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Volume 40, Issue 10, 15 May 1964
40(1964); http://dx.doi.org/10.1063/1.1724903View Description Hide Description
In the following article the absorption and emission spectra of CaF2:Er3+ are presented, discussed, and analyzed phenomenologically. The crystalline states are listed and identified with the free ion quantum numbers by comparison with the states of erbium chloride. The oscillator strengths are determined from the absorbance spectrum and compared with the oscillator strengths reported in the literature. The study of the emission properties of the erbium ion in CaF2 includes identification of transition schemes for the major emission groups from their excitation spectra,measurements of relative intensities, decay times of fluorescence, and quantum efficiencies. The natural lifetimes and fluorescence yields were calculated using data obtained from the absorbance spectrum. By combining data obtained from the absorption and emission spectra at 77° and 4°K, the crystalline field splitting of the ground 4 I 15/2 multiplet was determined. The wavelengths of all emission lines at 77°K are presented, including those whose origin could not be identified. The effects of temperature and ion concentration are discussed. All pertinent data are given in a table form. The important features of the absorption and emission spectra are amply illustrated by figures, graphs, and tables. In addition to the purely spectroscopic properties of CaF2:Er3+, its properties as a potential laser material are considered and discussed. The discussion is complemented by calculation of the threshold power requirements.
40(1964); http://dx.doi.org/10.1063/1.1724904View Description Hide Description
ESR and optical bleaching studies of n‐amyl disulfide, γ‐irradiated at 77°K in the amorphous state indicate the presence of ionic paramagnetic species in the irradiated material involving unpaired spins localized mainly at the sulfur. A comparison of ESR derivative peak positions from such samples with those arising from an apparent negative ion species produced from amyl disulfide in a tetrahydrofuran matrix indicates that this species may be common to both types of samples. This finding is supported by the fact that the threshold energy for the destruction of the ionic centers by optical bleaching is the same for both types of samples, being 2.1±0.2 eV. If the ESR spectrum of the negative‐ion species is substracted from the initial ionic species spectrum of amorphous amyl disulfide an ESRline shape is obtained which is postulated to result from a positive‐ion species. The principal g values obtained for this species are 2.003±0.001, 2.035±0.001, and approximately 2.018. Calculated g values based on a model in which the electron hole is localized on a nonbonding 3p sulfur orbital are in qualitative agreement with the observed g values. The The negative‐ion species appearing to be common to both types of samples exhibits an axially symmetric gtensor (g‖ = 2.003±0.001, g ⊥ = 2.022±0.001). This gtensor symmetry is obtained theoretically using a model in which the unpaired spin is in 3dσ bonding orbitals associated with both sulfurs.
40(1964); http://dx.doi.org/10.1063/1.1724905View Description Hide Description
The conditions that a set of molecular electronic wavefunctions for different nuclear configurations be optimized by incorporation of scale factors, in general different for each wavefunction of the starting set, are derived. The relationship of these conditions to the quantum‐mechanical virial theorem in Born—Oppenheimer approximation is pointed out. The quantitative effects of such optimization on a set of accurate wavefunctions for the hydrogen molecule and a partially optimized single‐configuration molecular‐orbital wavefunction for lithium fluoride are discussed. Expectation values and spectroscopic constants are investigated in detail. It is shown that as the total molecular energy decreases, the quantitative effects of scaling will become progressively smaller. A further conclusion is that, for sets of unscaled diatomic‐molecule wavefunctions only partially optimized, curves for kinetic energy and potential energy of the system as a function of internuclear separation are more accurately obtained from the total molecular‐energy curve by use of the virial theorem than by use of computed mean values.
40(1964); http://dx.doi.org/10.1063/1.1724906View Description Hide Description
Shock structure measurements were made on O2 in a 24‐in. diameter shock tube at initial pressures of 15 and 30 μ of Hg from Mach 4 to 21. An ultraviolet absorption technique using 1470‐Å radiation was employed to monitor the density of O2 molecules. In order to reduce shock front curvature effects, the knife‐edge technique was employed using only a 4‐in. optical path between knife edges. The data indicate that translational and rotational degrees of freedom are excited simultaneously. At about Mach 10 vibrational excitation begins to appear in the same zone as translational and rotational excitation; by Mach 14 all these processes occur simultaneously. Around Mach 16 dissociation starts to occur in the same zone. The thickness of the shock front decreases from three ambient mean free paths at Mach 4 to 2 ambient mean free paths at Mach 10 and remains essentially constant at higher Mach numbers.
40(1964); http://dx.doi.org/10.1063/1.1724907View Description Hide Description
The luminescence spectrum of europium tris‐hexafluoroacetylacetonate in various solutions is presented. While the presence of moisture has a marked effect on the spectral appearance of luminescence near 6100 Å, it does not appear to influence the long‐lived phosphorescence near 4500 Å. The presence of this blue phosphorescence poses some questions regarding the rates of various energy‐transfer processes.
40(1964); http://dx.doi.org/10.1063/1.1724908View Description Hide Description
Optical techniques have been used to study the condensation of water vapor on the inside surface of a glass section of a shock tube. Because of the thermal boundary layer, the gas (pure water vapor) at the walls experienced essentially an isothermal compression. By adjusting the initial conditions of the experiments, supersaturation of the water vapor was obtainable. The use of a shock tube resulted in very rapid compressions, permitting measurements to be made on a time scale the order of microseconds. This is a much faster time scale than has been reported by other investigators of condensation processes. The results of these measurements showed that the condensation process was very sensitive to the nature of the surface. For clean hydrophilicsurfaces it was found that condensation occurred in the form of discrete droplets having an average radius of the order of about 0.2 μ, until at least about 100 μsec after compression. Hydrophobicsurfaces produced condensation in the form of a continuous film. After reaching a thickness of about 100 Å in about 10 μsec after compression, the film appeared to begin to break up into many small droplets. The thin films of condensate were studied by measuring their optical transmissivity. The droplets were studied by making use of their light‐scattering properties. The results of the measurements are shown to be in agreement with mechanisms of the condensation process suggested by other authors.
Polyhedral Clathrate Hydrates. VII. Structure of the Monoclinic Form of the Tri‐n‐Butyl Sulfonium Fluoride Hydrate40(1964); http://dx.doi.org/10.1063/1.1724909View Description Hide Description
The monoclinic form of the clathrate hydrate of (n‐C4H9)3S+F— has 23 H2O per guest cation, as determined by a complete three‐dimensional crystal‐structure analysis.
The water framework consists of sheets of face‐sharing pentagonal dodecahedra, separated by layers of hydrogen‐bonded water molecules and anions containing large and irregular cavities in which the sulfonium ions are located. These cations are pyramidal in configuration and occupy the large cavities in pairs, with a S+–S+ nearest‐neighbor distance of 3.49 Å.
40(1964); http://dx.doi.org/10.1063/1.1724910View Description Hide Description
The vibrational energy transfer between an atom and an atomic oscillator is considered for a Morse potential interaction, from the point of view of thermal accommodation coefficient theory. An expression is obtained for the transition probabilities for the exchange of one quantum of energy. A comparison is made with the semiclassical theory. Inconsistencies in the literature are noted and discussed.
40(1964); http://dx.doi.org/10.1063/1.1724911View Description Hide Description
The probability of vibrational energy exchange in a molecular collision can be calculated using (1) a wave‐mechanical treatment using the method of ``distorted waves,'' (2) a semiclassical time‐dependent perturbation procedure in which the perturbationenergy is obtained as a function of time from the classical collision trajectory, and (3) a purely classical calculation of the energy transferred to a classical vibrator. These methods are reviewed, related, and compared.
40(1964); http://dx.doi.org/10.1063/1.1724912View Description Hide Description
By assuming the additivity of bond polarizabilities, a formal expression is derived for the difference Δγ in principal polarizabilities of a real polymer chain having constant end‐to‐end distance r. The expression is given as a series in powers of r 2, whose coefficients are functions of the differences α1κ—α2κ in principal polarizabilities of constituent bonds, 〈r 2k 〉, and 〈r 2k cos2Φ iκ〉, (k≥1). Here, Φ iκ is the angle between the end‐to‐end vector and the unit vector along the κth bond of the ith structural unit, and the averages refer to those about a polymer chain in free state. It is shown that if r 2 is in magnitude of the same order as 〈r 2〉, at the limit of infinite chain length the expression reduces towhere 〈r 2〉* is such a part of 〈r 2〉 as proportional to chain length.
The difference in principal polarizabilities of the ``equivalent random link'' is shown to beAn expression in a matrix form is derived for ΔΓ of the polyethylene chain. Numerical computations are made by a digital computer, using two geometrical models for this molecule recently proposed by Hoeve and by Nagai and Ishikawa, and also using Denbigh's and Bunn and Daubeny's values for bond polarizabilities. It is found that a good agreement is obtained between predictions of the theory and experimental values if Denbigh's values are used.
40(1964); http://dx.doi.org/10.1063/1.1724913View Description Hide Description
The first‐order density matrix is obtained for the state corresponding to a spin projection of a general different orbitals for different spins single determinental function. Explicit expressions are given for the natural orbitals and occupation numbers in terms of parameters characteristic of the unprojected state. The spin density and the charge density matrices are found to have the same natural orbitals in the projected state as in the unprojected state. A number of special and limiting cases are considered, including that of slightly different orbitals for different spins.
Organic Liquid Scintillators. VI. Substituted Distyrylbenzenes: Scintillation Properties and Spectra of Absorption and Fluorescence40(1964); http://dx.doi.org/10.1063/1.1724914View Description Hide Description
The preparation, spectra of absorption and fluorescence, and the scintillation properties of 28 derivatives of trans,trans‐p‐distyrylbenzene are described.
Most of the soluble derivatives are efficient primary scintillators in alkylbenzene solutions and are highly efficient secondary scintillators in alkylbenzene solution of p‐terphenyl. Solutions with efficiencies exceeding those of the best‐reported liquid scintillation systems are described.
40(1964); http://dx.doi.org/10.1063/1.1724915View Description Hide Description
An analysis of the mechanics of three‐body ion recombination is given. The relative efficiencies of various gases in promoting ion recombination are calculated and found to be in satisfactory agreement with experiment. The calculations lead to qualitative conclusions about how mass, relative velocity, and the nature of the deactivation criterion affect the magnitude of the recombination rate.
40(1964); http://dx.doi.org/10.1063/1.1724917View Description Hide Description
Ground‐state wavefunctions for CH4 have been calculated using the self‐consistent molecular orbital method of Roothaan. The molecular orbitals have been represented by linear combinations of atomic exponential orbital functions. The size of the basis set has been varied over wide limits; total energies, wave‐functions, and one‐electron energies are given for these cases.
40(1964); http://dx.doi.org/10.1063/1.1724918View Description Hide Description
The photoconductive sensitivity of additively colored KCl during bleaching of the F band has been measured at temperatures between —30°C and room temperature. At —30° and —15°C, a pronounced increase in sensitivity occurs during the early stages of bleaching which indicates the presence of traps of large cross section, unstable at higher temperatures. Estimated cross sections, combined with trap concentrations deduced from optical data, are used to account for the general form of the dependence of sensitivity upon exposure.
40(1964); http://dx.doi.org/10.1063/1.1724919View Description Hide Description
The formalism for a ``supercell'' theory of liquids is presented. Conceptually, it is analogous to the scheme employed by Kirkwood in ``justifying'' the single‐occupancy cell theory of Lennard‐Jones and Devonshire. The attractive feature of the theory lies in its ability to handle the large density fluctuations which the single‐occupancy theory is unable to treat adequately. The derivation of the numerically successful tunnel theory of Barker from our generalized supercell formalism by means of a certain number of well‐defined approximations is given.
40(1964); http://dx.doi.org/10.1063/1.1724920View Description Hide Description
Vacancies in graphite crystals can be rendered visible for electron microscopy by a technique which combines cleaving, etching, and decorating. The crystals are cleaved, and the vacant lattice sites in the exposed surface are attacked by a mixture of chlorine and oxygen, which expands these vacancies into monolayer loops of any desired diameter. These loops are decorated with gold to enhance their contrast. Numerous tests have established that the loop concentration is a quantitative measure of the vacancy concentration. The method is capable of determining vacancies at concentrations at least as low as 10—10 per carbon atom. The relative chemical reactivities of carbon atoms surrounding a vacancy, of carbon atoms at the edges of layers and of carbon atoms within layers have been measured.
40(1964); http://dx.doi.org/10.1063/1.1724921View Description Hide Description
The vapor pressures of LiF, LiCl, MgF2, and MgCl2 have been measured by the torsion‐effusion method. The lithium halide vaporization data have been analyzed to yield heats of sublimation of monomer and dimer species which are consistent with available data on vapor composition, heats of dimerization, and the normal boiling points. Derived heats of sublimation of monomer and dimer at 298°K are 66.5 and 71.6 kcal/mole for LiF and 51.0 and 52.0 kcal/mole for LiCl, respectively. An analysis of the data obtained here and other vaporization data on the magnesium halides indicates that the available entropy and free‐energy functions for MgF2(g) and MgCl2(g) may be low by 4 to 5 cal/mole deg. Possible reasons for the discrepancy are discussed. The heats of sublimation of MgF2(g) and MgCl2(g) at 298°K are calculated to be 93 and 59 kcal/mole, respectively.
Nuclear Magnetic Resonance in Molten Salts. I. Chemical Shift of Crystalline and Molten Thallium Salts40(1964); http://dx.doi.org/10.1063/1.1724922View Description Hide Description
Relatively large chemical shifts in the resonance frequency of the thallium nucleus are observed in both the crystalline and molten states of different thallium salts. Relative to TlNO3, which appears to be the most ionic of all thallium salts studied, the 205Tl resonance frequency at fixed field increases in the order: NO3 —<Cl—<Br—<I—. The results are interpreted in terms of a second‐order paramagnetic contribution to the field at the Tl nucleus, arising from an admixture of its excited states with the ground state, and the chemical shift is approximately proportional to the square of the overlap integral. Although cations and anions in the melts are partly associated, the NMR shifts of the Tl nucleus show that the cause arises from incipient covalency rather than polarization of the cation by the halide ions.
In both the crystalline and molten states, a linear paramagnetic shift with temperature is observed, which is attributed to the enhanced overlap of excited states which are induced by thermal vibrations.
40(1964); http://dx.doi.org/10.1063/1.1724923View Description Hide Description
The ligand‐field splitting of the antibonding orbitals of molecular oxygen is discussed for a general solvent environment. The results are combined with a previous calculation of the splittings of the 3Σ g —, 1Δ g , and 1Σ g + terms to give a possible interpretation of the observed 630 mμ emission line of dissolved molecular oxygen.