Volume 33, Issue 3, 01 September 1960
Index of content:
33(1960); http://dx.doi.org/10.1063/1.1731229View Description Hide Description
The complex dielectric constant of isoamyl bromide has been measured at 1, 3, and 9 kMc between —75° and 25°C. Complex plane plots indicate an asymmetric, skewed‐arc distribution of relaxation times, with the shape of the distribution function not being appreciably temperature dependent. A defect diffusion model is proposed to explain the dielectric behavior of this system. This model implies that the relaxation of a molecule is more probable immediately after one of its neighbors has relaxed than at an arbitrary time. A distribution of relaxation times is derived which, under the appropriate conditions, closely resembles that of the empirical skewed‐arc function.
33(1960); http://dx.doi.org/10.1063/1.1731230View Description Hide Description
The proton‐magnetic‐resonance doublets were obtained for rotation of the crystal around its c axis. From these data, the proton‐proton separation was computed to be 1.56±0.02 A. The hydrated water molecule was found to lie in one orientation whose proton‐proton axis makes direction angles of α0=89±1°, β0=1±1°, and γ0=90±6°, measured from the positive a, b, and c crystallographic axes, respectively. This orientation fits well into the crystal structure and indicates that the complex, BrI— —H–O–H— —BrII, exists.
Line widths range from 6.5 to 4.2 gauss and show a correlation with T 1 as a function of orientation. Observation was necessarily made with some saturation.
A new effect, an asymmetry of line areas in the doublets, was observed for narrow ranges near two crystal orientations. The two orientations were symmetrically close to that for which the proton‐proton line was parallel to the external magnetic field. It may be due to crossing of the bariumquadrupole resonance frequencies over the magnetic‐resonance frequencies of the protons.
Charge Transfer Reactions Producing Intrinsic Chemical Change: Methyl, Methylene, and Hydrogen Radicals Produced from Argon and Methane Reactions33(1960); http://dx.doi.org/10.1063/1.1731231View Description Hide Description
Charge transfer reactions producing intrinsic chemical changes in the neutral molecule have been proven by mass spectrometric techniques. The charge transfer reactionproducing an intrinsic chemical change in CH4 was found to be more probable by a factor of five than the simple charge transfer reactionCharge transfer reactions in mixtures of Ar and CH4 and Kr+CH4 were studied over the pressure range of 0.1–0.5 mm of Hg in the ionization chamber.Reactions were elucidated by catalytic and negative ion studies as well as by the usual pressure and appearance potential techniques. In the Kr+CH4 mixture, the reactionproducing the charged radical CH3 + was found to have a high probability. Absolute values for rate constants and cross sections are given for all of the charge transfer reactions observed in the Ar+CH4 mixture. Products from these elementary charge transfer reactions are correlated to previously reported radiolytic, α ionization (W value), and hydride ion transfer studies.
33(1960); http://dx.doi.org/10.1063/1.1731232View Description Hide Description
Diffusion in crystals by a vacancy mechanism is described by a model consisting of an isotope and a vacancy imbedded in a linear lattice of harmonic oscillators. Assuming a 6–12 potential between defects and lattice atoms, the anharmonic interaction is explicitly calculated. The usual approximation of assuming this interaction to depend linearly on the frequency is shown to be valid as long as the Debye approximation for the frequency spectrum is applicable.
The lattice with defects is analyzed using the formalism developed by Brout and Prigogine. In order to solve the equations, the concept of localized modes is introduced. The localized mode is approximated by the oscillation of the defect(isotope) in the lattice. The justification for this is investigated by a method due to Montroll and Potts.
The diffusion constant is calculated and shown to depend on the fourth power of the defect frequency. This is in agreement with an earlier result by Klemens, but deviates appreciably from the usual first power dependence.
33(1960); http://dx.doi.org/10.1063/1.1731233View Description Hide Description
33(1960); http://dx.doi.org/10.1063/1.1731234View Description Hide Description
The use of the mass‐action law in connection with solid‐state equilibria involving conduction electrons or holes assumes that the chemical potential of the species is related to its concentration by μ=μ0(T)+kT lnn. This approximation can fail at concentrations which are still very small by ordinary chemical standards. The formalism may be preserved in principle by introducing a suitable activity coefficient γ. It is shown theoretically, however, that γ increases almost exponentially with increasing n when n/λ≳0.1, where λ is the partition function in the quasi‐free‐particle approximation. As a consequence, the proper exponent of n in mass‐action equations becomes much larger than expected from stoichiometry considerations alone. The use of such equations becomes difficult, therefore, when n/λ≳0.5, and entirely unjustified when n/λ≳10. The determination of λ, which lies between 1016 and 1021 cm—3 for most semiconductors is discussed from an experimental viewpoint.
33(1960); http://dx.doi.org/10.1063/1.1731235View Description Hide Description
A theory is presented whereby the long‐range intermolecular forces, including the London dispersion forces, of pure nonelectrolytes may be calculated from optical and dielectric data. The method is based on the continuum‐model approach, where one molecule is treated explicitly while the others are replaced by a medium of uniform dielectric. The classical and quantum‐mechanical oscillators are used as working models and expressions are derived for computing the cohesive energy appropriate for both types of oscillators. The potential energy based on the quantum‐mechanical oscillator is calculated for a number of liquids and is shown to be in fair agreement with the experimental energy of vaporization.
33(1960); http://dx.doi.org/10.1063/1.1731237View Description Hide Description
The crystal structure of β‐Ga2O3 has been determined from single‐crystal three‐dimensional x‐ray diffraction data. The monoclinic crystal has cell dimensions a=12.23±0.02, b=3.04±0.01, c=5.80±0.01 A and β=103.7±0.3° as originally reported by Kohn, Katz, and Broder [Am. Mineral. 42, 398 (1957)]. There are 4 Ga2O3 in the unit cell. The most probable space group to which the crystal belongs is C 2h 3—C2/m; the atoms are in five sets of special positions 4i: (000, ½½0)±(x0z). There are two kinds of coordination for Ga3+ions in this structure, namely tetrahedral and octahedral. Average interionic distances are: tetrahedral Ga–O, 1.83 A; octahedral Ga–O, 2.00 A; tetrahedron edge O–O, 3.02 A; and octahedron edge O–O, 2.84 A. Because of the reduced coordination of half of the metal ions, the density of β‐Ga2O3 is lower than that of α‐Ga2O3 which has the α‐corundum structure. Also the closest approach of two Ga3+ions in β‐Ga2O3 is 3.04 A which is considerably larger than the closest approach of metal ions in the sesquioxides with the α‐corundum‐type structure and, in agreement with the results of thermodynamic measurements, the β phase appears to be the structurally more stable one.
The average Ga–O distances in the structure seem to account for the fact that although the Ga3+ ion is substantially larger than the Al3+ ion its quantitative preference for tetrahedrally coordinated sites when substituted for Fe3+ ion in the irongarnets is very nearly the same as that of the Al3+ ion.
The structure accounts for a recent result obtained by Peter and Schawlow from paramagnetic‐resonance measurements on Cr3+‐ion‐doped β‐Ga2O3, namely that the Cr3+ ion substitutes for the Ga3+ions in a single set of equivalent octahedral sites.
The magnetic aspects of the β‐Ga2O3structure are discussed and it is shown that a possible Fe2O3 isomorph could be expected to be at least antiferromagnetic with a Néel temperature of about 700°K Furthermore, a knowledge of the β‐Ga2O3structure and of the nature of site preferences of the Ga3+ and Fe3+ions in the garnets lead to a prediction regarding the structure of the ferrimagnetic crystals of formula Ga2—x Fe x O3 recently discovered by Remeika.
33(1960); http://dx.doi.org/10.1063/1.1731238View Description Hide Description
Our electron diffraction apparatus has been suitably modified for the study of vapors at high temperatures. A furnace and auxiliary power supply have been constructed, and a serviceable design for a sample container, with a nozzle, has been developed.
Data on two systems have been obtained. The diffraction pattern produced by cesium chloride vapor is that expected for a diatomic molecule; the interatomic distance determined in this experiment checks with the microwave value. In lithium chloride vapor, dimers predominate. Their structure is diamond shape (planar) with
The dimensions of the lithium halide dimers are compared and their thermodynamic functions tabulated.
33(1960); http://dx.doi.org/10.1063/1.1731239View Description Hide Description
The solution of the general open first‐order stochastic process representing the relaxation of an open multistate system is obtained by the generalization of a method of Krieger and Gans. The result is valid for a system containing an arbitrary number of absorbing and semiabsorbing states as well as allowing the presence of any number of emitting states. The stability of the solution is discussed in terms of the matrix of the transition probabilities. This is done with the aid of a theorem of Lévy and Hadamard. The result is applied to the corresponding closed system as well as the present work.
33(1960); http://dx.doi.org/10.1063/1.1731240View Description Hide Description
The dilute diffusionflame method for measuring the rates of fast gas reactions has been used to study the reaction 2NO+F2=2ONF. The reaction proceeds with the emission of visible light, and photographic methods were used to obtain concentration profiles in space. The results were interpreted in terms of the mechanism[Complex chemical formula]The interpretation of results is somewhat ambiguous. The observed rate may be that for the first step, in which case the rate constant has a pre‐exponential factor of 6×1011 cc/mole‐sec and an activation energy of 1.5±1.0 kcal between room temperature and dry ice temperature. Alternatively the observed rate may be a composite of at least four of the elementary steps given above. With a reasonable assignment of rate constants for the succeeding steps, the first alternative is favored, although the margin of safety is not great.
33(1960); http://dx.doi.org/10.1063/1.1731242View Description Hide Description
The radiolytic decomposition of CO induced by alpha particles appears to be initiated by two reactive species, CO+ and CO*. The products of the reaction are CO2 and the solids (C3O2) x and graphite.Carbon dioxide formed during the reaction depletes the CO+ by charge transfer. Thus, when CO2pressure becomes sufficiently high, CO* only initiates reaction. The reaction mechanism suggested is consistent with previous ionization and photochemical studies in the CO system.
33(1960); http://dx.doi.org/10.1063/1.1731243View Description Hide Description
Normal coordinate analysis, for XY 4‐type molecules of Td symmetry, has been carried out by the Wilson FG‐matrix method. Following Dennison, using the spectral data on NH4 + and ND4 +, the anharmonicity factors have been calculated. The constants of the most general quadratic potential‐energy function have been obtained for the ammonium ion.
33(1960); http://dx.doi.org/10.1063/1.1731244View Description Hide Description
The out‐of‐plane CH bands in a number of polynuclear aromatic molecules are analyzed. The CH bonds are considered as coupled oscillators. With each group of n neighboring CH bonds an n×n subdeterminant and a single vibrational frequency was associated. The method is applied to the methyl‐1,2‐benzanthracenes. Observed spectra agree with calculated frequencies well, and thus support the idea that observed CH bands are caused by splitting of n identical coupled oscillators. The spectra of some other polynuclear aromatic hydrocarbons are discussed as well.
33(1960); http://dx.doi.org/10.1063/1.1731245View Description Hide Description
The temperature dependence of the infrared spectra of N2O4 and N2O3 in the solid phase at liquid‐nitrogen temperatures has been investigated. From these spectra of both 14N and 15N isotopic molecules, absorption bands which may be assigned to unstable isomers of these nitrogen oxides have been identified. A reasonable interpretation of these absorption bands can be made by assuming the existence of two unstable forms of N2O4 and one of N2O3.
33(1960); http://dx.doi.org/10.1063/1.1731246View Description Hide Description
The proton hyperfine constants obtained from protonmagnetic resonance spectra of polycrystalline free radicals and from valence bond calculations of π‐orbital spin densities are compared for the free radicals α,α′‐diphenyl‐β‐picryl hydrazyl, and tris‐p‐chlorophenylaminium perchlorate. Two lines are observed in the protonmagnetic resonance spectra, one shifted upfield and one downfield from the normal resonance frequency. These are assigned to the ortho and paraprotons, and the metaprotons of the free radicals, respectively. Though the agreement between theory and experiment is not quantitative for the hyperfine constants, the theoretical and experimental ratios of hyperfine constants agree within experimental error. This serves to verify the existence of positive and negative spin densities and the signs of some of the relationships involved.
Nuclear Magnetic Resonance Spectra of Systems of the A 3 B 2 C Type: Proton Magnetic Resonance Spectra and the Absolute Signs of the Proton‐Proton Spin Coupling Constants in Ethyl Acetylene and Ethyl Mercaptan33(1960); http://dx.doi.org/10.1063/1.1731247View Description Hide Description
The high‐resolution protonmagnetic resonancespectra of ethyl acetylene and ethyl mercaptan have been studied at both 40 Mc and 60 Mc. Theoretical analysis of these spectra as systems of the A 3 B 2 C type enables one to determine the relative signs of the proton‐proton spin coupling constants in these molecules. It is thus shown that the spin coupling constants J CH3–CH2 and J CH2–CH are of opposite sign in ethyl acetylene, while J CH3–CH2 and J CH2–SH in ethyl mercaptan are of the same sign. Making use of the results of the valence bond theory regarding the absolute sign of J CH3–CH2 the present analysis has made possible determinations of the absolute sign of J CH2–CH and J CH2–SH in ethyl acetylene and ethyl mercaptan, respectively.
33(1960); http://dx.doi.org/10.1063/1.1731248View Description Hide Description
Two‐center integrals of operators for Slater‐type atomic orbitals are concisely expressed in terms of O functions which arise directly from the integral representation in spherical polar coordinates. The O functions are expressible in terms of A and B functions which lend themselves nicely to machine programs. Their greatest asset is their convenient correlation of A and B functions with Slater‐type atomic orbitals and operators expressed in spherical polar coordinates. Examples are given for dipole‐moment and quadrupole‐moment operators.
33(1960); http://dx.doi.org/10.1063/1.1731249View Description Hide Description
The Raman spectra of solutions containing cuprous, argentous, and mercuric ions together with cyanide ions indicate the presence of the di‐, tri‐, and tetra‐coordinated complexes. The spectra from solutions containing zinc and cadmium ions, respectively, with cyanide ions could be investigated in concentrations where only the tetra‐coordinated complex is observed.