Volume 42, Issue 7, 01 April 1965

Radiolysis of Hexafluoroethane
View Description Hide DescriptionThe radiolysis of C_{2}F_{6} at 3‐atm pressure has been examined. The products and 100 eV yields are CF_{4} (1.6), cyclo‐C_{3}F_{6} (0.30), C_{3}F_{8} (0.21), C_{4}H_{10} (0.14), and C_{2}F_{2} (0.03). Good material balance is obtained; the F/C ratio in the products is 3.0. Experiments using radical scavengers indicate that 50% of the CF_{4} comes from radical reactions and 50% from nonradical reactions, that C_{3}F_{8} and C_{4}H_{10} are entirely formed by radical reactions, and that C_{2}F_{2} and cyclo‐C_{3}F_{6} are probably formed by ionic reactions. In Ar–C_{2}F_{6} mixtures energy transfer, thought to be charge transfer, is observed and ionic production of C_{3}F_{8} is seen. C_{2}F_{6} is about one‐fifth as sensitive to radiation decomposition as is C_{2}H_{6}. It is concluded that excited molecule decompositions, particularly those giving molecular fluorine, are relatively unimportant in the radiolysis of perfluoroalkanes.

Melting Properties of the Alkali Nitrates to 10 000 Atmospheres
View Description Hide DescriptionThe melting points and the volumes of fusion of the alkali nitrates were determined at pressures up to 10 000 atm. LiNO_{3}, NaNO_{3}, and CsNO_{3} have normal melting curves. However, the RbNO_{3} melting curve exhibits an initial negative slope followed by normal behavior at higher pressures, whereas the KNO_{3} melting curve is initially normal, but goes through a maximum at elevated pressures. The results of this investigation indicate that the RbNO_{3} liquidus curve has two triple points, one at 310° and 200 atm and the other at 315° and 1900 atm.

On Semiclassical Scattering
View Description Hide DescriptionThe behavior of the quantum‐mechanical phase shifts for scattering by a potential well is examined in the classical limit. The phase shifts tend to zero in the classical limit for all cases in which the corresponding classical trajectory does not pass through the well. This disproves by counterexample the result of Curtiss and Powers which indicated that there should be a contribution to the phase shifts even in the classical limit from classically inaccessible but energetically possible regions between two inner classical turning points. The error in the latter result appears to arise from the neglect of bound states of positive energy which exist in the classical limit (and only in that limit).

Effect of Three Turning Points on Semiclassical Scattering
View Description Hide DescriptionWhen three turning points occur in the effective potential, the region between the two inner turning points is associated with classically bound trajectories or quantum‐mechanically metastable states. The effect of this portion of the effective potential‐energy curve on the semiclassical phase shifts and transport cross sections is discussed.

Infrared Spectroscopic Investigation of Ultraviolet‐Irradiated Sodium Azide Crystals
View Description Hide DescriptionThis study is concerned with new absorption bands which appear in the infrared spectrum when sodium azide crystals are irradiated with ultraviolet light at 77°K. The observed frequencies and frequency shifts of the irradiation bands produced by NaN_{3}, NaN^{15}NN, NaNN^{15}N, and Na^{15}N_{3} indicate that they are caused by some configuration of vibrating nitrogen atoms. Calculated frequency‐shift values for various polyatomic nitrogen defects, which have a high probability of being produced by ultraviolet photolysis, were obtained using expressions derived on the assumption of valence forces. By comparing calculated and observed values, considerations are given to the capability of several polyatomic nitrogen structures to produce the new infrared absorptions.

Experimental Study of the Absolute Temperature Scale. XI. Deviation of the International Practical from the Kelvin Temperature Scale in the Range 0° to 444.6°C
View Description Hide DescriptionThe deviations of the International Practical Temperature Scale from the thermodynamic Celsius scale were determined at eleven temperatures in the range 0° to 444.6°C by a comparison of the indications of four platinum resistance thermometers with those of two constant‐volume nitrogen‐gas thermometers in a stirred‐liquid thermostat. In each gas thermometer several different ice‐point pressures were used to permit corrections to be made for the imperfection of the thermometric fluid. The arithmetic means of the observed differences between temperatures on the thermodynamic Celsius scale as it was defined in 1954 and those on the IPTS at the eleven temperatures, each weighted in accordance with the number of observations, are represented by the equationwhere t in the right‐hand member is on the IPTS. The standard deviation of a determination of Δt of unit weight from the equation is 18×10^{−4} deg.

Causes of l‐Type Doubling in the 3p(E″) Rydberg State of Ammonia
View Description Hide DescriptionExpressions are developed for the rotational levels of an electronically degenerate planar XY _{3} molecule. It is shown that there can be strong l‐type doubling only in levels with no vibrational angular momentum and that this doubling has two main causes, namely, a rotational—electronic interaction and a rotational—Jahn—Teller interaction. The l‐type doubling of other levels is largely quenched by vibronic coupling.
Estimates of the observed l‐type doubling in the 3p(E″) state of ammonia indicate that the two above contributions act in opposite senses. A mechanism which accounts for the variation of the observed l‐type doubling with vibronic state is suggested.

Critical Opalescence of a Binary Liquid Mixture, n‐Decane—β,β′‐Dichloroethyl Ether. II. Small‐Angle X‐Ray Scattering
View Description Hide DescriptionThe small‐angle x‐ray scattering of n‐decane and β,β′‐dichloroethyl ether has been investigated at the critical‐solution concentration over a range of temperatures near the phase‐separation temperature in the one‐phase region. Composite light‐ and x‐ray scattering curves were constructed. The angular distribution of the scattering was analysed in terms of the Debye theory of critical opalescence. Deviations from the straight‐line behavior in plots of reciprocal scattered intensity versus (s/λ)^{2}(s=2 sin½θ, and λ is the wavelength in the medium) were observed.

Atomic‐Beam Scattering Studies on the Li–Hg System: Quantum Effects and Velocity Dependence of the Cross Sections
View Description Hide DescriptionMeasurements of the velocity dependence of the angular intensity distribution of ^{6}Li and ^{7}Li beamsscattered by a crossed Hgbeam are reported. The Li beams were velocity selected, the HgbeamMaxwellian. Angular intensity distributions were measured at various relative velocities (v_{r} ) from 700–1200 m/sec, relative total cross sections (q) from v_{r} =300 to 1350 m/sec. The differential cross sections show expected quantum interferences. Scattering patterns for ^{6}Li— and ^{7}Li–Hg are found to be identical at the same de Broglie wavelength. The over‐all angular dependence of the scattering at low angles follows the θ^{−7/3} relationship characteristic of an r ^{−6} long‐range potential. Extrema in the total cross sections q(v_{r} ) were also observed. The experimental data were analyzed in terms of a Lennard‐Jones (12, 6) potential, but it was not possible to determine a unique set of potential parameters. Comparison of observed and calculated results has yielded three nearly equivalent sets of σ, ε lying within the ranges 2.5≤σ≤3.5 Å, 480°≤ε/k≤1000°K.

On the Effect of the Ground‐State Dipole Moment on Optical Transition Probability
View Description Hide DescriptionThe customary procedure in the theory of transition probabilities of transforming the dipole‐velocity expression into the dipole‐length expression is subjected to a critical investigation. It is concluded that in the case of triplet—singlet transitions this transformation should follow rather than preceed the substitution of the perturbed triplet and singlet wavefunctions. The result is that the ground‐state dipole moment does not contribute to the transition probability. In many other cases, where approximate eigenfunctions are substituted, it is not clear whether the transformation should preceed or follow the substitution. Therefore it becomes uncertain as to whether ground‐state dipole moments contribute to the transition probability.

Entropy and Related Thermodynamic Properties of n‐Valeric Acid
View Description Hide DescriptionThe heat capacity from 15° to 300°K, the heat of fusion (3384.7±1.0 cal/mole), the temperature of fusion (239.49°±0.02°K), and the entropy of the ideal gas at 1 atm, 25°C (105.12±0.15 cal/deg·mole) of valeric acid have been determined experimentally.

Entropy and Related Thermodynamic Properties of Carbon Suboxide
View Description Hide DescriptionThe heat capacity, the temperature of fusion (160.962°±0.002°K), the heat of fusion (1290.9±0.4 cal/mole), the vapor pressures, the heat of vaporization, and the entropy of the ideal gas at 1 atm, 230°K 62.12±0.15 cal/deg·mole) have been determined for carbon suboxide. The known structure and the six known fundamental vibrations lead to a calculated entropy of 54.33 cal/deg·mole, exclusive of the unknown seventh fundamental. The unobserved, doubly degenerate bending mode must have a frequency of about 61.6±2.6 cm^{−1}.

Determination of the Excitation Functions for Formation of Metastable States of Some Rare Gases and Diatomic Molecules by Electron Impact
View Description Hide DescriptionAn apparatus for the determination of the excitation functions for formation of metastable states by impact of electrons of precisely defined energies in the energy range from threshold to the ionization potential is described. Results are given for Ne, Ar, Kr, H_{2}, N_{2}, and CO. Two sharp resonances are observed in each of the rare‐gas excitation functions, which correspond to excitation with electron exchange of the first two excited configurations of these atoms. For diatomic molecules, no such resonances are observed, except in nitrogen, where there is a resonance process with an onset energy of 11.8 eV. A partial explanation for the shapes of the excitation functions is offered, based on the location and character of the various excited triplet states of the molecules studied.

Radiolysis of Ethylene. IV. Unimolecular Dissociation of Intermediate Ion—Molecule Complexes
View Description Hide DescriptionKinetic analysis of free‐radical reactions in the radiolysis of ethylene demonstrates that the relative extent of radical addition to ethylene can be held constant by maintaining the ratio of accelerator beam current to ethylene pressure invariant. The pressure dependence of the methane and methyl radical yields when this ratio is constant reveals that the mechanism of their formation includes competition between unimolecular dissociation of an intermediate ion and its participation in an ion—molecule reaction. Consideration of known ion—molecule reactions suggests that the species involved in the competing steps are [C_{6}H_{11} ^{+}] (methane formation) and [C_{6}H_{12} ^{+}] or [C_{4}H_{8} ^{+}] (methyl radical formation). Rate constants of 4.2×10^{8} and 1.0×10^{9} sec^{−1}, respectively, are calculated for the dissociation processes on the basis of collision efficiency for the competing ion—molecule reactions.
About one‐fourth of the methane and one‐half of the methyl radicals are formed by reactions which are independent of pressure below 1 atm. This may be ascribed to rate constants larger than 10^{10} sec^{−1} for dissociation of [C_{8}H_{15} ^{+}] and [C_{8}H_{16} ^{+}] ion, respectively, or to the existence of at least two discrete energy levels for the dissociating species. Relative dissociation probabilities of intermediate ion—molecule complexes, determined by mass spectrometry, are used to estimate G(C_{2}H_{4} ^{+}) ≈ 1.5 and G(C_{2}H_{3} ^{+}) ≈ 1.0 ions/100 eV at approximately atmospheric pressure, in good agreement with values of 1.51 and 0.96, respectively, which may be calculated from W and fragmentation patterns for 70‐eV electrons.

Least‐Squares Adjustment of Anharmonic Potential Constants: Application to ^{12}CO_{2} and ^{13}CO_{2}
View Description Hide DescriptionAn algorithm for the calculation of anharmonic potential constants from the observed vibrational energy levels and rotational constants has been set up. Values have been obtained for the cubic and quartic force constants in the most general valence anharmonic potential for carbon dioxide.

On the High‐Temperature Electrical Conductivity of Alumina
View Description Hide DescriptionThe electrical conductivity of single‐crystal Al_{2}O_{3} and chromium‐doped Al_{2}O_{3} was measured in the temperature range of 1000°—1600°C. The measurements were made with the sample in air and in helium. The effects of the atmosphere on the measurements are discussed in detail.

Incoherent X‐Ray Scattering Factors
View Description Hide DescriptionIncoherent scattering factors for C, O, Cl, Al, and I are calculated from Hartree—Fock—Slater wavefunctions. Comparison of the values of C and Al with Hartree—Fock values show good agreement. Results for I, which represent the heaviest element for which calculations of this type have been performed, are compared with statistical Thomas—Fermi values.

Variation‐Perturbation Approach to Electron‐Cluster Wavefunctions
View Description Hide DescriptionSinanoğlu's cluster expansion formula for the exact wavefunction of a many‐electron system is investigated by variation‐perturbation techniques. The perturbation operator is the difference between the actual Hamiltonian and a symmetric sum of arbitrary one‐electron Hamiltonians. Each perturbation function is then expanded in accordance with the cluster formula.
When the occupied orbitals are chosen to be eigenfunctions of the one‐electron Hamiltonian the variational equations determining different nth‐order clusters are completely independent. If the orbitals are unitarily transformed to achieve greater localization the variational equations for each cluster are coupled.
The perturbation governing first‐order two‐electron clusters has the form of a dipole potential. This result does not depend on the nature of the one‐electron Hamiltonian. It is primarily useful, however, in studying the question of interorbital vs intraorbital correlation, i.e., when the one‐electron Hamiltonian is the Hartree—Fock operator. It is shown that interorbital correlation is small if the Hartree—Fock orbitals are well separated. The advantage of transforming to localized orbitals is shown to be questionable because of the coupling between the clusters.
Differential equations governing first‐ and second‐order orbital correction functions are derived and partially interpreted. In accordance with Brillouin'stheorem the first‐order corrections vanish as the one‐electron Hamiltonian approaches the form of the Hartree—Fock operator. In the Hartree—Fock case the role of the second‐order orbital correction functions is to relax the charge density subsequent to correlation. An investigation of the derivative of the correlation energy with respect to nuclear charge, a one‐electron property, suggests that the second order correction functions may be important whenever it is necessary to evaluate one‐electron properties to an accuracy beyond the Hartree—Fock estimate.
The second order four‐electron cluster is shown to be exactly expressible as a sum of products of first‐order two‐electron clusters.
Explicit variational equations are derived also for the second‐order two‐ and three‐electron Hartree—Fock clusters.

Energy‐Term Calculations with Hellmann‐Type Pseudopotential
View Description Hide DescriptionThe Hellmann pseudopotential method is used to calculate the energies of the ground states of the atoms Mg, Ca, Sr, Ba, Ra, Zn, Cd, and Hg. Two different types of wavefunctions were employed for the valence electrons:wavefunctions of Hylleraas type explicitly containing r _{12}, and a superposition of the configurations (1s)^{2 1} S and (2p)^{2 1} S. The agreement between the calculated and empirical energies is very good. The results are better with the superposition of configurations than with the wavefunction containing r _{12}.

Electron Energy for H_{2} ^{+} in the Ground State
View Description Hide DescriptionThe 1sσ_{ g } state of the hydrogen molecular ion is investigated. The result is given as a table in which the electronic energy for a two‐Coulomb center is given in seven decimal places for values of internuclear separation R up to 20 in steps of 0.05 a.u.