Volume 47, Issue 9, 01 November 1967
Index of content:
47(1967); http://dx.doi.org/10.1063/1.1712359View Description Hide Description
The manner in which a permanent dipole in a molecule affects capture collisions of the molecule with ions is investigated. Analytical capture cross sections are considered, and three cases are distinguished. None of these is strictly applicable to real collisions, but they are useful in establishment of the general magnitudes of cross sections. The Langevin cross section is somewhat of a lower limit. A strict upper limit to the cross section is derived; it depends on the magnitude of the dipole moment. A quantum‐mechanical treatment at small relative velocity uses the effective potential of interaction determined by the Stark effect; cross sections for this case depend explicitly on the rotational energy of the polar molecule. Molecules which have a first‐order Stark effect have a term ε−1 in their cross sections, whereas the second‐order Stark effect only leads to the ε−1/2 term of the Langevin theory (ε is the relative translational energy).
Numerical cross sections are obtained by using a computer study of collisions. The classical equations of motion are solved. Spiraling collisions (predicted in the Langevin theory) are not obtained, but it is found to be possible to define ``capture'' adequately and to set up a procedure for calculation of capture cross sections. This procedure involves averaging initial conditions with proper weighting. The real molecule HCl has been used in the calculations, and the results are compared with experiment as far as possible. A hypothetical molecule with the same dipole moment and polarizability of HCl but with a moment of inertia 100 times larger is also considered.
47(1967); http://dx.doi.org/10.1063/1.1712360View Description Hide Description
Results of numerical calculations of the electronic band structure of cubic boron nitride are reported. The calculations have been carried out using the augmented‐plane‐wave method of Slater. A total of 20 points in the first Brillouin zone have been examined which, by symmetry, determine eigenvalues at 256 different points from which a density‐of‐states histogram and curve have been plotted. The general shape and configuration of the energy bands resemble those obtained in previous energy‐band calculations. It proved necessary to use the average potential between the spheres and the Madelung correction for ionicity as adjustable parameters in order to obtain a satisfactory band picture. The potential used is a modification of the carbon potential of Keown scaled according to a scheme introduced by Herman and Skillman.
47(1967); http://dx.doi.org/10.1063/1.1712361View Description Hide Description
The data of Walton, Rhodin, and Rollins for the nucleation rate of silver on sodium chloride is analyzed using classical nucleation theory. The difference between the activation energies for desorption and surface diffusion, ΔG des—ΔG sd, is found to be 0.3 eV, essentially independent of the value used for γ, the surface free energy of silver. The product γ3 f(θ), where f(θ) is the contact angle function, is found to be 1.24×109 erg3/cm6. With γ=1140 erg/cm2, f(θ) is 0.839 and the contact angle, θ, is 119 deg. Using values of 1100 to 1600 erg/cm2 for γ results in contact angles of 133 to 75 deg. Since a Pound plot of the data produces a straight line, it is concluded that Walton's data may be interpreted by the formalism of classical nucleation theory. The radius of the critical sized nucleus, r *, is 2 to 3 Å, typical of other nucleation data analyzed in this manner.
Mass Spectrometry at High Temperatures. XVIII. The Stabilities of the Mono‐ and Difluorides of Scandium and Yttrium47(1967); http://dx.doi.org/10.1063/1.1712362View Description Hide Description
Mono‐, di‐, and trifluorides of Sc and Y have been identified in the vapors over mixtures of the corresponding metals and CaF2 in Ta‐Knudsen cells at high temperatures. Equilibria among these molecules and Ca and CaF have been studied by a mass spectrometer and their dissociation energies have been determined.
47(1967); http://dx.doi.org/10.1063/1.1712363View Description Hide Description
The nature of the four‐photon molecular scattering process involved in stimulated Raman scattering is considered by means of collision theory. An accurate expression is obtained for the scattering amplitude which explicitly illustrates its partitioning into coupled Stokes and anti‐Stokes scattering processes. The dependence of the cross section for stimulated Raman scattering upon the lifetime of the excited vibrational state is derived. Such a dependence was assumed from phenomenological considerations by Bloembergen and Shen and is consistent with the observation that stimulated Raman scattering is observed only for vibrations having narrow linewidths. The lifetime dependence of the cross section is shown to be in agreement with the two‐step mechanism of stimulated Raman scattering involving subsequent Stokes and anti‐Stokes scattering processes, and contradictory to a single‐step mechanism proposed by Buckingham. The single‐step mechanism is shown to correspond to a physically unrealizable limit of the two‐step process.
47(1967); http://dx.doi.org/10.1063/1.1712364View Description Hide Description
Fluorine and proton high‐resolution NMR lineshapes have been observed at 56.4 and 60 MHz, respectively, for a 50 mole % solution of 1‐fluoro‐1,1,2,2‐tetrachloroethane in carbon disulfide, between −120° and −14°C. Fluorine spin echoes were obtained at 25.27 MHz and protonspin echoes were obtained at 26.8 and 17.7 MHz. An iterative complete‐lineshape‐fitting computer program was used with the experimental lineshapes to obtain best‐fit exchange rates for interconversion of gauche and trans rotamers. A value of 18.9 ppm was found for the fluorine chemical shift from the low‐temperature high‐resolution spectrum and was used to fit the lineshapes at higher temperatures, as well as to fit the observed dependence of the fluorine relaxation rate on rf pulse spacing in the Carr—Purcell experiments.
Other parameters required in the analysis, i.e., the energy difference between trans and gauche rotamers and the proton‐fluorine coupling constants in each rotamer, were obtained from the temperature dependence of the proton spectrum under conditions of complete averaging (−90°−25°C). The values obtained for the coupling constants are in good agreement with an earlier determination by the same method but over a different temperature range. At −120°C the fluorine resonance consisted of a singlet and a doublet, with splittings in satisfactory agreement with the high‐temperature results. The protonspin echoes at −112°C are sensitive to the proton‐fluorine coupling constants, and can be calculated satisfactorily with coupling constants obtained from the high‐temperature proton lineshape.
Because of the large fluorine chemical shift, four orders of magnitude of the exchange rate were measurable. Exchange rates obtained from all four sets of data fall on the same, linear Arrhenius plot, with frequency factor (7.0±0.5)×1011 sec−1 and activation energy 7.85±0.05 kcal mole−1. The frequency factor is low compared with a value computed by assuming immediate deactivation from the eclipsed transition state, but agrees with a value calculated by assuming that the molecules undergo ``free'' internal rotation before deexcitation to any one of the stable rotamers.
47(1967); http://dx.doi.org/10.1063/1.1712365View Description Hide Description
The time‐of‐flight (TOF) method for the determination of electron‐diffusion coefficients D and drift velocities w described earlier could not be used to investigate a number of gases because a Gieger—Müller counter was used for an electron detector. A new experimental apparatus using differential pumping and an electron‐multiplier detector was developed to remove this restriction. Using this new apparatus, D and w have been measured for He, Ar, H2, N2, CO, CO2, CH4, and C2H4. Considerable divergence of D values from published values by the Townsend method have been obtained, indicating a fundamental difference in the methods.
47(1967); http://dx.doi.org/10.1063/1.1712366View Description Hide Description
A mathematical analysis of peak shapes in a Bendix time‐of‐flight mass spectrometer shows that ions formed with excess translational energy exhibit considerable peak broadening. A method is developed by which this translational energy can be readily determined from the peak width. Experimental results are presented which confirm the validity of the theoretical calculations.
47(1967); http://dx.doi.org/10.1063/1.1712367View Description Hide Description
A recently developed method has permitted the measurement of excess translational energy of ions formed in a time‐of‐flight mass spectrometer. The method, in conjunction with the RPD technique for determining appearance potentials, has been applied to the electron‐impact study of nitrogen, carbon monoxide, and nitric oxide. A total of 31 different ionization processes have been observed and identified, several of which had not been previously reported in the literature.
47(1967); http://dx.doi.org/10.1063/1.1712368View Description Hide Description
Construction of a statistical‐mechanical ensemble to represent a system known to be out of equilibrium is discussed. The consequences of the temperature, velocity, and chemical potential fields are formal time‐correlation‐function expressions for both linear‐ and higher‐order transport coefficients. Many different forms of correlation functions are equivalent, which permits choice of the most useful for a given purpose. Onsager‐type reciprocal relations appear to exist for only the linear coefficients.
47(1967); http://dx.doi.org/10.1063/1.1712369View Description Hide Description
Construction of a statistical mechanical ensemble to represent a homogeneous system not in chemical equilibrium is discussed. The consequences of the chemical driving forces are obtained as formal time‐correlation‐function expressions for both linear‐ and higher‐order chemical‐reaction rate constants. Onsager‐type reciprocal relations appear to exist for only the linear coefficients. Implications on the validity of using thermodynamic potentials for nonequilibrium systems are discussed.
47(1967); http://dx.doi.org/10.1063/1.1712370View Description Hide Description
Luminescence produced in nitrogen in small segments of the tracks of fission fragments was studied with a pulse technique. The amount of formation of the C 3π u state of nitrogen per unit distance, L *, was measured over the entire path length of the low‐mass fragment group as a function of track length. The energy loss per unit distance dE/dr can be approximated by L * over the entire fission fragment path length. The observance of light produced from the second positive group (C 3π u →B 3π g ) near the end of the track, despite a major change in the primary mode of energy deposition by the fission fragments, indicates that a more detailed theory of chemical production from the deposition of energy by a heavy charged particle needs to be formulated in the regime of nuclear elastic collisions which exists at the end of the particle's range.
Electronic Spectra and Coordination of Nickel Centers in Liquid Lithium Chloride—Potassium Chloride Mixtures47(1967); http://dx.doi.org/10.1063/1.1712371View Description Hide Description
The electronic absorption spectra (4–28 kK) of dilute solutions of NiCl2 in liquid LiCl–KCl mixtures were measured at representative solvent compositions and temperatures from pure LiCl to pure KCl and and from 363° to 1070°C. Phenomenologically the spectra respond to changes in temperature at high temperature and changes in solvent composition at low temperatures in ways that are quantitatively very regular. At intermediate temperatures the behavior is more intricate. The data agree well with the following model. Nickel is partitioned between two types of centers, labeled T and O, which are in equilibrium. The T/O concentration ratio increases with increasing temperature and KCl content in the solvent. At low temperatures the fraction of each kind of center varies linearly with the mole fraction of KCl. The O‐center concentration falls below the detection limit at 900°C in all solvents and in KCl at all temperatures. The coordination geometries of these centers are best described as being distributions about particular averages rather than as sharply defined arrangements. At low temperatures T centers have a distribution of coordination geometries that is narrow, composition invariant, and are clustered about a tetrahedral average. Their outer‐shell cations are mostly K+. At high temperatures the distribution broadens and in LiCl‐rich melts, Li+ ions invade their outer shells. The O centers are accurately studied only at rather low temperatures where they have a relatively broad coordination‐geometry distribution with an average distinctively different from tetrahedral. Their outer shells consist largely of Li+ ions.
Electronic Spectra and Coordination Geometry of Nickel Centers in Liquid Mixtures of Magnesium Chloride and Potassium Chloride47(1967); http://dx.doi.org/10.1063/1.1712372View Description Hide Description
The absorption spectra of nickel centers in MgCl2–KCl mixtures of various compositions were measured from about 5–28 kK at temperatures up to 1060°C. The observed behavior was qualitatively similar to that previously reported for nickel centers in liquid LiCl–KCl mixtures and, in a general way, fits the same model.
47(1967); http://dx.doi.org/10.1063/1.1712373View Description Hide Description
A method is described for measuring the optical absorptionspectra of the crystalline and liquid phases of a transition‐metal salt close to the melting point. Supercooling the liquid permits measuring both phases at the same temperature. This technique was applied to Cs3NiCl5 (mp 547°C) and CsNiCl3 (mp 758°C). It was shown that when Cs3NiCl5 melts, the approximately tetrahedral arrangement of chlorides about nickel is affected only in minor ways, but when CsNiCl3 melts, the octahedral coordination geometry in the crystal is completely destroyed and replaced by a different distribution of geometries. The spectrum of molten CsNiCl3 and its temperature dependence is closely similar to that of nickel centers in molten KMgCl3 at high temperatures. The latter are believed to consist of a single broad distribution of geometries rather than two distinctly separate distributions. It was previously supposed that there are two distinctly different coordination geometries in molten CsNiCl3.
47(1967); http://dx.doi.org/10.1063/1.1712374View Description Hide Description
It is shown that the sum of the squares of the fundamental frequencies of a molecule does not depend explicitly upon molecular geometry. Using this sum it is demonstrated that a set of effective Cartesian force constants which are measures of the potential environment of atoms in a molecule can be calculated with little difficulty.
47(1967); http://dx.doi.org/10.1063/1.1712375View Description Hide Description
The microwave absorption very far in the low‐frequency wing of the pure rotational spectra of HCl, DCl, and HBr has been measured in order to investigate the applicability of pressure‐broadening theory in the region many linewidths removed from the resonant frequencies. Data for mixtures of HCl and HBr with the foreign gases He, H2, Ar, N2, CH4, C2H6, CO, SF6, and CO2 are also reported. Experimental results are compared with the Van Vleck—Weisskopf equation, which is used to indicate an upper limit of the absorption. Data for the mixtures with He and H2 are in accord with this line shape. Data for the remaining mixtures and the pure gases are not in agreement, the observed absorption being from 2 to 8 times greater than predicted. These results suggest the presence of an additional absorption region which is centered at a lower frequency than the normal rotational spectrum and which may be attributed to interacting molecular pairs.
47(1967); http://dx.doi.org/10.1063/1.1712376View Description Hide Description
Microwave measurements have been made on the direct doublet splittings (ΔJ=0 transitions) of the 0110, 0220, 0310, and 0330 levels of DCN and the 0110 and 0220 levels of HCN. The sensitivity of the Δ and φ level splittings to certain vibrational and rotational constants enables us to obtain new values for those constants. New infrared measurements are given for ν1, 3ν2 1, 4ν2 0—ν2 1, and 4ν2 2—ν2 1 of HCN.
47(1967); http://dx.doi.org/10.1063/1.1712377View Description Hide Description
The purpose of the paper is to clarify the mechanism of excitation energy transfer between unlike trivalent rare‐earth ions in inorganic solids. We have measured the manner in which the intensities of the luminescences of Tb3+ (5 D 4→7 F 5) and Eu3+ (5 D 0→7 F 2) are quenched and the decay rates are made faster by the coexistence of other kinds of trivalent rare‐earth ions as a result of energy transfer. As the host material, calcium metaphosphate glass was used. The combination of Tb3+ donor and Nd3+ acceptor was studied most in detail. The results are discussed in terms of the resonance theory of energy transfer, and the experimental data are analyzed using the numerical calculations of the theory recently made by Inokuti and Hirayama. The overlap integrals of donor emission spectra with acceptor absorption spectra were estimated from the data of spectral measurements. Among the resonance mechanisms due to various electrostatic multipole interactions, the dipole—quadrupole interaction gave the best fit between theory and experiment. The transfer due to the exchange interaction was inferred not to be operative. It has been finally concluded that the mechanism of the energy transfer between unlike trivalent rare‐earth ions in inorganic solids is predominantly governed by the dipole—quadrupole interaction.
47(1967); http://dx.doi.org/10.1063/1.1712378View Description Hide Description
The difference bands of carbon tetrachloride are analyzed and it is found that, in the Raman spectrum at room temperature, the complex at 775 K is essentially all difference bands. This band has been previously assigned as the fundamental ν3, ν1+ν4 with a spacing of 28 K; the fundamental is present in the complex but its spacing is 15 K and it is weak. The difference bands of titanium tetrachloride are mentioned briefly.