Volume 64, Issue 6, 15 March 1976
Index of content:

Superstructure and modulation wave analysis for the unidimensional conductor hepta‐ (tetrathiafulvalene) pentaiodide
View Description Hide DescriptionWhen acetonitrile solutions of tetrathiafulvalene [i.e., (C_{3}S_{2}H_{2})_{2}; herein called TTF] and iodine, I_{2}, are allowed to mix by diffusion, monoclinic crystals are formed with the approximate composition (TTF)_{7}I_{5}. These crystals have an electrical conductivity along the needle axis c of 300 ohm^{−1}⋅cm^{−1} at room temperature. A complete crystal structure analysis based on an approximate supercell with a=48.016(16) Å, b= 16.041(6) Å, c=24.877(7) Å, β=91.31(2) °, Z=12 (RRF)_{7}I_{5} was carried out using space group P2_{1}/a with 225 nonhydrogen atoms in the asymmetric unit. The TTF molecules stack along c and form a TTF subcell a _{1}=a/3, b _{1}=b, c _{1}=c/7, Z _{1}=4 TTF and subcell symmetry C2/m. The iodine atoms are in chains along c and form an A‐centered sublattice complex (space group A2/m) with a _{2}=8.213 Å, b _{2}= b, c _{2}=5.023 Å, β_{2}=103.0°, and Z _{2}=2 I. The supercell space group P2_{1}/a is the mathematical intersection of the two subcell space groups. The supercell is only approximate because 5c _{2}=25.113(14) Å which is about 1% longer than 7 c _{1}; consequently, the particular crystal studied has the formula (TTF) I_{0.7076}. The crystallographic R (F ^{2}) index is 10% for the 3715 x‐ray data with intensity greater than 1 sigma and 12% for the complete set of 5733 independent reflections. The stacked TTF molecules are displaced from their ideal sublattice complex positions by displacement waves with rigid‐body translational and rotational components. One‐ and three‐dimensional Fourier analyses of the displacements show that TTF molecules are displaced predominantly by translational displacements along b and torsional rotations about c and that the periodicities are related to the iodine sublattice complex. A similar analysis for the iodine substructure show modulations related to the TTF sublattice complex; thus the modulation waves of the system are related to the dual sublattice complex geometries. Special techniques were developed for solving and refining dual‐sublattice‐complex crystal structures using a principle that interacting sublattice complexes Fourier transform as convoluting reciprocal lattices. Application of these principles to another dual‐sublattice‐complex problem, the chimney ladder structure Mn_{15}Si_{26}, is discussed.

On the evaporation of small ions from charged droplets
View Description Hide DescriptionExperiments are briefly reported which show that small ions separate or ’’evaporate’’ from evaporating droplets carrying electrical charges. A theoretical argument is developed to find in which conditions this ion evaporation can occur; to that end solvation free enthalpies of cluster ions are derived from existing experimental data and the absolute reaction rate theory is applied. The conditions for ion evaporation are compared with those for Rayleigh instability and it is shown that the first process should occur only when the drop reaches sizes of the order of 10^{−6} cm. The ion evaporation process must be operative in the evaporation of highly electrified cloud droplets when their solute concentration is low.

The Hugoniot and shock initiation threshold of lead azide
View Description Hide DescriptionThe Hugoniot of unreacted dextrinated lead azide has been determined using plate impact techniques in a 2.5 in. bore gas gun. The test specimens were compacted to a density of 3.4 gm/cc. Piezoresistive gauges were used to determine both the impact stress and the stress profile propagated through the sample. Each shot provided transmitted wave data for four sample thicknesses. The Hugoniot is linear up to 10 kbar. It can be represented by the equation σ=41.7 U _{ p } (σ in kilobars and U _{ p } in mm/μsec). The initiation threshold to long duration (3.5 μsec) shocks was 6.0 kbar based on evidence of reaction in the explosive inferred from increases in stress with propagation distance. Changes of wave speed were found to be noticeable only at higher stresses. Above 6 kbar the delay in initiation decreases with increasing stress levels. The initiation sensitivity to short duration (0.1 μsec) shocks was determined by impacting the lead azide with thin flyers accelerated by exploding foils. The impact velocity was determined by observation with a high‐speed framing camera and the transmitted stress profiles were measured by x‐cut quartz gauges. The short‐pulse initiation threshold for polyvinyl lead azide is 4.2 kbar for a density of 3.6 gm/cc, and 2.1 kbar for dextrinated lead azide for a density of 2.9 gm/cc. Comparison of initiation threshold measurements suggests that there is a minimum thickness, or a run‐up distance, before detonation occurs which is independent of pulse width with stresses up to 10 kbar. For long pulse (3.5 μsec) experiments with the gas gun, no evidence of detonation was detected for 1 mm thick samples. Detonation occurs with run distances in the range of 1–2 mm for impact stresses of 8.9 kbar. For stresses greater than 6.0 kbar, evidence of detonation was noted after a 2 mm run. In the thin flyer plate experiments at stresses of 8 kbar dextrinated lead azide displayed a 2 μsec initiation delay. Close to the initiation threshold the stress profiles in the explosive show a gradual transition from an unreactive shock to a stable detonation. It is postulated that reaction occuring behind the shock front produces pressure waves which travel through the explosive interacting with the unreacted explosive ahead of the reaction front causing a nonuniform rate of growth of the shock. This behavior is similar to that observed for heterogenous secondary explosives. The wave speed of the initial wave front propagating in the explosive changes abruptly from that appropriate to unreacted material to the detonation velocity.

Static and dynamic structure factors for interdimensional systems. I. Chainlike crystals
View Description Hide DescriptionThe displacement–displacement space–time correlation functions and static and dynamic structure factors are calculated for a chainlike harmonic lattice. The continuous transition from 3D to 1D behavior of the various quantities as functions of the interchain coupling is analyzed. Criteria for probing the 1D behavior are obtained along with suggestions and predictions for relevent scattering experiments. Existing experimental results are found to be compatible with the theory.

Study of the structure of molecular complexes. XIII. Monte Carlo simulation of liquid water with a configuration interaction pair potential
View Description Hide DescriptionA water–water interaction potential obtained from configuration interaction calculations has been used to simulate liquid water, at 25 °C, by a Monte Carlo technique. The resulting radial distribution functions and x‐ray and neutron scattering intensities are compared with experiment and found to be in satisfactory agreement. Some thermodynamic properties are also computed and discussed. The overall agreement seems to indicate that many‐body effects contribute little in determining the structure of liquid water, although they seem to be important for an accurate simulation of internal energy and related quantities.

A theoretical study of the electronic structure of ferrocene and ferricinium: Application to Mössbauer isomer shifts, ionization potentials, and conformation
View Description Hide DescriptionSelf‐consistent field wavefunctions have been obtained for ferrocene and several low‐lying states of the ferricinium ion using extended basis sets of contracted Gaussian functions. In agreement with the near minimal basis set results of Coutière e t a l., the electronic structure is found to change very considerably when ferricinium is formed by removing an electron from an Fe d molecular orbital of ferrocene. The ionicity of Fe, as determined by a Mulliken gross population analysis, is found to be +1.47 for the ion and +1.39 for ferrocene. The difference is less than 0.1 electrons, while a value close to one would have been expected. The major contribution to the change in structure comes from a greatly increased covalency of the ligand orbitals of e _{1g } symmetry in the ion. The change is shown to be responsible for the small differences found between the isomer shifts, and thus electron densities at the Fe nucleus, in ferrocene and ferricinium salts. Direct contributions from Fe 4s electrons are found to account for about half of the 0.93a ^{−3} _{0} difference in the electron density. A value of the change in nuclear radius, δR/R=−4.4×10^{−4}, is estimated from the computed densities. Computed values of the six lowest ionization potentials of ferrocene are compared with photoelectron spectra, and symmetry assignments of the ionic levels are made. The average error of the computed ionization potentials is 0.5 eV, giving confidence to these assignments. For the states considered, wavefunctions have been obtained for both the eclipsed and staggered conformations of the C_{5}H_{5} rings. Both absolute and relative total energies are found to be essentially the same for either conformation.

Discussion of Clarke’s ’’graph theoretic’’ method: Application—the Rayleigh–Bénard instability of a binary mixture
View Description Hide DescriptionThe ’’graph theoretic’’ method of Clarke is analyzed with a view to application to stability problems other than chemical reactions. The extended version—essentially the extension of the vertex aspects of the method is applied to the analysis of the Rayleigh–Bénard (convective instability) for a binary mixture.

The determination of optical absorption intensities using the X _{α} scattered wave method
View Description Hide DescriptionA density matrix formulation for optical absorption is developed within the X _{α}scattered wave theory using the transition state concept. Oscillator strengths for optical excitations in H^{+} _{2}, H_{2}, and FeCl_{4} ^{−1} are given for the f (∇V) form. In H^{+} _{2}, oscillator strengths accurate to about 10% are found for R?2.0 a _{0} (the equilibrium nuclear separation). In H_{2}, the intensity of the X ^{1}Σ_{ g }→B ^{1}Σ_{ u }transition at equilibrium is very accurately described (error ? 10%), but the X ^{1}Σ_{ g }→C ^{1}Π_{ u }transition intensity is not satisfactory due to the diffuse character of the ^{1}Π_{ u } state. The errors in the H_{2} and H^{+} _{2} intensities are associated with specific defects in the scattered wave model. These defects should not, however, cause significant errors in many systems of chemical interest. Consistent with this viewpoint, semiquantitative agreement is found between the theoretical and experimental intensities in FeCl_{4} ^{−1}.

Studies in fluctuation analysis: I. On relations between rate constants and relaxation times in chemical systems and the multivariate power spectrum of noise and fluctuations
View Description Hide DescriptionAn investigation of the stochastic fluctuations that occur in chemically reactive solutions is presented in terms of irreversible chemical thermodynamics. The approach considers in some detail the properties of the fluctuations in the frequency domain (e.g., the power spectrum) and it is found that (1) the kinetic rate constants of the reaction process can be obtained directly from the inverse of the normalized power spectrum extrapolated to the zero frequency point, (2) the Onsager flow coefficients are derived from the second moments and the inverse of the power spectrum at the zero frequency extrapolation, and (3) the eigenvalues of the normalized spectrum are the chemical relaxation times. It is suggested that the approach outlined in this article may prove useful in studies of chemical kinetics without the necessity of resorting to macroscopic relaxation methods.

Raman spectrum of ice VIII
View Description Hide DescriptionThe Raman spectra of H_{2}O and D_{2}O ice VIII recovered at ∼100 K and zero pressure have been measured in the range 4000–50 cm^{−1}. The three stretching, three rotational, and four translational bands expected from the symmetry of the crystal have been identified. Two bending bands are expected and have been tentatively identified among some weak bands. The relative intensity of the rotational and stretching bands is much smaller than in the vapor, and so if the intensity of the stretching bands is not greatly changed, the anisotropy of the polarizability is appreciably smaller in ice VIII than in the vapor.

Vibrational levels of heteronuclear rare gas van der Waals molecules
View Description Hide DescriptionVibrational levels for the diatomic heteronuclear van der Waals molecules formed from ground‐state helium, neon, argon, krypton, and xenon are calculated using available potential functions based on other kinds of experimental information.

Electron spin resonance studies of peroxy radicals labeled with ^{17}O in polytetrafluoroethylene
View Description Hide DescriptionThe ESR spectrum of the radicals formed by the reaction of oxygen with γ‐irradiated polytetrafluoroethylene (PTFE) has been obtained using oxygen isotopically labeled with ^{17}O. The presence of lines from two oxygen nuclei both labeled with ^{17}O confirms that peroxy radicals are formed. Two types of peroxy radicals are discussed; firstly, the peroxy chain radical (–CF_{2}–CF(O_{1}Ȯ_{2})–CF_{2}) with g _{⊥}=2.0220, g _{∥}=2.0060, a _{∥}(1) =40±1 G, a _{∥}(2) =89±1 G at 300 K, and g _{ z z }=2.0380, g _{ y y }=2.0065, g _{ x x }=2.0026, a _{ x x }(1) =46±1 G, a _{ x x }(2) =107±1 G at 77 K and secondly, the peroxy propagating radical (–CF_{2}–CF_{2}(O_{1}Ȯ_{2})) with g _{iso}=2.004, a _{iso}(1) =13±1 G, a _{iso}(2) =26.5±1 G at 300 K and identical parameters to the peroxy chain radical at 77 K. The temperature dependence of the ESR spectra is analyzed in terms of the rotational freedom in the polymer. The peroxy chain radical undergoes rotation along the polymer chain axis and the peroxy propagating radical also has this rotation about the chain axis and in addition rotates about the C–O bond which is nearly perpendicular to the main chain axis.

Generalized Langevin equation approach for atom/solid‐surface scattering: General formulation for classical scattering off harmonic solids
View Description Hide DescriptionA general theoretical framework for introducing many‐body or lattice effects into gas/solid scattering is presented. The theory is presently restricted to classical scattering off harmonic lattices but is otherwise completely general. It is nonperturbative and valid for arbitrary lattice temperature. The theory is based on a formulation of lattice dynamics suggested by and related to the Kubo–Mori theory of generalized Brownian motion. This formulation leads to a generalized Langevin equation (GLE) in which only the coordinates of the gas atom and the n∼1–6 surface atoms directly struck by the gas atom appear explicitly. The remainder of the lattice, which functions as a harmonic heat bath, affects the collision through a friction kernel and a Gaussian random force appearing in the GLE. The GLE can be solved in terms of a tractable number of (n+1) ‐particle gas–surface trajectories using approximate stochastic techniques. Stochastic solution yields thermally averaged temporal gas particle probability distribution functions (pdf). From the long time limit of these pdf’s all temperature dependent gas–surface cross sections can be found. In the limit of zero friction, the theory gives a convenient method for calculating atom–oscillator thermally averaged cross sections which circumvents laborious Monte Carlo classical trajectory sampling and which can be generalized to treat other gas phase collision problems.

Evidence for trapped‐exciton fluorescence in anthracene crystals at room temperature
View Description Hide DescriptionThe fluorescence variations due to imposed exciton–charge carrier interactions in anthracene are examined as a function of emission wavelength. In the short wavelength region of the emission spectrum, the observed modulation of the fluorescence intensity due to the presence of trapped charge carriers is relatively small and, with the exception of the highly reabsorbed fluorescence at very short wavelengths, is independent of emission wavelength. At longer wavelengths, however, a series of maxima develop along with a tenfold increase in the modulation. These observations are interpreted in terms of emission from trapped singlet excitons. Though the results are consistent with those expected with a discrete exciton trap at 0.43 eV, they may also be interpreted as indicating a series of exciton traps with depths in the range 0.4–1.0 eV. Results are also presented for tetracene‐doped anthracene crystals which support the hypothesis that the traps are perturbed molecules of the host crystals, rather than impurities.

Theory of dynamic light scattering from polydisperse systems
View Description Hide DescriptionAnalytical expressions for the light scattering autocorrelation function of Schulz distributed Rayleigh–Debye particles are presented. The theory is shown to be valid for spheres, thin rods, disks, and Gaussian coils executing translational diffusion. The polydisperse form factors for these shapes are also given. Analysis of polydisperse data with the expressions given yields the diffusion coefficient of the number average species and the Schulz polydispersity parameter. The effects of polydispersity on the angular dependence of the decay time and the conditions under which the form factor can be neglected are discussed.

Single‐rotational‐level lifetimes from measurements of linewidths in the B ^{3}Π_{0} _{ + }←X ^{1}Σ^{+} system of ICI
View Description Hide DescriptionLines in the 3−1 band of the B ^{3}Π_{0} _{ + }←X ^{1}Σ^{+} system of ICl vapor havew been recorded using a Fabry–Perot interferometer spectrometer. A striking increase in linewidths is observed for transitions ending on excited‐state rotational levels above J′=37. Even at low J′, the linewidths are approximately twice the expected value. Examination of the probable causes of the broadening in the spectrum points to shortened excited‐state lifetimes and yields 3×10^{−11} sec for the lifetime of I^{35}Cl in the J′=41 level and about 2×10^{−10} sec for J′ values below 20. These may be compared with the radiative lifetime, 9.8×10^{−7} sec, obtained from areas of some of the profiles measured here. The observed short lifetimes are discussed in terms of a homogeneous predissociation suggested also by earlier workers. The data require that the outer limb of the potential energy curve of the B state interact with an unstable O^{+} state. In addition it is suggested that a weaker, heterogeneous predissociation contributes to the widths for levels of low J′.

Collision‐induced spectra of rare gas mixtures: Experimental results and empirical relations
View Description Hide DescriptionTranslational absorption spectra were obtained for He–Kr and He–Xe mixtures at 300 °K and for He–Ar, He–Kr, He–Xe, Ne–Ar, Ne–Kr, and Ne–Xe mixtures at 480 °K. These spectra, as well as other rare gas translational spectra available from the literature, were found to obey a rule of corresponding states when expressed in terms of reduced frequencies and intensities. The peak frequencies and intensities, the half‐widths and spectral moments, were found empirically to vary as simple functions of the temperature and could be correlated quantitatively with molecular properties. On the basis of these correlations the characteristics of as yet unmeasured spectra could be predicted.

Uniform reduced interaction dipole for all rare gas pairs
View Description Hide DescriptionA large body of translational absorption spectra of the rare gases was used to evaluate a uniform reduced interaction dipole for all rare gas pairs. This dipole, obtained through the use of realistic intermolecular potentials, was free from artifacts which distorted previous dipoles, obtained from cruder models. Interesting correlations were found between individual dipole strengths and molecular properties. Similarities between the dipole and potential functions were noted.

Photoionization and Rydberg states of N_{2}
View Description Hide DescriptionThe frequencies and intensities of transitions to Rydberg levels, the direct photoionization cross section, and the angular distribution of photoelectrons of N_{2} have been calculated for processes associated with N^{+} _{2}(X ^{2}Σ^{+} _{ g }) and N^{+} _{2}(A ^{2}Π_{ u }). The theoretical model is based on a Hartree–Fock wavefunction for the ground state of N_{2}, and excited statewavefunctions derived from an irreducible‐tensorial one‐center representation of the effective potential of the N^{+} _{2} core. The calculations were carried out for several internuclear distances, especially to try to interpret the dependence of the angular distribution on the final vibrational state.

Autoionization of N_{2}
View Description Hide DescriptionAutoionization of N_{2} has been investigated theoretically, for the energy region between the threshold for production of N^{+} _{2} in its ground state, and the threshold for production of the first excited state of N^{+} _{2}. Both vibrationally induced and electronically induced autoionization were studied. Rates for the former process, originating with Rydberg states in the n pσ_{ u } ^{1}Σ^{+} _{ u }(v′≳0) and n pπ_{ u } ^{1}Π_{ u } (v′≳0) series, are of order 10^{10} sec^{−1} or slower, and correspond to linewidths of 0.2 cm^{−1} or less. Electronically induced autoionization is faster, with typical rates 10^{11}–10^{12} sec^{−1}, corresponding to linewidths of 0.5–5 cm^{−1}, consistent with observations.