Index of content:
Volume 45, Issue 9, 01 November 1966
Mass‐Spectrometric Studies at High Temperatures. XI. The Sublimation Pressure of NdF3 and the Stabilities of Gaseous NdF2 and NdF45(1966); http://dx.doi.org/10.1063/1.1728088View Description Hide Description
A mass spectrometer has been used to study the sublimation of NdF3 and gaseous equilibria involving NdF3, NdF2, NdF, Nd, BaF, and Ba.
The sublimation pressure of NdF3 is given by the equationwhere 1383°<T<1520°K. The heat of sublimation of NdF3 at 1448°K is 85.7±1.1 kcal mole−1.
Studies of the equilibria among gaseous species over the mixtures Nd+BaF2 and Nd+NdF3 yielded the heats of atomization of NdF3(g) and NdF2(g) and the heat of dissociation of NdF(g). The standard heat of formation of NdF3(s) is −399±10 kcal mole−1.
45(1966); http://dx.doi.org/10.1063/1.1728089View Description Hide Description
The hydroxyl group as a defect in inorganic crystals of more complicated structure has thus far received little attention. Most publications deal with water‐soluble substances. A more detailed study of the OH group has been made for rutile and anatase single crystals. The present paper investigates the hydroxyl group as anionic part in the Perovskite lattice. Results of ir spectroscopy and chemical analysis are compared with the data obtained on rutile.
45(1966); http://dx.doi.org/10.1063/1.1728090View Description Hide Description
For an analytical fluid it is shown that the relationship between coexisting phases is given bywhereand p with subscripts indicates partial derivatives of p evaluated at the critical point
Coexisting phases as a function of temperature are given bywhere
The reduced rectilinear diameter is given by
The reduced slope of the reduced rectilinear diameter is given by
Acceptor Action of Alkali Metals in II—VI Compounds as Detected by Electron Spin Resonance Techniques45(1966); http://dx.doi.org/10.1063/1.1728091View Description Hide Description
Experiments were performed to decide whether the introduction of alkali metals into II—VI compounds gives rise to the appearance of acceptor levels. In comparison with single crystals,powder samples are in most cases purer and it is much easier to dopepowders rapidly and reproducibly. For that reason polycrystalline materials were used in this investigation. In order to obtain a quick and decisive answer to the above‐mentioned question we used electron spin resonance techniques to study the influence of alkali metals on the Fermi level position in these samples. This requires at least one indicator, the presence of which can readily be detected by the employed techniques. For that purpose Fe was chosen since the valence change of divalent Fe to trivalent Fe, caused by the introduction of lower‐lying acceptors, is easily detected at 77°K due to the appearance of the electron spin resonance signal of the trivalent Fe. The use of Fe as an indicator has the additional advantage of setting an upper limit to the depth of the acceptors introduced by the alkali metals, since the position of the Fe level is quite accurately known.
If no acceptors were introduced the Fe was found to be introduced in the divalent form under the preparation conditions chosen and no resonance of trivalent Fe was detected. The simultaneous introduction of the alkali metals Li or Na in ZnS, CdS or ZnSe caused the appearance of resonances due to trivalent Fe. These results unequivocally show that these alkali metals introduce acceptor levels into the lattices investigated. The upper limit to the acceptor depth (optically, with respect to the valence band) are 1.4 eV for cubic ZnS, 1.3 eV for hexagonal CdS, and 1.1 eV for cubic ZnSe. The increase in the amount of Fe that is converted to the trivalent form by the introduction of the alkali metals on going from ZnS to CdS or ZnSe is discussed and explained in terms of the decreasing energy needed to ionize the electron from Fe centers into the conduction band.
45(1966); http://dx.doi.org/10.1063/1.1728092View Description Hide Description
Double‐quantum light scattering by a system of molecules is discussed in this paper. Expressions have been obtained for the scattered light intensity considering both the coherent and incoherent contributions. In that coherent contributions are also considered in this treatment, it goes beyond the scope of previous studies. It is shown that, for molecules of low symmetry, elliptically polarized light must be used in order to determine five independent quadratic forms in the 18 symmetric components (β ijk +β ikj ). According to the present results, the apparent discrepancy between the observed value of ⅓ for the depolarization ratio for CCl4 and the value to be expected from theory may be due to the fact that the coherent contribution had been neglected in previous theoretical considerations. In general, orientational correlation is essential if there is to be appreciable contribution from coherent scattering. For macromolecules, this constitutes a major difference between single‐ and double‐quantum scattering, and additional information may be expected if the latter is investigated experimentally.
45(1966); http://dx.doi.org/10.1063/1.1728093View Description Hide Description
The united‐atom (UA) method and the self‐consistent‐field one‐center‐expansion (OCE) treatment have been applied recently to the study of neonlike and argonlike molecules, namely, HF, H2O, NH3, NH4 +, CH4, HCl, H2S, PH3, PH4 +, and SiH4. In the present article, the values of physical properties predicted by each method are compared with the corresponding experimental quantities. For each molecule, comparisons with experiment have been made for the molecular energy, theoretical bond lengths, ``breathing'' force constants, and, for NH3 and PH3, the proton affinities. The radial density distribution of electrons, determined by us from the published OCE wavefunctions, has been used to calculate the coherent x‐ray scattering factor for the gaseous state of each molecule. The electron densities were also used to determine the purely diamagnetic contribution χ r to the total molar magnetic susceptibility. A comparison was made with the corresponding UA results and with the available experimental quantities. From the trend shown by the relationship between the theoretical and ``experimental'' values for χ r , it was possible, for a molecule with Td symmetry, to suggest a range of values for the diagonal components (gjj ″) of the electronic contribution (g″) to the molecular rotational gyromagnetic tensor (g). Hence, for SiH4, it was suggested that −1.48 < gjj ″ < −1.31. No experimental value for this quantity is known by the authors.
Although it is seen that the OCE results are, in most instances, superior to the results obtained from the UA approximation, the latter method still provides very useful results with comparatively little computation.
45(1966); http://dx.doi.org/10.1063/1.1728094View Description Hide Description
An electron beam served to charge the specimen and simultaneously was diffracted by this specimen. Analysis of the diffraction pattern obtained permits one to see that the easy polarization direction of tridymite lies parallel to the c axis of a hexagonal lattice. This diffraction pattern has been registered with the wavelength fluctuating between 0.0295 and 0.0333 Å. The inner field induced within the specimen was about 0.6 V/Å along the c axis.
45(1966); http://dx.doi.org/10.1063/1.1728095View Description Hide Description
Activated nitrogen produced by a microwavedischarge has a large number of absorption bands in the 600–1100‐Å region in addition to bands of ordinary nitrogen. The present analysis indicates that the additional bands belong to the same band systems as the ordinary nitrogen bands in this region, but the bands are produced by transitions from v>0 levels of the ground state. A brief note concerning the atomic absorptionspectrum of nitrogen in the same region is included.
45(1966); http://dx.doi.org/10.1063/1.1728096View Description Hide Description
The forbidden transitions observed in the nitrogen spectrum below 12.5 V have been studied by electron‐impact methods. Since the theory indicates that electric quadrupole transitions are preferred to singlet—triplet in electron‐impact spectra at intermediate energies, the observed transitions are probably electric quadrupole allowed. This has been demonstrated for the 12.25‐V transition by studying its relative intensity as a function of the scattering angle. The data on the 11.86‐V transition are also compatible with an electric quadrupole transition. In addition, new data on the Lyman—Birge—Hopfield bands in the 60–400‐V energy range indicate that the intensity distribution among vibrational levels is independent of energy.
45(1966); http://dx.doi.org/10.1063/1.1728097View Description Hide Description
The low‐lying valence levels of MgO are calculated by the LCAO MO SCF method using an extended basis set, in order to ascertain the nature of the ground state of the molecule. Three configurations were computed ab initio using open‐shell variational procedures for the excited states. Term values are obtained from the minima of the computed potential curves together with estimates of correlation energy differences between the configurations. The calculations indicate a closed‐shell 1Σ+ground state but with very low‐lying (0.3 eV) 3Π and 3Σ+ levels. The electronic partition function of the molecule is recalculated and hence the published dissociation energy adjusted. D 0°(MgO) is lowered by 4.5 kcal mole−1. Possible experimental consequences of the proximity of the triplet states to the ground state are discussed.
45(1966); http://dx.doi.org/10.1063/1.1728098View Description Hide Description
A gas‐phase chemical activation technique employing the H and Cl abstraction reactions by methylene from chloromethanes has been developed for the production of chloroethanes in the energy range between 85 and 95 kcal mole−1. In this paper the results from the reaction of methylene with chloromethane are reported. The abstraction reactions serve as a clean source of methyl and chloromethyl radicals; combination of these radicals at 25°C produces C2H5Cl and 1,2‐C2H4Cl2 at energies near 90 kcal mole−1. Since the critical energy for the unimolecular HCl elimination reactions is about 55 kcal mole−1, the molecules will react by this pathway unless deactivated by collisions with the bath molecules. By studying the system in the appropriate pressure ranges, the nonequilibrium rate constants were measured at 25°C as 3×109 and 1.8×108 sec−1 for C2H5Cl and 1,2‐C2H4Cl2, respectively.
Reaction of Methylene with Dichloromethane and Nonequilibrium Unimolecular Elimination Reactions of 1,1‐C2H4Cl2 and 1,1,2‐C2H3Cl3 Molecules45(1966); http://dx.doi.org/10.1063/1.1728099View Description Hide Description
The gas‐phase reaction of methylene with dichloromethane proceeds by Cl and H abstraction. The two reactions are competitive, although the ratio of rates depends upon the excess energy carried by the methylene and its electronic state. The total rates of reaction of CH2 with CH2Cl2 and with C2H4 are comparable. The methyl, chloromethyl, and dichloromethyl radicals that are generated by the CH2 abstraction reactions form a good chemical activation system for studying the HCl elimination reactions of C2H5Cl, 1,2‐C2H4Cl2, 1,1‐C2H4Cl2, and 1,1,2‐C2H3Cl3 at energies of ∼90 kcal mole−1. The results for the first two molecules agree with previous work; the rate constants for 1,1‐C2H4Cl2 and 1,1,2‐C2H3Cl2 are 1.2×1010 and 3.4×108 sec−1, respectively. Unusual ``disproportionation''‐type reactions in which chloroethenes and HCl are directly formed seem to occur between dichloromethyl and methyl or chloromethyl radicals.
RRKM Calculated Unimolecular Reaction Rates for Chemically and Thermally Activated C2H5Cl, 1,1‐C2H4Cl2, and 1,2‐C2H4Cl245(1966); http://dx.doi.org/10.1063/1.1728100View Description Hide Description
The RRKM theory of unimolecular reactions has been applied to the HCl elimination reactions of C2H5Cl, 1,1‐C2H4Cl2, and 1,2‐C2H4Cl2, in both chemical and thermal activation systems. The experimental data are adequately represented by a model which employs a four‐center transition state. For example, the model for C2H5Cl gives a pre‐exponential factor of 1.14×1013 compared to the experimental value of 0.97×1013. The calculated and experimental nonequilibrium rate constants for C2H5Cl formed by combination of CH3 and CH2Cl radicals are 1.7×109 and 2.6×109 sec−1, respectively. Various models for the molecule were investigated in an attempt to represent the torsional degree of freedom of the molecule and its interaction with over‐all rotation. Also several models for the activated complex were studied. For the present data, the conclusions presented are as follows: (1) RRKM theory with all internal degrees of freedom taken as active, satisfactorily reproduces the observed data for these four‐center elimination reactions; (2) the torsional degree of freedom can be adequately represented as a low‐frequency vibration and the over‐all rotational degree of freedom about the ``figure axis'' need not be considered active. The activated complex models developed in this work are significantly different from the models developed by Benson and Haugen for the empirical calculation of activation energies for the H—X+olefin reactions.
45(1966); http://dx.doi.org/10.1063/1.1728101View Description Hide Description
A theory of intensities in the diffraction of low‐energy (≲100‐eV) electrons by crystals is formulated on the basis of Lax's multiple‐scattering equations. The formulation is self‐consistent and is thus applicable regardless of the magnitude of the atomic‐scattering factor.
The qualitative conclusions of the theory are discussed in detail with reference to simplified model crystals. The theory predicts that the reflectivity curves (reflectivity associated with a given beam versus electron energy) should show two types of peaks in addition to the ordinary Bragg peaks: (a) a resonance peak in the specular reflectivity curve; (b) secondary Bragg peaks in all reflectivity curves. The resonance peak is predicted at an energy just below that of the first appearance of a nonspecular beam. It derives from multiple scattering in a single atom layer and is associated with a resonance (zero and phase discontinuity) in the effective field. The secondary Bragg peaks are predicted at energies given by conditions similar in form to the ordinary Bragg condition. They derive from multiple scattering between atom layers and are associated with the interference between four or more plane wave components of the effective field. Both types of peaks are prominent only when the atomic‐scattering cross section is large. All qualitative results are illustrated by an exact numerical application to a model crystal of isotropic (s‐wave) scatterers.
The relationship with existing theories is discussed. It is shown that the conventional modified kinematical approach to low‐energy electron diffraction is a limiting case that is approached when inelastic scattering is dominant. It is also shown that when certain assumptions are introduced, the most important being that of neglecting intralayer multiple scattering and the ``two‐beam'' assumption, the theory reduces to the Darwin dynamical theory.
45(1966); http://dx.doi.org/10.1063/1.1728102View Description Hide Description
The microwave spectra of CH3COI and CD3COI were investigated in the region 8000 to 27 000 Mc/sec. The effects of internal rotation and quadrupole perturbations were found to be essentially independent. The height of the potential barrier hindering the methyl group internal rotation was determined to be 1301±30 cal/mole from measured CH3COI doublet splittings. Level mixing was found for several pairs of rotational states, analogous to Fermi resonance in vibrational levels. Mixing effects permitted determination of the quadrupole coupling constant χ ab in both isotopic species. The values for quadrupole coupling constants in CH3COI are χ aa =−1563±2, χ bb =914±2, and χ ab =−135.6±2 Mc/sec. In CD3COI the values are χ aa =−1541±3, χ bb =892±2, and χ ab =−258.5±10 Mc/sec. Diagonalization of each of the above tensors gives χαα=−1569 and χββ=920 Mc/sec.
45(1966); http://dx.doi.org/10.1063/1.1728103View Description Hide Description
The scattering of low‐energy neutrons (0.005 eV) has been used to study translational and librational motions of H2O molecules in various configurations in crystals in a frequency region lying below 1000 cm−1. An attempt is made in this paper to determine the effects of various cations and anions on the frequencies of intermolecular motions of H2O molecules in crystalline salts. The neutron spectra were obtained for a series of hydrates in which the H2O is hydrogen bonded to the same anion, Cl−, but on the sphere of coordination of different cations (Al3+, Cr3+, Sr2+, Ca2+, Fe2+, Mg2+, Co2+, Ni2+) and for Al salts with different anions (NO3 −, SO4 2−, Cl−). This investigation tends to suggest that the vibrational frequencies of the H2O molecules are strongly dependent upon the degree and strength of coordination of the molecule as well as upon the degree and strength of the hydrogen bonds formed with neighboring anions or H2O molecules.
45(1966); http://dx.doi.org/10.1063/1.1728104View Description Hide Description
Since the chemical shift δ of the protonmagnetic resonance signal of water can be assumed to be approximately proportional to the degree of hydrogen bonding,x HB, the temperature dependence of the chemical shift is calculated using theoretical values of x HB vs t from various theories of water structure. These theoretical curves of δ are compared to the experimental temperature dependence of the chemical shift.
In addition, the chemical shift of water in some alcohol and carboxylic acidsolutions is measured and discussed.
45(1966); http://dx.doi.org/10.1063/1.1728105View Description Hide Description
Results have been obtained which indicate that a necessary condition for the phenomenological rate equation [Eq. (1)] to hold in dissociation—recombination of diatomic molecules A2 is that the concentration of Atoms A be sufficiently small. It is estimated that this condition is met for values of the atom concentration which have been obtained experimentally and that it would continue to be met for values of the atom concentration which are larger than the experimental values by several orders of magnitude.
45(1966); http://dx.doi.org/10.1063/1.1728106View Description Hide Description
The relationship between the specific luminescencedS/dx of organic scintillators and characteristic quantities of the ionizing particle is investigated. Considering the existence of the two scintillation components and the effect of δ rays, it is shown that dS/dx depends on the specific energy lossdE/dx and on the charge number z of the incident particle: For a given differential energy loss, the ion having the greatest charge number gives rise to the highest light output; for a given particle with increasing dE/dx, the specific luminescence goes through a maximum.
The theoretical conclusions are in agreement with experimental results obtained using α particles of 1 to 8 MeV, 3He ions in the energy range 1–3 MeV and protons from 0.3 to 3 MeV. An experimental device is described, which allows a direct measurement of the energy loss ΔE of particles passing through a thin organic scintillator, and of a quantity proportional to the number ΔS of emitted photons.
45(1966); http://dx.doi.org/10.1063/1.1728107View Description Hide Description
The m, n matrix element of an arbitrary potential function V(q) in the one‐dimensional harmonic‐oscillator representation is shown to be given bywhere α≡(2ω/ℏ)½, and g(αy) is the Fourier transform of V(q). This formula is specialized to the cases where V(q) is given by qj, qje −½γq 2 , ejαzq , and q −1 sin(αλq), where j is a nonnegative integer and γ, z, and λ are real parameters. Results are compared, where possible, with previous work.