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Volume 41, Issue 1, 01 July 1964

ESR Studies of Triplet States in Plastics: Effect of Temperature on the Spectra
View Description Hide DescriptionThe use of polymethylmethacrylate (Lucite) as a host medium for the study of aromatic triplet states by ESR has been explored. The zero‐field splitting parameter D ^{*} and the lifetime of the triplet state have been measured for a variety of aromatic molecules, and the effect of temperature on these parameters studied in the cases of coronene, triphenylene, and naphthalene.

On the Theory of Spin Relaxation of Gas Molecules: The Strong‐Collision Limit
View Description Hide DescriptionA model of spin relaxation of gas molecules based upon an assumption of strong collisions is developed. A relaxation matrix formally similar to that of Redfield, but with different spectral densities, is obtained. The nuclear magnetic relaxation of gaseous orthohydrogen is discussed in terms of these results, and it is shown that, in general, molecules in different J states are expected to exhibit different relaxation times (a conclusion that is independent of the strong collision assumption) whenever the collision mechanism is effective only in reorienting J but not in changing its magnitude. Otherwise statistical averages of relaxation times are obtained. Relaxation of more complex molecules is also discussed.

Perturbation Theory of the Heats of Mixing of Fused Salts
View Description Hide DescriptionA theory of the thermodynamic properties of molten salts including the effects of short‐range attractive interactions has been developed. The analysis builds upon the work of Reiss, Katz, and Kleppa who showed that many of the thermodynamic properties of molten salt mixtures could be understood in terms of a model ionic melt consisting of rigid impenetrable ions interacting with a long‐range Coulomb potential. The RKK theory is inadequate for the description of recent experimental measurements of the heats of mixing of salts whose short‐range attractive interactions are expected to be significant. Most of the molten salt data of Kleppa et al. have been fitted to the following equation for the heats of mixing:with x_{i} the mole fraction of the ith component, a<0, b<0, and c>0. The major contribution to a arises from Coulomb interactions, and is well accounted for by the RKK analysis which, however, does not completely account for b and gives c=0.
Using a perturbation analysis it is shown herein that the term c and part of b arise from short‐range interactions between ions; the theoretical relationship deduced reproduces the observed composition dependence of the heat of mixing shown above. The qualitative deductions which can be made from the formal analysis are all in agreement with the available experimental data. It is also shown that there is a short‐range potential contribution to the leading term (ax _{1} x _{2}) and explicit relationships for the coefficients a and b are obtained. A method of using the theorem of corresponding states to obtain information about the short‐range coupling is suggested.

Potential Function for the Stretching Region in Potassium Acid Fluoride
View Description Hide DescriptionA simple potential function is used to fit the observed fundamentals and overtones of the asymmetric and symmetric stretching frequencies of the bifluoride ion in KHF_{2} and KDF_{2} and also to account for the difference in mean FHF and FDF bond lengths. The agreement with experiment is good, considering the simplicity of the function and the uncertainties in the data. This potential function is based on a linear symmetric model for the bifluoride ion and there is thus no spectroscopic evidence in favor of an asymmetric model.

Paramagnetic Resonance of Mn^{++} in NaN_{3}, KN_{3}, and RbN_{3}
View Description Hide DescriptionThe paramagneticresonance of Mn^{++} in single crystals of NaN_{3}, KN_{3}, and RbN_{3} is studied at 9.1 Gc/sec as a function of crystal orientation in the magnetic field. In KN_{3} and RbN_{3} containing Mn^{++} the crystalline electric field is the resultant of a large axial field in the [001] direction plus a small cubic field. The g values for Mn^{++} in KN_{3} are g _{∥} = 1.9961±0.0005, g _{⊥} = 1.9878±0.0050; and for Mn^{++} in RbN_{3} g _{∥} = 2.0005±0.0005, g _{⊥} = 1.9971±0.0050. The axial electric field parameter D is —534±3.0 G for KN_{3} and —278±3.0 G for RbN_{3} at 25°C. The cubic field parameter a _{0} is 10±0.5 G for KN_{3} and 8.7±0.5 G for RbN_{3}. The Mn^{++} hyperfine coupling constants A and B are —89.7 and —91.1±0.5 G, respectively, in KN_{3}. In RbN_{3}, A and B are —88.0 and —88.9±0.5 G, respectively. The large magnitudes of D, A, and B allow the forbidden ΔM = ±1, Δm = ±1 transitions to be intense. Two inequivalent sites result from the displacement of the Mn^{++} from a cation site toward a bound nearest‐neighbor cation vacancy.
For an unheated crystal of NaN_{3}, the main Mn^{++}resonance is a single broad line at g = 1.95±0.01. Heating the NaN_{3} crystal changes this broad line into multiple sets of 30‐line spectra. At 25°C these sets of 30‐line spectra decay slowly and the original broad line regrows. A similar effect previously found for Mn^{++} in NaCl has been attributed to mobility of Mn^{++}‐cation vacancy complexes. One type of Mn^{++} spectrum in NaN_{3} is due to the vacancy‐associated complex and another type is due to the dissociated or excited complex. For both types of spectra g _{∥} = g _{⊥} = 2.001±0.002 and A≈B = 87±1.0 G. For the dissociated Mn^{++} complex state the spectrum has axial symmetry about the c axis and D = —240 G. For the vacancy‐paired Mn^{++} spectrum an additional rhombic distortion occurs, and D = —265 and E = +57 G.
The variation of linewidth with temperature is used to show that the KN_{3} spectra result from charge compensation by vacancy pairing. Additional effects produced by vacancy jumping are noted. Differences between the high‐temperature properties of Mn^{++} in NaN_{3} and KN_{3} are related to cation size effects. A low‐temperature line broadening of the Mn^{++} spectrum in KN_{3} and RbN_{3} is reported, and the similarity to the Mn^{++}resonances in solution‐grown KCl and KBr is noted.

Band Shape of the OH Stretching Vibration in Aliphatic Alcohols. Evidence for the Occurrence of an Intramolecular Interaction
View Description Hide DescriptionThe band shape of the OH stretching vibration in a series of aliphatic alcohols has been investigated. The asymmetric shape which occurs in the majority of alcohols is due to an overlapping band on the low‐frequency side of the major band. The asymmetry, which is concentration independent, is shown to occur in the deuterated species and in the first overtone vibration as well. The temperature dependence of the minor band has been investigated and a negative ΔH found which suggests that the minor band is due to an intramolecular interaction. A model is proposed in which the hydrogen of a CH group at the γ position interacts with the lone pair electrons at the hydroxyl oxygen atom. The model qualitatively predicts the correlation between the formation constant and the number of available γ‐CH groups which is experimentally observed.

Effect of Pressure on the Infrared Spectra of Some Hydrogen‐Bonded Solids
View Description Hide DescriptionBy using a diamond‐anvil pressure cell, the infrared spectra of oxalic acid, polyvinyl alcohol, nylon 6–6, and a number of other materials at various pressures up to 25 000 atm were obtained. Studies on two of the pressure‐induced changes, (1) the shift to lower frequencies of the hydrogen‐bonded —OH and —NH stretching bands, and (2) the intensity changes of the two —CH_{2} stretching bands, are reported.

Gas‐Phase Dosimetry by Use of Ionization Measurements
View Description Hide DescriptionA basis is provided for the use of ionization measurements to evaluate energy absorption in gas‐phase dosimetry when high‐energy electrons are employed as the radiationsource. It is concluded that total energy absorption can be determined and that stopping powers can be employed to calculate relative energy absorption in various gases. Scattering measurements indicate that irradiation cells should be short. Relative values of the energy required to form one ion pair (W) by 1‐MeV electrons are shown to be the same as those reported for lower energy electrons, and the following W values for the partial absorption of 1‐MeV electrons are reported with a probable error of about ±2%: C_{3}H_{8} 23.4, n‐C_{4}H_{10} 22.9, i‐C_{4}H_{10} 23.0, i‐C_{5}H_{12} 23.9, C_{3}H_{6} 24.8, 1‐C_{4}H_{8} 24.4, trans‐2‐C_{4}H_{8} 23.9, i‐C_{4}H_{8} 24.4, CH_{3}CHO 26.4, (C_{2}H_{5})_{2}O 23.8, CO 32.2, SO_{2} 30.4, NO 27.5, N_{2}O 32.9, and NH_{3} 26.5.
Chemical‐yield measurements on ethylene suggest that the formation of acetylene can be measured with an accuracy of better than ±3%; above 400 Torr and with dose rates in the order of 10^{15} eV cc^{—1}·sec^{—1} G(acetylene) = 3.07±0.08.

β‐Proton Hyperfine Splittings in the Vinyl Radical
View Description Hide DescriptionThe valence‐bond method is used to evaluate the β‐proton hyperfine splittings in vinyl‐type radicals (HC=CH_{2}) as a function of the H–C=C bond angle. Since only spin polarization is included, use is made of semiempirical exchange integrals to compensate for the neglect of charge transfer and the presence of other approximations in the present treatment. It is demonstrated theoretically that both β‐proton splitting constants should be positive and that the coupling with the protontrans to the sigma orbital occupied by the unpaired electron should be larger than the cis coupling. If the measured values of 68 and 34 Oe found in the vinyl radical are assigned accordingly (no experimental sign determination or assignment of cis versus trans has been made), good agreement with the calculated results is obtained for a bond angle in the reasonable range of 130°—150°.

Thermodynamics of Liquid In–Sb–Zn Solutions from Mass Spectrometry of Knudsen‐Cell Effusates
View Description Hide DescriptionSolution thermodynamics of the In–Sb system in the presence of 0.02 mole fraction zinc have been studied by a mass‐spectrometric Knudsen effusion technique. Activity coefficients for zinc and antimony were obtained, and partial molar heats of solution of antimony were determined from the partial molar heats of vaporization of the element. Partial molar heats and entropies of solution of zinc were calculated from the temperature dependence of the zinc activity coefficients.

Significant Structure Theory of Physical Adsorption
View Description Hide DescriptionThe significant structure theory of liquids has been modified to describe the physical adsorption of gases on homogeneous solids. Equations have been derived for the isotherm, the isosteric heat, and the critical properties. Good agreement with experiment is obtained for the systems Ar and Kr on graphite. The lack of mathematical rigor in the foundations of the significant structure theory is compensated for to a certain extent by its good results and its arithmetical and conceptual simplicity. Its departure from a rigorous foundation, however, makes it difficult to make improvements or to understand anomalies.
The third‐order dispersion energy correction for molecules adsorbed on a solid as derived by Sinanoğlu and Pitzer was used to determine the two‐dimensional lattice energy and the success of the present theory in predicting the heats of adsorption and the critical temperature is a measure of the validity of their work.

On the Radial Distribution Function in Fluids
View Description Hide DescriptionIt is shown that if g(r) is the radial distribution function and φ(r) the pair potential, then the function F(r)=g(r) exp[φ(r)/kT]—1 has a number of properties analogous to those of the pair correlation functionG(r)=g(r)—1 which are known from the Ornstein—Zernike theory. The integral of F(r) over all space is related to the fluctuations in a certain well‐defined physical quantity, in the same way that the integral of G(r) is related to fluctuations in density. The integral of F(r), furthermore, is shown to be always positive, so that on the average g(r) exceeds exp[—φ(r)/kT]. Finally, it is shown that if one makes a hypothesis analogous to one which is familiar in the Ornstein—Zernike theory, then it follows that the pair correlation functionG(r) cannot vanish more rapidly than the pair potential φ(r) as r→∞.

Microwave Spectrum of N‐Methyl Methylenimine
View Description Hide DescriptionThe rotational spectrum of CH_{3}NCH_{2} has been studied in the region 7000–49 000 Mc/sec. Several b‐type transitions have been identified. The barrier to the internal rotation of the methyl group has been found to be 1970±25 cal/mole. Quadrupole fine structure components for several transitions have been analyzed. The components of the quadrupoletensor χ_{ cc } and χ_{ aa } have been found to be 3.2±0.2 and 1.9±0.3 Mc/sec, respectively. The electric dipole moment has been found to be 1.53±0.020 D by measurement of Stark effects.

Some Mathematical Generalizations of the Schrödinger Equation for Two‐Electron Atoms
View Description Hide DescriptionWithin the past few years, considerable success has been found in using interelectron coordinates in atomic wavefunctions to describe atomic systems. The purpose of this paper is to supply a mathematical background for the generalization of this method for application to more complicated atomic, molecular, and solid systems.

Proton Spin—Lattice Relaxation of n‐Paraffins in Solution
View Description Hide DescriptionThe protonT _{1} values for carbon tetrachloride solutions of n‐paraffins have been measured as functions of concentration. The common relaxation theory in which molecules act as spheres whose translational and rotational diffusion coefficients are inversely proportional to the same viscosity is checked with the aid of diffusion coefficients. The simple theory is inadequate, especially for the greater chain lengths. Effects of changes of chain configuration with concentration may be important.

Lattice Heat Capacity of Solid Hydrogen
View Description Hide DescriptionThe lattice heat capacity of solid hydrogen was measured at zero pressure, and at three constant volumes. The measurements extend from 2°K to the triple point for the zero‐pressure data, from 2°K to the melting temperature at 22.56 cc/mole, and from 4° to 20°K at 19.83 and 18.73 cc/mole. The Debye thetas at 0°K are 128°, 169°, and 189°K at 22.56, 19.83, and 18.73 cc/mole, respectively. The temperature dependences of the Debye thetas are similar to those for other simple solids.
Some information about other thermodynamic properties was obtained from the heat capacities. The isothermal compressibility at 16.35°K at the melting pressure is essentially the same as at 4.2°K at the same pressure. The thermal expansion coefficient at 82 atm appears to have a maximum at about 12°K. At zero pressure the thermal expansion coefficient is approximately proportional to the temperature. The thermodynamic expression for the Grüneisen relation is not obeyed in solid hydrogen.

Lattice Vibrations of LaF_{3}
View Description Hide DescriptionThe infrared spectrum of LaF_{3} in the region from 50–575 cm^{—1} is presented. Four strong absorption bands at 185, 208, 275, and 358 cm^{—1} are observed. The Raman spectrum has been investigated and five lines are found at 75, 292, 310, 365, and 392 cm^{—1}. A group theoretical analysis has been carried out for the two slightly different crystal structures proposed for lanthanum trifluoride. The room temperature data seem to favor the more symmetrical bimolecular unit cell. Symmetry coordinates are discussed and some tentative assignments are made.

Electronic Structure of HCl
View Description Hide DescriptionAn approximate molecular Hartree—Fock electronic wavefunction has been obtained for the ground state of the hydrogen chloride molecule at three closely spaced internuclear distances. This work is of accuracy intermediate between the LCAO approximation and a true molecular Hartree—Fock calculation, since a double orbital basis set is used for the L and M shells of Cl together with extra H orbitals, but 3d basic orbitals are not included. There are 12 basis orbitals of σ symmetry and five of π symmetry. Orbital exponents are determined by variational calculations on atomic chlorine. The computed results include molecular electric dipole and quadrupole moments and their derivatives, estimates of the excitation energy of several low‐lying excited states of the neutral molecule and of the positive ion, estimates of the equilibrium internuclear distance of those states that are bound, and identification of the lowest purely repulsive state.

Proton Spin—Lattice Relaxation in Barium Chlorate Monohydrate
View Description Hide DescriptionThe protonic spin—lattice relaxation times were measured as functions of orientation and temperature in a single crystal of Ba(ClO_{3})_{2}·H_{2}O. Pulse methods were used. The proton—proton vector was the axis of rotation of the crystal. Values of T _{1} were found within the range from 6 to 2400 sec. The orientational dependence was characteristic of intermolecular relaxation of the kind described by Holcomb and Pedersen. The temperature dependence was characteristic of 180° flipping motion of the H_{2}O molecule whose activation energy was 5.0 kcal/mole. Sharp dips appeared in the values of T _{1} at certain orientations and temperatures. These probably are caused by cross relaxation between the protons and ^{35}Cl nuclei.

Ion—Molecule Reactions in Methanol and Ethanol
View Description Hide DescriptionProton‐transfer reactions in the methanol and ethanol systems have been investigated by the techniques of conventional mass spectrometry. Using isotopically substituted methanols, relative transfer probabilities from the carbon and hydroxyl positions of the parent molecule ion are found to be 1.00 and 0.81, respectively. The reaction involving CH_{2}OH^{+} has also been investigated quantitatively. In ethanol, only C_{2}H_{4}OH^{+} is found to participate significantly in proton transfer processes. Other secondary ions formed in the high‐pressure mass spectrum of methanol and ethanol are reported, as well as the rate constants for the various proton‐transfer processes.