Volume 37, Issue 1, 01 July 1962
Index of content:
37(1962); http://dx.doi.org/10.1063/1.1732927View Description Hide Description
The excess thermodynamic and molecular properties induced in a classical single‐component fluid by static external force fields are examined from several points of view. By utilizing the techniques of cluster theory, a local ``pressure,'' p̄(r), is constructed whose spatial integral yields directly and precisely the logarithm of the grand partition function, including the result of interaction with container vessel walls as well as other external fields (present, for example, in gravitational or centrifugal equilibrium). In particular, it is remarked that the problem arising from cluster integral dependence upon vessel volume in the usual imperfect gas theory is solved. The density expansion for p̄ is transformed into an integral involving a modification (Xg ) of the well‐known ``direct‐correlation function,'' or non‐nodal cluster function. Subsequent construction of local free energies provides a condition under which these quantities may be represented by uniform fluid values (evaluated at the local density), plus corrections involving just density gradients (or Laplacians). When the external force field is generated by a fixed set of particles, the formalism leads to new integral equations for molecular distribution functions. Comparison with similar previously known integral equations, in the pair distribution case, yields an explicit, formally exact, expression in terms of Xg for the troublesome ``elementary diagram cluster sum,'' which has prevented exact solution to the pair distribution problem. Finally, a new fluctuation theorem is derived, which relates the density derivative of surface tension for a fluid next to a planar wall of its vessel, to molecular distribution at this interface.
37(1962); http://dx.doi.org/10.1063/1.1732935View Description Hide Description
Free radicals produced by γ irradiation of single crystals of N‐acetyl methionine have been investigated through their electron spin resonance patterns for different orientations in the magnetic field. Two chemically different free radicals have been found, both relatively stable at room temperature. One of them has an ESR pattern very similar to that of cystine dihydrochloride. Analysis of this resonance shows that the electron spin density is concentrated mainly on the S in a free radical which probably has the chemical form[Complex chemical formula]The gtensor for this radical is anisotropic with principal values 2.004, 2.029, and 2.064. An isotropic doublet hyperfine structure of 9.5‐G spacing is observed. The second resonance has a complex, incompletely resolved, hyperfine structure with a total spread of about 26 G. Its almost isotropic gtensor with principal values from 2.002 to 2.005 indicates that the electron spin density is concentrated on a carbon. The free radical is believed to have the form[Complex chemical formula]but this structure is not proved.
37(1962); http://dx.doi.org/10.1063/1.1732945View Description Hide Description
The perchromate ion, CrO8 3—, in K3CrO8 has D 2d () symmetry and consists of a central pentavalent chromium ion surrounded by four peroxide groups. On the basis of a refinement of the previous structure determination, the chromium ion is nearer to one oxygen of each peroxide group than to the other and the peroxide oxygen—oxygen distance is shorter than normal. A ligand field calculation, based on the optical spectrum and the electron paramagnetic resonance spectrum, accounts for these structural features and leads to a description of the bonding in the perchromate ion.
37(1962); http://dx.doi.org/10.1063/1.1732968View Description Hide Description
A method for analyzing complex NMR spectra, which utilizes an iterative technique on the spin energy levels, is described. We show how the experimental energy levels and their errors are derived from the observed spectrum and the assignment of the various transitions. We discuss several techniques and methods that are helpful in obtaining this assignment. Sum rules for the energy levels and the intensities of the transitions, useful in the analysis, are also pointed out.
With the iterative procedure, which uses the eigenvectors of an approximate Hamiltonian, we then calculate the changes in the chemical shielding constants and the spin—spin coupling constants necessary to adjust the approximate energy levels toward the experimental ones. The probable errors in the derived magnetic parameters are also readily determined.
37(1962); http://dx.doi.org/10.1063/1.1732969View Description Hide Description
High‐resolution spectrum of Yb3+ in the cubic field of CaF2 is reported. The striking features of the spectrum are two strong sharp lines at 10 384.759 and 10 377.039 cm—1 at 4.2°K. The position of the two lines and their separation was measured as a function of the temperature. The line shape is Lorentzian. The possible position of the various Stark levels of the ground state is discussed.
37(1962); http://dx.doi.org/10.1063/1.1732970View Description Hide Description
The linear variation of nuclear magnetic shielding with electric field is calculated semiquantitatively by a variation method and by a perturbation method. The effect is sufficiently large to be significant for protons in molecules containing polar groups or in ions, as these protons experience intramolecular electric fields of ∼106 statV/cm. The effect on protons in solids for laboratory electric fields would only be a fraction of the (magnetic) dipolar linewidth and is therefore not observable. The calculation gives good agreement with the several experimental values from the literature. The intramolecular (electric) dipolar field is then used to explain the low‐field shift in resonance frequency of the methylene protons in in ethyl alcohol—an important example of the chemical ``inductive effect.''
37(1962); http://dx.doi.org/10.1063/1.1732971View Description Hide Description
For general spin systems of the type , it is shown that nuclear magnetic double‐resonance spectra recorded by sweeping magnetic field are mirror images if the frequency of the strong radio‐frequency field is set at equal intervals Δ above and below the resonance frequency of one type of nucleus. It is further proven that the double resonance spectrum is symmetric for Δ=O when field is swept, and for all values of Δ when frequency is swept. Finally, it is shown that the relative signs of all the coupling constants between nonequivalent or magnetically nonequivalent nuclei in a spin system can, in principle, be obtained in a double resonance experiment.
37(1962); http://dx.doi.org/10.1063/1.1732972View Description Hide Description
The mutual solubility of GeTe, SnTe, and PbTe was examined by x‐ray diffraction techniques. The rhombohedral to cubic phase transformation of GeTe and GeTe in various solid solutions were determined. The transformation temperature is shown to vary inversely with cation mass.
37(1962); http://dx.doi.org/10.1063/1.1732973View Description Hide Description
A method is described for recording the absorption spectra of gaseous atoms and molecules produced at strongly heated solid surfaces. A very intense pulse of light from a capacitor discharge lamp falls on light‐absorbing grids placed in the absorption path of a spectrograph. The diameter of the grid windings is sufficiently small that their temperatures rise several thousand degrees very rapidly. The gaseous thermal species that are formed in the optical path arise from the following reactions: (1) vaporization of the grid material; (2) vaporization of coatings applied to the grids; and (3) reactions of the grids with a surrounding gas. Flash spectroscopic recording is used.
The following illustrations of the technique are presented: the formation of atomic tungsten by the vaporization of tungsten grids; the formation of AlCl by the evaporation of AlCl3 from carbon grids; and the formation of CH3, CD3, and CF2 by the reaction of heated carbon grids with CH4, CD4, and CF4, respectively.
Flash heating compares favorably with flash photolysis as a way to produce labile species for kinetic absorption spectroscopy. Parent molecules need not absorb in the near ultraviolet since the dissociative processes that occur are thermal rather than photolytic. Container problems for high‐temperature studies are virtually eliminated because of the pulse nature of the experiment.
37(1962); http://dx.doi.org/10.1063/1.1732974View Description Hide Description
An independent‐electron molecular‐orbital theory is developed for the diamagnetic behavior of electrons in the presence of an applied magnetic field. The molecular orbitals are written as linear combinations of gauge‐invariant atomic orbitals, the dependence of the (complex) coefficients on the magnetic field being studied by perturbation theory. By making a systematic set of approximations involving the neglect of some interatomic terms, a general expression is derived for the diamagneticsusceptibilitytensor as a sum of atomic contributions. Each atomic contribution is made up of two parts, the first being a diamagnetic (Langevin‐type) term and the second being a paramagnetic contribution involving the details of the electronic excited states. At a lower level of approximation, this second term can be expressed in terms of atomic charge densities and bond orders together with a mean electronic excitation energy.
It is pointed out that the theory provides a convenient basis for detailed interpretation of the Pascal constants used for empirical calculations of diamagneticsusceptibilities of large molecules. In addition, a similar treatment of the theory of nuclear magnetic screening leads to an expression for the shielding constant involving a set of localized contributions closely related to corresponding contributions for the susceptibility.
Molecular‐Orbital Theory of Diamagnetism. II. Calculation of Pascal Constants for Some Noncyclic Molecules37(1962); http://dx.doi.org/10.1063/1.1732975View Description Hide Description
The general formulas for atomic contributions to diamagnetic susceptibilities derived in part I are used to calculate Pascal‐type constants for some simple molecules containing hydrogen, carbon, nitrogen, oxygen, and fluorine. For noncyclic saturated molecules, the theory reproduces the relative values of empirical atomic contributions fairly satisfactorily, although absolute numerical agreement is poor. For unsaturated groups, the theory provides an interpretation of the constitutive corrections required in the Pascal scheme. Considerable positive corrections are calculated for the carbon—carbon double bond and the carbonyl group, but not for the carbon—carbon triple bond. This is in agreement with the empirical rules. The theory also makes a number of predictions about diamagneticanisotropies.
37(1962); http://dx.doi.org/10.1063/1.1732976View Description Hide Description
An analysis of the resistivity and thermoelectric power of heavily dopedNb2O5 [over‐all composition where x varies from 0.0025 to 0.15] shows that mixed valence semiconduction has been observed. The major factor determining the value of the thermoelectric power at high temperatures appears to be an entropy of mixing term. In samples with x>0.10, it is concluded that the electrons can be trapped on tungsten ions as well as niobium ions. The low‐temperature resistivity data indicate that the conduction mechanism is not simply described at temperatures where the tungsten impurity ions are incompletely ionized.
37(1962); http://dx.doi.org/10.1063/1.1732977View Description Hide Description
Well‐known ideas suggest that the mass ratio of the constituents and the ionicity of a diatomic lattice will influence certain features of its vibrational spectrum: The splitting between the optical and acoustical branches increases with increasing mass ratio and the energy of the longitudinal optical branch is increased relative to that of the transverse optical branch by increasing ionicity. These effects are found to exist in the phonon frequencies which contribute to the lattice ``combination bands'' of zincblende‐type semiconductors.
37(1962); http://dx.doi.org/10.1063/1.1732978View Description Hide Description
A technique for measuring recombination rates in flames is described and some results showing the effect of temperature, pressure, and the presence of electronegative gases on recombination are presented. Experimental results are compared with predictions based on present‐day theories of recombination. Results are interpreted in terms of an ion—ion process with recombination occurring most probably between an OH— and an H3O+ ion. The importance of electron attachment in such a process is emphasized.
37(1962); http://dx.doi.org/10.1063/1.1732979View Description Hide Description
The effect of absorbed water upon the dielectric properties of polymethylmethacrylate, polyethylmethacrylate, and polyethylacrylate is experimentally investigated over a temperature range from 70°C to —195°C and at frequencies between 100 cps and 200 kc. It is found in each case that the absorbed water gives rise to a discernible loss index peak in the low‐temperature region (0° to —100°C). The 2.1% water absorbed in a specimen of polyethylacrylate acts as a plasticizer, apparently lowering the glass transition by 5C°. The facts that the apparent activation energy and the temperature location of the water induced peak changes with variations in the polymericstructure indicate that the induced loss peak is not to be identified with the loss peak found in ice, and furthermore suggests that the dielectric method can be employed to learn more about the water—polymer complex which is formed when water is absorbed into a polymer.
37(1962); http://dx.doi.org/10.1063/1.1732980View Description Hide Description
A theoretical treatment of nuclear‐magnetic double‐irradiation experiments is given which is applicable to two groups of nuclei of arbitrary spin, either of different nuclear species or in a situation where the chemical shift is large in comparison with the spin‐coupling constant. A convention is introduced whereby the group which experiences the ``strong'' rf field H 2 is given the symbol X, while the group to be investigated is represented by A. Particular attention is given to groups of spin ½ nuclei in A n X m type molecules where m, n≤3, and their spin‐decoupling behavior is presented in graphical form. Good correlations are observed with the experimental proton double‐resonance spectra of acetaldehyde, diethyl succinate, and 1,1,2 trichloroethane. When a single X transition is irradiated with a very weak H 2 a splitting of the A spin‐multiplet lines into submultiplets is observed; at the same time an Overhauser‐type redistribution of intensities may occur in certain molecules. Intermediate strengths of H 2 centered on the X multiplet coalesce the A spectrum to what is essentially a single line for AX m molecules, but for A n X m molecules where n>1 there is a ``residual splitting'' which, although it decreases as H 2 is made stronger, may never disappear completely. At high powers it is necessary to displace H 2 slightly off resonance for group X towards the A resonance in order to obtain optimum decoupling, a correction which can be important in the accurate measurement of protonchemical shifts by spin‐decoupling techniques.
37(1962); http://dx.doi.org/10.1063/1.1732928View Description Hide Description
The real and imaginary parts of the complex dielectric constant of the normal liquid phase of p‐azoxyanisole were measured at a temperature of 140°C for a frequency range from 900 Mc to 24 kMc. A plot of the complex dielectric constant in the complex plane satisfies the requirements for a Cole—Cole representation reasonably well. The temperature dependence of the dielectric loss at a frequency of 6 kMc shows an absorption maximum in the neighborhood of the clearing point (135°C) for both the anisotropic and normal liquid phases. Measurements of the dielectric loss at frequencies 500 and 900 Mc indicate an increase in the dielectric loss as the sample changes from the anisotropic to the normal liquid phase. This change could not be established for measurements at other frequencies reported in this paper.
37(1962); http://dx.doi.org/10.1063/1.1732929View Description Hide Description
The mean adsorption lifetime τ3 of Cs+ on tungsten has been measured in the 1000°—1200°K temperature range, using a pulsed beam technique. Under conditions of low surface coverage and with either Cs or CsI as beam materialswas obtained. The heat of desorption can be calculated as the energy required to remove an isolated Cs+ ion from the surface of an electrical conductor. The presence of an adsorbed contaminating layer, arising from residual vacuum gases, decreased the Cs+—W binding energy by 0.5 eV and increased the pre‐exponential factor by about two orders of magnitude. Anomalous results were obtained when CsCl was used for a beam material, suggesting a reaction between the surfacetungsten atoms and atomic chlorine.
37(1962); http://dx.doi.org/10.1063/1.1732930View Description Hide Description
The solubility of helium in liquid hydrogen has been measured as a function of temperature and pressure. It was found the solubility varied from 0.59 mole % for T=26.8°K and 1.98 atm partial pressure of helium to 11.1 mole % for T=19.8°K and 7.0 atm partial pressure of helium.
Relation between Ultrasonically Measured Properties and the Coefficients in the Solid Equation of State37(1962); http://dx.doi.org/10.1063/1.1732931View Description Hide Description
A relation is found by straight forward thermodynamic methods between the derivatives with respect to pressure of the isothermal and adiabatic bulk moduli which gives at zero pressure from the experimental plus temperature‐dependent‐only thermodynamic properties. Although BT<Bs is required by thermodynamics, we find for Cu, Ag, Au, Al, NaCl, and Na. The coefficients a 1 and a 2 in the equation of state are evaluated from ultrasonic experimental data and compared with those obtained by experiments in high pressure physics. Agreement between the a 1's is good but between the a 2's it is poor.