600 A with the sensitivity tailing off toward the red and infrared. The gain of the cell measured as a function of radiation intensity can be expressed empirically as a double exponential. The mechanism of the cell is explained on the basis of a model involving the formation of a quasi‐intrinsic region by diffusion of the barrier into the crystal.

Energy Levels of the Coaxial Internal Rotator with Rectangular Potential Function
View Description Hide DescriptionFor the coaxial internal rotator with rectangular potential function and freely variable valley breadth at constant periodicity, conditions are specified for an infinite number of points at which the borders of consecutive bands of energy levels must be exactly degenerate. As the valley breadth is changed through a degeneracy, the level of one symmetry relative to the potential function moves from the upper to the lower band of energy levels, or vice versa.
It follows that in the rotational region above the potential maximum the levels at the band limits can repeatedly cross and re‐cross when the potential maximum is increased with all other factors constant.
Similar behavior will presumably occur with other potential functions.

Infrared Absorption of Lanthanum, Scandium, and Indium Borate and the Force Constants of Borate Ion
View Description Hide DescriptionThe infrared absorption spectra of LaBO_{3}, InBO_{3}, and ScBO_{3} have been observed as crystalline powders in the wavelength range from 7 to 20 microns. The borates had a B^{10}/B^{11} ratio varying from the natural abundance (18/82) up to about 96/4. The four fundamental frequencies for B^{10} fell within the ranges, ω_{1} = 939, ω_{2} = 740–790, ω_{3} = 1265–1330, ω_{4} = 606–675, all in cm^{—1}. The totally symmetric frequency, ω_{1} is observed only in LaBO_{3}, which has less than threefold site symmetry, unlike the other two salts.
The GVF force constants have been calculated and are compared with those of BF_{3}. A very strong specific coupling of the out‐of‐plane bending mode (ω_{2}) is observed in LaBO_{3}, but the fine structure is not well resolved, and only a rough estimate of the coupling constant and dipole derivative can be made.