Volume 59, Issue 11, 01 December 1973

Characteristic energy losses by slow electron impact on thin‐film alkanes at 77 °K
View Description Hide DescriptionCharacteristic energy losses by slow electron impact have been measured on thin films of several alkanes at 77 °K. The cross section for the lowest loss at [inverted lazy s] 0.6 eV increases tenfold in the series n ‐pentane to n ‐nonane with increasing carbon number. For a given carbon number it decreases markedly with branching. Losses at [inverted lazy s] 3, [inverted lazy s] 6, [inverted lazy s] 9, and [inverted lazy s] 22 eV are common to all alkanes with no strong dependence on molecular size or configuration. The lowest losses may be due to temporary negative ion states or to pre‐existing trapping potentials. Losses at [inverted lazy s] 3 eV may be due to the highest temporary negative ions or to triplets. If the former is correct, then [inverted lazy s] 6 eV losses can be attributed to triplets. The [inverted lazy s] 9 eV losses are due to upper singlet states, and the [inverted lazy s] 22 eV losses may be due to collective excitations.

Temperature dependence of near resonant vibration → vibration energy transfer in HCl–D_{2} mixtures
View Description Hide DescriptionLaser‐excited vibrational fluorescencemeasurements have given rates for nearly resonant vibrational energy exchange between HCl and D_{2} molecules over the temperature range of 196–343°K. The energy transfer cross section σ_{ν ν} shows an inverse temperature dependence; namely, decreases as temperature increases. The magnitude and temperature dependence of these cross sections could be fit by first order calculations based on quadrupole‐quadrupole, and dipole‐quadrupole interactions. The rates of vibrational deactivation of HCl by He were found to increase with temperature. However, the results on HCl self‐relaxation also show an inverse temperature dependence over this temperature range studied. This enhancement observed at lower temperature is probably caused by the attractive chemical forces exerted between HCl molecules.

Application of an empirical equation of state to the critical region of methane and argon
View Description Hide DescriptionThe equation of state for the critical region of simple fluids proposed by Verbeke et al. is, with other options for the parameters, applied to methane and argon. The data on methane reported by Jansoone et al. are reanalyzed with this equation. In order to apply the equation in the critical region of argon the data of Verbeke et al. are utilized and expanded with additional new data. It is demonstrated that the proposed equation can be useful in the further investigation of the equation of state in the critical region of simple fluids.

Fermi‐contact hyperfine interaction and the electron spin g factor in H_{2} d(3p) ^{3}Π_{ u }
View Description Hide DescriptionMicrowave optical magnetic resonance induced by electrons (MOMRIE) experiments have been continued on the d(3p) ^{3}Π_{ u } states of ortho‐ and para‐H_{2}. Transitions that would at the high magnetic field limit be forbidden have been observed at low field (∼ 2 kG). Four such transitions in ortho‐H_{2} and two in para‐H_{2} have been accurately measured. Previously MOMRIE transitions within these states of H_{2} had been observed in the 12–15 kG range where selection rules permit only transitions which are insensitive to the electron spin g factorg_{s} and the Fermi‐contact hyperfine interaction a_{F} . The newly observed transitions are sensitive to these parameters and when combined with previous high field data determine g_{s} in the ν = 0–3 vibrational levels of ortho‐ and para‐H_{2} and a_{F} in the ν = 0–3 vibrational levels of ortho‐H_{2}. The values of a_{F} are comparable to those for the c(2p) ^{3}Π_{ u } state of H_{2} and the state of , but interestingly (for a given ν) are larger than either value. The values of g_{s} are found to be close to the free electron spin g factor for all the measured vibrational levels of ortho‐ and para‐H_{2}. However, they show a slight deviation to the high side of the free electron value, comparable to the experimental error.

Photoionization of atomic oxygen from 920 to 650 Å
View Description Hide DescriptionAtomic oxygen was produced in a low pressure gas discharge and was equilibrated in a small chamber to eliminate electronically excited species prior to the formation of an atomic beam which was photoionized. Relative photoionization cross sections were measured from 920 to 650 Å at a wavelength resolution (FWHM) of 0.42 Å. From the ratio of threshold intensities corresponding to ionization from the ^{3} P _{2}, ^{3} P _{1}, and ^{3} P _{0} states of O_{I}, the beam temperature was estimated to be 375 ± 25°K. Autoionization structure was observed corresponding to all of the transitions seen in absorption by Huffman, Larrabee, and Tanaka, including those transitions for which autoionization is forbidden on the basis of Russell‐Saunders coupling. The seven lowest energy autoionizing lines were measured at a wavelength resolution (FWHM) of 0.16 Å. The distribution of intensities within a multiplet corresponded to the theoretical intensities predicted for an approximately 375°K beam in all but two cases. These notable exceptions were the two most intense autoionization peaks in the spectra, both of which were forbidden in pure Russell‐Saunders coupling. The anomalous intensity distributions may be attributed to competition from emission which preferentially robs intensity from selected transitions within a multiplet, to nonstatistical autoionization probabilities, or to perturbations which alter the relative absorption intensities within a multiplet.

Self‐avoiding random walks, circle and star graphs, and a group of singular matrices
View Description Hide DescriptionThe self‐avoiding random walk problem in d ‐dimensional space is efficiently treated by use of a class of graphs of great generality, called circle graphs. Matrices associated with these graphs are shown to be submatrices of the matrix belonging to the complete star on the circle. The latter matrix possesses an interesting group property which is dependent on the notion of the generalized inverse. The self‐avoiding random walk problem is solved to all orders by graphical expansion, and a concise prescription suitable for numerical calculation of the coefficients is given. It is suggested that an analytical solution would be obtained from consideration of the properties of determinants of matrices in the generalized group.

Magnetothermodynamics of antiferromagnetic, ferroelectric, ferroelastic β‐Gd_{2}(MoO_{4})_{3}. IV Thermodynamic temperature and other properties without heat introduction below 0.5°K. Fields to 10 kG along the c ^{+} crystal axis
View Description Hide DescriptionUsing our previous magnetothermodynamic data on electrically polarized β‐Gd_{2}(MoO_{4})_{3} with high fields along the c axis [J. Chem. Phys. 56, 193 (1972)] above 0.5°K as a basis, measurements of magnetic moment on 62 demagnetization‐remagnetization isentropes were used to extend the properties to the region below 0.5°K. The isentropic change in enthalpyH was evaluated by means of the magnetic work (d H = − M d H)_{ s }. The thermodynamic temperature was obtained from . Thermodynamically correlated values for entropy,enthalpy,magnetic moment, internal energy, and heat capacity are tabulated over the temperature range 0.1–0.5°K and at fields of 0–10 000 G. At fields below 1615 G the substance remained in an essentially antiferromagnetic condition. At limiting low temperatures and fields of 0, 500, and 1000 G, the enthalpy varied as the 4/3 power of the entropy (C ∝ T ^{3}). Above 1615 G there was a region in which the classical dipole field balanced field increases as the transition continued gradually and reversibly toward saturation paramagnetism without abrupt spin reorientation (i.e., no irreversible ``spin flop''). In the region from about 1.7–2.9 kG, the limiting value of enthalpy varied approximately as the 6/5 power of the entropy. This indicates that the isoerstedic heat capacityC _{H} = 5S = constT ^{5}. It is pointed out that this implies five active degrees of freedom for the dipoles at the limiting low temperatures. Also, in the above region , while S, T, and C _{H} were essentially independent of field.

Fluctuations and noise in kinetic systems. II. Open ensembles at equilibrium and steady state
View Description Hide DescriptionWe consider the noise and fluctuations of an open ensemble of independent systems each of which can exist in a set of discrete states {0, 1, 2,..., x}. By an open ensemble we mean that the systems in the ensemble may be exchanged with one or more reservoirs. We derive the noise power spectrum of the quantity as a function of rate constants of the kinetic rate equations (α_{ ij } for the transition i →j, etc.). N _{i} is the number of systems of the ensemble in state i and the a _{i} 's are constants. This paper and a previous one [Y. Chen and T. L. Hill, Biophys. J. (to be published)] form a complete noise analysis for discrete linear kinetic systems and may be used in differentiating various kinetic schemes in complex biological problems. Also obtained is a Poissondistribution function for the number of systems of an open ensemble at cycling steady state (that is, some transition rate constants among the system states do not obey the Wegscheider relation). This extends the usual steady state results on open ensembles in which the Wegscheider relation holds.

High temperature negative ions: Electron impact of As_{4} vapor
View Description Hide DescriptionAppearance potentials and ion translational energies have been measured for the negative ions As^{−}, As_{2} ^{−}, and As_{3} ^{−} formed by dissociative resonance capture of As_{4}. The following thermochemical values (all in kilocalorie/mole) have been obtained: and . The measurement of the increase in translational energy through resonance gave α = 0.43 for the three processes studied.

^{15}N magnetic shielding anisotropies in ^{15}N^{15}NO
View Description Hide DescriptionThe ^{15}N magnetic shieldinganisotropies in nitrous oxide (^{15}N^{15}NO) have been determined using a pulsed FT NMR spectrometer. The shielding anisotropies obtained from the temperature dependence of the nematic phase chemical shifts are 512 ± 10 ppm (central ^{15}N) and 369 ± 15 ppm (end ^{15}N). The values obtained from the nematic‐isotropic phase difference method are 505 ± 10 ppm (central ^{15}N) and 366 ± 10 ppm (end ^{15}N). Theoretical estimates of the anisotropies from the so‐called atom dipole method are also reported. The indirect scalar coupling constant has been assigned to be negative. The signs of the ^{15}N spin‐rotation constants are predicted to be positive.

Vibrational relaxation in polyatomic molecules: SF_{6}
View Description Hide DescriptionVibrational relaxation in mixtures of 5%, 10%, and 25% SF_{6} in Ar has been studied behind incident shock waves over the temperature range 450–1050 K by time‐resolved measurement of postshock density gradients using a laser beam deflection technique. Short extrapolation of the results obtained yields excellent agreement with ultrasonic data in the range 200–420 K. Contrary to original reports, results from infrared fluorescence and double resonance measurements at 300 K are shown to be in disagreement with the ultrasonic data. A discussion of relaxation behavior in polyatomic molecules under differing conditions of departure from equilibrium shows that such a discrepancy is to be expected in general.

Multiple site effects on the Raman spectra of RbNO_{3} and CsNO_{3}
View Description Hide DescriptionMultiple band structure in the symmetric stretching region of the Raman spectra of RbNO_{3} IV and CsNO_{3} II confirms the presence of NO_{3} ^{−} ions on three distinct crystallographic C _{1} sites and supports the proposed or space group. Assignments were confirmed by ^{18}O‐isotopic dilution studies.

Excitation of metastable vibrational levels by electron impact
View Description Hide DescriptionAbsolute cross sections for the excitation of individual vibrational levels of the metastable state of nitrogen by electron impact were calculated using recent experimental data for the direct excitation of the state. The calculations include direct excitation as well as fast cascade contributions from the B ^{3}Π_{ g } and C ^{3}Π_{ u } states of N_{2}. The data input to the calculations consists of cross sections for direct excitation of the entire A, B, and C states, Franck‐Condon factors for the transition from the ground state to the vibrational levels of the A, B, and C states, and transition probabilities for the transitions C → B and B → A. The results obtained consist of graphs displaying the direct, cascade, and total cross sections of the A state both as a function of electron energy as well as vibrational quantum number. Electron energies range from threshold near 6 eV to 45 eV and vibrational quantum numbers range from ν = 0 to ν = 22. The results show that the population rates for the lowest vibrational levels of the A state are dominated by cascade, whereas the higher vibrational levels are directly excited from the N_{2}ground state. In general, the lowest vibrational levels of the A state are most efficiently populated by monoenergetic electrons and the nonmonoenergetic electron fluxes which are encountered in the aurora. Applications of the present results to processes in the upper atmosphere are briefly discussed.

Reduced 4f‐5d electrostatic interaction of Tm^{2+} in SrCl_{2}
View Description Hide DescriptionThe visible absorption and emission spectra of Tm^{2+} in SrCl_{2} sharpen at low temperatures and exhibit marked vibronic structure. The 4f ^{12} ^{3} H _{6} 5de_{g} excited states account for these transitions. The splitting of these states is almost entirely due to the 4f‐5delectrostaticinteraction. For theory and experiment to agree, the free‐ion electrostaticinteraction must be multiplied by 0.6. This suggests a strong nephelauxetic (cloud‐expanding) effect for the 5d electron on the divalent lathanides.

Study of the structure of molecular complexes. V. Heat of formation for the Li^{+}, Na^{+}, K^{+}, F^{−}, and Cl^{−} ion complexes with a single water molecule
View Description Hide DescriptionIn order to obtain the heat of formation ΔH, for the ion‐water complexes previously studied in the Hartree‐Fock approximation in the first three papers of this series, we have computed the normal frequencies of the complexes, the zero‐point energy correction to ΔH, and the molecular extra correlation energy. The main contribution to ΔH is due to the Hartree‐Fock binding; the least important contribution results from the correlation effects. The Hartree‐Fock binding varies from about 35 kcal/mole (Li^{+}–H_{2}O) to about 12 kcal/mole (Cl^{−}–H_{2}O); the zero‐point correction is between 1 and 2 kcal/mole; and the molecular extra correlation correction is less than 1 kcal/mole. The computation of ΔH is analyzed in order to estimate upper and lower bounds. We conclude that the calculated ΔH values are accurate to about 2.0 kcal/mole. Experimental data support this conclusion. In the Appendix, the potentials for water‐ion complexes have been presented in the form of a simple analytical expansion. The expansion has been obtained by fitting the Hartree‐Fock computed energies for the water‐ion complexes.

Effects of polymorphism on the Raman‐active longitudinal acoustical mode frequencies of n‐paraffins
View Description Hide DescriptionRaman spectroscopicmeasurements on the orthorhombic and monoclinic crystalline forms of n‐C_{36}H_{74} and n‐C_{94}H_{190} show that the frequencies of the longitudinal acoustical modes depend on the orientation of the chain axis relative to the planes containing the terminal methyl groups as well as the chain length. The frequency differences between the orthorhombic and monoclinic forms of a given n‐paraffin depend on the magnitude and direction of the regular stagger between neighboring end groups in the monoclinic forms. It is concluded that these frequency differences are most likely associated with variations in end group packing associated with differences in crystalline form. The implications of these observations to the use of Raman spectroscopic data to characterize the morphology of chain‐folded polyethylene crystals are discussed.

Electron spin resonance of chlorine dioxide in inert matrices at 4.2°K
View Description Hide DescriptionThe electron paramagnetic resonance spectrum of ClO_{2} trapped in neon, argon, and krypton matrices has been investigated at 4.2°K. The linewidths of the polycrystalline spectra were narrow enough so that forbidden transitions due to the nuclear Zeeman and nuclear quadrupoleinteractions could be resolved. The g, A, and Qtensors for each matrix were determined by comparison between experimental and computer simulated spectra. Partial orientation has been observed in all three matrices; the preferred orientation is with the molecular plane parallel to the deposition surface. Upon rotating the magnetic field to a position where it is either parallel or perpendicular to the deposition plane, marked differences in line intensities were apparent and an estimate of an orientation distribution function was made from comparison with simulated spectra. Annealing the argon matrix led to the appearance of a second trapping site with slightly different hyperfine and gtensors. This site is thought to be a substitutional one. The shifts of the hyperfine and gtensors in the three matrices have been qualitatively discussed in terms of van der Waals and Pauli interaction forces.

Vibrational spectra and structure of methyl chloroformate and methyl chloroformate‐d _{3}
View Description Hide DescriptionThe infrared spectra of methyl chloroformate and methyl chloroformate‐d _{3} are reported in the liquid and solid phases in the region 4000–50 cm^{−1}. The liquid phase Raman spectra of these compounds are also reported. It is found that the two compounds readily crystallize as oriented polycrystalline films when cooled in contact with cesium iodide windows. The polarized infrared spectra obtained with these films make possible an improved vibrational assignment for the light compound and a good first assignment for the deuterium‐substituted analog. The results are most consistent with a planar cisstructure and there is no indication of the existence of a second conformer. No clear cases of crystal splitting are observed.

Structural implications of the microwave spectrum of hexafluoropropene
View Description Hide DescriptionAnalysis of the microwave spectrum of hexafluoropropene, C_{3}F_{6}, has yielded rotational constants for the ground vibrational state of 2557.88, 1255.033, and 987.082 MHz. Assignments have also been made on the first four excited states of the CF_{3} torsional mode and on the first excited state of another low‐lying skeletal mode. A rough estimate of 350 cm^{−1} has been obtained for the barrier to internal rotation of the CF_{3} group. The ground‐state moments of inertia are consistent with the expected geometry of the molecule, in which all atoms are coplanar except for two equivalent F atoms in the CF_{3} group.

The Dufour effect
View Description Hide DescriptionEquations for the Dufour effect, which is the development of a temperature gradient due to diffusion, have been solved for geometrically well‐defined cells which have either all walls adiabatic or adiabatic lateral walls and diathermic ends. Two self‐consistent, well‐ordered perturbation schemes have been used, and heat of mixing, variability of all properties, and the barycentric velocity are included explicitly. For typical nonelectrolytes, the temperature difference produced by the Dufour effect could be as large as 0.2 deg for a diffusing mixture with initial mass fraction difference of 0.8. These results can be used (1) to design experiments to test the Onsager heat‐matter reciprocal relation and (2) to avoid undesired temperature variations in diffusionexperiments.