Reciprocal Distance Research Articles

Anodic behaviour of tungsten—I. Oxidation kinetics in acid media

Galvanostatic anodization of W has been studied in 10N solutions of HCl, H 2SO 4, HNO 3, H 3PO 4, and HClO 4 at 30°C. Experimental factors including electrode pre-treatment, stirring, acid concentration, temperature, open circuit decay, and cathodic polarization have been investigated in detail. The valve-metal behaviour of W is evident in all acids, and the electrode suffers but little from anodic dissolution. At constant c.d., the rate of oxide formation increases in the order HClO 4, H 3PO 4, HNO 3, H 2SO 4 and HCl, and increases with increase in c.d. The simple theory of anodization is applied, and data are given for reciprocal capacity, electrolytic parameters, activation distance, electric field, and pre-polarization thickness. The spark potential depends on the nature of electrolyte.

The adjustment of the Blue Nile Geodetic Control Project

The adjustment of the Ethiopian survey data was performed by methods developed and in current use by the U.S. Coast and Geodetic Survey. The basic level network furnished control for a least-squares solution of reciprocal zenith distance observations, after which a least-squares adjustment of the horizontal directions was made. Laplace azimuths and invar-taped bases were held fixed. Tellurometer lengths were introduced into the solution with appropriate weights. The Cholesky method for the solution of the normal equations was used. Different orders of accuracy were assigned different weights in the solution of the observational data.

An empirical method for calculating barriers to internal rotation in simple molecules

An empirical method has been proposed for the calculation of barriers to internal rotation in simple molecules, based on the hypothesis the main contribution to the barrier to arise from the interactions between non-bonded atoms the reciprocal distance of which varies with the molecular conformation. The repulsive energy between pairs of like atoms h as been calculated assuming the force lawU(r)=KU′(r), whereU′(r) is the Morse potential function deduced from spectroscopic data, andK a coefficient the value of which has been tentatively assumed to be -1. That corresponds to assume a coefficient twice the one assumed in the conventional valence-bond theory for the repulsive exchange integrals between nonbonded orbitals. For interactions between unlike atoms combination rules have been used, taking a geometrical mean of the quantities relative to interactions between like atoms. Other small contributions have been considered, such as the electrostatic interactions between effective charges localized on the nuclei and London dispersion forces. The reciprocal repulsion of dipoles has been assumed to be practically balanced by inductive effects that each dipole induces on the bond around which the internal rotation takes place. As a first approximation, interactions between bond dipoles have not therefore been taken into account. Barriers to internal rotation for thirty simple molecules having one degree of internal freedom and for ten molecules involving C-H interactions, have been computed by this method. The calculated values quantitatively agree with experimental ones deduced by microwave spectroscopy. It has been possible to conclude the present method by very simple calculations to give a satisfactory quantitative height and a correct shape for potential barriers in simple molecules

Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids

The procedures developed in a previous paper of the same main title are applied to the specific case of irreversible processes in fluids. The gross variables are chosen to be a finite number of the plane-wave expansion coefficients of the local particle, momentum and energy densities. As an example, the gross variables describing the local particle density are ∑ i=1Nexpik·xi,where pi and xi are the momentum and position of the ith molecule and N the total number. k runs over a finite number of values which are all small compared to the reciprocal mean distance between molecules. The phenomenonological equations are derived and expressions are given for the viscosity, diffusion, and heat conductivity in terms the autocorrelation coefficients of certain phase functions. These expressions are supposed to be valid for both liquids and gases. They are shown to coincide with the Chapman-Enskog expressions for dilute gases.

The non spherical potential field between two hydrogen molecules

The repulsive interaction energy between two hydrogen molecules is calculated by the quantummechanical perturbation theory, using the H e i t 1 e r-L o n d o n-W a n g wave-function for the unperturbed hydrogen molecule. The theoretical expression obtained, is developed into a series of powers of the reciprocal distance of the centre of the two molecules, the coefficients being functions of their mutual orientation. A suitable approximation for the attractive field is obtained by combining the theories of M a s s e y and B u c k i n g h a m and of J. H. d e B o e r and H e l l e r. The total theoretical field agrees within the experimental accuracy with the “experimental” field obtained by d e B o e r and M i c h e 1 s from the experimental values of the second virial coefficient of the equation of state.