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Volume 47, Issue 8, 15 October 1967
47(1967); http://dx.doi.org/10.1063/1.1712264View Description Hide Description
A physical‐cluster theory of condensation and critical phenomena is developed in which primary emphasis is placed on collective modes of oscillation of clusters under the restoring force of their surface tension. A procedure is advocated for self‐consistent inclusion of surface mode interaction leading to a nonlinear integral equation whose solution yields a wavelength‐dependent surface tension. An explicit expression is derived for the physical‐cluster‐size distribution near condensation, and from it follows prediction of critical exponents δ (critical isotherm degree), γ′ (initial compressibility below Tc ), ν′ (correlation length), and η (deviation from Ornstein—Zernike pair distribution at the critical point), in terms of the phenomenological coexistence curve (β) and surface tension (σ) exponents, as well as a parameter v, which is not directly measureable. The predictions are not consistent with the so‐called ``scaling laws,'' except for special v values that seem experimentally unacceptable. Reasons are listed indicating fundamental differences between the critical phenomena in lattice gases enjoying high current theoretical fashionability, and continuum fluid models. For a range of v values, the physical cluster theory predictions agree well with experiment. Appendices are devoted to an interfacial fluctuation theorem, and to an outline of the present physical‐cluster theory in two dimensions.
47(1967); http://dx.doi.org/10.1063/1.1712265View Description Hide Description
The weak‐coupling theory of molecular exciton states is extended to include the interaction of a vibronic (vibrational—electronic) exciton with its dissociated states in which vibrational and vibronic excitations occur on different sites. Only nondegenerate electronic states of the free molecule are considered. The spirit of the weak‐coupling limit is rigorously adhered to in that no approximations are made concerning the nature of the molecular potential‐energy surfaces. Analogy with exciton trapping by impurities leads to the notion of vibrational capture by vibronic excitons. There are also correlated or secondary capture states in which the vibrational exciton follows the vibronic exciton at a fixed distance as it moves through the crystal. Expressions containing the frequency shifts and Franck—Condon factors of the isolated molecule as parameters are derived for the energy and intensity of the capture state. In two special models the effects of large frequency shift and equal Franck—Condon factors are treated. For a linear chain with nearest‐neighbor interactions, explicit formulas are derived for the transition probability and compression of the exciton band due to coupling with dissociated states.
47(1967); http://dx.doi.org/10.1063/1.1712266View Description Hide Description
If a current the order of 1 mA is passed through 50–750 torr of a pure rare gas in a 10‐cm‐diam tube a diffuse discharge results filling the tube and emitting mainly a continuous spectrum, strong in the vacuum uv, weak in the near uv, visible and ir. The discharge is characterized by a very high voltage gradient and a substantially flat volt—ampere characteristic. The ion and electron concentration is 108−109 cm−3 and the electron energies are high. Energy losses are principally elastic and the ions and electrons reach the wall by ambipolar diffusion. The continuous spectra are of molecular origin. Continua from Xe, Kr, and Ar are whitish, that from Ne a light blue. In any of the above discharges if a critical current is exceeded the discharge goes to a filamentary form. The addition of 0.1% N2 to the pure rare gas has profound effects, lowering the gradient in Xe 18‐fold and bringing out the arc lines of Xe. New spectral structures are found at 3466 Å, 3650 Å, and at 1.3 μ which are believed to be due to complex molecules of Xe and N2. There is an afterglow lasting up to 10 sec that is spectroscopically much the same as the discharge itself. A high concentration (1013−1014 cm−3) of long‐lived energy carriers is indicated and are believed to be mainly N2(3Δ u ). Collisions of pairs of 3Δ u with Xe as a third body and/or of 3Δ u with N2(A) produce the higher excited states of Xe and probably Xe2 + and higher excited states of N2 and N atoms. Blue fluorescence of a Pyrex wall indicates strong vacuum uv in Xe. The Vegard—Kaplan (VK) bands are developed with fair intensity indicating a population of N2(A) of the order of 1010 cm−3. The discharges have a positive characteristic indicating that the ions and electrons are disappearing by recombination and that the metastable energy carriers are partially saturated with respect to current. Interruption of the current is followed by an abrupt fall in luminosity to ∼⅓ of the initial intensity, followed by a recovery to ∼¾ initial, and then a slow decay of ∼½ sec. In N2+Kr the first negative system of N2 + is strongly developed perhaps indicating the presence of a high‐energy metastable state of N2.
47(1967); http://dx.doi.org/10.1063/1.1712267View Description Hide Description
The paramagnetic resonance spectrum of NO2 has been studied at 4°K in gamma‐irradiated single crystals of KNO3. The g and hyperfine parameters are essentially the same as those for NO2 in NaNO2 but substantially different than those in KNO3 at 77°K, indicating that thermal motion at 77°K is frozen out at the lower temperature.
47(1967); http://dx.doi.org/10.1063/1.1712268View Description Hide Description
The stimulated Raman scattering of radiation is studied as an illustration of the fact that a correct quantum description of the interaction of a laser beam with matter is obtained by representing the field by means of Glauber coherent states. Any attempt to represent the field by means of incoherent, occupation‐number representation states will yield an incomplete description of the physical situation.
47(1967); http://dx.doi.org/10.1063/1.1712269View Description Hide Description
Mixed excimer fluorescence is observed when any one of a variety of aromatic hydrocarbons is added to solutions of 9‐cyanoanthracene or 9, 10‐dicyanoanthracene. The formation of a mixed excimer appears to be markedly dependent upon the ionization potential of the donor. The emission maxima of the 9, 10‐dicyanoanthracene mixed excimers vary linearly with the polarographic oxidation potentials of the donors, a results corresponding to that found for charge‐transfer absorption bands. It is concluded that charge‐transfer interaction is important in the excimer state.
47(1967); http://dx.doi.org/10.1063/1.1712270View Description Hide Description
Boron trifluoride adds to many Lewis bases to form 1:1 molecular addition compounds. Under favorable conditions, some of these adducts may be used to fractionate the isotopes of boron by means of the following reaction:The equilibrium constants for this reaction vary with donor, donor substituents, and temperature. At 30°C the following order is observed: . The ``anomalous'' concentration of boron‐10 in the molecular addition compound may be explained by the unique chemistry of the boron and fluorine atoms. A model is proposed which accounts for observed variations in the isotopic fractionation factor when different donors are used, as well as when different substituents are present on a selected donor. The model also explains the isotopic behavior of other boron halides.
47(1967); http://dx.doi.org/10.1063/1.1712271View Description Hide Description
The polarization ratios b/a, b/c′, and a 0/c 0 of the phosphorescence emission of 2‐chloro‐, 2‐bromo‐, 2‐iodo‐, and 2, 3‐dibromonaphthalene in biphenyl host crystal and 1‐bromonaphthalene in naphthalene host crystal are determined at 77°K. The relative transition probability of the emitting oscillators along the long axis (PL ), short axis (PM ) and normal to the halonaphthalene molecular plane (PN ) has been determined for each vibronic band in the spectrum. This is accomplished by a three‐dimensional analysis, using the observed polarization ratios from any two host crystal faces and the normalization condition: PL+PM+PN =100, applied to any vibronic emission band. The relative importance of the different spin‐allowed transitions in rendering the triplet—singlet spin‐forbidden transition allowed is concluded from the three‐dimensional analysis. In all the compounds studied, the out‐of‐plane electric dipole allowed transitions contribute 20%—40% of the intensity of the phosphorescence of the halonaphthalenes by direct spin—orbit perturbation [Subspectrum I:T. Pavlopoulos and M. A. El‐Sayed, J. Chem. Phys. 41, 1082 (1964)]. The in‐plane electric dipole allowed transitions contribute 60%—80% of the intensity via spin—orbit‐vibronic perturbation (Subspectrum II). The relative amounts of the long‐ and short‐axis polarized emissions are very sensitive to the position of the halogen atom in the naphthalene ring. The long‐axis polarized emission constitutes 52%, 21%, and 39% of the total emission of the 2‐halo‐, 1‐bromo‐, and 2, 3‐dibromonaphthalenes, respectively. The short‐axis polarized emission constitutes 10%—20%, 36%, and 44% of the total emission of the 2‐halo‐, 1‐bromo‐, and 2, 3‐dibromonaphthalenes, respectively. These observed variations in the long‐ and short‐axis in‐plane polarized emission are readily explained by the valence‐bond method if the perturbing transitions involve the (intramolecular) charge‐transfer (ionic) states formed from the linear combination of the ionic structures resulting from transferring electrons from the halogen atoms to the ring or to other halogens, if present. The relative amount of the out‐of‐plane emission is found to be largest for the 2, 3‐dibromo‐derivative (∼35%) in rigid glasses but lowest (∼17%) for the same compound in biphenyl host. This result shows that the decrease of the relative amount of the out‐of‐plane emission of 2, 3‐dibromonaphthalene in biphenyl host is a result of host—guest and not bromine—bromine interaction. The fact that the different bands involving the lattice vibrations of the host are found to have polarization similar to that of the phononless band indicates that the host—guest interaction is static in nature. Two mechanisms are proposed to explain the results. In the first mechanism, the intramolecular spin—orbit coupling scheme is changed by forcing the halogen to be slightly nonplanar with the aromatic ring due to the packing forces of the host lattice. In the second mechanism, mixing between the host and guest electronic states is proposed.
47(1967); http://dx.doi.org/10.1063/1.1712272View Description Hide Description
Proton and fluorine NMR data in NH4BF4 and its totally deuterated analog reflect the presence of isotropic and rapid BF4 − tumbling as well as onset of isotropic NH4 + ion motion in the orthorhombic phase. A linewidth transition in the 19F spin system from 19±1 G2 at 133°K to 2.5±0.5 G2 at 198°K and 19F thermal relaxation timesmeasured in ND4BF4 from 210° to 478°K yield a span of 19F correlation times from 3×10−4 sec (168°K) to 6.4×10−11 sec (472°K). The transition to the cubic modification at 472°K decreases the 19F correlation time to 2.6×10−12 sec (478°K). Above 318°K, fluorine relaxation in NH4BF4 is dominated by intraionic dipolar interactions, while below this temperature cross relaxation with protons located on neighboring ammonium ions becomes evident. Deuteration removes this contributor to the 19F relaxation. The apparent activation energy for BF4 − motion is slightly dependent upon temperature, and increases somewhat with increasing temperature. The pre‐exponential factor associated with 19F correlation times above 318°K is abnormally small, possibly reflecting a decrease in the effective moment of inertia by mechanical coupling between BF4 − motion and NH4 + motion. Crystallographic measurement of the orthorhombic unit cell parameters from 190° to 296°K shows rapid linear expansion of a and c axes in the range 190° to 260°K, with a marked decrease in the rate of variation of these axis lengths with temperature above 260°K. In the same temperature region a shallow protonT 1 minimum is observed, which may be associated with the modification of NH4 + ion motion by lattice expansion or simply due to cross relaxation with the 19F spin system. ProtonT 1 data also show a shallow plateau at higher temperatures due to interionic dipolar coupling and the BF4 − motion. The x‐ray data suggest the possibility of a subtle crystallographic change at low temperatures. A small linewidth transition is observed for the proton spin system in the range 173°K (4.0±0.1 G2) to 223°K (2.9±0.1 G2) apparently associated with interionic dipolar coupling.
47(1967); http://dx.doi.org/10.1063/1.1712273View Description Hide Description
The effect of pressure to 200 kbar has been measured on the Mössbauer resonance in a number of high‐spin ionic ferrous and ferric compounds. The isomer shift and quadrupole splitting characterize the ionic state and spin state of iron. In general, there is a decrease in the iosmer shift with increasing pressure correspinding to an increase of electron density at the iron nucleus. This can amount to 8%—20% of the difference in isomer shift between typical ferrous and ferric compounds. The pressure effect is usually larger in ferrous than in ferric compounds, and is associated with changes in the 3d−3s shielding. The quadrupole splitting usually increases with pressure. A quantitative interpretation depends on knowledge of changes in local symmetry and of spin—orbital coupling factors, as well as local compressibility. For six of the eight ferric compounds, we observed a significant amount of reduction to the ferrous state at high pressure. This phenomenon was definitely reversible. It appears to be associated with a general tendency for the ground state of the ferrous ion to decrease in energy relative to the ligands with increasing compression. Thus, electron transfer is facilitated. Some evidence exists that strong light also reduces iron compounds. These results tend to broaden the analogy previously noted between photochemical and high‐pressure reactions.
Effect of Pressure on the Mössbauer Resonance in Potassium Ferrocyanide, Potassium Ferricyanide, and Insoluble Prussian Blue47(1967); http://dx.doi.org/10.1063/1.1712274View Description Hide Description
The effect of pressure to 200 kbar has been measured on the Mössbauer resonance in potassium ferrocyanide, potassium ferricyanide, and insoluble Prussian blue. The ferrocyanide exhibits a decrease of isomer shift with pressure large compared with typical high‐spin ionic ferrous compounds. The ferricyanide exhibits an initial shift with pressure twice as large as the ferrous material. These large changes can be associated with changes in ``back donation'' and in 4s admixture in the binding. The ferricyanide reduces to ferrous compound with increasing pressure, paralleling to behavior of many high‐spin ferric compounds. As in the case of the high‐spin material, the phenomenon reverses with decreasing pressure. Near 50 kbar a first‐order phase transition occurs which apperantly relieves the internal compression of the ferricyanide ion. It is accompanied by an increase in the isomer shift of the ferric ion and the pressure‐induced ferrous ion as well as a decrease in the quadrupole splitting of the former. It is also accompanied by a large decrease in the percentage of Fe2+ ion present. This definitely relates the reversible reduction of ferric iron to overlap of the wavefunctions of metal and ligand. Insoluble Prussion blue contains high‐spin ferric ion and low‐spin ferrous ion. This compound also shows a reversible reduction of high‐spin ferric ion with increasing pressure.
47(1967); http://dx.doi.org/10.1063/1.1712275View Description Hide Description
The ground state and first excited state of the nitrogen‐molecule positive ion are calculated using the matrix Hartree—Fock approximation, which results in a reversal of the observed spectroscopic order of states. The inclusion of estimates of correlation‐energy differences between the levels corrects this and leads to a calculated term value of the excited state (1.17 eV) in extremely close agreement with experiment (1.16 eV).
Elastic Electron Scattering Amplitudes for Neutral Atoms Calculated Using the Partial Wave Method at 10, 40, 70, and 100 kV for Z = 1 to Z = 5447(1967); http://dx.doi.org/10.1063/1.1712276View Description Hide Description
Elastic electron scattering amplitudes for neutral atoms were calculated using the partial wave expansion method for 10‐, 40‐, 70‐, and 100‐kV incident electrons. The partial wave phase shifts were calculated by numerical intergration using the phase amplitude method until the results converged to values obtained using the WKBJ and first Born approxmations, which were then used in the remainder of the partial wave sum.
The static potential field of the target atoms was represented by an analytical expression involving a sum of Yukawa terms. Potential field parameters for the expression were obtained by a least‐squares fit of the radial electrondistribution function,D (r), using Hartree—Fock and relativistic wavefunctions for all the neutral atoms from Z=1 to Z=54. For the smaller atoms from Z=1 to Z=21, Clementi Hartree—Fock wavefunctions were used and for the atoms from Z=22 to 54 Liberman—Waber—Cromer D (r) curves calculated using the Dirac Hamiltonian incorporating a j—j coupling scheme and the Slater ⅔ approximation in the exchange potential were used.
47(1967); http://dx.doi.org/10.1063/1.1712277View Description Hide Description
The far‐infrared torsional vibration spectra in the 350–40‐cm−1spectral region are reported for the gaseous state of the following compounds: Ethyl chloride, propylene, deuterated ethyl bromide, 2‐chloropropane, 2‐bromopropane, 2‐iodopropane, dimethylamine, deuterated dimethylamine, dimethyl ether, deuterated dimethyl ether, 2,2‐difluoropropane, deuterated acetone, hexafluoroacetone, trimethylamine, tertiary butyl cyanide, and tertiary butyl acetylene. Using absorption bands assigned to torsional vibrations, the height of the potential barrier for internal rotation is calculated and compared to the available microwave data.
47(1967); http://dx.doi.org/10.1063/1.1712278View Description Hide Description
The kinetic theory of a small particle suspended in a Knudsen gas in which the temperature of the surface of both the particle and the boundary of the system obey arbitrary distributions has been established according to the revised law of thermal transpiration developed recently by Wu. The external force acting on the particle is mainly due to the radiometric force caused by the incident and the reflecting molecules in the absence of thermal‐creep effect in this limiting regime. Several particle shapes have been considered, such as a small disk, flat plate, sphere, and cube presented in a cylinder with uniform temperature gradient in a thermal transpiration system.
47(1967); http://dx.doi.org/10.1063/1.1712279View Description Hide Description
The Chapman—Enskog method is used to obtain estimates for the coefficients of diffusion,thermal diffusion, and thermal conductivity for a dilute gas composed of two species of loaded‐sphere molecules. Calculations are presented for the case in which the load eccentricity of one of the species is vanishingly small and the mass and size of both species are identical. The results of these calculations are in agreement with the observed thermal‐diffusive behavior of the D2—HT system.
47(1967); http://dx.doi.org/10.1063/1.1712280View Description Hide Description
The interchange‐symmetry concept for molecules and crystals is introduced. In a molecule it is the minimal symmetry establishing the physical equivalence among a given set of its constituent fragments (nuclei or collections thereof). In a crystal it is a minimal symmetry establishing the physical equivalence among a set of constituents (atoms or molecules) within the unit cell. The chief application of the interchange symmetry in this paper is for the classification of eigenstates and the interpretation of spectroscopic data encountered in investigations of molecular crystals. The existence of n‐1 pure, inequivalent, interchange elements in ideal crystals is proven group theoretically, where n is the number of molecules or atoms per primitive unit cell. The relations among interchange symmetries and interchange groups, site groups, unit cell groups, translation groups and space groups are discussed. These are related to crystal splittings, intermolecular coupling constants (including signs), selection rules and excitontheory (including k≠0). Examples: the benzene molecule (Höckel theory), the benzene, naphthalene, and anthracene crystals (exciton coupling constants and their signs), methyl halides, N2, CO, and CO2 crystals (interchange splittings), and the CS2 crystal (ground and distorted excited state). Nonhexagonal benzene and its energy splittings is the example in a separate chapter on isotopically substituted molecules that get distorted in excited states and/or in condensed phases like matrices and crystals.
47(1967); http://dx.doi.org/10.1063/1.1712281View Description Hide Description
The rates of the bimolecular and termolecular neutralization reactions of gaseous ions generated from the thallium and lead halides have been measured. The absolute values of the termolecular rate constants are generally consistent with Thomson's theory of ion recombination, although the experimental temperature dependence of the rate constant is somewhat greater than the theory predicts. The bimolecular rate constants are consistent with what is known about the energetics and masses of the systems. A mass spectrometric examination of gaseous ion‐neutral complex formation is presented.
47(1967); http://dx.doi.org/10.1063/1.1712282View Description Hide Description
Investigations have been made of the paramagneticrelaxation of the triplet molecules zinc 2,2′‐biquinoline randomly oriented in a rigid‐glass matrix of 2‐methyltetrahydrofuran. The saturation and relaxation behavior of these molecules is qualitatively consistent with the inhomogeneous nature of the ΔM=1 line‐shape. The relaxation times are such that a hole burned in the line can recover by spin—lattice relaxation and by cross relaxation to adjacent spin packets. The temperature dependence of the spin—lattice relaxation time is given by T 1 −1=1.37×105 exp(−22/T)+2.94T 2.
We interpret the exponential as indicating an Orbach process between the ground‐state triplet and the first excited singlet. The Orbach exponent implies that the triplet—singlet separation, which is determined by the value of the intramolecular exchange integral, is 15.5±1 cm−1. An expression for T 1 similar to that derived by Scott and Jeffries has been used to identify the dominant interaction participating in this process. From crude estimates of the spin‐vibronic matrix elements it seems unlikely that this interaction is large enough to account for the experimental value of T 1=1.3 msec at 4.2°K. The only interactions which are large enough to explain this value are second‐order vibronic effects which involve singlet—triplet mixing through static spin—orbit coupling. At this time we can offer no explanation of the T 2 dependence which predominates below 2°K.
Cross Sections for Electron‐Impact Fragmentation and Dissociation Energies of the Dimer and Tetramer of Bismuth47(1967); http://dx.doi.org/10.1063/1.1712283View Description Hide Description
Although molecules of bismuth have been the subject of numerous studies, the investigation reported here represents the first reliable mass‐spectrometric study of these molecules. First of all, this article describes a new method for handling the problem of apportionment of ion currents in mass‐spectrometric analyses when both direct ionization and electron‐impact fragmentation contribute comparable currents to a specific ion species. The study of the molecules Bi and Bi2 provides an experimental test of this apportionment method for the ion current of Bi+. Second, this article describes measurements of the heats of dissociation and atomization of Bi4. The results of these measurements provide the only reliable information now available on this molecule. The experimental heat of atomization of Bi4 at 298°K is found to be 139.7±1.9 kcal mole−1. Other thermodynamic data obtained for the dimer and monomer confirm the results of previous investigators.