Volume 10, Issue 4, 01 April 1942

The Diffraction of X‐Rays by Liquid Benzene‐Cyclohexane Mixtures
View Description Hide DescriptionThe x‐ray diffraction pattern of a liquid mixture of benzene and cyclohexane is investigated, using both the photographic method and the Geiger‐Mueller tube counter method. The fine structure on the main peak, and a secondary peak as reported by Bell and Davey, cannot be obtained. It is concluded that these features do not exist in this pattern.

The Infra‐Red Absorption of Silver Cyanide
View Description Hide DescriptionThe spectrum of powdered AgCN has been studied in the region 2500–1800 cm^{−1}. Intense absorption at 2178 cm^{−1} is attributed to an oscillation involving the CN group. The CN frequency for AgCN is almost 100 cm^{−1} higher than the CN frequencies of NaCN and KCN.

Second Virial Coefficients and the Forces Between Complex Molecules
View Description Hide DescriptionThe second virial coefficients of ethane, propane,n‐butane, n‐heptane, ammonia, methyl chloride, and the freons are computed from available experimental data. The causes for sizeable errors in second virial coefficients are considered. At temperatures above the critical, the second virial agrees with the theorem of corresponding states. Below the critical temperature, molecules with dipoles have unusually large virials and the values of their reduced dipole moment, μ/(T_{c}V_{c} )^{½}, determine the discrepancy. The data for isomeric hydrocarbons show that the second virial is not sensitive to the shape of the molecule. This makes it impossible to determine the exact laws of intermolecular interaction from the temperature variation of the second virial. The imperfections of a gas are considered to arise from the presence of double molecules which exist for the duration of a collision. The equilibrium constant for the formation of double molecules is related to the second virial and its temperature variation gives the entropy ΔS and the energy ΔE of their formation. These may be interpreted qualitatively in terms of the intermolecular forces. The second virial coefficient for all substances fits the equation:B(T) = b_{a} (1 — c exp (—ΔE/RT)) where b_{a}, c, and ΔE are taken as constants. Here b_{a}c=exp (ΔS/R). A corresponding states equation is given for estimating second virials when no experimental data are available.

Co‐Precipitation of Radium and Barium Salts as a Function of Temperature and Acidity
View Description Hide DescriptionCo‐precipitation of radium and barium salts which accompanies the cooling of a solution results in the deposition of a percentage of radium largely in excess of that of barium. Under similar conditions of cooling the relative amounts of radium and barium deposited have been determined at different temperatures throughout the cooling process and curves have been plotted. Determinations of the above nature have been made with radium‐barium solutions containing different concentrations of hydrobromic acid, and the variation in the form of the curves is shown. The first crystals formed in the solution contain a larger percentage of radium than succeeding crystals. It is pointed out that the efficiency of the refining process may be increased by separating liquor and crystals at a point above room temperature. In this way the factor of enrichment is increased, thereby hastening the process. Factor of enrichment curves for solutions of different acidity show that for cooling from boiling to room temperature an increase in acidity decreases the crystallization factor. However the inverse relationship is shown to be true when the solution is cooled through a small temperature interval. The rate at which the solution cools is a factor in the relative amounts of radium and barium deposited. With rapid cooling a smaller percentage of radium is precipitated than with slow cooling.

Intramolecular Energy Transfer The Fluorescence of Complexes of Europium
View Description Hide DescriptionThe characteristic line fluorescence of trivalent europium is excited in certain organoeuropium compounds by irradiation with light absorbed only by the organic part of the compound. The efficiency of excitation varies greatly with the nature of the compound, temperature, and solvent. Under optimum conditions, i.e., solution of a covalent compound at liquid‐air temperature, almost unit efficiency has been obtained. The decay time of the fluorescence is independent of quenching; quenching prevents excitation of the europium ion. There seems to be a steady gradation of efficiency of transfer from covalent to ionic compounds.

Frequency Spectrum of Crystalline Solids
View Description Hide DescriptionIt is generally accepted that a normal crystalline solid can be pictured at absolute zero as an assembly of molecules arranged at periodically placed lattice points. Since at higher temperatures each molecule becomes a harmonic oscillator about its lattice point, in order to calculate thermodynamic properties of the crystal it is necessary to know the distribution of its internal normal modes of vibration. On the basis of the Born‐von Kármán model these normal modes of vibration are roots of a secular determinant. In this paper it is shown that the 2nth moment of the distribution function of normal modes is proportional to the trace of the nth power of the matrix of the Born‐von Kármán determinant. By expressing the distribution function as a linear combination of Legendre polynomials it is shown that the coefficient of each polynomial is a linear combination of the moments. The frequency distribution function of a two‐dimensional simple cubic lattice is calculated by the above method and turns out to have two maxima. Usually the equation for a thermodynamic functionF(T) involves the integral of the product of the frequency distribution functiong(v) and a known function K(T, v). We show here that when F(T) is a known function of T an integral equation results with g(v) under the integral sign. This integral equation can be solved for g(v) by use of Fourier transforms.

The Viscosity of Certain ``Ferric Oxide'' Hydrosols
View Description Hide Description(1) The changes produced in the viscosities of ``ferric oxide'' hydrosols by aging, heating, and the addition of a number of electrolytes and a non‐electrolyte have been studied, in some instances together with the attendant changes in the pH values and specific conductances of the systems. (2) Agreement with Poiseuille's law has been demonstrated for typical cationic and anionic hydrosols. (3) The decrease in viscosity of hydrosols on aging and heating is accompanied by an increase in specific conductance. This conductance increase in the case of cationic sols is due almost entirely to the increase in hydrogen ion activity which occurs during the reaction. This is not so for anionic hydrosols, where the conductance increase is explained by the conversion of coordinated citrato groups to citrate ions. (4) The addition of salts and acids to these hydrosols first results in a viscosity decrease, followed by an increase in viscosity at higher electrolyte concentrations. (5) The viscosity increase occurs at lower salt concentrations for those salts which are potent precipitants than for those which are weak. For cationic hydrosols, salts of both weakly and strongly coordinating anions have the same effect in depressing the viscosity; in the case of anionic hydrosols, potassium citrate is less effective in this respect than potassium sulfate and nitrate. (6) The effects of acids in decreasing the viscosity of a sol, either cationic or anionic, was found to be the same for all acids used, when compared at the same pH values. The more powerful precipitants caused the subsequent viscosity increase to occur at lower electrolyte concentrations. (7) Acids are less effective than salts in decreasing the viscosities of cationic hydrosols. (8) Large concentrations of acetone produced a decrease in the relative viscosity of cationic hydrosols; this effect is, however, negligible in comparison with the magnitude of the changes caused by electrolytes. (9) The viscosity decrease produced by aging, heating, and the addition of electrolytes may be attributed in each case partly to the increase in electrolyte concentration of the system. (10) The viscosity resulting from these reactions is considered to be dependent also upon the micellar charge: the lower the charge, the lower the viscosity. (11) The viscosity increase at higher electrolyte concentrations may be ascribed to agglomeration of dispersed particles. (12) A mechanism based upon a Donnan equilibrium between the dispersed particle and the dispersion medium has been proposed to account for the effects observed.

The Approximate Solution of Schrödinger Equations by a Least Squares Method
View Description Hide DescriptionA method of approximation to the solution of a Schrödinger equation has been developed in which variation functions are used but no integrations are involved. The procedure involves the evaluation of the energy for a set of representative points in configuration space. The parameters in the variation function are then chosen by applying the condition that the mean square deviation of the energy from the average should be a minimum.
 LETTERS TO THE EDITOR


Surface Tension of Micelle‐Forming Solutions
View Description Hide Description 
Polarization of Luminescence in Crystals
View Description Hide Description 

The Absorption Spectrum of Chlorine Fluoride
View Description Hide Description
