Volume 37, Issue 9, 01 November 1962
Index of content:
37(1962); http://dx.doi.org/10.1063/1.1733403View Description Hide Description
The relations between second‐order derivatives of the thermodynamic properties of three‐dimensional systems have been evaluated. The method of Jacobians which was used previously for first‐order systems has been extended, and results are presented in tabular form.
Szilard—Chalmers Chemistry and Radiation Chemistry of Solid Hexabromoethane. Thermal Annealing and Radiation Annealing Effects37(1962); http://dx.doi.org/10.1063/1.1733404View Description Hide Description
The effects of ionizing radiation and thermal treatment on the chemical fate of Br82 atoms produced in solid C2Br6 by the Br81 (n,γ)Br82 process have been investigated. Three chemically distinguishable forms of Br82 are found, using two methods of analysis. One method involves determination of the fraction of the Br82 which is extractable into aqueous solution when the irradiated C2Br6 is dissolved in CS2 and the other involves dissolution in liquid Br2 followed by evaporation of the solvent. The ``aqueous yield'' of Br82 in C2Br6irradiated with neutrons at —196° and analyzed at 0° under the conditions of these investigations is 34%. This is lowered to about 24% by heating to 100° for an hour prior to analysis. Exposure of the crystals to 1020 eV g—1 of Co60 gamma radiation at —196° either before or after neutron irradiation does not affect the yield if analysis is made without thermal annealing but lowers it to 3.5% for samples annealed 1 h at 100°. Analyses of thermal annealing curves at several gamma doses and several temperatures indicate the existence of several processes by which gamma defects and Br82‐containing defects are annealed.G(Br2) from the radiolysis of C2Br6 is reduced by thermal annealing in a manner having similarity to the annealing of Br82. Implications of the data are discussed.
37(1962); http://dx.doi.org/10.1063/1.1733405View Description Hide Description
The difference between the energy of the best open‐shell and best closed‐shell wavefunctions for the hydrogen molecule was calculated for various values of the internuclear distance. Both left—right and in—out correlated functions were considered. The relative importance of the type of correlation reverses at an internuclear distance of 0.8 a 0.
37(1962); http://dx.doi.org/10.1063/1.1733406View Description Hide Description
A solution has been obtained for the differential equations describing the changes in concentrations with time and position in an ultracentrifuge cell during the sedimentation of an isomerizing substance. It is assumed that diffusion is negligable, and that the centrifugal field and cell cross section are constant. In addition to the general result, simple approximate solutions are presented for the cases where the chemical reactions are moderately slow and moderately fast, compared to the rate of separation of species by the centrifugal field.
37(1962); http://dx.doi.org/10.1063/1.1733407View Description Hide Description
Results are given for some numerical calculations, carried out on a high‐speed computer, for a simple model of sedimentation with concurrent dimerization. These results show that in a simple, dimerizing system anywhere from one to three concentration‐gradient peaks may be simultaneously observable. The numerical techniques used involved some interesting aspects in themselves and are therefore discussed briefly. Finally, a simple analytic expression for theoretical concentration‐gradient peak decay rates is presented.
37(1962); http://dx.doi.org/10.1063/1.1733408View Description Hide Description
The temperature dependence of the 20–28 kK optical absorption in K3Fe(CN)6 crystal is negligible below room temperature. The inference is made that this charge‐transfer absorption is electronically allowed (u←g). An alternate interpretation of Naiman that the band is of (g←g) type and thus activated by vibrations is not disproven, but it is restricted such that very stiff modes—i.e., those involving CN stretching— would have to be the only effective vibrational promoters. Arguments are made against this possibility.
37(1962); http://dx.doi.org/10.1063/1.1733409View Description Hide Description
Chemisorption of oxygen on highly ordered and relatively disordered tungstensurfaces at substrate temperatures of 20° and 300°K has been studied in the field‐emission microscope. Evidence is presented for the chemisorption of a monolayer of gas with a sticking coefficient of unity and the adsorption of a second, initially mobile layer of oxygen, also with a sticking coefficient of unity when the substrate temperature is 20°K. These results are independent of the degree of surface order over the range considered. The second adsorbed layer is not observed at substrate temperatures of 300°K, and use of the Langmuir postulate that only the clean surface contributes to the adsorption allows the definition of a constant sticking coefficient of 0.8 for oxygen on tungsten at 300°K. Variations in the dipole moment per adatom with crystallographic orientation are also reported.
37(1962); http://dx.doi.org/10.1063/1.1733410View Description Hide Description
Formulas are derived for the rotational relaxation times of gases composed of molecules interacting with square well potentials with rough spherical and spherocylindrical cores. The temperature dependence of the relaxation times is discussed and compared with previous theoretical results.
37(1962); http://dx.doi.org/10.1063/1.1733411View Description Hide Description
NMR spectra of tetravinylsilicon, methyl‐, and ethylvinylketone have been analyzed. The parameters found do not agree with those previously reported for the same compounds by other authors, although the source of several experimental data is the same; the coupling constants agree well with values already known for other vinyl compounds and correlate satisfactorily with the electronegativities of the elements bonded to the vinyl group.
37(1962); http://dx.doi.org/10.1063/1.1733412View Description Hide Description
The absorption coefficients of the ν3, 4.3‐μ CO2 band were measured over a temperature range of about 1200° to 2400°K at various pathlengths. The hot CO2 sample was investigated in the exhaust jet of a small supersonic burner, while the jet composition was obtained using a radiation temperature measurement and a simple thermochemical calculation. The present experimental results are compared with existing experimental values and theoretical calculations. The results indicate that above 2000°K a weak line approximation can be used to describe the absorption or emission of the band. The apparent integrated band intensity of the CO2 fundamental as a function of temperature is also reported and discussed in relation to other measurements.
37(1962); http://dx.doi.org/10.1063/1.1733413View Description Hide Description
A theory of electronic energy relaxation in the solid phase is presented. This process is sometimes called internal conversion when applied to states of the same multiplicity, or intersystem crossing when applied to states of different multiplicity. The physical limit where the electronic transition is slow compared with vibrational relaxation is shown to be a well‐defined mathematical limit in the theory. In the other limit, where the electronic transition is rapid compared with the vibrational relaxation time, vibrational relaxation plays the dominant role in the over‐all relaxation process. The result derived from a continuum model for the final states is justified only in the first limit and only then providing the assumption of a large number of final states is physically justified. Two different models are used to illustrate the source of the mathematical limitations and the range of applicability of the theory. These models remove the ambiguities which arise from the normalization of continuum states in the continuum model. The most important conclusions of the paper are embodied in Eqs. (22), (23), (40), (48), and (50).
37(1962); http://dx.doi.org/10.1063/1.1733414View Description Hide Description
The photolysis of the phenoxy radical trapped in solid nitrogen at 4.2°K is studied by use of infrared and visible‐ultraviolet absorption spectroscopy. The trapped phenoxy radicals are produced by the photolysis of a parent compound (phenol, anisole, or phenetole) suspended in the solid nitrogen. When light not absorbed by the parent compound is used to decompose the trapped phenoxy radical, product bands grow at 4.68 μ, 4.72 μ, and 2600 Å. The 4.68‐μ band has been assigned to carbon monoxide. The 4.72‐μ and 2600‐Å bands are probably due to trapped 6‐oxo‐1,3,5‐hexatrienyl‐1 radicals. The mechanism proposed to account for these products is that absorption of a light quantum by a phenoxy radical breaks the bond between the 1 and 2 ring carbon atoms to produce an excited 6‐oxo‐1,3,5‐hexatrienyl‐1 radical. This excited radical may either decompose to yield carbon monoxide or be deactivated and trapped.
37(1962); http://dx.doi.org/10.1063/1.1733415View Description Hide Description
The high‐resolution absorptionspectrum of C2HD has been studied in the 1900 to 3400 cm—1 region. Several bands at lower frequencies have been examined with medium resolution. Nineteen bands were analyzed for their rotational constants. Combination differences of four transitions from the ground state were averaged and the rotational constantsB 0=0.99156±0.00004 cm—1 and D 0=1.17±0.07×10—6 cm—1 obtained. This B 0 value together with those recently obtained for C2H2 and C2D2 have been used to calculate the ground‐state and equilibrium bond distances of the acetylene molecule. The l‐doubling constants for the degenerate modes were determined to be q 4=4.42×10—3 cm—1 and q 5=3.6×10—3 cm—1. The frequencies of the bending modes have been calculated by use of difference bands to be ν4 1=518.38 cm—1 and ν5 1=677.77 cm—1.
37(1962); http://dx.doi.org/10.1063/1.1733416View Description Hide Description
A microscopic description of the electromagnetic interactions among a set of charged particles, valid to terms of order c —2, is used to derive a number of well‐known expressions for macroscopic electrostatic and magnetostatic ``energy'' and ``work.'' Particular attention is paid to the assumptions required for the validity of these expressions, and to the relations between the various nonequivalent expressions bearing the same name (such as ``magnetic work'').
37(1962); http://dx.doi.org/10.1063/1.1733417View Description Hide Description
This paper is an extension of previous work by Magee and Funabashi on the influence of electronic coupling on dissociation mechanisms. The same model (linear chain of diatomic molecules) has again been considered. The use of a dynamical version of the Hellmann—Feynman theorem allows the development of a unified treatment valid for any coupling. An application to an infinite linear chain of hydrogen moleculeions is made, and the following results are found:
(1) In the weak‐coupling case, immediate dissociation occurs.
(2) In the intermediate case, the electronic excitation energy is converted into vibrational energy, mainly localized on the molecule initially excited. Redistribution of the vibrational energy then occurs.
(3) In the strong‐coupling case, dissociation does not occur. Many molecules vibrate with comparable amplitudes.
Short chains, containing two, three, four, and seven molecules, are also considered. For these it is found that two or more dissociations usually occur regardless of the type of coupling and initial position of the excitation.
Finally, an application to intramolecular energy transfer is attempted. The case of the radiation induced isomerization of cis‐polybutadiene into its trans isomer, studied by Golub, is examined. With certain restrictions, our results can be considered as supporting Golub's views.
37(1962); http://dx.doi.org/10.1063/1.1733418View Description Hide Description
The ESRpowderspectra of both pure K3CrO8 and of K3NbO8, containing small amounts of K3CrO8, have been obtained. The spectra have yielded the values: g∥=1.9434, g ‖=1.9848, for the two spin Hamiltonian parameters of chromium in the +5 oxidation state. It has been shown that the g factors can only be explained by assuming the ground state to be B 1(dxy ). Further, the optical spectrum of K3CrO8 in 30% H2O2 has been obtained and the single observed band at 20 000 cm—1, has been assigned to the B 1→E transition. Both the ESR and the optical spectra indicate a strong degree of covalent character in the bond between the chromium atom and the peroxide ions.
37(1962); http://dx.doi.org/10.1063/1.1733419View Description Hide Description
The scattering of helium and argon from the cleavage plane of lithium fluoride has been studied using molecular‐beam techniques and under vacuum conditions which were somewhat better than are typical for systems of this type. The helium measurements confirm the diffraction effects reported by O. Stern and co‐workers and reveal, in addition, a broad scattered beam approximately symmetrical about the specular position which apparently has not been previously recognized. Measurements with argon beams gave scattering patterns which were quite different from those obtained for helium. The scattered beams were very broad and had an intensity maximum between the specular position and the crystal normal. Analysis of the data showed that this deviation of the maximum from the specular position cannot be obtained by superposition of specular and cosine‐law scattering components. Furthermore, the experimental data on the scattering of argon seem to be inconsistent with a diffraction mechanism.
37(1962); http://dx.doi.org/10.1063/1.1733420View Description Hide Description
We show that in the Hartree—Fock approximation there exists a uniquely defined Hermitian potential which describes the interaction of a model subgroup of electrons with the rest of the system. This potential can be divided into two parts. The first part is the difference between the Hartree—Fock Hamiltonian for the system and the model Hamiltonian. The second part is a nonlocal potential which cancels (screens) some of the first part. The essential point in the derivation is our choice of definition for model orbitals in the system. The only condition that must be satisfied by the occupied orbitals of the system is that they be linearly independent. It is also shown that there exist equations describing the best orbitals to use in a calculation by a linear combination of atomic orbitals method. They are the best orbitals to use because they give the exact answer. As a concrete example of our ideas we have treated numerically the LiH molecule. In order to link our method with others that have been described we indicate how the pseudopotential form of the orthogonalized plane wave method may be derived.
Velocity Dependence of the Differential Cross Sections for the Scattering of Atomic Beams of K and Cs by Hg37(1962); http://dx.doi.org/10.1063/1.1733421View Description Hide Description
Measurements of the velocity dependence of the angular intensity distribution of potassium and cesium beamsscattered by a crossed beam of mercury are presented. The alkali beam was velocity selected, with a triangular velocity distribution (half‐intensity width 4.7% of peak velocity); the velocity was varied over the range 185–1000 m/sec. The Hgbeam had a thermal distribution; the average Hg speed was ∼235 meters per second. The scattering data have been converted to the center‐of‐mass system. The angular distributions show the expected strong forward scattering and evidence the phenomenon of rainbow scattering. The energy dependence of the rainbow angle is used to evaluate the interatomic potential well depth, interpreted as the dissociation energyDe of the 2Σ+ molecular ground state. Values (in erg×1014) thus obtained (±5%) are 7.46 for KHg and 7.72 for CsHg. Absolute values of differential cross sections could not be obtained; only relative cross sections D(θ) are reported. The observed low‐angle behavior D(θ) ∝θ‐ 7/3 serves as direct experimental confirmation of the r —6 dependence of the long‐range attractive potential for K–Hg and Cs–Hg systems.
Benzene Ring Distortion by One Substituent. Microwave Determination of the Complete Structure of Benzonitrile37(1962); http://dx.doi.org/10.1063/1.1733422View Description Hide Description
Microwave spectra of benzonitrile, C6H5CN, and 9 isotopic species are reported. Moments of inertia of these 10 molecules are combined to give the rs structure of benzonitrile. The final structure is: C(1)C(2) = 1.391 Å, C(2)C(3) = 1.393 Å, C(3)C(4) = 1.400 Å, C(1)C(7) = 1.455 Å, C≡N = 1.159 Å, C(2)H(2) = 1.069 Å, C(3)H(3) = 1.082 Å, C(4)H(4) = 1.081 Å, C(6)C(1)C(2) = 122.5°, C(1)C(2)C(3) = 118.45°, C(2)C(3)C(4) = 120.3°, C(3)C(4)C(5) = 120.0°, C(1)C(2)H(2) = 121.8°, C(4)C(3)H(3) = 119.9°.